LMFDB - Embedded newform 1960.2.q.r.961.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1960,2,Mod(361,1960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1960.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1960, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-1,0,-2,0,0,0,-11,0,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.6506787962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.r.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.68614 - 2.92048i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-4.18614 + 7.25061i) q^{9} +(-0.313859 - 0.543620i) q^{11} +1.37228 q^{13} +3.37228 q^{15} +(2.68614 + 4.65253i) q^{17} +(3.37228 - 5.84096i) q^{19} +(-3.37228 + 5.84096i) q^{23} +(-0.500000 - 0.866025i) q^{25} +18.1168 q^{27} +1.37228 q^{29} +(-4.00000 - 6.92820i) q^{31} +(-1.05842 + 1.83324i) q^{33} +(1.00000 - 1.73205i) q^{37} +(-2.31386 - 4.00772i) q^{39} +4.74456 q^{41} +2.74456 q^{43} +(-4.18614 - 7.25061i) q^{45} +(5.05842 - 8.76144i) q^{47} +(9.05842 - 15.6896i) q^{51} +(0.372281 + 0.644810i) q^{53} +0.627719 q^{55} -22.7446 q^{57} +(4.00000 + 6.92820i) q^{59} +(4.37228 - 7.57301i) q^{61} +(-0.686141 + 1.18843i) q^{65} +(2.00000 + 3.46410i) q^{67} +22.7446 q^{69} +8.00000 q^{71} +(-3.00000 - 5.19615i) q^{73} +(-1.68614 + 2.92048i) q^{75} +(1.05842 - 1.83324i) q^{79} +(-17.9891 - 31.1581i) q^{81} -13.4891 q^{83} -5.37228 q^{85} +(-2.31386 - 4.00772i) q^{87} +(1.62772 - 2.81929i) q^{89} +(-13.4891 + 23.3639i) q^{93} +(3.37228 + 5.84096i) q^{95} -18.8614 q^{97} +5.25544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 2 q^{5} - 11 q^{9} - 7 q^{11} - 6 q^{13} + 2 q^{15} + 5 q^{17} + 2 q^{19} - 2 q^{23} - 2 q^{25} + 38 q^{27} - 6 q^{29} - 16 q^{31} + 13 q^{33} + 4 q^{37} - 15 q^{39} - 4 q^{41} - 12 q^{43}+ \cdots + 44 q^{99}+O(q^{100}) $ 4 * q - q^3 - 2 * q^5 - 11 * q^9 - 7 * q^11 - 6 * q^13 + 2 * q^15 + 5 * q^17 + 2 * q^19 - 2 * q^23 - 2 * q^25 + 38 * q^27 - 6 * q^29 - 16 * q^31 + 13 * q^33 + 4 * q^37 - 15 * q^39 - 4 * q^41 - 12 * q^43 - 11 * q^45 + 3 * q^47 + 19 * q^51 - 10 * q^53 + 14 * q^55 - 68 * q^57 + 16 * q^59 + 6 * q^61 + 3 * q^65 + 8 * q^67 + 68 * q^69 + 32 * q^71 - 12 * q^73 - q^75 - 13 * q^79 - 26 * q^81 - 8 * q^83 - 10 * q^85 - 15 * q^87 + 18 * q^89 - 8 * q^93 + 2 * q^95 - 18 * q^97 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.68614	−	2.92048i	−0.973494	−	1.68614i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	−1.68614	−	2.92048i	−0.973494	−	1.68614i	−0.288675	−	0.957427i	$-0.593215\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−4.18614	+	7.25061i	−1.39538	+	2.41687i
$10$		0			0
$11$	−0.313859	−	0.543620i	−0.0946322	−	0.163908i	0.814823	−	0.579710i	$-0.196834\pi$
$11$	−0.313859	−	0.543620i	−0.0946322	−	0.163908i	−0.909455	+	0.415802i	$0.863501\pi$
$12$		0			0
$13$	1.37228			0.380602			0.190301	−	0.981726i	$-0.439054\pi$
$13$	1.37228			0.380602			0.190301	+	0.981726i	$0.439054\pi$
$14$		0			0
$15$	3.37228			0.870719
$16$		0			0
$17$	2.68614	+	4.65253i	0.651485	+	1.12840i	0.982763	+	0.184872i	$0.0591869\pi$
$17$	2.68614	+	4.65253i	0.651485	+	1.12840i	−0.331278	+	0.943533i	$0.607480\pi$
$18$		0			0
$19$	3.37228	−	5.84096i	0.773654	−	1.34001i	−0.161893	−	0.986808i	$-0.551760\pi$
$19$	3.37228	−	5.84096i	0.773654	−	1.34001i	0.935548	−	0.353200i	$-0.114907\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.37228	+	5.84096i	−0.703169	+	1.21792i	0.264179	+	0.964474i	$0.414899\pi$
$23$	−3.37228	+	5.84096i	−0.703169	+	1.21792i	−0.967348	+	0.253451i	$0.918434\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	18.1168			3.48659
$28$		0			0
$29$	1.37228			0.254826			0.127413	−	0.991850i	$-0.459333\pi$
$29$	1.37228			0.254826			0.127413	+	0.991850i	$0.459333\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$		0			0
$33$	−1.05842	+	1.83324i	−0.184248	+	0.319126i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$		0			0
$39$	−2.31386	−	4.00772i	−0.370514	−	0.641749i
$40$		0			0
$41$	4.74456			0.740976			0.370488	−	0.928837i	$-0.379190\pi$
$41$	4.74456			0.740976			0.370488	+	0.928837i	$0.379190\pi$
$42$		0			0
$43$	2.74456			0.418542			0.209271	−	0.977858i	$-0.432891\pi$
$43$	2.74456			0.418542			0.209271	+	0.977858i	$0.432891\pi$
$44$		0			0
$45$	−4.18614	−	7.25061i	−0.624033	−	1.08086i
$46$		0			0
$47$	5.05842	−	8.76144i	0.737847	−	1.27799i	−0.215616	−	0.976478i	$-0.569176\pi$
$47$	5.05842	−	8.76144i	0.737847	−	1.27799i	0.953463	−	0.301510i	$-0.0974906\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	9.05842	−	15.6896i	1.26843	−	2.19699i
$52$		0			0
$53$	0.372281	+	0.644810i	0.0511368	+	0.0885715i	0.890461	−	0.455060i	$-0.150382\pi$
$53$	0.372281	+	0.644810i	0.0511368	+	0.0885715i	−0.839324	+	0.543632i	$0.817049\pi$
$54$		0			0
$55$	0.627719			0.0846416
$56$		0			0
$57$	−22.7446			−3.01259
$58$		0			0
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	4.37228	−	7.57301i	0.559813	−	0.969625i	−0.437698	−	0.899122i	$-0.644206\pi$
$61$	4.37228	−	7.57301i	0.559813	−	0.969625i	0.997512	−	0.0705031i	$-0.0224605\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.686141	+	1.18843i	−0.0851053	+	0.147407i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$	22.7446			2.73812
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	−0.986447	+	0.164083i	$0.947534\pi$
$74$		0			0
$75$	−1.68614	+	2.92048i	−0.194699	+	0.337228i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.05842	−	1.83324i	0.119082	−	0.206256i	−0.800322	−	0.599570i	$-0.795338\pi$
$79$	1.05842	−	1.83324i	0.119082	−	0.206256i	0.919404	+	0.393314i	$0.128672\pi$
$80$		0			0
$81$	−17.9891	−	31.1581i	−1.99879	−	3.46201i
$82$		0			0
$83$	−13.4891			−1.48062			−0.740312	−	0.672264i	$-0.765322\pi$
$83$	−13.4891			−1.48062			−0.740312	+	0.672264i	$0.765322\pi$
$84$		0			0
$85$	−5.37228			−0.582706
$86$		0			0
$87$	−2.31386	−	4.00772i	−0.248072	−	0.429673i
$88$		0			0
$89$	1.62772	−	2.81929i	0.172538	−	0.298844i	−0.766769	−	0.641924i	$-0.778137\pi$
$89$	1.62772	−	2.81929i	0.172538	−	0.298844i	0.939306	+	0.343079i	$0.111470\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−13.4891	+	23.3639i	−1.39876	+	2.42272i
$94$		0			0
$95$	3.37228	+	5.84096i	0.345989	+	0.599270i
$96$		0			0
$97$	−18.8614			−1.91509			−0.957543	−	0.288291i	$-0.906913\pi$
$97$	−18.8614			−1.91509			−0.957543	+	0.288291i	$0.906913\pi$
$98$		0			0
$99$	5.25544			0.528191
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−5.68614	+	9.84868i	−0.560272	+	0.970420i	0.437200	+	0.899364i	$0.355970\pi$
$103$	−5.68614	+	9.84868i	−0.560272	+	0.970420i	−0.997472	+	0.0710555i	$0.977363\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.37228	−	2.37686i	0.132663	−	0.229780i	−0.792039	−	0.610470i	$-0.790980\pi$
$107$	1.37228	−	2.37686i	0.132663	−	0.229780i	0.924702	+	0.380691i	$0.124314\pi$
$108$		0			0
$109$	2.68614	+	4.65253i	0.257286	+	0.445632i	0.965514	−	0.260352i	$-0.0838386\pi$
$109$	2.68614	+	4.65253i	0.257286	+	0.445632i	−0.708228	+	0.705984i	$0.750505\pi$
$110$		0			0
$111$	−6.74456			−0.640166
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$		0			0
$115$	−3.37228	−	5.84096i	−0.314467	−	0.544673i
$116$		0			0
$117$	−5.74456	+	9.94987i	−0.531085	+	0.919866i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.30298	−	9.18504i	0.482090	−	0.835004i
$122$		0			0
$123$	−8.00000	−	13.8564i	−0.721336	−	1.24939i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	−4.62772	−	8.01544i	−0.407448	−	0.705720i
$130$		0			0
$131$	3.37228	−	5.84096i	0.294638	−	0.510327i	−0.680263	−	0.732968i	$-0.738134\pi$
$131$	3.37228	−	5.84096i	0.294638	−	0.510327i	0.974901	+	0.222641i	$0.0714677\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−9.05842	+	15.6896i	−0.779625	+	1.35035i
$136$		0			0
$137$	−1.62772	−	2.81929i	−0.139065	−	0.240868i	0.788078	−	0.615576i	$-0.211076\pi$
$137$	−1.62772	−	2.81929i	−0.139065	−	0.240868i	−0.927143	+	0.374707i	$0.877743\pi$
$138$		0			0
$139$	−6.74456			−0.572066			−0.286033	−	0.958220i	$-0.592337\pi$
$139$	−6.74456			−0.572066			−0.286033	+	0.958220i	$0.592337\pi$
$140$		0			0
$141$	−34.1168			−2.87316
$142$		0			0
$143$	−0.430703	−	0.746000i	−0.0360172	−	0.0623837i
$144$		0			0
$145$	−0.686141	+	1.18843i	−0.0569809	+	0.0986938i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.74456	−	6.48577i	0.306767	−	0.531335i	−0.670887	−	0.741560i	$-0.734086\pi$
$149$	3.74456	−	6.48577i	0.306767	−	0.531335i	0.977653	+	0.210225i	$0.0674196\pi$
$150$		0			0
$151$	1.05842	+	1.83324i	0.0861332	+	0.149187i	0.905874	−	0.423548i	$-0.139216\pi$
$151$	1.05842	+	1.83324i	0.0861332	+	0.149187i	−0.819740	+	0.572735i	$0.805882\pi$
$152$		0			0
$153$	−44.9783			−3.63628
$154$		0			0
$155$	8.00000			0.642575
$156$		0			0
$157$	3.74456	+	6.48577i	0.298849	+	0.517621i	0.975873	−	0.218340i	$-0.0700641\pi$
$157$	3.74456	+	6.48577i	0.298849	+	0.517621i	−0.677024	+	0.735961i	$0.736731\pi$
$158$		0			0
$159$	1.25544	−	2.17448i	0.0995627	−	0.172448i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.62772	−	4.55134i	0.205819	−	0.356489i	−0.744574	−	0.667539i	$-0.767348\pi$
$163$	2.62772	−	4.55134i	0.205819	−	0.356489i	0.950393	+	0.311051i	$0.100681\pi$
$164$		0			0
$165$	−1.05842	−	1.83324i	−0.0823980	−	0.142718i
$166$		0			0
$167$	11.3723			0.880014			0.440007	−	0.897994i	$-0.354976\pi$
$167$	11.3723			0.880014			0.440007	+	0.897994i	$0.354976\pi$
$168$		0			0
$169$	−11.1168			−0.855142
$170$		0			0
$171$	28.2337	+	48.9022i	2.15908	+	3.73964i
$172$		0			0
$173$	2.68614	−	4.65253i	0.204223	−	0.353725i	−0.745662	−	0.666325i	$-0.767866\pi$
$173$	2.68614	−	4.65253i	0.204223	−	0.353725i	0.949885	+	0.312599i	$0.101200\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	13.4891	−	23.3639i	1.01390	−	1.75613i
$178$		0			0
$179$	−11.4891	−	19.8997i	−0.858738	−	1.48738i	−0.873134	−	0.487481i	$-0.837916\pi$
$179$	−11.4891	−	19.8997i	−0.858738	−	1.48738i	0.0143962	−	0.999896i	$-0.495417\pi$
$180$		0			0
$181$	18.2337			1.35530			0.677650	−	0.735385i	$-0.262999\pi$
$181$	18.2337			1.35530			0.677650	+	0.735385i	$0.262999\pi$
$182$		0			0
$183$	−29.4891			−2.17990
$184$		0			0
$185$	1.00000	+	1.73205i	0.0735215	+	0.127343i
$186$		0			0
$187$	1.68614	−	2.92048i	0.123303	−	0.213567i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.4307	−	21.5306i	0.899454	−	1.55790i	0.0712608	−	0.997458i	$-0.477298\pi$
$191$	12.4307	−	21.5306i	0.899454	−	1.55790i	0.828193	−	0.560443i	$-0.189369\pi$
$192$		0			0
$193$	2.37228	+	4.10891i	0.170761	+	0.295766i	0.938686	−	0.344773i	$-0.112044\pi$
$193$	2.37228	+	4.10891i	0.170761	+	0.295766i	−0.767925	+	0.640539i	$0.778711\pi$
$194$		0			0
$195$	4.62772			0.331398
$196$		0			0
$197$	26.2337			1.86907			0.934536	−	0.355867i	$-0.115815\pi$
$197$	26.2337			1.86907			0.934536	+	0.355867i	$0.115815\pi$
$198$		0			0
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$		0			0
$201$	6.74456	−	11.6819i	0.475725	−	0.823979i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.37228	+	4.10891i	−0.165687	+	0.286979i
$206$		0			0
$207$	−28.2337	−	48.9022i	−1.96238	−	3.39894i
$208$		0			0
$209$	−4.23369			−0.292850
$210$		0			0
$211$	−8.62772			−0.593957			−0.296978	−	0.954884i	$-0.595979\pi$
$211$	−8.62772			−0.593957			−0.296978	+	0.954884i	$0.595979\pi$
$212$		0			0
$213$	−13.4891	−	23.3639i	−0.924260	−	1.60086i
$214$		0			0
$215$	−1.37228	+	2.37686i	−0.0935888	+	0.162101i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−10.1168	+	17.5229i	−0.683633	+	1.18409i
$220$		0			0
$221$	3.68614	+	6.38458i	0.247957	+	0.429474i
$222$		0			0
$223$	11.3723			0.761544			0.380772	−	0.924669i	$-0.375658\pi$
$223$	11.3723			0.761544			0.380772	+	0.924669i	$0.375658\pi$
$224$		0			0
$225$	8.37228			0.558152
$226$		0			0
$227$	−4.43070	−	7.67420i	−0.294076	−	0.509355i	0.680693	−	0.732568i	$-0.261679\pi$
$227$	−4.43070	−	7.67420i	−0.294076	−	0.509355i	−0.974770	+	0.223214i	$0.928345\pi$
$228$		0			0
$229$	11.1168	−	19.2549i	0.734622	−	1.27240i	−0.220267	−	0.975440i	$-0.570693\pi$
$229$	11.1168	−	19.2549i	0.734622	−	1.27240i	0.954889	−	0.296963i	$-0.0959737\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.37228	−	11.0371i	0.417462	−	0.723065i	−0.578221	−	0.815880i	$-0.696253\pi$
$233$	6.37228	−	11.0371i	0.417462	−	0.723065i	0.995683	+	0.0928145i	$0.0295863\pi$
$234$		0			0
$235$	5.05842	+	8.76144i	0.329975	+	0.571534i
$236$		0			0
$237$	−7.13859			−0.463701
$238$		0			0
$239$	19.3723			1.25309			0.626544	−	0.779386i	$-0.284469\pi$
$239$	19.3723			1.25309			0.626544	+	0.779386i	$0.284469\pi$
$240$		0			0
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	0.892058	+	0.451920i	$0.149261\pi$
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	−0.0546547	+	0.998505i	$0.517406\pi$
$242$		0			0
$243$	−33.4891	+	58.0049i	−2.14833	+	3.72101i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.62772	−	8.01544i	0.294455	−	0.510010i
$248$		0			0
$249$	22.7446	+	39.3947i	1.44138	+	2.49654i
$250$		0			0
$251$	6.74456			0.425713			0.212857	−	0.977083i	$-0.431723\pi$
$251$	6.74456			0.425713			0.212857	+	0.977083i	$0.431723\pi$
$252$		0			0
$253$	4.23369			0.266170
$254$		0			0
$255$	9.05842	+	15.6896i	0.567260	+	0.982524i
$256$		0			0
$257$	−0.255437	+	0.442430i	−0.0159337	+	0.0275981i	−0.873882	−	0.486137i	$-0.838405\pi$
$257$	−0.255437	+	0.442430i	−0.0159337	+	0.0275981i	0.857949	+	0.513736i	$0.171739\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−5.74456	+	9.94987i	−0.355580	+	0.615882i
$262$		0			0
$263$	6.11684	+	10.5947i	0.377181	+	0.653296i	0.990651	−	0.136422i	$-0.0435602\pi$
$263$	6.11684	+	10.5947i	0.377181	+	0.653296i	−0.613470	+	0.789718i	$0.710227\pi$
$264$		0			0
$265$	−0.744563			−0.0457381
$266$		0			0
$267$	−10.9783			−0.671858
$268$		0			0
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	−6.74456	+	11.6819i	−0.409703	+	0.709626i	−0.994856	−	0.101296i	$-0.967701\pi$
$271$	−6.74456	+	11.6819i	−0.409703	+	0.709626i	0.585153	+	0.810923i	$0.301034\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.313859	+	0.543620i	−0.0189264	+	0.0327815i
$276$		0			0
$277$	10.4891	+	18.1677i	0.630230	+	1.09159i	0.987504	+	0.157592i	$0.0503729\pi$
$277$	10.4891	+	18.1677i	0.630230	+	1.09159i	−0.357274	+	0.934000i	$0.616294\pi$
$278$		0			0
$279$	66.9783			4.00988
$280$		0			0
$281$	−21.6060			−1.28890			−0.644452	−	0.764645i	$-0.722914\pi$
$281$	−21.6060			−1.28890			−0.644452	+	0.764645i	$0.722914\pi$
$282$		0			0
$283$	−13.0584	−	22.6179i	−0.776243	−	1.34449i	−0.934093	−	0.357029i	$-0.883790\pi$
$283$	−13.0584	−	22.6179i	−0.776243	−	1.34449i	0.157851	−	0.987463i	$-0.449543\pi$
$284$		0			0
$285$	11.3723	−	19.6974i	0.673636	−	1.16677i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5.93070	+	10.2723i	−0.348865	+	0.604252i
$290$		0			0
$291$	31.8030	+	55.0844i	1.86432	+	3.22910i
$292$		0			0
$293$	−7.88316			−0.460539			−0.230269	−	0.973127i	$-0.573961\pi$
$293$	−7.88316			−0.460539			−0.230269	+	0.973127i	$0.573961\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$	−5.68614	−	9.84868i	−0.329943	−	0.571479i
$298$		0			0
$299$	−4.62772	+	8.01544i	−0.267628	+	0.463545i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−10.1168	+	17.5229i	−0.581198	+	1.00666i
$304$		0			0
$305$	4.37228	+	7.57301i	0.250356	+	0.433629i
$306$		0			0
$307$	−13.8832			−0.792354			−0.396177	−	0.918174i	$-0.629663\pi$
$307$	−13.8832			−0.792354			−0.396177	+	0.918174i	$0.629663\pi$
$308$		0			0
$309$	38.3505			2.18169
$310$		0			0
$311$	−0.627719	−	1.08724i	−0.0355947	−	0.0616518i	0.847679	−	0.530509i	$-0.177999\pi$
$311$	−0.627719	−	1.08724i	−0.0355947	−	0.0616518i	−0.883274	+	0.468857i	$0.844666\pi$
$312$		0			0
$313$	10.0584	−	17.4217i	0.568536	−	0.984733i	−0.428175	−	0.903696i	$-0.640843\pi$
$313$	10.0584	−	17.4217i	0.568536	−	0.984733i	0.996711	−	0.0810370i	$-0.0258232\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	−0.992864	−	0.119249i	$-0.961951\pi$
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	0.599705	+	0.800221i	$0.295285\pi$
$318$		0			0
$319$	−0.430703	−	0.746000i	−0.0241148	−	0.0417680i
$320$		0			0
$321$	−9.25544			−0.516588
$322$		0			0
$323$	36.2337			2.01610
$324$		0			0
$325$	−0.686141	−	1.18843i	−0.0380602	−	0.0659223i
$326$		0			0
$327$	9.05842	−	15.6896i	0.500932	−	0.867639i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	−0.982470	−	0.186421i	$-0.940311\pi$
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	0.652680	+	0.757634i	$0.273645\pi$
$332$		0			0
$333$	8.37228	+	14.5012i	0.458798	+	0.794662i
$334$		0			0
$335$	−4.00000			−0.218543
$336$		0			0
$337$	15.4891			0.843746			0.421873	−	0.906655i	$-0.361373\pi$
$337$	15.4891			0.843746			0.421873	+	0.906655i	$0.361373\pi$
$338$		0			0
$339$	−3.37228	−	5.84096i	−0.183157	−	0.317238i
$340$		0			0
$341$	−2.51087	+	4.34896i	−0.135971	+	0.235510i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−11.3723	+	19.6974i	−0.612263	+	1.06047i
$346$		0			0
$347$	6.62772	+	11.4795i	0.355795	+	0.616254i	0.987254	−	0.159155i	$-0.0508769\pi$
$347$	6.62772	+	11.4795i	0.355795	+	0.616254i	−0.631459	+	0.775409i	$0.717544\pi$
$348$		0			0
$349$	3.48913			0.186769			0.0933843	−	0.995630i	$-0.470231\pi$
$349$	3.48913			0.186769			0.0933843	+	0.995630i	$0.470231\pi$
$350$		0			0
$351$	24.8614			1.32700
$352$		0			0
$353$	13.4307	+	23.2627i	0.714844	+	1.23815i	0.963020	+	0.269431i	$0.0868357\pi$
$353$	13.4307	+	23.2627i	0.714844	+	1.23815i	−0.248175	+	0.968715i	$0.579831\pi$
$354$		0			0
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$		0			0
$361$	−13.2446	−	22.9403i	−0.697082	−	1.20738i
$362$		0			0
$363$	−35.7663			−1.87724
$364$		0			0
$365$	6.00000			0.314054
$366$		0			0
$367$	−4.43070	−	7.67420i	−0.231281	−	0.400590i	0.726904	−	0.686739i	$-0.240958\pi$
$367$	−4.43070	−	7.67420i	−0.231281	−	0.400590i	−0.958185	+	0.286148i	$0.907625\pi$
$368$		0			0
$369$	−19.8614	+	34.4010i	−1.03394	+	1.79084i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	9.62772	−	16.6757i	0.498504	−	0.863435i	−0.501494	−	0.865161i	$-0.667216\pi$
$373$	9.62772	−	16.6757i	0.498504	−	0.863435i	0.999999	+	0.00172614i	$0.000549447\pi$
$374$		0			0
$375$	−1.68614	−	2.92048i	−0.0870719	−	0.150813i
$376$		0			0
$377$	1.88316			0.0969875
$378$		0			0
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$		0			0
$381$	−13.4891	−	23.3639i	−0.691069	−	1.19697i
$382$		0			0
$383$	2.74456	−	4.75372i	0.140241	−	0.242904i	−0.787347	−	0.616511i	$-0.788546\pi$
$383$	2.74456	−	4.75372i	0.140241	−	0.242904i	0.927587	+	0.373607i	$0.121879\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−11.4891	+	19.8997i	−0.584025	+	1.01156i
$388$		0			0
$389$	5.43070	+	9.40625i	0.275348	+	0.476916i	0.970223	−	0.242214i	$-0.0778737\pi$
$389$	5.43070	+	9.40625i	0.275348	+	0.476916i	−0.694875	+	0.719130i	$0.744540\pi$
$390$		0			0
$391$	−36.2337			−1.83242
$392$		0			0
$393$	−22.7446			−1.14731
$394$		0			0
$395$	1.05842	+	1.83324i	0.0532550	+	0.0922403i
$396$		0			0
$397$	18.6861	−	32.3653i	0.937831	−	1.62437i	0.168323	−	0.985732i	$-0.446165\pi$
$397$	18.6861	−	32.3653i	0.937831	−	1.62437i	0.769507	−	0.638638i	$-0.220502\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.802985	+	1.39081i	−0.0400991	+	0.0694537i	−0.885378	−	0.464871i	$-0.846101\pi$
$401$	−0.802985	+	1.39081i	−0.0400991	+	0.0694537i	0.845279	+	0.534325i	$0.179434\pi$
$402$		0			0
$403$	−5.48913	−	9.50744i	−0.273433	−	0.473600i
$404$		0			0
$405$	35.9783			1.78777
$406$		0			0
$407$	−1.25544			−0.0622297
$408$		0			0
$409$	−5.74456	−	9.94987i	−0.284050	−	0.491990i	0.688328	−	0.725399i	$-0.258345\pi$
$409$	−5.74456	−	9.94987i	−0.284050	−	0.491990i	−0.972378	+	0.233410i	$0.925012\pi$
$410$		0			0
$411$	−5.48913	+	9.50744i	−0.270759	+	0.468968i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6.74456	−	11.6819i	0.331078	−	0.573443i
$416$		0			0
$417$	11.3723	+	19.6974i	0.556903	+	0.964584i
$418$		0			0
$419$	37.4891			1.83146			0.915732	−	0.401790i	$-0.131612\pi$
$419$	37.4891			1.83146			0.915732	+	0.401790i	$0.131612\pi$
$420$		0			0
$421$	21.6060			1.05301			0.526505	−	0.850172i	$-0.323502\pi$
$421$	21.6060			1.05301			0.526505	+	0.850172i	$0.323502\pi$
$422$		0			0
$423$	42.3505	+	73.3533i	2.05915	+	3.56656i
$424$		0			0
$425$	2.68614	−	4.65253i	0.130297	−	0.225681i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.45245	+	2.51572i	−0.0701251	+	0.121460i
$430$		0			0
$431$	−6.31386	−	10.9359i	−0.304128	−	0.526765i	0.672939	−	0.739698i	$-0.265032\pi$
$431$	−6.31386	−	10.9359i	−0.304128	−	0.526765i	−0.977067	+	0.212933i	$0.931698\pi$
$432$		0			0
$433$	16.9783			0.815923			0.407961	−	0.912999i	$-0.366240\pi$
$433$	16.9783			0.815923			0.407961	+	0.912999i	$0.366240\pi$
$434$		0			0
$435$	4.62772			0.221882
$436$		0			0
$437$	22.7446	+	39.3947i	1.08802	+	1.88451i
$438$		0			0
$439$	14.1168	−	24.4511i	0.673760	−	1.16699i	−0.303069	−	0.952968i	$-0.598011\pi$
$439$	14.1168	−	24.4511i	0.673760	−	1.16699i	0.976830	−	0.214018i	$-0.0686553\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.62772	−	4.55134i	0.124847	−	0.216241i	−0.796826	−	0.604208i	$-0.793489\pi$
$443$	2.62772	−	4.55134i	0.124847	−	0.216241i	0.921673	+	0.387968i	$0.126823\pi$
$444$		0			0
$445$	1.62772	+	2.81929i	0.0771613	+	0.133647i
$446$		0			0
$447$	−25.2554			−1.19454
$448$		0			0
$449$	−0.116844			−0.00551421			−0.00275710	−	0.999996i	$-0.500878\pi$
$449$	−0.116844			−0.00551421			−0.00275710	+	0.999996i	$0.500878\pi$
$450$		0			0
$451$	−1.48913	−	2.57924i	−0.0701202	−	0.121452i
$452$		0			0
$453$	3.56930	−	6.18220i	0.167700	−	0.290465i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.37228	+	14.5012i	−0.391639	+	0.678338i	−0.992666	−	0.120890i	$-0.961425\pi$
$457$	−8.37228	+	14.5012i	−0.391639	+	0.678338i	0.601027	+	0.799229i	$0.294758\pi$
$458$		0			0
$459$	48.6644	+	84.2892i	2.27146	+	3.93428i
$460$		0			0
$461$	12.7446			0.593573			0.296787	−	0.954944i	$-0.404085\pi$
$461$	12.7446			0.593573			0.296787	+	0.954944i	$0.404085\pi$
$462$		0			0
$463$	−29.4891			−1.37048			−0.685238	−	0.728319i	$-0.740302\pi$
$463$	−29.4891			−1.37048			−0.685238	+	0.728319i	$0.740302\pi$
$464$		0			0
$465$	−13.4891	−	23.3639i	−0.625543	−	1.08347i
$466$		0			0
$467$	−15.8030	+	27.3716i	−0.731275	+	1.26661i	0.225064	+	0.974344i	$0.427741\pi$
$467$	−15.8030	+	27.3716i	−0.731275	+	1.26661i	−0.956339	+	0.292261i	$0.905592\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	12.6277	−	21.8719i	0.581855	−	1.00780i
$472$		0			0
$473$	−0.861407	−	1.49200i	−0.0396075	−	0.0686022i
$474$		0			0
$475$	−6.74456			−0.309462
$476$		0			0
$477$	−6.23369			−0.285421
$478$		0			0
$479$	−6.11684	−	10.5947i	−0.279486	−	0.484083i	0.691771	−	0.722117i	$-0.256831\pi$
$479$	−6.11684	−	10.5947i	−0.279486	−	0.484083i	−0.971257	+	0.238033i	$0.923497\pi$
$480$		0			0
$481$	1.37228	−	2.37686i	0.0625706	−	0.108376i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.43070	−	16.3345i	0.428226	−	0.741709i
$486$		0			0
$487$	2.11684	+	3.66648i	0.0959234	+	0.166144i	0.909994	−	0.414622i	$-0.136086\pi$
$487$	2.11684	+	3.66648i	0.0959234	+	0.166144i	−0.814070	+	0.580766i	$0.802753\pi$
$488$		0			0
$489$	−17.7228			−0.801453
$490$		0			0
$491$	17.8832			0.807056			0.403528	−	0.914967i	$-0.367784\pi$
$491$	17.8832			0.807056			0.403528	+	0.914967i	$0.367784\pi$
$492$		0			0
$493$	3.68614	+	6.38458i	0.166015	+	0.287547i
$494$		0			0
$495$	−2.62772	+	4.55134i	−0.118107	+	0.204568i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.56930	+	2.71810i	−0.0702514	+	0.121679i	−0.899011	−	0.437925i	$-0.855713\pi$
$499$	−1.56930	+	2.71810i	−0.0702514	+	0.121679i	0.828760	+	0.559604i	$0.189047\pi$
$500$		0			0
$501$	−19.1753	−	33.2125i	−0.856688	−	1.48383i
$502$		0			0
$503$	12.6277			0.563042			0.281521	−	0.959555i	$-0.409161\pi$
$503$	12.6277			0.563042			0.281521	+	0.959555i	$0.409161\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$	18.7446	+	32.4665i	0.832475	+	1.44189i
$508$		0			0
$509$	2.48913	−	4.31129i	0.110329	−	0.191095i	−0.805574	−	0.592495i	$-0.798143\pi$
$509$	2.48913	−	4.31129i	0.110329	−	0.191095i	0.915903	+	0.401400i	$0.131476\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	61.0951	−	105.820i	2.69741	−	4.67206i
$514$		0			0
$515$	−5.68614	−	9.84868i	−0.250561	−	0.433985i
$516$		0			0
$517$	−6.35053			−0.279296
$518$		0			0
$519$	−18.1168			−0.795241
$520$		0			0
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	−0.981347	−	0.192244i	$-0.938423\pi$
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	0.324185	−	0.945994i	$-0.394910\pi$
$522$		0			0
$523$	16.2337	−	28.1176i	0.709850	−	1.22950i	−0.255063	−	0.966924i	$-0.582096\pi$
$523$	16.2337	−	28.1176i	0.709850	−	1.22950i	0.964913	−	0.262571i	$-0.0845704\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	21.4891	−	37.2203i	0.936081	−	1.62134i
$528$		0			0
$529$	−11.2446	−	19.4762i	−0.488894	−	0.846789i
$530$		0			0
$531$	−66.9783			−2.90661
$532$		0			0
$533$	6.51087			0.282017
$534$		0			0
$535$	1.37228	+	2.37686i	0.0593289	+	0.102761i
$536$		0			0
$537$	−38.7446	+	67.1076i	−1.67195	+	2.89590i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−10.1753	+	17.6241i	−0.437469	+	0.757718i	−0.997494	−	0.0707576i	$-0.977458\pi$
$541$	−10.1753	+	17.6241i	−0.437469	+	0.757718i	0.560025	+	0.828476i	$0.310792\pi$
$542$		0			0
$543$	−30.7446	−	53.2511i	−1.31938	−	2.28523i
$544$		0			0
$545$	−5.37228			−0.230123
$546$		0			0
$547$	14.9783			0.640424			0.320212	−	0.947346i	$-0.396246\pi$
$547$	14.9783			0.640424			0.320212	+	0.947346i	$0.396246\pi$
$548$		0			0
$549$	36.6060	+	63.4034i	1.56230	+	2.70599i
$550$		0			0
$551$	4.62772	−	8.01544i	0.197147	−	0.341469i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.37228	−	5.84096i	0.143145	−	0.247935i
$556$		0			0
$557$	19.1168	+	33.1113i	0.810007	+	1.40297i	0.912859	+	0.408276i	$0.133870\pi$
$557$	19.1168	+	33.1113i	0.810007	+	1.40297i	−0.102852	+	0.994697i	$0.532797\pi$
$558$		0			0
$559$	3.76631			0.159298
$560$		0			0
$561$	−11.3723			−0.480138
$562$		0			0
$563$	−2.74456	−	4.75372i	−0.115670	−	0.200345i	0.802378	−	0.596817i	$-0.203568\pi$
$563$	−2.74456	−	4.75372i	−0.115670	−	0.200345i	−0.918047	+	0.396471i	$0.870235\pi$
$564$		0			0
$565$	−1.00000	+	1.73205i	−0.0420703	+	0.0728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.4891	+	18.1677i	−0.439727	+	0.761630i	−0.997668	−	0.0682510i	$-0.978258\pi$
$569$	−10.4891	+	18.1677i	−0.439727	+	0.761630i	0.557941	+	0.829880i	$0.311591\pi$
$570$		0			0
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	0.995788	−	0.0916910i	$-0.0292272\pi$
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	−0.577301	+	0.816532i	$0.695894\pi$
$572$		0			0
$573$	−83.8397			−3.50245
$574$		0			0
$575$	6.74456			0.281268
$576$		0			0
$577$	8.80298	+	15.2472i	0.366473	+	0.634750i	0.989011	−	0.147839i	$-0.0472319\pi$
$577$	8.80298	+	15.2472i	0.366473	+	0.634750i	−0.622538	+	0.782589i	$0.713899\pi$
$578$		0			0
$579$	8.00000	−	13.8564i	0.332469	−	0.575853i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.233688	−	0.404759i	0.00967837	−	0.0167634i
$584$		0			0
$585$	−5.74456	−	9.94987i	−0.237508	−	0.411377i
$586$		0			0
$587$	−10.9783			−0.453121			−0.226560	−	0.973997i	$-0.572748\pi$
$587$	−10.9783			−0.453121			−0.226560	+	0.973997i	$0.572748\pi$
$588$		0			0
$589$	−53.9565			−2.22324
$590$		0			0
$591$	−44.2337	−	76.6150i	−1.81953	−	3.15152i
$592$		0			0
$593$	−12.6861	+	21.9730i	−0.520957	+	0.902325i	0.478746	+	0.877954i	$0.341092\pi$
$593$	−12.6861	+	21.9730i	−0.520957	+	0.902325i	−0.999703	+	0.0243710i	$0.992242\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−26.9783	+	46.7277i	−1.10415	+	1.91244i
$598$		0			0
$599$	−3.80298	−	6.58696i	−0.155386	−	0.269136i	0.777814	−	0.628495i	$-0.216329\pi$
$599$	−3.80298	−	6.58696i	−0.155386	−	0.269136i	−0.933199	+	0.359359i	$0.882995\pi$
$600$		0			0
$601$	−39.4891			−1.61080			−0.805398	−	0.592735i	$-0.798048\pi$
$601$	−39.4891			−1.61080			−0.805398	+	0.592735i	$0.798048\pi$
$602$		0			0
$603$	−33.4891			−1.36378
$604$		0			0
$605$	5.30298	+	9.18504i	0.215597	+	0.373425i
$606$		0			0
$607$	−7.80298	+	13.5152i	−0.316713	+	0.548564i	−0.979800	−	0.199979i	$-0.935913\pi$
$607$	−7.80298	+	13.5152i	−0.316713	+	0.548564i	0.663087	+	0.748542i	$0.269246\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.94158	−	12.0232i	0.280826	−	0.486405i
$612$		0			0
$613$	15.7446	+	27.2704i	0.635917	+	1.10144i	0.986320	+	0.164841i	$0.0527112\pi$
$613$	15.7446	+	27.2704i	0.635917	+	1.10144i	−0.350403	+	0.936599i	$0.613955\pi$
$614$		0			0
$615$	16.0000			0.645182
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	−0.627719	−	1.08724i	−0.0252301	−	0.0436999i	0.853135	−	0.521691i	$-0.174699\pi$
$619$	−0.627719	−	1.08724i	−0.0252301	−	0.0436999i	−0.878365	+	0.477991i	$0.841365\pi$
$620$		0			0
$621$	−61.0951	+	105.820i	−2.45166	+	4.24640i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	7.13859	+	12.3644i	0.285088	+	0.493787i
$628$		0			0
$629$	10.7446			0.428414
$630$		0			0
$631$	−3.37228			−0.134248			−0.0671242	−	0.997745i	$-0.521382\pi$
$631$	−3.37228			−0.134248			−0.0671242	+	0.997745i	$0.521382\pi$
$632$		0			0
$633$	14.5475	+	25.1971i	0.578213	+	1.00149i
$634$		0			0
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−33.4891	+	58.0049i	−1.32481	+	2.29464i
$640$		0			0
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	0.845601	−	0.533816i	$-0.179242\pi$
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	−0.885098	+	0.465404i	$0.845909\pi$
$642$		0			0
$643$	−12.6277			−0.497989			−0.248994	−	0.968505i	$-0.580100\pi$
$643$	−12.6277			−0.497989			−0.248994	+	0.968505i	$0.580100\pi$
$644$		0			0
$645$	9.25544			0.364432
$646$		0			0
$647$	−8.00000	−	13.8564i	−0.314512	−	0.544752i	0.664821	−	0.747002i	$-0.268508\pi$
$647$	−8.00000	−	13.8564i	−0.314512	−	0.544752i	−0.979334	+	0.202251i	$0.935174\pi$
$648$		0			0
$649$	2.51087	−	4.34896i	0.0985605	−	0.170712i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$		0			0
$655$	3.37228	+	5.84096i	0.131766	+	0.228225i
$656$		0			0
$657$	50.2337			1.95980
$658$		0			0
$659$	6.11684			0.238278			0.119139	−	0.992878i	$-0.461987\pi$
$659$	6.11684			0.238278			0.119139	+	0.992878i	$0.461987\pi$
$660$		0			0
$661$	1.62772	+	2.81929i	0.0633109	+	0.109658i	0.895943	−	0.444168i	$-0.146501\pi$
$661$	1.62772	+	2.81929i	0.0633109	+	0.109658i	−0.832633	+	0.553826i	$0.813167\pi$
$662$		0			0
$663$	12.4307	−	21.5306i	0.482769	−	0.836180i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.62772	+	8.01544i	−0.179186	+	0.310359i
$668$		0			0
$669$	−19.1753	−	33.2125i	−0.741359	−	1.28407i
$670$		0			0
$671$	−5.48913			−0.211905
$672$		0			0
$673$	−31.7228			−1.22282			−0.611412	−	0.791312i	$-0.709398\pi$
$673$	−31.7228			−1.22282			−0.611412	+	0.791312i	$0.709398\pi$
$674$		0			0
$675$	−9.05842	−	15.6896i	−0.348659	−	0.603895i
$676$		0			0
$677$	−18.1753	+	31.4805i	−0.698532	+	1.20989i	0.270443	+	0.962736i	$0.412830\pi$
$677$	−18.1753	+	31.4805i	−0.698532	+	1.20989i	−0.968975	+	0.247157i	$0.920504\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−14.9416	+	25.8796i	−0.572563	+	0.991707i
$682$		0			0
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	−0.972242	−	0.233977i	$-0.924826\pi$
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	0.283491	−	0.958975i	$-0.408507\pi$
$684$		0			0
$685$	3.25544			0.124384
$686$		0			0
$687$	−74.9783			−2.86060
$688$		0			0
$689$	0.510875	+	0.884861i	0.0194628	+	0.0337105i
$690$		0			0
$691$	6.74456	−	11.6819i	0.256575	−	0.444401i	−0.708747	−	0.705463i	$-0.750739\pi$
$691$	6.74456	−	11.6819i	0.256575	−	0.444401i	0.965322	+	0.261061i	$0.0840725\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.37228	−	5.84096i	0.127918	−	0.221560i
$696$		0			0
$697$	12.7446	+	22.0742i	0.482735	+	0.836121i
$698$		0			0
$699$	−42.9783			−1.62559
$700$		0			0
$701$	30.8614			1.16562			0.582810	−	0.812609i	$-0.301953\pi$
$701$	30.8614			1.16562			0.582810	+	0.812609i	$0.301953\pi$
$702$		0			0
$703$	−6.74456	−	11.6819i	−0.254376	−	0.440592i
$704$		0			0
$705$	17.0584	−	29.5461i	0.642457	−	1.11277i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	16.8030	−	29.1036i	0.631049	−	1.09301i	−0.356288	−	0.934376i	$-0.615958\pi$
$709$	16.8030	−	29.1036i	0.631049	−	1.09301i	0.987338	−	0.158633i	$-0.0507088\pi$
$710$		0			0
$711$	8.86141	+	15.3484i	0.332329	+	0.575610i
$712$		0			0
$713$	53.9565			2.02069
$714$		0			0
$715$	0.861407			0.0322148
$716$		0			0
$717$	−32.6644	−	56.5764i	−1.21987	−	2.11288i
$718$		0			0
$719$	7.37228	−	12.7692i	0.274940	−	0.476210i	−0.695180	−	0.718836i	$-0.744675\pi$
$719$	7.37228	−	12.7692i	0.274940	−	0.476210i	0.970120	+	0.242626i	$0.0780088\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	43.8397	−	75.9325i	1.63041	−	2.82396i
$724$		0			0
$725$	−0.686141	−	1.18843i	−0.0254826	−	0.0441372i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	117.935			4.36795
$730$		0			0
$731$	7.37228	+	12.7692i	0.272674	+	0.472285i
$732$		0			0
$733$	−19.4307	+	33.6550i	−0.717689	+	1.24307i	0.244224	+	0.969719i	$0.421467\pi$
$733$	−19.4307	+	33.6550i	−0.717689	+	1.24307i	−0.961913	+	0.273356i	$0.911866\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.25544	−	2.17448i	0.0462446	−	0.0800980i
$738$		0			0
$739$	−9.80298	−	16.9793i	−0.360609	−	0.624592i	0.627453	−	0.778655i	$-0.284098\pi$
$739$	−9.80298	−	16.9793i	−0.360609	−	0.624592i	−0.988061	+	0.154062i	$0.950764\pi$
$740$		0			0
$741$	−31.2119			−1.14660
$742$		0			0
$743$	−29.4891			−1.08185			−0.540926	−	0.841070i	$-0.681926\pi$
$743$	−29.4891			−1.08185			−0.540926	+	0.841070i	$0.681926\pi$
$744$		0			0
$745$	3.74456	+	6.48577i	0.137190	+	0.237620i
$746$		0			0
$747$	56.4674	−	97.8044i	2.06603	−	3.57847i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−24.4307	+	42.3152i	−0.891489	+	1.54410i	−0.0533984	+	0.998573i	$0.517005\pi$
$751$	−24.4307	+	42.3152i	−0.891489	+	1.54410i	−0.838091	+	0.545531i	$0.816328\pi$
$752$		0			0
$753$	−11.3723	−	19.6974i	−0.414429	−	0.717812i
$754$		0			0
$755$	−2.11684			−0.0770398
$756$		0			0
$757$	−38.2337			−1.38963			−0.694814	−	0.719190i	$-0.744513\pi$
$757$	−38.2337			−1.38963			−0.694814	+	0.719190i	$0.744513\pi$
$758$		0			0
$759$	−7.13859	−	12.3644i	−0.259115	−	0.448800i
$760$		0			0
$761$	−20.4891	+	35.4882i	−0.742730	+	1.28645i	0.208518	+	0.978019i	$0.433136\pi$
$761$	−20.4891	+	35.4882i	−0.742730	+	1.28645i	−0.951248	+	0.308428i	$0.900197\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	22.4891	−	38.9523i	0.813096	−	1.40832i
$766$		0			0
$767$	5.48913	+	9.50744i	0.198201	+	0.343294i
$768$		0			0
$769$	19.4891			0.702796			0.351398	−	0.936226i	$-0.385706\pi$
$769$	19.4891			0.702796			0.351398	+	0.936226i	$0.385706\pi$
$770$		0			0
$771$	1.72281			0.0620456
$772$		0			0
$773$	−0.686141	−	1.18843i	−0.0246788	−	0.0427449i	0.853422	−	0.521220i	$-0.174523\pi$
$773$	−0.686141	−	1.18843i	−0.0246788	−	0.0427449i	−0.878101	+	0.478475i	$0.841190\pi$
$774$		0			0
$775$	−4.00000	+	6.92820i	−0.143684	+	0.248868i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.0000	−	27.7128i	0.573259	−	0.992915i
$780$		0			0
$781$	−2.51087	−	4.34896i	−0.0898462	−	0.155618i
$782$		0			0
$783$	24.8614			0.888474
$784$		0			0
$785$	−7.48913			−0.267298
$786$		0			0
$787$	−6.94158	−	12.0232i	−0.247441	−	0.428580i	0.715374	−	0.698741i	$-0.246256\pi$
$787$	−6.94158	−	12.0232i	−0.247441	−	0.428580i	−0.962815	+	0.270162i	$0.912923\pi$
$788$		0			0
$789$	20.6277	−	35.7283i	0.734366	−	1.27196i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6.00000	−	10.3923i	0.213066	−	0.369042i
$794$		0			0
$795$	1.25544	+	2.17448i	0.0445258	+	0.0771209i
$796$		0			0
$797$	−21.3723			−0.757045			−0.378523	−	0.925592i	$-0.623568\pi$
$797$	−21.3723			−0.757045			−0.378523	+	0.925592i	$0.623568\pi$
$798$		0			0
$799$	54.3505			1.92278
$800$		0			0
$801$	13.6277	+	23.6039i	0.481512	+	0.834003i
$802$		0			0
$803$	−1.88316	+	3.26172i	−0.0664551	+	0.115104i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−10.1168	+	17.5229i	−0.356130	+	0.616835i
$808$		0			0
$809$	−7.31386	−	12.6680i	−0.257142	−	0.445382i	0.708333	−	0.705878i	$-0.249447\pi$
$809$	−7.31386	−	12.6680i	−0.257142	−	0.445382i	−0.965475	+	0.260496i	$0.916114\pi$
$810$		0			0
$811$	−1.25544			−0.0440844			−0.0220422	−	0.999757i	$-0.507017\pi$
$811$	−1.25544			−0.0440844			−0.0220422	+	0.999757i	$0.507017\pi$
$812$		0			0
$813$	45.4891			1.59537
$814$		0			0
$815$	2.62772	+	4.55134i	0.0920450	+	0.159427i
$816$		0			0
$817$	9.25544	−	16.0309i	0.323807	−	0.560850i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.94158	−	6.82701i	0.137562	−	0.238264i	−0.789011	−	0.614379i	$-0.789407\pi$
$821$	3.94158	−	6.82701i	0.137562	−	0.238264i	0.926573	+	0.376114i	$0.122740\pi$
$822$		0			0
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$		0			0
$825$	2.11684			0.0736990
$826$		0			0
$827$	13.2554			0.460937			0.230468	−	0.973080i	$-0.425974\pi$
$827$	13.2554			0.460937			0.230468	+	0.973080i	$0.425974\pi$
$828$		0			0
$829$	11.1168	+	19.2549i	0.386104	+	0.668752i	0.991922	−	0.126852i	$-0.0404873\pi$
$829$	11.1168	+	19.2549i	0.386104	+	0.668752i	−0.605818	+	0.795603i	$0.707154\pi$
$830$		0			0
$831$	35.3723	−	61.2666i	1.22705	−	2.12531i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−5.68614	+	9.84868i	−0.196777	+	0.340828i
$836$		0			0
$837$	−72.4674	−	125.517i	−2.50484	−	4.33851i
$838$		0			0
$839$	22.7446			0.785230			0.392615	−	0.919703i	$-0.371571\pi$
$839$	22.7446			0.785230			0.392615	+	0.919703i	$0.371571\pi$
$840$		0			0
$841$	−27.1168			−0.935064
$842$		0			0
$843$	36.4307	+	63.0998i	1.25474	+	2.17327i
$844$		0			0
$845$	5.55842	−	9.62747i	0.191216	−	0.331195i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−44.0367	+	76.2738i	−1.51133	+	2.61771i
$850$		0			0
$851$	6.74456	+	11.6819i	0.231201	+	0.400451i
$852$		0			0
$853$	16.5109			0.565322			0.282661	−	0.959220i	$-0.408783\pi$
$853$	16.5109			0.565322			0.282661	+	0.959220i	$0.408783\pi$
$854$		0			0
$855$	−56.4674			−1.93114
$856$		0			0
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$		0			0
$859$	−12.2337	+	21.1894i	−0.417408	+	0.722972i	−0.995678	−	0.0928736i	$-0.970395\pi$
$859$	−12.2337	+	21.1894i	−0.417408	+	0.722972i	0.578270	+	0.815846i	$0.303728\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.25544	+	2.17448i	−0.0427356	+	0.0740202i	−0.886602	−	0.462533i	$-0.846941\pi$
$863$	−1.25544	+	2.17448i	−0.0427356	+	0.0740202i	0.843866	+	0.536553i	$0.180274\pi$
$864$		0			0
$865$	2.68614	+	4.65253i	0.0913315	+	0.158191i
$866$		0			0
$867$	40.0000			1.35847
$868$		0			0
$869$	−1.32878			−0.0450759
$870$		0			0
$871$	2.74456	+	4.75372i	0.0929960	+	0.161074i
$872$		0			0
$873$	78.9565	−	136.757i	2.67227	−	4.62851i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	26.4891	−	45.8805i	0.894474	−	1.54927i	0.0600202	−	0.998197i	$-0.480883\pi$
$877$	26.4891	−	45.8805i	0.894474	−	1.54927i	0.834454	−	0.551078i	$-0.185783\pi$
$878$		0			0
$879$	13.2921	+	23.0226i	0.448332	+	0.776533i
$880$		0			0
$881$	36.7446			1.23796			0.618978	−	0.785408i	$-0.287547\pi$
$881$	36.7446			1.23796			0.618978	+	0.785408i	$0.287547\pi$
$882$		0			0
$883$	−33.4891			−1.12700			−0.563499	−	0.826116i	$-0.690545\pi$
$883$	−33.4891			−1.12700			−0.563499	+	0.826116i	$0.690545\pi$
$884$		0			0
$885$	13.4891	+	23.3639i	0.453432	+	0.785367i
$886$		0			0
$887$	−29.4891	+	51.0767i	−0.990148	+	1.71499i	−0.373808	+	0.927506i	$0.621948\pi$
$887$	−29.4891	+	51.0767i	−0.990148	+	1.71499i	−0.616339	+	0.787481i	$0.711385\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−11.2921	+	19.5585i	−0.378300	+	0.655235i
$892$		0			0
$893$	−34.1168	−	59.0921i	−1.14168	−	1.97744i
$894$		0			0
$895$	22.9783			0.768078
$896$		0			0
$897$	31.2119			1.04214
$898$		0			0
$899$	−5.48913	−	9.50744i	−0.183073	−	0.317091i
$900$		0			0
$901$	−2.00000	+	3.46410i	−0.0666297	+	0.115406i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.11684	+	15.7908i	−0.303054	+	0.524905i
$906$		0			0
$907$	22.8614	+	39.5971i	0.759101	+	1.31480i	0.943310	+	0.331914i	$0.107694\pi$
$907$	22.8614	+	39.5971i	0.759101	+	1.31480i	−0.184209	+	0.982887i	$0.558972\pi$
$908$		0			0
$909$	50.2337			1.66615
$910$		0			0
$911$	45.9565			1.52261			0.761303	−	0.648396i	$-0.224560\pi$
$911$	45.9565			1.52261			0.761303	+	0.648396i	$0.224560\pi$
$912$		0			0
$913$	4.23369	+	7.33296i	0.140115	+	0.242686i
$914$		0			0
$915$	14.7446	−	25.5383i	0.487440	−	0.844271i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−9.68614	+	16.7769i	−0.319516	+	0.553418i	−0.980387	−	0.197081i	$-0.936854\pi$
$919$	−9.68614	+	16.7769i	−0.319516	+	0.553418i	0.660871	+	0.750500i	$0.270187\pi$
$920$		0			0
$921$	23.4090	+	40.5455i	0.771351	+	1.33602i
$922$		0			0
$923$	10.9783			0.361354
$924$		0			0
$925$	−2.00000			−0.0657596
$926$		0			0
$927$	−47.6060	−	82.4560i	−1.56359	−	2.70821i
$928$		0			0
$929$	−21.1168	+	36.5754i	−0.692821	+	1.20000i	0.278089	+	0.960555i	$0.410299\pi$
$929$	−21.1168	+	36.5754i	−0.692821	+	1.20000i	−0.970910	+	0.239446i	$0.923034\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−2.11684	+	3.66648i	−0.0693024	+	0.120035i
$934$		0			0
$935$	1.68614	+	2.92048i	0.0551427	+	0.0955100i
$936$		0			0
$937$	35.0951			1.14651			0.573253	−	0.819378i	$-0.305681\pi$
$937$	35.0951			1.14651			0.573253	+	0.819378i	$0.305681\pi$
$938$		0			0
$939$	−67.8397			−2.21386
$940$		0			0
$941$	−1.11684	−	1.93443i	−0.0364081	−	0.0630606i	0.847247	−	0.531199i	$-0.178258\pi$
$941$	−1.11684	−	1.93443i	−0.0364081	−	0.0630606i	−0.883655	+	0.468138i	$0.844925\pi$
$942$		0			0
$943$	−16.0000	+	27.7128i	−0.521032	+	0.902453i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	−0.543746	−	0.839250i	$-0.682994\pi$
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	0.998685	+	0.0512727i	$0.0163278\pi$
$948$		0			0
$949$	−4.11684	−	7.13058i	−0.133638	−	0.231469i
$950$		0			0
$951$	47.2119			1.53095
$952$		0			0
$953$	48.7446			1.57899			0.789496	−	0.613756i	$-0.210342\pi$
$953$	48.7446			1.57899			0.789496	+	0.613756i	$0.210342\pi$
$954$		0			0
$955$	12.4307	+	21.5306i	0.402248	+	0.696714i
$956$		0			0
$957$	−1.45245	+	2.51572i	−0.0469511	+	0.0813217i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		0			0
$963$	11.4891	+	19.8997i	0.370232	+	0.641260i
$964$		0			0
$965$	−4.74456			−0.152733
$966$		0			0
$967$	36.2337			1.16520			0.582598	−	0.812760i	$-0.302036\pi$
$967$	36.2337			1.16520			0.582598	+	0.812760i	$0.302036\pi$
$968$		0			0
$969$	−61.0951	−	105.820i	−1.96266	−	3.39942i
$970$		0			0
$971$	5.25544	−	9.10268i	0.168655	−	0.292119i	−0.769292	−	0.638897i	$-0.779391\pi$
$971$	5.25544	−	9.10268i	0.168655	−	0.292119i	0.937947	+	0.346778i	$0.112724\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−2.31386	+	4.00772i	−0.0741028	+	0.128350i
$976$		0			0
$977$	−3.51087	−	6.08101i	−0.112323	−	0.194549i	0.804384	−	0.594110i	$-0.202496\pi$
$977$	−3.51087	−	6.08101i	−0.112323	−	0.194549i	−0.916706	+	0.399561i	$0.869162\pi$
$978$		0			0
$979$	−2.04350			−0.0653105
$980$		0			0
$981$	−44.9783			−1.43605
$982$		0			0
$983$	−2.31386	−	4.00772i	−0.0738007	−	0.127826i	0.826763	−	0.562550i	$-0.190180\pi$
$983$	−2.31386	−	4.00772i	−0.0738007	−	0.127826i	−0.900564	+	0.434723i	$0.856846\pi$
$984$		0			0
$985$	−13.1168	+	22.7190i	−0.417937	+	0.723889i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.25544	+	16.0309i	−0.294306	+	0.509753i
$990$		0			0
$991$	−26.9783	−	46.7277i	−0.856992	−	1.48435i	−0.874784	−	0.484513i	$-0.838997\pi$
$991$	−26.9783	−	46.7277i	−0.856992	−	1.48435i	0.0177919	−	0.999842i	$-0.494336\pi$
$992$		0			0
$993$	40.4674			1.28419
$994$		0			0
$995$	16.0000			0.507234
$996$		0			0
$997$	−12.0584	−	20.8858i	−0.381894	−	0.661460i	0.609439	−	0.792833i	$-0.291395\pi$
$997$	−12.0584	−	20.8858i	−0.381894	−	0.661460i	−0.991333	+	0.131373i	$0.958061\pi$
$998$		0			0
$999$	18.1168	−	31.3793i	0.573192	−	0.992797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.r.961.1		4
7.2	even	3		1960.2.a.s.1.2		2
7.3	odd	6		1960.2.q.t.361.2		4
7.4	even	3	inner	1960.2.q.r.361.1		4
7.5	odd	6		280.2.a.c.1.1	✓	2
7.6	odd	2		1960.2.q.t.961.2		4
21.5	even	6		2520.2.a.x.1.2		2
28.19	even	6		560.2.a.h.1.2		2
28.23	odd	6		3920.2.a.bt.1.1		2
35.9	even	6		9800.2.a.bu.1.1		2
35.12	even	12		1400.2.g.i.449.4		4
35.19	odd	6		1400.2.a.r.1.2		2
35.33	even	12		1400.2.g.i.449.1		4
56.5	odd	6		2240.2.a.bk.1.2		2
56.19	even	6		2240.2.a.bg.1.1		2
84.47	odd	6		5040.2.a.by.1.1		2
140.19	even	6		2800.2.a.bk.1.1		2
140.47	odd	12		2800.2.g.r.449.1		4
140.103	odd	12		2800.2.g.r.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.a.c.1.1	✓	2	7.5	odd	6
560.2.a.h.1.2		2	28.19	even	6
1400.2.a.r.1.2		2	35.19	odd	6
1400.2.g.i.449.1		4	35.33	even	12
1400.2.g.i.449.4		4	35.12	even	12
1960.2.a.s.1.2		2	7.2	even	3
1960.2.q.r.361.1		4	7.4	even	3	inner
1960.2.q.r.961.1		4	1.1	even	1	trivial
1960.2.q.t.361.2		4	7.3	odd	6
1960.2.q.t.961.2		4	7.6	odd	2
2240.2.a.bg.1.1		2	56.19	even	6
2240.2.a.bk.1.2		2	56.5	odd	6
2520.2.a.x.1.2		2	21.5	even	6
2800.2.a.bk.1.1		2	140.19	even	6
2800.2.g.r.449.1		4	140.47	odd	12
2800.2.g.r.449.4		4	140.103	odd	12
3920.2.a.bt.1.1		2	28.23	odd	6
5040.2.a.by.1.1		2	84.47	odd	6
9800.2.a.bu.1.1		2	35.9	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.68614 - 2.92048i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-4.18614 + 7.25061i) q^{9} +(-0.313859 - 0.543620i) q^{11} +1.37228 q^{13} +3.37228 q^{15} +(2.68614 + 4.65253i) q^{17} +(3.37228 - 5.84096i) q^{19} +(-3.37228 + 5.84096i) q^{23} +(-0.500000 - 0.866025i) q^{25} +18.1168 q^{27} +1.37228 q^{29} +(-4.00000 - 6.92820i) q^{31} +(-1.05842 + 1.83324i) q^{33} +(1.00000 - 1.73205i) q^{37} +(-2.31386 - 4.00772i) q^{39} +4.74456 q^{41} +2.74456 q^{43} +(-4.18614 - 7.25061i) q^{45} +(5.05842 - 8.76144i) q^{47} +(9.05842 - 15.6896i) q^{51} +(0.372281 + 0.644810i) q^{53} +0.627719 q^{55} -22.7446 q^{57} +(4.00000 + 6.92820i) q^{59} +(4.37228 - 7.57301i) q^{61} +(-0.686141 + 1.18843i) q^{65} +(2.00000 + 3.46410i) q^{67} +22.7446 q^{69} +8.00000 q^{71} +(-3.00000 - 5.19615i) q^{73} +(-1.68614 + 2.92048i) q^{75} +(1.05842 - 1.83324i) q^{79} +(-17.9891 - 31.1581i) q^{81} -13.4891 q^{83} -5.37228 q^{85} +(-2.31386 - 4.00772i) q^{87} +(1.62772 - 2.81929i) q^{89} +(-13.4891 + 23.3639i) q^{93} +(3.37228 + 5.84096i) q^{95} -18.8614 q^{97} +5.25544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 2 q^{5} - 11 q^{9} - 7 q^{11} - 6 q^{13} + 2 q^{15} + 5 q^{17} + 2 q^{19} - 2 q^{23} - 2 q^{25} + 38 q^{27} - 6 q^{29} - 16 q^{31} + 13 q^{33} + 4 q^{37} - 15 q^{39} - 4 q^{41} - 12 q^{43}+ \cdots + 44 q^{99}+O(q^{100}) \) 4 * q - q^3 - 2 * q^5 - 11 * q^9 - 7 * q^11 - 6 * q^13 + 2 * q^15 + 5 * q^17 + 2 * q^19 - 2 * q^23 - 2 * q^25 + 38 * q^27 - 6 * q^29 - 16 * q^31 + 13 * q^33 + 4 * q^37 - 15 * q^39 - 4 * q^41 - 12 * q^43 - 11 * q^45 + 3 * q^47 + 19 * q^51 - 10 * q^53 + 14 * q^55 - 68 * q^57 + 16 * q^59 + 6 * q^61 + 3 * q^65 + 8 * q^67 + 68 * q^69 + 32 * q^71 - 12 * q^73 - q^75 - 13 * q^79 - 26 * q^81 - 8 * q^83 - 10 * q^85 - 15 * q^87 + 18 * q^89 - 8 * q^93 + 2 * q^95 - 18 * q^97 + 44 * q^99

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