LMFDB - Embedded newform 1960.2.q.t.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			361.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	1960.361
Dual form			1960.2.q.t.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.68614	−	2.92048i	0.973494	−	1.68614i	0.684819	−	0.728714i	$-0.259881\pi$
$4$		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	−0.909455	−	0.415802i	$-0.863501\pi$
$11$	−0.313859	+	0.543620i	−0.0946322	+	0.163908i	0.814823	+	0.579710i	$0.196834\pi$
$12$		0			0
$13$	−1.37228			−0.380602			−0.190301	−	0.981726i	$-0.560946\pi$
$13$	−1.37228			−0.380602			−0.190301	+	0.981726i	$0.560946\pi$
$14$		0			0
$15$	3.37228			0.870719
$16$		0			0
$17$	−2.68614	+	4.65253i	−0.651485	+	1.12840i	0.331278	+	0.943533i	$0.392520\pi$
$17$	−2.68614	+	4.65253i	−0.651485	+	1.12840i	−0.982763	+	0.184872i	$0.940813\pi$
$18$		0			0
$19$	−3.37228	−	5.84096i	−0.773654	−	1.34001i	−0.935548	−	0.353200i	$-0.885093\pi$
$19$	−3.37228	−	5.84096i	−0.773654	−	1.34001i	0.161893	−	0.986808i	$-0.448240\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.37228	−	5.84096i	−0.703169	−	1.21792i	−0.967348	−	0.253451i	$-0.918434\pi$
$23$	−3.37228	−	5.84096i	−0.703169	−	1.21792i	0.264179	−	0.964474i	$-0.414899\pi$
$24$		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	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$		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	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$	−2.31386	+	4.00772i	−0.370514	+	0.641749i
$40$		0			0
$41$	−4.74456			−0.740976			−0.370488	−	0.928837i	$-0.620810\pi$
$41$	−4.74456			−0.740976			−0.370488	+	0.928837i	$0.620810\pi$
$42$		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	−0.953463	−	0.301510i	$-0.902509\pi$
$47$	−5.05842	−	8.76144i	−0.737847	−	1.27799i	0.215616	−	0.976478i	$-0.430824\pi$
$48$		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	−0.839324	−	0.543632i	$-0.817049\pi$
$53$	0.372281	−	0.644810i	0.0511368	−	0.0885715i	0.890461	+	0.455060i	$0.150382\pi$
$54$		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	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$		0			0
$61$	−4.37228	−	7.57301i	−0.559813	−	0.969625i	−0.997512	−	0.0705031i	$-0.977540\pi$
$61$	−4.37228	−	7.57301i	−0.559813	−	0.969625i	0.437698	−	0.899122i	$-0.355794\pi$
$62$		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	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$		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	$-0.719133\pi$
$73$	3.00000	−	5.19615i	0.351123	−	0.608164i	0.986447	+	0.164083i	$0.0524664\pi$
$74$		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	0.919404	−	0.393314i	$-0.128672\pi$
$79$	1.05842	+	1.83324i	0.119082	+	0.206256i	−0.800322	+	0.599570i	$0.795338\pi$
$80$		0			0
$81$	−17.9891	+	31.1581i	−1.99879	+	3.46201i
$82$		0			0
$83$	13.4891			1.48062			0.740312	−	0.672264i	$-0.234678\pi$
$83$	13.4891			1.48062			0.740312	+	0.672264i	$0.234678\pi$
$84$		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	$-0.221863\pi$
$89$	−1.62772	−	2.81929i	−0.172538	−	0.298844i	−0.939306	+	0.343079i	$0.888530\pi$
$90$		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	$-0.0930870\pi$
$97$	18.8614			1.91509			0.957543	+	0.288291i	$0.0930870\pi$
$98$		0			0
$99$	5.25544			0.528191
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	5.68614	+	9.84868i	0.560272	+	0.970420i	0.997472	+	0.0710555i	$0.0226368\pi$
$103$	5.68614	+	9.84868i	0.560272	+	0.970420i	−0.437200	+	0.899364i	$0.644030\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.37228	+	2.37686i	0.132663	+	0.229780i	0.924702	−	0.380691i	$-0.124314\pi$
$107$	1.37228	+	2.37686i	0.132663	+	0.229780i	−0.792039	+	0.610470i	$0.790980\pi$
$108$		0			0
$109$	2.68614	−	4.65253i	0.257286	−	0.445632i	−0.708228	−	0.705984i	$-0.750505\pi$
$109$	2.68614	−	4.65253i	0.257286	−	0.445632i	0.965514	+	0.260352i	$0.0838386\pi$
$110$		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	$-0.261866\pi$
$131$	−3.37228	−	5.84096i	−0.294638	−	0.510327i	−0.974901	+	0.222641i	$0.928532\pi$
$132$		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	−0.927143	−	0.374707i	$-0.877743\pi$
$137$	−1.62772	+	2.81929i	−0.139065	+	0.240868i	0.788078	+	0.615576i	$0.211076\pi$
$138$		0			0
$139$	6.74456			0.572066			0.286033	−	0.958220i	$-0.407663\pi$
$139$	6.74456			0.572066			0.286033	+	0.958220i	$0.407663\pi$
$140$		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	0.977653	−	0.210225i	$-0.0674196\pi$
$149$	3.74456	+	6.48577i	0.306767	+	0.531335i	−0.670887	+	0.741560i	$0.734086\pi$
$150$		0			0
$151$	1.05842	−	1.83324i	0.0861332	−	0.149187i	−0.819740	−	0.572735i	$-0.805882\pi$
$151$	1.05842	−	1.83324i	0.0861332	−	0.149187i	0.905874	+	0.423548i	$0.139216\pi$
$152$		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	$-0.929936\pi$
$157$	−3.74456	+	6.48577i	−0.298849	+	0.517621i	0.677024	+	0.735961i	$0.263269\pi$
$158$		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	0.950393	−	0.311051i	$-0.100681\pi$
$163$	2.62772	+	4.55134i	0.205819	+	0.356489i	−0.744574	+	0.667539i	$0.767348\pi$
$164$		0			0
$165$	−1.05842	+	1.83324i	−0.0823980	+	0.142718i
$166$		0			0
$167$	−11.3723			−0.880014			−0.440007	−	0.897994i	$-0.645024\pi$
$167$	−11.3723			−0.880014			−0.440007	+	0.897994i	$0.645024\pi$
$168$		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	$-0.232134\pi$
$173$	−2.68614	−	4.65253i	−0.204223	−	0.353725i	−0.949885	+	0.312599i	$0.898800\pi$
$174$		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	0.0143962	+	0.999896i	$0.495417\pi$
$179$	−11.4891	+	19.8997i	−0.858738	+	1.48738i	−0.873134	+	0.487481i	$0.837916\pi$
$180$		0			0
$181$	−18.2337			−1.35530			−0.677650	−	0.735385i	$-0.737001\pi$
$181$	−18.2337			−1.35530			−0.677650	+	0.735385i	$0.737001\pi$
$182$		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	0.828193	+	0.560443i	$0.189369\pi$
$191$	12.4307	+	21.5306i	0.899454	+	1.55790i	0.0712608	+	0.997458i	$0.477298\pi$
$192$		0			0
$193$	2.37228	−	4.10891i	0.170761	−	0.295766i	−0.767925	−	0.640539i	$-0.778711\pi$
$193$	2.37228	−	4.10891i	0.170761	−	0.295766i	0.938686	+	0.344773i	$0.112044\pi$
$194$		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	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$		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	$-0.624342\pi$
$223$	−11.3723			−0.761544			−0.380772	+	0.924669i	$0.624342\pi$
$224$		0			0
$225$	8.37228			0.558152
$226$		0			0
$227$	4.43070	−	7.67420i	0.294076	−	0.509355i	−0.680693	−	0.732568i	$-0.738321\pi$
$227$	4.43070	−	7.67420i	0.294076	−	0.509355i	0.974770	+	0.223214i	$0.0716548\pi$
$228$		0			0
$229$	−11.1168	−	19.2549i	−0.734622	−	1.27240i	−0.954889	−	0.296963i	$-0.904026\pi$
$229$	−11.1168	−	19.2549i	−0.734622	−	1.27240i	0.220267	−	0.975440i	$-0.429307\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.37228	+	11.0371i	0.417462	+	0.723065i	0.995683	−	0.0928145i	$-0.0295863\pi$
$233$	6.37228	+	11.0371i	0.417462	+	0.723065i	−0.578221	+	0.815880i	$0.696253\pi$
$234$		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	0.0546547	+	0.998505i	$0.482594\pi$
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	−0.892058	+	0.451920i	$0.850739\pi$
$242$		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	$-0.568277\pi$
$251$	−6.74456			−0.425713			−0.212857	+	0.977083i	$0.568277\pi$
$252$		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	$-0.161595\pi$
$257$	0.255437	+	0.442430i	0.0159337	+	0.0275981i	−0.857949	+	0.513736i	$0.828261\pi$
$258$		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	−0.613470	−	0.789718i	$-0.710227\pi$
$263$	6.11684	−	10.5947i	0.377181	−	0.653296i	0.990651	+	0.136422i	$0.0435602\pi$
$264$		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	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$		0			0
$271$	6.74456	+	11.6819i	0.409703	+	0.709626i	0.994856	−	0.101296i	$-0.0322990\pi$
$271$	6.74456	+	11.6819i	0.409703	+	0.709626i	−0.585153	+	0.810923i	$0.698966\pi$
$272$		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	−0.357274	−	0.934000i	$-0.616294\pi$
$277$	10.4891	−	18.1677i	0.630230	−	1.09159i	0.987504	−	0.157592i	$-0.0503729\pi$
$278$		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	−0.157851	−	0.987463i	$-0.550457\pi$
$283$	13.0584	−	22.6179i	0.776243	−	1.34449i	0.934093	−	0.357029i	$-0.116210\pi$
$284$		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	$-0.426039\pi$
$293$	7.88316			0.460539			0.230269	+	0.973127i	$0.426039\pi$
$294$		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	$-0.370337\pi$
$307$	13.8832			0.792354			0.396177	+	0.918174i	$0.370337\pi$
$308$		0			0
$309$	38.3505			2.18169
$310$		0			0
$311$	0.627719	−	1.08724i	0.0355947	−	0.0616518i	−0.847679	−	0.530509i	$-0.822001\pi$
$311$	0.627719	−	1.08724i	0.0355947	−	0.0616518i	0.883274	+	0.468857i	$0.155334\pi$
$312$		0			0
$313$	−10.0584	−	17.4217i	−0.568536	−	0.984733i	−0.996711	−	0.0810370i	$-0.974177\pi$
$313$	−10.0584	−	17.4217i	−0.568536	−	0.984733i	0.428175	−	0.903696i	$-0.359157\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.00000	−	12.1244i	−0.393159	−	0.680972i	0.599705	−	0.800221i	$-0.295285\pi$
$317$	−7.00000	−	12.1244i	−0.393159	−	0.680972i	−0.992864	+	0.119249i	$0.961951\pi$
$318$		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	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$		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	−0.631459	−	0.775409i	$-0.717544\pi$
$347$	6.62772	−	11.4795i	0.355795	−	0.616254i	0.987254	+	0.159155i	$0.0508769\pi$
$348$		0			0
$349$	−3.48913			−0.186769			−0.0933843	−	0.995630i	$-0.529769\pi$
$349$	−3.48913			−0.186769			−0.0933843	+	0.995630i	$0.529769\pi$
$350$		0			0
$351$	24.8614			1.32700
$352$		0			0
$353$	−13.4307	+	23.2627i	−0.714844	+	1.23815i	0.248175	+	0.968715i	$0.420169\pi$
$353$	−13.4307	+	23.2627i	−0.714844	+	1.23815i	−0.963020	+	0.269431i	$0.913164\pi$
$354$		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	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$		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	$-0.759042\pi$
$367$	4.43070	−	7.67420i	0.231281	−	0.400590i	0.958185	+	0.286148i	$0.0923750\pi$
$368$		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	0.999999	−	0.00172614i	$-0.000549447\pi$
$373$	9.62772	+	16.6757i	0.498504	+	0.863435i	−0.501494	+	0.865161i	$0.667216\pi$
$374$		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	$-0.211454\pi$
$383$	−2.74456	−	4.75372i	−0.140241	−	0.242904i	−0.927587	+	0.373607i	$0.878121\pi$
$384$		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	−0.694875	−	0.719130i	$-0.744540\pi$
$389$	5.43070	−	9.40625i	0.275348	−	0.476916i	0.970223	+	0.242214i	$0.0778737\pi$
$390$		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	−0.769507	−	0.638638i	$-0.779498\pi$
$397$	−18.6861	−	32.3653i	−0.937831	−	1.62437i	−0.168323	−	0.985732i	$-0.553835\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.802985	−	1.39081i	−0.0400991	−	0.0694537i	0.845279	−	0.534325i	$-0.179434\pi$
$401$	−0.802985	−	1.39081i	−0.0400991	−	0.0694537i	−0.885378	+	0.464871i	$0.846101\pi$
$402$		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	$-0.741655\pi$
$409$	5.74456	−	9.94987i	0.284050	−	0.491990i	0.972378	+	0.233410i	$0.0749884\pi$
$410$		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	$-0.868388\pi$
$419$	−37.4891			−1.83146			−0.915732	+	0.401790i	$0.868388\pi$
$420$		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	−0.977067	−	0.212933i	$-0.931698\pi$
$431$	−6.31386	+	10.9359i	−0.304128	+	0.526765i	0.672939	+	0.739698i	$0.265032\pi$
$432$		0			0
$433$	−16.9783			−0.815923			−0.407961	−	0.912999i	$-0.633760\pi$
$433$	−16.9783			−0.815923			−0.407961	+	0.912999i	$0.633760\pi$
$434$		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	−0.976830	−	0.214018i	$-0.931345\pi$
$439$	−14.1168	−	24.4511i	−0.673760	−	1.16699i	0.303069	−	0.952968i	$-0.401989\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.62772	+	4.55134i	0.124847	+	0.216241i	0.921673	−	0.387968i	$-0.126823\pi$
$443$	2.62772	+	4.55134i	0.124847	+	0.216241i	−0.796826	+	0.604208i	$0.793489\pi$
$444$		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	0.601027	−	0.799229i	$-0.294758\pi$
$457$	−8.37228	−	14.5012i	−0.391639	−	0.678338i	−0.992666	+	0.120890i	$0.961425\pi$
$458$		0			0
$459$	48.6644	−	84.2892i	2.27146	−	3.93428i
$460$		0			0
$461$	−12.7446			−0.593573			−0.296787	−	0.954944i	$-0.595915\pi$
$461$	−12.7446			−0.593573			−0.296787	+	0.954944i	$0.595915\pi$
$462$		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	0.956339	+	0.292261i	$0.0944077\pi$
$467$	15.8030	+	27.3716i	0.731275	+	1.26661i	−0.225064	+	0.974344i	$0.572259\pi$
$468$		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	$-0.743169\pi$
$479$	6.11684	−	10.5947i	0.279486	−	0.484083i	0.971257	+	0.238033i	$0.0765027\pi$
$480$		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	−0.814070	−	0.580766i	$-0.802753\pi$
$487$	2.11684	−	3.66648i	0.0959234	−	0.166144i	0.909994	+	0.414622i	$0.136086\pi$
$488$		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	0.828760	−	0.559604i	$-0.189047\pi$
$499$	−1.56930	−	2.71810i	−0.0702514	−	0.121679i	−0.899011	+	0.437925i	$0.855713\pi$
$500$		0			0
$501$	−19.1753	+	33.2125i	−0.856688	+	1.48383i
$502$		0			0
$503$	−12.6277			−0.563042			−0.281521	−	0.959555i	$-0.590839\pi$
$503$	−12.6277			−0.563042			−0.281521	+	0.959555i	$0.590839\pi$
$504$		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	$-0.201857\pi$
$509$	−2.48913	−	4.31129i	−0.110329	−	0.191095i	−0.915903	+	0.401400i	$0.868524\pi$
$510$		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	−0.324185	−	0.945994i	$-0.605090\pi$
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	0.981347	−	0.192244i	$-0.0615766\pi$
$522$		0			0
$523$	−16.2337	−	28.1176i	−0.709850	−	1.22950i	−0.964913	−	0.262571i	$-0.915430\pi$
$523$	−16.2337	−	28.1176i	−0.709850	−	1.22950i	0.255063	−	0.966924i	$-0.417904\pi$
$524$		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	0.560025	−	0.828476i	$-0.310792\pi$
$541$	−10.1753	−	17.6241i	−0.437469	−	0.757718i	−0.997494	+	0.0707576i	$0.977458\pi$
$542$		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	−0.102852	−	0.994697i	$-0.532797\pi$
$557$	19.1168	−	33.1113i	0.810007	−	1.40297i	0.912859	−	0.408276i	$-0.133870\pi$
$558$		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	$-0.796432\pi$
$563$	2.74456	−	4.75372i	0.115670	−	0.200345i	0.918047	+	0.396471i	$0.129765\pi$
$564$		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	0.557941	−	0.829880i	$-0.311591\pi$
$569$	−10.4891	−	18.1677i	−0.439727	−	0.761630i	−0.997668	+	0.0682510i	$0.978258\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$		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	$-0.952768\pi$
$577$	−8.80298	+	15.2472i	−0.366473	+	0.634750i	0.622538	+	0.782589i	$0.286101\pi$
$578$		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	$-0.427252\pi$
$587$	10.9783			0.453121			0.226560	+	0.973997i	$0.427252\pi$
$588$		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	0.999703	+	0.0243710i	$0.00775828\pi$
$593$	12.6861	+	21.9730i	0.520957	+	0.902325i	−0.478746	+	0.877954i	$0.658908\pi$
$594$		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	−0.933199	−	0.359359i	$-0.882995\pi$
$599$	−3.80298	+	6.58696i	−0.155386	+	0.269136i	0.777814	+	0.628495i	$0.216329\pi$
$600$		0			0
$601$	39.4891			1.61080			0.805398	−	0.592735i	$-0.201952\pi$
$601$	39.4891			1.61080			0.805398	+	0.592735i	$0.201952\pi$
$602$		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	$-0.0640873\pi$
$607$	7.80298	+	13.5152i	0.316713	+	0.548564i	−0.663087	+	0.748542i	$0.730754\pi$
$608$		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	−0.350403	−	0.936599i	$-0.613955\pi$
$613$	15.7446	−	27.2704i	0.635917	−	1.10144i	0.986320	−	0.164841i	$-0.0527112\pi$
$614$		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	$-0.825301\pi$
$619$	0.627719	−	1.08724i	0.0252301	−	0.0436999i	0.878365	+	0.477991i	$0.158635\pi$
$620$		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	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$		0			0
$643$	12.6277			0.497989			0.248994	−	0.968505i	$-0.419900\pi$
$643$	12.6277			0.497989			0.248994	+	0.968505i	$0.419900\pi$
$644$		0			0
$645$	9.25544			0.364432
$646$		0			0
$647$	8.00000	−	13.8564i	0.314512	−	0.544752i	−0.664821	−	0.747002i	$-0.731492\pi$
$647$	8.00000	−	13.8564i	0.314512	−	0.544752i	0.979334	+	0.202251i	$0.0648256\pi$
$648$		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	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$		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	$-0.853499\pi$
$661$	−1.62772	+	2.81929i	−0.0633109	+	0.109658i	0.832633	+	0.553826i	$0.186833\pi$
$662$		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	0.968975	+	0.247157i	$0.0794965\pi$
$677$	18.1753	+	31.4805i	0.698532	+	1.20989i	−0.270443	+	0.962736i	$0.587170\pi$
$678$		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	0.283491	+	0.958975i	$0.408507\pi$
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	−0.972242	+	0.233977i	$0.924826\pi$
$684$		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	$-0.249261\pi$
$691$	−6.74456	−	11.6819i	−0.256575	−	0.444401i	−0.965322	+	0.261061i	$0.915927\pi$
$692$		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	0.987338	+	0.158633i	$0.0507088\pi$
$709$	16.8030	+	29.1036i	0.631049	+	1.09301i	−0.356288	+	0.934376i	$0.615958\pi$
$710$		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	$-0.255325\pi$
$719$	−7.37228	−	12.7692i	−0.274940	−	0.476210i	−0.970120	+	0.242626i	$0.921991\pi$
$720$		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	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		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	0.961913	+	0.273356i	$0.0881336\pi$
$733$	19.4307	+	33.6550i	0.717689	+	1.24307i	−0.244224	+	0.969719i	$0.578533\pi$
$734$		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	−0.988061	−	0.154062i	$-0.950764\pi$
$739$	−9.80298	+	16.9793i	−0.360609	+	0.624592i	0.627453	+	0.778655i	$0.284098\pi$
$740$		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	−0.838091	−	0.545531i	$-0.816328\pi$
$751$	−24.4307	−	42.3152i	−0.891489	−	1.54410i	−0.0533984	−	0.998573i	$-0.517005\pi$
$752$		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	0.951248	+	0.308428i	$0.0998028\pi$
$761$	20.4891	+	35.4882i	0.742730	+	1.28645i	−0.208518	+	0.978019i	$0.566864\pi$
$762$		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	$-0.614294\pi$
$769$	−19.4891			−0.702796			−0.351398	+	0.936226i	$0.614294\pi$
$770$		0			0
$771$	1.72281			0.0620456
$772$		0			0
$773$	0.686141	−	1.18843i	0.0246788	−	0.0427449i	−0.853422	−	0.521220i	$-0.825477\pi$
$773$	0.686141	−	1.18843i	0.0246788	−	0.0427449i	0.878101	+	0.478475i	$0.158810\pi$
$774$		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	$-0.753744\pi$
$787$	6.94158	−	12.0232i	0.247441	−	0.428580i	0.962815	+	0.270162i	$0.0870772\pi$
$788$		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	$-0.376432\pi$
$797$	21.3723			0.757045			0.378523	+	0.925592i	$0.376432\pi$
$798$		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	−0.965475	−	0.260496i	$-0.916114\pi$
$809$	−7.31386	+	12.6680i	−0.257142	+	0.445382i	0.708333	+	0.705878i	$0.249447\pi$
$810$		0			0
$811$	1.25544			0.0440844			0.0220422	−	0.999757i	$-0.492983\pi$
$811$	1.25544			0.0440844			0.0220422	+	0.999757i	$0.492983\pi$
$812$		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	0.926573	−	0.376114i	$-0.122740\pi$
$821$	3.94158	+	6.82701i	0.137562	+	0.238264i	−0.789011	+	0.614379i	$0.789407\pi$
$822$		0			0
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$		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	$-0.959513\pi$
$829$	−11.1168	+	19.2549i	−0.386104	+	0.668752i	0.605818	+	0.795603i	$0.292846\pi$
$830$		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	$-0.628429\pi$
$839$	−22.7446			−0.785230			−0.392615	+	0.919703i	$0.628429\pi$
$840$		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	$-0.591217\pi$
$853$	−16.5109			−0.565322			−0.282661	+	0.959220i	$0.591217\pi$
$854$		0			0
$855$	−56.4674			−1.93114
$856$		0			0
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	12.2337	+	21.1894i	0.417408	+	0.722972i	0.995678	−	0.0928736i	$-0.0296053\pi$
$859$	12.2337	+	21.1894i	0.417408	+	0.722972i	−0.578270	+	0.815846i	$0.696272\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.25544	−	2.17448i	−0.0427356	−	0.0740202i	0.843866	−	0.536553i	$-0.180274\pi$
$863$	−1.25544	−	2.17448i	−0.0427356	−	0.0740202i	−0.886602	+	0.462533i	$0.846941\pi$
$864$		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	0.834454	+	0.551078i	$0.185783\pi$
$877$	26.4891	+	45.8805i	0.894474	+	1.54927i	0.0600202	+	0.998197i	$0.480883\pi$
$878$		0			0
$879$	13.2921	−	23.0226i	0.448332	−	0.776533i
$880$		0			0
$881$	−36.7446			−1.23796			−0.618978	−	0.785408i	$-0.712453\pi$
$881$	−36.7446			−1.23796			−0.618978	+	0.785408i	$0.712453\pi$
$882$		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	0.616339	+	0.787481i	$0.288615\pi$
$887$	29.4891	+	51.0767i	0.990148	+	1.71499i	0.373808	+	0.927506i	$0.378052\pi$
$888$		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	−0.184209	−	0.982887i	$-0.558972\pi$
$907$	22.8614	−	39.5971i	0.759101	−	1.31480i	0.943310	−	0.331914i	$-0.107694\pi$
$908$		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	0.660871	−	0.750500i	$-0.270187\pi$
$919$	−9.68614	−	16.7769i	−0.319516	−	0.553418i	−0.980387	+	0.197081i	$0.936854\pi$
$920$		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	0.970910	+	0.239446i	$0.0769658\pi$
$929$	21.1168	+	36.5754i	0.692821	+	1.20000i	−0.278089	+	0.960555i	$0.589701\pi$
$930$		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	$-0.694319\pi$
$937$	−35.0951			−1.14651			−0.573253	+	0.819378i	$0.694319\pi$
$938$		0			0
$939$	−67.8397			−2.21386
$940$		0			0
$941$	1.11684	−	1.93443i	0.0364081	−	0.0630606i	−0.847247	−	0.531199i	$-0.821742\pi$
$941$	1.11684	−	1.93443i	0.0364081	−	0.0630606i	0.883655	+	0.468138i	$0.155075\pi$
$942$		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	0.998685	−	0.0512727i	$-0.0163278\pi$
$947$	14.0000	+	24.2487i	0.454939	+	0.787977i	−0.543746	+	0.839250i	$0.682994\pi$
$948$		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	$-0.220609\pi$
$971$	−5.25544	−	9.10268i	−0.168655	−	0.292119i	−0.937947	+	0.346778i	$0.887276\pi$
$972$		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	−0.916706	−	0.399561i	$-0.869162\pi$
$977$	−3.51087	+	6.08101i	−0.112323	+	0.194549i	0.804384	+	0.594110i	$0.202496\pi$
$978$		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	$-0.809820\pi$
$983$	2.31386	−	4.00772i	0.0738007	−	0.127826i	0.900564	+	0.434723i	$0.143154\pi$
$984$		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	0.0177919	+	0.999842i	$0.494336\pi$
$991$	−26.9783	+	46.7277i	−0.856992	+	1.48435i	−0.874784	+	0.484513i	$0.838997\pi$
$992$		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	$-0.708605\pi$
$997$	12.0584	−	20.8858i	0.381894	−	0.661460i	0.991333	+	0.131373i	$0.0419386\pi$
$998$		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.t.361.2		4
7.2	even	3	inner	1960.2.q.t.961.2		4
7.3	odd	6		1960.2.a.s.1.2		2
7.4	even	3		280.2.a.c.1.1	✓	2
7.5	odd	6		1960.2.q.r.961.1		4
7.6	odd	2		1960.2.q.r.361.1		4
21.11	odd	6		2520.2.a.x.1.2		2
28.3	even	6		3920.2.a.bt.1.1		2
28.11	odd	6		560.2.a.h.1.2		2
35.4	even	6		1400.2.a.r.1.2		2
35.18	odd	12		1400.2.g.i.449.1		4
35.24	odd	6		9800.2.a.bu.1.1		2
35.32	odd	12		1400.2.g.i.449.4		4
56.11	odd	6		2240.2.a.bg.1.1		2
56.53	even	6		2240.2.a.bk.1.2		2
84.11	even	6		5040.2.a.by.1.1		2
140.39	odd	6		2800.2.a.bk.1.1		2
140.67	even	12		2800.2.g.r.449.1		4
140.123	even	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	7.4	even	3
560.2.a.h.1.2		2	28.11	odd	6
1400.2.a.r.1.2		2	35.4	even	6
1400.2.g.i.449.1		4	35.18	odd	12
1400.2.g.i.449.4		4	35.32	odd	12
1960.2.a.s.1.2		2	7.3	odd	6
1960.2.q.r.361.1		4	7.6	odd	2
1960.2.q.r.961.1		4	7.5	odd	6
1960.2.q.t.361.2		4	1.1	even	1	trivial
1960.2.q.t.961.2		4	7.2	even	3	inner
2240.2.a.bg.1.1		2	56.11	odd	6
2240.2.a.bk.1.2		2	56.53	even	6
2520.2.a.x.1.2		2	21.11	odd	6
2800.2.a.bk.1.1		2	140.39	odd	6
2800.2.g.r.449.1		4	140.67	even	12
2800.2.g.r.449.4		4	140.123	even	12
3920.2.a.bt.1.1		2	28.3	even	6
5040.2.a.by.1.1		2	84.11	even	6
9800.2.a.bu.1.1		2	35.24	odd	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 $\F_{q}$

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)

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