LMFDB - Embedded newform 1960.2.q.y.961.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.21913473024.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 11x^{6} - 2x^{5} + 51x^{4} + 162x^{2} + 112x + 196 $ x^8 - 2x^7 + 11x^6 - 2x^5 + 51x^4 + 162x^2 + 112x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$-0.591990 - 1.02536i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.y.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.591990 - 1.02536i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.799096 - 1.38408i) q^{9} +O(q^{10})$	\(q+(-0.591990 - 1.02536i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.799096 - 1.38408i) q^{9} +(-0.115117 - 0.199389i) q^{11} +2.27259 q^{13} -1.18398 q^{15} +(3.26639 + 5.65755i) q^{17} +(-0.130093 + 0.225328i) q^{19} +(4.43539 - 7.68233i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.44417 q^{27} +5.42662 q^{29} +(2.43539 + 4.21822i) q^{31} +(-0.136296 + 0.236072i) q^{33} +(0.577014 - 0.999417i) q^{37} +(-1.34535 - 2.33022i) q^{39} -4.43337 q^{41} +4.17723 q^{43} +(-0.799096 - 1.38408i) q^{45} +(0.461897 - 0.800028i) q^{47} +(3.86734 - 6.69843i) q^{51} +(1.06743 + 1.84885i) q^{53} -0.230234 q^{55} +0.308055 q^{57} +(-2.53553 - 4.39167i) q^{59} +(4.44417 - 7.69752i) q^{61} +(1.13630 - 1.96812i) q^{65} +(-4.07984 - 7.06649i) q^{67} -10.5028 q^{69} -9.06556 q^{71} +(3.00478 + 5.20442i) q^{73} +(-0.591990 + 1.02536i) q^{75} +(-0.0564558 + 0.0977843i) q^{79} +(0.825600 + 1.42998i) q^{81} -8.72065 q^{83} +6.53278 q^{85} +(-3.21250 - 5.56422i) q^{87} +(7.95852 - 13.7846i) q^{89} +(2.88345 - 4.99429i) q^{93} +(0.130093 + 0.225328i) q^{95} -4.29565 q^{97} -0.367959 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9	$ 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9} - 2 q^{11} - 20 q^{13} + 4 q^{15} + 6 q^{17} + 4 q^{23} - 4 q^{25} - 28 q^{27} - 4 q^{29} - 12 q^{31} + 18 q^{33} - 14 q^{39} - 24 q^{41} - 16 q^{43} + 6 q^{45} - 2 q^{47} - 2 q^{51} + 4 q^{53} - 4 q^{55} - 16 q^{57} + 8 q^{59} + 20 q^{61} - 10 q^{65} + 8 q^{67} - 48 q^{69} + 8 q^{71} + 16 q^{73} + 2 q^{75} - 22 q^{79} + 20 q^{81} - 72 q^{83} + 12 q^{85} - 18 q^{87} + 40 q^{89} + 32 q^{93} - 52 q^{97} + 24 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9 - 2 * q^11 - 20 * q^13 + 4 * q^15 + 6 * q^17 + 4 * q^23 - 4 * q^25 - 28 * q^27 - 4 * q^29 - 12 * q^31 + 18 * q^33 - 14 * q^39 - 24 * q^41 - 16 * q^43 + 6 * q^45 - 2 * q^47 - 2 * q^51 + 4 * q^53 - 4 * q^55 - 16 * q^57 + 8 * q^59 + 20 * q^61 - 10 * q^65 + 8 * q^67 - 48 * q^69 + 8 * q^71 + 16 * q^73 + 2 * q^75 - 22 * q^79 + 20 * q^81 - 72 * q^83 + 12 * q^85 - 18 * q^87 + 40 * q^89 + 32 * q^93 - 52 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.591990	−	1.02536i	−0.341785	−	0.591990i	0.642979	−	0.765884i	$-0.277698\pi$
$3$	−0.591990	−	1.02536i	−0.341785	−	0.591990i	−0.984764	+	0.173894i	$0.944365\pi$
$4$		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
$9$	0.799096	−	1.38408i	0.266365	−	0.461359i
$10$		0			0
$11$	−0.115117	−	0.199389i	−0.0347091	−	0.0601179i	0.848149	−	0.529758i	$-0.177717\pi$
$11$	−0.115117	−	0.199389i	−0.0347091	−	0.0601179i	−0.882858	+	0.469640i	$0.844384\pi$
$12$		0			0
$13$	2.27259			0.630304			0.315152	−	0.949041i	$-0.397945\pi$
$13$	2.27259			0.630304			0.315152	+	0.949041i	$0.397945\pi$
$14$		0			0
$15$	−1.18398			−0.305702
$16$		0			0
$17$	3.26639	+	5.65755i	0.792216	+	1.37216i	0.924592	+	0.380958i	$0.124406\pi$
$17$	3.26639	+	5.65755i	0.792216	+	1.37216i	−0.132376	+	0.991200i	$0.542261\pi$
$18$		0			0
$19$	−0.130093	+	0.225328i	−0.0298454	+	0.0516937i	−0.880562	−	0.473930i	$-0.842835\pi$
$19$	−0.130093	+	0.225328i	−0.0298454	+	0.0516937i	0.850717	+	0.525624i	$0.176168\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.43539	−	7.68233i	0.924843	−	1.60188i	0.133030	−	0.991112i	$-0.457529\pi$
$23$	4.43539	−	7.68233i	0.924843	−	1.60188i	0.791813	−	0.610764i	$-0.209137\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−5.44417			−1.04773
$28$		0			0
$29$	5.42662			1.00770			0.503849	−	0.863792i	$-0.331917\pi$
$29$	5.42662			1.00770			0.503849	+	0.863792i	$0.331917\pi$
$30$		0			0
$31$	2.43539	+	4.21822i	0.437409	+	0.757615i	0.997489	−	0.0708235i	$-0.0225627\pi$
$31$	2.43539	+	4.21822i	0.437409	+	0.757615i	−0.560079	+	0.828439i	$0.689229\pi$
$32$		0			0
$33$	−0.136296	+	0.236072i	−0.0237261	+	0.0410949i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.577014	−	0.999417i	0.0948605	−	0.164303i	−0.814690	−	0.579897i	$-0.803093\pi$
$37$	0.577014	−	0.999417i	0.0948605	−	0.164303i	0.909550	+	0.415594i	$0.136426\pi$
$38$		0			0
$39$	−1.34535	−	2.33022i	−0.215429	−	0.373133i
$40$		0			0
$41$	−4.43337			−0.692377			−0.346188	−	0.938165i	$-0.612524\pi$
$41$	−4.43337			−0.692377			−0.346188	+	0.938165i	$0.612524\pi$
$42$		0			0
$43$	4.17723			0.637021			0.318511	−	0.947919i	$-0.396817\pi$
$43$	4.17723			0.637021			0.318511	+	0.947919i	$0.396817\pi$
$44$		0			0
$45$	−0.799096	−	1.38408i	−0.119122	−	0.206326i
$46$		0			0
$47$	0.461897	−	0.800028i	0.0673745	−	0.116696i	−0.830370	−	0.557212i	$-0.811871\pi$
$47$	0.461897	−	0.800028i	0.0673745	−	0.116696i	0.897745	+	0.440516i	$0.145204\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3.86734	−	6.69843i	0.541536	−	0.937967i
$52$		0			0
$53$	1.06743	+	1.84885i	0.146623	+	0.253959i	0.929977	−	0.367617i	$-0.119826\pi$
$53$	1.06743	+	1.84885i	0.146623	+	0.253959i	−0.783354	+	0.621576i	$0.786493\pi$
$54$		0			0
$55$	−0.230234			−0.0310448
$56$		0			0
$57$	0.308055			0.0408029
$58$		0			0
$59$	−2.53553	−	4.39167i	−0.330098	−	0.571747i	0.652432	−	0.757847i	$-0.273749\pi$
$59$	−2.53553	−	4.39167i	−0.330098	−	0.571747i	−0.982531	+	0.186100i	$0.940415\pi$
$60$		0			0
$61$	4.44417	−	7.69752i	0.569017	−	0.985566i	−0.427646	−	0.903946i	$-0.640657\pi$
$61$	4.44417	−	7.69752i	0.569017	−	0.985566i	0.996663	−	0.0816204i	$-0.0260095\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.13630	−	1.96812i	0.140940	−	0.244116i
$66$		0			0
$67$	−4.07984	−	7.06649i	−0.498432	−	0.863309i	0.501567	−	0.865119i	$-0.332757\pi$
$67$	−4.07984	−	7.06649i	−0.498432	−	0.863309i	−0.999998	+	0.00180980i	$0.999424\pi$
$68$		0			0
$69$	−10.5028			−1.26439
$70$		0			0
$71$	−9.06556			−1.07588			−0.537942	−	0.842982i	$-0.680798\pi$
$71$	−9.06556			−1.07588			−0.537942	+	0.842982i	$0.680798\pi$
$72$		0			0
$73$	3.00478	+	5.20442i	0.351682	+	0.609132i	0.986544	−	0.163494i	$-0.0522764\pi$
$73$	3.00478	+	5.20442i	0.351682	+	0.609132i	−0.634862	+	0.772626i	$0.718943\pi$
$74$		0			0
$75$	−0.591990	+	1.02536i	−0.0683571	+	0.118398i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.0564558	+	0.0977843i	−0.00635177	+	0.0110016i	−0.869184	−	0.494489i	$-0.835355\pi$
$79$	−0.0564558	+	0.0977843i	−0.00635177	+	0.0110016i	0.862832	+	0.505491i	$0.168689\pi$
$80$		0			0
$81$	0.825600	+	1.42998i	0.0917334	+	0.158887i
$82$		0			0
$83$	−8.72065			−0.957216			−0.478608	−	0.878029i	$-0.658859\pi$
$83$	−8.72065			−0.957216			−0.478608	+	0.878029i	$0.658859\pi$
$84$		0			0
$85$	6.53278			0.708579
$86$		0			0
$87$	−3.21250	−	5.56422i	−0.344416	−	0.596547i
$88$		0			0
$89$	7.95852	−	13.7846i	0.843601	−	1.46116i	−0.0432288	−	0.999065i	$-0.513764\pi$
$89$	7.95852	−	13.7846i	0.843601	−	1.46116i	0.886830	−	0.462095i	$-0.152902\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.88345	−	4.99429i	0.299000	−	0.517884i
$94$		0			0
$95$	0.130093	+	0.225328i	0.0133473	+	0.0231181i
$96$		0			0
$97$	−4.29565			−0.436157			−0.218079	−	0.975931i	$-0.569979\pi$
$97$	−4.29565			−0.436157			−0.218079	+	0.975931i	$0.569979\pi$
$98$		0			0
$99$	−0.367959			−0.0369812
$100$		0			0
$101$	3.69356	+	6.39743i	0.367523	+	0.636568i	0.989178	−	0.146723i	$-0.0468726\pi$
$101$	3.69356	+	6.39743i	0.367523	+	0.636568i	−0.621655	+	0.783291i	$0.713539\pi$
$102$		0			0
$103$	−5.29032	+	9.16311i	−0.521271	+	0.902868i	0.478423	+	0.878130i	$0.341209\pi$
$103$	−5.29032	+	9.16311i	−0.521271	+	0.902868i	−0.999694	+	0.0247384i	$0.992125\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.73306	−	11.6620i	0.650910	−	1.12741i	−0.331993	−	0.943282i	$-0.607721\pi$
$107$	6.73306	−	11.6620i	0.650910	−	1.12741i	0.982903	−	0.184127i	$-0.0589456\pi$
$108$		0			0
$109$	−4.25284	−	7.36614i	−0.407348	−	0.705548i	0.587243	−	0.809410i	$-0.300213\pi$
$109$	−4.25284	−	7.36614i	−0.407348	−	0.705548i	−0.994592	+	0.103862i	$0.966880\pi$
$110$		0			0
$111$	−1.36634			−0.129688
$112$		0			0
$113$	18.3968			1.73063			0.865313	−	0.501232i	$-0.167120\pi$
$113$	18.3968			1.73063			0.865313	+	0.501232i	$0.167120\pi$
$114$		0			0
$115$	−4.43539	−	7.68233i	−0.413603	−	0.716381i
$116$		0			0
$117$	1.81602	−	3.14544i	0.167891	−	0.290796i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.47350	−	9.48037i	0.497591	−	0.861852i
$122$		0			0
$123$	2.62451	+	4.54579i	0.236644	+	0.409880i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.41032			0.746295			0.373147	−	0.927772i	$-0.378279\pi$
$127$	8.41032			0.746295			0.373147	+	0.927772i	$0.378279\pi$
$128$		0			0
$129$	−2.47287	−	4.28314i	−0.217724	−	0.377110i
$130$		0			0
$131$	−0.891086	+	1.54341i	−0.0778546	+	0.134848i	−0.902324	−	0.431058i	$-0.858140\pi$
$131$	−0.891086	+	1.54341i	−0.0778546	+	0.134848i	0.824470	+	0.565906i	$0.191474\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.72208	+	4.71479i	−0.234280	+	0.405784i
$136$		0			0
$137$	5.65685	+	9.79796i	0.483298	+	0.837096i	0.999816	−	0.0191800i	$-0.00610555\pi$
$137$	5.65685	+	9.79796i	0.483298	+	0.837096i	−0.516518	+	0.856276i	$0.672772\pi$
$138$		0			0
$139$	−15.4390			−1.30952			−0.654761	−	0.755836i	$-0.727231\pi$
$139$	−15.4390			−1.30952			−0.654761	+	0.755836i	$0.727231\pi$
$140$		0			0
$141$	−1.09375			−0.0921105
$142$		0			0
$143$	−0.261614	−	0.453129i	−0.0218773	−	0.0378926i
$144$		0			0
$145$	2.71331	−	4.69959i	0.225328	−	0.390280i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.6406	+	20.1620i	−0.953631	+	1.65174i	−0.216161	+	0.976358i	$0.569354\pi$
$149$	−11.6406	+	20.1620i	−0.953631	+	1.65174i	−0.737470	+	0.675380i	$0.763980\pi$
$150$		0			0
$151$	−11.1699	−	19.3468i	−0.908992	−	1.57442i	−0.815467	−	0.578804i	$-0.803520\pi$
$151$	−11.1699	−	19.3468i	−0.908992	−	1.57442i	−0.0935251	−	0.995617i	$-0.529814\pi$
$152$		0			0
$153$	10.4406			0.844076
$154$		0			0
$155$	4.87079			0.391231
$156$		0			0
$157$	−1.76301	−	3.05363i	−0.140704	−	0.243706i	0.787058	−	0.616879i	$-0.211603\pi$
$157$	−1.76301	−	3.05363i	−0.140704	−	0.243706i	−0.927762	+	0.373173i	$0.878270\pi$
$158$		0			0
$159$	1.26382	−	2.18900i	0.100227	−	0.173599i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	8.12610	−	14.0748i	0.636485	−	1.10242i	−0.349714	−	0.936857i	$-0.613721\pi$
$163$	8.12610	−	14.0748i	0.636485	−	1.10242i	0.986198	−	0.165568i	$-0.0529456\pi$
$164$		0			0
$165$	0.136296	+	0.236072i	0.0106107	+	0.0183782i
$166$		0			0
$167$	3.99714			0.309308			0.154654	−	0.987969i	$-0.450574\pi$
$167$	3.99714			0.309308			0.154654	+	0.987969i	$0.450574\pi$
$168$		0			0
$169$	−7.83532			−0.602717
$170$		0			0
$171$	0.207914	+	0.360117i	0.0158996	+	0.0275389i
$172$		0			0
$173$	8.81070	−	15.2606i	0.669865	−	1.16024i	−0.308077	−	0.951361i	$-0.599685\pi$
$173$	8.81070	−	15.2606i	0.669865	−	1.16024i	0.977942	−	0.208878i	$-0.0669813\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.00202	+	5.19965i	−0.225646	+	0.390830i
$178$		0			0
$179$	−12.6406	−	21.8941i	−0.944799	−	1.63644i	−0.756153	−	0.654395i	$-0.772923\pi$
$179$	−12.6406	−	21.8941i	−0.944799	−	1.63644i	−0.188646	−	0.982045i	$-0.560410\pi$
$180$		0			0
$181$	−18.4950			−1.37473			−0.687363	−	0.726315i	$-0.741232\pi$
$181$	−18.4950			−1.37473			−0.687363	+	0.726315i	$0.741232\pi$
$182$		0			0
$183$	−10.5236			−0.777927
$184$		0			0
$185$	−0.577014	−	0.999417i	−0.0424229	−	0.0734786i
$186$		0			0
$187$	0.752035	−	1.30256i	0.0549942	−	0.0952528i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.93289	+	17.2043i	−0.718719	+	1.24486i	0.242788	+	0.970079i	$0.421938\pi$
$191$	−9.93289	+	17.2043i	−0.718719	+	1.24486i	−0.961508	+	0.274779i	$0.911395\pi$
$192$		0			0
$193$	5.71676	+	9.90172i	0.411501	+	0.712741i	0.995054	−	0.0993341i	$-0.0316712\pi$
$193$	5.71676	+	9.90172i	0.411501	+	0.712741i	−0.583553	+	0.812075i	$0.698338\pi$
$194$		0			0
$195$	−2.69070			−0.192685
$196$		0			0
$197$	−4.56273			−0.325081			−0.162541	−	0.986702i	$-0.551969\pi$
$197$	−4.56273			−0.325081			−0.162541	+	0.986702i	$0.551969\pi$
$198$		0			0
$199$	−7.22146	−	12.5079i	−0.511916	−	0.886664i	−0.999905	−	0.0138143i	$-0.995603\pi$
$199$	−7.22146	−	12.5079i	−0.511916	−	0.886664i	0.487989	−	0.872850i	$-0.337731\pi$
$200$		0			0
$201$	−4.83045	+	8.36658i	−0.340713	+	0.590133i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.21669	+	3.83941i	−0.154820	+	0.268156i
$206$		0			0
$207$	−7.08861	−	12.2778i	−0.492693	−	0.853369i
$208$		0			0
$209$	0.0599037			0.00414363
$210$		0			0
$211$	6.63651			0.456876			0.228438	−	0.973558i	$-0.426638\pi$
$211$	6.63651			0.456876			0.228438	+	0.973558i	$0.426638\pi$
$212$		0			0
$213$	5.36672	+	9.29543i	0.367721	+	0.636912i
$214$		0			0
$215$	2.08861	−	3.61758i	0.142442	−	0.246717i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	3.55759	−	6.16193i	0.240400	−	0.416385i
$220$		0			0
$221$	7.42317	+	12.8573i	0.499337	+	0.864876i
$222$		0			0
$223$	20.3325			1.36156			0.680782	−	0.732486i	$-0.261640\pi$
$223$	20.3325			1.36156			0.680782	+	0.732486i	$0.261640\pi$
$224$		0			0
$225$	−1.59819			−0.106546
$226$		0			0
$227$	11.9656	+	20.7250i	0.794185	+	1.37557i	0.923355	+	0.383946i	$0.125435\pi$
$227$	11.9656	+	20.7250i	0.794185	+	1.37557i	−0.129171	+	0.991622i	$0.541231\pi$
$228$		0			0
$229$	1.29767	−	2.24763i	0.0857523	−	0.148527i	−0.819959	−	0.572422i	$-0.806004\pi$
$229$	1.29767	−	2.24763i	0.0857523	−	0.148527i	0.905712	+	0.423895i	$0.139337\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.58189	−	13.1322i	0.496706	−	0.860320i	−0.503287	−	0.864120i	$-0.667876\pi$
$233$	7.58189	−	13.1322i	0.496706	−	0.860320i	0.999993	+	0.00379927i	$0.00120935\pi$
$234$		0			0
$235$	−0.461897	−	0.800028i	−0.0301308	−	0.0521881i
$236$		0			0
$237$	0.133685			0.00868377
$238$		0			0
$239$	10.5656			0.683431			0.341716	−	0.939803i	$-0.388992\pi$
$239$	10.5656			0.683431			0.341716	+	0.939803i	$0.388992\pi$
$240$		0			0
$241$	9.83808	+	17.0401i	0.633726	+	1.09765i	0.986783	+	0.162044i	$0.0518088\pi$
$241$	9.83808	+	17.0401i	0.633726	+	1.09765i	−0.353057	+	0.935602i	$0.614858\pi$
$242$		0			0
$243$	−7.18875	+	12.4513i	−0.461159	+	0.798750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.295648	+	0.512078i	−0.0188117	+	0.0325828i
$248$		0			0
$249$	5.16254	+	8.94178i	0.327163	+	0.566662i
$250$		0			0
$251$	25.0498			1.58113			0.790564	−	0.612380i	$-0.209788\pi$
$251$	25.0498			1.58113			0.790564	+	0.612380i	$0.209788\pi$
$252$		0			0
$253$	−2.04236			−0.128402
$254$		0			0
$255$	−3.86734	−	6.69843i	−0.242182	−	0.419472i
$256$		0			0
$257$	0.857500	−	1.48523i	0.0534894	−	0.0926464i	−0.838041	−	0.545607i	$-0.816299\pi$
$257$	0.857500	−	1.48523i	0.0534894	−	0.0926464i	0.891530	+	0.452961i	$0.149632\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.33639	−	7.51085i	0.268416	−	0.464910i
$262$		0			0
$263$	11.0587	+	19.1542i	0.681906	+	1.18110i	0.974398	+	0.224828i	$0.0721821\pi$
$263$	11.0587	+	19.1542i	0.681906	+	1.18110i	−0.292492	+	0.956268i	$0.594485\pi$
$264$		0			0
$265$	2.13487			0.131144
$266$		0			0
$267$	−18.8454			−1.15332
$268$		0			0
$269$	−15.9630	−	27.6488i	−0.973283	−	1.68578i	−0.685488	−	0.728084i	$-0.740411\pi$
$269$	−15.9630	−	27.6488i	−0.973283	−	1.68578i	−0.287796	−	0.957692i	$-0.592922\pi$
$270$		0			0
$271$	−12.8883	+	22.3232i	−0.782910	+	1.35604i	0.147329	+	0.989088i	$0.452932\pi$
$271$	−12.8883	+	22.3232i	−0.782910	+	1.35604i	−0.930239	+	0.366953i	$0.880401\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.115117	+	0.199389i	−0.00694182	+	0.0120236i
$276$		0			0
$277$	4.00877	+	6.94340i	0.240864	+	0.417188i	0.960961	−	0.276685i	$-0.0892360\pi$
$277$	4.00877	+	6.94340i	0.240864	+	0.417188i	−0.720097	+	0.693874i	$0.755903\pi$
$278$		0			0
$279$	7.78445			0.466043
$280$		0			0
$281$	−3.13207			−0.186844			−0.0934218	−	0.995627i	$-0.529781\pi$
$281$	−3.13207			−0.186844			−0.0934218	+	0.995627i	$0.529781\pi$
$282$		0			0
$283$	1.58524	+	2.74571i	0.0942325	+	0.163216i	0.909288	−	0.416167i	$-0.136627\pi$
$283$	1.58524	+	2.74571i	0.0942325	+	0.163216i	−0.815056	+	0.579383i	$0.803294\pi$
$284$		0			0
$285$	0.154027	−	0.266783i	0.00912380	−	0.0158029i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−12.8386	+	22.2371i	−0.755212	+	1.30806i
$290$		0			0
$291$	2.54298	+	4.40457i	0.149072	+	0.258200i
$292$		0			0
$293$	17.5264			1.02390			0.511952	−	0.859014i	$-0.328923\pi$
$293$	17.5264			1.02390			0.511952	+	0.859014i	$0.328923\pi$
$294$		0			0
$295$	−5.07107			−0.295249
$296$		0			0
$297$	0.626717	+	1.08550i	0.0363658	+	0.0629874i
$298$		0			0
$299$	10.0798	−	17.4588i	0.582932	−	1.00967i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	4.37310	−	7.57443i	0.251228	−	0.435139i
$304$		0			0
$305$	−4.44417	−	7.69752i	−0.254472	−	0.440759i
$306$		0			0
$307$	−2.11063			−0.120460			−0.0602300	−	0.998185i	$-0.519183\pi$
$307$	−2.11063			−0.120460			−0.0602300	+	0.998185i	$0.519183\pi$
$308$		0			0
$309$	12.5273			0.712651
$310$		0			0
$311$	10.4075	+	18.0263i	0.590153	+	1.02217i	0.994211	+	0.107442i	$0.0342659\pi$
$311$	10.4075	+	18.0263i	0.590153	+	1.02217i	−0.404058	+	0.914733i	$0.632401\pi$
$312$		0			0
$313$	−10.6930	+	18.5208i	−0.604405	+	1.04686i	0.387741	+	0.921769i	$0.373256\pi$
$313$	−10.6930	+	18.5208i	−0.604405	+	1.04686i	−0.992145	+	0.125091i	$0.960078\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.74547	+	13.4155i	−0.435029	+	0.753492i	−0.997298	−	0.0734623i	$-0.976595\pi$
$317$	−7.74547	+	13.4155i	−0.435029	+	0.753492i	0.562269	+	0.826954i	$0.309928\pi$
$318$		0			0
$319$	−0.624697	−	1.08201i	−0.0349763	−	0.0605807i
$320$		0			0
$321$	−15.9436			−0.889886
$322$		0			0
$323$	−1.69974			−0.0945760
$324$		0			0
$325$	−1.13630	−	1.96812i	−0.0630304	−	0.109172i
$326$		0			0
$327$	−5.03528	+	8.72135i	−0.278451	+	0.482292i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.26180	−	7.38165i	0.234250	−	0.405732i	−0.724805	−	0.688954i	$-0.758070\pi$
$331$	4.26180	−	7.38165i	0.234250	−	0.405732i	0.959054	+	0.283222i	$0.0914033\pi$
$332$		0			0
$333$	−0.922179	−	1.59726i	−0.0505351	−	0.0875294i
$334$		0			0
$335$	−8.15968			−0.445811
$336$		0			0
$337$	−18.1246			−0.987309			−0.493655	−	0.869658i	$-0.664339\pi$
$337$	−18.1246			−0.987309			−0.493655	+	0.869658i	$0.664339\pi$
$338$		0			0
$339$	−10.8907	−	18.8633i	−0.591503	−	1.02451i
$340$		0			0
$341$	0.560711	−	0.971179i	0.0303642	−	0.0525923i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−5.25141	+	9.09571i	−0.282727	+	0.489697i
$346$		0			0
$347$	−2.05113	−	3.55266i	−0.110110	−	0.190717i	0.805704	−	0.592318i	$-0.201787\pi$
$347$	−2.05113	−	3.55266i	−0.110110	−	0.190717i	−0.915815	+	0.401601i	$0.868454\pi$
$348$		0			0
$349$	8.67850			0.464549			0.232275	−	0.972650i	$-0.425383\pi$
$349$	8.67850			0.464549			0.232275	+	0.972650i	$0.425383\pi$
$350$		0			0
$351$	−12.3724			−0.660388
$352$		0			0
$353$	15.0581	+	26.0814i	0.801462	+	1.38817i	0.918653	+	0.395064i	$0.129278\pi$
$353$	15.0581	+	26.0814i	0.801462	+	1.38817i	−0.117191	+	0.993109i	$0.537389\pi$
$354$		0			0
$355$	−4.53278	+	7.85100i	−0.240575	+	0.416688i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.1421	+	31.4231i	−0.957505	+	1.65845i	−0.228977	+	0.973432i	$0.573538\pi$
$359$	−18.1421	+	31.4231i	−0.957505	+	1.65845i	−0.728528	+	0.685016i	$0.759795\pi$
$360$		0			0
$361$	9.46615	+	16.3959i	0.498219	+	0.862940i
$362$		0			0
$363$	−12.9610			−0.680277
$364$		0			0
$365$	6.00955			0.314554
$366$		0			0
$367$	−5.35574	−	9.27641i	−0.279567	−	0.484225i	0.691710	−	0.722175i	$-0.256858\pi$
$367$	−5.35574	−	9.27641i	−0.279567	−	0.484225i	−0.971277	+	0.237951i	$0.923524\pi$
$368$		0			0
$369$	−3.54269	+	6.13612i	−0.184425	+	0.319434i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−2.82167	+	4.88728i	−0.146101	+	0.253054i	−0.929783	−	0.368108i	$-0.880006\pi$
$373$	−2.82167	+	4.88728i	−0.146101	+	0.253054i	0.783682	+	0.621162i	$0.213339\pi$
$374$		0			0
$375$	0.591990	+	1.02536i	0.0305702	+	0.0529492i
$376$		0			0
$377$	12.3325			0.635156
$378$		0			0
$379$	−1.59944			−0.0821575			−0.0410787	−	0.999156i	$-0.513079\pi$
$379$	−1.59944			−0.0821575			−0.0410787	+	0.999156i	$0.513079\pi$
$380$		0			0
$381$	−4.97882	−	8.62357i	−0.255073	−	0.441799i
$382$		0			0
$383$	−14.4447	+	25.0189i	−0.738089	+	1.27841i	0.215266	+	0.976555i	$0.430938\pi$
$383$	−14.4447	+	25.0189i	−0.738089	+	1.27841i	−0.953355	+	0.301852i	$0.902395\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.33801	−	5.78160i	0.169680	−	0.293895i
$388$		0			0
$389$	11.7613	+	20.3712i	0.596323	+	1.03286i	0.993359	+	0.115058i	$0.0367055\pi$
$389$	11.7613	+	20.3712i	0.596323	+	1.03286i	−0.397036	+	0.917803i	$0.629961\pi$
$390$		0			0
$391$	57.9509			2.93070
$392$		0			0
$393$	2.11006			0.106438
$394$		0			0
$395$	0.0564558	+	0.0977843i	0.00284060	+	0.00492006i
$396$		0			0
$397$	−8.29032	+	14.3593i	−0.416079	+	0.720671i	−0.995541	−	0.0943288i	$-0.969930\pi$
$397$	−8.29032	+	14.3593i	−0.416079	+	0.720671i	0.579462	+	0.814999i	$0.303263\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.760807	−	1.31776i	0.0379929	−	0.0658056i	−0.846404	−	0.532542i	$-0.821237\pi$
$401$	0.760807	−	1.31776i	0.0379929	−	0.0658056i	0.884397	+	0.466736i	$0.154570\pi$
$402$		0			0
$403$	5.53466	+	9.58630i	0.275701	+	0.477528i
$404$		0			0
$405$	1.65120			0.0820488
$406$		0			0
$407$	−0.265697			−0.0131701
$408$		0			0
$409$	−2.71464	−	4.70189i	−0.134230	−	0.232493i	0.791073	−	0.611722i	$-0.209523\pi$
$409$	−2.71464	−	4.70189i	−0.134230	−	0.232493i	−0.925303	+	0.379228i	$0.876189\pi$
$410$		0			0
$411$	6.69760	−	11.6006i	0.330368	−	0.572214i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−4.36033	+	7.55231i	−0.214040	+	0.370728i
$416$		0			0
$417$	9.13974	+	15.8305i	0.447575	+	0.775223i
$418$		0			0
$419$	−12.4199			−0.606750			−0.303375	−	0.952871i	$-0.598114\pi$
$419$	−12.4199			−0.606750			−0.303375	+	0.952871i	$0.598114\pi$
$420$		0			0
$421$	−20.6804			−1.00790			−0.503951	−	0.863732i	$-0.668121\pi$
$421$	−20.6804			−1.00790			−0.503951	+	0.863732i	$0.668121\pi$
$422$		0			0
$423$	−0.738200	−	1.27860i	−0.0358925	−	0.0621676i
$424$		0			0
$425$	3.26639	−	5.65755i	0.158443	−	0.274432i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.309746	+	0.536496i	−0.0149547	+	0.0259023i
$430$		0			0
$431$	15.8076	+	27.3795i	0.761424	+	1.31883i	0.942117	+	0.335286i	$0.108833\pi$
$431$	15.8076	+	27.3795i	0.761424	+	1.31883i	−0.180692	+	0.983540i	$0.557834\pi$
$432$		0			0
$433$	31.1247			1.49576			0.747880	−	0.663834i	$-0.231072\pi$
$433$	31.1247			1.49576			0.747880	+	0.663834i	$0.231072\pi$
$434$		0			0
$435$	−6.42501			−0.308055
$436$		0			0
$437$	1.15403	+	1.99883i	0.0552046	+	0.0956172i
$438$		0			0
$439$	0.122199	−	0.211655i	0.00583223	−	0.0101017i	−0.863095	−	0.505042i	$-0.831477\pi$
$439$	0.122199	−	0.211655i	0.00583223	−	0.0101017i	0.868927	+	0.494941i	$0.164810\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.72741	−	2.99196i	0.0820716	−	0.142152i	−0.822068	−	0.569389i	$-0.807180\pi$
$443$	1.72741	−	2.99196i	0.0820716	−	0.142152i	0.904140	+	0.427237i	$0.140513\pi$
$444$		0			0
$445$	−7.95852	−	13.7846i	−0.377270	−	0.653451i
$446$		0			0
$447$	27.5643			1.30375
$448$		0			0
$449$	−15.5329			−0.733044			−0.366522	−	0.930409i	$-0.619452\pi$
$449$	−15.5329			−0.733044			−0.366522	+	0.930409i	$0.619452\pi$
$450$		0			0
$451$	0.510357	+	0.883964i	0.0240318	+	0.0416243i
$452$		0			0
$453$	−13.2249	+	22.9062i	−0.621360	+	1.07623i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.26896	−	9.12610i	0.246471	−	0.426901i	−0.716073	−	0.698026i	$-0.754062\pi$
$457$	5.26896	−	9.12610i	0.246471	−	0.426901i	0.962544	+	0.271124i	$0.0873955\pi$
$458$		0			0
$459$	−17.7828	−	30.8007i	−0.830028	−	1.43765i
$460$		0			0
$461$	−5.98972			−0.278969			−0.139485	−	0.990224i	$-0.544545\pi$
$461$	−5.98972			−0.278969			−0.139485	+	0.990224i	$0.544545\pi$
$462$		0			0
$463$	−33.3601			−1.55038			−0.775188	−	0.631731i	$-0.782345\pi$
$463$	−33.3601			−1.55038			−0.775188	+	0.631731i	$0.782345\pi$
$464$		0			0
$465$	−2.88345	−	4.99429i	−0.133717	−	0.231605i
$466$		0			0
$467$	9.85379	−	17.0673i	0.455979	−	0.789779i	−0.542765	−	0.839885i	$-0.682623\pi$
$467$	9.85379	−	17.0673i	0.455979	−	0.789779i	0.998744	+	0.0501059i	$0.0159559\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.08737	+	3.61543i	−0.0961810	+	0.166590i
$472$		0			0
$473$	−0.480870	−	0.832892i	−0.0221104	−	0.0382964i
$474$		0			0
$475$	0.260186			0.0119382
$476$		0			0
$477$	3.41193			0.156222
$478$		0			0
$479$	0.162800	+	0.281978i	0.00743853	+	0.0128839i	0.869721	−	0.493544i	$-0.164299\pi$
$479$	0.162800	+	0.281978i	0.00743853	+	0.0128839i	−0.862282	+	0.506428i	$0.830966\pi$
$480$		0			0
$481$	1.31132	−	2.27127i	0.0597909	−	0.103561i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.14782	+	3.72014i	−0.0975277	+	0.168923i
$486$		0			0
$487$	8.46021	+	14.6535i	0.383369	+	0.664014i	0.991541	−	0.129791i	$-0.0414306\pi$
$487$	8.46021	+	14.6535i	0.383369	+	0.664014i	−0.608173	+	0.793805i	$0.708097\pi$
$488$		0			0
$489$	−19.2423			−0.870165
$490$		0			0
$491$	15.0203			0.677859			0.338929	−	0.940812i	$-0.389935\pi$
$491$	15.0203			0.677859			0.338929	+	0.940812i	$0.389935\pi$
$492$		0			0
$493$	17.7255	+	30.7014i	0.798314	+	1.38272i
$494$		0			0
$495$	−0.183979	+	0.318662i	−0.00826926	+	0.0143228i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−20.5215	+	35.5443i	−0.918670	+	1.59118i	−0.117233	+	0.993104i	$0.537402\pi$
$499$	−20.5215	+	35.5443i	−0.918670	+	1.59118i	−0.801437	+	0.598079i	$0.795931\pi$
$500$		0			0
$501$	−2.36627	−	4.09850i	−0.105717	−	0.183107i
$502$		0			0
$503$	−8.29741			−0.369963			−0.184982	−	0.982742i	$-0.559223\pi$
$503$	−8.29741			−0.369963			−0.184982	+	0.982742i	$0.559223\pi$
$504$		0			0
$505$	7.38712			0.328722
$506$		0			0
$507$	4.63843	+	8.03400i	0.206000	+	0.356802i
$508$		0			0
$509$	4.35633	−	7.54538i	0.193091	−	0.334443i	−0.753182	−	0.657812i	$-0.771482\pi$
$509$	4.35633	−	7.54538i	0.193091	−	0.334443i	0.946273	+	0.323369i	$0.104815\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.708248	−	1.22672i	0.0312699	−	0.0541611i
$514$		0			0
$515$	5.29032	+	9.16311i	0.233120	+	0.403775i
$516$		0			0
$517$	−0.212689			−0.00935404
$518$		0			0
$519$	−20.8634			−0.915800
$520$		0			0
$521$	−13.5528	−	23.4742i	−0.593760	−	1.02842i	−0.993721	−	0.111890i	$-0.964310\pi$
$521$	−13.5528	−	23.4742i	−0.593760	−	1.02842i	0.399961	−	0.916532i	$-0.369024\pi$
$522$		0			0
$523$	−0.685928	+	1.18806i	−0.0299935	+	0.0519503i	−0.880633	−	0.473800i	$-0.842882\pi$
$523$	−0.685928	+	1.18806i	−0.0299935	+	0.0519503i	0.850639	+	0.525750i	$0.176215\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.9099	+	27.5567i	−0.693045	+	1.20039i
$528$		0			0
$529$	−27.8454	−	48.2297i	−1.21067	−	2.09694i
$530$		0			0
$531$	−8.10454			−0.351707
$532$		0			0
$533$	−10.0753			−0.436408
$534$		0			0
$535$	−6.73306	−	11.6620i	−0.291096	−	0.504192i
$536$		0			0
$537$	−14.9662	+	25.9221i	−0.645837	+	1.11862i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−4.28279	+	7.41802i	−0.184132	+	0.318925i	−0.943284	−	0.331988i	$-0.892281\pi$
$541$	−4.28279	+	7.41802i	−0.184132	+	0.318925i	0.759152	+	0.650913i	$0.225614\pi$
$542$		0			0
$543$	10.9489	+	18.9640i	0.469861	+	0.813823i
$544$		0			0
$545$	−8.50568			−0.364343
$546$		0			0
$547$	44.2056			1.89009			0.945046	−	0.326936i	$-0.106016\pi$
$547$	44.2056			1.89009			0.945046	+	0.326936i	$0.106016\pi$
$548$		0			0
$549$	−7.10263	−	12.3021i	−0.303133	−	0.525042i
$550$		0			0
$551$	−0.705966	+	1.22277i	−0.0300751	+	0.0520917i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.683172	+	1.18329i	−0.0289991	+	0.0502278i
$556$		0			0
$557$	6.66926	+	11.5515i	0.282586	+	0.489453i	0.972021	−	0.234895i	$-0.0754745\pi$
$557$	6.66926	+	11.5515i	0.282586	+	0.489453i	−0.689435	+	0.724347i	$0.742141\pi$
$558$		0			0
$559$	9.49313			0.401517
$560$		0			0
$561$	−1.78079			−0.0751849
$562$		0			0
$563$	14.8660	+	25.7487i	0.626528	+	1.08518i	0.988243	+	0.152889i	$0.0488578\pi$
$563$	14.8660	+	25.7487i	0.626528	+	1.08518i	−0.361716	+	0.932288i	$0.617809\pi$
$564$		0			0
$565$	9.19841	−	15.9321i	0.386980	−	0.670269i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−11.7930	+	20.4260i	−0.494387	+	0.856303i	−0.999979	−	0.00646948i	$-0.997941\pi$
$569$	−11.7930	+	20.4260i	−0.494387	+	0.856303i	0.505592	+	0.862773i	$0.331274\pi$
$570$		0			0
$571$	−16.3217	−	28.2700i	−0.683042	−	1.18306i	−0.974048	−	0.226342i	$-0.927323\pi$
$571$	−16.3217	−	28.2700i	−0.683042	−	1.18306i	0.291006	−	0.956721i	$-0.406010\pi$
$572$		0			0
$573$	23.5207			0.982591
$574$		0			0
$575$	−8.87079			−0.369937
$576$		0			0
$577$	−14.4098	−	24.9584i	−0.599886	−	1.03903i	−0.992837	−	0.119474i	$-0.961879\pi$
$577$	−14.4098	−	24.9584i	−0.599886	−	1.03903i	0.392951	−	0.919559i	$-0.371454\pi$
$578$		0			0
$579$	6.76852	−	11.7234i	0.281290	−	0.487209i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.245760	−	0.425669i	0.0101783	−	0.0176294i
$584$		0			0
$585$	−1.81602	−	3.14544i	−0.0750832	−	0.130048i
$586$		0			0
$587$	1.82205			0.0752039			0.0376019	−	0.999293i	$-0.488028\pi$
$587$	1.82205			0.0752039			0.0376019	+	0.999293i	$0.488028\pi$
$588$		0			0
$589$	−1.26731			−0.0522186
$590$		0			0
$591$	2.70109	+	4.67842i	0.111108	+	0.192445i
$592$		0			0
$593$	15.4684	−	26.7921i	0.635212	−	1.10022i	−0.351258	−	0.936279i	$-0.614246\pi$
$593$	15.4684	−	26.7921i	0.635212	−	1.10022i	0.986470	−	0.163941i	$-0.0524207\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.55006	+	14.8091i	−0.349931	+	0.606098i
$598$		0			0
$599$	16.1456	+	27.9650i	0.659691	+	1.14262i	0.980696	+	0.195540i	$0.0626460\pi$
$599$	16.1456	+	27.9650i	0.659691	+	1.14262i	−0.321005	+	0.947077i	$0.604021\pi$
$600$		0			0
$601$	25.2829			1.03131			0.515655	−	0.856797i	$-0.327549\pi$
$601$	25.2829			1.03131			0.515655	+	0.856797i	$0.327549\pi$
$602$		0			0
$603$	−13.0407			−0.531060
$604$		0			0
$605$	−5.47350	−	9.48037i	−0.222529	−	0.385432i
$606$		0			0
$607$	−4.64426	+	8.04410i	−0.188505	+	0.326500i	−0.944752	−	0.327786i	$-0.893697\pi$
$607$	−4.64426	+	8.04410i	−0.188505	+	0.326500i	0.756247	+	0.654286i	$0.227031\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.04970	−	1.81814i	0.0424664	−	0.0735540i
$612$		0			0
$613$	−20.0305	−	34.6938i	−0.809023	−	1.40127i	−0.913541	−	0.406746i	$-0.866663\pi$
$613$	−20.0305	−	34.6938i	−0.809023	−	1.40127i	0.104518	−	0.994523i	$-0.466670\pi$
$614$		0			0
$615$	5.24902			0.211661
$616$		0			0
$617$	27.9860			1.12667			0.563336	−	0.826228i	$-0.309518\pi$
$617$	27.9860			1.12667			0.563336	+	0.826228i	$0.309518\pi$
$618$		0			0
$619$	−22.9024	−	39.6681i	−0.920525	−	1.59440i	−0.798605	−	0.601856i	$-0.794428\pi$
$619$	−22.9024	−	39.6681i	−0.920525	−	1.59440i	−0.121920	−	0.992540i	$-0.538905\pi$
$620$		0			0
$621$	−24.1470	+	41.8239i	−0.968986	+	1.67833i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−0.0354624	−	0.0614227i	−0.00141623	−	0.00245299i
$628$		0			0
$629$	7.53901			0.300600
$630$		0			0
$631$	22.5847			0.899082			0.449541	−	0.893260i	$-0.351588\pi$
$631$	22.5847			0.899082			0.449541	+	0.893260i	$0.351588\pi$
$632$		0			0
$633$	−3.92875	−	6.80479i	−0.156154	−	0.270466i
$634$		0			0
$635$	4.20516	−	7.28355i	0.166877	−	0.289039i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−7.24425	+	12.5474i	−0.286578	+	0.496368i
$640$		0			0
$641$	16.7563	+	29.0227i	0.661832	+	1.14633i	0.980134	+	0.198338i	$0.0635543\pi$
$641$	16.7563	+	29.0227i	0.661832	+	1.14633i	−0.318301	+	0.947990i	$0.603112\pi$
$642$		0			0
$643$	−46.4980			−1.83370			−0.916851	−	0.399231i	$-0.869277\pi$
$643$	−46.4980			−1.83370			−0.916851	+	0.399231i	$0.869277\pi$
$644$		0			0
$645$	−4.94575			−0.194739
$646$		0			0
$647$	−0.787826	−	1.36455i	−0.0309726	−	0.0536462i	0.850124	−	0.526583i	$-0.176527\pi$
$647$	−0.787826	−	1.36455i	−0.0309726	−	0.0536462i	−0.881096	+	0.472937i	$0.843194\pi$
$648$		0			0
$649$	−0.583767	+	1.01111i	−0.0229148	+	0.0396897i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.06556	+	10.5059i	−0.237364	+	0.411126i	−0.959957	−	0.280148i	$-0.909617\pi$
$653$	−6.06556	+	10.5059i	−0.237364	+	0.411126i	0.722593	+	0.691273i	$0.242950\pi$
$654$		0			0
$655$	0.891086	+	1.54341i	0.0348176	+	0.0603059i
$656$		0			0
$657$	9.60442			0.374704
$658$		0			0
$659$	35.1682			1.36996			0.684979	−	0.728563i	$-0.259811\pi$
$659$	35.1682			1.36996			0.684979	+	0.728563i	$0.259811\pi$
$660$		0			0
$661$	−0.812124	−	1.40664i	−0.0315880	−	0.0547120i	0.849799	−	0.527106i	$-0.176723\pi$
$661$	−0.812124	−	1.40664i	−0.0315880	−	0.0547120i	−0.881387	+	0.472395i	$0.843390\pi$
$662$		0			0
$663$	8.78888	−	15.2228i	0.341332	−	0.591204i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	24.0692	−	41.6891i	0.931963	−	1.61421i
$668$		0			0
$669$	−12.0366	−	20.8481i	−0.465363	−	0.806032i
$670$		0			0
$671$	−2.04640			−0.0790003
$672$		0			0
$673$	−24.3194			−0.937443			−0.468721	−	0.883346i	$-0.655285\pi$
$673$	−24.3194			−0.937443			−0.468721	+	0.883346i	$0.655285\pi$
$674$		0			0
$675$	2.72208	+	4.71479i	0.104773	+	0.181472i
$676$		0			0
$677$	6.07763	−	10.5268i	0.233582	−	0.404577i	−0.725277	−	0.688457i	$-0.758288\pi$
$677$	6.07763	−	10.5268i	0.233582	−	0.404577i	0.958860	+	0.283880i	$0.0916218\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	14.1670	−	24.5380i	0.542882	−	0.940299i
$682$		0			0
$683$	16.2579	+	28.1595i	0.622091	+	1.07749i	0.989096	+	0.147275i	$0.0470501\pi$
$683$	16.2579	+	28.1595i	0.622091	+	1.07749i	−0.367004	+	0.930219i	$0.619617\pi$
$684$		0			0
$685$	11.3137			0.432275
$686$		0			0
$687$	−3.07282			−0.117236
$688$		0			0
$689$	2.42584	+	4.20168i	0.0924172	+	0.160071i
$690$		0			0
$691$	10.1656	−	17.6073i	0.386716	−	0.669812i	−0.605290	−	0.796005i	$-0.706943\pi$
$691$	10.1656	−	17.6073i	0.386716	−	0.669812i	0.992006	+	0.126194i	$0.0402761\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.71951	+	13.3706i	−0.292818	+	0.507175i
$696$		0			0
$697$	−14.4811	−	25.0820i	−0.548512	−	0.950050i
$698$		0			0
$699$	−17.9536			−0.679068
$700$		0			0
$701$	7.35321			0.277727			0.138863	−	0.990312i	$-0.455655\pi$
$701$	7.35321			0.277727			0.138863	+	0.990312i	$0.455655\pi$
$702$		0			0
$703$	0.150131	+	0.260034i	0.00566230	+	0.00980738i
$704$		0			0
$705$	−0.546876	+	0.947217i	−0.0205965	+	0.0356743i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5.83188	−	10.1011i	0.219021	−	0.379355i	−0.735488	−	0.677538i	$-0.763047\pi$
$709$	5.83188	−	10.1011i	0.219021	−	0.379355i	0.954509	+	0.298183i	$0.0963805\pi$
$710$		0			0
$711$	0.0902272	+	0.156278i	0.00338378	+	0.00586089i
$712$		0			0
$713$	43.2077			1.61814
$714$		0			0
$715$	−0.523229			−0.0195676
$716$		0			0
$717$	−6.25472	−	10.8335i	−0.233587	−	0.404584i
$718$		0			0
$719$	−2.84285	+	4.92397i	−0.106021	+	0.183633i	−0.914155	−	0.405365i	$-0.867144\pi$
$719$	−2.84285	+	4.92397i	−0.106021	+	0.183633i	0.808134	+	0.588998i	$0.200478\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	11.6481	−	20.1751i	0.433197	−	0.750319i
$724$		0			0
$725$	−2.71331	−	4.69959i	−0.100770	−	0.174538i
$726$		0			0
$727$	−18.6873			−0.693074			−0.346537	−	0.938036i	$-0.612643\pi$
$727$	−18.6873			−0.693074			−0.346537	+	0.938036i	$0.612643\pi$
$728$		0			0
$729$	21.9763			0.813936
$730$		0			0
$731$	13.6444	+	23.6329i	0.504658	+	0.874094i
$732$		0			0
$733$	0.918469	−	1.59083i	0.0339244	−	0.0587588i	−0.848565	−	0.529092i	$-0.822533\pi$
$733$	0.918469	−	1.59083i	0.0339244	−	0.0587588i	0.882489	+	0.470333i	$0.155866\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.939319	+	1.62695i	−0.0346003	+	0.0599294i
$738$		0			0
$739$	12.2817	+	21.2725i	0.451789	+	0.782522i	0.998497	−	0.0548012i	$-0.0174525\pi$
$739$	12.2817	+	21.2725i	0.451789	+	0.782522i	−0.546708	+	0.837323i	$0.684119\pi$
$740$		0			0
$741$	0.700083			0.0257182
$742$		0			0
$743$	−27.1926			−0.997601			−0.498800	−	0.866717i	$-0.666226\pi$
$743$	−27.1926			−0.997601			−0.498800	+	0.866717i	$0.666226\pi$
$744$		0			0
$745$	11.6406	+	20.1620i	0.426477	+	0.738679i
$746$		0			0
$747$	−6.96864	+	12.0700i	−0.254969	+	0.441620i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.164228	+	0.284452i	−0.00599278	+	0.0103798i	−0.869006	−	0.494801i	$-0.835241\pi$
$751$	−0.164228	+	0.284452i	−0.00599278	+	0.0103798i	0.863013	+	0.505181i	$0.168574\pi$
$752$		0			0
$753$	−14.8292	−	25.6849i	−0.540406	−	0.936011i
$754$		0			0
$755$	−22.3398			−0.813027
$756$		0			0
$757$	−48.6331			−1.76760			−0.883801	−	0.467864i	$-0.845024\pi$
$757$	−48.6331			−1.76760			−0.883801	+	0.467864i	$0.845024\pi$
$758$		0			0
$759$	1.20906	+	2.09414i	0.0438859	+	0.0760126i
$760$		0			0
$761$	−4.01127	+	6.94772i	−0.145408	+	0.251854i	−0.929525	−	0.368759i	$-0.879783\pi$
$761$	−4.01127	+	6.94772i	−0.145408	+	0.251854i	0.784117	+	0.620613i	$0.213116\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	5.22032	−	9.04186i	0.188741	−	0.326909i
$766$		0			0
$767$	−5.76224	−	9.98048i	−0.208062	−	0.360374i
$768$		0			0
$769$	−35.6370			−1.28510			−0.642552	−	0.766242i	$-0.722124\pi$
$769$	−35.6370			−1.28510			−0.642552	+	0.766242i	$0.722124\pi$
$770$		0			0
$771$	−2.03053			−0.0731276
$772$		0			0
$773$	24.7978	+	42.9510i	0.891914	+	1.54484i	0.837579	+	0.546317i	$0.183971\pi$
$773$	24.7978	+	42.9510i	0.891914	+	1.54484i	0.0543350	+	0.998523i	$0.482696\pi$
$774$		0			0
$775$	2.43539	−	4.21822i	0.0874819	−	0.151523i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.576751	−	0.998962i	0.0206642	−	0.0357915i
$780$		0			0
$781$	1.04360	+	1.80757i	0.0373430	+	0.0646799i
$782$		0			0
$783$	−29.5434			−1.05580
$784$		0			0
$785$	−3.52603			−0.125849
$786$		0			0
$787$	10.7217	+	18.5706i	0.382188	+	0.661969i	0.991375	−	0.131058i	$-0.0418373\pi$
$787$	10.7217	+	18.5706i	0.382188	+	0.661969i	−0.609187	+	0.793027i	$0.708504\pi$
$788$		0			0
$789$	13.0932	−	22.6781i	0.466131	−	0.807363i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	10.0998	−	17.4933i	0.358654	−	0.621206i
$794$		0			0
$795$	−1.26382	−	2.18900i	−0.0448231	−	0.0776358i
$796$		0			0
$797$	−35.1429			−1.24482			−0.622412	−	0.782690i	$-0.713847\pi$
$797$	−35.1429			−1.24482			−0.622412	+	0.782690i	$0.713847\pi$
$798$		0			0
$799$	6.03494			0.213501
$800$		0			0
$801$	−12.7193	−	22.0304i	−0.449413	−	0.778405i
$802$		0			0
$803$	0.691802	−	1.19824i	0.0244132	−	0.0422848i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−18.8999	+	32.7356i	−0.665308	+	1.15235i
$808$		0			0
$809$	1.16299	+	2.01435i	0.0408884	+	0.0708208i	0.885745	−	0.464171i	$-0.153648\pi$
$809$	1.16299	+	2.01435i	0.0408884	+	0.0708208i	−0.844857	+	0.534992i	$0.820315\pi$
$810$		0			0
$811$	11.8045			0.414512			0.207256	−	0.978287i	$-0.433547\pi$
$811$	11.8045			0.414512			0.207256	+	0.978287i	$0.433547\pi$
$812$		0			0
$813$	30.5190			1.07035
$814$		0			0
$815$	−8.12610	−	14.0748i	−0.284645	−	0.493019i
$816$		0			0
$817$	−0.543428	+	0.941245i	−0.0190121	+	0.0329300i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	25.8895	−	44.8419i	0.903550	−	1.56499i	0.0806973	−	0.996739i	$-0.474285\pi$
$821$	25.8895	−	44.8419i	0.903550	−	1.56499i	0.822852	−	0.568255i	$-0.192381\pi$
$822$		0			0
$823$	20.3129	+	35.1830i	0.708064	+	1.22640i	0.965574	+	0.260128i	$0.0837646\pi$
$823$	20.3129	+	35.1830i	0.708064	+	1.22640i	−0.257510	+	0.966276i	$0.582902\pi$
$824$		0			0
$825$	0.272593			0.00949045
$826$		0			0
$827$	12.6201			0.438846			0.219423	−	0.975630i	$-0.429583\pi$
$827$	12.6201			0.438846			0.219423	+	0.975630i	$0.429583\pi$
$828$		0			0
$829$	−25.2452	−	43.7260i	−0.876803	−	1.51867i	−0.854829	−	0.518909i	$-0.826338\pi$
$829$	−25.2452	−	43.7260i	−0.876803	−	1.51867i	−0.0219739	−	0.999759i	$-0.506995\pi$
$830$		0			0
$831$	4.74630	−	8.22084i	0.164647	−	0.285178i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.99857	−	3.46163i	0.0691634	−	0.119795i
$836$		0			0
$837$	−13.2587	−	22.9647i	−0.458287	−	0.793776i
$838$		0			0
$839$	4.41032			0.152261			0.0761305	−	0.997098i	$-0.475743\pi$
$839$	4.41032			0.152261			0.0761305	+	0.997098i	$0.475743\pi$
$840$		0			0
$841$	0.448205			0.0154553
$842$		0			0
$843$	1.85415	+	3.21149i	0.0638604	+	0.110610i
$844$		0			0
$845$	−3.91766	+	6.78559i	−0.134772	+	0.233431i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.87689	−	3.25086i	0.0644146	−	0.111569i
$850$		0			0
$851$	−5.11857	−	8.86561i	−0.175462	−	0.303909i
$852$		0			0
$853$	−20.6785			−0.708018			−0.354009	−	0.935242i	$-0.615182\pi$
$853$	−20.6785			−0.708018			−0.354009	+	0.935242i	$0.615182\pi$
$854$		0			0
$855$	0.415828			0.0142210
$856$		0			0
$857$	−2.96527	−	5.13600i	−0.101292	−	0.175443i	0.810925	−	0.585150i	$-0.198964\pi$
$857$	−2.96527	−	5.13600i	−0.101292	−	0.175443i	−0.912217	+	0.409707i	$0.865631\pi$
$858$		0			0
$859$	15.6916	−	27.1786i	0.535390	−	0.927322i	−0.463755	−	0.885964i	$-0.653498\pi$
$859$	15.6916	−	27.1786i	0.535390	−	0.927322i	0.999144	−	0.0413587i	$-0.0131686\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−13.0855	+	22.6647i	−0.445435	+	0.771517i	−0.998082	−	0.0618987i	$-0.980284\pi$
$863$	−13.0855	+	22.6647i	−0.445435	+	0.771517i	0.552647	+	0.833415i	$0.313618\pi$
$864$		0			0
$865$	−8.81070	−	15.2606i	−0.299573	−	0.518875i
$866$		0			0
$867$	30.4013			1.03248
$868$		0			0
$869$	0.0259961			0.000881857
$870$		0			0
$871$	−9.27182	−	16.0593i	−0.314163	−	0.544147i
$872$		0			0
$873$	−3.43264	+	5.94550i	−0.116177	+	0.201225i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	26.1152	−	45.2328i	0.881847	−	1.52740i	0.0325618	−	0.999470i	$-0.489633\pi$
$877$	26.1152	−	45.2328i	0.881847	−	1.52740i	0.849285	−	0.527934i	$-0.177033\pi$
$878$		0			0
$879$	−10.3754	−	17.9708i	−0.349955	−	0.606140i
$880$		0			0
$881$	−33.5930			−1.13178			−0.565888	−	0.824482i	$-0.691467\pi$
$881$	−33.5930			−1.13178			−0.565888	+	0.824482i	$0.691467\pi$
$882$		0			0
$883$	30.5923			1.02951			0.514757	−	0.857336i	$-0.327882\pi$
$883$	30.5923			1.02951			0.514757	+	0.857336i	$0.327882\pi$
$884$		0			0
$885$	3.00202	+	5.19965i	0.100912	+	0.174784i
$886$		0			0
$887$	24.5152	−	42.4616i	0.823141	−	1.42572i	−0.0801908	−	0.996780i	$-0.525553\pi$
$887$	24.5152	−	42.4616i	0.823141	−	1.42572i	0.903332	−	0.428942i	$-0.141114\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.190081	−	0.329231i	0.00636797	−	0.0110296i
$892$		0			0
$893$	0.120179	+	0.208156i	0.00402164	+	0.00696568i
$894$		0			0
$895$	−25.2811			−0.845054
$896$		0			0
$897$	−23.8686			−0.796951
$898$		0			0
$899$	13.2160	+	22.8907i	0.440777	+	0.763448i
$900$		0			0
$901$	−6.97331	+	12.0781i	−0.232315	+	0.402381i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.24752	+	16.0172i	−0.307398	+	0.532429i
$906$		0			0
$907$	18.4507	+	31.9575i	0.612644	+	1.06113i	0.990793	+	0.135386i	$0.0432274\pi$
$907$	18.4507	+	31.9575i	0.612644	+	1.06113i	−0.378149	+	0.925745i	$0.623439\pi$
$908$		0			0
$909$	11.8060			0.391582
$910$		0			0
$911$	34.6118			1.14674			0.573371	−	0.819296i	$-0.305636\pi$
$911$	34.6118			1.14674			0.573371	+	0.819296i	$0.305636\pi$
$912$		0			0
$913$	1.00390	+	1.73880i	0.0332241	+	0.0575459i
$914$		0			0
$915$	−5.26180	+	9.11371i	−0.173950	+	0.301290i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	15.4085	−	26.6883i	0.508279	−	0.880365i	−0.491675	−	0.870779i	$-0.663615\pi$
$919$	15.4085	−	26.6883i	0.508279	−	0.880365i	0.999954	−	0.00958624i	$-0.00305144\pi$
$920$		0			0
$921$	1.24947	+	2.16415i	0.0411715	+	0.0713111i
$922$		0			0
$923$	−20.6023			−0.678134
$924$		0			0
$925$	−1.15403			−0.0379442
$926$		0			0
$927$	8.45496	+	14.6444i	0.277697	+	0.480986i
$928$		0			0
$929$	−8.66936	+	15.0158i	−0.284433	+	0.492652i	−0.972471	−	0.233022i	$-0.925139\pi$
$929$	−8.66936	+	15.0158i	−0.284433	+	0.492652i	0.688039	+	0.725674i	$0.258472\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	12.3222	−	21.3427i	0.403411	−	0.698729i
$934$		0			0
$935$	−0.752035	−	1.30256i	−0.0245942	−	0.0425983i
$936$		0			0
$937$	−44.3736			−1.44962			−0.724811	−	0.688948i	$-0.758073\pi$
$937$	−44.3736			−1.44962			−0.724811	+	0.688948i	$0.758073\pi$
$938$		0			0
$939$	25.3206			0.826307
$940$		0			0
$941$	0.829670	+	1.43703i	0.0270465	+	0.0468458i	0.879232	−	0.476394i	$-0.158056\pi$
$941$	0.829670	+	1.43703i	0.0270465	+	0.0468458i	−0.852185	+	0.523240i	$0.824723\pi$
$942$		0			0
$943$	−19.6638	+	34.0586i	−0.640340	+	1.10910i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.7243	−	32.4314i	0.608458	−	1.05388i	−0.383037	−	0.923733i	$-0.625122\pi$
$947$	18.7243	−	32.4314i	0.608458	−	1.05388i	0.991495	−	0.130147i	$-0.0415448\pi$
$948$		0			0
$949$	6.82863	+	11.8275i	0.221667	+	0.383938i
$950$		0			0
$951$	18.3409			0.594746
$952$		0			0
$953$	37.5875			1.21758			0.608789	−	0.793332i	$-0.291656\pi$
$953$	37.5875			1.21758			0.608789	+	0.793332i	$0.291656\pi$
$954$		0			0
$955$	9.93289	+	17.2043i	0.321421	+	0.556717i
$956$		0			0
$957$	−0.739628	+	1.28107i	−0.0239088	+	0.0414112i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	3.63772	−	6.30072i	0.117346	−	0.203249i
$962$		0			0
$963$	−10.7607	−	18.6381i	−0.346760	−	0.600605i
$964$		0			0
$965$	11.4335			0.368058
$966$		0			0
$967$	−24.5757			−0.790302			−0.395151	−	0.918616i	$-0.629308\pi$
$967$	−24.5757			−0.790302			−0.395151	+	0.918616i	$0.629308\pi$
$968$		0			0
$969$	1.00623	+	1.74284i	0.0323247	+	0.0559880i
$970$		0			0
$971$	24.3177	−	42.1195i	0.780392	−	1.35168i	−0.151321	−	0.988485i	$-0.548353\pi$
$971$	24.3177	−	42.1195i	0.780392	−	1.35168i	0.931713	−	0.363194i	$-0.118314\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−1.34535	+	2.33022i	−0.0430857	+	0.0746267i
$976$		0			0
$977$	−1.16872	−	2.02428i	−0.0373906	−	0.0647623i	0.846725	−	0.532032i	$-0.178571\pi$
$977$	−1.16872	−	2.02428i	−0.0373906	−	0.0647623i	−0.884115	+	0.467269i	$0.845238\pi$
$978$		0			0
$979$	−3.66465			−0.117123
$980$		0			0
$981$	−13.5937			−0.434014
$982$		0			0
$983$	14.3665	+	24.8836i	0.458221	+	0.793662i	0.998867	−	0.0475879i	$-0.0151534\pi$
$983$	14.3665	+	24.8836i	0.458221	+	0.793662i	−0.540646	+	0.841250i	$0.681820\pi$
$984$		0			0
$985$	−2.28137	+	3.95144i	−0.0726903	+	0.125903i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18.5276	−	32.0908i	0.589145	−	1.02043i
$990$		0			0
$991$	3.92394	+	6.79646i	0.124648	+	0.215897i	0.921595	−	0.388152i	$-0.126887\pi$
$991$	3.92394	+	6.79646i	0.124648	+	0.215897i	−0.796947	+	0.604049i	$0.793553\pi$
$992$		0			0
$993$	−10.0918			−0.320253
$994$		0			0
$995$	−14.4429			−0.457871
$996$		0			0
$997$	17.2262	+	29.8366i	0.545558	+	0.944934i	0.998572	+	0.0534302i	$0.0170155\pi$
$997$	17.2262	+	29.8366i	0.545558	+	0.944934i	−0.453014	+	0.891503i	$0.649651\pi$
$998$		0			0
$999$	−3.14136	+	5.44099i	−0.0993882	+	0.172145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.y.961.2		8
7.2	even	3		1960.2.a.x.1.3	✓	4
7.3	odd	6		1960.2.q.x.361.3		8
7.4	even	3	inner	1960.2.q.y.361.2		8
7.5	odd	6		1960.2.a.y.1.2	yes	4
7.6	odd	2		1960.2.q.x.961.3		8
28.19	even	6		3920.2.a.cd.1.3		4
28.23	odd	6		3920.2.a.ce.1.2		4
35.9	even	6		9800.2.a.cs.1.2		4
35.19	odd	6		9800.2.a.cl.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.x.1.3	✓	4	7.2	even	3
1960.2.a.y.1.2	yes	4	7.5	odd	6
1960.2.q.x.361.3		8	7.3	odd	6
1960.2.q.x.961.3		8	7.6	odd	2
1960.2.q.y.361.2		8	7.4	even	3	inner
1960.2.q.y.961.2		8	1.1	even	1	trivial
3920.2.a.cd.1.3		4	28.19	even	6
3920.2.a.ce.1.2		4	28.23	odd	6
9800.2.a.cl.1.3		4	35.19	odd	6
9800.2.a.cs.1.2		4	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(-0.591990 - 1.02536i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.799096 - 1.38408i) q^{9} +O(q^{10})\)	\(q+(-0.591990 - 1.02536i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.799096 - 1.38408i) q^{9} +(-0.115117 - 0.199389i) q^{11} +2.27259 q^{13} -1.18398 q^{15} +(3.26639 + 5.65755i) q^{17} +(-0.130093 + 0.225328i) q^{19} +(4.43539 - 7.68233i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.44417 q^{27} +5.42662 q^{29} +(2.43539 + 4.21822i) q^{31} +(-0.136296 + 0.236072i) q^{33} +(0.577014 - 0.999417i) q^{37} +(-1.34535 - 2.33022i) q^{39} -4.43337 q^{41} +4.17723 q^{43} +(-0.799096 - 1.38408i) q^{45} +(0.461897 - 0.800028i) q^{47} +(3.86734 - 6.69843i) q^{51} +(1.06743 + 1.84885i) q^{53} -0.230234 q^{55} +0.308055 q^{57} +(-2.53553 - 4.39167i) q^{59} +(4.44417 - 7.69752i) q^{61} +(1.13630 - 1.96812i) q^{65} +(-4.07984 - 7.06649i) q^{67} -10.5028 q^{69} -9.06556 q^{71} +(3.00478 + 5.20442i) q^{73} +(-0.591990 + 1.02536i) q^{75} +(-0.0564558 + 0.0977843i) q^{79} +(0.825600 + 1.42998i) q^{81} -8.72065 q^{83} +6.53278 q^{85} +(-3.21250 - 5.56422i) q^{87} +(7.95852 - 13.7846i) q^{89} +(2.88345 - 4.99429i) q^{93} +(0.130093 + 0.225328i) q^{95} -4.29565 q^{97} -0.367959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9	\( 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9} - 2 q^{11} - 20 q^{13} + 4 q^{15} + 6 q^{17} + 4 q^{23} - 4 q^{25} - 28 q^{27} - 4 q^{29} - 12 q^{31} + 18 q^{33} - 14 q^{39} - 24 q^{41} - 16 q^{43} + 6 q^{45} - 2 q^{47} - 2 q^{51} + 4 q^{53} - 4 q^{55} - 16 q^{57} + 8 q^{59} + 20 q^{61} - 10 q^{65} + 8 q^{67} - 48 q^{69} + 8 q^{71} + 16 q^{73} + 2 q^{75} - 22 q^{79} + 20 q^{81} - 72 q^{83} + 12 q^{85} - 18 q^{87} + 40 q^{89} + 32 q^{93} - 52 q^{97} + 24 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9 - 2 * q^11 - 20 * q^13 + 4 * q^15 + 6 * q^17 + 4 * q^23 - 4 * q^25 - 28 * q^27 - 4 * q^29 - 12 * q^31 + 18 * q^33 - 14 * q^39 - 24 * q^41 - 16 * q^43 + 6 * q^45 - 2 * q^47 - 2 * q^51 + 4 * q^53 - 4 * q^55 - 16 * q^57 + 8 * q^59 + 20 * q^61 - 10 * q^65 + 8 * q^67 - 48 * q^69 + 8 * q^71 + 16 * q^73 + 2 * q^75 - 22 * q^79 + 20 * q^81 - 72 * q^83 + 12 * q^85 - 18 * q^87 + 40 * q^89 + 32 * q^93 - 52 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more