LMFDB - Embedded newform 1960.2.q.p.961.1

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:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
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			961.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.p.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20711 - 2.09077i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(-1.20711 - 2.09077i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.41421 + 2.44949i) q^{9} +(0.500000 + 0.866025i) q^{11} -0.414214 q^{13} -2.41421 q^{15} +(-1.20711 - 2.09077i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-3.12132 + 5.40629i) q^{23} +(-0.500000 - 0.866025i) q^{25} -0.414214 q^{27} +1.00000 q^{29} +(-5.12132 - 8.87039i) q^{31} +(1.20711 - 2.09077i) q^{33} +(-5.94975 + 10.3053i) q^{37} +(0.500000 + 0.866025i) q^{39} +4.58579 q^{41} -11.6569 q^{43} +(1.41421 + 2.44949i) q^{45} +(-3.79289 + 6.56948i) q^{47} +(-2.91421 + 5.04757i) q^{51} +(-3.29289 - 5.70346i) q^{53} +1.00000 q^{55} +4.82843 q^{57} +(-0.878680 - 1.52192i) q^{59} +(3.41421 - 5.91359i) q^{61} +(-0.207107 + 0.358719i) q^{65} +(0.707107 + 1.22474i) q^{67} +15.0711 q^{69} -2.48528 q^{71} +(5.41421 + 9.37769i) q^{73} +(-1.20711 + 2.09077i) q^{75} +(1.67157 - 2.89525i) q^{79} +(4.74264 + 8.21449i) q^{81} -11.3137 q^{83} -2.41421 q^{85} +(-1.20711 - 2.09077i) q^{87} +(-4.82843 + 8.36308i) q^{89} +(-12.3640 + 21.4150i) q^{93} +(1.00000 + 1.73205i) q^{95} +14.0711 q^{97} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^5	$ 4 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 4 q^{13} - 4 q^{15} - 2 q^{17} - 4 q^{19} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} - 12 q^{31} + 2 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} - 24 q^{43} - 18 q^{47} - 6 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57} - 12 q^{59} + 8 q^{61} + 2 q^{65} + 32 q^{69} + 24 q^{71} + 16 q^{73} - 2 q^{75} + 18 q^{79} + 2 q^{81} - 4 q^{85} - 2 q^{87} - 8 q^{89} - 24 q^{93} + 4 q^{95} + 28 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 + 2 * q^11 + 4 * q^13 - 4 * q^15 - 2 * q^17 - 4 * q^19 - 4 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 - 12 * q^31 + 2 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 - 24 * q^43 - 18 * q^47 - 6 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 12 * q^59 + 8 * q^61 + 2 * q^65 + 32 * q^69 + 24 * q^71 + 16 * q^73 - 2 * q^75 + 18 * q^79 + 2 * q^81 - 4 * q^85 - 2 * q^87 - 8 * q^89 - 24 * q^93 + 4 * q^95 + 28 * q^97

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
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	−0.969528	−	0.244981i	$-0.921218\pi$
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	0.272605	−	0.962126i	$-0.412115\pi$
$4$		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
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$		0			0
$13$	−0.414214			−0.114882			−0.0574411	−	0.998349i	$-0.518294\pi$
$13$	−0.414214			−0.114882			−0.0574411	+	0.998349i	$0.518294\pi$
$14$		0			0
$15$	−2.41421			−0.623347
$16$		0			0
$17$	−1.20711	−	2.09077i	−0.292766	−	0.507086i	0.681696	−	0.731635i	$-0.261242\pi$
$17$	−1.20711	−	2.09077i	−0.292766	−	0.507086i	−0.974463	+	0.224549i	$0.927909\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.12132	+	5.40629i	−0.650840	+	1.12729i	0.332079	+	0.943252i	$0.392250\pi$
$23$	−3.12132	+	5.40629i	−0.650840	+	1.12729i	−0.982919	+	0.184037i	$0.941083\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	−5.12132	−	8.87039i	−0.919816	−	1.59317i	−0.799693	−	0.600410i	$-0.795004\pi$
$31$	−5.12132	−	8.87039i	−0.919816	−	1.59317i	−0.120124	−	0.992759i	$-0.538329\pi$
$32$		0			0
$33$	1.20711	−	2.09077i	0.210130	−	0.363956i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.94975	+	10.3053i	−0.978132	+	1.69418i	−0.308948	+	0.951079i	$0.599977\pi$
$37$	−5.94975	+	10.3053i	−0.978132	+	1.69418i	−0.669185	+	0.743096i	$0.733357\pi$
$38$		0			0
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	4.58579			0.716180			0.358090	−	0.933687i	$-0.383428\pi$
$41$	4.58579			0.716180			0.358090	+	0.933687i	$0.383428\pi$
$42$		0			0
$43$	−11.6569			−1.77765			−0.888827	−	0.458243i	$-0.848479\pi$
$43$	−11.6569			−1.77765			−0.888827	+	0.458243i	$0.848479\pi$
$44$		0			0
$45$	1.41421	+	2.44949i	0.210819	+	0.365148i
$46$		0			0
$47$	−3.79289	+	6.56948i	−0.553250	+	0.958258i	0.444787	+	0.895636i	$0.353279\pi$
$47$	−3.79289	+	6.56948i	−0.553250	+	0.958258i	−0.998037	+	0.0626213i	$0.980054\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.91421	+	5.04757i	−0.408072	+	0.706801i
$52$		0			0
$53$	−3.29289	−	5.70346i	−0.452314	−	0.783430i	0.546216	−	0.837645i	$-0.316068\pi$
$53$	−3.29289	−	5.70346i	−0.452314	−	0.783430i	−0.998529	+	0.0542143i	$0.982735\pi$
$54$		0			0
$55$	1.00000			0.134840
$56$		0			0
$57$	4.82843			0.639541
$58$		0			0
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	0.803143	−	0.595786i	$-0.203159\pi$
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	−0.917537	+	0.397649i	$0.869826\pi$
$60$		0			0
$61$	3.41421	−	5.91359i	0.437145	−	0.757158i	−0.560323	−	0.828274i	$-0.689323\pi$
$61$	3.41421	−	5.91359i	0.437145	−	0.757158i	0.997468	+	0.0711166i	$0.0226562\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.207107	+	0.358719i	−0.0256884	+	0.0444937i
$66$		0			0
$67$	0.707107	+	1.22474i	0.0863868	+	0.149626i	0.905981	−	0.423318i	$-0.139135\pi$
$67$	0.707107	+	1.22474i	0.0863868	+	0.149626i	−0.819594	+	0.572944i	$0.805801\pi$
$68$		0			0
$69$	15.0711			1.81434
$70$		0			0
$71$	−2.48528			−0.294949			−0.147474	−	0.989066i	$-0.547114\pi$
$71$	−2.48528			−0.294949			−0.147474	+	0.989066i	$0.547114\pi$
$72$		0			0
$73$	5.41421	+	9.37769i	0.633686	+	1.09758i	0.986792	+	0.161993i	$0.0517921\pi$
$73$	5.41421	+	9.37769i	0.633686	+	1.09758i	−0.353106	+	0.935583i	$0.614875\pi$
$74$		0			0
$75$	−1.20711	+	2.09077i	−0.139385	+	0.241421i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.67157	−	2.89525i	0.188067	−	0.325741i	−0.756539	−	0.653949i	$-0.773111\pi$
$79$	1.67157	−	2.89525i	0.188067	−	0.325741i	0.944606	+	0.328208i	$0.106445\pi$
$80$		0			0
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$		0			0
$83$	−11.3137			−1.24184			−0.620920	−	0.783874i	$-0.713241\pi$
$83$	−11.3137			−1.24184			−0.620920	+	0.783874i	$0.713241\pi$
$84$		0			0
$85$	−2.41421			−0.261858
$86$		0			0
$87$	−1.20711	−	2.09077i	−0.129415	−	0.224154i
$88$		0			0
$89$	−4.82843	+	8.36308i	−0.511812	+	0.886485i	0.488094	+	0.872791i	$0.337692\pi$
$89$	−4.82843	+	8.36308i	−0.511812	+	0.886485i	−0.999906	+	0.0136937i	$0.995641\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−12.3640	+	21.4150i	−1.28208	+	2.22063i
$94$		0			0
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$		0			0
$97$	14.0711			1.42870			0.714350	−	0.699788i	$-0.246722\pi$
$97$	14.0711			1.42870			0.714350	+	0.699788i	$0.246722\pi$
$98$		0			0
$99$	−2.82843			−0.284268
$100$		0			0
$101$	−5.24264	−	9.08052i	−0.521662	−	0.903546i	−0.999683	−	0.0251967i	$-0.991979\pi$
$101$	−5.24264	−	9.08052i	−0.521662	−	0.903546i	0.478020	−	0.878349i	$-0.341355\pi$
$102$		0			0
$103$	−3.37868	+	5.85204i	−0.332911	+	0.576619i	−0.983081	−	0.183170i	$-0.941364\pi$
$103$	−3.37868	+	5.85204i	−0.332911	+	0.576619i	0.650170	+	0.759789i	$0.274698\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.24264	−	12.5446i	0.700173	−	1.21273i	−0.268233	−	0.963354i	$-0.586440\pi$
$107$	7.24264	−	12.5446i	0.700173	−	1.21273i	0.968406	−	0.249380i	$-0.0802269\pi$
$108$		0			0
$109$	9.15685	+	15.8601i	0.877068	+	1.51913i	0.854544	+	0.519379i	$0.173837\pi$
$109$	9.15685	+	15.8601i	0.877068	+	1.51913i	0.0225237	+	0.999746i	$0.492830\pi$
$110$		0			0
$111$	28.7279			2.72673
$112$		0			0
$113$	−9.07107			−0.853334			−0.426667	−	0.904409i	$-0.640312\pi$
$113$	−9.07107			−0.853334			−0.426667	+	0.904409i	$0.640312\pi$
$114$		0			0
$115$	3.12132	+	5.40629i	0.291065	+	0.504139i
$116$		0			0
$117$	0.585786	−	1.01461i	0.0541560	−	0.0938009i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$	−5.53553	−	9.58783i	−0.499122	−	0.864505i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	3.75736			0.333412			0.166706	−	0.986007i	$-0.446687\pi$
$127$	3.75736			0.333412			0.166706	+	0.986007i	$0.446687\pi$
$128$		0			0
$129$	14.0711	+	24.3718i	1.23889	+	2.14582i
$130$		0			0
$131$	−10.1213	+	17.5306i	−0.884304	+	1.53166i	−0.0377944	+	0.999286i	$0.512033\pi$
$131$	−10.1213	+	17.5306i	−0.884304	+	1.53166i	−0.846509	+	0.532374i	$0.821300\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.207107	+	0.358719i	−0.0178249	+	0.0308737i
$136$		0			0
$137$	9.65685	+	16.7262i	0.825041	+	1.42901i	0.901888	+	0.431970i	$0.142181\pi$
$137$	9.65685	+	16.7262i	0.825041	+	1.42901i	−0.0768474	+	0.997043i	$0.524485\pi$
$138$		0			0
$139$	1.41421			0.119952			0.0599760	−	0.998200i	$-0.480898\pi$
$139$	1.41421			0.119952			0.0599760	+	0.998200i	$0.480898\pi$
$140$		0			0
$141$	18.3137			1.54229
$142$		0			0
$143$	−0.207107	−	0.358719i	−0.0173191	−	0.0299976i
$144$		0			0
$145$	0.500000	−	0.866025i	0.0415227	−	0.0719195i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.58579	−	7.94282i	0.375682	−	0.650701i	−0.614747	−	0.788725i	$-0.710742\pi$
$149$	4.58579	−	7.94282i	0.375682	−	0.650701i	0.990429	+	0.138024i	$0.0440751\pi$
$150$		0			0
$151$	3.32843	+	5.76500i	0.270864	+	0.469149i	0.969083	−	0.246734i	$-0.0793574\pi$
$151$	3.32843	+	5.76500i	0.270864	+	0.469149i	−0.698220	+	0.715884i	$0.746024\pi$
$152$		0			0
$153$	6.82843			0.552046
$154$		0			0
$155$	−10.2426			−0.822709
$156$		0			0
$157$	−5.24264	−	9.08052i	−0.418408	−	0.724704i	0.577371	−	0.816482i	$-0.304079\pi$
$157$	−5.24264	−	9.08052i	−0.418408	−	0.724704i	−0.995780	+	0.0917773i	$0.970745\pi$
$158$		0			0
$159$	−7.94975	+	13.7694i	−0.630456	+	1.09198i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.46447	+	2.53653i	−0.114706	+	0.198676i	−0.917662	−	0.397362i	$-0.869926\pi$
$163$	−1.46447	+	2.53653i	−0.114706	+	0.198676i	0.802956	+	0.596038i	$0.203259\pi$
$164$		0			0
$165$	−1.20711	−	2.09077i	−0.0939731	−	0.162766i
$166$		0			0
$167$	7.58579			0.587006			0.293503	−	0.955958i	$-0.405179\pi$
$167$	7.58579			0.587006			0.293503	+	0.955958i	$0.405179\pi$
$168$		0			0
$169$	−12.8284			−0.986802
$170$		0			0
$171$	−2.82843	−	4.89898i	−0.216295	−	0.374634i
$172$		0			0
$173$	6.86396	−	11.8887i	0.521857	−	0.903883i	−0.477819	−	0.878458i	$-0.658573\pi$
$173$	6.86396	−	11.8887i	0.521857	−	0.903883i	0.999677	−	0.0254253i	$-0.00809399\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.12132	+	3.67423i	−0.159448	+	0.276172i
$178$		0			0
$179$	−2.07107	−	3.58719i	−0.154799	−	0.268120i	0.778187	−	0.628033i	$-0.216140\pi$
$179$	−2.07107	−	3.58719i	−0.154799	−	0.268120i	−0.932986	+	0.359913i	$0.882806\pi$
$180$		0			0
$181$	−25.5563			−1.89959			−0.949794	−	0.312875i	$-0.898708\pi$
$181$	−25.5563			−1.89959			−0.949794	+	0.312875i	$0.898708\pi$
$182$		0			0
$183$	−16.4853			−1.21863
$184$		0			0
$185$	5.94975	+	10.3053i	0.437434	+	0.757658i
$186$		0			0
$187$	1.20711	−	2.09077i	0.0882724	−	0.152892i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.91421	+	11.9758i	−0.500295	+	0.866536i	0.499705	+	0.866196i	$0.333442\pi$
$191$	−6.91421	+	11.9758i	−0.500295	+	0.866536i	−1.00000		0.000340595i	$0.999892\pi$
$192$		0			0
$193$	−0.343146	−	0.594346i	−0.0247002	−	0.0427820i	0.853411	−	0.521238i	$-0.174530\pi$
$193$	−0.343146	−	0.594346i	−0.0247002	−	0.0427820i	−0.878111	+	0.478456i	$0.841196\pi$
$194$		0			0
$195$	1.00000			0.0716115
$196$		0			0
$197$	−12.2426			−0.872252			−0.436126	−	0.899886i	$-0.643650\pi$
$197$	−12.2426			−0.872252			−0.436126	+	0.899886i	$0.643650\pi$
$198$		0			0
$199$	6.19239	+	10.7255i	0.438967	+	0.760313i	0.997610	−	0.0690953i	$-0.0220113\pi$
$199$	6.19239	+	10.7255i	0.438967	+	0.760313i	−0.558643	+	0.829408i	$0.688678\pi$
$200$		0			0
$201$	1.70711	−	2.95680i	0.120410	−	0.208556i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.29289	−	3.97141i	0.160143	−	0.277375i
$206$		0			0
$207$	−8.82843	−	15.2913i	−0.613618	−	1.06282i
$208$		0			0
$209$	−2.00000			−0.138343
$210$		0			0
$211$	17.1421			1.18011			0.590057	−	0.807362i	$-0.299105\pi$
$211$	17.1421			1.18011			0.590057	+	0.807362i	$0.299105\pi$
$212$		0			0
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$		0			0
$215$	−5.82843	+	10.0951i	−0.397495	+	0.688482i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	13.0711	−	22.6398i	0.883261	−	1.52985i
$220$		0			0
$221$	0.500000	+	0.866025i	0.0336336	+	0.0582552i
$222$		0			0
$223$	−17.3848			−1.16417			−0.582085	−	0.813128i	$-0.697763\pi$
$223$	−17.3848			−1.16417			−0.582085	+	0.813128i	$0.697763\pi$
$224$		0			0
$225$	2.82843			0.188562
$226$		0			0
$227$	−0.792893	−	1.37333i	−0.0526262	−	0.0911512i	0.838512	−	0.544883i	$-0.183426\pi$
$227$	−0.792893	−	1.37333i	−0.0526262	−	0.0911512i	−0.891138	+	0.453732i	$0.850093\pi$
$228$		0			0
$229$	2.05025	−	3.55114i	0.135485	−	0.234666i	−0.790298	−	0.612723i	$-0.790074\pi$
$229$	2.05025	−	3.55114i	0.135485	−	0.234666i	0.925782	+	0.378057i	$0.123408\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.75736	+	3.04384i	−0.115128	+	0.199408i	−0.917831	−	0.396971i	$-0.870061\pi$
$233$	−1.75736	+	3.04384i	−0.115128	+	0.199408i	0.802703	+	0.596379i	$0.203395\pi$
$234$		0			0
$235$	3.79289	+	6.56948i	0.247421	+	0.428546i
$236$		0			0
$237$	−8.07107			−0.524272
$238$		0			0
$239$	−4.65685			−0.301227			−0.150613	−	0.988593i	$-0.548125\pi$
$239$	−4.65685			−0.301227			−0.150613	+	0.988593i	$0.548125\pi$
$240$		0			0
$241$	−5.19239	−	8.99348i	−0.334471	−	0.579321i	0.648912	−	0.760863i	$-0.275224\pi$
$241$	−5.19239	−	8.99348i	−0.334471	−	0.579321i	−0.983383	+	0.181543i	$0.941891\pi$
$242$		0			0
$243$	10.8284	−	18.7554i	0.694644	−	1.20316i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.414214	−	0.717439i	0.0263558	−	0.0456495i
$248$		0			0
$249$	13.6569	+	23.6544i	0.865468	+	1.49903i
$250$		0			0
$251$	7.55635			0.476953			0.238476	−	0.971148i	$-0.423352\pi$
$251$	7.55635			0.476953			0.238476	+	0.971148i	$0.423352\pi$
$252$		0			0
$253$	−6.24264			−0.392471
$254$		0			0
$255$	2.91421	+	5.04757i	0.182495	+	0.316091i
$256$		0			0
$257$	−5.24264	+	9.08052i	−0.327027	+	0.566427i	−0.981920	−	0.189294i	$-0.939380\pi$
$257$	−5.24264	+	9.08052i	−0.327027	+	0.566427i	0.654894	+	0.755721i	$0.272713\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.41421	+	2.44949i	−0.0875376	+	0.151620i
$262$		0			0
$263$	−9.48528	−	16.4290i	−0.584888	−	1.01305i	−0.994889	−	0.100970i	$-0.967805\pi$
$263$	−9.48528	−	16.4290i	−0.584888	−	1.01305i	0.410002	−	0.912085i	$-0.365528\pi$
$264$		0			0
$265$	−6.58579			−0.404562
$266$		0			0
$267$	23.3137			1.42678
$268$		0			0
$269$	−9.29289	−	16.0958i	−0.566598	−	0.981376i	−0.996899	−	0.0786907i	$-0.974926\pi$
$269$	−9.29289	−	16.0958i	−0.566598	−	0.981376i	0.430301	−	0.902685i	$-0.358407\pi$
$270$		0			0
$271$	−1.17157	+	2.02922i	−0.0711680	+	0.123267i	−0.899413	−	0.437099i	$-0.856006\pi$
$271$	−1.17157	+	2.02922i	−0.0711680	+	0.123267i	0.828245	+	0.560365i	$0.189339\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		0			0
$277$	6.53553	+	11.3199i	0.392682	+	0.680145i	0.992802	−	0.119764i	$-0.0382139\pi$
$277$	6.53553	+	11.3199i	0.392682	+	0.680145i	−0.600120	+	0.799910i	$0.704881\pi$
$278$		0			0
$279$	28.9706			1.73442
$280$		0			0
$281$	18.3137			1.09250			0.546252	−	0.837621i	$-0.316054\pi$
$281$	18.3137			1.09250			0.546252	+	0.837621i	$0.316054\pi$
$282$		0			0
$283$	−12.5208	−	21.6867i	−0.744285	−	1.28914i	−0.950528	−	0.310639i	$-0.899457\pi$
$283$	−12.5208	−	21.6867i	−0.744285	−	1.28914i	0.206243	−	0.978501i	$-0.433876\pi$
$284$		0			0
$285$	2.41421	−	4.18154i	0.143006	−	0.247693i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.58579	−	9.67487i	0.328576	−	0.569110i
$290$		0			0
$291$	−16.9853	−	29.4194i	−0.995695	−	1.72459i
$292$		0			0
$293$	−18.4142			−1.07577			−0.537885	−	0.843018i	$-0.680777\pi$
$293$	−18.4142			−1.07577			−0.537885	+	0.843018i	$0.680777\pi$
$294$		0			0
$295$	−1.75736			−0.102317
$296$		0			0
$297$	−0.207107	−	0.358719i	−0.0120176	−	0.0208150i
$298$		0			0
$299$	1.29289	−	2.23936i	0.0747699	−	0.129505i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−12.6569	+	21.9223i	−0.727117	+	1.25940i
$304$		0			0
$305$	−3.41421	−	5.91359i	−0.195497	−	0.338611i
$306$		0			0
$307$	−11.9289			−0.680820			−0.340410	−	0.940277i	$-0.610566\pi$
$307$	−11.9289			−0.680820			−0.340410	+	0.940277i	$0.610566\pi$
$308$		0			0
$309$	16.3137			0.928054
$310$		0			0
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	0.688726	−	0.725022i	$-0.258170\pi$
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	−0.972250	+	0.233944i	$0.924837\pi$
$312$		0			0
$313$	11.8640	−	20.5490i	0.670591	−	1.16150i	−0.307146	−	0.951662i	$-0.599374\pi$
$313$	11.8640	−	20.5490i	0.670591	−	1.16150i	0.977737	−	0.209835i	$-0.0672926\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.17157	+	10.6895i	−0.346630	+	0.600381i	−0.985649	−	0.168811i	$-0.946007\pi$
$317$	−6.17157	+	10.6895i	−0.346630	+	0.600381i	0.639018	+	0.769191i	$0.279341\pi$
$318$		0			0
$319$	0.500000	+	0.866025i	0.0279946	+	0.0484881i
$320$		0			0
$321$	−34.9706			−1.95187
$322$		0			0
$323$	4.82843			0.268661
$324$		0			0
$325$	0.207107	+	0.358719i	0.0114882	+	0.0198982i
$326$		0			0
$327$	22.1066	−	38.2898i	1.22250	−	2.11743i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4.75736	+	8.23999i	−0.261488	+	0.452911i	−0.966638	−	0.256148i	$-0.917547\pi$
$331$	−4.75736	+	8.23999i	−0.261488	+	0.452911i	0.705149	+	0.709059i	$0.250880\pi$
$332$		0			0
$333$	−16.8284	−	29.1477i	−0.922192	−	1.59728i
$334$		0			0
$335$	1.41421			0.0772667
$336$		0			0
$337$	−13.0711			−0.712026			−0.356013	−	0.934481i	$-0.615864\pi$
$337$	−13.0711			−0.712026			−0.356013	+	0.934481i	$0.615864\pi$
$338$		0			0
$339$	10.9497	+	18.9655i	0.594709	+	1.03007i
$340$		0			0
$341$	5.12132	−	8.87039i	0.277335	−	0.480358i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	7.53553	−	13.0519i	0.405700	−	0.702692i
$346$		0			0
$347$	−14.4350	−	25.0022i	−0.774913	−	1.34219i	−0.934843	−	0.355060i	$-0.884460\pi$
$347$	−14.4350	−	25.0022i	−0.774913	−	1.34219i	0.159930	−	0.987128i	$-0.448873\pi$
$348$		0			0
$349$	−6.68629			−0.357909			−0.178954	−	0.983857i	$-0.557271\pi$
$349$	−6.68629			−0.357909			−0.178954	+	0.983857i	$0.557271\pi$
$350$		0			0
$351$	0.171573			0.00915788
$352$		0			0
$353$	−15.1066	−	26.1654i	−0.804043	−	1.39264i	−0.916935	−	0.399037i	$-0.869345\pi$
$353$	−15.1066	−	26.1654i	−0.804043	−	1.39264i	0.112892	−	0.993607i	$-0.463989\pi$
$354$		0			0
$355$	−1.24264	+	2.15232i	−0.0659525	+	0.114233i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.8284	−	25.6836i	0.782614	−	1.35553i	−0.147799	−	0.989017i	$-0.547219\pi$
$359$	14.8284	−	25.6836i	0.782614	−	1.35553i	0.930414	−	0.366511i	$-0.119448\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	−24.1421			−1.26713
$364$		0			0
$365$	10.8284			0.566786
$366$		0			0
$367$	−5.62132	−	9.73641i	−0.293431	−	0.508237i	0.681188	−	0.732108i	$-0.261464\pi$
$367$	−5.62132	−	9.73641i	−0.293431	−	0.508237i	−0.974619	+	0.223872i	$0.928130\pi$
$368$		0			0
$369$	−6.48528	+	11.2328i	−0.337610	+	0.584758i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−11.4142	+	19.7700i	−0.591006	+	1.02365i	0.403092	+	0.915160i	$0.367936\pi$
$373$	−11.4142	+	19.7700i	−0.591006	+	1.02365i	−0.994097	+	0.108492i	$0.965398\pi$
$374$		0			0
$375$	1.20711	+	2.09077i	0.0623347	+	0.107967i
$376$		0			0
$377$	−0.414214			−0.0213331
$378$		0			0
$379$	28.6274			1.47049			0.735246	−	0.677801i	$-0.237067\pi$
$379$	28.6274			1.47049			0.735246	+	0.677801i	$0.237067\pi$
$380$		0			0
$381$	−4.53553	−	7.85578i	−0.232362	−	0.402464i
$382$		0			0
$383$	−11.4142	+	19.7700i	−0.583239	+	1.01020i	0.411853	+	0.911250i	$0.364882\pi$
$383$	−11.4142	+	19.7700i	−0.583239	+	1.01020i	−0.995092	+	0.0989496i	$0.968452\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	16.4853	−	28.5533i	0.837994	−	1.45145i
$388$		0			0
$389$	−5.39949	−	9.35220i	−0.273765	−	0.474175i	0.696058	−	0.717986i	$-0.254936\pi$
$389$	−5.39949	−	9.35220i	−0.273765	−	0.474175i	−0.969823	+	0.243811i	$0.921602\pi$
$390$		0			0
$391$	15.0711			0.762177
$392$		0			0
$393$	48.8701			2.46517
$394$		0			0
$395$	−1.67157	−	2.89525i	−0.0841060	−	0.145676i
$396$		0			0
$397$	2.79289	−	4.83743i	0.140171	−	0.242784i	−0.787390	−	0.616456i	$-0.788568\pi$
$397$	2.79289	−	4.83743i	0.140171	−	0.242784i	0.927561	+	0.373672i	$0.121901\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.2279	−	21.1794i	0.610633	−	1.05765i	−0.380501	−	0.924781i	$-0.624248\pi$
$401$	12.2279	−	21.1794i	0.610633	−	1.05765i	0.991134	−	0.132867i	$-0.0424184\pi$
$402$		0			0
$403$	2.12132	+	3.67423i	0.105670	+	0.183027i
$404$		0			0
$405$	9.48528			0.471327
$406$		0			0
$407$	−11.8995			−0.589836
$408$		0			0
$409$	16.5563	+	28.6764i	0.818659	+	1.41796i	0.906671	+	0.421839i	$0.138615\pi$
$409$	16.5563	+	28.6764i	0.818659	+	1.41796i	−0.0880119	+	0.996119i	$0.528051\pi$
$410$		0			0
$411$	23.3137	−	40.3805i	1.14998	−	1.99182i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−5.65685	+	9.79796i	−0.277684	+	0.480963i
$416$		0			0
$417$	−1.70711	−	2.95680i	−0.0835974	−	0.144795i
$418$		0			0
$419$	−28.5858			−1.39651			−0.698254	−	0.715851i	$-0.746039\pi$
$419$	−28.5858			−1.39651			−0.698254	+	0.715851i	$0.746039\pi$
$420$		0			0
$421$	−26.3137			−1.28245			−0.641226	−	0.767352i	$-0.721574\pi$
$421$	−26.3137			−1.28245			−0.641226	+	0.767352i	$0.721574\pi$
$422$		0			0
$423$	−10.7279	−	18.5813i	−0.521609	−	0.903454i
$424$		0			0
$425$	−1.20711	+	2.09077i	−0.0585533	+	0.101417i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.500000	+	0.866025i	−0.0241402	+	0.0418121i
$430$		0			0
$431$	−11.3284	−	19.6214i	−0.545671	−	0.945130i	−0.998564	−	0.0535654i	$-0.982941\pi$
$431$	−11.3284	−	19.6214i	−0.545671	−	0.945130i	0.452893	−	0.891565i	$-0.350392\pi$
$432$		0			0
$433$	6.97056			0.334984			0.167492	−	0.985873i	$-0.446433\pi$
$433$	6.97056			0.334984			0.167492	+	0.985873i	$0.446433\pi$
$434$		0			0
$435$	−2.41421			−0.115753
$436$		0			0
$437$	−6.24264	−	10.8126i	−0.298626	−	0.517235i
$438$		0			0
$439$	1.87868	−	3.25397i	0.0896645	−	0.155303i	−0.817705	−	0.575638i	$-0.804754\pi$
$439$	1.87868	−	3.25397i	0.0896645	−	0.155303i	0.907369	+	0.420334i	$0.138087\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.3848	−	30.1113i	0.825976	−	1.43063i	−0.0751957	−	0.997169i	$-0.523958\pi$
$443$	17.3848	−	30.1113i	0.825976	−	1.43063i	0.901171	−	0.433463i	$-0.142709\pi$
$444$		0			0
$445$	4.82843	+	8.36308i	0.228889	+	0.396448i
$446$		0			0
$447$	−22.1421			−1.04729
$448$		0			0
$449$	−27.4853			−1.29711			−0.648555	−	0.761168i	$-0.724626\pi$
$449$	−27.4853			−1.29711			−0.648555	+	0.761168i	$0.724626\pi$
$450$		0			0
$451$	2.29289	+	3.97141i	0.107968	+	0.187006i
$452$		0			0
$453$	8.03553	−	13.9180i	0.377542	−	0.653922i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.46447	+	4.26858i	−0.115283	+	0.199676i	−0.917893	−	0.396828i	$-0.870111\pi$
$457$	−2.46447	+	4.26858i	−0.115283	+	0.199676i	0.802610	+	0.596504i	$0.203444\pi$
$458$		0			0
$459$	0.500000	+	0.866025i	0.0233380	+	0.0404226i
$460$		0			0
$461$	−32.2843			−1.50363			−0.751814	−	0.659375i	$-0.770821\pi$
$461$	−32.2843			−1.50363			−0.751814	+	0.659375i	$0.770821\pi$
$462$		0			0
$463$	25.4558			1.18303			0.591517	−	0.806293i	$-0.298529\pi$
$463$	25.4558			1.18303			0.591517	+	0.806293i	$0.298529\pi$
$464$		0			0
$465$	12.3640	+	21.4150i	0.573365	+	0.993097i
$466$		0			0
$467$	−4.20711	+	7.28692i	−0.194682	+	0.337199i	−0.946796	−	0.321834i	$-0.895701\pi$
$467$	−4.20711	+	7.28692i	−0.194682	+	0.337199i	0.752114	+	0.659033i	$0.229034\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−12.6569	+	21.9223i	−0.583197	+	1.01013i
$472$		0			0
$473$	−5.82843	−	10.0951i	−0.267991	−	0.464175i
$474$		0			0
$475$	2.00000			0.0917663
$476$		0			0
$477$	18.6274			0.852891
$478$		0			0
$479$	20.2635	+	35.0973i	0.925861	+	1.60364i	0.790171	+	0.612887i	$0.209992\pi$
$479$	20.2635	+	35.0973i	0.925861	+	1.60364i	0.135690	+	0.990751i	$0.456675\pi$
$480$		0			0
$481$	2.46447	−	4.26858i	0.112370	−	0.194631i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.03553	−	12.1859i	0.319467	−	0.553333i
$486$		0			0
$487$	−0.636039	−	1.10165i	−0.0288217	−	0.0499206i	0.851255	−	0.524753i	$-0.175842\pi$
$487$	−0.636039	−	1.10165i	−0.0288217	−	0.0499206i	−0.880076	+	0.474832i	$0.842509\pi$
$488$		0			0
$489$	7.07107			0.319765
$490$		0			0
$491$	−11.4853			−0.518323			−0.259162	−	0.965834i	$-0.583446\pi$
$491$	−11.4853			−0.518323			−0.259162	+	0.965834i	$0.583446\pi$
$492$		0			0
$493$	−1.20711	−	2.09077i	−0.0543654	−	0.0941636i
$494$		0			0
$495$	−1.41421	+	2.44949i	−0.0635642	+	0.110096i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	13.3995	−	23.2086i	0.599844	−	1.03896i	−0.393000	−	0.919539i	$-0.628563\pi$
$499$	13.3995	−	23.2086i	0.599844	−	1.03896i	0.992844	−	0.119421i	$-0.0381039\pi$
$500$		0			0
$501$	−9.15685	−	15.8601i	−0.409098	−	0.708579i
$502$		0			0
$503$	−17.0416			−0.759849			−0.379924	−	0.925018i	$-0.624050\pi$
$503$	−17.0416			−0.759849			−0.379924	+	0.925018i	$0.624050\pi$
$504$		0			0
$505$	−10.4853			−0.466589
$506$		0			0
$507$	15.4853	+	26.8213i	0.687725	+	1.19118i
$508$		0			0
$509$	−8.12132	+	14.0665i	−0.359971	+	0.623488i	−0.987956	−	0.154738i	$-0.950547\pi$
$509$	−8.12132	+	14.0665i	−0.359971	+	0.623488i	0.627984	+	0.778226i	$0.283880\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.414214	−	0.717439i	0.0182880	−	0.0316757i
$514$		0			0
$515$	3.37868	+	5.85204i	0.148882	+	0.257872i
$516$		0			0
$517$	−7.58579			−0.333623
$518$		0			0
$519$	−33.1421			−1.45478
$520$		0			0
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$		0			0
$523$	7.75736	−	13.4361i	0.339206	−	0.587521i	−0.645078	−	0.764117i	$-0.723175\pi$
$523$	7.75736	−	13.4361i	0.339206	−	0.587521i	0.984284	+	0.176595i	$0.0565084\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.3640	+	21.4150i	−0.538583	+	0.932852i
$528$		0			0
$529$	−7.98528	−	13.8309i	−0.347186	−	0.601344i
$530$		0			0
$531$	4.97056			0.215704
$532$		0			0
$533$	−1.89949			−0.0822763
$534$		0			0
$535$	−7.24264	−	12.5446i	−0.313127	−	0.542351i
$536$		0			0
$537$	−5.00000	+	8.66025i	−0.215766	+	0.373718i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	6.15685	−	10.6640i	0.264704	−	0.458480i	−0.702782	−	0.711405i	$-0.748059\pi$
$541$	6.15685	−	10.6640i	0.264704	−	0.458480i	0.967486	+	0.252925i	$0.0813925\pi$
$542$		0			0
$543$	30.8492	+	53.4325i	1.32387	+	2.29301i
$544$		0			0
$545$	18.3137			0.784473
$546$		0			0
$547$	35.1127			1.50131			0.750655	−	0.660694i	$-0.229738\pi$
$547$	35.1127			1.50131			0.750655	+	0.660694i	$0.229738\pi$
$548$		0			0
$549$	9.65685	+	16.7262i	0.412144	+	0.713855i
$550$		0			0
$551$	−1.00000	+	1.73205i	−0.0426014	+	0.0737878i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	14.3640	−	24.8791i	0.609716	−	1.05606i
$556$		0			0
$557$	−1.07107	−	1.85514i	−0.0453826	−	0.0786050i	0.842442	−	0.538787i	$-0.181117\pi$
$557$	−1.07107	−	1.85514i	−0.0453826	−	0.0786050i	−0.887824	+	0.460182i	$0.847784\pi$
$558$		0			0
$559$	4.82843			0.204221
$560$		0			0
$561$	−5.82843			−0.246076
$562$		0			0
$563$	−13.9706	−	24.1977i	−0.588789	−	1.01981i	−0.994391	−	0.105763i	$-0.966272\pi$
$563$	−13.9706	−	24.1977i	−0.588789	−	1.01981i	0.405602	−	0.914050i	$-0.367062\pi$
$564$		0			0
$565$	−4.53553	+	7.85578i	−0.190811	+	0.330495i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.0711	−	29.5680i	0.715656	−	1.23955i	−0.247049	−	0.969003i	$-0.579461\pi$
$569$	17.0711	−	29.5680i	0.715656	−	1.23955i	0.962706	−	0.270550i	$-0.0872057\pi$
$570$		0			0
$571$	11.7279	+	20.3134i	0.490798	+	0.850088i	0.999944	−	0.0105929i	$-0.00337187\pi$
$571$	11.7279	+	20.3134i	0.490798	+	0.850088i	−0.509146	+	0.860680i	$0.670039\pi$
$572$		0			0
$573$	33.3848			1.39467
$574$		0			0
$575$	6.24264			0.260336
$576$		0			0
$577$	18.2071	+	31.5356i	0.757972	+	1.31285i	0.943883	+	0.330279i	$0.107143\pi$
$577$	18.2071	+	31.5356i	0.757972	+	1.31285i	−0.185912	+	0.982566i	$0.559524\pi$
$578$		0			0
$579$	−0.828427	+	1.43488i	−0.0344283	+	0.0596315i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	3.29289	−	5.70346i	0.136378	−	0.236213i
$584$		0			0
$585$	−0.585786	−	1.01461i	−0.0242193	−	0.0419490i
$586$		0			0
$587$	−13.8579			−0.571975			−0.285988	−	0.958233i	$-0.592322\pi$
$587$	−13.8579			−0.571975			−0.285988	+	0.958233i	$0.592322\pi$
$588$		0			0
$589$	20.4853			0.844081
$590$		0			0
$591$	14.7782	+	25.5965i	0.607893	+	1.05290i
$592$		0			0
$593$	−4.72183	+	8.17844i	−0.193902	+	0.335848i	−0.946540	−	0.322586i	$-0.895448\pi$
$593$	−4.72183	+	8.17844i	−0.193902	+	0.335848i	0.752638	+	0.658435i	$0.228781\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	14.9497	−	25.8937i	0.611852	−	1.05976i
$598$		0			0
$599$	18.1569	+	31.4486i	0.741869	+	1.28495i	0.951643	+	0.307205i	$0.0993937\pi$
$599$	18.1569	+	31.4486i	0.741869	+	1.28495i	−0.209774	+	0.977750i	$0.567273\pi$
$600$		0			0
$601$	−18.2843			−0.745831			−0.372915	−	0.927865i	$-0.621642\pi$
$601$	−18.2843			−0.745831			−0.372915	+	0.927865i	$0.621642\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$		0			0
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$		0			0
$607$	−10.0355	+	17.3821i	−0.407330	+	0.705516i	−0.994590	−	0.103883i	$-0.966873\pi$
$607$	−10.0355	+	17.3821i	−0.407330	+	0.705516i	0.587260	+	0.809398i	$0.300207\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.57107	−	2.72117i	0.0635586	−	0.110087i
$612$		0			0
$613$	−14.6569	−	25.3864i	−0.591985	−	1.02535i	−0.993965	−	0.109699i	$-0.965011\pi$
$613$	−14.6569	−	25.3864i	−0.591985	−	1.02535i	0.401980	−	0.915648i	$-0.368322\pi$
$614$		0			0
$615$	−11.0711			−0.446429
$616$		0			0
$617$	−11.4142			−0.459519			−0.229759	−	0.973247i	$-0.573794\pi$
$617$	−11.4142			−0.459519			−0.229759	+	0.973247i	$0.573794\pi$
$618$		0			0
$619$	7.53553	+	13.0519i	0.302879	+	0.524601i	0.976787	−	0.214214i	$-0.0687190\pi$
$619$	7.53553	+	13.0519i	0.302879	+	0.524601i	−0.673908	+	0.738815i	$0.735386\pi$
$620$		0			0
$621$	1.29289	−	2.23936i	0.0518820	−	0.0898623i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	2.41421	+	4.18154i	0.0964144	+	0.166995i
$628$		0			0
$629$	28.7279			1.14546
$630$		0			0
$631$	−37.6274			−1.49792			−0.748962	−	0.662613i	$-0.769447\pi$
$631$	−37.6274			−1.49792			−0.748962	+	0.662613i	$0.769447\pi$
$632$		0			0
$633$	−20.6924	−	35.8403i	−0.822449	−	1.42452i
$634$		0			0
$635$	1.87868	−	3.25397i	0.0745531	−	0.129130i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	3.51472	−	6.08767i	0.139040	−	0.240825i
$640$		0			0
$641$	−16.1421	−	27.9590i	−0.637576	−	1.10431i	−0.985963	−	0.166963i	$-0.946604\pi$
$641$	−16.1421	−	27.9590i	−0.637576	−	1.10431i	0.348387	−	0.937351i	$-0.386729\pi$
$642$		0			0
$643$	−30.2132			−1.19149			−0.595746	−	0.803173i	$-0.703144\pi$
$643$	−30.2132			−1.19149			−0.595746	+	0.803173i	$0.703144\pi$
$644$		0			0
$645$	28.1421			1.10810
$646$		0			0
$647$	−9.07107	−	15.7116i	−0.356620	−	0.617685i	0.630773	−	0.775967i	$-0.282738\pi$
$647$	−9.07107	−	15.7116i	−0.356620	−	0.617685i	−0.987394	+	0.158282i	$0.949404\pi$
$648$		0			0
$649$	0.878680	−	1.52192i	0.0344912	−	0.0597405i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.1421	−	19.2987i	0.436025	−	0.755218i	−0.561353	−	0.827576i	$-0.689719\pi$
$653$	11.1421	−	19.2987i	0.436025	−	0.755218i	0.997379	+	0.0723580i	$0.0230524\pi$
$654$		0			0
$655$	10.1213	+	17.5306i	0.395473	+	0.684979i
$656$		0			0
$657$	−30.6274			−1.19489
$658$		0			0
$659$	17.4853			0.681130			0.340565	−	0.940221i	$-0.389382\pi$
$659$	17.4853			0.681130			0.340565	+	0.940221i	$0.389382\pi$
$660$		0			0
$661$	15.4142	+	26.6982i	0.599543	+	1.03844i	0.992888	+	0.119049i	$0.0379845\pi$
$661$	15.4142	+	26.6982i	0.599543	+	1.03844i	−0.393345	+	0.919391i	$0.628682\pi$
$662$		0			0
$663$	1.20711	−	2.09077i	0.0468801	−	0.0811988i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.12132	+	5.40629i	−0.120858	+	0.209332i
$668$		0			0
$669$	20.9853	+	36.3476i	0.811338	+	1.40528i
$670$		0			0
$671$	6.82843			0.263609
$672$		0			0
$673$	50.8284			1.95929			0.979646	−	0.200733i	$-0.0643324\pi$
$673$	50.8284			1.95929			0.979646	+	0.200733i	$0.0643324\pi$
$674$		0			0
$675$	0.207107	+	0.358719i	0.00797154	+	0.0138071i
$676$		0			0
$677$	−18.0355	+	31.2385i	−0.693162	+	1.20059i	0.277635	+	0.960687i	$0.410450\pi$
$677$	−18.0355	+	31.2385i	−0.693162	+	1.20059i	−0.970796	+	0.239905i	$0.922884\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.91421	+	3.31552i	−0.0733528	+	0.127051i
$682$		0			0
$683$	6.58579	+	11.4069i	0.251998	+	0.436474i	0.964076	−	0.265627i	$-0.0855790\pi$
$683$	6.58579	+	11.4069i	0.251998	+	0.436474i	−0.712078	+	0.702101i	$0.752246\pi$
$684$		0			0
$685$	19.3137			0.737939
$686$		0			0
$687$	−9.89949			−0.377689
$688$		0			0
$689$	1.36396	+	2.36245i	0.0519628	+	0.0900022i
$690$		0			0
$691$	−5.07107	+	8.78335i	−0.192913	+	0.334134i	−0.946214	−	0.323541i	$-0.895127\pi$
$691$	−5.07107	+	8.78335i	−0.192913	+	0.334134i	0.753302	+	0.657675i	$0.228460\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.707107	−	1.22474i	0.0268221	−	0.0464572i
$696$		0			0
$697$	−5.53553	−	9.58783i	−0.209673	−	0.363165i
$698$		0			0
$699$	8.48528			0.320943
$700$		0			0
$701$	−37.1421			−1.40284			−0.701420	−	0.712749i	$-0.747450\pi$
$701$	−37.1421			−1.40284			−0.701420	+	0.712749i	$0.747450\pi$
$702$		0			0
$703$	−11.8995	−	20.6105i	−0.448798	−	0.777341i
$704$		0			0
$705$	9.15685	−	15.8601i	0.344867	−	0.597327i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	10.6716	−	18.4837i	0.400779	−	0.694170i	−0.593041	−	0.805172i	$-0.702073\pi$
$709$	10.6716	−	18.4837i	0.400779	−	0.694170i	0.993820	+	0.111002i	$0.0354061\pi$
$710$		0			0
$711$	4.72792	+	8.18900i	0.177311	+	0.307112i
$712$		0			0
$713$	63.9411			2.39461
$714$		0			0
$715$	−0.414214			−0.0154907
$716$		0			0
$717$	5.62132	+	9.73641i	0.209932	+	0.363613i
$718$		0			0
$719$	−24.8492	+	43.0402i	−0.926720	+	1.60513i	−0.137950	+	0.990439i	$0.544051\pi$
$719$	−24.8492	+	43.0402i	−0.926720	+	1.60513i	−0.788771	+	0.614688i	$0.789282\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−12.5355	+	21.7122i	−0.466202	+	0.807485i
$724$		0			0
$725$	−0.500000	−	0.866025i	−0.0185695	−	0.0321634i
$726$		0			0
$727$	41.3137			1.53224			0.766120	−	0.642697i	$-0.222185\pi$
$727$	41.3137			1.53224			0.766120	+	0.642697i	$0.222185\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	14.0711	+	24.3718i	0.520437	+	0.901424i
$732$		0			0
$733$	13.3492	−	23.1216i	0.493066	−	0.854015i	−0.506903	−	0.862003i	$-0.669210\pi$
$733$	13.3492	−	23.1216i	0.493066	−	0.854015i	0.999968	+	0.00798883i	$0.00254295\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.707107	+	1.22474i	−0.0260466	+	0.0451141i
$738$		0			0
$739$	2.39949	+	4.15605i	0.0882668	+	0.152883i	0.906779	−	0.421607i	$-0.138534\pi$
$739$	2.39949	+	4.15605i	0.0882668	+	0.152883i	−0.818512	+	0.574490i	$0.805201\pi$
$740$		0			0
$741$	−2.00000			−0.0734718
$742$		0			0
$743$	−5.89949			−0.216431			−0.108216	−	0.994127i	$-0.534514\pi$
$743$	−5.89949			−0.216431			−0.108216	+	0.994127i	$0.534514\pi$
$744$		0			0
$745$	−4.58579	−	7.94282i	−0.168010	−	0.291002i
$746$		0			0
$747$	16.0000	−	27.7128i	0.585409	−	1.01396i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−12.8137	+	22.1940i	−0.467579	+	0.809870i	−0.999314	−	0.0370405i	$-0.988207\pi$
$751$	−12.8137	+	22.1940i	−0.467579	+	0.809870i	0.531735	+	0.846911i	$0.321540\pi$
$752$		0			0
$753$	−9.12132	−	15.7986i	−0.332399	−	0.575733i
$754$		0			0
$755$	6.65685			0.242268
$756$		0			0
$757$	−36.7696			−1.33641			−0.668206	−	0.743976i	$-0.732938\pi$
$757$	−36.7696			−1.33641			−0.668206	+	0.743976i	$0.732938\pi$
$758$		0			0
$759$	7.53553	+	13.0519i	0.273523	+	0.473755i
$760$		0			0
$761$	−2.22183	+	3.84831i	−0.0805411	+	0.139501i	−0.903482	−	0.428625i	$-0.858998\pi$
$761$	−2.22183	+	3.84831i	−0.0805411	+	0.139501i	0.822941	+	0.568126i	$0.192331\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.41421	−	5.91359i	0.123441	−	0.213806i
$766$		0			0
$767$	0.363961	+	0.630399i	0.0131419	+	0.0227624i
$768$		0			0
$769$	−18.4853			−0.666596			−0.333298	−	0.942821i	$-0.608162\pi$
$769$	−18.4853			−0.666596			−0.333298	+	0.942821i	$0.608162\pi$
$770$		0			0
$771$	25.3137			0.911651
$772$		0			0
$773$	10.6924	+	18.5198i	0.384578	+	0.666109i	0.991711	−	0.128491i	$-0.0410135\pi$
$773$	10.6924	+	18.5198i	0.384578	+	0.666109i	−0.607132	+	0.794601i	$0.707680\pi$
$774$		0			0
$775$	−5.12132	+	8.87039i	−0.183963	+	0.318634i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.58579	+	7.94282i	−0.164303	+	0.284581i
$780$		0			0
$781$	−1.24264	−	2.15232i	−0.0444652	−	0.0770160i
$782$		0			0
$783$	−0.414214			−0.0148028
$784$		0			0
$785$	−10.4853			−0.374236
$786$		0			0
$787$	21.4203	+	37.1011i	0.763552	+	1.32251i	0.941009	+	0.338382i	$0.109879\pi$
$787$	21.4203	+	37.1011i	0.763552	+	1.32251i	−0.177457	+	0.984128i	$0.556787\pi$
$788$		0			0
$789$	−22.8995	+	39.6631i	−0.815244	+	1.41204i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.41421	+	2.44949i	−0.0502202	+	0.0869839i
$794$		0			0
$795$	7.94975	+	13.7694i	0.281948	+	0.488349i
$796$		0			0
$797$	35.9289			1.27267			0.636334	−	0.771414i	$-0.280450\pi$
$797$	35.9289			1.27267			0.636334	+	0.771414i	$0.280450\pi$
$798$		0			0
$799$	18.3137			0.647892
$800$		0			0
$801$	−13.6569	−	23.6544i	−0.482541	−	0.835786i
$802$		0			0
$803$	−5.41421	+	9.37769i	−0.191063	+	0.330932i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−22.4350	+	38.8586i	−0.789750	+	1.36789i
$808$		0			0
$809$	−24.4706	−	42.3843i	−0.860339	−	1.49015i	−0.871602	−	0.490215i	$-0.836918\pi$
$809$	−24.4706	−	42.3843i	−0.860339	−	1.49015i	0.0112626	−	0.999937i	$-0.496415\pi$
$810$		0			0
$811$	−39.5563			−1.38901			−0.694506	−	0.719487i	$-0.744377\pi$
$811$	−39.5563			−1.38901			−0.694506	+	0.719487i	$0.744377\pi$
$812$		0			0
$813$	5.65685			0.198395
$814$		0			0
$815$	1.46447	+	2.53653i	0.0512980	+	0.0888508i
$816$		0			0
$817$	11.6569	−	20.1903i	0.407822	−	0.706368i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.7426	+	18.6068i	−0.374921	+	0.649382i	−0.990315	−	0.138838i	$-0.955663\pi$
$821$	−10.7426	+	18.6068i	−0.374921	+	0.649382i	0.615394	+	0.788219i	$0.288997\pi$
$822$		0			0
$823$	18.0208	+	31.2130i	0.628166	+	1.08802i	0.987919	+	0.154968i	$0.0495275\pi$
$823$	18.0208	+	31.2130i	0.628166	+	1.08802i	−0.359753	+	0.933047i	$0.617139\pi$
$824$		0			0
$825$	−2.41421			−0.0840521
$826$		0			0
$827$	−54.0416			−1.87921			−0.939606	−	0.342259i	$-0.888808\pi$
$827$	−54.0416			−1.87921			−0.939606	+	0.342259i	$0.888808\pi$
$828$		0			0
$829$	−3.70711	−	6.42090i	−0.128753	−	0.223007i	0.794441	−	0.607342i	$-0.207764\pi$
$829$	−3.70711	−	6.42090i	−0.128753	−	0.223007i	−0.923194	+	0.384335i	$0.874431\pi$
$830$		0			0
$831$	15.7782	−	27.3286i	0.547339	−	0.948019i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	3.79289	−	6.56948i	0.131258	−	0.227346i
$836$		0			0
$837$	2.12132	+	3.67423i	0.0733236	+	0.127000i
$838$		0			0
$839$	7.75736			0.267814			0.133907	−	0.990994i	$-0.457248\pi$
$839$	7.75736			0.267814			0.133907	+	0.990994i	$0.457248\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$	−22.1066	−	38.2898i	−0.761392	−	1.31877i
$844$		0			0
$845$	−6.41421	+	11.1097i	−0.220656	+	0.382187i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−30.2279	+	52.3563i	−1.03742	+	1.79686i
$850$		0			0
$851$	−37.1421	−	64.3321i	−1.27322	−	2.20527i
$852$		0			0
$853$	9.31371			0.318895			0.159448	−	0.987206i	$-0.449029\pi$
$853$	9.31371			0.318895			0.159448	+	0.987206i	$0.449029\pi$
$854$		0			0
$855$	−5.65685			−0.193460
$856$		0			0
$857$	−27.2426	−	47.1856i	−0.930591	−	1.61183i	−0.782314	−	0.622885i	$-0.785960\pi$
$857$	−27.2426	−	47.1856i	−0.930591	−	1.61183i	−0.148277	−	0.988946i	$-0.547373\pi$
$858$		0			0
$859$	26.7279	−	46.2941i	0.911945	−	1.57953i	0.100631	−	0.994924i	$-0.467914\pi$
$859$	26.7279	−	46.2941i	0.911945	−	1.57953i	0.811314	−	0.584611i	$-0.198753\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11.0919	+	19.2117i	−0.377572	+	0.653974i	−0.990708	−	0.136003i	$-0.956574\pi$
$863$	−11.0919	+	19.2117i	−0.377572	+	0.653974i	0.613136	+	0.789977i	$0.289908\pi$
$864$		0			0
$865$	−6.86396	−	11.8887i	−0.233382	−	0.404229i
$866$		0			0
$867$	−26.9706			−0.915968
$868$		0			0
$869$	3.34315			0.113408
$870$		0			0
$871$	−0.292893	−	0.507306i	−0.00992431	−	0.0171894i
$872$		0			0
$873$	−19.8995	+	34.4669i	−0.673496	+	1.16653i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.4853	+	23.3572i	−0.455366	+	0.788716i	−0.998709	−	0.0507941i	$-0.983825\pi$
$877$	−13.4853	+	23.3572i	−0.455366	+	0.788716i	0.543344	+	0.839510i	$0.317158\pi$
$878$		0			0
$879$	22.2279	+	38.4999i	0.749729	+	1.29857i
$880$		0			0
$881$	17.6569			0.594875			0.297437	−	0.954741i	$-0.403868\pi$
$881$	17.6569			0.594875			0.297437	+	0.954741i	$0.403868\pi$
$882$		0			0
$883$	35.1127			1.18164			0.590818	−	0.806805i	$-0.298805\pi$
$883$	35.1127			1.18164			0.590818	+	0.806805i	$0.298805\pi$
$884$		0			0
$885$	2.12132	+	3.67423i	0.0713074	+	0.123508i
$886$		0			0
$887$	9.14214	−	15.8346i	0.306963	−	0.531675i	−0.670734	−	0.741698i	$-0.734021\pi$
$887$	9.14214	−	15.8346i	0.306963	−	0.531675i	0.977696	+	0.210023i	$0.0673539\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−4.74264	+	8.21449i	−0.158884	+	0.275196i
$892$		0			0
$893$	−7.58579	−	13.1390i	−0.253849	−	0.439679i
$894$		0			0
$895$	−4.14214			−0.138456
$896$		0			0
$897$	−6.24264			−0.208436
$898$		0			0
$899$	−5.12132	−	8.87039i	−0.170806	−	0.295844i
$900$		0			0
$901$	−7.94975	+	13.7694i	−0.264844	+	0.458724i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.7782	+	22.1324i	−0.424761	+	0.735707i
$906$		0			0
$907$	3.84924	+	6.66708i	0.127812	+	0.221377i	0.922829	−	0.385211i	$-0.125871\pi$
$907$	3.84924	+	6.66708i	0.127812	+	0.221377i	−0.795017	+	0.606588i	$0.792538\pi$
$908$		0			0
$909$	29.6569			0.983656
$910$		0			0
$911$	20.6863			0.685367			0.342684	−	0.939451i	$-0.388664\pi$
$911$	20.6863			0.685367			0.342684	+	0.939451i	$0.388664\pi$
$912$		0			0
$913$	−5.65685	−	9.79796i	−0.187215	−	0.324265i
$914$		0			0
$915$	−8.24264	+	14.2767i	−0.272493	+	0.471972i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−14.2990	+	24.7666i	−0.471680	+	0.816974i	−0.999475	−	0.0323979i	$-0.989686\pi$
$919$	−14.2990	+	24.7666i	−0.471680	+	0.816974i	0.527795	+	0.849372i	$0.323019\pi$
$920$		0			0
$921$	14.3995	+	24.9407i	0.474479	+	0.821823i
$922$		0			0
$923$	1.02944			0.0338843
$924$		0			0
$925$	11.8995			0.391253
$926$		0			0
$927$	−9.55635	−	16.5521i	−0.313872	−	0.543642i
$928$		0			0
$929$	17.2635	−	29.9012i	0.566396	−	0.981026i	−0.430523	−	0.902580i	$-0.641671\pi$
$929$	17.2635	−	29.9012i	0.566396	−	0.981026i	0.996918	−	0.0784462i	$-0.0249959\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−12.0711	+	20.9077i	−0.395189	+	0.684487i
$934$		0			0
$935$	−1.20711	−	2.09077i	−0.0394766	−	0.0683755i
$936$		0			0
$937$	14.2132			0.464325			0.232163	−	0.972677i	$-0.425420\pi$
$937$	14.2132			0.464325			0.232163	+	0.972677i	$0.425420\pi$
$938$		0			0
$939$	−57.2843			−1.86940
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$		0			0
$943$	−14.3137	+	24.7921i	−0.466118	+	0.807341i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.94975	+	8.57321i	−0.160845	+	0.278592i	−0.935172	−	0.354194i	$-0.884755\pi$
$947$	−4.94975	+	8.57321i	−0.160845	+	0.278592i	0.774327	+	0.632786i	$0.218089\pi$
$948$		0			0
$949$	−2.24264	−	3.88437i	−0.0727992	−	0.126092i
$950$		0			0
$951$	29.7990			0.966298
$952$		0			0
$953$	58.3848			1.89127			0.945634	−	0.325232i	$-0.105442\pi$
$953$	58.3848			1.89127			0.945634	+	0.325232i	$0.105442\pi$
$954$		0			0
$955$	6.91421	+	11.9758i	0.223739	+	0.387527i
$956$		0			0
$957$	1.20711	−	2.09077i	0.0390202	−	0.0675850i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−36.9558	+	64.0094i	−1.19212	+	2.06482i
$962$		0			0
$963$	20.4853	+	35.4815i	0.660129	+	1.14338i
$964$		0			0
$965$	−0.686292			−0.0220925
$966$		0			0
$967$	28.8284			0.927060			0.463530	−	0.886081i	$-0.346583\pi$
$967$	28.8284			0.927060			0.463530	+	0.886081i	$0.346583\pi$
$968$		0			0
$969$	−5.82843	−	10.0951i	−0.187236	−	0.324302i
$970$		0			0
$971$	14.0919	−	24.4079i	0.452230	−	0.783285i	−0.546294	−	0.837593i	$-0.683962\pi$
$971$	14.0919	−	24.4079i	0.452230	−	0.783285i	0.998524	+	0.0543080i	$0.0172953\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$		0			0
$977$	−21.0416	−	36.4452i	−0.673181	−	1.16598i	−0.976997	−	0.213254i	$-0.931594\pi$
$977$	−21.0416	−	36.4452i	−0.673181	−	1.16598i	0.303815	−	0.952731i	$-0.401739\pi$
$978$		0			0
$979$	−9.65685			−0.308634
$980$		0			0
$981$	−51.7990			−1.65381
$982$		0			0
$983$	−16.6924	−	28.9121i	−0.532404	−	0.922152i	−0.999284	−	0.0378308i	$-0.987955\pi$
$983$	−16.6924	−	28.9121i	−0.532404	−	0.922152i	0.466880	−	0.884321i	$-0.345378\pi$
$984$		0			0
$985$	−6.12132	+	10.6024i	−0.195041	+	0.337822i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	36.3848	−	63.0203i	1.15697	−	2.00393i
$990$		0			0
$991$	2.65685	+	4.60181i	0.0843978	+	0.146181i	0.905134	−	0.425125i	$-0.139770\pi$
$991$	2.65685	+	4.60181i	0.0843978	+	0.146181i	−0.820737	+	0.571307i	$0.806437\pi$
$992$		0			0
$993$	22.9706			0.728949
$994$		0			0
$995$	12.3848			0.392624
$996$		0			0
$997$	6.44975	+	11.1713i	0.204266	+	0.353798i	0.949898	−	0.312559i	$-0.101186\pi$
$997$	6.44975	+	11.1713i	0.204266	+	0.353798i	−0.745633	+	0.666357i	$0.767853\pi$
$998$		0			0
$999$	2.46447	−	4.26858i	0.0779723	−	0.135052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.p.961.1		4
7.2	even	3		1960.2.a.u.1.2	yes	2
7.3	odd	6		1960.2.q.v.361.2		4
7.4	even	3	inner	1960.2.q.p.361.1		4
7.5	odd	6		1960.2.a.q.1.1	✓	2
7.6	odd	2		1960.2.q.v.961.2		4
28.19	even	6		3920.2.a.by.1.2		2
28.23	odd	6		3920.2.a.bn.1.1		2
35.9	even	6		9800.2.a.bs.1.1		2
35.19	odd	6		9800.2.a.ca.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.q.1.1	✓	2	7.5	odd	6
1960.2.a.u.1.2	yes	2	7.2	even	3
1960.2.q.p.361.1		4	7.4	even	3	inner
1960.2.q.p.961.1		4	1.1	even	1	trivial
1960.2.q.v.361.2		4	7.3	odd	6
1960.2.q.v.961.2		4	7.6	odd	2
3920.2.a.bn.1.1		2	28.23	odd	6
3920.2.a.by.1.2		2	28.19	even	6
9800.2.a.bs.1.1		2	35.9	even	6
9800.2.a.ca.1.2		2	35.19	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)

\(f(q)\)	\(=\)	\(q+(-1.20711 - 2.09077i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(-1.20711 - 2.09077i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.41421 + 2.44949i) q^{9} +(0.500000 + 0.866025i) q^{11} -0.414214 q^{13} -2.41421 q^{15} +(-1.20711 - 2.09077i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-3.12132 + 5.40629i) q^{23} +(-0.500000 - 0.866025i) q^{25} -0.414214 q^{27} +1.00000 q^{29} +(-5.12132 - 8.87039i) q^{31} +(1.20711 - 2.09077i) q^{33} +(-5.94975 + 10.3053i) q^{37} +(0.500000 + 0.866025i) q^{39} +4.58579 q^{41} -11.6569 q^{43} +(1.41421 + 2.44949i) q^{45} +(-3.79289 + 6.56948i) q^{47} +(-2.91421 + 5.04757i) q^{51} +(-3.29289 - 5.70346i) q^{53} +1.00000 q^{55} +4.82843 q^{57} +(-0.878680 - 1.52192i) q^{59} +(3.41421 - 5.91359i) q^{61} +(-0.207107 + 0.358719i) q^{65} +(0.707107 + 1.22474i) q^{67} +15.0711 q^{69} -2.48528 q^{71} +(5.41421 + 9.37769i) q^{73} +(-1.20711 + 2.09077i) q^{75} +(1.67157 - 2.89525i) q^{79} +(4.74264 + 8.21449i) q^{81} -11.3137 q^{83} -2.41421 q^{85} +(-1.20711 - 2.09077i) q^{87} +(-4.82843 + 8.36308i) q^{89} +(-12.3640 + 21.4150i) q^{93} +(1.00000 + 1.73205i) q^{95} +14.0711 q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^5	\( 4 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 4 q^{13} - 4 q^{15} - 2 q^{17} - 4 q^{19} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} - 12 q^{31} + 2 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} - 24 q^{43} - 18 q^{47} - 6 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57} - 12 q^{59} + 8 q^{61} + 2 q^{65} + 32 q^{69} + 24 q^{71} + 16 q^{73} - 2 q^{75} + 18 q^{79} + 2 q^{81} - 4 q^{85} - 2 q^{87} - 8 q^{89} - 24 q^{93} + 4 q^{95} + 28 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 + 2 * q^11 + 4 * q^13 - 4 * q^15 - 2 * q^17 - 4 * q^19 - 4 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 - 12 * q^31 + 2 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 - 24 * q^43 - 18 * q^47 - 6 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 12 * q^59 + 8 * q^61 + 2 * q^65 + 32 * q^69 + 24 * q^71 + 16 * q^73 - 2 * q^75 + 18 * q^79 + 2 * q^81 - 4 * q^85 - 2 * q^87 - 8 * q^89 - 24 * q^93 + 4 * q^95 + 28 * q^97

Introduction

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