LMFDB - Embedded newform 960.2.cp.a.299.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(59,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 1, 8, 8]))

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

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

chi := DirichletCharacter("960.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cp (of order $16$, degree $8$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{16}]$

Embedding invariants

Embedding label			299.2
Character	$\chi$	$=$	960.299
Dual form			960.2.cp.a.899.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0989274 - 1.41075i) q^{2} +(1.69877 - 0.337906i) q^{3} +(-1.98043 + 0.279124i) q^{4} +(-1.85922 + 1.24229i) q^{5} +(-0.644756 - 2.36311i) q^{6} +(0.589692 + 2.76627i) q^{8} +(2.77164 - 1.14805i) q^{9} +O(q^{10})$	\(q+(-0.0989274 - 1.41075i) q^{2} +(1.69877 - 0.337906i) q^{3} +(-1.98043 + 0.279124i) q^{4} +(-1.85922 + 1.24229i) q^{5} +(-0.644756 - 2.36311i) q^{6} +(0.589692 + 2.76627i) q^{8} +(2.77164 - 1.14805i) q^{9} +(1.93649 + 2.50000i) q^{10} +(-3.26997 + 1.14337i) q^{12} +(-2.73861 + 2.73861i) q^{15} +(3.84418 - 1.10557i) q^{16} +(5.35106 - 5.35106i) q^{17} +(-1.89380 - 3.79651i) q^{18} +(-6.96563 - 4.65428i) q^{19} +(3.33530 - 2.97922i) q^{20} +(8.64884 - 3.58247i) q^{23} +(1.93649 + 4.50000i) q^{24} +(1.91342 - 4.61940i) q^{25} +(4.32044 - 2.88683i) q^{27} +(4.13442 + 3.59257i) q^{30} +4.42678 q^{31} +(-1.93997 - 5.31380i) q^{32} +(-8.07838 - 7.01964i) q^{34} +(-5.16858 + 3.04726i) q^{36} +(-5.87694 + 10.2872i) q^{38} +(-4.53289 - 4.41055i) q^{40} +(-3.72688 + 5.57767i) q^{45} +(-5.90957 - 11.8469i) q^{46} +(7.63665 + 7.63665i) q^{47} +(6.15680 - 3.17708i) q^{48} +(-4.94975 - 4.94975i) q^{49} +(-6.70610 - 2.24237i) q^{50} +(7.28207 - 10.8984i) q^{51} +(-1.14840 - 0.228432i) q^{53} +(-4.50000 - 5.80948i) q^{54} +(-13.4057 - 5.55283i) q^{57} +(4.65921 - 6.18803i) q^{60} +(0.206943 + 1.04037i) q^{61} +(-0.437930 - 6.24508i) q^{62} +(-7.30453 + 3.26250i) q^{64} +(-9.10378 + 12.0910i) q^{68} +(13.4819 - 9.00829i) q^{69} +(4.81023 + 6.99011i) q^{72} +(1.68953 - 8.49385i) q^{75} +(15.0940 + 7.27320i) q^{76} +(-11.8730 + 11.8730i) q^{79} +(-5.77375 + 6.83109i) q^{80} +(6.36396 - 6.36396i) q^{81} +(8.35300 + 5.58129i) q^{83} +(-3.30123 + 16.5964i) q^{85} +(8.23738 + 4.70591i) q^{90} +(-16.1285 + 9.50891i) q^{92} +(7.52009 - 1.49584i) q^{93} +(10.0179 - 11.5289i) q^{94} +18.7326 q^{95} +(-5.09114 - 8.37140i) q^{96} +(-6.49319 + 7.47252i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 192 q^{51} - 144 q^{54} + 208 q^{76} - 256 q^{79} + 16 q^{94}+O(q^{100}) $ 32 * q + 192 * q^51 - 144 * q^54 + 208 * q^76 - 256 * q^79 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−0.0989274	−	1.41075i	−0.0699522	−	0.997550i
$2$	−0.0989274	−	1.41075i	−0.0699522	−	0.997550i
$3$	1.69877	−	0.337906i	0.980785	−	0.195090i
$3$	1.69877	−	0.337906i	0.980785	−	0.195090i
$4$	−1.98043	+	0.279124i	−0.990213	+	0.139562i
$5$	−1.85922	+	1.24229i	−0.831470	+	0.555570i
$5$	−1.85922	+	1.24229i	−0.831470	+	0.555570i
$6$	−0.644756	−	2.36311i	−0.263221	−	0.964736i
$7$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$7$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$8$	0.589692	+	2.76627i	0.208488	+	0.978025i
$9$	2.77164	−	1.14805i	0.923880	−	0.382683i
$10$	1.93649	+	2.50000i	0.612372	+	0.790569i
$11$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$11$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$12$	−3.26997	+	1.14337i	−0.943960	+	0.330061i
$13$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$13$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$14$		0			0
$15$	−2.73861	+	2.73861i	−0.707107	+	0.707107i
$16$	3.84418	−	1.10557i	0.961045	−	0.276392i
$17$	5.35106	−	5.35106i	1.29782	−	1.29782i	0.367997	−	0.929827i	$-0.380044\pi$
$17$	5.35106	−	5.35106i	1.29782	−	1.29782i	0.929827	−	0.367997i	$-0.119956\pi$
$18$	−1.89380	−	3.79651i	−0.446373	−	0.894847i
$19$	−6.96563	−	4.65428i	−1.59803	−	1.06777i	−0.952724	−	0.303838i	$-0.901732\pi$
$19$	−6.96563	−	4.65428i	−1.59803	−	1.06777i	−0.645301	−	0.763928i	$-0.723268\pi$
$20$	3.33530	−	2.97922i	0.745796	−	0.666174i
$21$		0			0
$22$		0			0
$23$	8.64884	−	3.58247i	1.80341	−	0.746996i	0.818363	−	0.574701i	$-0.194882\pi$
$23$	8.64884	−	3.58247i	1.80341	−	0.746996i	0.985045	−	0.172295i	$-0.0551183\pi$
$24$	1.93649	+	4.50000i	0.395285	+	0.918559i
$25$	1.91342	−	4.61940i	0.382683	−	0.923880i
$26$		0			0
$27$	4.32044	−	2.88683i	0.831470	−	0.555570i
$28$		0			0
$29$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$29$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$30$	4.13442	+	3.59257i	0.754838	+	0.655911i
$31$	4.42678			0.795074			0.397537	−	0.917586i	$-0.369865\pi$
$31$	4.42678			0.795074			0.397537	+	0.917586i	$0.369865\pi$
$32$	−1.93997	−	5.31380i	−0.342942	−	0.939357i
$33$		0			0
$34$	−8.07838	−	7.01964i	−1.38543	−	1.20386i
$35$		0			0
$36$	−5.16858	+	3.04726i	−0.861430	+	0.507877i
$37$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$37$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$38$	−5.87694	+	10.2872i	−0.953365	+	1.66880i
$39$		0			0
$40$	−4.53289	−	4.41055i	−0.716713	−	0.697369i
$41$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$41$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$42$		0			0
$43$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$43$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$44$		0			0
$45$	−3.72688	+	5.57767i	−0.555570	+	0.831470i
$46$	−5.90957	−	11.8469i	−0.871319	−	1.74674i
$47$	7.63665	+	7.63665i	1.11392	+	1.11392i	0.992615	+	0.121304i	$0.0387076\pi$
$47$	7.63665	+	7.63665i	1.11392	+	1.11392i	0.121304	+	0.992615i	$0.461292\pi$
$48$	6.15680	−	3.17708i	0.888657	−	0.458572i
$49$	−4.94975	−	4.94975i	−0.707107	−	0.707107i
$50$	−6.70610	−	2.24237i	−0.948386	−	0.317119i
$51$	7.28207	−	10.8984i	1.01969	−	1.52608i
$52$		0			0
$53$	−1.14840	−	0.228432i	−0.157745	−	0.0313775i	0.115586	−	0.993298i	$-0.463125\pi$
$53$	−1.14840	−	0.228432i	−0.157745	−	0.0313775i	−0.273331	+	0.961920i	$0.588125\pi$
$54$	−4.50000	−	5.80948i	−0.612372	−	0.790569i
$55$		0			0
$56$		0			0
$57$	−13.4057	−	5.55283i	−1.77563	−	0.735490i
$58$		0			0
$59$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$59$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$60$	4.65921	−	6.18803i	0.601502	−	0.798872i
$61$	0.206943	+	1.04037i	0.0264964	+	0.133206i	0.991769	−	0.128037i	$-0.0408676\pi$
$61$	0.206943	+	1.04037i	0.0264964	+	0.133206i	−0.965273	+	0.261243i	$0.915868\pi$
$62$	−0.437930	−	6.24508i	−0.0556172	−	0.793126i
$63$		0			0
$64$	−7.30453	+	3.26250i	−0.913066	+	0.407812i
$65$		0			0
$66$		0			0
$67$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$67$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$68$	−9.10378	+	12.0910i	−1.10400	+	1.46625i
$69$	13.4819	−	9.00829i	1.62303	−	1.08447i
$70$		0			0
$71$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$71$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$72$	4.81023	+	6.99011i	0.566891	+	0.823793i
$73$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$73$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$74$		0			0
$75$	1.68953	−	8.49385i	0.195090	−	0.980785i
$76$	15.0940	+	7.27320i	1.73141	+	0.834293i
$77$		0			0
$78$		0			0
$79$	−11.8730	+	11.8730i	−1.33581	+	1.33581i	−0.435745	+	0.900070i	$0.643515\pi$
$79$	−11.8730	+	11.8730i	−1.33581	+	1.33581i	−0.900070	+	0.435745i	$0.856485\pi$
$80$	−5.77375	+	6.83109i	−0.645525	+	0.763739i
$81$	6.36396	−	6.36396i	0.707107	−	0.707107i
$82$		0			0
$83$	8.35300	+	5.58129i	0.916860	+	0.612626i	0.921928	−	0.387361i	$-0.126613\pi$
$83$	8.35300	+	5.58129i	0.916860	+	0.612626i	−0.00506792	+	0.999987i	$0.501613\pi$
$84$		0			0
$85$	−3.30123	+	16.5964i	−0.358069	+	1.80013i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$89$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$90$	8.23738	+	4.70591i	0.868296	+	0.496046i
$91$		0			0
$92$	−16.1285	+	9.50891i	−1.68151	+	0.991373i
$93$	7.52009	−	1.49584i	0.779797	−	0.155111i
$94$	10.0179	−	11.5289i	1.03327	−	1.18911i
$95$	18.7326			1.92193
$96$	−5.09114	−	8.37140i	−0.519612	−	0.854402i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	−6.49319	+	7.47252i	−0.655911	+	0.754838i
$99$		0			0
$100$	−2.50000	+	9.68246i	−0.250000	+	0.968246i
$101$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$101$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$102$	−16.0953	−	9.19502i	−1.59367	−	0.910443i
$103$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$103$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$104$		0			0
$105$		0			0
$106$	−0.208651	+	1.64271i	−0.0202660	+	0.159554i
$107$	−20.1098	−	4.00010i	−1.94409	−	0.386704i	−0.998031	−	0.0627149i	$-0.980024\pi$
$107$	−20.1098	−	4.00010i	−1.94409	−	0.386704i	−0.946061	−	0.323989i	$-0.894976\pi$
$108$	−7.75054	+	6.92309i	−0.745796	+	0.666174i
$109$	6.92407	−	10.3626i	0.663206	−	0.992557i	−0.335517	−	0.942034i	$-0.608911\pi$
$109$	6.92407	−	10.3626i	0.663206	−	0.992557i	0.998723	−	0.0505232i	$-0.0160889\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	13.7976	+	13.7976i	1.29797	+	1.29797i	0.929731	+	0.368239i	$0.120039\pi$
$113$	13.7976	+	13.7976i	1.29797	+	1.29797i	0.368239	+	0.929731i	$0.379961\pi$
$114$	−6.50746	+	19.4614i	−0.609479	+	1.82273i
$115$	−11.6297	+	17.4050i	−1.08447	+	1.62303i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−9.19069	−	5.96081i	−0.838991	−	0.544145i
$121$	−10.1627	−	4.20952i	−0.923880	−	0.382683i
$122$	1.44723	−	0.394866i	0.131026	−	0.0357495i
$123$		0			0
$124$	−8.76692	+	1.23562i	−0.787293	+	0.110962i
$125$	2.18118	+	10.9655i	0.195090	+	0.980785i
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	5.32518	+	9.98211i	0.470684	+	0.882302i
$129$		0			0
$130$		0			0
$131$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$131$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−4.44638	+	10.7345i	−0.382683	+	0.923880i
$136$	17.9580	+	11.6470i	1.53988	+	0.998724i
$137$	10.3081	−	4.26976i	0.880682	−	0.364791i	0.103921	−	0.994586i	$-0.466861\pi$
$137$	10.3081	−	4.26976i	0.880682	−	0.364791i	0.776761	+	0.629795i	$0.216861\pi$
$138$	−14.0422	−	18.1284i	−1.19535	−	1.54319i
$139$	1.86983	−	9.40025i	0.158596	−	0.797318i	−0.816810	−	0.576906i	$-0.804260\pi$
$139$	1.86983	−	9.40025i	0.158596	−	0.797318i	0.975407	−	0.220412i	$-0.0707402\pi$
$140$		0			0
$141$	15.5534	+	10.3924i	1.30983	+	0.875201i
$142$		0			0
$143$		0			0
$144$	9.38543	−	7.47755i	0.782119	−	0.623129i
$145$		0			0
$146$		0			0
$147$	−10.0810	−	6.73593i	−0.831470	−	0.555570i
$148$		0			0
$149$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$149$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$150$	−12.1498	−	1.54323i	−0.992030	−	0.126004i
$151$	−17.0064	+	7.04427i	−1.38396	+	0.573254i	−0.945537	−	0.325515i	$-0.894462\pi$
$151$	−17.0064	+	7.04427i	−1.38396	+	0.573254i	−0.438421	+	0.898770i	$0.644462\pi$
$152$	8.76745	−	22.0134i	0.711134	−	1.78552i
$153$	8.68793	−	20.9745i	0.702377	−	1.69569i
$154$		0			0
$155$	−8.23038	+	5.49936i	−0.661080	+	0.441719i
$156$		0			0
$157$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$157$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$158$	17.9244	+	15.5752i	1.42599	+	1.23910i
$159$	−2.02806			−0.160836
$160$	10.2081	+	7.46953i	0.807024	+	0.590518i
$161$		0			0
$162$	−9.60752	−	8.34838i	−0.754838	−	0.655911i
$163$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$163$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$164$		0			0
$165$		0			0
$166$	7.04746	−	12.3361i	0.546989	−	0.957469i
$167$	−23.2182	−	9.61731i	−1.79668	−	0.744210i	−0.987697	−	0.156379i	$-0.950018\pi$
$167$	−23.2182	−	9.61731i	−1.79668	−	0.744210i	−0.808984	−	0.587831i	$-0.799982\pi$
$168$		0			0
$169$	4.97488	+	12.0104i	0.382683	+	0.923880i
$170$	23.7400	+	3.01537i	1.82077	+	0.231268i
$171$	−24.6496	−	4.90310i	−1.88500	−	0.374950i
$172$		0			0
$173$	11.8663	−	17.7591i	0.902175	−	1.35020i	−0.0342793	−	0.999412i	$-0.510914\pi$
$173$	11.8663	−	17.7591i	0.902175	−	1.35020i	0.936455	−	0.350789i	$-0.114086\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$179$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$180$	5.82395	−	12.0864i	0.434092	−	0.900869i
$181$	−9.49937	−	1.88954i	−0.706083	−	0.140449i	−0.171028	−	0.985266i	$-0.554709\pi$
$181$	−9.49937	−	1.88954i	−0.706083	−	0.140449i	−0.535054	+	0.844818i	$0.679709\pi$
$182$		0			0
$183$	0.703098	+	1.69743i	0.0519745	+	0.125477i
$184$	15.0102	+	21.8125i	1.10657	+	1.60804i
$185$		0			0
$186$	−2.85420	−	10.4610i	−0.209280	−	0.767036i
$187$		0			0
$188$	−17.2554	−	12.9923i	−1.25848	−	0.947557i
$189$		0			0
$190$	−1.85317	−	26.4271i	−0.134443	−	1.91722i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	−11.3063	+	8.01048i	−0.815961	+	0.578106i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$		0			0
$196$	11.1842	+	8.42102i	0.798872	+	0.601502i
$197$	−13.6641	+	9.13004i	−0.973525	+	0.650489i	−0.937178	−	0.348851i	$-0.886572\pi$
$197$	−13.6641	+	9.13004i	−0.973525	+	0.650489i	−0.0363466	+	0.999339i	$0.511572\pi$
$198$		0			0
$199$	1.95856	−	4.72839i	0.138839	−	0.335186i	−0.839132	−	0.543928i	$-0.816937\pi$
$199$	1.95856	−	4.72839i	0.138839	−	0.335186i	0.977971	+	0.208741i	$0.0669366\pi$
$200$	13.9068	+	2.56901i	0.983362	+	0.181657i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−11.3796	+	23.6161i	−0.796732	+	1.65345i
$205$		0			0
$206$		0			0
$207$	19.8586	−	19.8586i	1.38027	−	1.38027i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	24.0903	+	16.0966i	1.65844	+	1.10814i	0.870043	+	0.492975i	$0.164091\pi$
$211$	24.0903	+	16.0966i	1.65844	+	1.10814i	0.788401	+	0.615162i	$0.210909\pi$
$212$	2.33809	+	0.131846i	0.160581	+	0.00905520i
$213$		0			0
$214$	−3.65372	+	28.7657i	−0.249763	+	1.96638i
$215$		0			0
$216$	10.5335	+	10.2492i	0.716713	+	0.697369i
$217$		0			0
$218$	−15.3040	−	8.74298i	−1.03652	−	0.592149i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$		−	15.0000i		−	1.00000i
$226$	18.1000	−	20.8299i	1.20399	−	1.38559i
$227$	3.03507	+	15.2583i	0.201444	+	1.01273i	0.940683	+	0.339286i	$0.110186\pi$
$227$	3.03507	+	15.2583i	0.201444	+	1.01273i	−0.739239	+	0.673443i	$0.764814\pi$
$228$	28.0990	+	7.25512i	1.86090	+	0.480482i
$229$	−0.868775	−	1.30021i	−0.0574103	−	0.0859206i	0.801654	−	0.597788i	$-0.203954\pi$
$229$	−0.868775	−	1.30021i	−0.0574103	−	0.0859206i	−0.859064	+	0.511868i	$0.828954\pi$
$230$	25.7046	+	14.6847i	1.69491	+	0.968280i
$231$		0			0
$232$		0			0
$233$	−11.3675	−	27.4436i	−0.744709	−	1.79789i	−0.585553	−	0.810634i	$-0.699122\pi$
$233$	−11.3675	−	27.4436i	−0.744709	−	1.79789i	−0.159157	−	0.987253i	$-0.550878\pi$
$234$		0			0
$235$	−23.6852	−	4.71127i	−1.54505	−	0.307330i
$236$		0			0
$237$	−16.1575	+	24.1814i	−1.04954	+	1.57075i
$238$		0			0
$239$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$239$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$240$	−7.50000	+	13.5554i	−0.484123	+	0.875000i
$241$	20.7824	+	20.7824i	1.33871	+	1.33871i	0.897310	+	0.441401i	$0.145518\pi$
$241$	20.7824	+	20.7824i	1.33871	+	1.33871i	0.441401	+	0.897310i	$0.354482\pi$
$242$	−4.93321	+	14.7534i	−0.317119	+	0.948386i
$243$	8.66048	−	12.9613i	0.555570	−	0.831470i
$244$	−0.700229	−	2.00262i	−0.0448275	−	0.128205i
$245$	15.3517	+	3.05365i	0.980785	+	0.195090i
$246$		0			0
$247$		0			0
$248$	2.61044	+	12.2457i	0.165763	+	0.777602i
$249$	16.0758	+	6.65880i	1.01876	+	0.421984i
$250$	15.2538	−	4.16188i	0.964736	−	0.263221i
$251$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$251$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$			29.3090i			1.83540i
$256$	13.5554	−	8.50000i	0.847215	−	0.531250i
$257$	23.1527			1.44423			0.722113	−	0.691776i	$-0.243171\pi$
$257$	23.1527			1.44423			0.722113	+	0.691776i	$0.243171\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.01855	+	19.3585i	−0.494445	+	1.19370i	0.457991	+	0.888957i	$0.348569\pi$
$263$	−8.01855	+	19.3585i	−0.494445	+	1.19370i	−0.952436	+	0.304739i	$0.901431\pi$
$264$		0			0
$265$	2.41892	−	1.00195i	0.148593	−	0.0615492i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$269$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$270$	15.5836	+	5.21079i	0.948386	+	0.317119i
$271$	−22.6274	+	22.6274i	−1.37452	+	1.37452i	−0.520900	+	0.853618i	$0.674404\pi$
$271$	−22.6274	+	22.6274i	−1.37452	+	1.37452i	−0.853618	+	0.520900i	$0.825596\pi$
$272$	14.6545	−	26.4864i	0.888559	−	1.60598i
$273$		0			0
$274$	−7.04332	−	14.1198i	−0.425503	−	0.853007i
$275$		0			0
$276$	−24.1854	+	21.6034i	−1.45579	+	1.30037i
$277$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$277$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$278$	−13.4464	−	1.70791i	−0.806459	−	0.102434i
$279$	12.2694	−	5.08217i	0.734552	−	0.304262i
$280$		0			0
$281$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$281$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$282$	13.1225	−	22.9700i	0.781431	−	1.36784i
$283$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$283$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$284$		0			0
$285$	31.8224	−	6.32988i	1.88500	−	0.374950i
$286$		0			0
$287$		0			0
$288$	−11.4774	−	12.5008i	−0.676313	−	0.736614i
$289$		−	40.2678i		−	2.36869i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	19.0142	+	28.4567i	1.11082	+	1.66246i	0.575369	+	0.817894i	$0.304859\pi$
$293$	19.0142	+	28.4567i	1.11082	+	1.66246i	0.535452	+	0.844566i	$0.320141\pi$
$294$	−8.50542	+	14.8882i	−0.496046	+	0.868296i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.975161	+	17.2930i	−0.0563009	+	0.998414i
$301$		0			0
$302$	11.6201	+	23.2948i	0.668661	+	1.34047i
$303$		0			0
$304$	−31.9228	−	10.1909i	−1.83090	−	0.584490i
$305$	−1.67720	−	1.67720i	−0.0960363	−	0.0960363i
$306$	−30.4492	−	10.1815i	−1.74067	−	0.582039i
$307$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$307$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$308$		0			0
$309$		0			0
$310$	8.57243	+	11.0670i	0.486881	+	0.628561i
$311$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$311$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$312$		0			0
$313$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$313$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$314$		0			0
$315$		0			0
$316$	20.1995	−	26.8276i	1.13631	−	1.50917i
$317$	−0.738325	−	3.71181i	−0.0414685	−	0.208476i	0.954496	−	0.298223i	$-0.0963940\pi$
$317$	−0.738325	−	3.71181i	−0.0414685	−	0.208476i	−0.995965	+	0.0897473i	$0.971394\pi$
$318$	0.200631	+	2.86109i	0.0112508	+	0.160442i
$319$		0			0
$320$	9.52777	−	15.1401i	0.532618	−	0.846356i
$321$	−35.5137			−1.98218
$322$		0			0
$323$	−62.1789	+	12.3682i	−3.45973	+	0.688183i
$324$	−10.8270	+	14.3797i	−0.601502	+	0.798872i
$325$		0			0
$326$		0			0
$327$	8.26081	−	19.9434i	0.456824	−	1.10287i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.734640	+	3.69329i	−0.0403795	+	0.203001i	−0.995709	−	0.0925421i	$-0.970501\pi$
$331$	−0.734640	+	3.69329i	−0.0403795	+	0.203001i	0.955329	+	0.295543i	$0.0955007\pi$
$332$	−18.1004	−	8.72182i	−0.993387	−	0.478672i
$333$		0			0
$334$	−11.2707	+	33.7065i	−0.616705	+	1.84434i
$335$		0			0
$336$		0			0
$337$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$337$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$338$	16.4516	−	8.20648i	0.894847	−	0.446373i
$339$	28.1013	+	18.7767i	1.52625	+	1.01981i
$340$	1.90540	−	33.7894i	0.103335	−	1.83249i
$341$		0			0
$342$	−4.47853	+	35.2594i	−0.242171	+	1.90661i
$343$		0			0
$344$		0			0
$345$	−13.8748	+	33.4968i	−0.746996	+	1.80341i
$346$	−26.2276	−	14.9835i	−1.41000	−	0.805516i
$347$	−14.9247	+	9.97235i	−0.801198	+	0.535344i	−0.887436	−	0.460931i	$-0.847516\pi$
$347$	−14.9247	+	9.97235i	−0.801198	+	0.535344i	0.0862376	+	0.996275i	$0.472516\pi$
$348$		0			0
$349$	29.7417	−	5.91599i	1.59204	−	0.316676i	0.682048	−	0.731308i	$-0.261090\pi$
$349$	29.7417	−	5.91599i	1.59204	−	0.316676i	0.909989	+	0.414632i	$0.136090\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	26.6486i		−	1.41836i	−0.705028	−	0.709180i	$-0.749065\pi$
$353$		−	26.6486i		−	1.41836i	0.705028	−	0.709180i	$-0.250935\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$359$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$360$	−17.6271	−	7.02046i	−0.929028	−	0.370011i
$361$	19.5866	+	47.2863i	1.03088	+	2.48875i
$362$	−1.72592	+	13.5882i	−0.0907125	+	0.714178i
$363$	−18.6865	−	3.71697i	−0.980785	−	0.195090i
$364$		0			0
$365$		0			0
$366$	2.32509	−	1.15982i	0.121534	−	0.0606246i
$367$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$367$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$368$	29.2871	−	23.3335i	1.52669	−	1.21634i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−14.4755	+	5.06143i	−0.750517	+	0.262423i
$373$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$373$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$374$		0			0
$375$	7.41063	+	17.8909i	0.382683	+	0.923880i
$376$	−16.6218	+	25.6283i	−0.857203	+	1.32168i
$377$		0			0
$378$		0			0
$379$	16.6562	+	24.9278i	0.855572	+	1.28045i	0.958306	+	0.285746i	$0.0922412\pi$
$379$	16.6562	+	24.9278i	0.855572	+	1.28045i	−0.102733	+	0.994709i	$0.532759\pi$
$380$	−37.0986	+	5.22872i	−1.90312	+	0.268228i
$381$		0			0
$382$		0			0
$383$			35.6280i			1.82051i	0.414053	+	0.910253i	$0.364113\pi$
$383$			35.6280i			1.82051i	−0.414053	+	0.910253i	$0.635887\pi$
$384$	12.4193	+	15.1579i	0.633769	+	0.773523i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$389$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$390$		0			0
$391$	27.1105	−	65.4506i	1.37104	−	3.30998i
$392$	10.7735	−	16.6112i	0.544145	−	0.838991i
$393$		0			0
$394$	14.2319	+	18.3734i	0.716995	+	0.925637i
$395$	7.32480	−	36.8242i	0.368551	−	1.85283i
$396$		0			0
$397$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$397$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$398$	−6.86432	−	2.29527i	−0.344077	−	0.115052i
$399$		0			0
$400$	2.24847	−	19.8732i	0.112423	−	0.993660i
$401$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$401$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−3.92612	+	19.7379i	−0.195090	+	0.980785i
$406$		0			0
$407$		0			0
$408$	34.4421	+	13.7175i	1.70514	+	0.679117i
$409$	−4.65491	+	11.2379i	−0.230170	+	0.555680i	−0.996197	−	0.0871284i	$-0.972231\pi$
$409$	−4.65491	+	11.2379i	−0.230170	+	0.555680i	0.766027	+	0.642809i	$0.222231\pi$
$410$		0			0
$411$	16.0683	−	10.7365i	0.792593	−	0.529594i
$412$		0			0
$413$		0			0
$414$	−29.9801	−	26.0510i	−1.47344	−	1.28034i
$415$	−22.4637			−1.10270
$416$		0			0
$417$		−	16.6007i		−	0.812939i
$418$		0			0
$419$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$419$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$420$		0			0
$421$	−18.8854	−	28.2639i	−0.920416	−	1.37750i	−0.926003	−	0.377515i	$-0.876779\pi$
$421$	−18.8854	−	28.2639i	−0.920416	−	1.37750i	0.00558746	−	0.999984i	$-0.498221\pi$
$422$	20.3251	−	35.5778i	0.989411	−	1.73190i
$423$	29.9333	+	12.3988i	1.45541	+	0.602849i
$424$	−0.0452999	−	3.31150i	−0.00219996	−	0.160821i
$425$	−14.4799	−	34.9575i	−0.702377	−	1.69569i
$426$		0			0
$427$		0			0
$428$	40.9426	+	2.30877i	1.97904	+	0.111599i
$429$		0			0
$430$		0			0
$431$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$431$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$432$	13.4170	−	15.8740i	0.645525	−	0.763739i
$433$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$433$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$434$		0			0
$435$		0			0
$436$	−10.8202	+	22.4550i	−0.518192	+	1.07540i
$437$	−76.9185	−	15.3000i	−3.67951	−	0.731900i
$438$		0			0
$439$	−14.8098	−	35.7540i	−0.706833	−	1.70644i	−0.707768	−	0.706445i	$-0.750298\pi$
$439$	−14.8098	−	35.7540i	−0.706833	−	1.70644i	0.000935292	−	1.00000i	$-0.499702\pi$
$440$		0			0
$441$	−19.4015	−	8.03635i	−0.923880	−	0.382683i
$442$		0			0
$443$	−17.2833	−	25.8662i	−0.821153	−	1.22894i	−0.970726	−	0.240191i	$-0.922790\pi$
$443$	−17.2833	−	25.8662i	−0.821153	−	1.22894i	0.149573	−	0.988751i	$-0.452210\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−21.1612	+	1.48391i	−0.997550	+	0.0699522i
$451$		0			0
$452$	−31.1764	−	23.4739i	−1.46641	−	1.10412i
$453$	−26.5096	+	17.7131i	−1.24553	+	0.832236i
$454$	21.2254	−	5.79118i	0.996157	−	0.271794i
$455$		0			0
$456$	7.45540	−	40.3583i	0.349131	−	1.88995i
$457$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$457$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$458$	−1.74833	+	1.35425i	−0.0816941	+	0.0632800i
$459$	7.67137	−	38.5666i	0.358069	−	1.80013i
$460$	18.1735	−	37.7154i	0.847345	−	1.75849i
$461$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$461$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$462$		0			0
$463$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$463$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$464$		0			0
$465$	−12.1232	+	12.1232i	−0.562202	+	0.562202i
$466$	−37.5914	+	18.7516i	−1.74139	+	0.868651i
$467$	−6.77797	−	4.52889i	−0.313647	−	0.209572i	0.388775	−	0.921333i	$-0.372898\pi$
$467$	−6.77797	−	4.52889i	−0.313647	−	0.209572i	−0.702422	+	0.711760i	$0.747898\pi$
$468$		0			0
$469$		0			0
$470$	−4.30331	+	33.8799i	−0.198497	+	1.56276i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	35.7123	+	20.4020i	1.64032	+	0.937094i
$475$	−34.8281	+	23.2714i	−1.59803	+	1.06777i
$476$		0			0
$477$	−3.44521	+	0.685295i	−0.157745	+	0.0313775i
$478$		0			0
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$	19.8653	+	9.23961i	0.906722	+	0.421729i
$481$		0			0
$482$	27.2628	−	31.3747i	1.24179	−	1.42908i
$483$		0			0
$484$	21.3014	+	5.50000i	0.968246	+	0.250000i
$485$		0			0
$486$	−19.1419	−	10.9355i	−0.868296	−	0.496046i
$487$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$487$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$488$	−2.75592	+	1.18596i	−0.124755	+	0.0536859i
$489$		0			0
$490$	2.78922	−	21.9595i	0.126004	−	0.992030i
$491$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$491$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	17.0174	−	4.89411i	0.764102	−	0.219752i
$497$		0			0
$498$	7.80357	−	23.3376i	0.349686	−	1.04578i
$499$	−17.9345	+	26.8409i	−0.802858	+	1.20156i	0.173379	+	0.984855i	$0.444532\pi$
$499$	−17.9345	+	26.8409i	−0.802858	+	1.20156i	−0.976237	+	0.216707i	$0.930468\pi$
$500$	−7.38039	−	21.1076i	−0.330061	−	0.943960i
$501$	−42.6922	−	8.49200i	−1.90735	−	0.379395i
$502$		0			0
$503$	16.5267	+	39.8989i	0.736887	+	1.77900i	0.618124	+	0.786081i	$0.287893\pi$
$503$	16.5267	+	39.8989i	0.736887	+	1.77900i	0.118763	+	0.992923i	$0.462107\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.5096	+	18.7219i	0.555570	+	0.831470i
$508$		0			0
$509$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$509$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$510$	41.3476	−	2.89946i	1.83090	−	0.128390i
$511$		0			0
$512$	−13.3324	−	18.2824i	−0.589213	−	0.807978i
$513$	−43.5307			−1.92193
$514$	−2.29044	−	32.6626i	−0.101027	−	1.44069i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	14.1571	−	34.1783i	0.621429	−	1.50026i
$520$		0			0
$521$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$521$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$522$		0			0
$523$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$523$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$524$		0			0
$525$		0			0
$526$	28.1032	+	9.39708i	1.22536	+	0.409732i
$527$	23.6880	−	23.6880i	1.03187	−	1.03187i
$528$		0			0
$529$	45.7050	−	45.7050i	1.98717	−	1.98717i
$530$	−1.65280	−	3.31337i	−0.0717928	−	0.143923i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	42.3580	−	17.5452i	1.83129	−	0.758547i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	5.80948	−	22.5000i	0.250000	−	0.968246i
$541$	−23.6934	+	4.71292i	−1.01866	+	0.202624i	−0.676052	−	0.736854i	$-0.736311\pi$
$541$	−23.6934	+	4.71292i	−1.01866	+	0.202624i	−0.342609	+	0.939478i	$0.611311\pi$
$542$	34.1601	+	29.6831i	1.46730	+	1.27500i
$543$	−16.7757			−0.719916
$544$	−38.8154	−	18.0536i	−1.66420	−	0.774041i
$545$			27.8681i			1.19374i
$546$		0			0
$547$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$547$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$548$	−19.2227	+	11.3332i	−0.821153	+	0.484130i
$549$	1.76797	+	2.64596i	0.0754552	+	0.112927i
$550$		0			0
$551$		0			0
$552$	32.8695	+	31.9824i	1.39902	+	1.36126i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.07922	+	19.1384i	−0.0457692	+	0.811649i
$557$	−20.3152	+	30.4039i	−0.860783	+	1.28825i	0.0953863	+	0.995440i	$0.469591\pi$
$557$	−20.3152	+	30.4039i	−0.860783	+	1.28825i	−0.956170	+	0.292813i	$0.905409\pi$
$558$	−8.38345	−	16.8063i	−0.354900	−	0.711469i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−26.3027	+	39.3648i	−1.10853	+	1.65903i	−0.497271	+	0.867596i	$0.665664\pi$
$563$	−26.3027	+	39.3648i	−1.10853	+	1.65903i	−0.611257	+	0.791433i	$0.709336\pi$
$564$	−33.7031	−	16.2401i	−1.41916	−	0.683833i
$565$	−42.7935	−	8.51216i	−1.80034	−	0.358109i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$569$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$570$	−12.0780	−	44.2673i	−0.505891	−	1.85415i
$571$	−0.980030	−	1.46672i	−0.0410130	−	0.0613802i	0.810397	−	0.585882i	$-0.199252\pi$
$571$	−0.980030	−	1.46672i	−0.0410130	−	0.0613802i	−0.851410	+	0.524502i	$0.824252\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	46.8072i		−	1.95200i
$576$	−16.5000	+	17.4284i	−0.687500	+	0.726184i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−56.8078	+	3.98359i	−2.36289	+	0.165695i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	38.2643	−	29.6394i	1.58068	−	1.22439i
$587$	0.137860	−	0.693068i	0.00569009	−	0.0286060i	−0.977836	−	0.209373i	$-0.932858\pi$
$587$	0.137860	−	0.693068i	0.00569009	−	0.0286060i	0.983526	+	0.180767i	$0.0578579\pi$
$588$	21.8449	+	10.5262i	0.900869	+	0.434092i
$589$	−30.8353	−	20.6035i	−1.27055	−	0.848953i
$590$		0			0
$591$	−20.1270	+	20.1270i	−0.827915	+	0.827915i
$592$		0			0
$593$	30.2703	−	30.2703i	1.24305	−	1.24305i	0.284326	−	0.958728i	$-0.408230\pi$
$593$	30.2703	−	30.2703i	1.24305	−	1.24305i	0.958728	−	0.284326i	$-0.0917698\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.72939	−	8.69425i	0.0707794	−	0.355832i
$598$		0			0
$599$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$599$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$600$	24.4926	−	0.335048i	0.999906	−	0.0136783i
$601$	−17.9725	+	43.3895i	−0.733114	+	1.76989i	−0.101185	+	0.994868i	$0.532263\pi$
$601$	−17.9725	+	43.3895i	−0.733114	+	1.76989i	−0.631929	+	0.775026i	$0.717737\pi$
$602$		0			0
$603$		0			0
$604$	31.7136	−	18.6975i	1.29041	−	0.760792i
$605$	24.1241	−	4.79859i	0.980785	−	0.195090i
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−11.2188	+	46.0432i	−0.454983	+	1.86730i
$609$		0			0
$610$	−2.20019	+	2.53203i	−0.0890831	+	0.102519i
$611$		0			0
$612$	−11.3513	+	43.9635i	−0.458850	+	1.77712i
$613$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$613$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.07232	+	2.58880i	0.0431698	+	0.104221i	0.943994	−	0.329964i	$-0.107036\pi$
$617$	1.07232	+	2.58880i	0.0431698	+	0.104221i	−0.900824	+	0.434185i	$0.857036\pi$
$618$		0			0
$619$	−37.8790	−	7.53460i	−1.52248	−	0.302841i	−0.638230	−	0.769846i	$-0.720333\pi$
$619$	−37.8790	−	7.53460i	−1.52248	−	0.302841i	−0.884255	+	0.467005i	$0.845333\pi$
$620$	14.7647	−	13.1884i	0.592963	−	0.529658i
$621$	27.0249	−	40.4456i	1.08447	−	1.62303i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−17.6777	−	17.6777i	−0.707107	−	0.707107i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	12.2459	+	29.5641i	0.487500	+	1.17693i	0.955974	+	0.293452i	$0.0948042\pi$
$631$	12.2459	+	29.5641i	0.487500	+	1.17693i	−0.468473	+	0.883478i	$0.655196\pi$
$632$	−39.8453	−	25.8425i	−1.58496	−	1.02796i
$633$	46.3630	+	19.2042i	1.84276	+	0.763298i
$634$	−5.16339	+	1.40879i	−0.205065	+	0.0559503i
$635$		0			0
$636$	4.01643	−	0.566080i	0.159262	−	0.0224465i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−22.3014	−	11.9435i	−0.881540	−	0.472109i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	3.51327	+	50.1009i	0.138658	+	1.97732i
$643$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$643$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$644$		0			0
$645$		0			0
$646$	23.5996	+	86.4953i	0.928512	+	3.40311i
$647$	5.76248	−	13.9118i	0.226546	−	0.546931i	−0.769206	−	0.639001i	$-0.779348\pi$
$647$	5.76248	−	13.9118i	0.226546	−	0.546931i	0.995753	+	0.0920694i	$0.0293482\pi$
$648$	21.3572	+	13.8517i	0.838991	+	0.544145i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.00868	−	3.34669i	−0.196005	−	0.130966i	0.453695	−	0.891157i	$-0.350105\pi$
$653$	−5.00868	−	3.34669i	−0.196005	−	0.130966i	−0.649700	+	0.760191i	$0.725105\pi$
$654$	−28.9523	−	9.68099i	−1.13212	−	0.378557i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$659$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$660$		0			0
$661$	−9.73008	+	48.9164i	−0.378456	+	1.90263i	0.0493940	+	0.998779i	$0.484271\pi$
$661$	−9.73008	+	48.9164i	−0.378456	+	1.90263i	−0.427850	+	0.903850i	$0.640729\pi$
$662$	5.28298	+	0.671026i	0.205329	+	0.0260802i
$663$		0			0
$664$	−10.5137	+	26.3979i	−0.408010	+	1.02444i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	48.6664	+	12.5656i	1.88296	+	0.486178i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0			−	1.00000i	$-0.5\pi$
$673$		0			0				1.00000i	$0.5\pi$
$674$		0			0
$675$	−5.06860	−	25.4815i	−0.195090	−	0.980785i
$676$	−13.2048	−	22.3972i	−0.507877	−	0.861430i
$677$	27.9923	+	41.8935i	1.07583	+	1.61010i	0.745856	+	0.666107i	$0.232041\pi$
$677$	27.9923	+	41.8935i	1.07583	+	1.61010i	0.329976	+	0.943989i	$0.392959\pi$
$678$	23.7092	−	41.5014i	0.910546	−	1.59385i
$679$		0			0
$680$	−47.8569	+	0.654661i	−1.83523	+	0.0251051i
$681$	10.3118	+	24.8948i	0.395148	+	0.953970i
$682$		0			0
$683$	−1.61454	−	0.321151i	−0.0617785	−	0.0122885i	0.164104	−	0.986443i	$-0.447527\pi$
$683$	−1.61454	−	0.321151i	−0.0617785	−	0.0122885i	−0.225883	+	0.974154i	$0.572527\pi$
$684$	50.1852	+	2.82996i	1.91888	+	0.108206i
$685$	−13.8608	+	20.7441i	−0.529594	+	0.792593i
$686$		0			0
$687$	−1.91520	−	1.91520i	−0.0730694	−	0.0730694i
$688$		0			0
$689$		0			0
$690$	48.6282	+	16.2602i	1.85125	+	0.619014i
$691$	12.4721	−	18.6658i	0.474460	−	0.710079i	−0.514627	−	0.857414i	$-0.672070\pi$
$691$	12.4721	−	18.6658i	0.474460	−	0.710079i	0.989087	+	0.147335i	$0.0470696\pi$
$692$	−18.5433	+	38.4828i	−0.704910	+	1.46290i
$693$		0			0
$694$	15.5449	+	20.0684i	0.590078	+	0.761787i
$695$	8.20144	+	19.8000i	0.311098	+	0.751058i
$696$		0			0
$697$		0			0
$698$	−11.2882	−	41.3728i	−0.427267	−	1.56598i
$699$	−28.5841	−	42.7792i	−1.08115	−	1.61806i
$700$		0			0
$701$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$701$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−41.8276			−1.57532
$706$	−37.5944	+	2.63627i	−1.41489	+	0.0992174i
$707$		0			0
$708$		0			0
$709$	−28.7417	+	19.2046i	−1.07942	+	0.721245i	−0.962332	−	0.271877i	$-0.912356\pi$
$709$	−28.7417	+	19.2046i	−1.07942	+	0.721245i	−0.117087	+	0.993122i	$0.537356\pi$
$710$		0			0
$711$	−19.2768	+	46.5384i	−0.722938	+	1.74533i
$712$		0			0
$713$	38.2866	−	15.8588i	1.43384	−	0.593917i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$719$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$720$	−8.16030	+	25.5619i	−0.304117	+	0.952635i
$721$		0			0
$722$	64.7715	−	32.3098i	2.41055	−	1.20244i
$723$	42.3270	+	28.2820i	1.57416	+	1.05182i
$724$	19.3402	+	1.09060i	0.718774	+	0.0405319i
$725$		0			0
$726$	−3.39511	+	26.7296i	−0.126004	+	0.992030i
$727$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$727$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$728$		0			0
$729$	10.3325	−	24.9447i	0.382683	−	0.923880i
$730$		0			0
$731$		0			0
$732$	−1.86623	−	3.16538i	−0.0689777	−	0.116996i
$733$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$733$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$734$		0			0
$735$	27.1109			1.00000
$736$	−35.8151	−	39.0084i	−1.32016	−	1.43787i
$737$		0			0
$738$		0			0
$739$	2.82906	+	14.2226i	0.104069	+	0.523188i	0.997290	+	0.0735712i	$0.0234396\pi$
$739$	2.82906	+	14.2226i	0.104069	+	0.523188i	−0.893221	+	0.449617i	$0.851560\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−36.3108	−	15.0404i	−1.33212	−	0.551780i	−0.400857	−	0.916141i	$-0.631288\pi$
$743$	−36.3108	−	15.0404i	−1.33212	−	0.551780i	−0.931258	+	0.364360i	$0.881288\pi$
$744$	8.57243	+	19.9205i	0.314280	+	0.730322i
$745$		0			0
$746$		0			0
$747$	29.5591	+	5.87967i	1.08151	+	0.215126i
$748$		0			0
$749$		0			0
$750$	24.5064	−	12.2244i	0.894847	−	0.446373i
$751$	−19.8986	−	19.8986i	−0.726109	−	0.726109i	0.243734	−	0.969842i	$-0.421628\pi$
$751$	−19.8986	−	19.8986i	−0.726109	−	0.726109i	−0.969842	+	0.243734i	$0.921628\pi$
$752$	37.7995	+	20.9138i	1.37840	+	0.762648i
$753$		0			0
$754$		0			0
$755$	22.8676	−	34.2237i	0.832236	−	1.24553i
$756$		0			0
$757$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$757$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$758$	33.5191	−	25.9638i	1.21747	−	0.943047i
$759$		0			0
$760$	11.0465	+	51.8196i	0.400698	+	1.87969i
$761$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$761$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	9.90369	+	49.7892i	0.358069	+	1.80013i
$766$	50.2622	−	3.52459i	1.81605	−	0.127348i
$767$		0			0
$768$	20.1554	−	19.0200i	0.727294	−	0.686326i
$769$	11.0219			0.397461			0.198730	−	0.980054i	$-0.436318\pi$
$769$	11.0219			0.397461			0.198730	+	0.980054i	$0.436318\pi$
$770$		0			0
$771$	39.3311	−	7.82344i	1.41647	−	0.281754i
$772$		0			0
$773$	46.0847	−	30.7928i	1.65755	−	1.10754i	0.784094	−	0.620642i	$-0.213128\pi$
$773$	46.0847	−	30.7928i	1.65755	−	1.10754i	0.873458	−	0.486899i	$-0.161872\pi$
$774$		0			0
$775$	8.47028	−	20.4491i	0.304262	−	0.734552i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−95.0163	−	31.7713i	−3.39778	−	1.13614i
$783$		0			0
$784$	−24.5000	−	13.5554i	−0.875000	−	0.484123i
$785$		0			0
$786$		0			0
$787$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$787$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$788$	24.5123	−	21.8953i	0.873214	−	0.779989i
$789$	−7.08032	+	35.5952i	−0.252066	+	1.26722i
$790$	−52.6744	−	6.69052i	−1.87407	−	0.238038i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	3.77062	−	2.51945i	0.133730	−	0.0893556i
$796$	−2.55898	+	9.91090i	−0.0907008	+	0.351283i
$797$	53.3361	−	10.6092i	1.88926	−	0.375797i	0.892148	−	0.451743i	$-0.149198\pi$
$797$	53.3361	−	10.6092i	1.88926	−	0.375797i	0.997112	+	0.0759458i	$0.0241976\pi$
$798$		0			0
$799$	81.7284			2.89134
$800$	−28.2585	−	1.20602i	−0.999091	−	0.0426391i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$809$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$810$	28.2337	+	3.58615i	0.992030	+	0.126004i
$811$	12.4037	+	2.46725i	0.435552	+	0.0866368i	0.407997	−	0.912983i	$-0.366228\pi$
$811$	12.4037	+	2.46725i	0.435552	+	0.0866368i	0.0275560	+	0.999620i	$0.491228\pi$
$812$		0			0
$813$	−30.7928	+	46.0847i	−1.07995	+	1.61626i
$814$		0			0
$815$		0			0
$816$	15.9447	−	49.9462i	0.558176	−	1.74847i
$817$		0			0
$818$	16.3144	+	5.45516i	0.570420	+	0.190735i
$819$		0			0
$820$		0			0
$821$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$821$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$822$	−16.7361	−	21.6063i	−0.583740	−	0.753605i
$823$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$823$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	31.7462	+	47.5115i	1.10392	+	1.65214i	0.646581	+	0.762845i	$0.276198\pi$
$827$	31.7462	+	47.5115i	1.10392	+	1.65214i	0.457341	+	0.889291i	$0.348802\pi$
$828$	−33.7855	+	44.8715i	−1.17413	+	1.55939i
$829$	0.477853	+	2.40233i	0.0165965	+	0.0834364i	0.988196	−	0.153196i	$-0.0489564\pi$
$829$	0.477853	+	2.40233i	0.0165965	+	0.0834364i	−0.971599	+	0.236632i	$0.923956\pi$
$830$	2.22227	+	31.6906i	0.0771362	+	1.10000i
$831$		0			0
$832$		0			0
$833$	−52.9728			−1.83540
$834$	−23.4194	+	1.64226i	−0.810947	+	0.0568669i
$835$	55.1154	−	10.9631i	1.90735	−	0.379395i
$836$		0			0
$837$	19.1257	−	12.7794i	0.661080	−	0.441719i
$838$		0			0
$839$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$839$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$840$		0			0
$841$	26.7925	−	11.0978i	0.923880	−	0.382683i
$842$	−38.0050	+	29.4386i	−1.30974	+	1.01452i
$843$		0			0
$844$	−52.2020	−	25.1540i	−1.79687	−	0.865837i
$845$	−24.1699	−	16.1498i	−0.831470	−	0.555570i
$846$	14.5303	−	43.4549i	0.499563	−	1.49401i
$847$		0			0
$848$	−4.66722	+	0.391505i	−0.160273	+	0.0134443i
$849$		0			0
$850$	−47.8838	+	23.8857i	−1.64240	+	0.819274i
$851$		0			0
$852$		0			0
$853$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$853$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$854$		0			0
$855$	51.9201	−	21.5060i	1.77563	−	0.735490i
$856$	−0.793252	−	57.9881i	−0.0271128	−	1.98199i
$857$	−21.3036	+	51.4315i	−0.727718	+	1.75687i	−0.0776619	+	0.996980i	$0.524745\pi$
$857$	−21.3036	+	51.4315i	−0.727718	+	1.75687i	−0.650056	+	0.759886i	$0.725255\pi$
$858$		0			0
$859$	24.4466	−	16.3347i	0.834107	−	0.557333i	−0.0635745	−	0.997977i	$-0.520250\pi$
$859$	24.4466	−	16.3347i	0.834107	−	0.557333i	0.897682	+	0.440644i	$0.145250\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.0144			−0.545136			−0.272568	−	0.962137i	$-0.587873\pi$
$863$	−16.0144			−0.545136			−0.272568	+	0.962137i	$0.587873\pi$
$864$	−23.7216	−	17.3576i	−0.807024	−	0.590518i
$865$			47.7595i			1.62387i
$866$		0			0
$867$	−13.6067	−	68.4057i	−0.462109	−	2.32318i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	32.7488	+	13.0431i	1.10902	+	0.441696i
$873$		0			0
$874$	−13.9752	+	110.026i	−0.472717	+	3.72169i
$875$		0			0
$876$		0			0
$877$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$877$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$878$	−48.9748	+	24.4299i	−1.65282	+	0.824471i
$879$	41.9164	+	41.9164i	1.41381	+	1.41381i
$880$		0			0
$881$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$881$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$882$	−9.41794	+	28.1656i	−0.317119	+	0.948386i
$883$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$883$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$884$		0			0
$885$		0			0
$886$	−34.7810	+	26.9412i	−1.16849	+	0.905108i
$887$	15.3664	+	37.0977i	0.515952	+	1.24562i	0.940370	+	0.340153i	$0.110479\pi$
$887$	15.3664	+	37.0977i	0.515952	+	1.24562i	−0.424418	+	0.905466i	$0.639521\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−17.6509	−	88.7372i	−0.590666	−	2.96948i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	4.18685	+	29.7064i	0.139562	+	0.990213i
$901$	−7.36754	+	4.92283i	−0.245448	+	0.164003i
$902$		0			0
$903$		0			0
$904$	−30.0316	+	46.3043i	−0.998837	+	1.54006i
$905$	20.0088	−	8.28792i	0.665115	−	0.275500i
$906$	27.6113	+	35.6461i	0.917325	+	1.18426i
$907$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$907$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$908$	−10.2697	−	29.3708i	−0.340811	−	0.974704i
$909$		0			0
$910$		0			0
$911$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$911$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$912$	−57.6730	−	6.52515i	−1.90974	−	0.216069i
$913$		0			0
$914$		0			0
$915$	−3.41592	−	2.28244i	−0.112927	−	0.0754552i
$916$	2.08347	+	2.33248i	0.0688397	+	0.0770674i
$917$		0			0
$918$	−55.1667	−	7.00709i	−1.82077	−	0.231268i
$919$	39.6338	−	16.4168i	1.30740	−	0.541542i	0.383274	−	0.923635i	$-0.374797\pi$
$919$	39.6338	−	16.4168i	1.30740	−	0.541542i	0.924124	+	0.382093i	$0.124797\pi$
$920$	−55.0049	−	21.9072i	−1.81346	−	0.722259i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$	18.3022	+	15.9035i	0.600152	+	0.521498i
$931$	11.4406	+	57.5156i	0.374950	+	1.88500i
$932$	30.1726	+	51.1770i	0.988338	+	1.67636i
$933$		0			0
$934$	−5.71861	+	10.0100i	−0.187119	+	0.327539i
$935$		0			0
$936$		0			0
$937$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$937$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$938$		0			0
$939$		0			0
$940$	48.2218	+	2.71924i	1.57282	+	0.0886920i
$941$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$941$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	34.0302	−	50.9297i	1.10583	−	1.65499i	0.471733	−	0.881741i	$-0.343629\pi$
$947$	34.0302	−	50.9297i	1.10583	−	1.65499i	0.634098	−	0.773252i	$-0.281371\pi$
$948$	25.2492	−	52.3995i	0.820055	−	1.70186i
$949$		0			0
$950$	36.2756	+	46.8316i	1.17694	+	1.51942i
$951$	−2.50849	−	6.05603i	−0.0813433	−	0.196380i
$952$		0			0
$953$	−33.9918	−	14.0799i	−1.10110	−	0.456092i	−0.243238	−	0.969967i	$-0.578210\pi$
$953$	−33.9918	−	14.0799i	−1.10110	−	0.456092i	−0.857865	+	0.513875i	$0.828210\pi$
$954$	1.30761	+	4.79253i	0.0423353	+	0.155164i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	11.0696	−	28.9390i	0.357268	−	0.934002i
$961$	−11.4036			−0.367858
$962$		0			0
$963$	−60.3295	+	12.0003i	−1.94409	+	0.386704i
$964$	−46.9588	−	35.3571i	−1.51244	−	1.13878i
$965$		0			0
$966$		0			0
$967$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$967$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$968$	5.65183	−	30.5950i	0.181657	−	0.983362i
$969$	−101.448	+	42.0213i	−3.25899	+	1.34992i
$970$		0			0
$971$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$971$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$972$	−13.5336	+	28.0863i	−0.434092	+	0.900869i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.94573	+	3.77059i	0.0622813	+	0.120694i
$977$	34.9033	−	34.9033i	1.11666	−	1.11666i	0.124427	−	0.992229i	$-0.460291\pi$
$977$	34.9033	−	34.9033i	1.11666	−	1.11666i	0.992229	−	0.124427i	$-0.0397092\pi$
$978$		0			0
$979$		0			0
$980$	−31.2553	−	1.76250i	−0.998414	−	0.0563009i
$981$	7.29423	−	36.6706i	0.232887	−	1.17080i
$982$		0			0
$983$	−34.7975	+	14.4136i	−1.10987	+	0.459722i	−0.860892	−	0.508788i	$-0.830094\pi$
$983$	−34.7975	+	14.4136i	−1.10987	+	0.459722i	−0.248975	+	0.968510i	$0.580094\pi$
$984$		0			0
$985$	14.0624	−	33.9496i	0.448064	−	1.08172i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$	−8.58784	−	23.5231i	−0.272664	−	0.746858i
$993$			6.52228i			0.206978i
$994$		0			0
$995$	2.23264	+	11.2242i	0.0707794	+	0.355832i
$996$	−33.6955	−	8.70014i	−1.06768	−	0.275675i
$997$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$997$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$998$	39.6399	+	22.6458i	1.25478	+	0.716839i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cp.a.299.2	✓	32
3.2	odd	2	inner	960.2.cp.a.299.3	yes	32
5.4	even	2	inner	960.2.cp.a.299.3	yes	32
15.14	odd	2	CM	960.2.cp.a.299.2	✓	32
64.3	odd	16	inner	960.2.cp.a.899.2	yes	32
192.131	even	16	inner	960.2.cp.a.899.3	yes	32
320.259	odd	16	inner	960.2.cp.a.899.3	yes	32
960.899	even	16	inner	960.2.cp.a.899.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cp.a.299.2	✓	32	1.1	even	1	trivial
960.2.cp.a.299.2	✓	32	15.14	odd	2	CM
960.2.cp.a.299.3	yes	32	3.2	odd	2	inner
960.2.cp.a.299.3	yes	32	5.4	even	2	inner
960.2.cp.a.899.2	yes	32	64.3	odd	16	inner
960.2.cp.a.899.2	yes	32	960.899	even	16	inner
960.2.cp.a.899.3	yes	32	192.131	even	16	inner
960.2.cp.a.899.3	yes	32	320.259	odd	16	inner

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cp (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0989274 - 1.41075i) q^{2} +(1.69877 - 0.337906i) q^{3} +(-1.98043 + 0.279124i) q^{4} +(-1.85922 + 1.24229i) q^{5} +(-0.644756 - 2.36311i) q^{6} +(0.589692 + 2.76627i) q^{8} +(2.77164 - 1.14805i) q^{9} +O(q^{10})\)	\(q+(-0.0989274 - 1.41075i) q^{2} +(1.69877 - 0.337906i) q^{3} +(-1.98043 + 0.279124i) q^{4} +(-1.85922 + 1.24229i) q^{5} +(-0.644756 - 2.36311i) q^{6} +(0.589692 + 2.76627i) q^{8} +(2.77164 - 1.14805i) q^{9} +(1.93649 + 2.50000i) q^{10} +(-3.26997 + 1.14337i) q^{12} +(-2.73861 + 2.73861i) q^{15} +(3.84418 - 1.10557i) q^{16} +(5.35106 - 5.35106i) q^{17} +(-1.89380 - 3.79651i) q^{18} +(-6.96563 - 4.65428i) q^{19} +(3.33530 - 2.97922i) q^{20} +(8.64884 - 3.58247i) q^{23} +(1.93649 + 4.50000i) q^{24} +(1.91342 - 4.61940i) q^{25} +(4.32044 - 2.88683i) q^{27} +(4.13442 + 3.59257i) q^{30} +4.42678 q^{31} +(-1.93997 - 5.31380i) q^{32} +(-8.07838 - 7.01964i) q^{34} +(-5.16858 + 3.04726i) q^{36} +(-5.87694 + 10.2872i) q^{38} +(-4.53289 - 4.41055i) q^{40} +(-3.72688 + 5.57767i) q^{45} +(-5.90957 - 11.8469i) q^{46} +(7.63665 + 7.63665i) q^{47} +(6.15680 - 3.17708i) q^{48} +(-4.94975 - 4.94975i) q^{49} +(-6.70610 - 2.24237i) q^{50} +(7.28207 - 10.8984i) q^{51} +(-1.14840 - 0.228432i) q^{53} +(-4.50000 - 5.80948i) q^{54} +(-13.4057 - 5.55283i) q^{57} +(4.65921 - 6.18803i) q^{60} +(0.206943 + 1.04037i) q^{61} +(-0.437930 - 6.24508i) q^{62} +(-7.30453 + 3.26250i) q^{64} +(-9.10378 + 12.0910i) q^{68} +(13.4819 - 9.00829i) q^{69} +(4.81023 + 6.99011i) q^{72} +(1.68953 - 8.49385i) q^{75} +(15.0940 + 7.27320i) q^{76} +(-11.8730 + 11.8730i) q^{79} +(-5.77375 + 6.83109i) q^{80} +(6.36396 - 6.36396i) q^{81} +(8.35300 + 5.58129i) q^{83} +(-3.30123 + 16.5964i) q^{85} +(8.23738 + 4.70591i) q^{90} +(-16.1285 + 9.50891i) q^{92} +(7.52009 - 1.49584i) q^{93} +(10.0179 - 11.5289i) q^{94} +18.7326 q^{95} +(-5.09114 - 8.37140i) q^{96} +(-6.49319 + 7.47252i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 192 q^{51} - 144 q^{54} + 208 q^{76} - 256 q^{79} + 16 q^{94}+O(q^{100}) \) 32 * q + 192 * q^51 - 144 * q^54 + 208 * q^76 - 256 * q^79 + 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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