LMFDB - Embedded newform 960.2.t.b.719.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(239,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))

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

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

chi := DirichletCharacter("960.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.t (of order $4$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			719.39
Character	$\chi$	$=$	960.719
Dual form			960.2.t.b.239.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71929 + 0.209895i) q^{3} +(0.768175 + 2.09998i) q^{5} +4.08340i q^{7} +(2.91189 + 0.721739i) q^{9} +O(q^{10})$	\(q+(1.71929 + 0.209895i) q^{3} +(0.768175 + 2.09998i) q^{5} +4.08340i q^{7} +(2.91189 + 0.721739i) q^{9} +(-3.73399 - 3.73399i) q^{11} +(0.658169 + 0.658169i) q^{13} +(0.879937 + 3.77170i) q^{15} -2.37750 q^{17} +(3.49873 + 3.49873i) q^{19} +(-0.857084 + 7.02053i) q^{21} +4.63710 q^{23} +(-3.81982 + 3.22630i) q^{25} +(4.85488 + 1.85207i) q^{27} +(-1.57201 - 1.57201i) q^{29} -0.107179i q^{31} +(-5.63606 - 7.20355i) q^{33} +(-8.57504 + 3.13676i) q^{35} +(0.798876 - 0.798876i) q^{37} +(0.993434 + 1.26973i) q^{39} -8.35437 q^{41} +(-0.742112 - 0.742112i) q^{43} +(0.721203 + 6.66932i) q^{45} -1.98407i q^{47} -9.67413 q^{49} +(-4.08761 - 0.499026i) q^{51} +(2.31137 + 2.31137i) q^{53} +(4.97295 - 10.7097i) q^{55} +(5.28095 + 6.74968i) q^{57} +(4.24336 + 4.24336i) q^{59} +(-0.129772 + 0.129772i) q^{61} +(-2.94715 + 11.8904i) q^{63} +(-0.876552 + 1.88773i) q^{65} +(10.8687 - 10.8687i) q^{67} +(7.97250 + 0.973304i) q^{69} -0.137907i q^{71} +7.69107 q^{73} +(-7.24454 + 4.74517i) q^{75} +(15.2474 - 15.2474i) q^{77} +9.66245i q^{79} +(7.95819 + 4.20325i) q^{81} +(-6.95219 - 6.95219i) q^{83} +(-1.82634 - 4.99271i) q^{85} +(-2.37277 - 3.03268i) q^{87} +6.69332 q^{89} +(-2.68757 + 2.68757i) q^{91} +(0.0224962 - 0.184271i) q^{93} +(-4.65962 + 10.0349i) q^{95} -0.584506i q^{97} +(-8.17800 - 13.5679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q - 16 q^{19} + 8 q^{21} + 8 q^{39} - 12 q^{45} - 112 q^{49} - 32 q^{51} + 40 q^{55} + 16 q^{61} - 40 q^{69} + 36 q^{75} + 64 q^{81} - 64 q^{85} - 48 q^{91} + 8 q^{99}+O(q^{100}) $ 80 * q - 16 * q^19 + 8 * q^21 + 8 * q^39 - 12 * q^45 - 112 * q^49 - 32 * q^51 + 40 * q^55 + 16 * q^61 - 40 * q^69 + 36 * q^75 + 64 * q^81 - 64 * q^85 - 48 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	1.71929	+	0.209895i	0.992630	+	0.121183i
$3$	1.71929	+	0.209895i	0.992630	+	0.121183i
$4$		0			0
$5$	0.768175	+	2.09998i	0.343538	+	0.939139i
$5$	0.768175	+	2.09998i	0.343538	+	0.939139i
$6$		0			0
$7$			4.08340i			1.54338i	0.636000	+	0.771689i	$0.280588\pi$
$7$			4.08340i			1.54338i	−0.636000	+	0.771689i	$0.719412\pi$
$8$		0			0
$9$	2.91189	+	0.721739i	0.970629	+	0.240580i
$10$		0			0
$11$	−3.73399	−	3.73399i	−1.12584	−	1.12584i	−0.990846	−	0.134995i	$-0.956898\pi$
$11$	−3.73399	−	3.73399i	−1.12584	−	1.12584i	−0.134995	−	0.990846i	$-0.543102\pi$
$12$		0			0
$13$	0.658169	+	0.658169i	0.182543	+	0.182543i	0.792463	−	0.609920i	$-0.208798\pi$
$13$	0.658169	+	0.658169i	0.182543	+	0.182543i	−0.609920	+	0.792463i	$0.708798\pi$
$14$		0			0
$15$	0.879937	+	3.77170i	0.227199	+	0.973848i
$16$		0			0
$17$	−2.37750			−0.576630			−0.288315	−	0.957536i	$-0.593095\pi$
$17$	−2.37750			−0.576630			−0.288315	+	0.957536i	$0.593095\pi$
$18$		0			0
$19$	3.49873	+	3.49873i	0.802663	+	0.802663i	0.983511	−	0.180848i	$-0.0578842\pi$
$19$	3.49873	+	3.49873i	0.802663	+	0.802663i	−0.180848	+	0.983511i	$0.557884\pi$
$20$		0			0
$21$	−0.857084	+	7.02053i	−0.187031	+	1.53200i
$22$		0			0
$23$	4.63710			0.966902			0.483451	−	0.875371i	$-0.339383\pi$
$23$	4.63710			0.966902			0.483451	+	0.875371i	$0.339383\pi$
$24$		0			0
$25$	−3.81982	+	3.22630i	−0.763963	+	0.645260i
$26$		0			0
$27$	4.85488	+	1.85207i	0.934322	+	0.356430i
$28$		0			0
$29$	−1.57201	−	1.57201i	−0.291914	−	0.291914i	0.545922	−	0.837836i	$-0.316180\pi$
$29$	−1.57201	−	1.57201i	−0.291914	−	0.291914i	−0.837836	+	0.545922i	$0.816180\pi$
$30$		0			0
$31$		−	0.107179i		−	0.0192498i	−0.999954	−	0.00962491i	$-0.996936\pi$
$31$		−	0.107179i		−	0.0192498i	0.999954	−	0.00962491i	$-0.00306375\pi$
$32$		0			0
$33$	−5.63606	−	7.20355i	−0.981111	−	1.25398i
$34$		0			0
$35$	−8.57504	+	3.13676i	−1.44945	+	0.530210i
$36$		0			0
$37$	0.798876	−	0.798876i	0.131334	−	0.131334i	−0.638384	−	0.769718i	$-0.720397\pi$
$37$	0.798876	−	0.798876i	0.131334	−	0.131334i	0.769718	+	0.638384i	$0.220397\pi$
$38$		0			0
$39$	0.993434	+	1.26973i	0.159077	+	0.203319i
$40$		0			0
$41$	−8.35437			−1.30473			−0.652366	−	0.757904i	$-0.726224\pi$
$41$	−8.35437			−1.30473			−0.652366	+	0.757904i	$0.726224\pi$
$42$		0			0
$43$	−0.742112	−	0.742112i	−0.113171	−	0.113171i	0.648254	−	0.761425i	$-0.275500\pi$
$43$	−0.742112	−	0.742112i	−0.113171	−	0.113171i	−0.761425	+	0.648254i	$0.775500\pi$
$44$		0			0
$45$	0.721203	+	6.66932i	0.107511	+	0.994204i
$46$		0			0
$47$		−	1.98407i		−	0.289407i	−0.989475	−	0.144703i	$-0.953777\pi$
$47$		−	1.98407i		−	0.289407i	0.989475	−	0.144703i	$-0.0462228\pi$
$48$		0			0
$49$	−9.67413			−1.38202
$50$		0			0
$51$	−4.08761	−	0.499026i	−0.572380	−	0.0698776i
$52$		0			0
$53$	2.31137	+	2.31137i	0.317491	+	0.317491i	0.847803	−	0.530312i	$-0.177925\pi$
$53$	2.31137	+	2.31137i	0.317491	+	0.317491i	−0.530312	+	0.847803i	$0.677925\pi$
$54$		0			0
$55$	4.97295	−	10.7097i	0.670552	−	1.44409i
$56$		0			0
$57$	5.28095	+	6.74968i	0.699479	+	0.894017i
$58$		0			0
$59$	4.24336	+	4.24336i	0.552438	+	0.552438i	0.927144	−	0.374706i	$-0.122256\pi$
$59$	4.24336	+	4.24336i	0.552438	+	0.552438i	−0.374706	+	0.927144i	$0.622256\pi$
$60$		0			0
$61$	−0.129772	+	0.129772i	−0.0166156	+	0.0166156i	−0.715366	−	0.698750i	$-0.753740\pi$
$61$	−0.129772	+	0.129772i	−0.0166156	+	0.0166156i	0.698750	+	0.715366i	$0.253740\pi$
$62$		0			0
$63$	−2.94715	+	11.8904i	−0.371305	+	1.49805i
$64$		0			0
$65$	−0.876552	+	1.88773i	−0.108723	+	0.234144i
$66$		0			0
$67$	10.8687	−	10.8687i	1.32782	−	1.32782i	0.420553	−	0.907268i	$-0.361836\pi$
$67$	10.8687	−	10.8687i	1.32782	−	1.32782i	0.907268	−	0.420553i	$-0.138164\pi$
$68$		0			0
$69$	7.97250	+	0.973304i	0.959776	+	0.117172i
$70$		0			0
$71$		−	0.137907i		−	0.0163665i	−0.999967	−	0.00818327i	$-0.997395\pi$
$71$		−	0.137907i		−	0.0163665i	0.999967	−	0.00818327i	$-0.00260484\pi$
$72$		0			0
$73$	7.69107			0.900171			0.450086	−	0.892985i	$-0.351393\pi$
$73$	7.69107			0.900171			0.450086	+	0.892985i	$0.351393\pi$
$74$		0			0
$75$	−7.24454	+	4.74517i	−0.836527	+	0.547925i
$76$		0			0
$77$	15.2474	−	15.2474i	1.73760	−	1.73760i
$78$		0			0
$79$			9.66245i			1.08711i	0.839373	+	0.543555i	$0.182922\pi$
$79$			9.66245i			1.08711i	−0.839373	+	0.543555i	$0.817078\pi$
$80$		0			0
$81$	7.95819	+	4.20325i	0.884243	+	0.467027i
$82$		0			0
$83$	−6.95219	−	6.95219i	−0.763101	−	0.763101i	0.213780	−	0.976882i	$-0.431422\pi$
$83$	−6.95219	−	6.95219i	−0.763101	−	0.763101i	−0.976882	+	0.213780i	$0.931422\pi$
$84$		0			0
$85$	−1.82634	−	4.99271i	−0.198094	−	0.541535i
$86$		0			0
$87$	−2.37277	−	3.03268i	−0.254388	−	0.325138i
$88$		0			0
$89$	6.69332			0.709491			0.354745	−	0.934963i	$-0.384568\pi$
$89$	6.69332			0.709491			0.354745	+	0.934963i	$0.384568\pi$
$90$		0			0
$91$	−2.68757	+	2.68757i	−0.281733	+	0.281733i
$92$		0			0
$93$	0.0224962	−	0.184271i	0.00233275	−	0.0191080i
$94$		0			0
$95$	−4.65962	+	10.0349i	−0.478067	+	1.02956i
$96$		0			0
$97$		−	0.584506i		−	0.0593476i	−0.999560	−	0.0296738i	$-0.990553\pi$
$97$		−	0.584506i		−	0.0593476i	0.999560	−	0.0296738i	$-0.00944685\pi$
$98$		0			0
$99$	−8.17800	−	13.5679i	−0.821920	−	1.36363i
$100$		0			0
$101$	5.52152	−	5.52152i	0.549412	−	0.549412i	−0.376859	−	0.926271i	$-0.622996\pi$
$101$	5.52152	−	5.52152i	0.549412	−	0.549412i	0.926271	+	0.376859i	$0.122996\pi$
$102$		0			0
$103$			14.1043i			1.38974i	0.719136	+	0.694869i	$0.244538\pi$
$103$			14.1043i			1.38974i	−0.719136	+	0.694869i	$0.755462\pi$
$104$		0			0
$105$	−15.4013	+	3.59313i	−1.50302	+	0.350654i
$106$		0			0
$107$	10.4095	−	10.4095i	1.00632	−	1.00632i	0.00634270	−	0.999980i	$-0.497981\pi$
$107$	10.4095	−	10.4095i	1.00632	−	1.00632i	0.999980	−	0.00634270i	$-0.00201896\pi$
$108$		0			0
$109$	10.7908	−	10.7908i	1.03357	−	1.03357i	0.0341516	−	0.999417i	$-0.489127\pi$
$109$	10.7908	−	10.7908i	1.03357	−	1.03357i	0.999417	−	0.0341516i	$-0.0108729\pi$
$110$		0			0
$111$	1.54118	−	1.20582i	0.146282	−	0.114451i
$112$		0			0
$113$	−1.84969			−0.174004			−0.0870019	−	0.996208i	$-0.527729\pi$
$113$	−1.84969			−0.174004			−0.0870019	+	0.996208i	$0.527729\pi$
$114$		0			0
$115$	3.56210	+	9.73781i	0.332168	+	0.908055i
$116$		0			0
$117$	1.44149	+	2.39154i	0.133266	+	0.221098i
$118$		0			0
$119$		−	9.70829i		−	0.889958i
$120$		0			0
$121$			16.8854i			1.53504i
$122$		0			0
$123$	−14.3635	−	1.75354i	−1.29512	−	0.158111i
$124$		0			0
$125$	−9.70944	−	5.54317i	−0.868439	−	0.495796i
$126$		0			0
$127$	−6.44438			−0.571846			−0.285923	−	0.958253i	$-0.592300\pi$
$127$	−6.44438			−0.571846			−0.285923	+	0.958253i	$0.592300\pi$
$128$		0			0
$129$	−1.12014	−	1.43167i	−0.0986226	−	0.126051i
$130$		0			0
$131$	4.98942	−	4.98942i	0.435928	−	0.435928i	−0.454711	−	0.890639i	$-0.650257\pi$
$131$	4.98942	−	4.98942i	0.435928	−	0.435928i	0.890639	+	0.454711i	$0.150257\pi$
$132$		0			0
$133$	−14.2867	+	14.2867i	−1.23881	+	1.23881i
$134$		0			0
$135$	−0.159903	+	11.6178i	−0.0137622	+	0.999905i
$136$		0			0
$137$		−	16.1748i		−	1.38191i	−0.722898	−	0.690955i	$-0.757190\pi$
$137$		−	16.1748i		−	1.38191i	0.722898	−	0.690955i	$-0.242810\pi$
$138$		0			0
$139$	12.8546	−	12.8546i	1.09031	−	1.09031i	0.0948192	−	0.995495i	$-0.469773\pi$
$139$	12.8546	−	12.8546i	1.09031	−	1.09031i	0.995495	−	0.0948192i	$-0.0302273\pi$
$140$		0			0
$141$	0.416447	−	3.41119i	0.0350712	−	0.287274i
$142$		0			0
$143$		−	4.91520i		−	0.411030i
$144$		0			0
$145$	2.09360	−	4.50875i	0.173864	−	0.374432i
$146$		0			0
$147$	−16.6326	−	2.03055i	−1.37183	−	0.167477i
$148$		0			0
$149$	−5.90204	+	5.90204i	−0.483514	+	0.483514i	−0.906252	−	0.422738i	$-0.861069\pi$
$149$	−5.90204	+	5.90204i	−0.483514	+	0.483514i	0.422738	+	0.906252i	$0.361069\pi$
$150$		0			0
$151$	−20.1902			−1.64305			−0.821527	−	0.570169i	$-0.806878\pi$
$151$	−20.1902			−1.64305			−0.821527	+	0.570169i	$0.806878\pi$
$152$		0			0
$153$	−6.92303	−	1.71594i	−0.559694	−	0.138725i
$154$		0			0
$155$	0.225073	−	0.0823318i	0.0180783	−	0.00661305i
$156$		0			0
$157$	14.2660	+	14.2660i	1.13855	+	1.13855i	0.988710	+	0.149843i	$0.0478767\pi$
$157$	14.2660	+	14.2660i	1.13855	+	1.13855i	0.149843	+	0.988710i	$0.452123\pi$
$158$		0			0
$159$	3.48876	+	4.45905i	0.276677	+	0.353626i
$160$		0			0
$161$			18.9351i			1.49230i
$162$		0			0
$163$	5.06752	−	5.06752i	0.396919	−	0.396919i	−0.480226	−	0.877145i	$-0.659445\pi$
$163$	5.06752	−	5.06752i	0.396919	−	0.396919i	0.877145	+	0.480226i	$0.159445\pi$
$164$		0			0
$165$	10.7978	−	17.3692i	0.840609	−	1.35219i
$166$		0			0
$167$	8.86797			0.686224			0.343112	−	0.939295i	$-0.388519\pi$
$167$	8.86797			0.686224			0.343112	+	0.939295i	$0.388519\pi$
$168$		0			0
$169$		−	12.1336i		−	0.933356i
$170$		0			0
$171$	7.66273	+	12.7131i	0.585984	+	0.972193i
$172$		0			0
$173$	−2.26621	+	2.26621i	−0.172297	+	0.172297i	−0.787988	−	0.615691i	$-0.788877\pi$
$173$	−2.26621	+	2.26621i	−0.172297	+	0.172297i	0.615691	+	0.787988i	$0.288877\pi$
$174$		0			0
$175$	−13.1743	−	15.5978i	−0.995881	−	1.17908i
$176$		0			0
$177$	6.40488	+	8.18620i	0.481420	+	0.615312i
$178$		0			0
$179$	−1.87635	+	1.87635i	−0.140245	+	0.140245i	−0.773744	−	0.633499i	$-0.781618\pi$
$179$	−1.87635	+	1.87635i	−0.140245	+	0.140245i	0.633499	+	0.773744i	$0.281618\pi$
$180$		0			0
$181$	−1.67944	−	1.67944i	−0.124832	−	0.124832i	0.641931	−	0.766763i	$-0.278134\pi$
$181$	−1.67944	−	1.67944i	−0.124832	−	0.124832i	−0.766763	+	0.641931i	$0.778134\pi$
$182$		0			0
$183$	−0.250354	+	0.195877i	−0.0185067	+	0.0144797i
$184$		0			0
$185$	2.29130	+	1.06395i	0.168460	+	0.0782229i
$186$		0			0
$187$	8.87759	+	8.87759i	0.649193	+	0.649193i
$188$		0			0
$189$	−7.56272	+	19.8244i	−0.550107	+	1.44201i
$190$		0			0
$191$	14.8761			1.07640			0.538200	−	0.842817i	$-0.319105\pi$
$191$	14.8761			1.07640			0.538200	+	0.842817i	$0.319105\pi$
$192$		0			0
$193$		−	5.60930i		−	0.403766i	−0.979410	−	0.201883i	$-0.935294\pi$
$193$		−	5.60930i		−	0.403766i	0.979410	−	0.201883i	$-0.0647061\pi$
$194$		0			0
$195$	−1.90327	+	3.06156i	−0.136296	+	0.219243i
$196$		0			0
$197$	−9.31889	−	9.31889i	−0.663944	−	0.663944i	0.292364	−	0.956307i	$-0.405558\pi$
$197$	−9.31889	−	9.31889i	−0.663944	−	0.663944i	−0.956307	+	0.292364i	$0.905558\pi$
$198$		0			0
$199$	−9.51884			−0.674773			−0.337386	−	0.941366i	$-0.609543\pi$
$199$	−9.51884			−0.674773			−0.337386	+	0.941366i	$0.609543\pi$
$200$		0			0
$201$	20.9677	−	16.4051i	1.47894	−	1.15713i
$202$		0			0
$203$	6.41912	−	6.41912i	0.450534	−	0.450534i
$204$		0			0
$205$	−6.41761	−	17.5440i	−0.448225	−	1.22532i
$206$		0			0
$207$	13.5027	+	3.34678i	0.938504	+	0.232617i
$208$		0			0
$209$		−	26.1284i		−	1.80734i
$210$		0			0
$211$	−6.17042	−	6.17042i	−0.424789	−	0.424789i	0.462060	−	0.886849i	$-0.347111\pi$
$211$	−6.17042	−	6.17042i	−0.424789	−	0.424789i	−0.886849	+	0.462060i	$0.847111\pi$
$212$		0			0
$213$	0.0289460	−	0.237101i	0.00198334	−	0.0162459i
$214$		0			0
$215$	0.988347	−	2.12849i	0.0674047	−	0.145162i
$216$		0			0
$217$	0.437652			0.0297098
$218$		0			0
$219$	13.2231	+	1.61432i	0.893537	+	0.109085i
$220$		0			0
$221$	−1.56480	−	1.56480i	−0.105260	−	0.105260i
$222$		0			0
$223$	−2.88059			−0.192898			−0.0964492	−	0.995338i	$-0.530749\pi$
$223$	−2.88059			−0.192898			−0.0964492	+	0.995338i	$0.530749\pi$
$224$		0			0
$225$	−13.4514	+	6.63772i	−0.896761	+	0.442514i
$226$		0			0
$227$	1.95092	+	1.95092i	0.129487	+	0.129487i	0.768880	−	0.639393i	$-0.220814\pi$
$227$	1.95092	+	1.95092i	0.129487	+	0.129487i	−0.639393	+	0.768880i	$0.720814\pi$
$228$		0			0
$229$	0.0765008	+	0.0765008i	0.00505532	+	0.00505532i	0.709630	−	0.704575i	$-0.248862\pi$
$229$	0.0765008	+	0.0765008i	0.00505532	+	0.00505532i	−0.704575	+	0.709630i	$0.748862\pi$
$230$		0			0
$231$	29.4149	−	23.0143i	1.93536	−	1.51423i
$232$		0			0
$233$			12.3612i			0.809808i	0.914359	+	0.404904i	$0.132695\pi$
$233$			12.3612i			0.809808i	−0.914359	+	0.404904i	$0.867305\pi$
$234$		0			0
$235$	4.16651	−	1.52411i	0.271793	−	0.0994223i
$236$		0			0
$237$	−2.02810	+	16.6125i	−0.131739	+	1.07910i
$238$		0			0
$239$	−19.0058			−1.22938			−0.614692	−	0.788767i	$-0.710720\pi$
$239$	−19.0058			−1.22938			−0.614692	+	0.788767i	$0.710720\pi$
$240$		0			0
$241$	−11.4896			−0.740108			−0.370054	−	0.929010i	$-0.620661\pi$
$241$	−11.4896			−0.740108			−0.370054	+	0.929010i	$0.620661\pi$
$242$		0			0
$243$	12.8002	+	8.89696i	0.821130	+	0.570740i
$244$		0			0
$245$	−7.43142	−	20.3155i	−0.474776	−	1.29791i
$246$		0			0
$247$			4.60551i			0.293041i
$248$		0			0
$249$	−10.4936	−	13.4120i	−0.665003	−	0.849952i
$250$		0			0
$251$	−14.1571	−	14.1571i	−0.893589	−	0.893589i	0.101270	−	0.994859i	$-0.467709\pi$
$251$	−14.1571	−	14.1571i	−0.893589	−	0.893589i	−0.994859	+	0.101270i	$0.967709\pi$
$252$		0			0
$253$	−17.3149	−	17.3149i	−1.08858	−	1.08858i
$254$		0			0
$255$	−2.09205	−	8.96723i	−0.131010	−	0.561550i
$256$		0			0
$257$	1.89934			0.118478			0.0592388	−	0.998244i	$-0.481133\pi$
$257$	1.89934			0.118478			0.0592388	+	0.998244i	$0.481133\pi$
$258$		0			0
$259$	3.26213	+	3.26213i	0.202699	+	0.202699i
$260$		0			0
$261$	−3.44293	−	5.71208i	−0.213112	−	0.353569i
$262$		0			0
$263$	−14.3225			−0.883164			−0.441582	−	0.897221i	$-0.645583\pi$
$263$	−14.3225			−0.883164			−0.441582	+	0.897221i	$0.645583\pi$
$264$		0			0
$265$	−3.07829	+	6.62936i	−0.189098	+	0.407239i
$266$		0			0
$267$	11.5077	+	1.40489i	0.704262	+	0.0859782i
$268$		0			0
$269$	8.45418	+	8.45418i	0.515460	+	0.515460i	0.916194	−	0.400734i	$-0.131245\pi$
$269$	8.45418	+	8.45418i	0.515460	+	0.515460i	−0.400734	+	0.916194i	$0.631245\pi$
$270$		0			0
$271$		−	27.3338i		−	1.66041i	−0.557457	−	0.830206i	$-0.688223\pi$
$271$		−	27.3338i		−	1.66041i	0.557457	−	0.830206i	$-0.311777\pi$
$272$		0			0
$273$	−5.18480	+	4.05659i	−0.313798	+	0.245516i
$274$		0			0
$275$	26.3101	+	2.21618i	1.58656	+	0.133641i
$276$		0			0
$277$	9.07408	−	9.07408i	0.545209	−	0.545209i	−0.379843	−	0.925051i	$-0.624022\pi$
$277$	9.07408	−	9.07408i	0.545209	−	0.545209i	0.925051	+	0.379843i	$0.124022\pi$
$278$		0			0
$279$	0.0773549	−	0.312092i	0.00463112	−	0.0186845i
$280$		0			0
$281$	−5.07486			−0.302741			−0.151370	−	0.988477i	$-0.548369\pi$
$281$	−5.07486			−0.302741			−0.151370	+	0.988477i	$0.548369\pi$
$282$		0			0
$283$	−16.1709	−	16.1709i	−0.961262	−	0.961262i	0.0380152	−	0.999277i	$-0.487896\pi$
$283$	−16.1709	−	16.1709i	−0.961262	−	0.961262i	−0.999277	+	0.0380152i	$0.987896\pi$
$284$		0			0
$285$	−10.1175	+	16.2748i	−0.599308	+	0.964036i
$286$		0			0
$287$		−	34.1142i		−	2.01370i
$288$		0			0
$289$	−11.3475			−0.667498
$290$		0			0
$291$	0.122685	−	1.00493i	0.00719191	−	0.0589102i
$292$		0			0
$293$	11.3911	+	11.3911i	0.665473	+	0.665473i	0.956665	−	0.291192i	$-0.0940518\pi$
$293$	11.3911	+	11.3911i	0.665473	+	0.665473i	−0.291192	+	0.956665i	$0.594052\pi$
$294$		0			0
$295$	−5.65131	+	12.1706i	−0.329032	+	0.708599i
$296$		0			0
$297$	−11.2125	−	25.0437i	−0.650614	−	1.45318i
$298$		0			0
$299$	3.05200	+	3.05200i	0.176502	+	0.176502i
$300$		0			0
$301$	3.03034	−	3.03034i	0.174666	−	0.174666i
$302$		0			0
$303$	10.6520	−	8.33414i	0.611942	−	0.478784i
$304$		0			0
$305$	−0.372207	−	0.172831i	−0.0213125	−	0.00989628i
$306$		0			0
$307$	−17.3451	+	17.3451i	−0.989935	+	0.989935i	−0.999950	−	0.0100151i	$-0.996812\pi$
$307$	−17.3451	+	17.3451i	−0.989935	+	0.989935i	0.0100151	+	0.999950i	$0.496812\pi$
$308$		0			0
$309$	−2.96042	+	24.2493i	−0.168413	+	1.37950i
$310$		0			0
$311$			24.7223i			1.40188i	0.713223	+	0.700938i	$0.247235\pi$
$311$			24.7223i			1.40188i	−0.713223	+	0.700938i	$0.752765\pi$
$312$		0			0
$313$	10.4396			0.590079			0.295039	−	0.955485i	$-0.404667\pi$
$313$	10.4396			0.590079			0.295039	+	0.955485i	$0.404667\pi$
$314$		0			0
$315$	−27.2335	+	2.94496i	−1.53443	+	0.165930i
$316$		0			0
$317$	2.57617	−	2.57617i	0.144692	−	0.144692i	−0.631050	−	0.775742i	$-0.717376\pi$
$317$	2.57617	−	2.57617i	0.144692	−	0.144692i	0.775742	+	0.631050i	$0.217376\pi$
$318$		0			0
$319$			11.7397i			0.657298i
$320$		0			0
$321$	20.0818	−	15.7120i	1.12086	−	0.876957i
$322$		0			0
$323$	−8.31824	−	8.31824i	−0.462839	−	0.462839i
$324$		0			0
$325$	−4.63754	−	0.390634i	−0.257244	−	0.0216685i
$326$		0			0
$327$	20.8173	−	16.2875i	1.15120	−	0.900700i
$328$		0			0
$329$	8.10176			0.446664
$330$		0			0
$331$	−12.3750	+	12.3750i	−0.680193	+	0.680193i	−0.960044	−	0.279850i	$-0.909715\pi$
$331$	−12.3750	+	12.3750i	−0.680193	+	0.680193i	0.279850	+	0.960044i	$0.409715\pi$
$332$		0			0
$333$	2.90282	−	1.74966i	0.159073	−	0.0958807i
$334$		0			0
$335$	31.1730	+	14.4749i	1.70317	+	0.790851i
$336$		0			0
$337$			9.83951i			0.535992i	0.963420	+	0.267996i	$0.0863614\pi$
$337$			9.83951i			0.535992i	−0.963420	+	0.267996i	$0.913639\pi$
$338$		0			0
$339$	−3.18014	−	0.388240i	−0.172721	−	0.0210863i
$340$		0			0
$341$	−0.400204	+	0.400204i	−0.0216723	+	0.0216723i
$342$		0			0
$343$		−	10.9195i		−	0.589599i
$344$		0			0
$345$	4.08036	+	17.4897i	0.219679	+	0.941616i
$346$		0			0
$347$	−9.16621	+	9.16621i	−0.492068	+	0.492068i	−0.908957	−	0.416889i	$-0.863120\pi$
$347$	−9.16621	+	9.16621i	−0.492068	+	0.492068i	0.416889	+	0.908957i	$0.363120\pi$
$348$		0			0
$349$	13.3149	−	13.3149i	0.712732	−	0.712732i	−0.254374	−	0.967106i	$-0.581869\pi$
$349$	13.3149	−	13.3149i	0.712732	−	0.712732i	0.967106	+	0.254374i	$0.0818694\pi$
$350$		0			0
$351$	1.97636	+	4.41430i	0.105490	+	0.235618i
$352$		0			0
$353$	23.3939			1.24513			0.622566	−	0.782567i	$-0.286090\pi$
$353$	23.3939			1.24513			0.622566	+	0.782567i	$0.286090\pi$
$354$		0			0
$355$	0.289601	−	0.105937i	0.0153704	−	0.00562253i
$356$		0			0
$357$	2.03772	−	16.6913i	0.107848	−	0.883399i
$358$		0			0
$359$			10.2744i			0.542262i	0.962542	+	0.271131i	$0.0873977\pi$
$359$			10.2744i			0.542262i	−0.962542	+	0.271131i	$0.912602\pi$
$360$		0			0
$361$			5.48218i			0.288536i
$362$		0			0
$363$	−3.54416	+	29.0309i	−0.186020	+	1.52372i
$364$		0			0
$365$	5.90808	+	16.1511i	0.309243	+	0.845386i
$366$		0			0
$367$	33.8052			1.76462			0.882309	−	0.470670i	$-0.155988\pi$
$367$	33.8052			1.76462			0.882309	+	0.470670i	$0.155988\pi$
$368$		0			0
$369$	−24.3270	−	6.02967i	−1.26641	−	0.313892i
$370$		0			0
$371$	−9.43824	+	9.43824i	−0.490009	+	0.490009i
$372$		0			0
$373$	12.8667	−	12.8667i	0.666212	−	0.666212i	−0.290625	−	0.956837i	$-0.593863\pi$
$373$	12.8667	−	12.8667i	0.666212	−	0.666212i	0.956837	+	0.290625i	$0.0938631\pi$
$374$		0			0
$375$	−15.5298	−	11.5683i	−0.801957	−	0.597382i
$376$		0			0
$377$		−	2.06929i		−	0.106574i
$378$		0			0
$379$	6.45281	−	6.45281i	0.331459	−	0.331459i	−0.521681	−	0.853140i	$-0.674695\pi$
$379$	6.45281	−	6.45281i	0.331459	−	0.331459i	0.853140	+	0.521681i	$0.174695\pi$
$380$		0			0
$381$	−11.0797	−	1.35264i	−0.567632	−	0.0692980i
$382$		0			0
$383$		−	8.29165i		−	0.423683i	−0.977304	−	0.211842i	$-0.932054\pi$
$383$		−	8.29165i		−	0.423683i	0.977304	−	0.211842i	$-0.0679461\pi$
$384$		0			0
$385$	43.7318	+	20.3065i	2.22878	+	1.03492i
$386$		0			0
$387$	−1.62534	−	2.69656i	−0.0826205	−	0.137074i
$388$		0			0
$389$	−23.7779	+	23.7779i	−1.20559	+	1.20559i	−0.233143	+	0.972443i	$0.574901\pi$
$389$	−23.7779	+	23.7779i	−1.20559	+	1.20559i	−0.972443	+	0.233143i	$0.925099\pi$
$390$		0			0
$391$	−11.0247			−0.557544
$392$		0			0
$393$	9.62550	−	7.53099i	0.485542	−	0.379888i
$394$		0			0
$395$	−20.2909	+	7.42245i	−1.02095	+	0.373464i
$396$		0			0
$397$	−19.3636	−	19.3636i	−0.971831	−	0.971831i	0.0277826	−	0.999614i	$-0.491155\pi$
$397$	−19.3636	−	19.3636i	−0.971831	−	0.971831i	−0.999614	+	0.0277826i	$0.991155\pi$
$398$		0			0
$399$	−27.5616	+	21.5642i	−1.37981	+	1.07956i
$400$		0			0
$401$		−	26.8842i		−	1.34253i	−0.741216	−	0.671266i	$-0.765751\pi$
$401$		−	26.8842i		−	1.34253i	0.741216	−	0.671266i	$-0.234249\pi$
$402$		0			0
$403$	0.0705416	−	0.0705416i	0.00351393	−	0.00351393i
$404$		0			0
$405$	−2.71345	+	19.9408i	−0.134832	+	0.990868i
$406$		0			0
$407$	−5.96600			−0.295724
$408$		0			0
$409$			28.3692i			1.40276i	0.712785	+	0.701382i	$0.247433\pi$
$409$			28.3692i			1.40276i	−0.712785	+	0.701382i	$0.752567\pi$
$410$		0			0
$411$	3.39502	−	27.8092i	0.167464	−	1.37173i
$412$		0			0
$413$	−17.3273	+	17.3273i	−0.852621	+	0.852621i
$414$		0			0
$415$	9.25894	−	19.9399i	0.454504	−	0.978813i
$416$		0			0
$417$	24.7989	−	19.4026i	1.21441	−	0.950151i
$418$		0			0
$419$	9.93798	−	9.93798i	0.485502	−	0.485502i	−0.421381	−	0.906884i	$-0.638455\pi$
$419$	9.93798	−	9.93798i	0.485502	−	0.485502i	0.906884	+	0.421381i	$0.138455\pi$
$420$		0			0
$421$	−26.3543	−	26.3543i	−1.28443	−	1.28443i	−0.938121	−	0.346307i	$-0.887436\pi$
$421$	−26.3543	−	26.3543i	−1.28443	−	1.28443i	−0.346307	−	0.938121i	$-0.612564\pi$
$422$		0			0
$423$	1.43198	−	5.77740i	0.0696254	−	0.280907i
$424$		0			0
$425$	9.08163	−	7.67054i	0.440524	−	0.372076i
$426$		0			0
$427$	−0.529912	−	0.529912i	−0.0256442	−	0.0256442i
$428$		0			0
$429$	1.03168	−	8.45063i	0.0498097	−	0.408000i
$430$		0			0
$431$	−13.9667			−0.672753			−0.336377	−	0.941728i	$-0.609202\pi$
$431$	−13.9667			−0.672753			−0.336377	+	0.941728i	$0.609202\pi$
$432$		0			0
$433$			23.5387i			1.13120i	0.824680	+	0.565599i	$0.191355\pi$
$433$			23.5387i			1.13120i	−0.824680	+	0.565599i	$0.808645\pi$
$434$		0			0
$435$	4.54587	−	7.31240i	0.217958	−	0.350603i
$436$		0			0
$437$	16.2239	+	16.2239i	0.776097	+	0.776097i
$438$		0			0
$439$	−17.9084			−0.854721			−0.427361	−	0.904081i	$-0.640556\pi$
$439$	−17.9084			−0.854721			−0.427361	+	0.904081i	$0.640556\pi$
$440$		0			0
$441$	−28.1700	−	6.98219i	−1.34143	−	0.332485i
$442$		0			0
$443$	−8.23902	+	8.23902i	−0.391448	+	0.391448i	−0.875203	−	0.483755i	$-0.839272\pi$
$443$	−8.23902	+	8.23902i	−0.391448	+	0.391448i	0.483755	+	0.875203i	$0.339272\pi$
$444$		0			0
$445$	5.14164	+	14.0558i	0.243737	+	0.666310i
$446$		0			0
$447$	−11.3861	+	8.90848i	−0.538544	+	0.421357i
$448$		0			0
$449$			11.2483i			0.530842i	0.964133	+	0.265421i	$0.0855110\pi$
$449$			11.2483i			0.530842i	−0.964133	+	0.265421i	$0.914489\pi$
$450$		0			0
$451$	31.1951	+	31.1951i	1.46892	+	1.46892i
$452$		0			0
$453$	−34.7127	−	4.23782i	−1.63095	−	0.199110i
$454$		0			0
$455$	−7.70835	−	3.57931i	−0.361373	−	0.167801i
$456$		0			0
$457$	27.3670			1.28017			0.640087	−	0.768302i	$-0.278898\pi$
$457$	27.3670			1.28017			0.640087	+	0.768302i	$0.278898\pi$
$458$		0			0
$459$	−11.5425	−	4.40329i	−0.538758	−	0.205528i
$460$		0			0
$461$	9.47250	+	9.47250i	0.441178	+	0.441178i	0.892408	−	0.451230i	$-0.149014\pi$
$461$	9.47250	+	9.47250i	0.441178	+	0.441178i	−0.451230	+	0.892408i	$0.649014\pi$
$462$		0			0
$463$	−2.00138			−0.0930119			−0.0465059	−	0.998918i	$-0.514809\pi$
$463$	−2.00138			−0.0930119			−0.0465059	+	0.998918i	$0.514809\pi$
$464$		0			0
$465$	0.404245	−	0.0943104i	0.0187464	−	0.00437354i
$466$		0			0
$467$	20.3367	+	20.3367i	0.941071	+	0.941071i	0.998358	−	0.0572864i	$-0.0182448\pi$
$467$	20.3367	+	20.3367i	0.941071	+	0.941071i	−0.0572864	+	0.998358i	$0.518245\pi$
$468$		0			0
$469$	44.3811	+	44.3811i	2.04933	+	2.04933i
$470$		0			0
$471$	21.5330	+	27.5217i	0.992189	+	1.26813i
$472$		0			0
$473$			5.54208i			0.254825i
$474$		0			0
$475$	−24.6524	−	2.07655i	−1.13113	−	0.0952786i
$476$		0			0
$477$	5.06225	+	8.39866i	0.231784	+	0.384548i
$478$		0			0
$479$	−31.7808			−1.45210			−0.726051	−	0.687641i	$-0.758646\pi$
$479$	−31.7808			−1.45210			−0.726051	+	0.687641i	$0.758646\pi$
$480$		0			0
$481$	1.05159			0.0479484
$482$		0			0
$483$	−3.97439	+	32.5549i	−0.180841	+	1.48130i
$484$		0			0
$485$	1.22745	−	0.449003i	0.0557356	−	0.0203882i
$486$		0			0
$487$		−	2.12487i		−	0.0962873i	−0.998840	−	0.0481436i	$-0.984669\pi$
$487$		−	2.12487i		−	0.0962873i	0.998840	−	0.0481436i	$-0.0153305\pi$
$488$		0			0
$489$	9.77616	−	7.64886i	0.442093	−	0.345894i
$490$		0			0
$491$	16.3251	+	16.3251i	0.736742	+	0.736742i	0.971946	−	0.235204i	$-0.0755758\pi$
$491$	16.3251	+	16.3251i	0.736742	+	0.736742i	−0.235204	+	0.971946i	$0.575576\pi$
$492$		0			0
$493$	3.73745	+	3.73745i	0.168326	+	0.168326i
$494$		0			0
$495$	22.2102	−	27.5962i	0.998276	−	1.24036i
$496$		0			0
$497$	0.563129			0.0252598
$498$		0			0
$499$	3.87438	+	3.87438i	0.173441	+	0.173441i	0.788489	−	0.615048i	$-0.210864\pi$
$499$	3.87438	+	3.87438i	0.173441	+	0.173441i	−0.615048	+	0.788489i	$0.710864\pi$
$500$		0			0
$501$	15.2466	+	1.86134i	0.681167	+	0.0831586i
$502$		0			0
$503$	−5.30301			−0.236450			−0.118225	−	0.992987i	$-0.537720\pi$
$503$	−5.30301			−0.236450			−0.118225	+	0.992987i	$0.537720\pi$
$504$		0			0
$505$	15.8366	+	7.35358i	0.704718	+	0.327230i
$506$		0			0
$507$	2.54679	−	20.8612i	0.113107	−	0.926477i
$508$		0			0
$509$	−14.4372	−	14.4372i	−0.639917	−	0.639917i	0.310618	−	0.950535i	$-0.399464\pi$
$509$	−14.4372	−	14.4372i	−0.639917	−	0.639917i	−0.950535	+	0.310618i	$0.899464\pi$
$510$		0			0
$511$			31.4057i			1.38931i
$512$		0			0
$513$	10.5060	+	23.4658i	0.463852	+	1.03604i
$514$		0			0
$515$	−29.6187	+	10.8346i	−1.30516	+	0.477428i
$516$		0			0
$517$	−7.40852	+	7.40852i	−0.325826	+	0.325826i
$518$		0			0
$519$	−4.37193	+	3.42060i	−0.191906	+	0.150148i
$520$		0			0
$521$	−0.00929696			−0.000407307			−0.000203654	−	1.00000i	$-0.500065\pi$
$521$	−0.00929696			−0.000407307			−0.000203654		1.00000i	$0.500065\pi$
$522$		0			0
$523$	4.31180	+	4.31180i	0.188542	+	0.188542i	0.795066	−	0.606524i	$-0.207436\pi$
$523$	4.31180	+	4.31180i	0.188542	+	0.188542i	−0.606524	+	0.795066i	$0.707436\pi$
$524$		0			0
$525$	−19.3764	−	29.5823i	−0.845656	−	1.29108i
$526$		0			0
$527$			0.254817i			0.0111000i
$528$		0			0
$529$	−1.49730			−0.0650999
$530$		0			0
$531$	9.29358	+	15.4188i	0.403307	+	0.669118i
$532$		0			0
$533$	−5.49859	−	5.49859i	−0.238170	−	0.238170i
$534$		0			0
$535$	29.8560	+	13.8634i	1.29079	+	0.599366i
$536$		0			0
$537$	−3.61983	+	2.83215i	−0.156207	+	0.122216i
$538$		0			0
$539$	36.1231	+	36.1231i	1.55593	+	1.55593i
$540$		0			0
$541$	−32.8523	+	32.8523i	−1.41243	+	1.41243i	−0.670730	+	0.741701i	$0.734019\pi$
$541$	−32.8523	+	32.8523i	−1.41243	+	1.41243i	−0.741701	+	0.670730i	$0.765981\pi$
$542$		0			0
$543$	−2.53494	−	3.23995i	−0.108785	−	0.139040i
$544$		0			0
$545$	30.9496	+	14.3712i	1.32573	+	0.615594i
$546$		0			0
$547$	3.27241	−	3.27241i	0.139918	−	0.139918i	−0.633678	−	0.773597i	$-0.718456\pi$
$547$	3.27241	−	3.27241i	0.139918	−	0.139918i	0.773597	+	0.633678i	$0.218456\pi$
$548$		0			0
$549$	−0.471544	+	0.284221i	−0.0201250	+	0.0121302i
$550$		0			0
$551$		−	11.0000i		−	0.468617i
$552$		0			0
$553$	−39.4556			−1.67782
$554$		0			0
$555$	3.71608	+	2.31016i	0.157739	+	0.0980608i
$556$		0			0
$557$	−9.94610	+	9.94610i	−0.421430	+	0.421430i	−0.885696	−	0.464266i	$-0.846318\pi$
$557$	−9.94610	+	9.94610i	−0.421430	+	0.421430i	0.464266	+	0.885696i	$0.346318\pi$
$558$		0			0
$559$		−	0.976870i		−	0.0413172i
$560$		0			0
$561$	13.3997	+	17.1265i	0.565738	+	0.723080i
$562$		0			0
$563$	19.4453	+	19.4453i	0.819523	+	0.819523i	0.986039	−	0.166516i	$-0.0532516\pi$
$563$	19.4453	+	19.4453i	0.819523	+	0.819523i	−0.166516	+	0.986039i	$0.553252\pi$
$564$		0			0
$565$	−1.42088	−	3.88430i	−0.0597770	−	0.163414i
$566$		0			0
$567$	−17.1635	+	32.4964i	−0.720800	+	1.36472i
$568$		0			0
$569$	−29.5741			−1.23981			−0.619905	−	0.784677i	$-0.712829\pi$
$569$	−29.5741			−1.23981			−0.619905	+	0.784677i	$0.712829\pi$
$570$		0			0
$571$	−16.7406	+	16.7406i	−0.700572	+	0.700572i	−0.964533	−	0.263961i	$-0.914971\pi$
$571$	−16.7406	+	16.7406i	−0.700572	+	0.700572i	0.263961	+	0.964533i	$0.414971\pi$
$572$		0			0
$573$	25.5763	+	3.12243i	1.06847	+	0.130441i
$574$		0			0
$575$	−17.7129	+	14.9607i	−0.738678	+	0.623903i
$576$		0			0
$577$			17.2485i			0.718063i	0.933325	+	0.359032i	$0.116893\pi$
$577$			17.2485i			0.718063i	−0.933325	+	0.359032i	$0.883107\pi$
$578$		0			0
$579$	1.17736	−	9.64398i	0.0489295	−	0.400790i
$580$		0			0
$581$	28.3885	−	28.3885i	1.17775	−	1.17775i
$582$		0			0
$583$		−	17.2613i		−	0.714889i
$584$		0			0
$585$	−3.91487	+	4.86422i	−0.161860	+	0.201111i
$586$		0			0
$587$	−15.6372	+	15.6372i	−0.645415	+	0.645415i	−0.951881	−	0.306466i	$-0.900853\pi$
$587$	−15.6372	+	15.6372i	−0.645415	+	0.645415i	0.306466	+	0.951881i	$0.400853\pi$
$588$		0			0
$589$	0.374988	−	0.374988i	0.0154511	−	0.0154511i
$590$		0			0
$591$	−14.0659	−	17.9778i	−0.578592	−	0.739509i
$592$		0			0
$593$	−15.1360			−0.621561			−0.310781	−	0.950482i	$-0.600590\pi$
$593$	−15.1360			−0.621561			−0.310781	+	0.950482i	$0.600590\pi$
$594$		0			0
$595$	20.3872	−	7.45767i	0.835794	−	0.305734i
$596$		0			0
$597$	−16.3656	−	1.99796i	−0.669800	−	0.0817709i
$598$		0			0
$599$		−	42.4714i		−	1.73533i	−0.497145	−	0.867667i	$-0.665618\pi$
$599$		−	42.4714i		−	1.73533i	0.497145	−	0.867667i	$-0.334382\pi$
$600$		0			0
$601$			7.07055i			0.288414i	0.989548	+	0.144207i	$0.0460631\pi$
$601$			7.07055i			0.288414i	−0.989548	+	0.144207i	$0.953937\pi$
$602$		0			0
$603$	39.4927	−	23.8040i	1.60827	−	0.969376i
$604$		0			0
$605$	−35.4590	+	12.9709i	−1.44161	+	0.527344i
$606$		0			0
$607$	−2.22367			−0.0902561			−0.0451281	−	0.998981i	$-0.514370\pi$
$607$	−2.22367			−0.0902561			−0.0451281	+	0.998981i	$0.514370\pi$
$608$		0			0
$609$	12.3836	−	9.68897i	0.501811	−	0.392617i
$610$		0			0
$611$	1.30586	−	1.30586i	0.0528293	−	0.0528293i
$612$		0			0
$613$	31.9461	−	31.9461i	1.29029	−	1.29029i	0.355683	−	0.934607i	$-0.384248\pi$
$613$	31.9461	−	31.9461i	1.29029	−	1.29029i	0.934607	−	0.355683i	$-0.115752\pi$
$614$		0			0
$615$	−7.35132	−	31.5101i	−0.296434	−	1.27061i
$616$		0			0
$617$			33.0436i			1.33029i	0.746716	+	0.665143i	$0.231630\pi$
$617$			33.0436i			1.33029i	−0.746716	+	0.665143i	$0.768370\pi$
$618$		0			0
$619$	24.5945	−	24.5945i	0.988537	−	0.988537i	−0.0113984	−	0.999935i	$-0.503628\pi$
$619$	24.5945	−	24.5945i	0.988537	−	0.988537i	0.999935	+	0.0113984i	$0.00362831\pi$
$620$		0			0
$621$	22.5126	+	8.58822i	0.903398	+	0.344633i
$622$		0			0
$623$			27.3315i			1.09501i
$624$		0			0
$625$	4.18198	−	24.6477i	0.167279	−	0.985910i
$626$		0			0
$627$	5.48423	−	44.9223i	0.219019	−	1.79402i
$628$		0			0
$629$	−1.89933	+	1.89933i	−0.0757313	+	0.0757313i
$630$		0			0
$631$	5.55087			0.220977			0.110488	−	0.993877i	$-0.464759\pi$
$631$	5.55087			0.220977			0.110488	+	0.993877i	$0.464759\pi$
$632$		0			0
$633$	−9.31357	−	11.9038i	−0.370181	−	0.473135i
$634$		0			0
$635$	−4.95041	−	13.5331i	−0.196451	−	0.537043i
$636$		0			0
$637$	−6.36721	−	6.36721i	−0.252278	−	0.252278i
$638$		0			0
$639$	0.0995328	−	0.401569i	0.00393745	−	0.0158858i
$640$		0			0
$641$			18.9176i			0.747200i	0.927590	+	0.373600i	$0.121877\pi$
$641$			18.9176i			0.747200i	−0.927590	+	0.373600i	$0.878123\pi$
$642$		0			0
$643$	−8.14527	+	8.14527i	−0.321218	+	0.321218i	−0.849234	−	0.528016i	$-0.822936\pi$
$643$	−8.14527	+	8.14527i	−0.321218	+	0.321218i	0.528016	+	0.849234i	$0.322936\pi$
$644$		0			0
$645$	2.14601	−	3.45203i	0.0844991	−	0.135924i
$646$		0			0
$647$	−32.1389			−1.26351			−0.631755	−	0.775168i	$-0.717665\pi$
$647$	−32.1389			−1.26351			−0.631755	+	0.775168i	$0.717665\pi$
$648$		0			0
$649$		−	31.6893i		−	1.24391i
$650$		0			0
$651$	0.752450	+	0.0918610i	0.0294908	+	0.00360032i
$652$		0			0
$653$	−16.6066	+	16.6066i	−0.649866	+	0.649866i	−0.952961	−	0.303094i	$-0.901980\pi$
$653$	−16.6066	+	16.6066i	−0.649866	+	0.649866i	0.303094	+	0.952961i	$0.401980\pi$
$654$		0			0
$655$	14.3104	+	6.64493i	0.559155	+	0.259639i
$656$		0			0
$657$	22.3955	+	5.55094i	0.873733	+	0.216563i
$658$		0			0
$659$	9.70238	−	9.70238i	0.377951	−	0.377951i	−0.492412	−	0.870363i	$-0.663884\pi$
$659$	9.70238	−	9.70238i	0.377951	−	0.377951i	0.870363	+	0.492412i	$0.163884\pi$
$660$		0			0
$661$	−8.55783	−	8.55783i	−0.332861	−	0.332861i	0.520811	−	0.853672i	$-0.325630\pi$
$661$	−8.55783	−	8.55783i	−0.332861	−	0.332861i	−0.853672	+	0.520811i	$0.825630\pi$
$662$		0			0
$663$	−2.36189	−	3.01878i	−0.0917284	−	0.117240i
$664$		0			0
$665$	−40.9764	−	19.0271i	−1.58900	−	0.737838i
$666$		0			0
$667$	−7.28955	−	7.28955i	−0.282252	−	0.282252i
$668$		0			0
$669$	−4.95255	−	0.604621i	−0.191477	−	0.0233760i
$670$		0			0
$671$	0.969138			0.0374131
$672$		0			0
$673$		−	50.4678i		−	1.94539i	−0.232087	−	0.972695i	$-0.574555\pi$
$673$		−	50.4678i		−	1.94539i	0.232087	−	0.972695i	$-0.425445\pi$
$674$		0			0
$675$	−24.5201	+	8.58875i	−0.943778	+	0.330581i
$676$		0			0
$677$	−0.103733	−	0.103733i	−0.00398677	−	0.00398677i	0.705111	−	0.709097i	$-0.250897\pi$
$677$	−0.103733	−	0.103733i	−0.00398677	−	0.00398677i	−0.709097	+	0.705111i	$0.750897\pi$
$678$		0			0
$679$	2.38677			0.0915958
$680$		0			0
$681$	2.94470	+	3.76368i	0.112841	+	0.144224i
$682$		0			0
$683$	6.39553	−	6.39553i	0.244718	−	0.244718i	−0.574081	−	0.818799i	$-0.694640\pi$
$683$	6.39553	−	6.39553i	0.244718	−	0.244718i	0.818799	+	0.574081i	$0.194640\pi$
$684$		0			0
$685$	33.9668	−	12.4251i	1.29781	−	0.474739i
$686$		0			0
$687$	0.115470	+	0.147584i	0.00440544	+	0.00563068i
$688$		0			0
$689$			3.04254i			0.115912i
$690$		0			0
$691$	−10.3797	−	10.3797i	−0.394861	−	0.394861i	0.481555	−	0.876416i	$-0.340072\pi$
$691$	−10.3797	−	10.3797i	−0.394861	−	0.394861i	−0.876416	+	0.481555i	$0.840072\pi$
$692$		0			0
$693$	55.4033	−	33.3940i	2.10460	−	1.26853i
$694$		0			0
$695$	36.8690	+	17.1198i	1.39852	+	0.649391i
$696$		0			0
$697$	19.8625			0.752347
$698$		0			0
$699$	−2.59455	+	21.2524i	−0.0981349	+	0.803840i
$700$		0			0
$701$	−4.02073	−	4.02073i	−0.151861	−	0.151861i	0.627088	−	0.778949i	$-0.284247\pi$
$701$	−4.02073	−	4.02073i	−0.151861	−	0.151861i	−0.778949	+	0.627088i	$0.784247\pi$
$702$		0			0
$703$	5.59010			0.210835
$704$		0			0
$705$	7.48333	−	1.74586i	0.281838	−	0.0657529i
$706$		0			0
$707$	22.5466	+	22.5466i	0.847951	+	0.847951i
$708$		0			0
$709$	−12.9713	−	12.9713i	−0.487149	−	0.487149i	0.420257	−	0.907405i	$-0.361940\pi$
$709$	−12.9713	−	12.9713i	−0.487149	−	0.487149i	−0.907405	+	0.420257i	$0.861940\pi$
$710$		0			0
$711$	−6.97377	+	28.1360i	−0.261537	+	1.05518i
$712$		0			0
$713$		−	0.496998i		−	0.0186127i
$714$		0			0
$715$	10.3218	−	3.77573i	0.386014	−	0.141204i
$716$		0			0
$717$	−32.6764	−	3.98922i	−1.22032	−	0.148980i
$718$		0			0
$719$	27.1715			1.01332			0.506662	−	0.862145i	$-0.330879\pi$
$719$	27.1715			1.01332			0.506662	+	0.862145i	$0.330879\pi$
$720$		0			0
$721$	−57.5935			−2.14489
$722$		0			0
$723$	−19.7539	−	2.41160i	−0.734654	−	0.0896885i
$724$		0			0
$725$	11.0765	+	0.933010i	0.411372	+	0.0346511i
$726$		0			0
$727$		−	8.78770i		−	0.325918i	−0.986633	−	0.162959i	$-0.947896\pi$
$727$		−	8.78770i		−	0.325918i	0.986633	−	0.162959i	$-0.0521038\pi$
$728$		0			0
$729$	20.1397	+	17.9831i	0.745915	+	0.666041i
$730$		0			0
$731$	1.76437	+	1.76437i	0.0652577	+	0.0652577i
$732$		0			0
$733$	10.8147	+	10.8147i	0.399449	+	0.399449i	0.878039	−	0.478590i	$-0.158852\pi$
$733$	10.8147	+	10.8147i	0.399449	+	0.399449i	−0.478590	+	0.878039i	$0.658852\pi$
$734$		0			0
$735$	−8.51263	−	36.4879i	−0.313993	−	1.34588i
$736$		0			0
$737$	−81.1672			−2.98983
$738$		0			0
$739$	−22.4470	−	22.4470i	−0.825725	−	0.825725i	0.161197	−	0.986922i	$-0.448465\pi$
$739$	−22.4470	−	22.4470i	−0.825725	−	0.825725i	−0.986922	+	0.161197i	$0.948465\pi$
$740$		0			0
$741$	−0.966673	+	7.91818i	−0.0355116	+	0.290882i
$742$		0			0
$743$	32.8288			1.20437			0.602187	−	0.798355i	$-0.294296\pi$
$743$	32.8288			1.20437			0.602187	+	0.798355i	$0.294296\pi$
$744$		0			0
$745$	−16.9279	−	7.86035i	−0.620192	−	0.287981i
$746$		0			0
$747$	−15.2263	−	25.2616i	−0.557102	−	0.924275i
$748$		0			0
$749$	42.5060	+	42.5060i	1.55314	+	1.55314i
$750$		0			0
$751$			11.6289i			0.424346i	0.977232	+	0.212173i	$0.0680541\pi$
$751$			11.6289i			0.424346i	−0.977232	+	0.212173i	$0.931946\pi$
$752$		0			0
$753$	−21.3686	−	27.3116i	−0.778716	−	0.995291i
$754$		0			0
$755$	−15.5096	−	42.3990i	−0.564452	−	1.54306i
$756$		0			0
$757$	−35.0528	+	35.0528i	−1.27401	+	1.27401i	−0.330051	+	0.943963i	$0.607066\pi$
$757$	−35.0528	+	35.0528i	−1.27401	+	1.27401i	−0.943963	+	0.330051i	$0.892934\pi$
$758$		0			0
$759$	−26.1350	−	33.4036i	−0.948639	−	1.21247i
$760$		0			0
$761$	34.3245			1.24426			0.622132	−	0.782912i	$-0.286267\pi$
$761$	34.3245			1.24426			0.622132	+	0.782912i	$0.286267\pi$
$762$		0			0
$763$	44.0630	+	44.0630i	1.59519	+	1.59519i
$764$		0			0
$765$	−1.71466	−	15.8563i	−0.0619938	−	0.573287i
$766$		0			0
$767$			5.58569i			0.201688i
$768$		0			0
$769$	0.873616			0.0315034			0.0157517	−	0.999876i	$-0.494986\pi$
$769$	0.873616			0.0315034			0.0157517	+	0.999876i	$0.494986\pi$
$770$		0			0
$771$	3.26551	+	0.398662i	0.117604	+	0.0143575i
$772$		0			0
$773$	−23.8387	−	23.8387i	−0.857420	−	0.857420i	0.133614	−	0.991033i	$-0.457342\pi$
$773$	−23.8387	−	23.8387i	−0.857420	−	0.857420i	−0.991033	+	0.133614i	$0.957342\pi$
$774$		0			0
$775$	0.345790	+	0.409402i	0.0124211	+	0.0147062i
$776$		0			0
$777$	4.92383	+	6.29324i	0.176641	+	0.225769i
$778$		0			0
$779$	−29.2296	−	29.2296i	−1.04726	−	1.04726i
$780$		0			0
$781$	−0.514943	+	0.514943i	−0.0184261	+	0.0184261i
$782$		0			0
$783$	−4.72044	−	10.5434i	−0.168695	−	0.376789i
$784$		0			0
$785$	−18.9995	+	40.9171i	−0.678123	+	1.46040i
$786$		0			0
$787$	11.2684	−	11.2684i	0.401674	−	0.401674i	−0.477148	−	0.878823i	$-0.658330\pi$
$787$	11.2684	−	11.2684i	0.401674	−	0.401674i	0.878823	+	0.477148i	$0.158330\pi$
$788$		0			0
$789$	−24.6245	−	3.00622i	−0.876656	−	0.107024i
$790$		0			0
$791$		−	7.55300i		−	0.268554i
$792$		0			0
$793$	−0.170824			−0.00606614
$794$		0			0
$795$	−6.68393	+	10.7517i	−0.237055	+	0.381322i
$796$		0			0
$797$	36.0183	−	36.0183i	1.27583	−	1.27583i	0.332855	−	0.942978i	$-0.391988\pi$
$797$	36.0183	−	36.0183i	1.27583	−	1.27583i	0.942978	−	0.332855i	$-0.108012\pi$
$798$		0			0
$799$			4.71714i			0.166880i
$800$		0			0
$801$	19.4902	+	4.83083i	0.688653	+	0.170689i
$802$		0			0
$803$	−28.7184	−	28.7184i	−1.01345	−	1.01345i
$804$		0			0
$805$	−39.7633	+	14.5455i	−1.40147	+	0.512661i
$806$		0			0
$807$	12.7607	+	16.3096i	0.449197	+	0.574127i
$808$		0			0
$809$	47.3602			1.66510			0.832548	−	0.553953i	$-0.186881\pi$
$809$	47.3602			1.66510			0.832548	+	0.553953i	$0.186881\pi$
$810$		0			0
$811$	−10.0673	+	10.0673i	−0.353512	+	0.353512i	−0.861415	−	0.507903i	$-0.830421\pi$
$811$	−10.0673	+	10.0673i	−0.353512	+	0.353512i	0.507903	+	0.861415i	$0.330421\pi$
$812$		0			0
$813$	5.73723	−	46.9947i	0.201213	−	1.64817i
$814$		0			0
$815$	14.5344	+	6.74894i	0.509118	+	0.236405i
$816$		0			0
$817$		−	5.19289i		−	0.181676i
$818$		0			0
$819$	−9.76561	+	5.88617i	−0.341238	+	0.205679i
$820$		0			0
$821$	−29.4088	+	29.4088i	−1.02637	+	1.02637i	−0.0267305	+	0.999643i	$0.508510\pi$
$821$	−29.4088	+	29.4088i	−1.02637	+	1.02637i	−0.999643	+	0.0267305i	$0.991490\pi$
$822$		0			0
$823$		−	8.03877i		−	0.280214i	−0.990136	−	0.140107i	$-0.955255\pi$
$823$		−	8.03877i		−	0.280214i	0.990136	−	0.140107i	$-0.0447446\pi$
$824$		0			0
$825$	44.7695	+	9.33262i	1.55867	+	0.324920i
$826$		0			0
$827$	−25.7224	+	25.7224i	−0.894456	+	0.894456i	−0.994939	−	0.100482i	$-0.967961\pi$
$827$	−25.7224	+	25.7224i	−0.894456	+	0.894456i	0.100482	+	0.994939i	$0.467961\pi$
$828$		0			0
$829$	−7.82520	+	7.82520i	−0.271780	+	0.271780i	−0.829817	−	0.558036i	$-0.811555\pi$
$829$	−7.82520	+	7.82520i	−0.271780	+	0.271780i	0.558036	+	0.829817i	$0.311555\pi$
$830$		0			0
$831$	17.5055	−	13.6963i	0.607261	−	0.475121i
$832$		0			0
$833$	23.0003			0.796913
$834$		0			0
$835$	6.81215	+	18.6225i	0.235744	+	0.644459i
$836$		0			0
$837$	0.198502	−	0.520339i	0.00686122	−	0.0179855i
$838$		0			0
$839$			49.5577i			1.71092i	0.517866	+	0.855461i	$0.326726\pi$
$839$			49.5577i			1.71092i	−0.517866	+	0.855461i	$0.673274\pi$
$840$		0			0
$841$		−	24.0576i		−	0.829572i
$842$		0			0
$843$	−8.72513	−	1.06519i	−0.300509	−	0.0366870i
$844$		0			0
$845$	25.4803	−	9.32074i	0.876551	−	0.320643i
$846$		0			0
$847$	−68.9499			−2.36914
$848$		0			0
$849$	−24.4083	−	31.1966i	−0.837689	−	1.07067i
$850$		0			0
$851$	3.70447	−	3.70447i	0.126988	−	0.126988i
$852$		0			0
$853$	−27.2084	+	27.2084i	−0.931598	+	0.931598i	−0.997806	−	0.0662080i	$-0.978910\pi$
$853$	−27.2084	+	27.2084i	−0.931598	+	0.931598i	0.0662080	+	0.997806i	$0.478910\pi$
$854$		0			0
$855$	−20.8108	+	25.8574i	−0.711716	+	0.884306i
$856$		0			0
$857$			39.9345i			1.36414i	0.731289	+	0.682068i	$0.238919\pi$
$857$			39.9345i			1.36414i	−0.731289	+	0.682068i	$0.761081\pi$
$858$		0			0
$859$	33.5029	−	33.5029i	1.14311	−	1.14311i	0.155227	−	0.987879i	$-0.450389\pi$
$859$	33.5029	−	33.5029i	1.14311	−	1.14311i	0.987879	−	0.155227i	$-0.0496107\pi$
$860$		0			0
$861$	7.16040	−	58.6520i	0.244026	−	1.99886i
$862$		0			0
$863$		−	4.15052i		−	0.141285i	−0.997502	−	0.0706426i	$-0.977495\pi$
$863$		−	4.15052i		−	0.141285i	0.997502	−	0.0706426i	$-0.0225050\pi$
$864$		0			0
$865$	−6.49984	−	3.01815i	−0.221001	−	0.102620i
$866$		0			0
$867$	−19.5096	−	2.38178i	−0.662579	−	0.0808894i
$868$		0			0
$869$	36.0795	−	36.0795i	1.22391	−	1.22391i
$870$		0			0
$871$	14.3069			0.484770
$872$		0			0
$873$	0.421861	−	1.70202i	0.0142778	−	0.0576045i
$874$		0			0
$875$	22.6349	−	39.6475i	0.765201	−	1.34033i
$876$		0			0
$877$	−19.6248	−	19.6248i	−0.662681	−	0.662681i	0.293330	−	0.956011i	$-0.405236\pi$
$877$	−19.6248	−	19.6248i	−0.662681	−	0.662681i	−0.956011	+	0.293330i	$0.905236\pi$
$878$		0			0
$879$	17.1936	+	21.9754i	0.579924	+	0.741212i
$880$		0			0
$881$		−	20.6430i		−	0.695481i	−0.937591	−	0.347740i	$-0.886949\pi$
$881$		−	20.6430i		−	0.695481i	0.937591	−	0.347740i	$-0.113051\pi$
$882$		0			0
$883$	−2.68626	+	2.68626i	−0.0904000	+	0.0904000i	−0.750861	−	0.660461i	$-0.770361\pi$
$883$	−2.68626	+	2.68626i	−0.0904000	+	0.0904000i	0.660461	+	0.750861i	$0.270361\pi$
$884$		0			0
$885$	−12.2708	+	19.7385i	−0.412477	+	0.663504i
$886$		0			0
$887$	5.25621			0.176486			0.0882432	−	0.996099i	$-0.471875\pi$
$887$	5.25621			0.176486			0.0882432	+	0.996099i	$0.471875\pi$
$888$		0			0
$889$		−	26.3149i		−	0.882575i
$890$		0			0
$891$	−14.0209	−	45.4107i	−0.469719	−	1.52132i
$892$		0			0
$893$	6.94173	−	6.94173i	0.232296	−	0.232296i
$894$		0			0
$895$	−5.38167	−	2.49894i	−0.179889	−	0.0835302i
$896$		0			0
$897$	4.60666	+	5.88785i	0.153812	+	0.196590i
$898$		0			0
$899$	−0.168485	+	0.168485i	−0.00561930	+	0.00561930i
$900$		0			0
$901$	−5.49529	−	5.49529i	−0.183075	−	0.183075i
$902$		0			0
$903$	5.84607	−	4.57396i	0.194545	−	0.152212i
$904$		0			0
$905$	2.23669	−	4.81690i	0.0743500	−	0.160119i
$906$		0			0
$907$	−25.4215	−	25.4215i	−0.844108	−	0.844108i	0.145282	−	0.989390i	$-0.453591\pi$
$907$	−25.4215	−	25.4215i	−0.844108	−	0.844108i	−0.989390	+	0.145282i	$0.953591\pi$
$908$		0			0
$909$	20.0632	−	12.0930i	0.665453	−	0.401098i
$910$		0			0
$911$	29.2937			0.970544			0.485272	−	0.874363i	$-0.338721\pi$
$911$	29.2937			0.970544			0.485272	+	0.874363i	$0.338721\pi$
$912$		0			0
$913$			51.9188i			1.71826i
$914$		0			0
$915$	−0.603653	−	0.375270i	−0.0199562	−	0.0124061i
$916$		0			0
$917$	20.3738	+	20.3738i	0.672802	+	0.672802i
$918$		0			0
$919$	42.0179			1.38604			0.693022	−	0.720917i	$-0.256279\pi$
$919$	42.0179			1.38604			0.693022	+	0.720917i	$0.256279\pi$
$920$		0			0
$921$	−33.4618	+	26.1805i	−1.10260	+	0.862676i
$922$		0			0
$923$	0.0907661	−	0.0907661i	0.00298760	−	0.00298760i
$924$		0			0
$925$	−0.474146	+	5.62897i	−0.0155898	+	0.185080i
$926$		0			0
$927$	−10.1796	+	41.0702i	−0.334343	+	1.34892i
$928$		0			0
$929$		−	50.1590i		−	1.64566i	−0.568286	−	0.822831i	$-0.692393\pi$
$929$		−	50.1590i		−	1.64566i	0.568286	−	0.822831i	$-0.307607\pi$
$930$		0			0
$931$	−33.8471	−	33.8471i	−1.10930	−	1.10930i
$932$		0			0
$933$	−5.18909	+	42.5048i	−0.169883	+	1.39154i
$934$		0			0
$935$	−11.8232	+	25.4623i	−0.386660	+	0.832705i
$936$		0			0
$937$	−46.0881			−1.50563			−0.752817	−	0.658230i	$-0.771305\pi$
$937$	−46.0881			−1.50563			−0.752817	+	0.658230i	$0.771305\pi$
$938$		0			0
$939$	17.9486	+	2.19121i	0.585730	+	0.0715074i
$940$		0			0
$941$	−30.3573	−	30.3573i	−0.989619	−	0.989619i	0.0103277	−	0.999947i	$-0.496713\pi$
$941$	−30.3573	−	30.3573i	−0.989619	−	0.989619i	−0.999947	+	0.0103277i	$0.996713\pi$
$942$		0			0
$943$	−38.7400			−1.26155
$944$		0			0
$945$	−47.4403	−	0.652946i	−1.54323	−	0.0212403i
$946$		0			0
$947$	12.0328	+	12.0328i	0.391012	+	0.391012i	0.875048	−	0.484036i	$-0.160830\pi$
$947$	12.0328	+	12.0328i	0.391012	+	0.391012i	−0.484036	+	0.875048i	$0.660830\pi$
$948$		0			0
$949$	5.06202	+	5.06202i	0.164320	+	0.164320i
$950$		0			0
$951$	4.96990	−	3.88845i	0.161160	−	0.126092i
$952$		0			0
$953$		−	0.810875i		−	0.0262668i	−0.999914	−	0.0131334i	$-0.995819\pi$
$953$		−	0.810875i		−	0.0262668i	0.999914	−	0.0131334i	$-0.00418062\pi$
$954$		0			0
$955$	11.4275	+	31.2396i	0.369784	+	1.01089i
$956$		0			0
$957$	−2.46411	+	20.1839i	−0.0796533	+	0.652454i
$958$		0			0
$959$	66.0483			2.13281
$960$		0			0
$961$	30.9885			0.999629
$962$		0			0
$963$	37.8242	−	22.7983i	1.21887	−	0.734666i
$964$		0			0
$965$	11.7794	−	4.30892i	0.379192	−	0.138709i
$966$		0			0
$967$		−	3.61644i		−	0.116297i	−0.998308	−	0.0581484i	$-0.981480\pi$
$967$		−	3.61644i		−	0.116297i	0.998308	−	0.0581484i	$-0.0185196\pi$
$968$		0			0
$969$	−12.5555	−	16.0474i	−0.403340	−	0.515516i
$970$		0			0
$971$	13.6779	+	13.6779i	0.438946	+	0.438946i	0.891657	−	0.452711i	$-0.149543\pi$
$971$	13.6779	+	13.6779i	0.438946	+	0.438946i	−0.452711	+	0.891657i	$0.649543\pi$
$972$		0			0
$973$	52.4905	+	52.4905i	1.68277	+	1.68277i
$974$		0			0
$975$	−7.89126	−	1.64501i	−0.252722	−	0.0526824i
$976$		0			0
$977$	−10.3013			−0.329567			−0.164784	−	0.986330i	$-0.552693\pi$
$977$	−10.3013			−0.329567			−0.164784	+	0.986330i	$0.552693\pi$
$978$		0			0
$979$	−24.9928	−	24.9928i	−0.798774	−	0.798774i
$980$		0			0
$981$	39.2096	−	23.6334i	1.25187	−	0.754556i
$982$		0			0
$983$	−5.71041			−0.182134			−0.0910668	−	0.995845i	$-0.529028\pi$
$983$	−5.71041			−0.182134			−0.0910668	+	0.995845i	$0.529028\pi$
$984$		0			0
$985$	12.4109	−	26.7280i	0.395445	−	0.851625i
$986$		0			0
$987$	13.9292	+	1.70052i	0.443372	+	0.0541281i
$988$		0			0
$989$	−3.44125	−	3.44125i	−0.109425	−	0.109425i
$990$		0			0
$991$		−	30.7989i		−	0.978358i	−0.872183	−	0.489179i	$-0.837297\pi$
$991$		−	30.7989i		−	0.978358i	0.872183	−	0.489179i	$-0.162703\pi$
$992$		0			0
$993$	−23.8737	+	18.6788i	−0.757608	+	0.592753i
$994$		0			0
$995$	−7.31213	−	19.9894i	−0.231810	−	0.633705i
$996$		0			0
$997$	13.0092	−	13.0092i	0.412005	−	0.412005i	−0.470431	−	0.882437i	$-0.655902\pi$
$997$	13.0092	−	13.0092i	0.412005	−	0.412005i	0.882437	+	0.470431i	$0.155902\pi$
$998$		0			0
$999$	5.35802	−	2.39888i	0.169520	−	0.0758971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.t.b.719.39		80
3.2	odd	2	inner	960.2.t.b.719.19		80
4.3	odd	2		240.2.t.b.59.39	yes	80
5.4	even	2	inner	960.2.t.b.719.2		80
12.11	even	2		240.2.t.b.59.1	✓	80
15.14	odd	2	inner	960.2.t.b.719.22		80
16.3	odd	4	inner	960.2.t.b.239.22		80
16.13	even	4		240.2.t.b.179.40	yes	80
20.19	odd	2		240.2.t.b.59.2	yes	80
48.29	odd	4		240.2.t.b.179.2	yes	80
48.35	even	4	inner	960.2.t.b.239.2		80
60.59	even	2		240.2.t.b.59.40	yes	80
80.19	odd	4	inner	960.2.t.b.239.19		80
80.29	even	4		240.2.t.b.179.1	yes	80
240.29	odd	4		240.2.t.b.179.39	yes	80
240.179	even	4	inner	960.2.t.b.239.39		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.t.b.59.1	✓	80	12.11	even	2
240.2.t.b.59.2	yes	80	20.19	odd	2
240.2.t.b.59.39	yes	80	4.3	odd	2
240.2.t.b.59.40	yes	80	60.59	even	2
240.2.t.b.179.1	yes	80	80.29	even	4
240.2.t.b.179.2	yes	80	48.29	odd	4
240.2.t.b.179.39	yes	80	240.29	odd	4
240.2.t.b.179.40	yes	80	16.13	even	4
960.2.t.b.239.2		80	48.35	even	4	inner
960.2.t.b.239.19		80	80.19	odd	4	inner
960.2.t.b.239.22		80	16.3	odd	4	inner
960.2.t.b.239.39		80	240.179	even	4	inner
960.2.t.b.719.2		80	5.4	even	2	inner
960.2.t.b.719.19		80	3.2	odd	2	inner
960.2.t.b.719.22		80	15.14	odd	2	inner
960.2.t.b.719.39		80	1.1	even	1	trivial

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.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71929 + 0.209895i) q^{3} +(0.768175 + 2.09998i) q^{5} +4.08340i q^{7} +(2.91189 + 0.721739i) q^{9} +O(q^{10})\)	\(q+(1.71929 + 0.209895i) q^{3} +(0.768175 + 2.09998i) q^{5} +4.08340i q^{7} +(2.91189 + 0.721739i) q^{9} +(-3.73399 - 3.73399i) q^{11} +(0.658169 + 0.658169i) q^{13} +(0.879937 + 3.77170i) q^{15} -2.37750 q^{17} +(3.49873 + 3.49873i) q^{19} +(-0.857084 + 7.02053i) q^{21} +4.63710 q^{23} +(-3.81982 + 3.22630i) q^{25} +(4.85488 + 1.85207i) q^{27} +(-1.57201 - 1.57201i) q^{29} -0.107179i q^{31} +(-5.63606 - 7.20355i) q^{33} +(-8.57504 + 3.13676i) q^{35} +(0.798876 - 0.798876i) q^{37} +(0.993434 + 1.26973i) q^{39} -8.35437 q^{41} +(-0.742112 - 0.742112i) q^{43} +(0.721203 + 6.66932i) q^{45} -1.98407i q^{47} -9.67413 q^{49} +(-4.08761 - 0.499026i) q^{51} +(2.31137 + 2.31137i) q^{53} +(4.97295 - 10.7097i) q^{55} +(5.28095 + 6.74968i) q^{57} +(4.24336 + 4.24336i) q^{59} +(-0.129772 + 0.129772i) q^{61} +(-2.94715 + 11.8904i) q^{63} +(-0.876552 + 1.88773i) q^{65} +(10.8687 - 10.8687i) q^{67} +(7.97250 + 0.973304i) q^{69} -0.137907i q^{71} +7.69107 q^{73} +(-7.24454 + 4.74517i) q^{75} +(15.2474 - 15.2474i) q^{77} +9.66245i q^{79} +(7.95819 + 4.20325i) q^{81} +(-6.95219 - 6.95219i) q^{83} +(-1.82634 - 4.99271i) q^{85} +(-2.37277 - 3.03268i) q^{87} +6.69332 q^{89} +(-2.68757 + 2.68757i) q^{91} +(0.0224962 - 0.184271i) q^{93} +(-4.65962 + 10.0349i) q^{95} -0.584506i q^{97} +(-8.17800 - 13.5679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q - 16 q^{19} + 8 q^{21} + 8 q^{39} - 12 q^{45} - 112 q^{49} - 32 q^{51} + 40 q^{55} + 16 q^{61} - 40 q^{69} + 36 q^{75} + 64 q^{81} - 64 q^{85} - 48 q^{91} + 8 q^{99}+O(q^{100}) \) 80 * q - 16 * q^19 + 8 * q^21 + 8 * q^39 - 12 * q^45 - 112 * q^49 - 32 * q^51 + 40 * q^55 + 16 * q^61 - 40 * q^69 + 36 * q^75 + 64 * q^81 - 64 * q^85 - 48 * q^91 + 8 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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