LMFDB - Embedded newform 936.2.g.f.469.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(469,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("936.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.g (of order $2$, degree $1$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.10
Character	$\chi$	$=$	936.469
Dual form			936.2.g.f.469.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.900006 + 1.09087i) q^{2} +(-0.379977 - 1.96357i) q^{4} -3.06504i q^{5} -1.53955 q^{7} +(2.48398 + 1.35272i) q^{8} +(3.34355 + 2.75856i) q^{10} -4.08464i q^{11} +1.00000i q^{13} +(1.38560 - 1.67944i) q^{14} +(-3.71123 + 1.49222i) q^{16} +4.47763 q^{17} +2.68495i q^{19} +(-6.01843 + 1.16465i) q^{20} +(4.45580 + 3.67620i) q^{22} -3.24471 q^{23} -4.39448 q^{25} +(-1.09087 - 0.900006i) q^{26} +(0.584993 + 3.02301i) q^{28} -8.41043i q^{29} -5.14476 q^{31} +(1.71232 - 5.39147i) q^{32} +(-4.02990 + 4.88449i) q^{34} +4.71878i q^{35} +5.60521i q^{37} +(-2.92892 - 2.41647i) q^{38} +(4.14616 - 7.61349i) q^{40} -5.34539 q^{41} -8.91439i q^{43} +(-8.02049 + 1.55207i) q^{44} +(2.92026 - 3.53955i) q^{46} -10.6143 q^{47} -4.62979 q^{49} +(3.95506 - 4.79379i) q^{50} +(1.96357 - 0.379977i) q^{52} -2.48127i q^{53} -12.5196 q^{55} +(-3.82420 - 2.08258i) q^{56} +(9.17465 + 7.56944i) q^{58} +3.09287i q^{59} +8.47358i q^{61} +(4.63032 - 5.61224i) q^{62} +(4.34028 + 6.72027i) q^{64} +3.06504 q^{65} -9.32998i q^{67} +(-1.70140 - 8.79215i) q^{68} +(-5.14755 - 4.24693i) q^{70} -7.52766 q^{71} -5.60521 q^{73} +(-6.11453 - 5.04473i) q^{74} +(5.27209 - 1.02022i) q^{76} +6.28850i q^{77} -11.3742 q^{79} +(4.57373 + 11.3751i) q^{80} +(4.81089 - 5.83110i) q^{82} +4.46652i q^{83} -13.7241i q^{85} +(9.72440 + 8.02301i) q^{86} +(5.52539 - 10.1462i) q^{88} +5.90303 q^{89} -1.53955i q^{91} +(1.23292 + 6.37123i) q^{92} +(9.55293 - 11.5788i) q^{94} +8.22948 q^{95} +14.0149 q^{97} +(4.16684 - 5.05049i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} + 8 q^{28} + 40 q^{31} - 16 q^{34} - 36 q^{40} - 24 q^{46} + 24 q^{49} - 4 q^{52} - 16 q^{55} - 24 q^{58} + 8 q^{64} - 16 q^{70} - 16 q^{76}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q + 8 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 + 8 * q^28 + 40 * q^31 - 16 * q^34 - 36 * q^40 - 24 * q^46 + 24 * q^49 - 4 * q^52 - 16 * q^55 - 24 * q^58 + 8 * q^64 - 16 * q^70 - 16 * q^76 + 68 * q^82 + 28 * q^88 + 12 * q^94 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.900006	+	1.09087i	−0.636401	+	0.771359i
$2$	−0.900006	+	1.09087i	−0.636401	+	0.771359i
$3$		0			0
$3$		0			0
$4$	−0.379977	−	1.96357i	−0.189989	−	0.981786i
$5$		−	3.06504i		−	1.37073i	−0.728200	−	0.685364i	$-0.759643\pi$
$5$		−	3.06504i		−	1.37073i	0.728200	−	0.685364i	$-0.240357\pi$
$6$		0			0
$7$	−1.53955			−0.581894			−0.290947	−	0.956739i	$-0.593970\pi$
$7$	−1.53955			−0.581894			−0.290947	+	0.956739i	$0.593970\pi$
$8$	2.48398	+	1.35272i	0.878218	+	0.478260i
$9$		0			0
$10$	3.34355	+	2.75856i	1.05732	+	0.872332i
$11$		−	4.08464i		−	1.23157i	−0.787916	−	0.615783i	$-0.788840\pi$
$11$		−	4.08464i		−	1.23157i	0.787916	−	0.615783i	$-0.211160\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	1.38560	−	1.67944i	0.370318	−	0.448849i
$15$		0			0
$16$	−3.71123	+	1.49222i	−0.927809	+	0.373056i
$17$	4.47763			1.08598			0.542992	−	0.839738i	$-0.317291\pi$
$17$	4.47763			1.08598			0.542992	+	0.839738i	$0.317291\pi$
$18$		0			0
$19$			2.68495i			0.615969i	0.951391	+	0.307985i	$0.0996546\pi$
$19$			2.68495i			0.615969i	−0.951391	+	0.307985i	$0.900345\pi$
$20$	−6.01843	+	1.16465i	−1.34576	+	0.260423i
$21$		0			0
$22$	4.45580	+	3.67620i	0.949979	+	0.783769i
$23$	−3.24471			−0.676569			−0.338285	−	0.941044i	$-0.609847\pi$
$23$	−3.24471			−0.676569			−0.338285	+	0.941044i	$0.609847\pi$
$24$		0			0
$25$	−4.39448			−0.878896
$26$	−1.09087	−	0.900006i	−0.213936	−	0.176506i
$27$		0			0
$28$	0.584993	+	3.02301i	0.110553	+	0.571296i
$29$		−	8.41043i		−	1.56178i	−0.624670	−	0.780889i	$-0.714766\pi$
$29$		−	8.41043i		−	1.56178i	0.624670	−	0.780889i	$-0.285234\pi$
$30$		0			0
$31$	−5.14476			−0.924026			−0.462013	−	0.886873i	$-0.652873\pi$
$31$	−5.14476			−0.924026			−0.462013	+	0.886873i	$0.652873\pi$
$32$	1.71232	−	5.39147i	0.302698	−	0.953087i
$33$		0			0
$34$	−4.02990	+	4.88449i	−0.691121	+	0.837684i
$35$			4.71878i			0.797619i
$36$		0			0
$37$			5.60521i			0.921491i	0.887532	+	0.460746i	$0.152418\pi$
$37$			5.60521i			0.921491i	−0.887532	+	0.460746i	$0.847582\pi$
$38$	−2.92892	−	2.41647i	−0.475133	−	0.392003i
$39$		0			0
$40$	4.14616	−	7.61349i	0.655565	−	1.20380i
$41$	−5.34539			−0.834810			−0.417405	−	0.908721i	$-0.637060\pi$
$41$	−5.34539			−0.834810			−0.417405	+	0.908721i	$0.637060\pi$
$42$		0			0
$43$		−	8.91439i		−	1.35943i	−0.733476	−	0.679716i	$-0.762103\pi$
$43$		−	8.91439i		−	1.35943i	0.733476	−	0.679716i	$-0.237897\pi$
$44$	−8.02049	+	1.55207i	−1.20913	+	0.233983i
$45$		0			0
$46$	2.92026	−	3.53955i	0.430569	−	0.521878i
$47$	−10.6143			−1.54825			−0.774127	−	0.633031i	$-0.781811\pi$
$47$	−10.6143			−1.54825			−0.774127	+	0.633031i	$0.781811\pi$
$48$		0			0
$49$	−4.62979			−0.661399
$50$	3.95506	−	4.79379i	0.559330	−	0.677944i
$51$		0			0
$52$	1.96357	−	0.379977i	0.272299	−	0.0526933i
$53$		−	2.48127i		−	0.340829i	−0.985372	−	0.170415i	$-0.945489\pi$
$53$		−	2.48127i		−	0.340829i	0.985372	−	0.170415i	$-0.0545107\pi$
$54$		0			0
$55$	−12.5196			−1.68814
$56$	−3.82420	−	2.08258i	−0.511030	−	0.278297i
$57$		0			0
$58$	9.17465	+	7.56944i	1.20469	+	0.993916i
$59$			3.09287i			0.402658i	0.979524	+	0.201329i	$0.0645260\pi$
$59$			3.09287i			0.402658i	−0.979524	+	0.201329i	$0.935474\pi$
$60$		0			0
$61$			8.47358i			1.08493i	0.840078	+	0.542465i	$0.182509\pi$
$61$			8.47358i			1.08493i	−0.840078	+	0.542465i	$0.817491\pi$
$62$	4.63032	−	5.61224i	0.588051	−	0.712755i
$63$		0			0
$64$	4.34028	+	6.72027i	0.542534	+	0.840034i
$65$	3.06504			0.380172
$66$		0			0
$67$		−	9.32998i		−	1.13984i	−0.821701	−	0.569919i	$-0.806975\pi$
$67$		−	9.32998i		−	1.13984i	0.821701	−	0.569919i	$-0.193025\pi$
$68$	−1.70140	−	8.79215i	−0.206325	−	1.06620i
$69$		0			0
$70$	−5.14755	−	4.24693i	−0.615250	−	0.507605i
$71$	−7.52766			−0.893368			−0.446684	−	0.894692i	$-0.647395\pi$
$71$	−7.52766			−0.893368			−0.446684	+	0.894692i	$0.647395\pi$
$72$		0			0
$73$	−5.60521			−0.656040			−0.328020	−	0.944671i	$-0.606381\pi$
$73$	−5.60521			−0.656040			−0.328020	+	0.944671i	$0.606381\pi$
$74$	−6.11453	−	5.04473i	−0.710800	−	0.586437i
$75$		0			0
$76$	5.27209	−	1.02022i	0.604750	−	0.117027i
$77$			6.28850i			0.716641i
$78$		0			0
$79$	−11.3742			−1.27970			−0.639849	−	0.768501i	$-0.721003\pi$
$79$	−11.3742			−1.27970			−0.639849	+	0.768501i	$0.721003\pi$
$80$	4.57373	+	11.3751i	0.511359	+	1.27177i
$81$		0			0
$82$	4.81089	−	5.83110i	0.531273	−	0.643938i
$83$			4.46652i			0.490264i	0.969490	+	0.245132i	$0.0788314\pi$
$83$			4.46652i			0.490264i	−0.969490	+	0.245132i	$0.921169\pi$
$84$		0			0
$85$		−	13.7241i		−	1.48859i
$86$	9.72440	+	8.02301i	1.04861	+	0.865143i
$87$		0			0
$88$	5.52539	−	10.1462i	0.589009	−	1.08158i
$89$	5.90303			0.625720			0.312860	−	0.949799i	$-0.398713\pi$
$89$	5.90303			0.625720			0.312860	+	0.949799i	$0.398713\pi$
$90$		0			0
$91$		−	1.53955i		−	0.161388i
$92$	1.23292	+	6.37123i	0.128540	+	0.664247i
$93$		0			0
$94$	9.55293	−	11.5788i	0.985309	−	1.19426i
$95$	8.22948			0.844327
$96$		0			0
$97$	14.0149			1.42300			0.711500	−	0.702686i	$-0.248016\pi$
$97$	14.0149			1.42300			0.711500	+	0.702686i	$0.248016\pi$
$98$	4.16684	−	5.05049i	0.420915	−	0.510176i
$99$		0			0
$100$	1.66980	+	8.62888i	0.166980	+	0.862888i
$101$		−	5.30645i		−	0.528012i	−0.964521	−	0.264006i	$-0.914956\pi$
$101$		−	5.30645i		−	0.528012i	0.964521	−	0.264006i	$-0.0850438\pi$
$102$		0			0
$103$	12.6342			1.24489			0.622443	−	0.782665i	$-0.286140\pi$
$103$	12.6342			1.24489			0.622443	+	0.782665i	$0.286140\pi$
$104$	−1.35272	+	2.48398i	−0.132645	+	0.243574i
$105$		0			0
$106$	2.70674	+	2.23316i	0.262902	+	0.216904i
$107$		−	5.45968i		−	0.527807i	−0.964549	−	0.263904i	$-0.914990\pi$
$107$		−	5.45968i		−	0.527807i	0.964549	−	0.263904i	$-0.0850101\pi$
$108$		0			0
$109$		−	16.3549i		−	1.56651i	−0.621698	−	0.783257i	$-0.713557\pi$
$109$		−	16.3549i		−	1.56651i	0.621698	−	0.783257i	$-0.286443\pi$
$110$	11.2677	−	13.6572i	1.07433	−	1.30216i
$111$		0			0
$112$	5.71362	−	2.29735i	0.539886	−	0.217079i
$113$	20.0002			1.88146			0.940730	−	0.339156i	$-0.110142\pi$
$113$	20.0002			1.88146			0.940730	+	0.339156i	$0.110142\pi$
$114$		0			0
$115$			9.94518i			0.927393i
$116$	−16.5145	+	3.19577i	−1.53333	+	0.296720i
$117$		0			0
$118$	−3.37391	−	2.78361i	−0.310594	−	0.256252i
$119$	−6.89352			−0.631928
$120$		0			0
$121$	−5.68431			−0.516755
$122$	−9.24353	−	7.62627i	−0.836870	−	0.690450i
$123$		0			0
$124$	1.95489	+	10.1021i	0.175554	+	0.907196i
$125$		−	1.85594i		−	0.166000i
$126$		0			0
$127$	9.95513			0.883375			0.441688	−	0.897169i	$-0.354380\pi$
$127$	9.95513			0.883375			0.441688	+	0.897169i	$0.354380\pi$
$128$	−11.2372	−	1.31363i	−0.993236	−	0.116109i
$129$		0			0
$130$	−2.75856	+	3.34355i	−0.241941	+	0.293249i
$131$			12.8881i			1.12604i	0.826445	+	0.563018i	$0.190360\pi$
$131$			12.8881i			1.12604i	−0.826445	+	0.563018i	$0.809640\pi$
$132$		0			0
$133$		−	4.13361i		−	0.358429i
$134$	10.1778	+	8.39704i	0.879224	+	0.725394i
$135$		0			0
$136$	11.1223	+	6.05700i	0.953732	+	0.519383i
$137$	−11.2772			−0.963474			−0.481737	−	0.876316i	$-0.659994\pi$
$137$	−11.2772			−0.963474			−0.481737	+	0.876316i	$0.659994\pi$
$138$		0			0
$139$			0.953667i			0.0808890i	0.999182	+	0.0404445i	$0.0128774\pi$
$139$			0.953667i			0.0808890i	−0.999182	+	0.0404445i	$0.987123\pi$
$140$	9.26566	−	1.79303i	0.783091	−	0.151538i
$141$		0			0
$142$	6.77494	−	8.21166i	0.568540	−	0.689107i
$143$	4.08464			0.341575
$144$		0			0
$145$	−25.7783			−2.14077
$146$	5.04473	−	6.11453i	0.417504	−	0.506042i
$147$		0			0
$148$	11.0062	−	2.12985i	0.904707	−	0.175073i
$149$		−	5.35820i		−	0.438961i	−0.975617	−	0.219481i	$-0.929564\pi$
$149$		−	5.35820i		−	0.438961i	0.975617	−	0.219481i	$-0.0704363\pi$
$150$		0			0
$151$	−6.90944			−0.562283			−0.281141	−	0.959666i	$-0.590713\pi$
$151$	−6.90944			−0.562283			−0.281141	+	0.959666i	$0.590713\pi$
$152$	−3.63199	+	6.66935i	−0.294594	+	0.540956i
$153$		0			0
$154$	−6.85991	−	5.65969i	−0.552787	−	0.456071i
$155$			15.7689i			1.26659i
$156$		0			0
$157$		−	5.01523i		−	0.400259i	−0.979769	−	0.200130i	$-0.935864\pi$
$157$		−	5.01523i		−	0.400259i	0.979769	−	0.200130i	$-0.0641363\pi$
$158$	10.2369	−	12.4077i	0.814400	−	0.987106i
$159$		0			0
$160$	−16.5251	−	5.24833i	−1.30642	−	0.414917i
$161$	4.99539			0.393692
$162$		0			0
$163$			23.4882i			1.83974i	0.392229	+	0.919868i	$0.371704\pi$
$163$			23.4882i			1.83974i	−0.392229	+	0.919868i	$0.628296\pi$
$164$	2.03113	+	10.4961i	0.158604	+	0.819605i
$165$		0			0
$166$	−4.87238	−	4.01990i	−0.378170	−	0.312005i
$167$	−21.0636			−1.62995			−0.814975	−	0.579497i	$-0.803249\pi$
$167$	−21.0636			−1.62995			−0.814975	+	0.579497i	$0.803249\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	14.9712	+	12.3518i	1.14824	+	0.947340i
$171$		0			0
$172$	−17.5040	+	3.38726i	−1.33467	+	0.258276i
$173$		−	2.84062i		−	0.215968i	−0.994153	−	0.107984i	$-0.965560\pi$
$173$		−	2.84062i		−	0.215968i	0.994153	−	0.107984i	$-0.0344396\pi$
$174$		0			0
$175$	6.76551			0.511425
$176$	6.09521	+	15.1591i	0.459443	+	1.14266i
$177$		0			0
$178$	−5.31277	+	6.43942i	−0.398209	+	0.482655i
$179$			6.01451i			0.449546i	0.974411	+	0.224773i	$0.0721640\pi$
$179$			6.01451i			0.449546i	−0.974411	+	0.224773i	$0.927836\pi$
$180$		0			0
$181$			3.30604i			0.245736i	0.992423	+	0.122868i	$0.0392091\pi$
$181$			3.30604i			0.245736i	−0.992423	+	0.122868i	$0.960791\pi$
$182$	1.67944	+	1.38560i	0.124488	+	0.102708i
$183$		0			0
$184$	−8.05979	−	4.38920i	−0.594176	−	0.323576i
$185$	17.1802			1.26311
$186$		0			0
$187$		−	18.2895i		−	1.33746i
$188$	4.03319	+	20.8419i	0.294150	+	1.52005i
$189$		0			0
$190$	−7.40658	+	8.97726i	−0.537330	+	0.651279i
$191$	18.8424			1.36339			0.681693	−	0.731638i	$-0.261244\pi$
$191$	18.8424			1.36339			0.681693	+	0.731638i	$0.261244\pi$
$192$		0			0
$193$	−26.4738			−1.90563			−0.952813	−	0.303558i	$-0.901826\pi$
$193$	−26.4738			−1.90563			−0.952813	+	0.303558i	$0.901826\pi$
$194$	−12.6135	+	15.2884i	−0.905598	+	1.09764i
$195$		0			0
$196$	1.75922	+	9.09094i	0.125658	+	0.649353i
$197$		−	12.8619i		−	0.916375i	−0.888856	−	0.458188i	$-0.848499\pi$
$197$		−	12.8619i		−	0.916375i	0.888856	−	0.458188i	$-0.151501\pi$
$198$		0			0
$199$	−8.29510			−0.588024			−0.294012	−	0.955802i	$-0.594991\pi$
$199$	−8.29510			−0.588024			−0.294012	+	0.955802i	$0.594991\pi$
$200$	−10.9158	−	5.94452i	−0.771863	−	0.420341i
$201$		0			0
$202$	5.78863	+	4.77584i	0.407286	+	0.336027i
$203$			12.9483i			0.908789i
$204$		0			0
$205$			16.3838i			1.14430i
$206$	−11.3709	+	13.7822i	−0.792246	+	0.960253i
$207$		0			0
$208$	−1.49222	−	3.71123i	−0.103467	−	0.257328i
$209$	10.9671			0.758607
$210$		0			0
$211$			8.42146i			0.579757i	0.957063	+	0.289879i	$0.0936149\pi$
$211$			8.42146i			0.579757i	−0.957063	+	0.289879i	$0.906385\pi$
$212$	−4.87216	+	0.942827i	−0.334622	+	0.0647537i
$213$		0			0
$214$	5.95578	+	4.91375i	0.407129	+	0.335897i
$215$	−27.3230			−1.86341
$216$		0			0
$217$	7.92060			0.537685
$218$	17.8410	+	14.7195i	1.20834	+	0.996931i
$219$		0			0
$220$	4.75716	+	24.5831i	0.320728	+	1.65740i
$221$			4.47763i			0.301198i
$222$		0			0
$223$	15.9829			1.07029			0.535147	−	0.844759i	$-0.320256\pi$
$223$	15.9829			1.07029			0.535147	+	0.844759i	$0.320256\pi$
$224$	−2.63619	+	8.30042i	−0.176138	+	0.554595i
$225$		0			0
$226$	−18.0003	+	21.8175i	−1.19736	+	1.45128i
$227$		−	22.0283i		−	1.46207i	−0.682341	−	0.731034i	$-0.739038\pi$
$227$		−	22.0283i		−	1.46207i	0.682341	−	0.731034i	$-0.260962\pi$
$228$		0			0
$229$		−	22.1183i		−	1.46162i	−0.682582	−	0.730809i	$-0.739143\pi$
$229$		−	22.1183i		−	1.46162i	0.682582	−	0.730809i	$-0.260857\pi$
$230$	−10.8489	−	8.95073i	−0.715353	−	0.590193i
$231$		0			0
$232$	11.3770	−	20.8913i	0.746936	−	1.37158i
$233$	18.2955			1.19858			0.599289	−	0.800533i	$-0.295450\pi$
$233$	18.2955			1.19858			0.599289	+	0.800533i	$0.295450\pi$
$234$		0			0
$235$			32.5332i			2.12223i
$236$	6.07308	−	1.17522i	0.395324	−	0.0765003i
$237$		0			0
$238$	6.20421	−	7.51991i	0.402159	−	0.487443i
$239$	14.4015			0.931555			0.465777	−	0.884902i	$-0.345775\pi$
$239$	14.4015			0.931555			0.465777	+	0.884902i	$0.345775\pi$
$240$		0			0
$241$	27.8275			1.79253			0.896263	−	0.443523i	$-0.146271\pi$
$241$	27.8275			1.79253			0.896263	+	0.443523i	$0.146271\pi$
$242$	5.11591	−	6.20082i	0.328863	−	0.398604i
$243$		0			0
$244$	16.6385	−	3.21976i	1.06517	−	0.206124i
$245$			14.1905i			0.906599i
$246$		0			0
$247$	−2.68495			−0.170839
$248$	−12.7795	−	6.95944i	−0.811496	−	0.441925i
$249$		0			0
$250$	2.02458	+	1.67036i	0.128046	+	0.105643i
$251$			11.0370i			0.696647i	0.937374	+	0.348324i	$0.113249\pi$
$251$			11.0370i			0.696647i	−0.937374	+	0.348324i	$0.886751\pi$
$252$		0			0
$253$			13.2535i			0.833240i
$254$	−8.95968	+	10.8597i	−0.562181	+	0.681399i
$255$		0			0
$256$	11.5465	−	11.0760i	0.721658	−	0.692250i
$257$	−15.5226			−0.968271			−0.484135	−	0.874993i	$-0.660866\pi$
$257$	−15.5226			−0.968271			−0.484135	+	0.874993i	$0.660866\pi$
$258$		0			0
$259$		−	8.62949i		−	0.536210i
$260$	−1.16465	−	6.01843i	−0.0722282	−	0.373247i
$261$		0			0
$262$	−14.0591	−	11.5993i	−0.868577	−	0.716609i
$263$	−7.75769			−0.478360			−0.239180	−	0.970975i	$-0.576879\pi$
$263$	−7.75769			−0.478360			−0.239180	+	0.970975i	$0.576879\pi$
$264$		0			0
$265$	−7.60521			−0.467184
$266$	4.50921	+	3.72027i	0.276477	+	0.228104i
$267$		0			0
$268$	−18.3201	+	3.54518i	−1.11908	+	0.216556i
$269$		−	17.3913i		−	1.06037i	−0.847883	−	0.530184i	$-0.822123\pi$
$269$		−	17.3913i		−	1.06037i	0.847883	−	0.530184i	$-0.177877\pi$
$270$		0			0
$271$	11.5240			0.700034			0.350017	−	0.936743i	$-0.386176\pi$
$271$	11.5240			0.700034			0.350017	+	0.936743i	$0.386176\pi$
$272$	−16.6175	+	6.68163i	−1.00759	+	0.405133i
$273$		0			0
$274$	10.1495	−	12.3019i	0.613155	−	0.743184i
$275$			17.9499i			1.08242i
$276$		0			0
$277$			5.37979i			0.323240i	0.986853	+	0.161620i	$0.0516719\pi$
$277$			5.37979i			0.323240i	−0.986853	+	0.161620i	$0.948328\pi$
$278$	−1.04032	−	0.858306i	−0.0623944	−	0.0514778i
$279$		0			0
$280$	−6.38320	+	11.7213i	−0.381469	+	0.700483i
$281$	−11.8348			−0.706006			−0.353003	−	0.935622i	$-0.614839\pi$
$281$	−11.8348			−0.706006			−0.353003	+	0.935622i	$0.614839\pi$
$282$		0			0
$283$		−	4.29013i		−	0.255022i	−0.991837	−	0.127511i	$-0.959301\pi$
$283$		−	4.29013i		−	0.255022i	0.991837	−	0.127511i	$-0.0406988\pi$
$284$	2.86034	+	14.7811i	0.169730	+	0.877097i
$285$		0			0
$286$	−3.67620	+	4.45580i	−0.217379	+	0.263477i
$287$	8.22948			0.485771
$288$		0			0
$289$	3.04917			0.179363
$290$	23.2007	−	28.1207i	1.36239	−	1.65130i
$291$		0			0
$292$	2.12985	+	11.0062i	0.124640	+	0.644091i
$293$			1.85244i			0.108221i	0.998535	+	0.0541103i	$0.0172322\pi$
$293$			1.85244i			0.108221i	−0.998535	+	0.0541103i	$0.982768\pi$
$294$		0			0
$295$	9.47978			0.551934
$296$	−7.58230	+	13.9232i	−0.440712	+	0.809270i
$297$		0			0
$298$	5.84508	+	4.82242i	0.338597	+	0.279355i
$299$		−	3.24471i		−	0.187647i
$300$		0			0
$301$			13.7241i			0.791045i
$302$	6.21854	−	7.53728i	0.357837	−	0.433722i
$303$		0			0
$304$	−4.00655	−	9.96448i	−0.229791	−	0.571502i
$305$	25.9719			1.48714
$306$		0			0
$307$		−	24.1569i		−	1.37871i	−0.724424	−	0.689354i	$-0.757894\pi$
$307$		−	24.1569i		−	1.37871i	0.724424	−	0.689354i	$-0.242106\pi$
$308$	12.3479	−	2.38949i	0.703588	−	0.136154i
$309$		0			0
$310$	−17.2018	−	14.1921i	−0.976994	−	0.806058i
$311$	−23.8271			−1.35111			−0.675557	−	0.737308i	$-0.736097\pi$
$311$	−23.8271			−1.35111			−0.675557	+	0.737308i	$0.736097\pi$
$312$		0			0
$313$	34.8419			1.96938			0.984690	−	0.174316i	$-0.0557715\pi$
$313$	34.8419			1.96938			0.984690	+	0.174316i	$0.0557715\pi$
$314$	5.47095	+	4.51374i	0.308743	+	0.254725i
$315$		0			0
$316$	4.32193	+	22.3341i	0.243128	+	1.25639i
$317$		−	24.0822i		−	1.35259i	−0.736631	−	0.676295i	$-0.763585\pi$
$317$		−	24.0822i		−	1.35259i	0.736631	−	0.676295i	$-0.236415\pi$
$318$		0			0
$319$	−34.3536			−1.92343
$320$	20.5979	−	13.3031i	1.15146	−	0.743667i
$321$		0			0
$322$	−4.49588	+	5.44930i	−0.250546	+	0.303678i
$323$			12.0222i			0.668933i
$324$		0			0
$325$		−	4.39448i		−	0.243762i
$326$	−25.6224	−	21.1395i	−1.41910	−	1.17081i
$327$		0			0
$328$	−13.2778	−	7.23084i	−0.733145	−	0.399256i
$329$	16.3412			0.900919
$330$		0			0
$331$		−	18.9047i		−	1.03910i	−0.854441	−	0.519549i	$-0.826100\pi$
$331$		−	18.9047i		−	1.03910i	0.854441	−	0.519549i	$-0.173900\pi$
$332$	8.77034	−	1.69718i	0.481335	−	0.0931446i
$333$		0			0
$334$	18.9574	−	22.9775i	1.03730	−	1.25728i
$335$	−28.5968			−1.56241
$336$		0			0
$337$	19.0547			1.03798			0.518989	−	0.854781i	$-0.326309\pi$
$337$	19.0547			1.03798			0.518989	+	0.854781i	$0.326309\pi$
$338$	0.900006	−	1.09087i	0.0489539	−	0.0593353i
$339$		0			0
$340$	−26.9483	+	5.21485i	−1.46148	+	0.282815i
$341$			21.0145i			1.13800i
$342$		0			0
$343$	17.9046			0.966758
$344$	12.0587	−	22.1431i	0.650162	−	1.19388i
$345$		0			0
$346$	3.09873	+	2.55657i	0.166589	+	0.137442i
$347$		−	5.85643i		−	0.314390i	−0.987568	−	0.157195i	$-0.949755\pi$
$347$		−	5.85643i		−	0.314390i	0.987568	−	0.157195i	$-0.0502451\pi$
$348$		0			0
$349$			36.7471i			1.96703i	0.180833	+	0.983514i	$0.442121\pi$
$349$			36.7471i			1.96703i	−0.180833	+	0.983514i	$0.557879\pi$
$350$	−6.08900	+	7.38026i	−0.325471	+	0.394492i
$351$		0			0
$352$	−22.0222	−	6.99421i	−1.17379	−	0.372792i
$353$	−4.29572			−0.228638			−0.114319	−	0.993444i	$-0.536469\pi$
$353$	−4.29572			−0.228638			−0.114319	+	0.993444i	$0.536469\pi$
$354$		0			0
$355$			23.0726i			1.22457i
$356$	−2.24302	−	11.5910i	−0.118880	−	0.614324i
$357$		0			0
$358$	−6.56103	−	5.41310i	−0.346761	−	0.286091i
$359$	−2.76866			−0.146124			−0.0730621	−	0.997327i	$-0.523277\pi$
$359$	−2.76866			−0.146124			−0.0730621	+	0.997327i	$0.523277\pi$
$360$		0			0
$361$	11.7911			0.620582
$362$	−3.60644	−	2.97545i	−0.189550	−	0.156386i
$363$		0			0
$364$	−3.02301	+	0.584993i	−0.158449	+	0.0306619i
$365$			17.1802i			0.899253i
$366$		0			0
$367$	−8.47535			−0.442410			−0.221205	−	0.975227i	$-0.570999\pi$
$367$	−8.47535			−0.442410			−0.221205	+	0.975227i	$0.570999\pi$
$368$	12.0419	−	4.84184i	0.627727	−	0.252398i
$369$		0			0
$370$	−15.4623	+	18.7413i	−0.803846	+	0.974314i
$371$			3.82004i			0.198327i
$372$		0			0
$373$		−	1.08038i		−	0.0559400i	−0.999609	−	0.0279700i	$-0.991096\pi$
$373$		−	1.08038i		−	0.0559400i	0.999609	−	0.0279700i	$-0.00890429\pi$
$374$	19.9514	+	16.4607i	1.03166	+	0.851162i
$375$		0			0
$376$	−26.3656	−	14.3582i	−1.35970	−	0.740468i
$377$	8.41043			0.433159
$378$		0			0
$379$		−	28.8581i		−	1.48234i	−0.671318	−	0.741170i	$-0.734271\pi$
$379$		−	28.8581i		−	1.48234i	0.671318	−	0.741170i	$-0.265729\pi$
$380$	−3.12701	−	16.1592i	−0.160412	−	0.828949i
$381$		0			0
$382$	−16.9583	+	20.5545i	−0.867660	+	1.05166i
$383$	30.8123			1.57444			0.787218	−	0.616675i	$-0.211521\pi$
$383$	30.8123			1.57444			0.787218	+	0.616675i	$0.211521\pi$
$384$		0			0
$385$	19.2745			0.982320
$386$	23.8266	−	28.8794i	1.21274	−	1.46992i
$387$		0			0
$388$	−5.32535	−	27.5193i	−0.270354	−	1.39708i
$389$			14.4458i			0.732429i	0.930530	+	0.366214i	$0.119346\pi$
$389$			14.4458i			0.732429i	−0.930530	+	0.366214i	$0.880654\pi$
$390$		0			0
$391$	−14.5286			−0.734744
$392$	−11.5003	−	6.26283i	−0.580853	−	0.316321i
$393$		0			0
$394$	14.0306	+	11.5758i	0.706854	+	0.583182i
$395$			34.8624i			1.75412i
$396$		0			0
$397$		−	19.3194i		−	0.969615i	−0.874621	−	0.484808i	$-0.838890\pi$
$397$		−	19.3194i		−	0.969615i	0.874621	−	0.484808i	$-0.161110\pi$
$398$	7.46565	−	9.04885i	0.374219	−	0.453578i
$399$		0			0
$400$	16.3090	−	6.55755i	0.815448	−	0.327878i
$401$	−17.0808			−0.852972			−0.426486	−	0.904494i	$-0.640249\pi$
$401$	−17.0808			−0.852972			−0.426486	+	0.904494i	$0.640249\pi$
$402$		0			0
$403$		−	5.14476i		−	0.256279i
$404$	−10.4196	+	2.01633i	−0.518395	+	0.100316i
$405$		0			0
$406$	−14.1248	−	11.6535i	−0.701003	−	0.578354i
$407$	22.8953			1.13488
$408$		0			0
$409$	2.17373			0.107484			0.0537420	−	0.998555i	$-0.482885\pi$
$409$	2.17373			0.107484			0.0537420	+	0.998555i	$0.482885\pi$
$410$	−17.8726	−	14.7456i	−0.882664	−	0.728231i
$411$		0			0
$412$	−4.80071	−	24.8082i	−0.236514	−	1.22221i
$413$		−	4.76162i		−	0.234304i
$414$		0			0
$415$	13.6901			0.672019
$416$	5.39147	+	1.71232i	0.264339	+	0.0839533i
$417$		0			0
$418$	−9.87042	+	11.9636i	−0.482778	+	0.585158i
$419$		−	14.0890i		−	0.688295i	−0.938916	−	0.344147i	$-0.888168\pi$
$419$		−	14.0890i		−	0.688295i	0.938916	−	0.344147i	$-0.111832\pi$
$420$		0			0
$421$			26.8194i			1.30710i	0.756884	+	0.653549i	$0.226721\pi$
$421$			26.8194i			1.30710i	−0.756884	+	0.653549i	$0.773279\pi$
$422$	−9.18668	−	7.57937i	−0.447201	−	0.368958i
$423$		0			0
$424$	3.35648	−	6.16343i	0.163005	−	0.299323i
$425$	−19.6769			−0.954468
$426$		0			0
$427$		−	13.0455i		−	0.631314i
$428$	−10.7205	+	2.07455i	−0.518194	+	0.100277i
$429$		0			0
$430$	24.5909	−	29.8057i	1.18588	−	1.43736i
$431$	10.6793			0.514405			0.257203	−	0.966357i	$-0.417199\pi$
$431$	10.6793			0.514405			0.257203	+	0.966357i	$0.417199\pi$
$432$		0			0
$433$	25.6827			1.23423			0.617116	−	0.786872i	$-0.288301\pi$
$433$	25.6827			1.23423			0.617116	+	0.786872i	$0.288301\pi$
$434$	−7.12859	+	8.64031i	−0.342183	+	0.414748i
$435$		0			0
$436$	−32.1140	+	6.21448i	−1.53798	+	0.297620i
$437$		−	8.71189i		−	0.416746i
$438$		0			0
$439$	39.1318			1.86766			0.933828	−	0.357722i	$-0.116446\pi$
$439$	39.1318			1.86766			0.933828	+	0.357722i	$0.116446\pi$
$440$	−31.0984	−	16.9356i	−1.48256	−	0.807371i
$441$		0			0
$442$	−4.88449	−	4.02990i	−0.232332	−	0.191683i
$443$		−	28.0513i		−	1.33276i	−0.745614	−	0.666378i	$-0.767844\pi$
$443$		−	28.0513i		−	1.33276i	0.745614	−	0.666378i	$-0.232156\pi$
$444$		0			0
$445$		−	18.0930i		−	0.857692i
$446$	−14.3847	+	17.4352i	−0.681135	+	0.825580i
$447$		0			0
$448$	−6.68206	−	10.3462i	−0.315698	−	0.488811i
$449$	−24.1923			−1.14171			−0.570853	−	0.821052i	$-0.693387\pi$
$449$	−24.1923			−1.14171			−0.570853	+	0.821052i	$0.693387\pi$
$450$		0			0
$451$			21.8340i			1.02812i
$452$	−7.59961	−	39.2718i	−0.357456	−	1.84719i
$453$		0			0
$454$	24.0299	+	19.8256i	1.12778	+	0.930461i
$455$	−4.71878			−0.221220
$456$		0			0
$457$	−4.64631			−0.217345			−0.108673	−	0.994078i	$-0.534660\pi$
$457$	−4.64631			−0.217345			−0.108673	+	0.994078i	$0.534660\pi$
$458$	24.1281	+	19.9066i	1.12743	+	0.930175i
$459$		0			0
$460$	19.5281	−	3.77894i	0.910502	−	0.176194i
$461$		−	8.95432i		−	0.417044i	−0.978018	−	0.208522i	$-0.933135\pi$
$461$		−	8.95432i		−	0.417044i	0.978018	−	0.208522i	$-0.0668653\pi$
$462$		0			0
$463$	1.07881			0.0501365			0.0250682	−	0.999686i	$-0.492020\pi$
$463$	1.07881			0.0501365			0.0250682	+	0.999686i	$0.492020\pi$
$464$	12.5503	+	31.2131i	0.582631	+	1.44903i
$465$		0			0
$466$	−16.4661	+	19.9579i	−0.762775	+	0.924533i
$467$		−	22.8953i		−	1.05947i	−0.848164	−	0.529734i	$-0.822292\pi$
$467$		−	22.8953i		−	1.05947i	0.848164	−	0.529734i	$-0.177708\pi$
$468$		0			0
$469$			14.3639i			0.663265i
$470$	−35.4894	−	29.2801i	−1.63700	−	1.35059i
$471$		0			0
$472$	−4.18380	+	7.68262i	−0.192575	+	0.353621i
$473$	−36.4121			−1.67423
$474$		0			0
$475$		−	11.7990i		−	0.541373i
$476$	2.61938	+	13.5359i	0.120059	+	0.620418i
$477$		0			0
$478$	−12.9614	+	15.7101i	−0.592842	+	0.718563i
$479$	−9.79548			−0.447567			−0.223783	−	0.974639i	$-0.571841\pi$
$479$	−9.79548			−0.447567			−0.223783	+	0.974639i	$0.571841\pi$
$480$		0			0
$481$	−5.60521			−0.255576
$482$	−25.0449	+	30.3561i	−1.14076	+	1.38268i
$483$		0			0
$484$	2.15991	+	11.1615i	0.0981775	+	0.507343i
$485$		−	42.9563i		−	1.95055i
$486$		0			0
$487$	38.1722			1.72975			0.864874	−	0.501989i	$-0.167398\pi$
$487$	38.1722			1.72975			0.864874	+	0.501989i	$0.167398\pi$
$488$	−11.4624	+	21.0482i	−0.518879	+	0.952805i
$489$		0			0
$490$	−15.4799	−	12.7716i	−0.699313	−	0.576960i
$491$		−	36.8387i		−	1.66251i	−0.555893	−	0.831254i	$-0.687623\pi$
$491$		−	36.8387i		−	1.66251i	0.555893	−	0.831254i	$-0.312377\pi$
$492$		0			0
$493$		−	37.6588i		−	1.69607i
$494$	2.41647	−	2.92892i	0.108722	−	0.131778i
$495$		0			0
$496$	19.0934	−	7.67714i	0.857319	−	0.344714i
$497$	11.5892			0.519846
$498$		0			0
$499$			9.44767i			0.422936i	0.977385	+	0.211468i	$0.0678244\pi$
$499$			9.44767i			0.422936i	−0.977385	+	0.211468i	$0.932176\pi$
$500$	−3.64428	+	0.705215i	−0.162977	+	0.0315382i
$501$		0			0
$502$	−12.0399	−	9.93334i	−0.537365	−	0.443347i
$503$	−3.12104			−0.139160			−0.0695802	−	0.997576i	$-0.522166\pi$
$503$	−3.12104			−0.139160			−0.0695802	+	0.997576i	$0.522166\pi$
$504$		0			0
$505$	−16.2645			−0.723760
$506$	−14.4578	−	11.9282i	−0.642727	−	0.530274i
$507$		0			0
$508$	−3.78272	−	19.5476i	−0.167831	−	0.867286i
$509$			1.82216i			0.0807658i	0.999184	+	0.0403829i	$0.0128578\pi$
$509$			1.82216i			0.0807658i	−0.999184	+	0.0403829i	$0.987142\pi$
$510$		0			0
$511$	8.62949			0.381746
$512$	1.69047	+	22.5642i	0.0747091	+	0.997205i
$513$		0			0
$514$	13.9704	−	16.9330i	0.616208	−	0.746884i
$515$		−	38.7244i		−	1.70640i
$516$		0			0
$517$			43.3556i			1.90678i
$518$	9.41361	+	7.76659i	0.413610	+	0.341245i
$519$		0			0
$520$	7.61349	+	4.14616i	0.333874	+	0.181821i
$521$	8.67898			0.380233			0.190117	−	0.981762i	$-0.439113\pi$
$521$	8.67898			0.380233			0.190117	+	0.981762i	$0.439113\pi$
$522$		0			0
$523$		−	11.8477i		−	0.518064i	−0.965869	−	0.259032i	$-0.916596\pi$
$523$		−	11.8477i		−	0.518064i	0.965869	−	0.259032i	$-0.0834036\pi$
$524$	25.3066	−	4.89717i	1.10553	−	0.213934i
$525$		0			0
$526$	6.98197	−	8.46260i	0.304429	−	0.368987i
$527$	−23.0363			−1.00348
$528$		0			0
$529$	−12.4718			−0.542254
$530$	6.84474	−	8.29627i	0.297316	−	0.360367i
$531$		0			0
$532$	−8.11663	+	1.57067i	−0.351901	+	0.0680974i
$533$		−	5.34539i		−	0.231535i
$534$		0			0
$535$	−16.7341			−0.723480
$536$	12.6209	−	23.1754i	0.545139	−	1.00103i
$537$		0			0
$538$	18.9716	+	15.6523i	0.817924	+	0.674819i
$539$			18.9111i			0.814557i
$540$		0			0
$541$		−	12.0878i		−	0.519696i	−0.965649	−	0.259848i	$-0.916327\pi$
$541$		−	12.0878i		−	0.519696i	0.965649	−	0.259848i	$-0.0836725\pi$
$542$	−10.3717	+	12.5711i	−0.445502	+	0.539977i
$543$		0			0
$544$	7.66712	−	24.1410i	0.328725	−	1.03504i
$545$	−50.1284			−2.14727
$546$		0			0
$547$			45.8603i			1.96084i	0.196911	+	0.980421i	$0.436909\pi$
$547$			45.8603i			1.96084i	−0.196911	+	0.980421i	$0.563091\pi$
$548$	4.28507	+	22.1436i	0.183049	+	0.945926i
$549$		0			0
$550$	−19.5809	−	16.1550i	−0.834933	−	0.688852i
$551$	22.5816			0.962008
$552$		0			0
$553$	17.5111			0.744648
$554$	−5.86863	−	4.84184i	−0.249334	−	0.205710i
$555$		0			0
$556$	1.87259	−	0.362372i	0.0794157	−	0.0153680i
$557$			23.1714i			0.981804i	0.871215	+	0.490902i	$0.163333\pi$
$557$			23.1714i			0.981804i	−0.871215	+	0.490902i	$0.836667\pi$
$558$		0			0
$559$	8.91439			0.377038
$560$	−7.04148	−	17.5125i	−0.297557	−	0.740038i
$561$		0			0
$562$	10.6514	−	12.9102i	0.449303	−	0.544584i
$563$		−	30.8773i		−	1.30132i	−0.759368	−	0.650662i	$-0.774492\pi$
$563$		−	30.8773i		−	1.30132i	0.759368	−	0.650662i	$-0.225508\pi$
$564$		0			0
$565$		−	61.3014i		−	2.57897i
$566$	4.67996	+	3.86115i	0.196713	+	0.162296i
$567$		0			0
$568$	−18.6985	−	10.1828i	−0.784572	−	0.427262i
$569$	12.3484			0.517673			0.258836	−	0.965921i	$-0.416661\pi$
$569$	12.3484			0.517673			0.258836	+	0.965921i	$0.416661\pi$
$570$		0			0
$571$		−	28.6787i		−	1.20016i	−0.799938	−	0.600082i	$-0.795135\pi$
$571$		−	28.6787i		−	1.20016i	0.799938	−	0.600082i	$-0.204865\pi$
$572$	−1.55207	−	8.02049i	−0.0648953	−	0.335354i
$573$		0			0
$574$	−7.40658	+	8.97726i	−0.309145	+	0.374704i
$575$	14.2588			0.594634
$576$		0			0
$577$	2.40971			0.100318			0.0501588	−	0.998741i	$-0.484027\pi$
$577$	2.40971			0.100318			0.0501588	+	0.998741i	$0.484027\pi$
$578$	−2.74427	+	3.32623i	−0.114147	+	0.138353i
$579$		0			0
$580$	9.79517	+	50.6176i	0.406722	+	2.10178i
$581$		−	6.87642i		−	0.285282i
$582$		0			0
$583$	−10.1351			−0.419754
$584$	−13.9232	−	7.58230i	−0.576147	−	0.313758i
$585$		0			0
$586$	−2.02076	−	1.66720i	−0.0834768	−	0.0688716i
$587$		−	2.78354i		−	0.114889i	−0.998349	−	0.0574444i	$-0.981705\pi$
$587$		−	2.78354i		−	0.114889i	0.998349	−	0.0574444i	$-0.0182952\pi$
$588$		0			0
$589$		−	13.8134i		−	0.569172i
$590$	−8.53187	+	10.3412i	−0.351251	+	0.425739i
$591$		0			0
$592$	−8.36424	−	20.8023i	−0.343768	−	0.854967i
$593$	1.14404			0.0469799			0.0234900	−	0.999724i	$-0.492522\pi$
$593$	1.14404			0.0469799			0.0234900	+	0.999724i	$0.492522\pi$
$594$		0			0
$595$			21.1289i			0.866202i
$596$	−10.5212	+	2.03599i	−0.430966	+	0.0833976i
$597$		0			0
$598$	3.53955	+	2.92026i	0.144743	+	0.119418i
$599$	2.31285			0.0945005			0.0472503	−	0.998883i	$-0.484954\pi$
$599$	2.31285			0.0945005			0.0472503	+	0.998883i	$0.484954\pi$
$600$		0			0
$601$	17.9439			0.731947			0.365973	−	0.930625i	$-0.380736\pi$
$601$	17.9439			0.731947			0.365973	+	0.930625i	$0.380736\pi$
$602$	−14.9712	−	12.3518i	−0.610180	−	0.503422i
$603$		0			0
$604$	2.62543	+	13.5672i	0.106827	+	0.552041i
$605$			17.4226i			0.708331i
$606$		0			0
$607$	−5.60428			−0.227471			−0.113735	−	0.993511i	$-0.536282\pi$
$607$	−5.60428			−0.227471			−0.113735	+	0.993511i	$0.536282\pi$
$608$	14.4758	+	4.59749i	0.587072	+	0.186453i
$609$		0			0
$610$	−23.3748	+	28.3318i	−0.946420	+	1.14712i
$611$		−	10.6143i		−	0.429408i
$612$		0			0
$613$			2.81625i			0.113747i	0.998381	+	0.0568736i	$0.0181132\pi$
$613$			2.81625i			0.113747i	−0.998381	+	0.0568736i	$0.981887\pi$
$614$	26.3520	+	21.7414i	1.06348	+	0.877411i
$615$		0			0
$616$	−8.50660	+	15.6205i	−0.342741	+	0.629367i
$617$	30.2020			1.21589			0.607943	−	0.793981i	$-0.291995\pi$
$617$	30.2020			1.21589			0.607943	+	0.793981i	$0.291995\pi$
$618$		0			0
$619$		−	21.4184i		−	0.860879i	−0.902619	−	0.430440i	$-0.858359\pi$
$619$		−	21.4184i		−	0.860879i	0.902619	−	0.430440i	$-0.141641\pi$
$620$	30.9634	−	5.99182i	1.24352	−	0.240637i
$621$		0			0
$622$	21.4446	−	25.9922i	0.859850	−	1.04219i
$623$	−9.08800			−0.364103
$624$		0			0
$625$	−27.6609			−1.10644
$626$	−31.3579	+	38.0078i	−1.25331	+	1.51910i
$627$		0			0
$628$	−9.84777	+	1.90567i	−0.392969	+	0.0760446i
$629$			25.0981i			1.00073i
$630$		0			0
$631$	−11.8944			−0.473510			−0.236755	−	0.971569i	$-0.576084\pi$
$631$	−11.8944			−0.473510			−0.236755	+	0.971569i	$0.576084\pi$
$632$	−28.2532	−	15.3862i	−1.12385	−	0.612028i
$633$		0			0
$634$	26.2704	+	21.6741i	1.04333	+	0.860789i
$635$		−	30.5129i		−	1.21087i
$636$		0			0
$637$		−	4.62979i		−	0.183439i
$638$	30.9185	−	37.4752i	1.22407	−	1.48366i
$639$		0			0
$640$	−4.02632	+	34.4424i	−0.159154	+	1.36146i
$641$	−12.0823			−0.477224			−0.238612	−	0.971115i	$-0.576692\pi$
$641$	−12.0823			−0.477224			−0.238612	+	0.971115i	$0.576692\pi$
$642$		0			0
$643$			8.29078i			0.326956i	0.986547	+	0.163478i	$0.0522713\pi$
$643$			8.29078i			0.326956i	−0.986547	+	0.163478i	$0.947729\pi$
$644$	−1.89813	−	9.80881i	−0.0747969	−	0.386521i
$645$		0			0
$646$	−13.1146	−	10.8201i	−0.515988	−	0.425710i
$647$	31.3814			1.23373			0.616865	−	0.787069i	$-0.288402\pi$
$647$	31.3814			1.23373			0.616865	+	0.787069i	$0.288402\pi$
$648$		0			0
$649$	12.6333			0.495900
$650$	4.79379	+	3.95506i	0.188028	+	0.155130i
$651$		0			0
$652$	46.1207	−	8.92496i	1.80623	−	0.349529i
$653$		−	1.52441i		−	0.0596546i	−0.999555	−	0.0298273i	$-0.990504\pi$
$653$		−	1.52441i		−	0.0596546i	0.999555	−	0.0298273i	$-0.00949574\pi$
$654$		0			0
$655$	39.5024			1.54349
$656$	19.8380	−	7.97652i	0.774544	−	0.311431i
$657$		0			0
$658$	−14.7072	+	17.8261i	−0.573346	+	0.694932i
$659$			32.1348i			1.25179i	0.779906	+	0.625897i	$0.215267\pi$
$659$			32.1348i			1.25179i	−0.779906	+	0.625897i	$0.784733\pi$
$660$		0			0
$661$			45.2896i			1.76156i	0.473525	+	0.880780i	$0.342981\pi$
$661$			45.2896i			1.76156i	−0.473525	+	0.880780i	$0.657019\pi$
$662$	20.6225	+	17.0144i	0.801517	+	0.661282i
$663$		0			0
$664$	−6.04197	+	11.0947i	−0.234474	+	0.430559i
$665$	−12.6697			−0.491309
$666$		0			0
$667$			27.2894i			1.05665i
$668$	8.00368	+	41.3599i	0.309672	+	1.60026i
$669$		0			0
$670$	25.7373	−	31.1952i	0.994318	−	1.20518i
$671$	34.6115			1.33616
$672$		0			0
$673$	−31.6596			−1.22039			−0.610195	−	0.792251i	$-0.708909\pi$
$673$	−31.6596			−1.22039			−0.610195	+	0.792251i	$0.708909\pi$
$674$	−17.1494	+	20.7862i	−0.660570	+	0.800653i
$675$		0			0
$676$	0.379977	+	1.96357i	0.0146145	+	0.0755220i
$677$		−	39.5883i		−	1.52150i	−0.649043	−	0.760752i	$-0.724830\pi$
$677$		−	39.5883i		−	1.52150i	0.649043	−	0.760752i	$-0.275170\pi$
$678$		0			0
$679$	−21.5766			−0.828035
$680$	18.5649	−	34.0904i	0.711933	−	1.30731i
$681$		0			0
$682$	−22.9240	−	18.9132i	−0.877805	−	0.724223i
$683$			25.6951i			0.983196i	0.870822	+	0.491598i	$0.163587\pi$
$683$			25.6951i			0.983196i	−0.870822	+	0.491598i	$0.836413\pi$
$684$		0			0
$685$			34.5650i			1.32066i
$686$	−16.1143	+	19.5315i	−0.615246	+	0.745718i
$687$		0			0
$688$	13.3023	+	33.0834i	0.507144	+	1.26129i
$689$	2.48127			0.0945290
$690$		0			0
$691$			33.9215i			1.29043i	0.764000	+	0.645217i	$0.223233\pi$
$691$			33.9215i			1.29043i	−0.764000	+	0.645217i	$0.776767\pi$
$692$	−5.57776	+	1.07937i	−0.212035	+	0.0410315i
$693$		0			0
$694$	6.38859	+	5.27083i	0.242507	+	0.200078i
$695$	2.92303			0.110877
$696$		0			0
$697$	−23.9347			−0.906591
$698$	−40.0862	−	33.0726i	−1.51728	−	1.25182i
$699$		0			0
$700$	−2.57074	−	13.2846i	−0.0971648	−	0.502110i
$701$			38.5695i			1.45675i	0.685179	+	0.728375i	$0.259724\pi$
$701$			38.5695i			1.45675i	−0.685179	+	0.728375i	$0.740276\pi$
$702$		0			0
$703$	−15.0497			−0.567610
$704$	27.4499	−	17.7285i	1.03456	−	0.668167i
$705$		0			0
$706$	3.86617	−	4.68605i	0.145505	−	0.176362i
$707$			8.16953i			0.307247i
$708$		0			0
$709$		−	0.628816i		−	0.0236157i	−0.999930	−	0.0118078i	$-0.996241\pi$
$709$		−	0.628816i		−	0.0236157i	0.999930	−	0.0118078i	$-0.00375864\pi$
$710$	−25.1691	−	20.7655i	−0.944579	−	0.779314i
$711$		0			0
$712$	14.6630	+	7.98517i	0.549519	+	0.299257i
$713$	16.6933			0.625168
$714$		0			0
$715$		−	12.5196i		−	0.468206i
$716$	11.8099	−	2.28538i	0.441358	−	0.0854086i
$717$		0			0
$718$	2.49181	−	3.02024i	0.0929936	−	0.112714i
$719$	−14.6658			−0.546942			−0.273471	−	0.961880i	$-0.588172\pi$
$719$	−14.6658			−0.546942			−0.273471	+	0.961880i	$0.588172\pi$
$720$		0			0
$721$	−19.4510			−0.724392
$722$	−10.6120	+	12.8625i	−0.394939	+	0.478691i
$723$		0			0
$724$	6.49164	−	1.25622i	0.241260	−	0.0466870i
$725$			36.9595i			1.37264i
$726$		0			0
$727$	−25.6145			−0.949991			−0.474996	−	0.879988i	$-0.657550\pi$
$727$	−25.6145			−0.949991			−0.474996	+	0.879988i	$0.657550\pi$
$728$	2.08258	−	3.82420i	0.0771856	−	0.141734i
$729$		0			0
$730$	−18.7413	−	15.4623i	−0.693647	−	0.572285i
$731$		−	39.9153i		−	1.47632i
$732$		0			0
$733$		−	3.38122i		−	0.124888i	−0.998048	−	0.0624440i	$-0.980111\pi$
$733$		−	3.38122i		−	0.124888i	0.998048	−	0.0624440i	$-0.0198895\pi$
$734$	7.62787	−	9.24547i	0.281550	−	0.341257i
$735$		0			0
$736$	−5.55598	+	17.4938i	−0.204796	+	0.644829i
$737$	−38.1096			−1.40379
$738$		0			0
$739$			23.7865i			0.875000i	0.899218	+	0.437500i	$0.144136\pi$
$739$			23.7865i			0.875000i	−0.899218	+	0.437500i	$0.855864\pi$
$740$	−6.52808	−	33.7346i	−0.239977	−	1.24011i
$741$		0			0
$742$	−4.16715	−	3.43806i	−0.152981	−	0.126215i
$743$	39.6656			1.45519			0.727595	−	0.686007i	$-0.240638\pi$
$743$	39.6656			1.45519			0.727595	+	0.686007i	$0.240638\pi$
$744$		0			0
$745$	−16.4231			−0.601697
$746$	1.17855	+	0.972349i	0.0431498	+	0.0356002i
$747$		0			0
$748$	−35.9128	+	6.94960i	−1.31310	+	0.254102i
$749$			8.40543i			0.307128i
$750$		0			0
$751$	−11.4232			−0.416837			−0.208419	−	0.978040i	$-0.566832\pi$
$751$	−11.4232			−0.416837			−0.208419	+	0.978040i	$0.566832\pi$
$752$	39.3921	−	15.8389i	1.43648	−	0.577585i
$753$		0			0
$754$	−7.56944	+	9.17465i	−0.275663	+	0.334121i
$755$			21.1777i			0.770737i
$756$		0			0
$757$		−	45.1067i		−	1.63943i	−0.572772	−	0.819715i	$-0.694132\pi$
$757$		−	45.1067i		−	1.63943i	0.572772	−	0.819715i	$-0.305868\pi$
$758$	31.4803	+	25.9724i	1.14342	+	0.943362i
$759$		0			0
$760$	20.4418	+	11.1322i	0.741503	+	0.403808i
$761$	−38.2864			−1.38788			−0.693941	−	0.720032i	$-0.744127\pi$
$761$	−38.2864			−1.38788			−0.693941	+	0.720032i	$0.744127\pi$
$762$		0			0
$763$			25.1791i			0.911546i
$764$	−7.15967	−	36.9984i	−0.259028	−	1.33855i
$765$		0			0
$766$	−27.7313	+	33.6121i	−1.00197	+	1.21445i
$767$	−3.09287			−0.111677
$768$		0			0
$769$	13.0069			0.469039			0.234520	−	0.972111i	$-0.424648\pi$
$769$	13.0069			0.469039			0.234520	+	0.972111i	$0.424648\pi$
$770$	−17.3472	+	21.0259i	−0.625149	+	0.757721i
$771$		0			0
$772$	10.0594	+	51.9832i	0.362047	+	1.87092i
$773$			43.3238i			1.55825i	0.626869	+	0.779124i	$0.284336\pi$
$773$			43.3238i			1.55825i	−0.626869	+	0.779124i	$0.715664\pi$
$774$		0			0
$775$	22.6085			0.812123
$776$	34.8127	+	18.9583i	1.24970	+	0.680564i
$777$		0			0
$778$	−15.7584	−	13.0013i	−0.564965	−	0.466118i
$779$		−	14.3521i		−	0.514217i
$780$		0			0
$781$			30.7478i			1.10024i
$782$	13.0759	−	15.8488i	0.467592	−	0.566751i
$783$		0			0
$784$	17.1823	−	6.90870i	0.613652	−	0.246739i
$785$	−15.3719			−0.548647
$786$		0			0
$787$		−	12.0517i		−	0.429597i	−0.976658	−	0.214798i	$-0.931091\pi$
$787$		−	12.0517i		−	0.429597i	0.976658	−	0.214798i	$-0.0689094\pi$
$788$	−25.2553	+	4.88724i	−0.899684	+	0.174101i
$789$		0			0
$790$	−38.0302	−	31.3764i	−1.35305	−	1.11632i
$791$	−30.7912			−1.09481
$792$		0			0
$793$	−8.47358			−0.300905
$794$	21.0749	+	17.3876i	0.747921	+	0.617064i
$795$		0			0
$796$	3.15195	+	16.2880i	0.111718	+	0.577314i
$797$			28.0211i			0.992558i	0.868163	+	0.496279i	$0.165301\pi$
$797$			28.0211i			0.992558i	−0.868163	+	0.496279i	$0.834699\pi$
$798$		0			0
$799$	−47.5269			−1.68138
$800$	−7.52475	+	23.6927i	−0.266040	+	0.837664i
$801$		0			0
$802$	15.3728	−	18.6328i	0.542832	−	0.657947i
$803$			22.8953i			0.807957i
$804$		0			0
$805$		−	15.3111i		−	0.539644i
$806$	5.61224	+	4.63032i	0.197683	+	0.163096i
$807$		0			0
$808$	7.17816	−	13.1811i	0.252527	−	0.463709i
$809$	35.2588			1.23963			0.619817	−	0.784746i	$-0.287207\pi$
$809$	35.2588			1.23963			0.619817	+	0.784746i	$0.287207\pi$
$810$		0			0
$811$		−	46.3530i		−	1.62767i	−0.581094	−	0.813836i	$-0.697375\pi$
$811$		−	46.3530i		−	1.62767i	0.581094	−	0.813836i	$-0.302625\pi$
$812$	25.4248	−	4.92004i	0.892237	−	0.172660i
$813$		0			0
$814$	−20.6059	+	24.9757i	−0.722237	+	0.875397i
$815$	71.9922			2.52178
$816$		0			0
$817$	23.9347			0.837368
$818$	−1.95637	+	2.37125i	−0.0684029	+	0.0829087i
$819$		0			0
$820$	32.1709	−	6.22548i	1.12346	−	0.217403i
$821$		−	23.1380i		−	0.807520i	−0.914865	−	0.403760i	$-0.867703\pi$
$821$		−	23.1380i		−	0.807520i	0.914865	−	0.403760i	$-0.132297\pi$
$822$		0			0
$823$	8.31783			0.289941			0.144971	−	0.989436i	$-0.453691\pi$
$823$	8.31783			0.289941			0.144971	+	0.989436i	$0.453691\pi$
$824$	31.3831	+	17.0906i	1.09328	+	0.595379i
$825$		0			0
$826$	5.19429	+	4.28549i	0.180733	+	0.149111i
$827$			35.6621i			1.24009i	0.784565	+	0.620046i	$0.212886\pi$
$827$			35.6621i			1.24009i	−0.784565	+	0.620046i	$0.787114\pi$
$828$		0			0
$829$		−	6.05505i		−	0.210301i	−0.994456	−	0.105150i	$-0.966468\pi$
$829$		−	6.05505i		−	0.210301i	0.994456	−	0.105150i	$-0.0335324\pi$
$830$	−12.3212	+	14.9340i	−0.427673	+	0.518368i
$831$		0			0
$832$	−6.72027	+	4.34028i	−0.232983	+	0.150472i
$833$	−20.7305			−0.718269
$834$		0			0
$835$			64.5608i			2.23422i
$836$	−4.16723	−	21.5346i	−0.144127	−	0.744790i
$837$		0			0
$838$	15.3693	+	12.6802i	0.530922	+	0.438031i
$839$	45.5223			1.57160			0.785802	−	0.618478i	$-0.212251\pi$
$839$	45.5223			1.57160			0.785802	+	0.618478i	$0.212251\pi$
$840$		0			0
$841$	−41.7354			−1.43915
$842$	−29.2564	−	24.1377i	−1.00824	−	0.831839i
$843$		0			0
$844$	16.5362	−	3.19996i	0.569198	−	0.110147i
$845$			3.06504i			0.105441i
$846$		0			0
$847$	8.75126			0.300697
$848$	3.70262	+	9.20859i	0.127149	+	0.316224i
$849$		0			0
$850$	17.7093	−	21.4648i	0.607424	−	0.736237i
$851$		−	18.1873i		−	0.623453i
$852$		0			0
$853$			7.21422i			0.247010i	0.992344	+	0.123505i	$0.0394135\pi$
$853$			7.21422i			0.247010i	−0.992344	+	0.123505i	$0.960586\pi$
$854$	14.2309	+	11.7410i	0.486970	+	0.401769i
$855$		0			0
$856$	7.38544	−	13.5617i	0.252429	−	0.463530i
$857$	−25.2860			−0.863754			−0.431877	−	0.901933i	$-0.642149\pi$
$857$	−25.2860			−0.863754			−0.431877	+	0.901933i	$0.642149\pi$
$858$		0			0
$859$		−	27.1905i		−	0.927727i	−0.885907	−	0.463864i	$-0.846463\pi$
$859$		−	27.1905i		−	0.927727i	0.885907	−	0.463864i	$-0.153537\pi$
$860$	10.3821	+	53.6506i	0.354027	+	1.82947i
$861$		0			0
$862$	−9.61147	+	11.6497i	−0.327368	+	0.396791i
$863$	−52.6961			−1.79380			−0.896898	−	0.442237i	$-0.854185\pi$
$863$	−52.6961			−1.79380			−0.896898	+	0.442237i	$0.854185\pi$
$864$		0			0
$865$	−8.70661			−0.296034
$866$	−23.1146	+	28.0164i	−0.785466	+	0.952036i
$867$		0			0
$868$	−3.00965	−	15.5527i	−0.102154	−	0.527892i
$869$			46.4595i			1.57603i
$870$		0			0
$871$	9.32998			0.316134
$872$	22.1237	−	40.6252i	0.749202	−	1.37574i
$873$		0			0
$874$	9.50350	+	7.84076i	0.321461	+	0.265218i
$875$			2.85731i			0.0965947i
$876$		0			0
$877$		−	20.0897i		−	0.678380i	−0.940718	−	0.339190i	$-0.889847\pi$
$877$		−	20.0897i		−	0.678380i	0.940718	−	0.339190i	$-0.110153\pi$
$878$	−35.2188	+	42.6875i	−1.18858	+	1.44063i
$879$		0			0
$880$	46.4632	−	18.6821i	1.56627	−	0.629772i
$881$	52.8711			1.78127			0.890636	−	0.454718i	$-0.150260\pi$
$881$	52.8711			1.78127			0.890636	+	0.454718i	$0.150260\pi$
$882$		0			0
$883$		−	20.1563i		−	0.678313i	−0.940730	−	0.339157i	$-0.889858\pi$
$883$		−	20.1563i		−	0.678313i	0.940730	−	0.339157i	$-0.110142\pi$
$884$	8.79215	−	1.70140i	0.295712	−	0.0572242i
$885$		0			0
$886$	30.6002	+	25.2463i	1.02803	+	0.848167i
$887$	19.3446			0.649528			0.324764	−	0.945795i	$-0.394715\pi$
$887$	19.3446			0.649528			0.324764	+	0.945795i	$0.394715\pi$
$888$		0			0
$889$	−15.3264			−0.514031
$890$	19.7371	+	16.2839i	0.661588	+	0.545836i
$891$		0			0
$892$	−6.07313	−	31.3836i	−0.203343	−	1.05080i
$893$		−	28.4988i		−	0.953677i
$894$		0			0
$895$	18.4347			0.616205
$896$	17.3002	+	2.02239i	0.577958	+	0.0675632i
$897$		0			0
$898$	21.7732	−	26.3906i	0.726582	−	0.880664i
$899$			43.2696i			1.44312i
$900$		0			0
$901$		−	11.1102i		−	0.370135i
$902$	−23.8180	−	19.6507i	−0.793052	−	0.654298i
$903$		0			0
$904$	49.6800	+	27.0547i	1.65233	+	0.899827i
$905$	10.1331			0.336837
$906$		0			0
$907$		−	32.0311i		−	1.06358i	−0.846877	−	0.531788i	$-0.821520\pi$
$907$		−	32.0311i		−	1.06358i	0.846877	−	0.531788i	$-0.178480\pi$
$908$	−43.2541	+	8.37024i	−1.43544	+	0.277776i
$909$		0			0
$910$	4.24693	−	5.14755i	0.140784	−	0.170640i
$911$	−16.3856			−0.542880			−0.271440	−	0.962455i	$-0.587500\pi$
$911$	−16.3856			−0.542880			−0.271440	+	0.962455i	$0.587500\pi$
$912$		0			0
$913$	18.2441			0.603793
$914$	4.18171	−	5.06851i	0.138319	−	0.167651i
$915$		0			0
$916$	−43.4309	+	8.40444i	−1.43500	+	0.277691i
$917$		−	19.8418i		−	0.655233i
$918$		0			0
$919$	−21.1754			−0.698513			−0.349257	−	0.937027i	$-0.613566\pi$
$919$	−21.1754			−0.698513			−0.349257	+	0.937027i	$0.613566\pi$
$920$	−13.4531	+	24.7036i	−0.443535	+	0.814453i
$921$		0			0
$922$	9.76796	+	8.05894i	0.321691	+	0.265407i
$923$		−	7.52766i		−	0.247776i
$924$		0			0
$925$		−	24.6320i		−	0.809895i
$926$	−0.970934	+	1.17683i	−0.0319069	+	0.0386732i
$927$		0			0
$928$	−45.3446	−	14.4013i	−1.48851	−	0.472747i
$929$	−30.7749			−1.00969			−0.504846	−	0.863210i	$-0.668451\pi$
$929$	−30.7749			−1.00969			−0.504846	+	0.863210i	$0.668451\pi$
$930$		0			0
$931$		−	12.4308i		−	0.407402i
$932$	−6.95187	−	35.9245i	−0.227716	−	1.17675i
$933$		0			0
$934$	24.9757	+	20.6059i	0.817229	+	0.674246i
$935$	−56.0581			−1.83330
$936$		0			0
$937$	−6.23750			−0.203770			−0.101885	−	0.994796i	$-0.532487\pi$
$937$	−6.23750			−0.203770			−0.101885	+	0.994796i	$0.532487\pi$
$938$	−15.6691	−	12.9276i	−0.511615	−	0.422102i
$939$		0			0
$940$	63.8814	−	12.3619i	2.08358	−	0.403200i
$941$		−	17.8567i		−	0.582112i	−0.956706	−	0.291056i	$-0.905993\pi$
$941$		−	17.8567i		−	0.582112i	0.956706	−	0.291056i	$-0.0940067\pi$
$942$		0			0
$943$	17.3443			0.564807
$944$	−4.61526	−	11.4784i	−0.150214	−	0.373589i
$945$		0			0
$946$	32.7711	−	39.7207i	1.06548	−	1.29143i
$947$		−	48.2716i		−	1.56861i	−0.620372	−	0.784307i	$-0.713019\pi$
$947$		−	48.2716i		−	1.56861i	0.620372	−	0.784307i	$-0.286981\pi$
$948$		0			0
$949$		−	5.60521i		−	0.181953i
$950$	12.8711	+	10.6191i	0.417593	+	0.344530i
$951$		0			0
$952$	−17.1233	−	9.32503i	−0.554971	−	0.302226i
$953$	11.8061			0.382436			0.191218	−	0.981548i	$-0.438756\pi$
$953$	11.8061			0.382436			0.191218	+	0.981548i	$0.438756\pi$
$954$		0			0
$955$		−	57.7527i		−	1.86883i
$956$	−5.47224	−	28.2784i	−0.176985	−	0.914588i
$957$		0			0
$958$	8.81599	−	10.6856i	0.284832	−	0.345234i
$959$	17.3617			0.560640
$960$		0			0
$961$	−4.53146			−0.146176
$962$	5.04473	−	6.11453i	0.162648	−	0.197140i
$963$		0			0
$964$	−10.5738	−	54.6413i	−0.340559	−	1.75988i
$965$			81.1433i			2.61210i
$966$		0			0
$967$	−46.9298			−1.50916			−0.754581	−	0.656207i	$-0.772160\pi$
$967$	−46.9298			−1.50916			−0.754581	+	0.656207i	$0.772160\pi$
$968$	−14.1197	−	7.68930i	−0.453824	−	0.247143i
$969$		0			0
$970$	46.8596	+	38.6610i	1.50457	+	1.24133i
$971$		−	3.92771i		−	0.126046i	−0.998012	−	0.0630230i	$-0.979926\pi$
$971$		−	3.92771i		−	0.126046i	0.998012	−	0.0630230i	$-0.0200742\pi$
$972$		0			0
$973$		−	1.46822i		−	0.0470688i
$974$	−34.3552	+	41.6408i	−1.10081	+	1.33426i
$975$		0			0
$976$	−12.6445	−	31.4474i	−0.404740	−	1.00661i
$977$	−52.9280			−1.69332			−0.846659	−	0.532136i	$-0.821389\pi$
$977$	−52.9280			−1.69332			−0.846659	+	0.532136i	$0.821389\pi$
$978$		0			0
$979$		−	24.1118i		−	0.770616i
$980$	27.8641	−	5.39207i	0.890086	−	0.172243i
$981$		0			0
$982$	40.1861	+	33.1551i	1.28239	+	1.05802i
$983$	22.3899			0.714128			0.357064	−	0.934080i	$-0.383778\pi$
$983$	22.3899			0.714128			0.357064	+	0.934080i	$0.383778\pi$
$984$		0			0
$985$	−39.4224			−1.25610
$986$	41.0807	+	33.8932i	1.30828	+	1.07938i
$987$		0			0
$988$	1.02022	+	5.27209i	0.0324575	+	0.167728i
$989$			28.9246i			0.919750i
$990$		0			0
$991$	−14.5258			−0.461426			−0.230713	−	0.973022i	$-0.574106\pi$
$991$	−14.5258			−0.461426			−0.230713	+	0.973022i	$0.574106\pi$
$992$	−8.80946	+	27.7378i	−0.279701	+	0.880677i
$993$		0			0
$994$	−10.4303	+	12.6422i	−0.330830	+	0.400988i
$995$			25.4248i			0.806022i
$996$		0			0
$997$			33.6376i			1.06531i	0.846332	+	0.532656i	$0.178806\pi$
$997$			33.6376i			1.06531i	−0.846332	+	0.532656i	$0.821194\pi$
$998$	−10.3061	−	8.50296i	−0.326235	−	0.269156i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.f.469.10	yes	24
3.2	odd	2	inner	936.2.g.f.469.15	yes	24
4.3	odd	2		3744.2.g.f.1873.9		24
8.3	odd	2		3744.2.g.f.1873.10		24
8.5	even	2	inner	936.2.g.f.469.9	✓	24
12.11	even	2		3744.2.g.f.1873.14		24
24.5	odd	2	inner	936.2.g.f.469.16	yes	24
24.11	even	2		3744.2.g.f.1873.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.g.f.469.9	✓	24	8.5	even	2	inner
936.2.g.f.469.10	yes	24	1.1	even	1	trivial
936.2.g.f.469.15	yes	24	3.2	odd	2	inner
936.2.g.f.469.16	yes	24	24.5	odd	2	inner
3744.2.g.f.1873.9		24	4.3	odd	2
3744.2.g.f.1873.10		24	8.3	odd	2
3744.2.g.f.1873.13		24	24.11	even	2
3744.2.g.f.1873.14		24	12.11	even	2

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900006 + 1.09087i) q^{2} +(-0.379977 - 1.96357i) q^{4} -3.06504i q^{5} -1.53955 q^{7} +(2.48398 + 1.35272i) q^{8} +(3.34355 + 2.75856i) q^{10} -4.08464i q^{11} +1.00000i q^{13} +(1.38560 - 1.67944i) q^{14} +(-3.71123 + 1.49222i) q^{16} +4.47763 q^{17} +2.68495i q^{19} +(-6.01843 + 1.16465i) q^{20} +(4.45580 + 3.67620i) q^{22} -3.24471 q^{23} -4.39448 q^{25} +(-1.09087 - 0.900006i) q^{26} +(0.584993 + 3.02301i) q^{28} -8.41043i q^{29} -5.14476 q^{31} +(1.71232 - 5.39147i) q^{32} +(-4.02990 + 4.88449i) q^{34} +4.71878i q^{35} +5.60521i q^{37} +(-2.92892 - 2.41647i) q^{38} +(4.14616 - 7.61349i) q^{40} -5.34539 q^{41} -8.91439i q^{43} +(-8.02049 + 1.55207i) q^{44} +(2.92026 - 3.53955i) q^{46} -10.6143 q^{47} -4.62979 q^{49} +(3.95506 - 4.79379i) q^{50} +(1.96357 - 0.379977i) q^{52} -2.48127i q^{53} -12.5196 q^{55} +(-3.82420 - 2.08258i) q^{56} +(9.17465 + 7.56944i) q^{58} +3.09287i q^{59} +8.47358i q^{61} +(4.63032 - 5.61224i) q^{62} +(4.34028 + 6.72027i) q^{64} +3.06504 q^{65} -9.32998i q^{67} +(-1.70140 - 8.79215i) q^{68} +(-5.14755 - 4.24693i) q^{70} -7.52766 q^{71} -5.60521 q^{73} +(-6.11453 - 5.04473i) q^{74} +(5.27209 - 1.02022i) q^{76} +6.28850i q^{77} -11.3742 q^{79} +(4.57373 + 11.3751i) q^{80} +(4.81089 - 5.83110i) q^{82} +4.46652i q^{83} -13.7241i q^{85} +(9.72440 + 8.02301i) q^{86} +(5.52539 - 10.1462i) q^{88} +5.90303 q^{89} -1.53955i q^{91} +(1.23292 + 6.37123i) q^{92} +(9.55293 - 11.5788i) q^{94} +8.22948 q^{95} +14.0149 q^{97} +(4.16684 - 5.05049i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} + 8 q^{28} + 40 q^{31} - 16 q^{34} - 36 q^{40} - 24 q^{46} + 24 q^{49} - 4 q^{52} - 16 q^{55} - 24 q^{58} + 8 q^{64} - 16 q^{70} - 16 q^{76}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q + 8 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 + 8 * q^28 + 40 * q^31 - 16 * q^34 - 36 * q^40 - 24 * q^46 + 24 * q^49 - 4 * q^52 - 16 * q^55 - 24 * q^58 + 8 * q^64 - 16 * q^70 - 16 * q^76 + 68 * q^82 + 28 * q^88 + 12 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

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