LMFDB - Embedded newform 1264.2.n.i.767.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1264,2,Mod(735,1264)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1264, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1264.735");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1264 = 2^{4} \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1264.n (of order $6$, degree $2$, 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:	$10.0930908155$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			767.6
Character	$\chi$	$=$	1264.767
Dual form			1264.2.n.i.735.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.214059 - 0.370761i) q^{3} +(0.323998 - 0.561181i) q^{5} +(2.03778 - 3.52953i) q^{7} +(1.40836 - 2.43935i) q^{9} +O(q^{10})$	\(q+(-0.214059 - 0.370761i) q^{3} +(0.323998 - 0.561181i) q^{5} +(2.03778 - 3.52953i) q^{7} +(1.40836 - 2.43935i) q^{9} +(0.217813 + 0.125754i) q^{11} +(-1.64580 - 2.85061i) q^{13} -0.277419 q^{15} +1.82066i q^{17} +(-5.79726 - 3.34705i) q^{19} -1.74482 q^{21} +(-3.50593 - 2.02415i) q^{23} +(2.29005 + 3.96648i) q^{25} -2.49024 q^{27} +(3.46896 + 2.00281i) q^{29} +(1.92075 + 1.10895i) q^{31} -0.107676i q^{33} +(-1.32047 - 2.28712i) q^{35} +(-1.78297 + 1.02940i) q^{37} +(-0.704596 + 1.22040i) q^{39} +11.9481i q^{41} +(-1.51660 - 2.62683i) q^{43} +(-0.912609 - 1.58069i) q^{45} +(1.32047 - 2.28712i) q^{47} +(-4.80508 - 8.32264i) q^{49} +(0.675030 - 0.389729i) q^{51} +(-4.27622 - 2.46887i) q^{53} +(0.141142 - 0.0814883i) q^{55} +2.86587i q^{57} +(-4.25897 - 7.37676i) q^{59} +0.126162i q^{61} +(-5.73984 - 9.94169i) q^{63} -2.13294 q^{65} -1.30540i q^{67} +1.73315i q^{69} +8.95357 q^{71} +(3.80224 - 6.58568i) q^{73} +(0.980413 - 1.69812i) q^{75} +(0.887709 - 0.512519i) q^{77} +(-5.88156 - 6.66387i) q^{79} +(-3.69201 - 6.39475i) q^{81} +(1.06076 + 0.612431i) q^{83} +(1.02172 + 0.589890i) q^{85} -1.71488i q^{87} +10.9283 q^{89} -13.4151 q^{91} -0.949521i q^{93} +(-3.75660 + 2.16887i) q^{95} +1.93543 q^{97} +(0.613517 - 0.354214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 20 q^{9}+O(q^{10}) $ 28 * q - 20 * q^9	$ 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) $ 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1264\mathbb{Z}\right)^\times$.

$n$	$159$	$161$	$949$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.214059	−	0.370761i	−0.123587	−	0.214059i	0.797593	−	0.603196i	$-0.206107\pi$
$3$	−0.214059	−	0.370761i	−0.123587	−	0.214059i	−0.921180	+	0.389137i	$0.872773\pi$
$4$		0			0
$5$	0.323998	−	0.561181i	0.144896	−	0.250968i	−0.784438	−	0.620207i	$-0.787049\pi$
$5$	0.323998	−	0.561181i	0.144896	−	0.250968i	0.929334	+	0.369240i	$0.120382\pi$
$6$		0			0
$7$	2.03778	−	3.52953i	0.770208	−	1.33404i	−0.167241	−	0.985916i	$-0.553486\pi$
$7$	2.03778	−	3.52953i	0.770208	−	1.33404i	0.937449	−	0.348123i	$-0.113181\pi$
$8$		0			0
$9$	1.40836	−	2.43935i	0.469452	−	0.813115i
$10$		0			0
$11$	0.217813	+	0.125754i	0.0656731	+	0.0379164i	0.532477	−	0.846444i	$-0.321261\pi$
$11$	0.217813	+	0.125754i	0.0656731	+	0.0379164i	−0.466804	+	0.884361i	$0.654595\pi$
$12$		0			0
$13$	−1.64580	−	2.85061i	−0.456462	−	0.790616i	0.542309	−	0.840179i	$-0.317550\pi$
$13$	−1.64580	−	2.85061i	−0.456462	−	0.790616i	−0.998771	+	0.0495635i	$0.984217\pi$
$14$		0			0
$15$	−0.277419			−0.0716292
$16$		0			0
$17$			1.82066i			0.441575i	0.975322	+	0.220787i	$0.0708627\pi$
$17$			1.82066i			0.441575i	−0.975322	+	0.220787i	$0.929137\pi$
$18$		0			0
$19$	−5.79726	−	3.34705i	−1.32998	−	0.767866i	−0.344686	−	0.938718i	$-0.612014\pi$
$19$	−5.79726	−	3.34705i	−1.32998	−	0.767866i	−0.985297	+	0.170853i	$0.945348\pi$
$20$		0			0
$21$	−1.74482			−0.380751
$22$		0			0
$23$	−3.50593	−	2.02415i	−0.731037	−	0.422065i	0.0877642	−	0.996141i	$-0.472028\pi$
$23$	−3.50593	−	2.02415i	−0.731037	−	0.422065i	−0.818802	+	0.574077i	$0.805361\pi$
$24$		0			0
$25$	2.29005	+	3.96648i	0.458010	+	0.793297i
$26$		0			0
$27$	−2.49024			−0.479247
$28$		0			0
$29$	3.46896	+	2.00281i	0.644170	+	0.371912i	0.786219	−	0.617948i	$-0.212036\pi$
$29$	3.46896	+	2.00281i	0.644170	+	0.371912i	−0.142049	+	0.989860i	$0.545369\pi$
$30$		0			0
$31$	1.92075	+	1.10895i	0.344977	+	0.199173i	0.662471	−	0.749088i	$-0.269508\pi$
$31$	1.92075	+	1.10895i	0.344977	+	0.199173i	−0.317494	+	0.948260i	$0.602841\pi$
$32$		0			0
$33$		−	0.107676i		−	0.0187439i
$34$		0			0
$35$	−1.32047	−	2.28712i	−0.223200	−	0.386594i
$36$		0			0
$37$	−1.78297	+	1.02940i	−0.293118	+	0.169232i	−0.639347	−	0.768918i	$-0.720795\pi$
$37$	−1.78297	+	1.02940i	−0.293118	+	0.169232i	0.346229	+	0.938150i	$0.387462\pi$
$38$		0			0
$39$	−0.704596	+	1.22040i	−0.112826	+	0.195420i
$40$		0			0
$41$			11.9481i			1.86598i	0.359904	+	0.932989i	$0.382809\pi$
$41$			11.9481i			1.86598i	−0.359904	+	0.932989i	$0.617191\pi$
$42$		0			0
$43$	−1.51660	−	2.62683i	−0.231279	−	0.400588i	0.726906	−	0.686737i	$-0.240958\pi$
$43$	−1.51660	−	2.62683i	−0.231279	−	0.400588i	−0.958185	+	0.286150i	$0.907624\pi$
$44$		0			0
$45$	−0.912609	−	1.58069i	−0.136044	−	0.235635i
$46$		0			0
$47$	1.32047	−	2.28712i	0.192610	−	0.333611i	−0.753504	−	0.657443i	$-0.771638\pi$
$47$	1.32047	−	2.28712i	0.192610	−	0.333611i	0.946115	+	0.323832i	$0.104971\pi$
$48$		0			0
$49$	−4.80508	−	8.32264i	−0.686440	−	1.18895i
$50$		0			0
$51$	0.675030	−	0.389729i	0.0945231	−	0.0545730i
$52$		0			0
$53$	−4.27622	−	2.46887i	−0.587383	−	0.339126i	0.176679	−	0.984269i	$-0.443465\pi$
$53$	−4.27622	−	2.46887i	−0.587383	−	0.339126i	−0.764062	+	0.645143i	$0.776798\pi$
$54$		0			0
$55$	0.141142	−	0.0814883i	0.0190316	−	0.0109879i
$56$		0			0
$57$			2.86587i			0.379593i
$58$		0			0
$59$	−4.25897	−	7.37676i	−0.554471	−	0.960372i	−0.997944	−	0.0640847i	$-0.979587\pi$
$59$	−4.25897	−	7.37676i	−0.554471	−	0.960372i	0.443473	−	0.896288i	$-0.353746\pi$
$60$		0			0
$61$			0.126162i			0.0161534i	0.999967	+	0.00807671i	$0.00257092\pi$
$61$			0.126162i			0.0161534i	−0.999967	+	0.00807671i	$0.997429\pi$
$62$		0			0
$63$	−5.73984	−	9.94169i	−0.723152	−	1.25254i
$64$		0			0
$65$	−2.13294			−0.264559
$66$		0			0
$67$		−	1.30540i		−	0.159480i	−0.996816	−	0.0797401i	$-0.974591\pi$
$67$		−	1.30540i		−	0.159480i	0.996816	−	0.0797401i	$-0.0254090\pi$
$68$		0			0
$69$			1.73315i			0.208647i
$70$		0			0
$71$	8.95357			1.06259			0.531297	−	0.847186i	$-0.321705\pi$
$71$	8.95357			1.06259			0.531297	+	0.847186i	$0.321705\pi$
$72$		0			0
$73$	3.80224	−	6.58568i	0.445019	−	0.770795i	−0.553035	−	0.833158i	$-0.686530\pi$
$73$	3.80224	−	6.58568i	0.445019	−	0.770795i	0.998054	+	0.0623629i	$0.0198636\pi$
$74$		0			0
$75$	0.980413	−	1.69812i	0.113208	−	0.196083i
$76$		0			0
$77$	0.887709	−	0.512519i	0.101164	−	0.0584070i
$78$		0			0
$79$	−5.88156	−	6.66387i	−0.661728	−	0.749744i
$79$	−5.88156	−	6.66387i	−0.661728	−	0.749744i
$80$		0			0
$81$	−3.69201	−	6.39475i	−0.410224	−	0.710528i
$82$		0			0
$83$	1.06076	+	0.612431i	0.116434	+	0.0672231i	0.557086	−	0.830455i	$-0.311919\pi$
$83$	1.06076	+	0.612431i	0.116434	+	0.0672231i	−0.440652	+	0.897678i	$0.645253\pi$
$84$		0			0
$85$	1.02172	+	0.589890i	0.110821	+	0.0639825i
$86$		0			0
$87$		−	1.71488i		−	0.183854i
$88$		0			0
$89$	10.9283			1.15840			0.579201	−	0.815185i	$-0.303365\pi$
$89$	10.9283			1.15840			0.579201	+	0.815185i	$0.303365\pi$
$90$		0			0
$91$	−13.4151			−1.40628
$92$		0			0
$93$		−	0.949521i		−	0.0984608i
$94$		0			0
$95$	−3.75660	+	2.16887i	−0.385419	+	0.222522i
$96$		0			0
$97$	1.93543			0.196513			0.0982565	−	0.995161i	$-0.468673\pi$
$97$	1.93543			0.196513			0.0982565	+	0.995161i	$0.468673\pi$
$98$		0			0
$99$	0.613517	−	0.354214i	0.0616608	−	0.0355999i
$100$		0			0
$101$	5.53221			0.550475			0.275238	−	0.961376i	$-0.411243\pi$
$101$	5.53221			0.550475			0.275238	+	0.961376i	$0.411243\pi$
$102$		0			0
$103$	4.29337	+	7.43633i	0.423038	+	0.732724i	0.996235	−	0.0866941i	$-0.0276303\pi$
$103$	4.29337	+	7.43633i	0.423038	+	0.732724i	−0.573197	+	0.819418i	$0.694297\pi$
$104$		0			0
$105$	−0.565318	+	0.979159i	−0.0551694	+	0.0955562i
$106$		0			0
$107$	−3.65735	−	6.33472i	−0.353570	−	0.612400i	0.633303	−	0.773904i	$-0.281699\pi$
$107$	−3.65735	−	6.33472i	−0.353570	−	0.612400i	−0.986872	+	0.161504i	$0.948366\pi$
$108$		0			0
$109$	10.2976	−	5.94534i	0.986334	−	0.569460i	0.0821574	−	0.996619i	$-0.473819\pi$
$109$	10.2976	−	5.94534i	0.986334	−	0.569460i	0.904176	+	0.427159i	$0.140486\pi$
$110$		0			0
$111$	0.763320	+	0.440703i	0.0724511	+	0.0418297i
$112$		0			0
$113$	−5.61258	+	3.24043i	−0.527987	+	0.304834i	−0.740197	−	0.672391i	$-0.765268\pi$
$113$	−5.61258	+	3.24043i	−0.527987	+	0.304834i	0.212209	+	0.977224i	$0.431934\pi$
$114$		0			0
$115$	−2.27183	+	1.31164i	−0.211849	+	0.122311i
$116$		0			0
$117$	−9.27149			−0.857149
$118$		0			0
$119$	6.42608	+	3.71010i	0.589078	+	0.340104i
$120$		0			0
$121$	−5.46837	−	9.47150i	−0.497125	−	0.861045i
$122$		0			0
$123$	4.42989	−	2.55760i	0.399430	−	0.230611i
$124$		0			0
$125$	6.20786			0.555248
$126$		0			0
$127$	8.72691	−	15.1155i	0.774388	−	1.34128i	−0.160749	−	0.986995i	$-0.551391\pi$
$127$	8.72691	−	15.1155i	0.774388	−	1.34128i	0.935138	−	0.354285i	$-0.115276\pi$
$128$		0			0
$129$	−0.649284	+	1.12459i	−0.0571663	+	0.0990149i
$130$		0			0
$131$			3.25418i			0.284319i	0.989844	+	0.142159i	$0.0454046\pi$
$131$			3.25418i			0.284319i	−0.989844	+	0.142159i	$0.954595\pi$
$132$		0			0
$133$	−23.6270	+	13.6411i	−2.04872	+	1.18283i
$134$		0			0
$135$	−0.806833	+	1.39748i	−0.0694411	+	0.120276i
$136$		0			0
$137$		−	12.7326i		−	1.08782i	−0.839145	−	0.543908i	$-0.816944\pi$
$137$		−	12.7326i		−	1.08782i	0.839145	−	0.543908i	$-0.183056\pi$
$138$		0			0
$139$	−9.01282	+	15.6107i	−0.764458	+	1.32408i	0.176075	+	0.984377i	$0.443660\pi$
$139$	−9.01282	+	15.6107i	−0.764458	+	1.32408i	−0.940533	+	0.339703i	$0.889673\pi$
$140$		0			0
$141$	−1.13064			−0.0952167
$142$		0			0
$143$		−	0.827865i		−	0.0692296i
$144$		0			0
$145$	2.24787	−	1.29781i	0.186676	−	0.107777i
$146$		0			0
$147$	−2.05714	+	3.56307i	−0.169670	+	0.293877i
$148$		0			0
$149$	14.3862	+	8.30586i	1.17856	+	0.680442i	0.955681	−	0.294404i	$-0.0951211\pi$
$149$	14.3862	+	8.30586i	1.17856	+	0.680442i	0.222879	+	0.974846i	$0.428454\pi$
$150$		0			0
$151$	−8.37145	−	4.83326i	−0.681259	−	0.393325i	0.119070	−	0.992886i	$-0.462009\pi$
$151$	−8.37145	−	4.83326i	−0.681259	−	0.393325i	−0.800329	+	0.599561i	$0.795342\pi$
$152$		0			0
$153$	4.44122	+	2.56414i	0.359051	+	0.207298i
$154$		0			0
$155$	1.24464	−	0.718593i	0.0999718	−	0.0577188i
$156$		0			0
$157$			16.4350i			1.31166i	0.754910	+	0.655829i	$0.227681\pi$
$157$			16.4350i			1.31166i	−0.754910	+	0.655829i	$0.772319\pi$
$158$		0			0
$159$			2.11394i			0.167646i
$160$		0			0
$161$	−14.2886	+	8.24954i	−1.12610	+	0.650155i
$162$		0			0
$163$	6.84978	+	3.95472i	0.536516	+	0.309758i	0.743666	−	0.668551i	$-0.233085\pi$
$163$	6.84978	+	3.95472i	0.536516	+	0.309758i	−0.207149	+	0.978309i	$0.566419\pi$
$164$		0			0
$165$	−0.0604254	−	0.0348866i	−0.00470411	−	0.00271592i
$166$		0			0
$167$	18.3902	+	10.6176i	1.42307	+	0.821612i	0.996560	−	0.0828698i	$-0.0264086\pi$
$167$	18.3902	+	10.6176i	1.42307	+	0.821612i	0.426513	+	0.904481i	$0.359742\pi$
$168$		0			0
$169$	1.08270	−	1.87529i	0.0832845	−	0.144253i
$170$		0			0
$171$	−16.3292	+	9.42768i	−1.24873	+	0.720953i
$172$		0			0
$173$		−	7.27842i		−	0.553368i	−0.960961	−	0.276684i	$-0.910765\pi$
$173$		−	7.27842i		−	0.553368i	0.960961	−	0.276684i	$-0.0892355\pi$
$174$		0			0
$175$	18.6665			1.41105
$176$		0			0
$177$	−1.82335	+	3.15813i	−0.137051	+	0.237379i
$178$		0			0
$179$		−	8.50441i		−	0.635650i	−0.948149	−	0.317825i	$-0.897048\pi$
$179$		−	8.50441i		−	0.635650i	0.948149	−	0.317825i	$-0.102952\pi$
$180$		0			0
$181$	1.34138	−	2.32334i	0.0997039	−	0.172692i	−0.811858	−	0.583855i	$-0.801544\pi$
$181$	1.34138	−	2.32334i	0.0997039	−	0.172692i	0.911562	+	0.411163i	$0.134877\pi$
$182$		0			0
$183$	0.0467761	−	0.0270062i	0.00345779	−	0.00199636i
$184$		0			0
$185$			1.33409i			0.0980841i
$186$		0			0
$187$	−0.228956	+	0.396563i	−0.0167429	+	0.0289996i
$188$		0			0
$189$	−5.07456	+	8.78940i	−0.369120	+	0.639335i
$190$		0			0
$191$	22.8345			1.65225			0.826124	−	0.563489i	$-0.190541\pi$
$191$	22.8345			1.65225			0.826124	+	0.563489i	$0.190541\pi$
$192$		0			0
$193$	−0.121216	+	0.0699839i	−0.00872529	+	0.00503755i	−0.504356	−	0.863496i	$-0.668270\pi$
$193$	−0.121216	+	0.0699839i	−0.00872529	+	0.00503755i	0.495631	+	0.868533i	$0.334937\pi$
$194$		0			0
$195$	0.456575	+	0.790812i	0.0326960	+	0.0566312i
$196$		0			0
$197$	6.36138	+	3.67275i	0.453230	+	0.261672i	0.709193	−	0.705014i	$-0.249059\pi$
$197$	6.36138	+	3.67275i	0.453230	+	0.261672i	−0.255963	+	0.966686i	$0.582393\pi$
$198$		0			0
$199$	−4.34860			−0.308264			−0.154132	−	0.988050i	$-0.549258\pi$
$199$	−4.34860			−0.308264			−0.154132	+	0.988050i	$0.549258\pi$
$200$		0			0
$201$	−0.483993	+	0.279433i	−0.0341382	+	0.0197097i
$202$		0			0
$203$	14.1379	−	8.16255i	0.992289	−	0.572899i
$204$		0			0
$205$	6.70504	+	3.87116i	0.468300	+	0.270373i
$206$		0			0
$207$	−9.87521	+	5.70146i	−0.686375	+	0.396279i
$208$		0			0
$209$	−0.841812	−	1.45806i	−0.0582294	−	0.100856i
$210$		0			0
$211$	−10.5023	+	18.1905i	−0.723007	+	1.25228i	0.236782	+	0.971563i	$0.423907\pi$
$211$	−10.5023	+	18.1905i	−0.723007	+	1.25228i	−0.959789	+	0.280722i	$0.909426\pi$
$212$		0			0
$213$	−1.91659	−	3.31964i	−0.131323	−	0.227458i
$214$		0			0
$215$	−1.96550			−0.134046
$216$		0			0
$217$	7.82813	−	4.51958i	0.531408	−	0.306809i
$218$		0			0
$219$	−3.25562			−0.219994
$220$		0			0
$221$	5.18998	−	2.99644i	0.349116	−	0.201562i
$222$		0			0
$223$			7.68996i			0.514958i	0.966284	+	0.257479i	$0.0828918\pi$
$223$			7.68996i			0.514958i	−0.966284	+	0.257479i	$0.917108\pi$
$224$		0			0
$225$	12.9008			0.860056
$226$		0			0
$227$	−19.8021			−1.31431			−0.657156	−	0.753755i	$-0.728241\pi$
$227$	−19.8021			−1.31431			−0.657156	+	0.753755i	$0.728241\pi$
$228$		0			0
$229$		−	4.50599i		−	0.297764i	−0.988855	−	0.148882i	$-0.952433\pi$
$229$		−	4.50599i		−	0.297764i	0.988855	−	0.148882i	$-0.0475675\pi$
$230$		0			0
$231$	−0.380045	−	0.219419i	−0.0250051	−	0.0144367i
$232$		0			0
$233$	−12.2258	−	7.05859i	−0.800941	−	0.462423i	0.0428593	−	0.999081i	$-0.486353\pi$
$233$	−12.2258	−	7.05859i	−0.800941	−	0.462423i	−0.843800	+	0.536658i	$0.819687\pi$
$234$		0			0
$235$	−0.855659	−	1.48205i	−0.0558171	−	0.0966780i
$236$		0			0
$237$	−1.21170	+	3.60712i	−0.0787086	+	0.234308i
$238$		0			0
$239$	8.23117	−	4.75227i	0.532430	−	0.307399i	−0.209575	−	0.977792i	$-0.567208\pi$
$239$	8.23117	−	4.75227i	0.532430	−	0.307399i	0.742005	+	0.670394i	$0.233875\pi$
$240$		0			0
$241$	−2.03509	+	3.52488i	−0.131092	+	0.227058i	−0.924098	−	0.382156i	$-0.875182\pi$
$241$	−2.03509	+	3.52488i	−0.131092	+	0.227058i	0.793006	+	0.609214i	$0.208515\pi$
$242$		0			0
$243$	−5.31598	+	9.20755i	−0.341020	+	0.590665i
$244$		0			0
$245$	−6.22734			−0.397850
$246$		0			0
$247$			22.0343i			1.40201i
$248$		0			0
$249$		−	0.524386i		−	0.0332316i
$250$		0			0
$251$	20.5951			1.29995			0.649976	−	0.759955i	$-0.274779\pi$
$251$	20.5951			1.29995			0.649976	+	0.759955i	$0.274779\pi$
$252$		0			0
$253$	−0.509092	−	0.881773i	−0.0320063	−	0.0554366i
$254$		0			0
$255$		−	0.505085i		−	0.0316297i
$256$		0			0
$257$	−7.02256	−	12.1634i	−0.438055	−	0.758734i	0.559484	−	0.828841i	$-0.310999\pi$
$257$	−7.02256	−	12.1634i	−0.438055	−	0.758734i	−0.997539	+	0.0701069i	$0.977666\pi$
$258$		0			0
$259$			8.39072i			0.521374i
$260$		0			0
$261$	9.77108	−	5.64133i	0.604814	−	0.349190i
$262$		0			0
$263$	13.1299	+	7.58055i	0.809624	+	0.467437i	0.846825	−	0.531871i	$-0.178511\pi$
$263$	13.1299	+	7.58055i	0.809624	+	0.467437i	−0.0372013	+	0.999308i	$0.511844\pi$
$264$		0			0
$265$	−2.77097	+	1.59982i	−0.170219	+	0.0982761i
$266$		0			0
$267$	−2.33931	−	4.05181i	−0.143164	−	0.247967i
$268$		0			0
$269$	13.8062	−	23.9130i	0.841779	−	1.45800i	−0.0466102	−	0.998913i	$-0.514842\pi$
$269$	13.8062	−	23.9130i	0.841779	−	1.45800i	0.888389	−	0.459091i	$-0.151825\pi$
$270$		0			0
$271$	10.8644	+	18.8177i	0.659964	+	1.14309i	0.980624	+	0.195898i	$0.0627620\pi$
$271$	10.8644	+	18.8177i	0.659964	+	1.14309i	−0.320660	+	0.947194i	$0.603905\pi$
$272$		0			0
$273$	2.87162	+	4.97379i	0.173798	+	0.301028i
$274$		0			0
$275$			1.15194i			0.0694644i
$276$		0			0
$277$	7.88524	−	13.6576i	0.473778	−	0.820608i	−0.525771	−	0.850626i	$-0.676223\pi$
$277$	7.88524	−	13.6576i	0.473778	−	0.820608i	0.999549	+	0.0300183i	$0.00955655\pi$
$278$		0			0
$279$	5.41021	−	3.12359i	0.323901	−	0.187004i
$280$		0			0
$281$	4.99206	+	8.64651i	0.297802	+	0.515807i	0.975633	−	0.219410i	$-0.0704133\pi$
$281$	4.99206	+	8.64651i	0.297802	+	0.515807i	−0.677831	+	0.735218i	$0.737080\pi$
$282$		0			0
$283$		−	18.5877i		−	1.10492i	−0.833539	−	0.552461i	$-0.813689\pi$
$283$		−	18.5877i		−	1.10492i	0.833539	−	0.552461i	$-0.186311\pi$
$284$		0			0
$285$	1.60827	+	0.928534i	0.0952656	+	0.0550016i
$286$		0			0
$287$	42.1712	+	24.3476i	2.48929	+	1.43719i
$288$		0			0
$289$	13.6852			0.805012
$290$		0			0
$291$	−0.414296	−	0.717582i	−0.0242865	−	0.0420654i
$292$		0			0
$293$	−10.1425	−	5.85576i	−0.592529	−	0.342097i	0.173568	−	0.984822i	$-0.444470\pi$
$293$	−10.1425	−	5.85576i	−0.592529	−	0.342097i	−0.766097	+	0.642725i	$0.777804\pi$
$294$		0			0
$295$	−5.51959			−0.321363
$296$		0			0
$297$	−0.542407	−	0.313159i	−0.0314737	−	0.0181713i
$298$		0			0
$299$			13.3254i			0.770626i
$300$		0			0
$301$	−12.3620			−0.712532
$302$		0			0
$303$	−1.18422	−	2.05113i	−0.0680317	−	0.117834i
$304$		0			0
$305$	0.0707998	+	0.0408763i	0.00405399	+	0.00234057i
$306$		0			0
$307$	−10.3842	+	17.9859i	−0.592656	+	1.02651i	0.401218	+	0.915983i	$0.368587\pi$
$307$	−10.3842	+	17.9859i	−0.592656	+	1.02651i	−0.993873	+	0.110527i	$0.964746\pi$
$308$		0			0
$309$	1.83807	−	3.18363i	0.104564	−	0.181110i
$310$		0			0
$311$	−8.31463	+	14.4014i	−0.471480	+	0.816627i	−0.999468	−	0.0326251i	$-0.989613\pi$
$311$	−8.31463	+	14.4014i	−0.471480	+	0.816627i	0.527988	+	0.849252i	$0.322947\pi$
$312$		0			0
$313$	12.3010	+	21.3060i	0.695295	+	1.20429i	0.970081	+	0.242781i	$0.0780595\pi$
$313$	12.3010	+	21.3060i	0.695295	+	1.20429i	−0.274786	+	0.961505i	$0.588607\pi$
$314$		0			0
$315$	−7.43878			−0.419128
$316$		0			0
$317$	−6.37605			−0.358115			−0.179057	−	0.983839i	$-0.557305\pi$
$317$	−6.37605			−0.358115			−0.179057	+	0.983839i	$0.557305\pi$
$318$		0			0
$319$	0.503723	+	0.872475i	0.0282031	+	0.0488492i
$320$		0			0
$321$	−1.56578	+	2.71201i	−0.0873933	+	0.151370i
$322$		0			0
$323$	6.09384	−	10.5548i	0.339070	−	0.587287i
$324$		0			0
$325$	7.53792	−	13.0561i	0.418129	−	0.724220i
$326$		0			0
$327$	−4.40860	−	2.54531i	−0.243796	−	0.140756i
$328$		0			0
$329$	−5.38165	−	9.32130i	−0.296700	−	0.513900i
$330$		0			0
$331$	−9.62347			−0.528954			−0.264477	−	0.964392i	$-0.585199\pi$
$331$	−9.62347			−0.528954			−0.264477	+	0.964392i	$0.585199\pi$
$332$		0			0
$333$			5.79903i			0.317785i
$334$		0			0
$335$	−0.732566	−	0.422947i	−0.0400244	−	0.0231081i
$336$		0			0
$337$	−25.2743			−1.37678			−0.688389	−	0.725342i	$-0.741682\pi$
$337$	−25.2743			−1.37678			−0.688389	+	0.725342i	$0.741682\pi$
$338$		0			0
$339$	2.40285	+	1.38729i	0.130505	+	0.0753470i
$340$		0			0
$341$	0.278910	+	0.483086i	0.0151038	+	0.0261606i
$342$		0			0
$343$	−10.6378			−0.574389
$344$		0			0
$345$	0.972612	+	0.561538i	0.0523636	+	0.0302322i
$346$		0			0
$347$	25.1964	+	14.5472i	1.35262	+	0.780933i	0.988615	−	0.150466i	$-0.0480775\pi$
$347$	25.1964	+	14.5472i	1.35262	+	0.780933i	0.364000	+	0.931399i	$0.381411\pi$
$348$		0			0
$349$			22.8231i			1.22169i	0.791749	+	0.610847i	$0.209171\pi$
$349$			22.8231i			1.22169i	−0.791749	+	0.610847i	$0.790829\pi$
$350$		0			0
$351$	4.09844	+	7.09870i	0.218758	+	0.378901i
$352$		0			0
$353$	−16.3547	+	9.44239i	−0.870473	+	0.502568i	−0.867505	−	0.497428i	$-0.834278\pi$
$353$	−16.3547	+	9.44239i	−0.870473	+	0.502568i	−0.00296746	+	0.999996i	$0.500945\pi$
$354$		0			0
$355$	2.90094	−	5.02457i	0.153966	−	0.266677i
$356$		0			0
$357$		−	3.17672i		−	0.168130i
$358$		0			0
$359$	7.21599	+	12.4985i	0.380845	+	0.659644i	0.991183	−	0.132498i	$-0.0422997\pi$
$359$	7.21599	+	12.4985i	0.380845	+	0.659644i	−0.610338	+	0.792141i	$0.708966\pi$
$360$		0			0
$361$	12.9055	+	22.3529i	0.679235	+	1.17647i
$362$		0			0
$363$	−2.34111	+	4.05492i	−0.122876	+	0.212828i
$364$		0			0
$365$	−2.46384	−	4.26749i	−0.128963	−	0.223371i
$366$		0			0
$367$	13.8709	−	8.00838i	0.724056	−	0.418034i	−0.0921878	−	0.995742i	$-0.529386\pi$
$367$	13.8709	−	8.00838i	0.724056	−	0.418034i	0.816244	+	0.577708i	$0.196053\pi$
$368$		0			0
$369$	29.1455	+	16.8272i	1.51726	+	0.875988i
$370$		0			0
$371$	−17.4280	+	10.0620i	−0.904814	+	0.522395i
$372$		0			0
$373$		−	11.6904i		−	0.605305i	−0.953101	−	0.302652i	$-0.902128\pi$
$373$		−	11.6904i		−	0.605305i	0.953101	−	0.302652i	$-0.0978721\pi$
$374$		0			0
$375$	−1.32885	−	2.30164i	−0.0686215	−	0.118856i
$376$		0			0
$377$		−	13.1849i		−	0.679055i
$378$		0			0
$379$	−14.8390	−	25.7019i	−0.762228	−	1.32022i	−0.941700	−	0.336455i	$-0.890772\pi$
$379$	−14.8390	−	25.7019i	−0.762228	−	1.32022i	0.179471	−	0.983763i	$-0.442561\pi$
$380$		0			0
$381$	−7.47230			−0.382818
$382$		0			0
$383$		−	29.9847i		−	1.53215i	−0.642753	−	0.766074i	$-0.722208\pi$
$383$		−	29.9847i		−	1.53215i	0.642753	−	0.766074i	$-0.277792\pi$
$384$		0			0
$385$		−	0.664220i		−	0.0338518i
$386$		0			0
$387$	−8.54366			−0.434299
$388$		0			0
$389$	−17.4045	+	30.1455i	−0.882445	+	1.52844i	−0.0338308	+	0.999428i	$0.510771\pi$
$389$	−17.4045	+	30.1455i	−0.882445	+	1.52844i	−0.848614	+	0.529012i	$0.822563\pi$
$390$		0			0
$391$	3.68529	−	6.38311i	0.186373	−	0.322808i
$392$		0			0
$393$	1.20652	−	0.696586i	0.0608610	−	0.0351381i
$394$		0			0
$395$	−5.64525	+	1.14154i	−0.284043	+	0.0574371i
$396$		0			0
$397$	−12.5291	−	21.7010i	−0.628815	−	1.08914i	−0.987790	−	0.155793i	$-0.950207\pi$
$397$	−12.5291	−	21.7010i	−0.628815	−	1.08914i	0.358974	−	0.933347i	$-0.383127\pi$
$398$		0			0
$399$	10.1152	+	5.84000i	0.506392	+	0.292366i
$400$		0			0
$401$	−21.4052	−	12.3583i	−1.06892	−	0.617143i	−0.141036	−	0.990005i	$-0.545043\pi$
$401$	−21.4052	−	12.3583i	−1.06892	−	0.617143i	−0.927887	+	0.372862i	$0.878377\pi$
$402$		0			0
$403$		−	7.30041i		−	0.363659i
$404$		0			0
$405$	−4.78482			−0.237759
$406$		0			0
$407$	−0.517804			−0.0256666
$408$		0			0
$409$			18.7975i			0.929478i	0.885448	+	0.464739i	$0.153852\pi$
$409$			18.7975i			0.929478i	−0.885448	+	0.464739i	$0.846148\pi$
$410$		0			0
$411$	−4.72074	+	2.72552i	−0.232857	+	0.134440i
$412$		0			0
$413$	−34.7154			−1.70823
$414$		0			0
$415$	0.687369	−	0.396853i	0.0337416	−	0.0194807i
$416$		0			0
$417$	7.71711			0.377909
$418$		0			0
$419$	17.1062	+	29.6289i	0.835694	+	1.44746i	0.893464	+	0.449134i	$0.148268\pi$
$419$	17.1062	+	29.6289i	0.835694	+	1.44746i	−0.0577703	+	0.998330i	$0.518399\pi$
$420$		0			0
$421$	2.13861	−	3.70419i	0.104230	−	0.180531i	−0.809194	−	0.587542i	$-0.800096\pi$
$421$	2.13861	−	3.70419i	0.104230	−	0.180531i	0.913423	+	0.407011i	$0.133429\pi$
$422$		0			0
$423$	−3.71939	−	6.44217i	−0.180843	−	0.313229i
$424$		0			0
$425$	−7.22162	+	4.16940i	−0.350300	+	0.202246i
$426$		0			0
$427$	0.445294	+	0.257091i	0.0215493	+	0.0124415i
$428$		0			0
$429$	−0.306941	+	0.177212i	−0.0148192	+	0.00855589i
$430$		0			0
$431$	−20.4216	+	11.7904i	−0.983674	+	0.567925i	−0.903377	−	0.428846i	$-0.858920\pi$
$431$	−20.4216	+	11.7904i	−0.983674	+	0.567925i	−0.0802970	+	0.996771i	$0.525587\pi$
$432$		0			0
$433$	24.3783			1.17155			0.585774	−	0.810475i	$-0.300791\pi$
$433$	24.3783			1.17155			0.585774	+	0.810475i	$0.300791\pi$
$434$		0			0
$435$	−0.962355	−	0.555616i	−0.0461414	−	0.0266398i
$436$		0			0
$437$	13.5499	+	23.4690i	0.648178	+	1.12268i
$438$		0			0
$439$	17.7602	−	10.2539i	0.847648	−	0.489390i	−0.0122085	−	0.999925i	$-0.503886\pi$
$439$	17.7602	−	10.2539i	0.847648	−	0.489390i	0.859857	+	0.510536i	$0.170553\pi$
$440$		0			0
$441$	−27.0691			−1.28900
$442$		0			0
$443$	18.2591	−	31.6258i	0.867518	−	1.50258i	0.00299253	−	0.999996i	$-0.499047\pi$
$443$	18.2591	−	31.6258i	0.867518	−	1.50258i	0.864525	−	0.502589i	$-0.167619\pi$
$444$		0			0
$445$	3.54076	−	6.13278i	0.167848	−	0.290722i
$446$		0			0
$447$		−	7.11178i		−	0.336376i
$448$		0			0
$449$	1.76503	−	1.01904i	0.0832969	−	0.0480915i	−0.457773	−	0.889069i	$-0.651353\pi$
$449$	1.76503	−	1.01904i	0.0832969	−	0.0480915i	0.541070	+	0.840978i	$0.318019\pi$
$450$		0			0
$451$	−1.50253	+	2.60245i	−0.0707512	+	0.122545i
$452$		0			0
$453$			4.13841i			0.194440i
$454$		0			0
$455$	−4.34646	+	7.52828i	−0.203765	+	0.352931i
$456$		0			0
$457$	2.54795			0.119188			0.0595939	−	0.998223i	$-0.481019\pi$
$457$	2.54795			0.119188			0.0595939	+	0.998223i	$0.481019\pi$
$458$		0			0
$459$		−	4.53388i		−	0.211624i
$460$		0			0
$461$	31.5946	−	18.2411i	1.47151	−	0.849575i	0.472019	−	0.881588i	$-0.343525\pi$
$461$	31.5946	−	18.2411i	1.47151	−	0.849575i	0.999487	+	0.0320132i	$0.0101919\pi$
$462$		0			0
$463$	9.38770	−	16.2600i	0.436283	−	0.755665i	−0.561116	−	0.827737i	$-0.689628\pi$
$463$	9.38770	−	16.2600i	0.436283	−	0.755665i	0.997399	+	0.0720721i	$0.0229612\pi$
$464$		0			0
$465$	−0.532853	−	0.307643i	−0.0247105	−	0.0142666i
$466$		0			0
$467$	11.7847	+	6.80390i	0.545331	+	0.314847i	0.747237	−	0.664558i	$-0.231380\pi$
$467$	11.7847	+	6.80390i	0.545331	+	0.314847i	−0.201906	+	0.979405i	$0.564713\pi$
$468$		0			0
$469$	−4.60746	−	2.66012i	−0.212753	−	0.122833i
$470$		0			0
$471$	6.09347	−	3.51807i	0.280772	−	0.162104i
$472$		0			0
$473$		−	0.762877i		−	0.0350771i
$474$		0			0
$475$		−	30.6596i		−	1.40676i
$476$		0			0
$477$	−12.0449	+	6.95411i	−0.551497	+	0.318407i
$478$		0			0
$479$	−2.22736	−	1.28597i	−0.101771	−	0.0587572i	0.448251	−	0.893908i	$-0.352047\pi$
$479$	−2.22736	−	1.28597i	−0.101771	−	0.0587572i	−0.550021	+	0.835151i	$0.685380\pi$
$480$		0			0
$481$	5.86880	+	3.38835i	0.267594	+	0.154496i
$482$		0			0
$483$	6.11722	+	3.53178i	0.278343	+	0.160702i
$484$		0			0
$485$	0.627075	−	1.08613i	0.0284740	−	0.0493184i
$486$		0			0
$487$	−26.0836	+	15.0594i	−1.18196	+	0.682407i	−0.956468	−	0.291838i	$-0.905733\pi$
$487$	−26.0836	+	15.0594i	−1.18196	+	0.682407i	−0.225495	+	0.974244i	$0.572400\pi$
$488$		0			0
$489$		−	3.38618i		−	0.153128i
$490$		0			0
$491$	37.6098			1.69731			0.848654	−	0.528948i	$-0.177413\pi$
$491$	37.6098			1.69731			0.848654	+	0.528948i	$0.177413\pi$
$492$		0			0
$493$	−3.64643	+	6.31580i	−0.164227	+	0.284449i
$494$		0			0
$495$		−	0.459059i		−	0.0206331i
$496$		0			0
$497$	18.2454	−	31.6020i	0.818418	−	1.41754i
$498$		0			0
$499$	−30.6866	+	17.7169i	−1.37372	+	0.793119i	−0.991395	−	0.130908i	$-0.958211\pi$
$499$	−30.6866	+	17.7169i	−1.37372	+	0.793119i	−0.382328	+	0.924027i	$0.624877\pi$
$500$		0			0
$501$		−	9.09115i		−	0.406163i
$502$		0			0
$503$	−4.42363	+	7.66195i	−0.197240	+	0.341630i	−0.947633	−	0.319363i	$-0.896531\pi$
$503$	−4.42363	+	7.66195i	−0.197240	+	0.341630i	0.750393	+	0.660992i	$0.229864\pi$
$504$		0			0
$505$	1.79242	−	3.10457i	0.0797618	−	0.138151i
$506$		0			0
$507$	−0.927046			−0.0411716
$508$		0			0
$509$	−3.65270	+	2.10889i	−0.161903	+	0.0934747i	−0.578762	−	0.815496i	$-0.696464\pi$
$509$	−3.65270	+	2.10889i	−0.161903	+	0.0934747i	0.416859	+	0.908971i	$0.363131\pi$
$510$		0			0
$511$	−15.4963	−	26.8403i	−0.685514	−	1.18734i
$512$		0			0
$513$	14.4366	+	8.33496i	0.637391	+	0.367998i
$514$		0			0
$515$	5.56417			0.245187
$516$		0			0
$517$	0.575232	−	0.332110i	0.0252987	−	0.0146062i
$518$		0			0
$519$	−2.69856	+	1.55801i	−0.118453	+	0.0683891i
$520$		0			0
$521$	22.7980	+	13.1624i	0.998797	+	0.576656i	0.907892	−	0.419204i	$-0.137691\pi$
$521$	22.7980	+	13.1624i	0.998797	+	0.576656i	0.0909046	+	0.995860i	$0.471024\pi$
$522$		0			0
$523$	−12.4848	+	7.20808i	−0.545920	+	0.315187i	−0.747475	−	0.664290i	$-0.768734\pi$
$523$	−12.4848	+	7.20808i	−0.545920	+	0.315187i	0.201555	+	0.979477i	$0.435401\pi$
$524$		0			0
$525$	−3.99573	−	6.92080i	−0.174388	−	0.302049i
$526$		0			0
$527$	−2.01901	+	3.49704i	−0.0879497	+	0.152333i
$528$		0			0
$529$	−3.30563	−	5.72551i	−0.143723	−	0.248935i
$530$		0			0
$531$	−23.9926			−1.04119
$532$		0			0
$533$	34.0593	−	19.6641i	1.47527	−	0.851749i
$534$		0			0
$535$	−4.73990			−0.204924
$536$		0			0
$537$	−3.15311	+	1.82045i	−0.136067	+	0.0785581i
$538$		0			0
$539$		−	2.41704i		−	0.104109i
$540$		0			0
$541$	11.2183			0.482313			0.241157	−	0.970486i	$-0.422473\pi$
$541$	11.2183			0.482313			0.241157	+	0.970486i	$0.422473\pi$
$542$		0			0
$543$	−1.14854			−0.0492885
$544$		0			0
$545$		−	7.70511i		−	0.330050i
$546$		0			0
$547$	−13.3680	−	7.71801i	−0.571574	−	0.329998i	0.186204	−	0.982511i	$-0.440381\pi$
$547$	−13.3680	−	7.71801i	−0.571574	−	0.329998i	−0.757778	+	0.652513i	$0.773715\pi$
$548$		0			0
$549$	0.307753	+	0.177682i	0.0131346	+	0.00758326i
$550$		0			0
$551$	−13.4070	−	23.2216i	−0.571157	−	0.989272i
$552$		0			0
$553$	−35.5057	+	7.17969i	−1.50986	+	0.305312i
$554$		0			0
$555$	0.494628	−	0.285574i	0.0209958	−	0.0121219i
$556$		0			0
$557$	2.85349	−	4.94239i	0.120906	−	0.209416i	−0.799219	−	0.601040i	$-0.794753\pi$
$557$	2.85349	−	4.94239i	0.120906	−	0.209416i	0.920125	+	0.391624i	$0.128087\pi$
$558$		0			0
$559$	−4.99203	+	8.64646i	−0.211141	+	0.365706i
$560$		0			0
$561$	0.196041			0.00827684
$562$		0			0
$563$			15.6251i			0.658520i	0.944239	+	0.329260i	$0.106799\pi$
$563$			15.6251i			0.658520i	−0.944239	+	0.329260i	$0.893201\pi$
$564$		0			0
$565$			4.19956i			0.176677i
$566$		0			0
$567$	−30.0940			−1.26383
$568$		0			0
$569$	−15.7932	−	27.3546i	−0.662084	−	1.14676i	−0.980067	−	0.198667i	$-0.936339\pi$
$569$	−15.7932	−	27.3546i	−0.662084	−	1.14676i	0.317983	−	0.948097i	$-0.396995\pi$
$570$		0			0
$571$			19.3532i			0.809906i	0.914338	+	0.404953i	$0.132712\pi$
$571$			19.3532i			0.809906i	−0.914338	+	0.404953i	$0.867288\pi$
$572$		0			0
$573$	−4.88794	−	8.46616i	−0.204197	−	0.353679i
$574$		0			0
$575$		−	18.5416i		−	0.773240i
$576$		0			0
$577$	10.5503	−	6.09124i	0.439216	−	0.253581i	−0.264049	−	0.964509i	$-0.585058\pi$
$577$	10.5503	−	6.09124i	0.439216	−	0.253581i	0.703265	+	0.710928i	$0.251725\pi$
$578$		0			0
$579$	0.0518946	+	0.0299614i	0.00215667	+	0.00124515i
$580$		0			0
$581$	4.32319	−	2.49600i	0.179356	−	0.103551i
$582$		0			0
$583$	−0.620944	−	1.07551i	−0.0257169	−	0.0445429i
$584$		0			0
$585$	−3.00394	+	5.20298i	−0.124198	+	0.215117i
$586$		0			0
$587$	−11.6762	−	20.2237i	−0.481928	−	0.834723i	0.517857	−	0.855467i	$-0.326730\pi$
$587$	−11.6762	−	20.2237i	−0.481928	−	0.834723i	−0.999785	+	0.0207437i	$0.993397\pi$
$588$		0			0
$589$	−7.42340	−	12.8577i	−0.305876	−	0.529792i
$590$		0			0
$591$		−	3.14474i		−	0.129357i
$592$		0			0
$593$	1.23972	−	2.14726i	0.0509092	−	0.0881772i	−0.839448	−	0.543440i	$-0.817121\pi$
$593$	1.23972	−	2.14726i	0.0509092	−	0.0881772i	0.890357	+	0.455263i	$0.150455\pi$
$594$		0			0
$595$	4.16407	−	2.40413i	0.170710	−	0.0985596i
$596$		0			0
$597$	0.930858	+	1.61229i	0.0380975	+	0.0659868i
$598$		0			0
$599$		−	12.8535i		−	0.525180i	−0.964907	−	0.262590i	$-0.915423\pi$
$599$		−	12.8535i		−	0.525180i	0.964907	−	0.262590i	$-0.0845767\pi$
$600$		0			0
$601$	−20.9240	−	12.0805i	−0.853507	−	0.492772i	0.00832565	−	0.999965i	$-0.497350\pi$
$601$	−20.9240	−	12.0805i	−0.853507	−	0.492772i	−0.861833	+	0.507193i	$0.830683\pi$
$602$		0			0
$603$	−3.18433	−	1.83847i	−0.129676	−	0.0748684i
$604$		0			0
$605$	−7.08696			−0.288126
$606$		0			0
$607$	−14.8293	−	25.6851i	−0.601903	−	1.04253i	−0.992533	−	0.121978i	$-0.961076\pi$
$607$	−14.8293	−	25.6851i	−0.601903	−	1.04253i	0.390630	−	0.920548i	$-0.372257\pi$
$608$		0			0
$609$	−6.05272	−	3.49454i	−0.245268	−	0.141606i
$610$		0			0
$611$	−8.69291			−0.351678
$612$		0			0
$613$	35.2853	+	20.3720i	1.42516	+	0.822816i	0.996734	−	0.0807602i	$-0.0257348\pi$
$613$	35.2853	+	20.3720i	1.42516	+	0.822816i	0.428426	+	0.903577i	$0.359068\pi$
$614$		0			0
$615$		−	3.31463i		−	0.133659i
$616$		0			0
$617$	11.2107			0.451326			0.225663	−	0.974205i	$-0.427545\pi$
$617$	11.2107			0.451326			0.225663	+	0.974205i	$0.427545\pi$
$618$		0			0
$619$	23.3506	+	40.4445i	0.938541	+	1.62560i	0.768195	+	0.640216i	$0.221155\pi$
$619$	23.3506	+	40.4445i	0.938541	+	1.62560i	0.170346	+	0.985384i	$0.445511\pi$
$620$		0			0
$621$	8.73062	+	5.04063i	0.350348	+	0.202273i
$622$		0			0
$623$	22.2695	−	38.5720i	0.892210	−	1.54535i
$624$		0			0
$625$	−9.43892	+	16.3487i	−0.377557	+	0.653948i
$626$		0			0
$627$	−0.360395	+	0.624223i	−0.0143928	+	0.0249291i
$628$		0			0
$629$	−1.87418	−	3.24617i	−0.0747284	−	0.129433i
$630$		0			0
$631$	−0.0645560			−0.00256993			−0.00128497	−	0.999999i	$-0.500409\pi$
$631$	−0.0645560			−0.00256993			−0.00128497	+	0.999999i	$0.500409\pi$
$632$		0			0
$633$	8.99244			0.357417
$634$		0			0
$635$	−5.65500	−	9.79475i	−0.224412	−	0.388693i
$636$		0			0
$637$	−15.8164	+	27.3948i	−0.626667	+	1.08542i
$638$		0			0
$639$	12.6098	−	21.8409i	0.498837	−	0.864011i
$640$		0			0
$641$	−15.6387	+	27.0870i	−0.617690	+	1.06987i	0.372216	+	0.928146i	$0.378598\pi$
$641$	−15.6387	+	27.0870i	−0.617690	+	1.06987i	−0.989906	+	0.141725i	$0.954735\pi$
$642$		0			0
$643$	−12.5547	−	7.24844i	−0.495108	−	0.285851i	0.231583	−	0.972815i	$-0.425609\pi$
$643$	−12.5547	−	7.24844i	−0.495108	−	0.285851i	−0.726691	+	0.686965i	$0.758943\pi$
$644$		0			0
$645$	0.420733	+	0.728732i	0.0165664	+	0.0286938i
$646$		0			0
$647$	−24.3074			−0.955621			−0.477811	−	0.878463i	$-0.658569\pi$
$647$	−24.3074			−0.955621			−0.477811	+	0.878463i	$0.658569\pi$
$648$		0			0
$649$		−	2.14234i		−	0.0840942i
$650$		0			0
$651$	−3.35137	−	1.93491i	−0.131350	−	0.0758352i
$652$		0			0
$653$	32.4454			1.26969			0.634844	−	0.772640i	$-0.281064\pi$
$653$	32.4454			1.26969			0.634844	+	0.772640i	$0.281064\pi$
$654$		0			0
$655$	1.82618	+	1.05435i	0.0713548	+	0.0411967i
$656$		0			0
$657$	−10.7098	−	18.5500i	−0.417830	−	0.723704i
$658$		0			0
$659$	1.12101			0.0436685			0.0218343	−	0.999762i	$-0.493049\pi$
$659$	1.12101			0.0436685			0.0218343	+	0.999762i	$0.493049\pi$
$660$		0			0
$661$	−1.96751	−	1.13594i	−0.0765271	−	0.0441830i	0.461248	−	0.887271i	$-0.347402\pi$
$661$	−1.96751	−	1.13594i	−0.0765271	−	0.0441830i	−0.537775	+	0.843088i	$0.680735\pi$
$662$		0			0
$663$	−2.22193	−	1.28283i	−0.0862925	−	0.0498210i
$664$		0			0
$665$			17.6787i			0.685551i
$666$		0			0
$667$	−8.10796	−	14.0434i	−0.313942	−	0.543763i
$668$		0			0
$669$	2.85114	−	1.64611i	0.110232	−	0.0636422i
$670$		0			0
$671$	−0.0158655	+	0.0274798i	−0.000612479	+	0.00106085i
$672$		0			0
$673$		−	41.8519i		−	1.61327i	−0.591047	−	0.806637i	$-0.701285\pi$
$673$		−	41.8519i		−	1.61327i	0.591047	−	0.806637i	$-0.298715\pi$
$674$		0			0
$675$	−5.70278	−	9.87751i	−0.219500	−	0.380185i
$676$		0			0
$677$	18.3876	+	31.8483i	0.706693	+	1.22403i	0.966077	+	0.258254i	$0.0831473\pi$
$677$	18.3876	+	31.8483i	0.706693	+	1.22403i	−0.259384	+	0.965774i	$0.583519\pi$
$678$		0			0
$679$	3.94397	−	6.83116i	0.151356	−	0.262156i
$680$		0			0
$681$	4.23882	+	7.34185i	0.162432	+	0.281340i
$682$		0			0
$683$	39.4444	−	22.7732i	1.50930	−	0.871394i	0.509357	−	0.860555i	$-0.329883\pi$
$683$	39.4444	−	22.7732i	1.50930	−	0.871394i	0.999941	−	0.0108384i	$-0.00345005\pi$
$684$		0			0
$685$	−7.14527	−	4.12532i	−0.273007	−	0.157620i
$686$		0			0
$687$	−1.67065	+	0.964548i	−0.0637391	+	0.0367998i
$688$		0			0
$689$			16.2531i			0.619193i
$690$		0			0
$691$	−20.8519	−	36.1166i	−0.793245	−	1.37394i	−0.923947	−	0.382520i	$-0.875056\pi$
$691$	−20.8519	−	36.1166i	−0.793245	−	1.37394i	0.130702	−	0.991422i	$-0.458277\pi$
$692$		0			0
$693$		−	2.88724i		−	0.109677i
$694$		0			0
$695$	5.84027	+	10.1156i	0.221534	+	0.383708i
$696$		0			0
$697$	−21.7534			−0.823969
$698$		0			0
$699$			6.04382i			0.228598i
$700$		0			0
$701$			45.4596i			1.71699i	0.512824	+	0.858493i	$0.328599\pi$
$701$			45.4596i			1.71699i	−0.512824	+	0.858493i	$0.671401\pi$
$702$		0			0
$703$	13.7817			0.519788
$704$		0			0
$705$	−0.366324	+	0.634491i	−0.0137965	+	0.0238963i
$706$		0			0
$707$	11.2734	−	19.5261i	0.423980	−	0.734356i
$708$		0			0
$709$	−20.0517	+	11.5769i	−0.753057	+	0.434778i	−0.826798	−	0.562500i	$-0.809840\pi$
$709$	−20.0517	+	11.5769i	−0.753057	+	0.434778i	0.0737401	+	0.997277i	$0.476506\pi$
$710$		0			0
$711$	−24.5388	+	4.96206i	−0.920278	+	0.186092i
$712$		0			0
$713$	−4.48935	−	7.77579i	−0.168128	−	0.291205i
$714$		0			0
$715$	−0.464582	−	0.268227i	−0.0173744	−	0.0100311i
$716$		0			0
$717$	−3.52391	−	2.03453i	−0.131603	−	0.0759810i
$718$		0			0
$719$		−	22.2715i		−	0.830587i	−0.909687	−	0.415294i	$-0.863679\pi$
$719$		−	22.2715i		−	0.830587i	0.909687	−	0.415294i	$-0.136321\pi$
$720$		0			0
$721$	34.9957			1.30331
$722$		0			0
$723$	1.74252			0.0648051
$724$		0			0
$725$			18.3461i			0.681358i
$726$		0			0
$727$	−13.6563	+	7.88445i	−0.506483	+	0.292418i	−0.731387	−	0.681963i	$-0.761127\pi$
$727$	−13.6563	+	7.88445i	−0.506483	+	0.292418i	0.224904	+	0.974381i	$0.427793\pi$
$728$		0			0
$729$	−17.6003			−0.651864
$730$		0			0
$731$	4.78256	−	2.76121i	0.176889	−	0.102127i
$732$		0			0
$733$	−0.161586			−0.00596832			−0.00298416	−	0.999996i	$-0.500950\pi$
$733$	−0.161586			−0.00596832			−0.00298416	+	0.999996i	$0.500950\pi$
$734$		0			0
$735$	1.33302	+	2.30886i	0.0491691	+	0.0851634i
$736$		0			0
$737$	0.164160	−	0.284334i	0.00604691	−	0.0104736i
$738$		0			0
$739$	−7.76076	−	13.4420i	−0.285484	−	0.494473i	0.687242	−	0.726428i	$-0.258821\pi$
$739$	−7.76076	−	13.4420i	−0.285484	−	0.494473i	−0.972726	+	0.231955i	$0.925488\pi$
$740$		0			0
$741$	8.16945	−	4.71664i	0.300112	−	0.173270i
$742$		0			0
$743$	42.5993	+	24.5947i	1.56282	+	0.902293i	0.996970	+	0.0777828i	$0.0247841\pi$
$743$	42.5993	+	24.5947i	1.56282	+	0.902293i	0.565847	+	0.824510i	$0.308549\pi$
$744$		0			0
$745$	9.32217	−	5.38216i	0.341538	−	0.197187i
$746$		0			0
$747$	2.98786	−	1.72504i	0.109320	−	0.0631161i
$748$		0			0
$749$	−29.8115			−1.08929
$750$		0			0
$751$	−38.1288	−	22.0137i	−1.39134	−	0.803291i	−0.397877	−	0.917439i	$-0.630253\pi$
$751$	−38.1288	−	22.0137i	−1.39134	−	0.803291i	−0.993464	+	0.114147i	$0.963586\pi$
$752$		0			0
$753$	−4.40857	−	7.63587i	−0.160657	−	0.278267i
$754$		0			0
$755$	−5.42466	+	3.13193i	−0.197424	+	0.113983i
$756$		0			0
$757$	1.96798			0.0715274			0.0357637	−	0.999360i	$-0.488614\pi$
$757$	1.96798			0.0715274			0.0357637	+	0.999360i	$0.488614\pi$
$758$		0			0
$759$	−0.217952	+	0.377503i	−0.00791114	+	0.0137025i
$760$		0			0
$761$	−7.78928	+	13.4914i	−0.282361	+	0.489064i	−0.971966	−	0.235122i	$-0.924451\pi$
$761$	−7.78928	+	13.4914i	−0.282361	+	0.489064i	0.689605	+	0.724186i	$0.257784\pi$
$762$		0			0
$763$		−	48.4611i		−	1.75441i
$764$		0			0
$765$	2.87789	−	1.66155i	0.104050	−	0.0600735i
$766$		0			0
$767$	−14.0188	+	24.2813i	−0.506190	+	0.876747i
$768$		0			0
$769$		−	7.38704i		−	0.266383i	−0.991090	−	0.133192i	$-0.957477\pi$
$769$		−	7.38704i		−	0.266383i	0.991090	−	0.133192i	$-0.0425226\pi$
$770$		0			0
$771$	−3.00649	+	5.20739i	−0.108276	+	0.187540i
$772$		0			0
$773$	−8.84600			−0.318168			−0.159084	−	0.987265i	$-0.550854\pi$
$773$	−8.84600			−0.318168			−0.159084	+	0.987265i	$0.550854\pi$
$774$		0			0
$775$			10.1582i			0.364893i
$776$		0			0
$777$	3.11095	−	1.79611i	0.111605	−	0.0644351i
$778$		0			0
$779$	39.9908	−	69.2662i	1.43282	−	2.48172i
$780$		0			0
$781$	1.95021	+	1.12595i	0.0697838	+	0.0402897i
$782$		0			0
$783$	−8.63856	−	4.98747i	−0.308717	−	0.178238i
$784$		0			0
$785$	9.22301	+	5.32491i	0.329183	+	0.190054i
$786$		0			0
$787$	5.69364	−	3.28722i	0.202956	−	0.117177i	−0.395077	−	0.918648i	$-0.629282\pi$
$787$	5.69364	−	3.28722i	0.202956	−	0.117177i	0.598034	+	0.801471i	$0.295949\pi$
$788$		0			0
$789$		−	6.49074i		−	0.231077i
$790$		0			0
$791$			26.4131i			0.939141i
$792$		0			0
$793$	0.359639	−	0.207638i	0.0127711	−	0.00737343i
$794$		0			0
$795$	1.18630	+	0.684912i	0.0420738	+	0.0242913i
$796$		0			0
$797$	−21.5375	−	12.4347i	−0.762897	−	0.440459i	0.0674381	−	0.997723i	$-0.478517\pi$
$797$	−21.5375	−	12.4347i	−0.762897	−	0.440459i	−0.830335	+	0.557265i	$0.811851\pi$
$798$		0			0
$799$	4.16407	+	2.40413i	0.147314	+	0.0850519i
$800$		0			0
$801$	15.3910	−	26.6580i	0.543815	−	0.941915i
$802$		0			0
$803$	1.65636	−	0.956298i	0.0584515	−	0.0337470i
$804$		0			0
$805$			10.6913i			0.376820i
$806$		0			0
$807$	−11.8214			−0.416132
$808$		0			0
$809$	13.1786	−	22.8260i	0.463335	−	0.802519i	−0.535790	−	0.844351i	$-0.679986\pi$
$809$	13.1786	−	22.8260i	0.463335	−	0.802519i	0.999125	+	0.0418322i	$0.0133195\pi$
$810$		0			0
$811$			42.6435i			1.49742i	0.662900	+	0.748708i	$0.269326\pi$
$811$			42.6435i			1.49742i	−0.662900	+	0.748708i	$0.730674\pi$
$812$		0			0
$813$	4.65124	−	8.05619i	0.163126	−	0.282543i
$814$		0			0
$815$	4.43863	−	2.56264i	0.155478	−	0.0897655i
$816$		0			0
$817$			20.3045i			0.710366i
$818$		0			0
$819$	−18.8932	+	32.7240i	−0.660183	+	1.14347i
$820$		0			0
$821$	−14.2120	+	24.6159i	−0.496002	+	0.859101i	−0.999989	−	0.00461035i	$-0.998532\pi$
$821$	−14.2120	+	24.6159i	−0.496002	+	0.859101i	0.503987	+	0.863711i	$0.331866\pi$
$822$		0			0
$823$	−1.98464			−0.0691803			−0.0345901	−	0.999402i	$-0.511013\pi$
$823$	−1.98464			−0.0691803			−0.0345901	+	0.999402i	$0.511013\pi$
$824$		0			0
$825$	0.427093	−	0.246582i	0.0148695	−	0.00858490i
$826$		0			0
$827$	2.54889	+	4.41480i	0.0886335	+	0.153518i	0.906934	−	0.421273i	$-0.138417\pi$
$827$	2.54889	+	4.41480i	0.0886335	+	0.153518i	−0.818300	+	0.574791i	$0.805083\pi$
$828$		0			0
$829$	−20.4342	−	11.7977i	−0.709710	−	0.409751i	0.101244	−	0.994862i	$-0.467718\pi$
$829$	−20.4342	−	11.7977i	−0.709710	−	0.409751i	−0.810954	+	0.585111i	$0.801051\pi$
$830$		0			0
$831$	−6.75163			−0.234211
$832$		0			0
$833$	15.1527	−	8.74841i	0.525010	−	0.303114i
$834$		0			0
$835$	11.9167	−	6.88013i	0.412396	−	0.238097i
$836$		0			0
$837$	−4.78314	−	2.76155i	−0.165329	−	0.0954530i
$838$		0			0
$839$	−27.9043	+	16.1106i	−0.963365	+	0.556199i	−0.897207	−	0.441610i	$-0.854407\pi$
$839$	−27.9043	+	16.1106i	−0.963365	+	0.556199i	−0.0661577	+	0.997809i	$0.521074\pi$
$840$		0			0
$841$	−6.47753	−	11.2194i	−0.223363	−	0.386876i
$842$		0			0
$843$	2.13719	−	3.70173i	0.0736089	−	0.127494i
$844$		0			0
$845$	−0.701584	−	1.21518i	−0.0241352	−	0.0418034i
$846$		0			0
$847$	−44.5733			−1.53156
$848$		0			0
$849$	−6.89159	+	3.97886i	−0.236519	+	0.136554i
$850$		0			0
$851$	8.33461			0.285707
$852$		0			0
$853$	21.1601	−	12.2168i	0.724507	−	0.418294i	−0.0919023	−	0.995768i	$-0.529295\pi$
$853$	21.1601	−	12.2168i	0.724507	−	0.418294i	0.816409	+	0.577474i	$0.195961\pi$
$854$		0			0
$855$			12.2182i			0.417853i
$856$		0			0
$857$	14.8659			0.507810			0.253905	−	0.967229i	$-0.418285\pi$
$857$	14.8659			0.507810			0.253905	+	0.967229i	$0.418285\pi$
$858$		0			0
$859$	−11.0933			−0.378500			−0.189250	−	0.981929i	$-0.560606\pi$
$859$	−11.0933			−0.378500			−0.189250	+	0.981929i	$0.560606\pi$
$860$		0			0
$861$		−	20.8473i		−	0.710473i
$862$		0			0
$863$	−18.7007	−	10.7968i	−0.636578	−	0.367528i	0.146717	−	0.989178i	$-0.453129\pi$
$863$	−18.7007	−	10.7968i	−0.636578	−	0.367528i	−0.783295	+	0.621650i	$0.786463\pi$
$864$		0			0
$865$	−4.08451	−	2.35819i	−0.138877	−	0.0801809i
$866$		0			0
$867$	−2.92944	−	5.07394i	−0.0994891	−	0.172320i
$868$		0			0
$869$	−0.443070	−	2.19111i	−0.0150301	−	0.0743283i
$870$		0			0
$871$	−3.72119	+	2.14843i	−0.126088	+	0.0727967i
$872$		0			0
$873$	2.72577	−	4.72118i	0.0922535	−	0.159788i
$874$		0			0
$875$	12.6502	−	21.9109i	0.427656	−	0.740723i
$876$		0			0
$877$	11.4740			0.387450			0.193725	−	0.981056i	$-0.437943\pi$
$877$	11.4740			0.387450			0.193725	+	0.981056i	$0.437943\pi$
$878$		0			0
$879$			5.01392i			0.169115i
$880$		0			0
$881$			33.3584i			1.12387i	0.827180	+	0.561937i	$0.189944\pi$
$881$			33.3584i			1.12387i	−0.827180	+	0.561937i	$0.810056\pi$
$882$		0			0
$883$	33.0578			1.11248			0.556242	−	0.831020i	$-0.312243\pi$
$883$	33.0578			1.11248			0.556242	+	0.831020i	$0.312243\pi$
$884$		0			0
$885$	1.18152	+	2.04645i	0.0397163	+	0.0687907i
$886$		0			0
$887$			25.7081i			0.863193i	0.902067	+	0.431596i	$0.142049\pi$
$887$			25.7081i			0.863193i	−0.902067	+	0.431596i	$0.857951\pi$
$888$		0			0
$889$	−35.5670	−	61.6039i	−1.19288	−	2.06613i
$890$		0			0
$891$		−	1.85715i		−	0.0622168i
$892$		0			0
$893$	−15.3102	+	8.83936i	−0.512337	+	0.295798i
$894$		0			0
$895$	−4.77251	−	2.75541i	−0.159527	−	0.0921032i
$896$		0			0
$897$	4.94053	−	2.85242i	0.164960	−	0.0952395i
$898$		0			0
$899$	4.44201	+	7.69379i	0.148149	+	0.256602i
$900$		0			0
$901$	4.49498	−	7.78553i	0.149749	−	0.259374i
$902$		0			0
$903$	2.64619	+	4.58334i	0.0880598	+	0.152524i
$904$		0			0
$905$	−0.869207	−	1.50551i	−0.0288934	−	0.0500449i
$906$		0			0
$907$			44.1471i			1.46588i	0.680294	+	0.732939i	$0.261852\pi$
$907$			44.1471i			1.46588i	−0.680294	+	0.732939i	$0.738148\pi$
$908$		0			0
$909$	7.79133	−	13.4950i	0.258422	−	0.447600i
$910$		0			0
$911$	−3.99320	+	2.30547i	−0.132300	+	0.0763837i	−0.564689	−	0.825303i	$-0.691004\pi$
$911$	−3.99320	+	2.30547i	−0.132300	+	0.0763837i	0.432389	+	0.901687i	$0.357671\pi$
$912$		0			0
$913$	0.154032	+	0.266791i	0.00509771	+	0.00882949i
$914$		0			0
$915$		−	0.0349998i		−	0.00115706i
$916$		0			0
$917$	11.4857	+	6.63129i	0.379292	+	0.218984i
$918$		0			0
$919$	−4.90138	−	2.82981i	−0.161682	−	0.0933470i	0.416976	−	0.908918i	$-0.363090\pi$
$919$	−4.90138	−	2.82981i	−0.161682	−	0.0933470i	−0.578658	+	0.815571i	$0.696423\pi$
$920$		0			0
$921$	8.89130			0.292978
$922$		0			0
$923$	−14.7358	−	25.5231i	−0.485034	−	0.840103i
$924$		0			0
$925$	−8.16616	−	4.71474i	−0.268502	−	0.155020i
$926$		0			0
$927$	24.1864			0.794385
$928$		0			0
$929$	14.1205	+	8.15248i	0.463279	+	0.267474i	0.713422	−	0.700735i	$-0.247144\pi$
$929$	14.1205	+	8.15248i	0.463279	+	0.267474i	−0.250143	+	0.968209i	$0.580478\pi$
$930$		0			0
$931$			64.3313i			2.10837i
$932$		0			0
$933$	7.11930			0.233075
$934$		0			0
$935$	0.148362	+	0.256971i	0.00485197	+	0.00840386i
$936$		0			0
$937$	33.4207	+	19.2954i	1.09181	+	0.630354i	0.934056	−	0.357125i	$-0.116243\pi$
$937$	33.4207	+	19.2954i	1.09181	+	0.630354i	0.157749	+	0.987479i	$0.449576\pi$
$938$		0			0
$939$	5.26629	−	9.12149i	0.171859	−	0.297669i
$940$		0			0
$941$	10.4001	−	18.0134i	0.339033	−	0.587222i	−0.645218	−	0.763998i	$-0.723234\pi$
$941$	10.4001	−	18.0134i	0.339033	−	0.587222i	0.984251	+	0.176777i	$0.0565670\pi$
$942$		0			0
$943$	24.1847	−	41.8892i	0.787564	−	1.36410i
$944$		0			0
$945$	3.28829	+	5.69549i	0.106968	+	0.185274i
$946$		0			0
$947$	21.7971			0.708310			0.354155	−	0.935187i	$-0.384768\pi$
$947$	21.7971			0.708310			0.354155	+	0.935187i	$0.384768\pi$
$948$		0			0
$949$	−25.0309			−0.812537
$950$		0			0
$951$	1.36485	+	2.36399i	0.0442584	+	0.0766577i
$952$		0			0
$953$	3.48839	−	6.04207i	0.113000	−	0.195722i	−0.803978	−	0.594658i	$-0.797287\pi$
$953$	3.48839	−	6.04207i	0.113000	−	0.195722i	0.916979	+	0.398937i	$0.130621\pi$
$954$		0			0
$955$	7.39833	−	12.8143i	0.239404	−	0.414661i
$956$		0			0
$957$	0.215653	−	0.373522i	0.00697108	−	0.0120743i
$958$		0			0
$959$	−44.9400	−	25.9461i	−1.45119	−	0.837845i
$960$		0			0
$961$	−13.0405	−	22.5868i	−0.420660	−	0.728605i
$962$		0			0
$963$	−20.6034			−0.663936
$964$		0			0
$965$			0.0906985i			0.00291969i
$966$		0			0
$967$	−4.74544	−	2.73978i	−0.152603	−	0.0881055i	0.421754	−	0.906710i	$-0.361415\pi$
$967$	−4.74544	−	2.73978i	−0.152603	−	0.0881055i	−0.574357	+	0.818605i	$0.694748\pi$
$968$		0			0
$969$	−5.21777			−0.167619
$970$		0			0
$971$	25.6027	+	14.7817i	0.821629	+	0.474368i	0.850978	−	0.525202i	$-0.176010\pi$
$971$	25.6027	+	14.7817i	0.821629	+	0.474368i	−0.0293491	+	0.999569i	$0.509343\pi$
$972$		0			0
$973$	36.7323	+	63.6221i	1.17758	+	2.03963i
$974$		0			0
$975$	−6.45425			−0.206701
$976$		0			0
$977$	32.1287	+	18.5495i	1.02789	+	0.593451i	0.916379	−	0.400312i	$-0.131098\pi$
$977$	32.1287	+	18.5495i	1.02789	+	0.593451i	0.111509	+	0.993763i	$0.464432\pi$
$978$		0			0
$979$	2.38034	+	1.37429i	0.0760759	+	0.0439224i
$980$		0			0
$981$		−	33.4926i		−	1.06934i
$982$		0			0
$983$	19.9452	+	34.5462i	0.636154	+	1.10185i	0.986269	+	0.165145i	$0.0528092\pi$
$983$	19.9452	+	34.5462i	0.636154	+	1.10185i	−0.350115	+	0.936707i	$0.613858\pi$
$984$		0			0
$985$	4.12215	−	2.37992i	0.131343	−	0.0758307i
$986$		0			0
$987$	−2.30398	+	3.99062i	−0.0733366	+	0.127023i
$988$		0			0
$989$			12.2793i			0.390459i
$990$		0			0
$991$	11.2528	+	19.4904i	0.357456	+	0.619132i	0.987535	−	0.157399i	$-0.0503109\pi$
$991$	11.2528	+	19.4904i	0.357456	+	0.619132i	−0.630079	+	0.776531i	$0.716978\pi$
$992$		0			0
$993$	2.05999	+	3.56801i	0.0653719	+	0.113227i
$994$		0			0
$995$	−1.40894	+	2.44035i	−0.0446663	+	0.0773643i
$996$		0			0
$997$	−30.9578	−	53.6205i	−0.980443	−	1.69818i	−0.660658	−	0.750687i	$-0.729722\pi$
$997$	−30.9578	−	53.6205i	−0.980443	−	1.69818i	−0.319786	−	0.947490i	$-0.603611\pi$
$998$		0			0
$999$	4.44002	−	2.56344i	0.140476	−	0.0811038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1264.2.n.i.767.6	yes	28
4.3	odd	2	inner	1264.2.n.i.767.9	yes	28
79.24	odd	6	inner	1264.2.n.i.735.9	yes	28
316.103	even	6	inner	1264.2.n.i.735.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1264.2.n.i.735.6	✓	28	316.103	even	6	inner
1264.2.n.i.735.9	yes	28	79.24	odd	6	inner
1264.2.n.i.767.6	yes	28	1.1	even	1	trivial
1264.2.n.i.767.9	yes	28	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1264 = 2^{4} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1264.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.214059 - 0.370761i) q^{3} +(0.323998 - 0.561181i) q^{5} +(2.03778 - 3.52953i) q^{7} +(1.40836 - 2.43935i) q^{9} +O(q^{10})\)	\(q+(-0.214059 - 0.370761i) q^{3} +(0.323998 - 0.561181i) q^{5} +(2.03778 - 3.52953i) q^{7} +(1.40836 - 2.43935i) q^{9} +(0.217813 + 0.125754i) q^{11} +(-1.64580 - 2.85061i) q^{13} -0.277419 q^{15} +1.82066i q^{17} +(-5.79726 - 3.34705i) q^{19} -1.74482 q^{21} +(-3.50593 - 2.02415i) q^{23} +(2.29005 + 3.96648i) q^{25} -2.49024 q^{27} +(3.46896 + 2.00281i) q^{29} +(1.92075 + 1.10895i) q^{31} -0.107676i q^{33} +(-1.32047 - 2.28712i) q^{35} +(-1.78297 + 1.02940i) q^{37} +(-0.704596 + 1.22040i) q^{39} +11.9481i q^{41} +(-1.51660 - 2.62683i) q^{43} +(-0.912609 - 1.58069i) q^{45} +(1.32047 - 2.28712i) q^{47} +(-4.80508 - 8.32264i) q^{49} +(0.675030 - 0.389729i) q^{51} +(-4.27622 - 2.46887i) q^{53} +(0.141142 - 0.0814883i) q^{55} +2.86587i q^{57} +(-4.25897 - 7.37676i) q^{59} +0.126162i q^{61} +(-5.73984 - 9.94169i) q^{63} -2.13294 q^{65} -1.30540i q^{67} +1.73315i q^{69} +8.95357 q^{71} +(3.80224 - 6.58568i) q^{73} +(0.980413 - 1.69812i) q^{75} +(0.887709 - 0.512519i) q^{77} +(-5.88156 - 6.66387i) q^{79} +(-3.69201 - 6.39475i) q^{81} +(1.06076 + 0.612431i) q^{83} +(1.02172 + 0.589890i) q^{85} -1.71488i q^{87} +10.9283 q^{89} -13.4151 q^{91} -0.949521i q^{93} +(-3.75660 + 2.16887i) q^{95} +1.93543 q^{97} +(0.613517 - 0.354214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 20 q^{9}+O(q^{10}) \) 28 * q - 20 * q^9	\( 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) \) 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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