LMFDB - Embedded newform 1764.2.i.h.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(373,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("1764.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + 16x^{8} - 39x^{6} + 144x^{4} - 162x^{2} + 729 $ x^12 - 2x^10 + 16x^8 - 39x^6 + 144x^4 - 162*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$0.965975 - 1.43767i$ of defining polynomial
Character	$\chi$	$=$	1764.373
Dual form			1764.2.i.h.1537.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.762070 - 1.55539i) q^{3} +(-1.95014 - 3.37774i) q^{5} +(-1.83850 + 2.37064i) q^{9} +O(q^{10})$	\(q+(-0.762070 - 1.55539i) q^{3} +(-1.95014 - 3.37774i) q^{5} +(-1.83850 + 2.37064i) q^{9} +(2.13378 - 3.69582i) q^{11} +(2.71221 - 4.69768i) q^{13} +(-3.76757 + 5.60730i) q^{15} +(-2.49012 - 4.31301i) q^{17} +(0.222091 - 0.384673i) q^{19} +(-4.10607 - 7.11191i) q^{23} +(-5.10607 + 8.84396i) q^{25} +(5.08834 + 1.05300i) q^{27} +(1.33850 + 2.31835i) q^{29} +0.851993 q^{31} +(-7.37455 - 0.502398i) q^{33} +(4.90135 - 8.48939i) q^{37} +(-9.37363 - 0.638587i) q^{39} +(2.69402 - 4.66618i) q^{41} +(4.31078 + 7.46649i) q^{43} +(11.5927 + 1.58689i) q^{45} +3.49246 q^{47} +(-4.81078 + 7.15992i) q^{51} +(2.83850 + 4.91642i) q^{53} -16.6447 q^{55} +(-0.767567 - 0.0522912i) q^{57} -1.89558 q^{59} -11.2566 q^{61} -21.1567 q^{65} +2.59057 q^{67} +(-7.93272 + 11.8063i) q^{69} +0.141862 q^{71} +(5.16595 + 8.94769i) q^{73} +(17.6470 + 1.20222i) q^{75} -0.409429 q^{79} +(-2.23985 - 8.71683i) q^{81} +(2.08231 + 3.60666i) q^{83} +(-9.71213 + 16.8219i) q^{85} +(2.58591 - 3.84863i) q^{87} +(-1.20625 + 2.08929i) q^{89} +(-0.649278 - 1.32518i) q^{93} -1.73243 q^{95} +(3.80448 + 6.58955i) q^{97} +(4.83850 + 11.8532i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{9}+O(q^{10}) $ 12 * q - 8 * q^9	$ 12 q - 8 q^{9} + 8 q^{11} - 10 q^{15} - 12 q^{25} + 2 q^{29} + 6 q^{37} - 28 q^{39} + 6 q^{43} - 12 q^{51} + 20 q^{53} + 26 q^{57} - 92 q^{65} + 24 q^{67} + 44 q^{71} - 12 q^{79} + 40 q^{81} - 18 q^{85} + 52 q^{93} - 56 q^{95} + 44 q^{99}+O(q^{100}) $ 12 * q - 8 * q^9 + 8 * q^11 - 10 * q^15 - 12 * q^25 + 2 * q^29 + 6 * q^37 - 28 * q^39 + 6 * q^43 - 12 * q^51 + 20 * q^53 + 26 * q^57 - 92 * q^65 + 24 * q^67 + 44 * q^71 - 12 * q^79 + 40 * q^81 - 18 * q^85 + 52 * q^93 - 56 * q^95 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.762070	−	1.55539i	−0.439981	−	0.898007i
$3$	−0.762070	−	1.55539i	−0.439981	−	0.898007i
$4$		0			0
$5$	−1.95014	−	3.37774i	−0.872128	−	1.51057i	−0.859791	−	0.510645i	$-0.829407\pi$
$5$	−1.95014	−	3.37774i	−0.872128	−	1.51057i	−0.0123362	−	0.999924i	$-0.503927\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.83850	+	2.37064i	−0.612833	+	0.790213i
$10$		0			0
$11$	2.13378	−	3.69582i	0.643360	−	1.11433i	−0.341318	−	0.939948i	$-0.610873\pi$
$11$	2.13378	−	3.69582i	0.643360	−	1.11433i	0.984678	−	0.174384i	$-0.0557935\pi$
$12$		0			0
$13$	2.71221	−	4.69768i	0.752231	−	1.30290i	−0.194508	−	0.980901i	$-0.562311\pi$
$13$	2.71221	−	4.69768i	0.752231	−	1.30290i	0.946739	−	0.322001i	$-0.104355\pi$
$14$		0			0
$15$	−3.76757	+	5.60730i	−0.972782	+	1.44780i
$16$		0			0
$17$	−2.49012	−	4.31301i	−0.603942	−	1.04606i	−0.992218	−	0.124515i	$-0.960263\pi$
$17$	−2.49012	−	4.31301i	−0.603942	−	1.04606i	0.388276	−	0.921543i	$-0.373071\pi$
$18$		0			0
$19$	0.222091	−	0.384673i	0.0509512	−	0.0882501i	−0.839425	−	0.543476i	$-0.817108\pi$
$19$	0.222091	−	0.384673i	0.0509512	−	0.0882501i	0.890376	+	0.455226i	$0.150441\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.10607	−	7.11191i	−0.856174	−	1.48294i	−0.875552	−	0.483124i	$-0.839502\pi$
$23$	−4.10607	−	7.11191i	−0.856174	−	1.48294i	0.0193779	−	0.999812i	$-0.493831\pi$
$24$		0			0
$25$	−5.10607	+	8.84396i	−1.02121	+	1.76879i
$26$		0			0
$27$	5.08834	+	1.05300i	0.979251	+	0.202649i
$28$		0			0
$29$	1.33850	+	2.31835i	0.248553	+	0.430506i	0.963125	−	0.269056i	$-0.0867117\pi$
$29$	1.33850	+	2.31835i	0.248553	+	0.430506i	−0.714572	+	0.699562i	$0.753378\pi$
$30$		0			0
$31$	0.851993			0.153022			0.0765112	−	0.997069i	$-0.475622\pi$
$31$	0.851993			0.153022			0.0765112	+	0.997069i	$0.475622\pi$
$32$		0			0
$33$	−7.37455	−	0.502398i	−1.28374	−	0.0874562i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.90135	−	8.48939i	0.805777	−	1.39565i	−0.109988	−	0.993933i	$-0.535081\pi$
$37$	4.90135	−	8.48939i	0.805777	−	1.39565i	0.915765	−	0.401714i	$-0.131585\pi$
$38$		0			0
$39$	−9.37363	−	0.638587i	−1.50098	−	0.102256i
$40$		0			0
$41$	2.69402	−	4.66618i	0.420735	−	0.728735i	−0.575276	−	0.817959i	$-0.695105\pi$
$41$	2.69402	−	4.66618i	0.420735	−	0.728735i	0.996012	+	0.0892242i	$0.0284388\pi$
$42$		0			0
$43$	4.31078	+	7.46649i	0.657388	+	1.13863i	0.981289	+	0.192538i	$0.0616720\pi$
$43$	4.31078	+	7.46649i	0.657388	+	1.13863i	−0.323902	+	0.946091i	$0.604995\pi$
$44$		0			0
$45$	11.5927	+	1.58689i	1.72814	+	0.236560i
$46$		0			0
$47$	3.49246			0.509428			0.254714	−	0.967016i	$-0.418019\pi$
$47$	3.49246			0.509428			0.254714	+	0.967016i	$0.418019\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.81078	+	7.15992i	−0.673644	+	1.00259i
$52$		0			0
$53$	2.83850	+	4.91642i	0.389898	+	0.675323i	0.992435	−	0.122768i	$-0.0391770\pi$
$53$	2.83850	+	4.91642i	0.389898	+	0.675323i	−0.602538	+	0.798090i	$0.705844\pi$
$54$		0			0
$55$	−16.6447			−2.24437
$56$		0			0
$57$	−0.767567	−	0.0522912i	−0.101667	−	0.00692614i
$58$		0			0
$59$	−1.89558			−0.246783			−0.123392	−	0.992358i	$-0.539377\pi$
$59$	−1.89558			−0.246783			−0.123392	+	0.992358i	$0.539377\pi$
$60$		0			0
$61$	−11.2566			−1.44126			−0.720632	−	0.693317i	$-0.756148\pi$
$61$	−11.2566			−1.44126			−0.720632	+	0.693317i	$0.756148\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−21.1567			−2.62416
$66$		0			0
$67$	2.59057			0.316489			0.158244	−	0.987400i	$-0.449417\pi$
$67$	2.59057			0.316489			0.158244	+	0.987400i	$0.449417\pi$
$68$		0			0
$69$	−7.93272	+	11.8063i	−0.954987	+	1.42131i
$70$		0			0
$71$	0.141862			0.0168359			0.00841794	−	0.999965i	$-0.497320\pi$
$71$	0.141862			0.0168359			0.00841794	+	0.999965i	$0.497320\pi$
$72$		0			0
$73$	5.16595	+	8.94769i	0.604629	+	1.04725i	0.992110	+	0.125370i	$0.0400118\pi$
$73$	5.16595	+	8.94769i	0.604629	+	1.04725i	−0.387481	+	0.921878i	$0.626655\pi$
$74$		0			0
$75$	17.6470	+	1.20222i	2.03770	+	0.138820i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.409429			−0.0460644			−0.0230322	−	0.999735i	$-0.507332\pi$
$79$	−0.409429			−0.0460644			−0.0230322	+	0.999735i	$0.507332\pi$
$80$		0			0
$81$	−2.23985	−	8.71683i	−0.248872	−	0.968536i
$82$		0			0
$83$	2.08231	+	3.60666i	0.228563	+	0.395882i	0.957382	−	0.288823i	$-0.0932641\pi$
$83$	2.08231	+	3.60666i	0.228563	+	0.395882i	−0.728820	+	0.684706i	$0.759931\pi$
$84$		0			0
$85$	−9.71213	+	16.8219i	−1.05343	+	1.82459i
$86$		0			0
$87$	2.58591	−	3.84863i	0.277239	−	0.412617i
$88$		0			0
$89$	−1.20625	+	2.08929i	−0.127863	+	0.221464i	−0.922848	−	0.385164i	$-0.874145\pi$
$89$	−1.20625	+	2.08929i	−0.127863	+	0.221464i	0.794986	+	0.606628i	$0.207478\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.649278	−	1.32518i	−0.0673270	−	0.137415i
$94$		0			0
$95$	−1.73243			−0.177744
$96$		0			0
$97$	3.80448	+	6.58955i	0.386286	+	0.669067i	0.991947	−	0.126656i	$-0.0404244\pi$
$97$	3.80448	+	6.58955i	0.386286	+	0.669067i	−0.605661	+	0.795723i	$0.707091\pi$
$98$		0			0
$99$	4.83850	+	11.8532i	0.486287	+	1.19129i
$100$		0			0
$101$	−2.56185	+	4.43726i	−0.254914	+	0.441524i	−0.964872	−	0.262720i	$-0.915380\pi$
$101$	−2.56185	+	4.43726i	−0.254914	+	0.441524i	0.709958	+	0.704244i	$0.248714\pi$
$102$		0			0
$103$	6.48031	+	11.2242i	0.638524	+	1.10596i	0.985757	+	0.168177i	$0.0537880\pi$
$103$	6.48031	+	11.2242i	0.638524	+	1.10596i	−0.347233	+	0.937779i	$0.612879\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.76757	−	9.98972i	0.557572	−	0.965743i	−0.440127	−	0.897936i	$-0.645066\pi$
$107$	5.76757	−	9.98972i	0.557572	−	0.965743i	0.997698	−	0.0678070i	$-0.0216002\pi$
$108$		0			0
$109$	0.204714	+	0.354576i	0.0196081	+	0.0339622i	0.875663	−	0.482923i	$-0.160425\pi$
$109$	0.204714	+	0.354576i	0.0196081	+	0.0339622i	−0.856055	+	0.516885i	$0.827091\pi$
$110$		0			0
$111$	−16.9395	−	1.15402i	−1.60783	−	0.109535i
$112$		0			0
$113$	−6.94456	+	12.0283i	−0.653290	+	1.13153i	0.329030	+	0.944319i	$0.393278\pi$
$113$	−6.94456	+	12.0283i	−0.653290	+	1.13153i	−0.982320	+	0.187211i	$0.940055\pi$
$114$		0			0
$115$	−16.0148	+	27.7384i	−1.49339	+	2.58662i
$116$		0			0
$117$	6.15011	+	15.0663i	0.568578	+	1.39288i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.60607	−	6.24589i	−0.327824	−	0.567808i
$122$		0			0
$123$	−9.31078	−	0.634305i	−0.839525	−	0.0571934i
$124$		0			0
$125$	20.3287			1.81826
$126$		0			0
$127$	11.6216			1.03125			0.515623	−	0.856815i	$-0.327560\pi$
$127$	11.6216			1.03125			0.515623	+	0.856815i	$0.327560\pi$
$128$		0			0
$129$	8.32821	−	12.3949i	0.733258	−	1.09131i
$130$		0			0
$131$	−2.02775	−	3.51216i	−0.177165	−	0.306859i	0.763743	−	0.645520i	$-0.223359\pi$
$131$	−2.02775	−	3.51216i	−0.177165	−	0.306859i	−0.940908	+	0.338661i	$0.890026\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−6.36622	−	19.2406i	−0.547917	−	1.65596i
$136$		0			0
$137$	−4.57835	+	7.92993i	−0.391155	+	0.677500i	−0.992602	−	0.121413i	$-0.961258\pi$
$137$	−4.57835	+	7.92993i	−0.391155	+	0.677500i	0.601448	+	0.798912i	$0.294591\pi$
$138$		0			0
$139$	5.23869	−	9.07369i	0.444340	−	0.769620i	−0.553666	−	0.832739i	$-0.686771\pi$
$139$	5.23869	−	9.07369i	0.444340	−	0.769620i	0.998006	+	0.0631191i	$0.0201048\pi$
$140$		0			0
$141$	−2.66150	−	5.43215i	−0.224139	−	0.457470i
$142$		0			0
$143$	−11.5745	−	20.0477i	−0.967910	−	1.67647i
$144$		0			0
$145$	5.22051	−	9.04219i	0.433540	−	0.750913i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.13378	+	14.0881i	0.666346	+	1.15414i	0.978919	+	0.204251i	$0.0654757\pi$
$149$	8.13378	+	14.0881i	0.666346	+	1.15414i	−0.312573	+	0.949894i	$0.601191\pi$
$150$		0			0
$151$	3.60607	−	6.24589i	0.293457	−	0.508283i	−0.681167	−	0.732128i	$-0.738527\pi$
$151$	3.60607	−	6.24589i	0.293457	−	0.508283i	0.974625	+	0.223844i	$0.0718608\pi$
$152$		0			0
$153$	14.8027	+	2.02629i	1.19672	+	0.163816i
$154$		0			0
$155$	−1.66150	−	2.87781i	−0.133455	−	0.231151i
$156$		0			0
$157$	1.18706			0.0947376			0.0473688	−	0.998877i	$-0.484916\pi$
$157$	1.18706			0.0947376			0.0473688	+	0.998877i	$0.484916\pi$
$158$		0			0
$159$	5.48384	−	8.16164i	0.434897	−	0.647260i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.5074	+	18.1994i	−0.823004	+	1.42549i	0.0804306	+	0.996760i	$0.474370\pi$
$163$	−10.5074	+	18.1994i	−0.823004	+	1.42549i	−0.903435	+	0.428725i	$0.858963\pi$
$164$		0			0
$165$	12.6844	+	25.8890i	0.987480	+	2.01546i
$166$		0			0
$167$	10.0322	−	17.3763i	0.776315	−	1.34462i	−0.157738	−	0.987481i	$-0.550420\pi$
$167$	10.0322	−	17.3763i	0.776315	−	1.34462i	0.934053	−	0.357136i	$-0.116247\pi$
$168$		0			0
$169$	−8.21213	−	14.2238i	−0.631702	−	1.09414i
$170$		0			0
$171$	0.503607	+	1.23372i	0.0385118	+	0.0943448i
$172$		0			0
$173$	6.06019			0.460748			0.230374	−	0.973102i	$-0.426005\pi$
$173$	6.06019			0.460748			0.230374	+	0.973102i	$0.426005\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.44456	+	2.94837i	0.108580	+	0.221613i
$178$		0			0
$179$	−4.41685	−	7.65020i	−0.330131	−	0.571803i	0.652407	−	0.757869i	$-0.273759\pi$
$179$	−4.41685	−	7.65020i	−0.330131	−	0.571803i	−0.982537	+	0.186066i	$0.940426\pi$
$180$		0			0
$181$	−24.1809			−1.79735			−0.898676	−	0.438614i	$-0.855470\pi$
$181$	−24.1809			−1.79735			−0.898676	+	0.438614i	$0.855470\pi$
$182$		0			0
$183$	8.57835	+	17.5085i	0.634130	+	1.29427i
$184$		0			0
$185$	−38.2332			−2.81096
$186$		0			0
$187$	−21.2535			−1.55421
$188$		0			0
$189$		0			0
$190$		0			0
$191$	20.2270			1.46357			0.731786	−	0.681535i	$-0.238687\pi$
$191$	20.2270			1.46357			0.731786	+	0.681535i	$0.238687\pi$
$192$		0			0
$193$	−12.3933			−0.892087			−0.446044	−	0.895011i	$-0.647167\pi$
$193$	−12.3933			−0.892087			−0.446044	+	0.895011i	$0.647167\pi$
$194$		0			0
$195$	16.1229	+	32.9070i	1.15458	+	2.35652i
$196$		0			0
$197$	14.3933			1.02548			0.512739	−	0.858544i	$-0.328631\pi$
$197$	14.3933			1.02548			0.512739	+	0.858544i	$0.328631\pi$
$198$		0			0
$199$	−5.25688	−	9.10518i	−0.372650	−	0.645449i	0.617322	−	0.786711i	$-0.288218\pi$
$199$	−5.25688	−	9.10518i	−0.372650	−	0.645449i	−0.989972	+	0.141261i	$0.954884\pi$
$200$		0			0
$201$	−1.97420	−	4.02936i	−0.139249	−	0.284209i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−21.0148			−1.46774
$206$		0			0
$207$	24.4088	+	3.34125i	1.69653	+	0.232233i
$208$		0			0
$209$	−0.947789	−	1.64162i	−0.0655599	−	0.113553i
$210$		0			0
$211$	11.7121	−	20.2860i	0.806296	−	1.39655i	−0.109116	−	0.994029i	$-0.534802\pi$
$211$	11.7121	−	20.2860i	0.806296	−	1.39655i	0.915412	−	0.402517i	$-0.131865\pi$
$212$		0			0
$213$	−0.108109	−	0.220651i	−0.00740747	−	0.0151187i
$214$		0			0
$215$	16.8132	−	29.1214i	1.14665	−	1.98606i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	9.98036	−	14.8539i	0.674410	−	1.00373i
$220$		0			0
$221$	−27.0148			−1.81721
$222$		0			0
$223$	−12.6727	−	21.9497i	−0.848625	−	1.46986i	−0.882436	−	0.470433i	$-0.844098\pi$
$223$	−12.6727	−	21.9497i	−0.848625	−	1.46986i	0.0338111	−	0.999428i	$-0.489236\pi$
$224$		0			0
$225$	−11.5783	−	28.3642i	−0.771890	−	1.89095i
$226$		0			0
$227$	9.01267	−	15.6104i	0.598192	−	1.03610i	−0.394896	−	0.918726i	$-0.629219\pi$
$227$	9.01267	−	15.6104i	0.598192	−	1.03610i	0.993088	−	0.117373i	$-0.0374474\pi$
$228$		0			0
$229$	2.71221	+	4.69768i	0.179228	+	0.310431i	0.941616	−	0.336688i	$-0.109307\pi$
$229$	2.71221	+	4.69768i	0.179228	+	0.310431i	−0.762389	+	0.647120i	$0.775973\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.42165	−	2.46237i	0.0931356	−	0.161316i	−0.815693	−	0.578484i	$-0.803644\pi$
$233$	1.42165	−	2.46237i	0.0931356	−	0.161316i	0.908829	+	0.417169i	$0.136978\pi$
$234$		0			0
$235$	−6.81078	−	11.7966i	−0.444286	−	0.769526i
$236$		0			0
$237$	0.312014	+	0.636823i	0.0202675	+	0.0413661i
$238$		0			0
$239$	−6.09057	+	10.5492i	−0.393966	+	0.682370i	−0.992969	−	0.118378i	$-0.962231\pi$
$239$	−6.09057	+	10.5492i	−0.393966	+	0.682370i	0.599002	+	0.800747i	$0.295564\pi$
$240$		0			0
$241$	−9.31237	+	16.1295i	−0.599863	+	1.03899i	0.392978	+	0.919548i	$0.371445\pi$
$241$	−9.31237	+	16.1295i	−0.599863	+	1.03899i	−0.992841	+	0.119445i	$0.961888\pi$
$242$		0			0
$243$	−11.8512	+	10.1267i	−0.760253	+	0.649627i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.20471	−	2.08663i	−0.0766541	−	0.132769i
$248$		0			0
$249$	4.02291	−	5.98733i	0.254942	−	0.379432i
$250$		0			0
$251$	7.14015			0.450682			0.225341	−	0.974280i	$-0.427650\pi$
$251$	7.14015			0.450682			0.225341	+	0.974280i	$0.427650\pi$
$252$		0			0
$253$	−35.0458			−2.20331
$254$		0			0
$255$	33.5660	+	2.28671i	2.10198	+	0.143200i
$256$		0			0
$257$	0.672148	+	1.16419i	0.0419274	+	0.0726204i	0.886228	−	0.463250i	$-0.153317\pi$
$257$	0.672148	+	1.16419i	0.0419274	+	0.0726204i	−0.844300	+	0.535871i	$0.819984\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−7.95679	−	1.08918i	−0.492513	−	0.0674187i
$262$		0			0
$263$	12.1493	−	21.0432i	0.749157	−	1.29758i	−0.199071	−	0.979985i	$-0.563792\pi$
$263$	12.1493	−	21.0432i	0.749157	−	1.29758i	0.948227	−	0.317592i	$-0.102874\pi$
$264$		0			0
$265$	11.0709	−	19.1754i	0.680081	−	1.17794i
$266$		0			0
$267$	4.16892	+	0.284011i	0.255134	+	0.0173812i
$268$		0			0
$269$	−2.69989	−	4.67636i	−0.164615	−	0.285122i	0.771903	−	0.635740i	$-0.219305\pi$
$269$	−2.69989	−	4.67636i	−0.164615	−	0.285122i	−0.936519	+	0.350618i	$0.885972\pi$
$270$		0			0
$271$	−6.78589	+	11.7535i	−0.412213	+	0.713974i	−0.995131	−	0.0985565i	$-0.968577\pi$
$271$	−6.78589	+	11.7535i	−0.412213	+	0.713974i	0.582918	+	0.812531i	$0.301911\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	21.7905	+	37.7422i	1.31402	+	2.27594i
$276$		0			0
$277$	14.5074	−	25.1276i	0.871666	−	1.50977i	0.0113940	−	0.999935i	$-0.496373\pi$
$277$	14.5074	−	25.1276i	0.871666	−	1.50977i	0.860272	−	0.509835i	$-0.170294\pi$
$278$		0			0
$279$	−1.56639	+	2.01977i	−0.0937771	+	0.120920i
$280$		0			0
$281$	0.885857	+	1.53435i	0.0528458	+	0.0915316i	0.891238	−	0.453536i	$-0.149837\pi$
$281$	0.885857	+	1.53435i	0.0528458	+	0.0915316i	−0.838392	+	0.545067i	$0.816504\pi$
$282$		0			0
$283$	24.2536			1.44173			0.720864	−	0.693076i	$-0.243745\pi$
$283$	24.2536			1.44173			0.720864	+	0.693076i	$0.243745\pi$
$284$		0			0
$285$	1.32024	+	2.69461i	0.0782040	+	0.159615i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−3.90135	+	6.75734i	−0.229491	+	0.397490i
$290$		0			0
$291$	7.35006	−	10.9392i	0.430868	−	0.641265i
$292$		0			0
$293$	−7.52491	+	13.0335i	−0.439610	+	0.761426i	−0.997659	−	0.0683813i	$-0.978217\pi$
$293$	−7.52491	+	13.0335i	−0.439610	+	0.761426i	0.558050	+	0.829808i	$0.311550\pi$
$294$		0			0
$295$	3.69664	+	6.40276i	0.215226	+	0.372783i
$296$		0			0
$297$	14.7491	−	16.5587i	0.855830	−	0.960835i
$298$		0			0
$299$	−44.5460			−2.57616
$300$		0			0
$301$		0			0
$302$		0			0
$303$	8.85399	+	0.603186i	0.508649	+	0.0346521i
$304$		0			0
$305$	21.9520	+	38.0219i	1.25697	+	2.17713i
$306$		0			0
$307$	−4.01912			−0.229383			−0.114692	−	0.993401i	$-0.536588\pi$
$307$	−4.01912			−0.229383			−0.114692	+	0.993401i	$0.536588\pi$
$308$		0			0
$309$	12.5196	−	18.6331i	0.712217	−	1.06000i
$310$		0			0
$311$	1.59688			0.0905510			0.0452755	−	0.998975i	$-0.485583\pi$
$311$	1.59688			0.0905510			0.0452755	+	0.998975i	$0.485583\pi$
$312$		0			0
$313$	−4.87111			−0.275332			−0.137666	−	0.990479i	$-0.543960\pi$
$313$	−4.87111			−0.275332			−0.137666	+	0.990479i	$0.543960\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.37844			−0.470580			−0.235290	−	0.971925i	$-0.575604\pi$
$317$	−8.37844			−0.470580			−0.235290	+	0.971925i	$0.575604\pi$
$318$		0			0
$319$	11.4243			0.639636
$320$		0			0
$321$	−19.9332	−	1.35797i	−1.11256	−	0.0757945i
$322$		0			0
$323$	−2.21213			−0.123086
$324$		0			0
$325$	27.6974	+	47.9733i	1.53638	+	2.66108i
$326$		0			0
$327$	0.395498	−	0.588623i	0.0218711	−	0.0325509i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	25.8337			1.41995			0.709974	−	0.704228i	$-0.248707\pi$
$331$	25.8337			1.41995			0.709974	+	0.704228i	$0.248707\pi$
$332$		0			0
$333$	11.1141	+	27.2271i	0.609051	+	1.49203i
$334$		0			0
$335$	−5.05197	−	8.75026i	−0.276018	−	0.478078i
$336$		0			0
$337$	9.81820	−	17.0056i	0.534831	−	0.926355i	−0.464340	−	0.885657i	$-0.653709\pi$
$337$	9.81820	−	17.0056i	0.534831	−	0.926355i	0.999171	−	0.0406980i	$-0.0129582\pi$
$338$		0			0
$339$	24.0010	+	1.63509i	1.30356	+	0.0888060i
$340$		0			0
$341$	1.81797	−	3.14881i	0.0984485	−	0.170518i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	55.3485	+	3.77067i	2.97986	+	0.203006i
$346$		0			0
$347$	−22.4094			−1.20300			−0.601501	−	0.798872i	$-0.705430\pi$
$347$	−22.4094			−1.20300			−0.601501	+	0.798872i	$0.705430\pi$
$348$		0			0
$349$	−5.38804	−	9.33236i	−0.288415	−	0.499550i	0.685016	−	0.728528i	$-0.259795\pi$
$349$	−5.38804	−	9.33236i	−0.288415	−	0.499550i	−0.973432	+	0.228978i	$0.926462\pi$
$350$		0			0
$351$	18.7473	−	21.0474i	1.00066	−	1.12343i
$352$		0			0
$353$	5.70106	−	9.87453i	0.303437	−	0.525568i	−0.673475	−	0.739210i	$-0.735199\pi$
$353$	5.70106	−	9.87453i	0.303437	−	0.525568i	0.976912	+	0.213642i	$0.0685325\pi$
$354$		0			0
$355$	−0.276650	−	0.479171i	−0.0146830	−	0.0254318i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.38171	−	16.2496i	0.495148	−	0.857621i	−0.504837	−	0.863215i	$-0.668447\pi$
$359$	9.38171	−	16.2496i	0.495148	−	0.857621i	0.999984	+	0.00559386i	$0.00178059\pi$
$360$		0			0
$361$	9.40135	+	16.2836i	0.494808	+	0.857033i
$362$		0			0
$363$	−6.96674	+	10.3687i	−0.365659	+	0.544213i
$364$		0			0
$365$	20.1486	−	34.8984i	1.05463	−	1.82667i
$366$		0			0
$367$	−0.833806	+	1.44420i	−0.0435243	+	0.0753864i	−0.886967	−	0.461833i	$-0.847192\pi$
$367$	−0.833806	+	1.44420i	−0.0435243	+	0.0753864i	0.843443	+	0.537219i	$0.180525\pi$
$368$		0			0
$369$	6.10887	+	14.9653i	0.318015	+	0.779063i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	12.5229	+	21.6903i	0.648412	+	1.12308i	0.983502	+	0.180896i	$0.0578998\pi$
$373$	12.5229	+	21.6903i	0.648412	+	1.12308i	−0.335090	+	0.942186i	$0.608767\pi$
$374$		0			0
$375$	−15.4919	−	31.6192i	−0.799999	−	1.63281i
$376$		0			0
$377$	14.5211			0.747876
$378$		0			0
$379$	5.21213			0.267729			0.133865	−	0.991000i	$-0.457261\pi$
$379$	5.21213			0.267729			0.133865	+	0.991000i	$0.457261\pi$
$380$		0			0
$381$	−8.85644	−	18.0761i	−0.453729	−	0.926067i
$382$		0			0
$383$	−11.2385	−	19.4656i	−0.574258	−	0.994644i	−0.996122	−	0.0879849i	$-0.971957\pi$
$383$	−11.2385	−	19.4656i	−0.574258	−	0.994644i	0.421864	−	0.906659i	$-0.361376\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−25.6257	−	3.50783i	−1.30263	−	0.178313i
$388$		0			0
$389$	5.20471	−	9.01483i	0.263889	−	0.457070i	−0.703383	−	0.710811i	$-0.748328\pi$
$389$	5.20471	−	9.01483i	0.263889	−	0.457070i	0.967272	+	0.253741i	$0.0816612\pi$
$390$		0			0
$391$	−20.4492	+	35.4190i	−1.03416	+	1.79121i
$392$		0			0
$393$	−3.91751	+	5.83046i	−0.197612	+	0.294108i
$394$		0			0
$395$	0.798442	+	1.38294i	0.0401740	+	0.0695834i
$396$		0			0
$397$	−1.31436	+	2.27654i	−0.0659659	+	0.114256i	−0.897122	−	0.441783i	$-0.854346\pi$
$397$	−1.31436	+	2.27654i	−0.0659659	+	0.114256i	0.831156	+	0.556039i	$0.187680\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.59865	+	9.69714i	0.279583	+	0.484252i	0.971281	−	0.237935i	$-0.0764704\pi$
$401$	5.59865	+	9.69714i	0.279583	+	0.484252i	−0.691698	+	0.722187i	$0.743137\pi$
$402$		0			0
$403$	2.31078	−	4.00239i	0.115108	−	0.199373i
$404$		0			0
$405$	−25.0751	+	24.5646i	−1.24599	+	1.22063i
$406$		0			0
$407$	−20.9168	−	36.2290i	−1.03681	−	1.79581i
$408$		0			0
$409$	−31.7309			−1.56899			−0.784495	−	0.620135i	$-0.787078\pi$
$409$	−31.7309			−1.56899			−0.784495	+	0.620135i	$0.787078\pi$
$410$		0			0
$411$	15.8232	+	1.07797i	0.780500	+	0.0531723i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	8.12156	−	14.0670i	0.398672	−	0.690520i
$416$		0			0
$417$	−18.1054	−	1.23345i	−0.886625	−	0.0604022i
$418$		0			0
$419$	19.0449	−	32.9867i	0.930403	−	1.61151i	0.147770	−	0.989022i	$-0.452791\pi$
$419$	19.0449	−	32.9867i	0.930403	−	1.61151i	0.782633	−	0.622483i	$-0.213876\pi$
$420$		0			0
$421$	−0.614143	−	1.06373i	−0.0299315	−	0.0518429i	0.850672	−	0.525697i	$-0.176196\pi$
$421$	−0.614143	−	1.06373i	−0.0299315	−	0.0518429i	−0.880603	+	0.473855i	$0.842862\pi$
$422$		0			0
$423$	−6.42089	+	8.27937i	−0.312194	+	0.402557i
$424$		0			0
$425$	50.8588			2.46701
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−22.3614	+	33.2807i	−1.07962	+	1.60681i
$430$		0			0
$431$	4.66150	+	8.07396i	0.224537	+	0.388909i	0.956180	−	0.292778i	$-0.0945798\pi$
$431$	4.66150	+	8.07396i	0.224537	+	0.388909i	−0.731644	+	0.681687i	$0.761246\pi$
$432$		0			0
$433$	−15.3849			−0.739350			−0.369675	−	0.929161i	$-0.620531\pi$
$433$	−15.3849			−0.739350			−0.369675	+	0.929161i	$0.620531\pi$
$434$		0			0
$435$	−18.0426	−	1.22917i	−0.865074	−	0.0589340i
$436$		0			0
$437$	−3.64768			−0.174492
$438$		0			0
$439$	−5.08935			−0.242901			−0.121451	−	0.992597i	$-0.538755\pi$
$439$	−5.08935			−0.242901			−0.121451	+	0.992597i	$0.538755\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−34.7865			−1.65276			−0.826379	−	0.563114i	$-0.809603\pi$
$443$	−34.7865			−1.65276			−0.826379	+	0.563114i	$0.809603\pi$
$444$		0			0
$445$	9.40943			0.446050
$446$		0			0
$447$	15.7141	−	23.3874i	0.743250	−	1.10618i
$448$		0			0
$449$	−23.8337			−1.12478			−0.562391	−	0.826872i	$-0.690118\pi$
$449$	−23.8337			−1.12478			−0.562391	+	0.826872i	$0.690118\pi$
$450$		0			0
$451$	−11.4969	−	19.9132i	−0.541369	−	0.937678i
$452$		0			0
$453$	−12.4629	−	0.849046i	−0.585558	−	0.0398916i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.8337			0.787447			0.393723	−	0.919229i	$-0.371187\pi$
$457$	16.8337			0.787447			0.393723	+	0.919229i	$0.371187\pi$
$458$		0			0
$459$	−8.12898	−	24.5681i	−0.379428	−	1.14674i
$460$		0			0
$461$	6.13780	+	10.6310i	0.285866	+	0.495134i	0.972819	−	0.231568i	$-0.0743855\pi$
$461$	6.13780	+	10.6310i	0.285866	+	0.495134i	−0.686953	+	0.726702i	$0.741052\pi$
$462$		0			0
$463$	6.10607	−	10.5760i	0.283773	−	0.491509i	−0.688538	−	0.725200i	$-0.741747\pi$
$463$	6.10607	−	10.5760i	0.283773	−	0.491509i	0.972311	+	0.233691i	$0.0750805\pi$
$464$		0			0
$465$	−3.20994	+	4.77738i	−0.148857	+	0.221546i
$466$		0			0
$467$	−16.8791	+	29.2354i	−0.781071	+	1.35285i	0.150248	+	0.988648i	$0.451993\pi$
$467$	−16.8791	+	29.2354i	−0.781071	+	1.35285i	−0.931318	+	0.364206i	$0.881340\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.904622	−	1.84634i	−0.0416828	−	0.0850750i
$472$		0			0
$473$	36.7931			1.69175
$474$		0			0
$475$	2.26802	+	3.92833i	0.104064	+	0.180244i
$476$		0			0
$477$	−16.8736	−	2.30978i	−0.772591	−	0.105758i
$478$		0			0
$479$	−11.9593	+	20.7141i	−0.546434	+	0.946451i	0.452082	+	0.891977i	$0.350682\pi$
$479$	−11.9593	+	20.7141i	−0.546434	+	0.946451i	−0.998515	+	0.0544741i	$0.982652\pi$
$480$		0			0
$481$	−26.5870	−	46.0500i	−1.21226	−	2.09970i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	14.8385	−	25.7010i	0.673781	−	1.16702i
$486$		0			0
$487$	5.19664	+	9.00084i	0.235482	+	0.407867i	0.959413	−	0.282006i	$-0.0909998\pi$
$487$	5.19664	+	9.00084i	0.235482	+	0.407867i	−0.723931	+	0.689873i	$0.757666\pi$
$488$		0			0
$489$	36.3146	+	2.47396i	1.64220	+	0.111877i
$490$		0			0
$491$	−2.68922	+	4.65787i	−0.121363	+	0.210207i	−0.920305	−	0.391201i	$-0.872060\pi$
$491$	−2.68922	+	4.65787i	−0.121363	+	0.210207i	0.798943	+	0.601407i	$0.205393\pi$
$492$		0			0
$493$	6.66603	−	11.5459i	0.300223	−	0.520001i
$494$		0			0
$495$	30.6012	−	39.4585i	1.37542	−	1.77353i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	9.62156	+	16.6650i	0.430720	+	0.746029i	0.996935	−	0.0782282i	$-0.0249263\pi$
$499$	9.62156	+	16.6650i	0.430720	+	0.746029i	−0.566215	+	0.824257i	$0.691593\pi$
$500$		0			0
$501$	−34.6722	−	2.36207i	−1.54904	−	0.105530i
$502$		0			0
$503$	22.3334			0.995798			0.497899	−	0.867235i	$-0.334105\pi$
$503$	22.3334			0.995798			0.497899	+	0.867235i	$0.334105\pi$
$504$		0			0
$505$	19.9838			0.889269
$506$		0			0
$507$	−15.8654	+	23.6127i	−0.704608	+	1.04867i
$508$		0			0
$509$	20.1131	+	34.8369i	0.891497	+	1.54412i	0.838081	+	0.545545i	$0.183677\pi$
$509$	20.1131	+	34.8369i	0.891497	+	1.54412i	0.0534152	+	0.998572i	$0.482989\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	1.53513	−	1.72349i	0.0677779	−	0.0760938i
$514$		0			0
$515$	25.2750	−	43.7776i	1.11375	−	1.92907i
$516$		0			0
$517$	7.45216	−	12.9075i	0.327746	−	0.567672i
$518$		0			0
$519$	−4.61829	−	9.42598i	−0.202720	−	0.413755i
$520$		0			0
$521$	−18.3497	−	31.7826i	−0.803914	−	1.39242i	−0.917022	−	0.398837i	$-0.869414\pi$
$521$	−18.3497	−	31.7826i	−0.803914	−	1.39242i	0.113108	−	0.993583i	$-0.463919\pi$
$522$		0			0
$523$	−14.1727	+	24.5479i	−0.619731	+	1.07341i	0.369804	+	0.929110i	$0.379425\pi$
$523$	−14.1727	+	24.5479i	−0.619731	+	1.07341i	−0.989535	+	0.144296i	$0.953908\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.12156	−	3.67465i	−0.0924166	−	0.160070i
$528$		0			0
$529$	−22.2195	+	38.4854i	−0.966067	+	1.67328i
$530$		0			0
$531$	3.48502	−	4.49373i	0.151237	−	0.195011i
$532$		0			0
$533$	−14.6135	−	25.3113i	−0.632980	−	1.09635i
$534$		0			0
$535$	−44.9902			−1.94509
$536$		0			0
$537$	−8.53313	+	12.6999i	−0.368232	+	0.548042i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	12.3027	−	21.3089i	0.528934	−	0.916141i	−0.470496	−	0.882402i	$-0.655925\pi$
$541$	12.3027	−	21.3089i	0.528934	−	0.916141i	0.999431	−	0.0337394i	$-0.0107416\pi$
$542$		0			0
$543$	18.4275	+	37.6108i	0.790801	+	1.61403i
$544$		0			0
$545$	0.798442	−	1.38294i	0.0342015	−	0.0592388i
$546$		0			0
$547$	−0.106065	−	0.183711i	−0.00453503	−	0.00785491i	0.863749	−	0.503922i	$-0.168110\pi$
$547$	−0.106065	−	0.183711i	−0.00453503	−	0.00785491i	−0.868284	+	0.496067i	$0.834777\pi$
$548$		0			0
$549$	20.6953	−	26.6854i	0.883254	−	1.13891i
$550$		0			0
$551$	1.18907			0.0506563
$552$		0			0
$553$		0			0
$554$		0			0
$555$	29.1364	+	59.4677i	1.23677	+	2.52426i
$556$		0			0
$557$	−9.40877	−	16.2965i	−0.398662	−	0.690503i	0.594899	−	0.803801i	$-0.297192\pi$
$557$	−9.40877	−	16.2965i	−0.398662	−	0.690503i	−0.993561	+	0.113297i	$0.963859\pi$
$558$		0			0
$559$	46.7669			1.97803
$560$		0			0
$561$	16.1966	+	33.0575i	0.683823	+	1.39569i
$562$		0			0
$563$	−12.8781			−0.542749			−0.271375	−	0.962474i	$-0.587478\pi$
$563$	−12.8781			−0.542749			−0.271375	+	0.962474i	$0.587478\pi$
$564$		0			0
$565$	54.1714			2.27901
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−27.0000			−1.13190			−0.565949	−	0.824440i	$-0.691490\pi$
$569$	−27.0000			−1.13190			−0.565949	+	0.824440i	$0.691490\pi$
$570$		0			0
$571$	−10.8498			−0.454052			−0.227026	−	0.973889i	$-0.572900\pi$
$571$	−10.8498			−0.454052			−0.227026	+	0.973889i	$0.572900\pi$
$572$		0			0
$573$	−15.4144	−	31.4609i	−0.643944	−	1.31430i
$574$		0			0
$575$	83.8634			3.49734
$576$		0			0
$577$	10.6085	+	18.3745i	0.441640	+	0.764942i	0.997811	−	0.0661250i	$-0.0210636\pi$
$577$	10.6085	+	18.3745i	0.441640	+	0.764942i	−0.556172	+	0.831067i	$0.687730\pi$
$578$		0			0
$579$	9.44454	+	19.2764i	0.392502	+	0.801101i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	24.2270			1.00338
$584$		0			0
$585$	38.8965	−	50.1549i	1.60817	−	2.07365i
$586$		0			0
$587$	7.92684	+	13.7297i	0.327176	+	0.566685i	0.981950	−	0.189139i	$-0.0605698\pi$
$587$	7.92684	+	13.7297i	0.327176	+	0.566685i	−0.654775	+	0.755824i	$0.727236\pi$
$588$		0			0
$589$	0.189220	−	0.327739i	0.00779668	−	0.0135042i
$590$		0			0
$591$	−10.9687	−	22.3872i	−0.451191	−	0.920887i
$592$		0			0
$593$	12.2580	−	21.2314i	0.503375	−	0.871871i	−0.496618	−	0.867969i	$-0.665425\pi$
$593$	12.2580	−	21.2314i	0.503375	−	0.871871i	0.999992	−	0.00390123i	$-0.00124180\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.1560	+	15.1153i	−0.415659	+	0.618628i
$598$		0			0
$599$	4.42426			0.180770			0.0903852	−	0.995907i	$-0.471190\pi$
$599$	4.42426			0.180770			0.0903852	+	0.995907i	$0.471190\pi$
$600$		0			0
$601$	−4.47075	−	7.74357i	−0.182366	−	0.315867i	0.760320	−	0.649549i	$-0.225042\pi$
$601$	−4.47075	−	7.74357i	−0.182366	−	0.315867i	−0.942686	+	0.333682i	$0.891709\pi$
$602$		0			0
$603$	−4.76276	+	6.14131i	−0.193955	+	0.250093i
$604$		0			0
$605$	−14.0646	+	24.3607i	−0.571809	+	0.990402i
$606$		0			0
$607$	18.9127	+	32.7578i	0.767643	+	1.32960i	0.938838	+	0.344359i	$0.111904\pi$
$607$	18.9127	+	32.7578i	0.767643	+	1.32960i	−0.171195	+	0.985237i	$0.554763\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.47228	−	16.4065i	0.383208	−	0.663735i
$612$		0			0
$613$	9.33369	+	16.1664i	0.376984	+	0.652956i	0.990622	−	0.136632i	$-0.0436278\pi$
$613$	9.33369	+	16.1664i	0.376984	+	0.652956i	−0.613638	+	0.789588i	$0.710294\pi$
$614$		0			0
$615$	16.0148	+	32.6863i	0.645778	+	1.31804i
$616$		0			0
$617$	−14.9365	+	25.8708i	−0.601320	+	1.04152i	0.391301	+	0.920263i	$0.372025\pi$
$617$	−14.9365	+	25.8708i	−0.601320	+	1.04152i	−0.992621	+	0.121255i	$0.961308\pi$
$618$		0			0
$619$	−1.90789	+	3.30456i	−0.0766846	+	0.132822i	−0.901818	−	0.432117i	$-0.857767\pi$
$619$	−1.90789	+	3.30456i	−0.0766846	+	0.132822i	0.825133	+	0.564938i	$0.191100\pi$
$620$		0			0
$621$	−13.4042	−	40.5115i	−0.537894	−	1.62567i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−14.1135	−	24.4453i	−0.564539	−	0.977811i
$626$		0			0
$627$	−1.83108	+	2.72521i	−0.0731264	+	0.108835i
$628$		0			0
$629$	−48.8197			−1.94657
$630$		0			0
$631$	20.0458			0.798012			0.399006	−	0.916948i	$-0.369355\pi$
$631$	20.0458			0.798012			0.399006	+	0.916948i	$0.369355\pi$
$632$		0			0
$633$	−40.4782	−	2.75761i	−1.60886	−	0.109605i
$634$		0			0
$635$	−22.6636	−	39.2546i	−0.899379	−	1.55777i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.260812	+	0.336303i	−0.0103176	+	0.0133039i
$640$		0			0
$641$	4.75207	−	8.23083i	0.187696	−	0.325098i	−0.756786	−	0.653663i	$-0.773231\pi$
$641$	4.75207	−	8.23083i	0.187696	−	0.325098i	0.944482	+	0.328564i	$0.106565\pi$
$642$		0			0
$643$	−15.0611	+	26.0866i	−0.593952	+	1.02876i	0.399741	+	0.916628i	$0.369100\pi$
$643$	−15.0611	+	26.0866i	−0.593952	+	1.02876i	−0.993694	+	0.112128i	$0.964233\pi$
$644$		0			0
$645$	−58.1080	−	3.95866i	−2.28800	−	0.155872i
$646$		0			0
$647$	10.6267	+	18.4060i	0.417780	+	0.723616i	0.995716	−	0.0924659i	$-0.0294749\pi$
$647$	10.6267	+	18.4060i	0.417780	+	0.723616i	−0.577936	+	0.816082i	$0.696142\pi$
$648$		0			0
$649$	−4.04475	+	7.00572i	−0.158770	+	0.274999i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.225016	+	0.389739i	0.00880556	+	0.0152517i	0.870395	−	0.492355i	$-0.163864\pi$
$653$	0.225016	+	0.389739i	0.00880556	+	0.0152517i	−0.861589	+	0.507606i	$0.830530\pi$
$654$		0			0
$655$	−7.90877	+	13.6984i	−0.309021	+	0.535240i
$656$		0			0
$657$	−30.7093	−	4.20371i	−1.19808	−	0.164002i
$658$		0			0
$659$	8.68441	+	15.0418i	0.338297	+	0.585947i	0.984112	−	0.177546i	$-0.0568159\pi$
$659$	8.68441	+	15.0418i	0.338297	+	0.585947i	−0.645816	+	0.763493i	$0.723483\pi$
$660$		0			0
$661$	34.0096			1.32282			0.661411	−	0.750024i	$-0.269958\pi$
$661$	34.0096			1.32282			0.661411	+	0.750024i	$0.269958\pi$
$662$		0			0
$663$	20.5872	+	42.0187i	0.799541	+	1.63187i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	10.9919	−	19.0386i	0.425609	−	0.737176i
$668$		0			0
$669$	−24.4830	+	36.4382i	−0.946566	+	1.40878i
$670$		0			0
$671$	−24.0192	+	41.6025i	−0.927252	+	1.60605i
$672$		0			0
$673$	−10.5825	−	18.3294i	−0.407925	−	0.706547i	0.586732	−	0.809781i	$-0.300414\pi$
$673$	−10.5825	−	18.3294i	−0.407925	−	0.706547i	−0.994657	+	0.103234i	$0.967081\pi$
$674$		0			0
$675$	−35.2941	+	39.6244i	−1.35847	+	1.52515i
$676$		0			0
$677$	−17.7149			−0.680839			−0.340420	−	0.940274i	$-0.610569\pi$
$677$	−17.7149			−0.680839			−0.340420	+	0.940274i	$0.610569\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−31.1486	−	2.12203i	−1.19362	−	0.0813163i
$682$		0			0
$683$	16.2676	+	28.1763i	0.622461	+	1.07813i	0.989026	+	0.147742i	$0.0472005\pi$
$683$	16.2676	+	28.1763i	0.622461	+	1.07813i	−0.366565	+	0.930393i	$0.619466\pi$
$684$		0			0
$685$	35.7136			1.36455
$686$		0			0
$687$	5.23985	−	7.79851i	0.199913	−	0.297532i
$688$		0			0
$689$	30.7944			1.17317
$690$		0			0
$691$	31.3820			1.19383			0.596914	−	0.802305i	$-0.296393\pi$
$691$	31.3820			1.19383			0.596914	+	0.802305i	$0.296393\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−40.8647			−1.55009
$696$		0			0
$697$	−26.8337			−1.01640
$698$		0			0
$699$	−4.91336	−	0.334727i	−0.185840	−	0.0126605i
$700$		0			0
$701$	−11.7163			−0.442518			−0.221259	−	0.975215i	$-0.571017\pi$
$701$	−11.7163			−0.442518			−0.221259	+	0.975215i	$0.571017\pi$
$702$		0			0
$703$	−2.17709	−	3.77084i	−0.0821106	−	0.142220i
$704$		0			0
$705$	−13.1581	+	19.5833i	−0.495562	+	0.737549i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	7.18114			0.269693			0.134847	−	0.990866i	$-0.456946\pi$
$709$	7.18114			0.269693			0.134847	+	0.990866i	$0.456946\pi$
$710$		0			0
$711$	0.752734	−	0.970608i	0.0282297	−	0.0364006i
$712$		0			0
$713$	−3.49834	−	6.05930i	−0.131014	−	0.226922i
$714$		0			0
$715$	−45.1438	+	78.1914i	−1.68828	+	2.92419i
$716$		0			0
$717$	21.0496	+	1.43402i	0.786110	+	0.0535545i
$718$		0			0
$719$	−7.82360	+	13.5509i	−0.291771	+	0.505362i	−0.974229	−	0.225563i	$-0.927578\pi$
$719$	−7.82360	+	13.5509i	−0.291771	+	0.505362i	0.682458	+	0.730925i	$0.260911\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	32.1844	+	2.19259i	1.19695	+	0.0815434i
$724$		0			0
$725$	−27.3378			−1.01530
$726$		0			0
$727$	−22.5678	−	39.0886i	−0.836995	−	1.44972i	−0.892396	−	0.451253i	$-0.850977\pi$
$727$	−22.5678	−	39.0886i	−0.836995	−	1.44972i	0.0554015	−	0.998464i	$-0.482356\pi$
$728$		0			0
$729$	24.7824	+	10.7160i	0.917867	+	0.396889i
$730$		0			0
$731$	21.4687	−	37.1848i	0.794048	−	1.37533i
$732$		0			0
$733$	−20.6167	−	35.7092i	−0.761495	−	1.31895i	−0.942080	−	0.335388i	$-0.891133\pi$
$733$	−20.6167	−	35.7092i	−0.761495	−	1.31895i	0.180585	−	0.983559i	$-0.442201\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.52772	−	9.57429i	0.203616	−	0.352673i
$738$		0			0
$739$	−16.6209	−	28.7882i	−0.611410	−	1.05899i	−0.991003	−	0.133839i	$-0.957269\pi$
$739$	−16.6209	−	28.7882i	−0.611410	−	1.05899i	0.379593	−	0.925153i	$-0.376064\pi$
$740$		0			0
$741$	−2.32745	+	3.46396i	−0.0855010	+	0.127252i
$742$		0			0
$743$	−16.3263	+	28.2779i	−0.598953	+	1.03742i	0.394023	+	0.919101i	$0.371083\pi$
$743$	−16.3263	+	28.2779i	−0.598953	+	1.03742i	−0.992976	+	0.118316i	$0.962250\pi$
$744$		0			0
$745$	31.7240	−	54.9475i	1.16228	−	2.01312i
$746$		0			0
$747$	−12.3784	−	1.69444i	−0.452902	−	0.0619964i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−20.0384	−	34.7075i	−0.731212	−	1.26650i	−0.956366	−	0.292173i	$-0.905622\pi$
$751$	−20.0384	−	34.7075i	−0.731212	−	1.26650i	0.225154	−	0.974323i	$-0.427712\pi$
$752$		0			0
$753$	−5.44129	−	11.1057i	−0.198292	−	0.404716i
$754$		0			0
$755$	−28.1293			−1.02373
$756$		0			0
$757$	21.8337			0.793559			0.396779	−	0.917914i	$-0.370128\pi$
$757$	21.8337			0.793559			0.396779	+	0.917914i	$0.370128\pi$
$758$		0			0
$759$	26.7074	+	54.5100i	0.969416	+	1.97859i
$760$		0			0
$761$	−4.56067	−	7.89932i	−0.165324	−	0.286350i	0.771446	−	0.636295i	$-0.219534\pi$
$761$	−4.56067	−	7.89932i	−0.165324	−	0.286350i	−0.936770	+	0.349945i	$0.886200\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−22.0229	−	53.9510i	−0.796240	−	1.95060i
$766$		0			0
$767$	−5.14120	+	8.90482i	−0.185638	+	0.321534i
$768$		0			0
$769$	−14.3654	+	24.8815i	−0.518028	+	0.897250i	0.481753	+	0.876307i	$0.340000\pi$
$769$	−14.3654	+	24.8815i	−0.518028	+	0.897250i	−0.999781	+	0.0209433i	$0.993333\pi$
$770$		0			0
$771$	1.29856	−	1.93265i	0.0467664	−	0.0696028i
$772$		0			0
$773$	19.7283	+	34.1705i	0.709578	+	1.22903i	0.965014	+	0.262200i	$0.0844479\pi$
$773$	19.7283	+	34.1705i	0.709578	+	1.22903i	−0.255435	+	0.966826i	$0.582219\pi$
$774$		0			0
$775$	−4.35033	+	7.53499i	−0.156268	+	0.270665i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.19664	−	2.07264i	−0.0428740	−	0.0742599i
$780$		0			0
$781$	0.302702	−	0.524295i	0.0108315	−	0.0187608i
$782$		0			0
$783$	4.36952	+	13.2060i	0.156154	+	0.471943i
$784$		0			0
$785$	−2.31493	−	4.00957i	−0.0826232	−	0.143108i
$786$		0			0
$787$	11.0307			0.393202			0.196601	−	0.980484i	$-0.437010\pi$
$787$	11.0307			0.393202			0.196601	+	0.980484i	$0.437010\pi$
$788$		0			0
$789$	−41.9890	−	2.86054i	−1.49485	−	0.101838i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−30.5303	+	52.8801i	−1.08416	+	1.87783i
$794$		0			0
$795$	−38.2621	−	2.60664i	−1.35702	−	0.0924480i
$796$		0			0
$797$	−1.15757	+	2.00497i	−0.0410032	+	0.0710196i	−0.885799	−	0.464070i	$-0.846389\pi$
$797$	−1.15757	+	2.00497i	−0.0410032	+	0.0710196i	0.844796	+	0.535089i	$0.179722\pi$
$798$		0			0
$799$	−8.69664	−	15.0630i	−0.307665	−	0.532891i
$800$		0			0
$801$	−2.73526	−	6.70075i	−0.0966456	−	0.236759i
$802$		0			0
$803$	44.0921			1.55598
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.21606	+	7.76311i	−0.183614	+	0.273274i
$808$		0			0
$809$	3.70471	+	6.41675i	0.130251	+	0.225601i	0.923773	−	0.382940i	$-0.125088\pi$
$809$	3.70471	+	6.41675i	0.130251	+	0.225601i	−0.793522	+	0.608541i	$0.791755\pi$
$810$		0			0
$811$	12.8879			0.452555			0.226277	−	0.974063i	$-0.427344\pi$
$811$	12.8879			0.452555			0.226277	+	0.974063i	$0.427344\pi$
$812$		0			0
$813$	23.4526	+	1.59773i	0.822520	+	0.0560349i
$814$		0			0
$815$	81.9636			2.87106
$816$		0			0
$817$	3.82955			0.133979
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.8743			−0.903019			−0.451510	−	0.892266i	$-0.649114\pi$
$821$	−25.8743			−0.903019			−0.451510	+	0.892266i	$0.649114\pi$
$822$		0			0
$823$	44.0620			1.53590			0.767952	−	0.640507i	$-0.221276\pi$
$823$	44.0620			1.53590			0.767952	+	0.640507i	$0.221276\pi$
$824$		0			0
$825$	42.0981	−	62.6550i	1.46567	−	2.18137i
$826$		0			0
$827$	−6.81753			−0.237069			−0.118534	−	0.992950i	$-0.537820\pi$
$827$	−6.81753			−0.237069			−0.118534	+	0.992950i	$0.537820\pi$
$828$		0			0
$829$	−4.27759	−	7.40900i	−0.148567	−	0.257325i	0.782131	−	0.623114i	$-0.214133\pi$
$829$	−4.27759	−	7.40900i	−0.148567	−	0.257325i	−0.930698	+	0.365789i	$0.880799\pi$
$830$		0			0
$831$	−50.1389	−	3.41576i	−1.73930	−	0.118491i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−78.2566			−2.70818
$836$		0			0
$837$	4.33523	+	0.897144i	0.149847	+	0.0310098i
$838$		0			0
$839$	−18.0971	−	31.3451i	−0.624781	−	1.08215i	−0.988583	−	0.150676i	$-0.951855\pi$
$839$	−18.0971	−	31.3451i	−0.624781	−	1.08215i	0.363803	−	0.931476i	$-0.381478\pi$
$840$		0			0
$841$	10.9168	−	18.9085i	0.376443	−	0.652018i
$842$		0			0
$843$	1.71143	−	2.54714i	0.0589448	−	0.0877281i
$844$		0			0
$845$	−32.0296	+	55.4768i	−1.10185	+	1.90846i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−18.4830	−	37.7239i	−0.634334	−	1.29468i
$850$		0			0
$851$	−80.5011			−2.75954
$852$		0			0
$853$	3.97889	+	6.89164i	0.136235	+	0.235965i	0.926068	−	0.377356i	$-0.123167\pi$
$853$	3.97889	+	6.89164i	0.136235	+	0.235965i	−0.789834	+	0.613321i	$0.789833\pi$
$854$		0			0
$855$	3.18507	−	4.10697i	0.108927	−	0.140455i
$856$		0			0
$857$	−22.7899	+	39.4733i	−0.778489	+	1.34838i	0.154324	+	0.988020i	$0.450680\pi$
$857$	−22.7899	+	39.4733i	−0.778489	+	1.34838i	−0.932813	+	0.360362i	$0.882653\pi$
$858$		0			0
$859$	10.4518	+	18.1030i	0.356609	+	0.617666i	0.987392	−	0.158294i	$-0.0505994\pi$
$859$	10.4518	+	18.1030i	0.356609	+	0.617666i	−0.630783	+	0.775960i	$0.717266\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.88586	−	6.73050i	0.132276	−	0.229109i	−0.792278	−	0.610161i	$-0.791105\pi$
$863$	3.88586	−	6.73050i	0.132276	−	0.229109i	0.924554	+	0.381052i	$0.124438\pi$
$864$		0			0
$865$	−11.8182	−	20.4697i	−0.401831	−	0.695991i
$866$		0			0
$867$	13.4834	+	0.918570i	0.457921	+	0.0311963i
$868$		0			0
$869$	−0.873633	+	1.51318i	−0.0296360	+	0.0513310i
$870$		0			0
$871$	7.02616	−	12.1697i	0.238072	−	0.412354i
$872$		0			0
$873$	−22.6160	−	3.09583i	−0.765434	−	0.104778i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19.6886	+	34.1016i	0.664835	+	1.15153i	0.979330	+	0.202269i	$0.0648317\pi$
$877$	19.6886	+	34.1016i	0.664835	+	1.15153i	−0.314495	+	0.949259i	$0.601835\pi$
$878$		0			0
$879$	26.0068	+	1.77173i	0.877186	+	0.0597591i
$880$		0			0
$881$	−26.7967			−0.902805			−0.451402	−	0.892320i	$-0.649076\pi$
$881$	−26.7967			−0.902805			−0.451402	+	0.892320i	$0.649076\pi$
$882$		0			0
$883$	−43.0755			−1.44961			−0.724803	−	0.688956i	$-0.758069\pi$
$883$	−43.0755			−1.44961			−0.724803	+	0.688956i	$0.758069\pi$
$884$		0			0
$885$	7.14172	−	10.6291i	0.240066	−	0.357293i
$886$		0			0
$887$	18.6253	+	32.2600i	0.625377	+	1.08318i	0.988468	+	0.151431i	$0.0483881\pi$
$887$	18.6253	+	32.2600i	0.625377	+	1.08318i	−0.363091	+	0.931754i	$0.618279\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−36.9952	−	10.3217i	−1.23939	−	0.345791i
$892$		0			0
$893$	0.775645	−	1.34346i	0.0259560	−	0.0449571i
$894$		0			0
$895$	−17.2269	+	29.8379i	−0.575832	+	0.997370i
$896$		0			0
$897$	33.9472	+	69.2866i	1.13346	+	2.31341i
$898$		0			0
$899$	1.14039	+	1.97521i	0.0380342	+	0.0658771i
$900$		0			0
$901$	14.1364	−	24.4849i	0.470951	−	0.815711i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	47.1560	+	81.6766i	1.56752	+	2.71502i
$906$		0			0
$907$	4.89327	−	8.47540i	0.162478	−	0.281421i	−0.773279	−	0.634067i	$-0.781385\pi$
$907$	4.89327	−	8.47540i	0.162478	−	0.281421i	0.935757	+	0.352646i	$0.114718\pi$
$908$		0			0
$909$	−5.80917	−	14.2311i	−0.192678	−	0.472016i
$910$		0			0
$911$	14.2979	+	24.7647i	0.473710	+	0.820490i	0.999547	−	0.0300951i	$-0.00958102\pi$
$911$	14.2979	+	24.7647i	0.473710	+	0.820490i	−0.525837	+	0.850586i	$0.676248\pi$
$912$		0			0
$913$	17.7728			0.588192
$914$		0			0
$915$	42.4101	−	63.1194i	1.40204	−	2.08666i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	8.61348	−	14.9190i	0.284133	−	0.492132i	−0.688266	−	0.725459i	$-0.741628\pi$
$919$	8.61348	−	14.9190i	0.284133	−	0.492132i	0.972398	+	0.233326i	$0.0749611\pi$
$920$		0			0
$921$	3.06285	+	6.25132i	0.100924	+	0.205988i
$922$		0			0
$923$	0.384758	−	0.666420i	0.0126645	−	0.0219355i
$924$		0			0
$925$	50.0532	+	86.6948i	1.64574	+	2.85051i
$926$		0			0
$927$	−38.5226	−	5.27325i	−1.26525	−	0.173196i
$928$		0			0
$929$	−26.8597			−0.881240			−0.440620	−	0.897694i	$-0.645241\pi$
$929$	−26.8597			−0.881240			−0.440620	+	0.897694i	$0.645241\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.21694	−	2.48378i	−0.0398408	−	0.0813154i
$934$		0			0
$935$	41.4472	+	71.7886i	1.35547	+	2.34774i
$936$		0			0
$937$	51.5653			1.68456			0.842282	−	0.539037i	$-0.181212\pi$
$937$	51.5653			1.68456			0.842282	+	0.539037i	$0.181212\pi$
$938$		0			0
$939$	3.71213	+	7.57650i	0.121141	+	0.247250i
$940$		0			0
$941$	−41.8004			−1.36266			−0.681328	−	0.731979i	$-0.738597\pi$
$941$	−41.8004			−1.36266			−0.681328	+	0.731979i	$0.738597\pi$
$942$		0			0
$943$	−44.2473			−1.44089
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.50415			0.308843			0.154422	−	0.988005i	$-0.450649\pi$
$947$	9.50415			0.308843			0.154422	+	0.988005i	$0.450649\pi$
$948$		0			0
$949$	56.0445			1.81928
$950$		0			0
$951$	6.38496	+	13.0318i	0.207046	+	0.422584i
$952$		0			0
$953$	−58.4539			−1.89351			−0.946754	−	0.321957i	$-0.895659\pi$
$953$	−58.4539			−1.89351			−0.946754	+	0.321957i	$0.895659\pi$
$954$		0			0
$955$	−39.4453	−	68.3213i	−1.27642	−	2.21083i
$956$		0			0
$957$	−8.70609	−	17.7692i	−0.281428	−	0.574397i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−30.2741			−0.976584
$962$		0			0
$963$	13.0783	+	32.0389i	0.421444	+	1.03244i
$964$		0			0
$965$	24.1686	+	41.8612i	0.778014	+	1.34756i
$966$		0			0
$967$	−5.09799	+	8.82997i	−0.163940	+	0.283953i	−0.936278	−	0.351259i	$-0.885754\pi$
$967$	−5.09799	+	8.82997i	−0.163940	+	0.283953i	0.772338	+	0.635212i	$0.219087\pi$
$968$		0			0
$969$	1.68580	+	3.44073i	0.0541557	+	0.110532i
$970$		0			0
$971$	19.4238	−	33.6429i	0.623338	−	1.07965i	−0.365522	−	0.930803i	$-0.619109\pi$
$971$	19.4238	−	33.6429i	0.623338	−	1.07965i	0.988860	−	0.148850i	$-0.0475572\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	53.5100	−	79.6394i	1.71369	−	2.55050i
$976$		0			0
$977$	−42.1322			−1.34793			−0.673965	−	0.738763i	$-0.735410\pi$
$977$	−42.1322			−1.34793			−0.673965	+	0.738763i	$0.735410\pi$
$978$		0			0
$979$	5.14776	+	8.91619i	0.164523	+	0.284963i
$980$		0			0
$981$	−1.21694	−	0.166583i	−0.0388538	−	0.00531859i
$982$		0			0
$983$	17.0284	−	29.4941i	0.543123	−	0.940716i	−0.455600	−	0.890185i	$-0.650575\pi$
$983$	17.0284	−	29.4941i	0.543123	−	0.940716i	0.998722	−	0.0505312i	$-0.0160914\pi$
$984$		0			0
$985$	−28.0688	−	48.6167i	−0.894348	−	1.54906i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	35.4007	−	61.3158i	1.12568	−	1.94973i
$990$		0			0
$991$	−20.5980	−	35.6768i	−0.654317	−	1.13331i	−0.982065	−	0.188544i	$-0.939623\pi$
$991$	−20.5980	−	35.6768i	−0.654317	−	1.13331i	0.327748	−	0.944765i	$-0.393710\pi$
$992$		0			0
$993$	−19.6871	−	40.1816i	−0.624751	−	1.27512i
$994$		0			0
$995$	−20.5033	+	35.5127i	−0.649997	+	1.12583i
$996$		0			0
$997$	15.7199	−	27.2277i	0.497856	−	0.862311i	−0.502141	−	0.864786i	$-0.667454\pi$
$997$	15.7199	−	27.2277i	0.497856	−	0.862311i	0.999997	+	0.00247444i	$0.000787640\pi$
$998$		0			0
$999$	33.8790	−	38.0358i	1.07189	−	1.20340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.i.h.373.2		12
3.2	odd	2		5292.2.i.h.1549.6		12
7.2	even	3		1764.2.j.f.589.6	yes	12
7.3	odd	6		1764.2.l.h.949.4		12
7.4	even	3		1764.2.l.h.949.3		12
7.5	odd	6		1764.2.j.f.589.1	✓	12
7.6	odd	2	inner	1764.2.i.h.373.5		12
9.2	odd	6		5292.2.l.h.3313.1		12
9.7	even	3		1764.2.l.h.961.3		12
21.2	odd	6		5292.2.j.f.1765.6		12
21.5	even	6		5292.2.j.f.1765.1		12
21.11	odd	6		5292.2.l.h.361.1		12
21.17	even	6		5292.2.l.h.361.6		12
21.20	even	2		5292.2.i.h.1549.1		12
63.2	odd	6		5292.2.j.f.3529.6		12
63.11	odd	6		5292.2.i.h.2125.6		12
63.16	even	3		1764.2.j.f.1177.6	yes	12
63.20	even	6		5292.2.l.h.3313.6		12
63.25	even	3	inner	1764.2.i.h.1537.2		12
63.34	odd	6		1764.2.l.h.961.4		12
63.38	even	6		5292.2.i.h.2125.1		12
63.47	even	6		5292.2.j.f.3529.1		12
63.52	odd	6	inner	1764.2.i.h.1537.5		12
63.61	odd	6		1764.2.j.f.1177.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.h.373.2		12	1.1	even	1	trivial
1764.2.i.h.373.5		12	7.6	odd	2	inner
1764.2.i.h.1537.2		12	63.25	even	3	inner
1764.2.i.h.1537.5		12	63.52	odd	6	inner
1764.2.j.f.589.1	✓	12	7.5	odd	6
1764.2.j.f.589.6	yes	12	7.2	even	3
1764.2.j.f.1177.1	yes	12	63.61	odd	6
1764.2.j.f.1177.6	yes	12	63.16	even	3
1764.2.l.h.949.3		12	7.4	even	3
1764.2.l.h.949.4		12	7.3	odd	6
1764.2.l.h.961.3		12	9.7	even	3
1764.2.l.h.961.4		12	63.34	odd	6
5292.2.i.h.1549.1		12	21.20	even	2
5292.2.i.h.1549.6		12	3.2	odd	2
5292.2.i.h.2125.1		12	63.38	even	6
5292.2.i.h.2125.6		12	63.11	odd	6
5292.2.j.f.1765.1		12	21.5	even	6
5292.2.j.f.1765.6		12	21.2	odd	6
5292.2.j.f.3529.1		12	63.47	even	6
5292.2.j.f.3529.6		12	63.2	odd	6
5292.2.l.h.361.1		12	21.11	odd	6
5292.2.l.h.361.6		12	21.17	even	6
5292.2.l.h.3313.1		12	9.2	odd	6
5292.2.l.h.3313.6		12	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.762070 - 1.55539i) q^{3} +(-1.95014 - 3.37774i) q^{5} +(-1.83850 + 2.37064i) q^{9} +O(q^{10})\)	\(q+(-0.762070 - 1.55539i) q^{3} +(-1.95014 - 3.37774i) q^{5} +(-1.83850 + 2.37064i) q^{9} +(2.13378 - 3.69582i) q^{11} +(2.71221 - 4.69768i) q^{13} +(-3.76757 + 5.60730i) q^{15} +(-2.49012 - 4.31301i) q^{17} +(0.222091 - 0.384673i) q^{19} +(-4.10607 - 7.11191i) q^{23} +(-5.10607 + 8.84396i) q^{25} +(5.08834 + 1.05300i) q^{27} +(1.33850 + 2.31835i) q^{29} +0.851993 q^{31} +(-7.37455 - 0.502398i) q^{33} +(4.90135 - 8.48939i) q^{37} +(-9.37363 - 0.638587i) q^{39} +(2.69402 - 4.66618i) q^{41} +(4.31078 + 7.46649i) q^{43} +(11.5927 + 1.58689i) q^{45} +3.49246 q^{47} +(-4.81078 + 7.15992i) q^{51} +(2.83850 + 4.91642i) q^{53} -16.6447 q^{55} +(-0.767567 - 0.0522912i) q^{57} -1.89558 q^{59} -11.2566 q^{61} -21.1567 q^{65} +2.59057 q^{67} +(-7.93272 + 11.8063i) q^{69} +0.141862 q^{71} +(5.16595 + 8.94769i) q^{73} +(17.6470 + 1.20222i) q^{75} -0.409429 q^{79} +(-2.23985 - 8.71683i) q^{81} +(2.08231 + 3.60666i) q^{83} +(-9.71213 + 16.8219i) q^{85} +(2.58591 - 3.84863i) q^{87} +(-1.20625 + 2.08929i) q^{89} +(-0.649278 - 1.32518i) q^{93} -1.73243 q^{95} +(3.80448 + 6.58955i) q^{97} +(4.83850 + 11.8532i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{9}+O(q^{10}) \) 12 * q - 8 * q^9	\( 12 q - 8 q^{9} + 8 q^{11} - 10 q^{15} - 12 q^{25} + 2 q^{29} + 6 q^{37} - 28 q^{39} + 6 q^{43} - 12 q^{51} + 20 q^{53} + 26 q^{57} - 92 q^{65} + 24 q^{67} + 44 q^{71} - 12 q^{79} + 40 q^{81} - 18 q^{85} + 52 q^{93} - 56 q^{95} + 44 q^{99}+O(q^{100}) \) 12 * q - 8 * q^9 + 8 * q^11 - 10 * q^15 - 12 * q^25 + 2 * q^29 + 6 * q^37 - 28 * q^39 + 6 * q^43 - 12 * q^51 + 20 * q^53 + 26 * q^57 - 92 * q^65 + 24 * q^67 + 44 * q^71 - 12 * q^79 + 40 * q^81 - 18 * q^85 + 52 * q^93 - 56 * q^95 + 44 * q^99

Introduction

L-functions

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