LMFDB - Embedded newform 325.3.h.b.168.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(168,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.168"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.h (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			168.10
Character	$\chi$	$=$	325.168
Dual form			325.3.h.b.207.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.78036 + 1.78036i) q^{2} +(-0.433767 - 0.433767i) q^{3} +2.33933i q^{4} -1.54452i q^{6} +(5.63522 + 5.63522i) q^{7} +(2.95658 - 2.95658i) q^{8} -8.62369i q^{9} +7.95860i q^{11} +(1.01472 - 1.01472i) q^{12} +(7.09417 + 10.8937i) q^{13} +20.0654i q^{14} +19.8849 q^{16} +(-4.22084 + 4.22084i) q^{17} +(15.3532 - 15.3532i) q^{18} +28.4044 q^{19} -4.88875i q^{21} +(-14.1691 + 14.1691i) q^{22} +(-16.8593 - 16.8593i) q^{23} -2.56494 q^{24} +(-6.76452 + 32.0248i) q^{26} +(-7.64458 + 7.64458i) q^{27} +(-13.1826 + 13.1826i) q^{28} +50.7219i q^{29} +5.26889i q^{31} +(23.5758 + 23.5758i) q^{32} +(3.45218 - 3.45218i) q^{33} -15.0292 q^{34} +20.1736 q^{36} +(-16.4223 - 16.4223i) q^{37} +(50.5700 + 50.5700i) q^{38} +(1.64811 - 7.80255i) q^{39} -61.6304i q^{41} +(8.70370 - 8.70370i) q^{42} +(18.6744 + 18.6744i) q^{43} -18.6178 q^{44} -60.0309i q^{46} +(-21.8727 - 21.8727i) q^{47} +(-8.62540 - 8.62540i) q^{48} +14.5113i q^{49} +3.66173 q^{51} +(-25.4840 + 16.5956i) q^{52} +(-38.2818 - 38.2818i) q^{53} -27.2201 q^{54} +33.3220 q^{56} +(-12.3209 - 12.3209i) q^{57} +(-90.3030 + 90.3030i) q^{58} +12.8470 q^{59} -45.4020 q^{61} +(-9.38049 + 9.38049i) q^{62} +(48.5964 - 48.5964i) q^{63} +4.40705i q^{64} +12.2922 q^{66} +(-22.7910 - 22.7910i) q^{67} +(-9.87393 - 9.87393i) q^{68} +14.6260i q^{69} +0.496956i q^{71} +(-25.4967 - 25.4967i) q^{72} +(-18.8385 + 18.8385i) q^{73} -58.4750i q^{74} +66.4473i q^{76} +(-44.8484 + 44.8484i) q^{77} +(16.8255 - 10.9571i) q^{78} -73.0902i q^{79} -70.9813 q^{81} +(109.724 - 109.724i) q^{82} +(70.8434 - 70.8434i) q^{83} +11.4364 q^{84} +66.4941i q^{86} +(22.0015 - 22.0015i) q^{87} +(23.5303 + 23.5303i) q^{88} -2.26468 q^{89} +(-21.4112 + 101.366i) q^{91} +(39.4393 - 39.4393i) q^{92} +(2.28547 - 2.28547i) q^{93} -77.8822i q^{94} -20.4528i q^{96} +(85.2235 + 85.2235i) q^{97} +(-25.8353 + 25.8353i) q^{98} +68.6325 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 72 q^{12} + 36 q^{13} - 104 q^{16} + 48 q^{17} - 8 q^{22} + 104 q^{23} + 88 q^{26} - 56 q^{27} + 256 q^{36} - 124 q^{38} - 216 q^{42} - 8 q^{43} - 196 q^{48} - 296 q^{51} - 16 q^{52} - 220 q^{53}+ \cdots - 812 q^{92}+O(q^{100}) $ 24 * q + 4 * q^3 - 72 * q^12 + 36 * q^13 - 104 * q^16 + 48 * q^17 - 8 * q^22 + 104 * q^23 + 88 * q^26 - 56 * q^27 + 256 * q^36 - 124 * q^38 - 216 * q^42 - 8 * q^43 - 196 * q^48 - 296 * q^51 - 16 * q^52 - 220 * q^53 + 584 * q^56 - 8 * q^61 + 596 * q^62 - 360 * q^66 + 640 * q^68 - 388 * q^77 + 636 * q^78 - 224 * q^81 + 1004 * q^82 + 52 * q^87 - 780 * q^88 - 512 * q^91 - 812 * q^92

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.78036	+	1.78036i	0.890178	+	0.890178i	0.994539	−	0.104362i	$-0.0332800\pi$
$2$	1.78036	+	1.78036i	0.890178	+	0.890178i	−0.104362	+	0.994539i	$0.533280\pi$
$3$	−0.433767	−	0.433767i	−0.144589	−	0.144589i	0.631107	−	0.775696i	$-0.282601\pi$
$3$	−0.433767	−	0.433767i	−0.144589	−	0.144589i	−0.775696	+	0.631107i	$0.782601\pi$
$4$			2.33933i			0.584832i
$5$		0			0
$5$		0			0
$6$		−	1.54452i		−	0.257420i
$7$	5.63522	+	5.63522i	0.805031	+	0.805031i	0.983877	−	0.178846i	$-0.0572364\pi$
$7$	5.63522	+	5.63522i	0.805031	+	0.805031i	−0.178846	+	0.983877i	$0.557236\pi$
$8$	2.95658	−	2.95658i	0.369573	−	0.369573i
$9$		−	8.62369i		−	0.958188i
$10$		0			0
$11$			7.95860i			0.723509i	0.932273	+	0.361755i	$0.117822\pi$
$11$			7.95860i			0.723509i	−0.932273	+	0.361755i	$0.882178\pi$
$12$	1.01472	−	1.01472i	0.0845604	−	0.0845604i
$13$	7.09417	+	10.8937i	0.545705	+	0.837977i
$13$	7.09417	+	10.8937i	0.545705	+	0.837977i
$14$			20.0654i			1.43324i
$15$		0			0
$16$	19.8849			1.24280
$17$	−4.22084	+	4.22084i	−0.248285	+	0.248285i	−0.820266	−	0.571982i	$-0.806175\pi$
$17$	−4.22084	+	4.22084i	−0.248285	+	0.248285i	0.571982	+	0.820266i	$0.306175\pi$
$18$	15.3532	−	15.3532i	0.852957	−	0.852957i
$19$	28.4044			1.49497			0.747485	−	0.664279i	$-0.231261\pi$
$19$	28.4044			1.49497			0.747485	+	0.664279i	$0.231261\pi$
$20$		0			0
$21$		−	4.88875i		−	0.232797i
$22$	−14.1691	+	14.1691i	−0.644052	+	0.644052i
$23$	−16.8593	−	16.8593i	−0.733011	−	0.733011i	0.238204	−	0.971215i	$-0.423441\pi$
$23$	−16.8593	−	16.8593i	−0.733011	−	0.733011i	−0.971215	+	0.238204i	$0.923441\pi$
$24$	−2.56494			−0.106873
$25$		0			0
$26$	−6.76452	+	32.0248i	−0.260174	+	1.23172i
$27$	−7.64458	+	7.64458i	−0.283133	+	0.283133i
$28$	−13.1826	+	13.1826i	−0.470808	+	0.470808i
$29$			50.7219i			1.74903i	0.484998	+	0.874515i	$0.338820\pi$
$29$			50.7219i			1.74903i	−0.484998	+	0.874515i	$0.661180\pi$
$30$		0			0
$31$			5.26889i			0.169964i	0.996382	+	0.0849821i	$0.0270833\pi$
$31$			5.26889i			0.169964i	−0.996382	+	0.0849821i	$0.972917\pi$
$32$	23.5758	+	23.5758i	0.736743	+	0.736743i
$33$	3.45218	−	3.45218i	0.104612	−	0.104612i
$34$	−15.0292			−0.442035
$35$		0			0
$36$	20.1736			0.560379
$37$	−16.4223	−	16.4223i	−0.443845	−	0.443845i	0.449457	−	0.893302i	$-0.351618\pi$
$37$	−16.4223	−	16.4223i	−0.443845	−	0.443845i	−0.893302	+	0.449457i	$0.851618\pi$
$38$	50.5700	+	50.5700i	1.33079	+	1.33079i
$39$	1.64811	−	7.80255i	0.0422593	−	0.200065i
$40$		0			0
$41$		−	61.6304i		−	1.50318i	−0.659631	−	0.751590i	$-0.729287\pi$
$41$		−	61.6304i		−	1.50318i	0.659631	−	0.751590i	$-0.270713\pi$
$42$	8.70370	−	8.70370i	0.207231	−	0.207231i
$43$	18.6744	+	18.6744i	0.434288	+	0.434288i	0.890084	−	0.455796i	$-0.150645\pi$
$43$	18.6744	+	18.6744i	0.434288	+	0.434288i	−0.455796	+	0.890084i	$0.650645\pi$
$44$	−18.6178			−0.423131
$45$		0			0
$46$		−	60.0309i		−	1.30502i
$47$	−21.8727	−	21.8727i	−0.465376	−	0.465376i	0.435037	−	0.900413i	$-0.356735\pi$
$47$	−21.8727	−	21.8727i	−0.465376	−	0.465376i	−0.900413	+	0.435037i	$0.856735\pi$
$48$	−8.62540	−	8.62540i	−0.179696	−	0.179696i
$49$			14.5113i			0.296149i
$50$		0			0
$51$	3.66173			0.0717985
$52$	−25.4840	+	16.5956i	−0.490076	+	0.319146i
$53$	−38.2818	−	38.2818i	−0.722298	−	0.722298i	0.246775	−	0.969073i	$-0.420629\pi$
$53$	−38.2818	−	38.2818i	−0.722298	−	0.722298i	−0.969073	+	0.246775i	$0.920629\pi$
$54$	−27.2201			−0.504077
$55$		0			0
$56$	33.3220			0.595036
$57$	−12.3209	−	12.3209i	−0.216156	−	0.216156i
$58$	−90.3030	+	90.3030i	−1.55695	+	1.55695i
$59$	12.8470			0.217746			0.108873	−	0.994056i	$-0.465276\pi$
$59$	12.8470			0.217746			0.108873	+	0.994056i	$0.465276\pi$
$60$		0			0
$61$	−45.4020			−0.744296			−0.372148	−	0.928173i	$-0.621379\pi$
$61$	−45.4020			−0.744296			−0.372148	+	0.928173i	$0.621379\pi$
$62$	−9.38049	+	9.38049i	−0.151298	+	0.151298i
$63$	48.5964	−	48.5964i	0.771371	−	0.771371i
$64$			4.40705i			0.0688601i
$65$		0			0
$66$	12.2922			0.186246
$67$	−22.7910	−	22.7910i	−0.340164	−	0.340164i	0.516265	−	0.856429i	$-0.327322\pi$
$67$	−22.7910	−	22.7910i	−0.340164	−	0.340164i	−0.856429	+	0.516265i	$0.827322\pi$
$68$	−9.87393	−	9.87393i	−0.145205	−	0.145205i
$69$			14.6260i			0.211971i
$70$		0			0
$71$			0.496956i			0.00699938i	0.999994	+	0.00349969i	$0.00111399\pi$
$71$			0.496956i			0.00699938i	−0.999994	+	0.00349969i	$0.998886\pi$
$72$	−25.4967	−	25.4967i	−0.354120	−	0.354120i
$73$	−18.8385	+	18.8385i	−0.258061	+	0.258061i	−0.824265	−	0.566204i	$-0.808412\pi$
$73$	−18.8385	+	18.8385i	−0.258061	+	0.258061i	0.566204	+	0.824265i	$0.308412\pi$
$74$		−	58.4750i		−	0.790203i
$75$		0			0
$76$			66.4473i			0.874306i
$77$	−44.8484	+	44.8484i	−0.582447	+	0.582447i
$78$	16.8255	−	10.9571i	0.215712	−	0.140475i
$79$		−	73.0902i		−	0.925192i	−0.886569	−	0.462596i	$-0.846918\pi$
$79$		−	73.0902i		−	0.925192i	0.886569	−	0.462596i	$-0.153082\pi$
$80$		0			0
$81$	−70.9813			−0.876312
$82$	109.724	−	109.724i	1.33810	−	1.33810i
$83$	70.8434	−	70.8434i	0.853536	−	0.853536i	−0.137031	−	0.990567i	$-0.543756\pi$
$83$	70.8434	−	70.8434i	0.853536	−	0.853536i	0.990567	+	0.137031i	$0.0437561\pi$
$84$	11.4364			0.136147
$85$		0			0
$86$			66.4941i			0.773187i
$87$	22.0015	−	22.0015i	0.252891	−	0.252891i
$88$	23.5303	+	23.5303i	0.267390	+	0.267390i
$89$	−2.26468			−0.0254459			−0.0127229	−	0.999919i	$-0.504050\pi$
$89$	−2.26468			−0.0254459			−0.0127229	+	0.999919i	$0.504050\pi$
$90$		0			0
$91$	−21.4112	+	101.366i	−0.235288	+	1.11391i
$92$	39.4393	−	39.4393i	0.428688	−	0.428688i
$93$	2.28547	−	2.28547i	0.0245750	−	0.0245750i
$94$		−	77.8822i		−	0.828534i
$95$		0			0
$96$		−	20.4528i		−	0.213050i
$97$	85.2235	+	85.2235i	0.878593	+	0.878593i	0.993389	−	0.114796i	$-0.0366215\pi$
$97$	85.2235	+	85.2235i	0.878593	+	0.878593i	−0.114796	+	0.993389i	$0.536622\pi$
$98$	−25.8353	+	25.8353i	−0.263626	+	0.263626i
$99$	68.6325			0.693258
$100$		0			0
$101$	−30.6953			−0.303914			−0.151957	−	0.988387i	$-0.548557\pi$
$101$	−30.6953			−0.303914			−0.151957	+	0.988387i	$0.548557\pi$
$102$	6.51917	+	6.51917i	0.0639135	+	0.0639135i
$103$	−120.944	−	120.944i	−1.17421	−	1.17421i	−0.981195	−	0.193020i	$-0.938172\pi$
$103$	−120.944	−	120.944i	−1.17421	−	1.17421i	−0.193020	−	0.981195i	$-0.561828\pi$
$104$	53.1827	+	11.2336i	0.511372	+	0.108016i
$105$		0			0
$106$		−	136.310i		−	1.28595i
$107$	−92.6405	+	92.6405i	−0.865799	+	0.865799i	−0.992004	−	0.126205i	$-0.959720\pi$
$107$	−92.6405	+	92.6405i	−0.865799	+	0.865799i	0.126205	+	0.992004i	$0.459720\pi$
$108$	−17.8832	−	17.8832i	−0.165585	−	0.165585i
$109$	−116.041			−1.06460			−0.532298	−	0.846557i	$-0.678671\pi$
$109$	−116.041			−1.06460			−0.532298	+	0.846557i	$0.678671\pi$
$110$		0			0
$111$			14.2469i			0.128350i
$112$	112.055	+	112.055i	1.00050	+	1.00050i
$113$	−67.8000	−	67.8000i	−0.600000	−	0.600000i	0.340313	−	0.940312i	$-0.389467\pi$
$113$	−67.8000	−	67.8000i	−0.600000	−	0.600000i	−0.940312	+	0.340313i	$0.889467\pi$
$114$		−	43.8712i		−	0.384835i
$115$		0			0
$116$	−118.655			−1.02289
$117$	93.9439	−	61.1779i	0.802940	−	0.522888i
$118$	22.8722	+	22.8722i	0.193832	+	0.193832i
$119$	−47.5707			−0.399754
$120$		0			0
$121$	57.6607			0.476534
$122$	−80.8317	−	80.8317i	−0.662555	−	0.662555i
$123$	−26.7332	+	26.7332i	−0.217343	+	0.217343i
$124$	−12.3257			−0.0994005
$125$		0			0
$126$	173.038			1.37331
$127$	128.144	−	128.144i	1.00901	−	1.00901i	0.00904741	−	0.999959i	$-0.497120\pi$
$127$	128.144	−	128.144i	1.00901	−	1.00901i	0.999959	−	0.00904741i	$-0.00287992\pi$
$128$	86.4570	−	86.4570i	0.675445	−	0.675445i
$129$		−	16.2007i		−	0.125587i
$130$		0			0
$131$	−165.385			−1.26248			−0.631239	−	0.775589i	$-0.717453\pi$
$131$	−165.385			−1.26248			−0.631239	+	0.775589i	$0.717453\pi$
$132$	8.07579	+	8.07579i	0.0611802	+	0.0611802i
$133$	160.065	+	160.065i	1.20350	+	1.20350i
$134$		−	81.1521i		−	0.605613i
$135$		0			0
$136$			24.9585i			0.183519i
$137$	71.1667	+	71.1667i	0.519465	+	0.519465i	0.917409	−	0.397945i	$-0.130276\pi$
$137$	71.1667	+	71.1667i	0.519465	+	0.519465i	−0.397945	+	0.917409i	$0.630276\pi$
$138$	−26.0395	+	26.0395i	−0.188692	+	0.188692i
$139$			87.3453i			0.628384i	0.949360	+	0.314192i	$0.101733\pi$
$139$			87.3453i			0.628384i	−0.949360	+	0.314192i	$0.898267\pi$
$140$		0			0
$141$			18.9753i			0.134577i
$142$	−0.884758	+	0.884758i	−0.00623069	+	0.00623069i
$143$	−86.6986	+	56.4597i	−0.606284	+	0.394823i
$144$		−	171.481i		−	1.19084i
$145$		0			0
$146$	−67.0784			−0.459441
$147$	6.29454	−	6.29454i	0.0428200	−	0.0428200i
$148$	38.4171	−	38.4171i	0.259575	−	0.259575i
$149$	200.517			1.34575			0.672875	−	0.739756i	$-0.265059\pi$
$149$	200.517			1.34575			0.672875	+	0.739756i	$0.265059\pi$
$150$		0			0
$151$			282.461i			1.87061i	0.353849	+	0.935303i	$0.384873\pi$
$151$			282.461i			1.87061i	−0.353849	+	0.935303i	$0.615127\pi$
$152$	83.9801	−	83.9801i	0.552501	−	0.552501i
$153$	36.3992	+	36.3992i	0.237903	+	0.237903i
$154$	−159.692			−1.03696
$155$		0			0
$156$	18.2527	+	3.85548i	0.117005	+	0.0247146i
$157$	−144.002	+	144.002i	−0.917212	+	0.917212i	−0.996826	−	0.0796134i	$-0.974631\pi$
$157$	−144.002	+	144.002i	−0.917212	+	0.917212i	0.0796134	+	0.996826i	$0.474631\pi$
$158$	130.126	−	130.126i	0.823585	−	0.823585i
$159$			33.2108i			0.208873i
$160$		0			0
$161$		−	190.011i		−	1.18019i
$162$	−126.372	−	126.372i	−0.780073	−	0.780073i
$163$	−78.4288	+	78.4288i	−0.481158	+	0.481158i	−0.905502	−	0.424343i	$-0.860505\pi$
$163$	−78.4288	+	78.4288i	−0.481158	+	0.481158i	0.424343	+	0.905502i	$0.360505\pi$
$164$	144.174			0.879108
$165$		0			0
$166$	252.253			1.51960
$167$	−125.294	−	125.294i	−0.750263	−	0.750263i	0.224265	−	0.974528i	$-0.428002\pi$
$167$	−125.294	−	125.294i	−0.750263	−	0.750263i	−0.974528	+	0.224265i	$0.928002\pi$
$168$	−14.4540	−	14.4540i	−0.0860357	−	0.0860357i
$169$	−68.3455	+	154.564i	−0.404411	+	0.914577i
$170$		0			0
$171$		−	244.951i		−	1.43246i
$172$	−43.6855	+	43.6855i	−0.253986	+	0.253986i
$173$	−144.598	−	144.598i	−0.835825	−	0.835825i	0.152481	−	0.988306i	$-0.451274\pi$
$173$	−144.598	−	144.598i	−0.835825	−	0.835825i	−0.988306	+	0.152481i	$0.951274\pi$
$174$	78.3410			0.450235
$175$		0			0
$176$			158.256i			0.899180i
$177$	−5.57261	−	5.57261i	−0.0314837	−	0.0314837i
$178$	−4.03194	−	4.03194i	−0.0226514	−	0.0226514i
$179$		−	14.1047i		−	0.0787971i	−0.999224	−	0.0393985i	$-0.987456\pi$
$179$		−	14.1047i		−	0.0787971i	0.999224	−	0.0393985i	$-0.0125442\pi$
$180$		0			0
$181$	149.600			0.826517			0.413259	−	0.910614i	$-0.364391\pi$
$181$	149.600			0.826517			0.413259	+	0.910614i	$0.364391\pi$
$182$	−218.586	+	142.347i	−1.20102	+	0.782127i
$183$	19.6939	+	19.6939i	0.107617	+	0.107617i
$184$	−99.6916			−0.541802
$185$		0			0
$186$	8.13790			0.0437522
$187$	−33.5920	−	33.5920i	−0.179636	−	0.179636i
$188$	51.1673	−	51.1673i	0.272167	−	0.272167i
$189$	−86.1578			−0.455861
$190$		0			0
$191$	−202.051			−1.05786			−0.528930	−	0.848665i	$-0.677407\pi$
$191$	−202.051			−1.05786			−0.528930	+	0.848665i	$0.677407\pi$
$192$	1.91163	−	1.91163i	0.00995642	−	0.00995642i
$193$	−120.889	+	120.889i	−0.626366	+	0.626366i	−0.947152	−	0.320786i	$-0.896053\pi$
$193$	−120.889	+	120.889i	−0.626366	+	0.626366i	0.320786	+	0.947152i	$0.396053\pi$
$194$			303.456i			1.56421i
$195$		0			0
$196$	−33.9468			−0.173198
$197$	−24.3108	−	24.3108i	−0.123405	−	0.123405i	0.642707	−	0.766112i	$-0.277811\pi$
$197$	−24.3108	−	24.3108i	−0.123405	−	0.123405i	−0.766112	+	0.642707i	$0.777811\pi$
$198$	122.190	+	122.190i	0.617123	+	0.617123i
$199$		−	111.235i		−	0.558969i	−0.960150	−	0.279485i	$-0.909836\pi$
$199$		−	111.235i		−	0.558969i	0.960150	−	0.279485i	$-0.0901636\pi$
$200$		0			0
$201$			19.7720i			0.0983681i
$202$	−54.6485	−	54.6485i	−0.270537	−	0.270537i
$203$	−285.829	+	285.829i	−1.40802	+	1.40802i
$204$			8.56598i			0.0419901i
$205$		0			0
$206$		−	430.647i		−	2.09052i
$207$	−145.389	+	145.389i	−0.702362	+	0.702362i
$208$	141.067	+	216.620i	0.678205	+	1.04144i
$209$			226.060i			1.08162i
$210$		0			0
$211$	−86.7166			−0.410979			−0.205490	−	0.978659i	$-0.565879\pi$
$211$	−86.7166			−0.410979			−0.205490	+	0.978659i	$0.565879\pi$
$212$	89.5537	−	89.5537i	0.422423	−	0.422423i
$213$	0.215563	−	0.215563i	0.00101203	−	0.00101203i
$214$	−329.866			−1.54143
$215$		0			0
$216$			45.2037i			0.209276i
$217$	−29.6913	+	29.6913i	−0.136826	+	0.136826i
$218$	−206.594	−	206.594i	−0.947679	−	0.947679i
$219$	16.3430			0.0746258
$220$		0			0
$221$	−75.9239	−	16.0372i	−0.343547	−	0.0725666i
$222$	−25.3645	+	25.3645i	−0.114255	+	0.114255i
$223$	185.893	−	185.893i	0.833601	−	0.833601i	−0.154406	−	0.988007i	$-0.549346\pi$
$223$	185.893	−	185.893i	0.833601	−	0.833601i	0.988007	+	0.154406i	$0.0493465\pi$
$224$			265.709i			1.18620i
$225$		0			0
$226$		−	241.416i		−	1.06821i
$227$	34.9372	+	34.9372i	0.153908	+	0.153908i	0.779861	−	0.625953i	$-0.215290\pi$
$227$	34.9372	+	34.9372i	0.153908	+	0.153908i	−0.625953	+	0.779861i	$0.715290\pi$
$228$	28.8227	−	28.8227i	0.126415	−	0.126415i
$229$	242.528			1.05907			0.529537	−	0.848287i	$-0.322366\pi$
$229$	242.528			1.05907			0.529537	+	0.848287i	$0.322366\pi$
$230$		0			0
$231$	38.9076			0.168431
$232$	149.964	+	149.964i	0.646395	+	0.646395i
$233$	238.192	+	238.192i	1.02228	+	1.02228i	0.999746	+	0.0225371i	$0.00717440\pi$
$233$	238.192	+	238.192i	1.02228	+	1.02228i	0.0225371	+	0.999746i	$0.492826\pi$
$234$	276.172	+	58.3351i	1.18022	+	0.249295i
$235$		0			0
$236$			30.0534i			0.127345i
$237$	−31.7041	+	31.7041i	−0.133773	+	0.133773i
$238$	−84.6927	−	84.6927i	−0.355852	−	0.355852i
$239$	−342.001			−1.43097			−0.715484	−	0.698629i	$-0.753794\pi$
$239$	−342.001			−1.43097			−0.715484	+	0.698629i	$0.753794\pi$
$240$		0			0
$241$			176.477i			0.732268i	0.930562	+	0.366134i	$0.119319\pi$
$241$			176.477i			0.732268i	−0.930562	+	0.366134i	$0.880681\pi$
$242$	102.656	+	102.656i	0.424200	+	0.424200i
$243$	99.5906	+	99.5906i	0.409838	+	0.409838i
$244$		−	106.210i		−	0.435288i
$245$		0			0
$246$	−95.1893			−0.386948
$247$	201.506	+	309.429i	0.815813	+	1.25275i
$248$	15.5779	+	15.5779i	0.0628142	+	0.0628142i
$249$	−61.4592			−0.246824
$250$		0			0
$251$	314.765			1.25404			0.627022	−	0.779002i	$-0.284274\pi$
$251$	314.765			1.25404			0.627022	+	0.779002i	$0.284274\pi$
$252$	113.683	+	113.683i	0.451123	+	0.451123i
$253$	134.176	−	134.176i	0.530340	−	0.530340i
$254$	456.283			1.79639
$255$		0			0
$256$	325.476			1.27139
$257$	13.8093	−	13.8093i	0.0537327	−	0.0537327i	−0.679730	−	0.733463i	$-0.737903\pi$
$257$	13.8093	−	13.8093i	0.0537327	−	0.0537327i	0.733463	+	0.679730i	$0.237903\pi$
$258$	28.8430	−	28.8430i	0.111794	−	0.111794i
$259$		−	185.086i		−	0.714619i
$260$		0			0
$261$	437.410			1.67590
$262$	−294.443	−	294.443i	−1.12383	−	1.12383i
$263$	−108.910	−	108.910i	−0.414106	−	0.414106i	0.469060	−	0.883166i	$-0.344593\pi$
$263$	−108.910	−	108.910i	−0.414106	−	0.414106i	−0.883166	+	0.469060i	$0.844593\pi$
$264$		−	20.4133i		−	0.0773232i
$265$		0			0
$266$			569.945i			2.14265i
$267$	0.982346	+	0.982346i	0.00367920	+	0.00367920i
$268$	53.3156	−	53.3156i	0.198939	−	0.198939i
$269$		−	43.8038i		−	0.162839i	−0.996680	−	0.0814197i	$-0.974055\pi$
$269$		−	43.8038i		−	0.162839i	0.996680	−	0.0814197i	$-0.0259454\pi$
$270$		0			0
$271$		−	243.960i		−	0.900220i	−0.892973	−	0.450110i	$-0.851385\pi$
$271$		−	243.960i		−	0.900220i	0.892973	−	0.450110i	$-0.148615\pi$
$272$	−83.9308	+	83.9308i	−0.308569	+	0.308569i
$273$	53.2566	−	34.6816i	0.195079	−	0.127039i
$274$			253.404i			0.924832i
$275$		0			0
$276$	−34.2150			−0.123967
$277$	120.428	−	120.428i	0.434758	−	0.434758i	−0.455486	−	0.890243i	$-0.650534\pi$
$277$	120.428	−	120.428i	0.434758	−	0.434758i	0.890243	+	0.455486i	$0.150534\pi$
$278$	−155.506	+	155.506i	−0.559373	+	0.559373i
$279$	45.4373			0.162858
$280$		0			0
$281$			358.582i			1.27609i	0.769999	+	0.638045i	$0.220257\pi$
$281$			358.582i			1.27609i	−0.769999	+	0.638045i	$0.779743\pi$
$282$	−33.7828	+	33.7828i	−0.119797	+	0.119797i
$283$	−175.165	−	175.165i	−0.618959	−	0.618959i	0.326305	−	0.945264i	$-0.394196\pi$
$283$	−175.165	−	175.165i	−0.618959	−	0.618959i	−0.945264	+	0.326305i	$0.894196\pi$
$284$	−1.16254			−0.00409346
$285$		0			0
$286$	−254.873	−	53.8361i	−0.891163	−	0.188238i
$287$	347.300	−	347.300i	1.21011	−	1.21011i
$288$	203.310	−	203.310i	0.705938	−	0.705938i
$289$			253.369i			0.876709i
$290$		0			0
$291$		−	73.9344i		−	0.254070i
$292$	−44.0694	−	44.0694i	−0.150923	−	0.150923i
$293$	221.222	−	221.222i	0.755025	−	0.755025i	−0.220388	−	0.975412i	$-0.570732\pi$
$293$	221.222	−	221.222i	0.755025	−	0.755025i	0.975412	+	0.220388i	$0.0707323\pi$
$294$	22.4130			0.0762348
$295$		0			0
$296$	−97.1077			−0.328067
$297$	−60.8402	−	60.8402i	−0.204849	−	0.204849i
$298$	356.991	+	356.991i	1.19796	+	1.19796i
$299$	64.0573	−	303.262i	0.214238	−	1.01425i
$300$		0			0
$301$			210.468i			0.699231i
$302$	−502.882	+	502.882i	−1.66517	+	1.66517i
$303$	13.3146	+	13.3146i	0.0439426	+	0.0439426i
$304$	564.818			1.85795
$305$		0			0
$306$			129.607i			0.423553i
$307$	−2.13802	−	2.13802i	−0.00696423	−	0.00696423i	0.703616	−	0.710580i	$-0.251568\pi$
$307$	−2.13802	−	2.13802i	−0.00696423	−	0.00696423i	−0.710580	+	0.703616i	$0.751568\pi$
$308$	−104.915	−	104.915i	−0.340634	−	0.340634i
$309$			104.923i			0.339557i
$310$		0			0
$311$	−464.344			−1.49307			−0.746534	−	0.665347i	$-0.768284\pi$
$311$	−464.344			−1.49307			−0.746534	+	0.665347i	$0.768284\pi$
$312$	−18.1961	−	27.9417i	−0.0583209	−	0.0895567i
$313$	29.3689	+	29.3689i	0.0938304	+	0.0938304i	0.752464	−	0.658633i	$-0.228865\pi$
$313$	29.3689	+	29.3689i	0.0938304	+	0.0938304i	−0.658633	+	0.752464i	$0.728865\pi$
$314$	−512.751			−1.63296
$315$		0			0
$316$	170.982			0.541082
$317$	133.383	+	133.383i	0.420765	+	0.420765i	0.885467	−	0.464702i	$-0.153839\pi$
$317$	133.383	+	133.383i	0.420765	+	0.420765i	−0.464702	+	0.885467i	$0.653839\pi$
$318$	−59.1270	+	59.1270i	−0.185934	+	0.185934i
$319$	−403.675			−1.26544
$320$		0			0
$321$	80.3689			0.250370
$322$	338.287	−	338.287i	1.05058	−	1.05058i
$323$	−119.891	+	119.891i	−0.371178	+	0.371178i
$324$		−	166.049i		−	0.512496i
$325$		0			0
$326$	−279.262			−0.856633
$327$	50.3348	+	50.3348i	0.153929	+	0.153929i
$328$	−182.215	−	182.215i	−0.555535	−	0.555535i
$329$		−	246.514i		−	0.749284i
$330$		0			0
$331$			83.9623i			0.253663i	0.991924	+	0.126831i	$0.0404807\pi$
$331$			83.9623i			0.253663i	−0.991924	+	0.126831i	$0.959519\pi$
$332$	165.726	+	165.726i	0.499175	+	0.499175i
$333$	−141.621	+	141.621i	−0.425287	+	0.425287i
$334$		−	446.135i		−	1.33573i
$335$		0			0
$336$		−	97.2120i		−	0.289321i
$337$	−92.5815	+	92.5815i	−0.274722	+	0.274722i	−0.830998	−	0.556276i	$-0.812230\pi$
$337$	−92.5815	+	92.5815i	−0.274722	+	0.274722i	0.556276	+	0.830998i	$0.312230\pi$
$338$	−396.857	+	153.499i	−1.17413	+	0.454138i
$339$			58.8188i			0.173507i
$340$		0			0
$341$	−41.9330			−0.122971
$342$	436.100	−	436.100i	1.27515	−	1.27515i
$343$	194.351	−	194.351i	0.566621	−	0.566621i
$344$	110.425			0.321002
$345$		0			0
$346$		−	514.871i		−	1.48807i
$347$	263.764	−	263.764i	0.760126	−	0.760126i	−0.216219	−	0.976345i	$-0.569372\pi$
$347$	263.764	−	263.764i	0.760126	−	0.760126i	0.976345	+	0.216219i	$0.0693725\pi$
$348$	51.4687	+	51.4687i	0.147899	+	0.147899i
$349$	479.339			1.37346			0.686732	−	0.726911i	$-0.259045\pi$
$349$	479.339			1.37346			0.686732	+	0.726911i	$0.259045\pi$
$350$		0			0
$351$	−137.510	−	29.0458i	−0.391766	−	0.0827517i
$352$	−187.630	+	187.630i	−0.533040	+	0.533040i
$353$	10.9905	−	10.9905i	0.0311344	−	0.0311344i	−0.691368	−	0.722503i	$-0.742992\pi$
$353$	10.9905	−	10.9905i	0.0311344	−	0.0311344i	0.722503	+	0.691368i	$0.242992\pi$
$354$		−	19.8424i		−	0.0560521i
$355$		0			0
$356$		−	5.29784i		−	0.0148816i
$357$	20.6346	+	20.6346i	0.0578000	+	0.0578000i
$358$	25.1113	−	25.1113i	0.0701434	−	0.0701434i
$359$	−394.878			−1.09994			−0.549969	−	0.835185i	$-0.685361\pi$
$359$	−394.878			−1.09994			−0.549969	+	0.835185i	$0.685361\pi$
$360$		0			0
$361$	445.811			1.23493
$362$	266.340	+	266.340i	0.735747	+	0.735747i
$363$	−25.0113	−	25.0113i	−0.0689017	−	0.0689017i
$364$	−237.127	−	50.0878i	−0.651449	−	0.137604i
$365$		0			0
$366$			70.1244i			0.191597i
$367$	32.7622	−	32.7622i	0.0892703	−	0.0892703i	−0.661061	−	0.750332i	$-0.729894\pi$
$367$	32.7622	−	32.7622i	0.0892703	−	0.0892703i	0.750332	+	0.661061i	$0.229894\pi$
$368$	−335.244	−	335.244i	−0.910989	−	0.910989i
$369$	−531.481			−1.44033
$370$		0			0
$371$		−	431.452i		−	1.16294i
$372$	5.34647	+	5.34647i	0.0143722	+	0.0143722i
$373$	42.9772	+	42.9772i	0.115221	+	0.115221i	0.762366	−	0.647146i	$-0.224037\pi$
$373$	42.9772	+	42.9772i	0.115221	+	0.115221i	−0.647146	+	0.762366i	$0.724037\pi$
$374$		−	119.611i		−	0.319816i
$375$		0			0
$376$	−129.337			−0.343981
$377$	−552.549	+	359.830i	−1.46565	+	0.954455i
$378$	−153.391	−	153.391i	−0.405797	−	0.405797i
$379$	494.557			1.30490			0.652449	−	0.757832i	$-0.273742\pi$
$379$	494.557			1.30490			0.652449	+	0.757832i	$0.273742\pi$
$380$		0			0
$381$	−111.169			−0.291783
$382$	−359.723	−	359.723i	−0.941684	−	0.941684i
$383$	43.8046	−	43.8046i	0.114372	−	0.114372i	−0.647604	−	0.761977i	$-0.724229\pi$
$383$	43.8046	−	43.8046i	0.114372	−	0.114372i	0.761977	+	0.647604i	$0.224229\pi$
$384$	−75.0044			−0.195324
$385$		0			0
$386$	−430.450			−1.11515
$387$	161.042	−	161.042i	0.416130	−	0.416130i
$388$	−199.366	+	199.366i	−0.513829	+	0.513829i
$389$			341.940i			0.879023i	0.898237	+	0.439511i	$0.144848\pi$
$389$			341.940i			0.879023i	−0.898237	+	0.439511i	$0.855152\pi$
$390$		0			0
$391$	142.320			0.363991
$392$	42.9040	+	42.9040i	0.109449	+	0.109449i
$393$	71.7384	+	71.7384i	0.182541	+	0.182541i
$394$		−	86.5637i		−	0.219705i
$395$		0			0
$396$			160.554i			0.405439i
$397$	−266.811	−	266.811i	−0.672069	−	0.672069i	0.286124	−	0.958193i	$-0.407633\pi$
$397$	−266.811	−	266.811i	−0.672069	−	0.672069i	−0.958193	+	0.286124i	$0.907633\pi$
$398$	198.038	−	198.038i	0.497582	−	0.497582i
$399$		−	138.862i		−	0.348025i
$400$		0			0
$401$			259.256i			0.646523i	0.946310	+	0.323261i	$0.104779\pi$
$401$			259.256i			0.646523i	−0.946310	+	0.323261i	$0.895221\pi$
$402$	−35.2011	+	35.2011i	−0.0875650	+	0.0875650i
$403$	−57.3977	+	37.3784i	−0.142426	+	0.0927503i
$404$		−	71.8064i		−	0.177739i
$405$		0			0
$406$	−1017.75			−2.50678
$407$	130.698	−	130.698i	0.321126	−	0.321126i
$408$	10.8262	−	10.8262i	0.0265348	−	0.0265348i
$409$	422.900			1.03399			0.516993	−	0.855990i	$-0.327051\pi$
$409$	422.900			1.03399			0.516993	+	0.855990i	$0.327051\pi$
$410$		0			0
$411$		−	61.7396i		−	0.150218i
$412$	282.928	−	282.928i	0.686719	−	0.686719i
$413$	72.3956	+	72.3956i	0.175292	+	0.175292i
$414$	−517.688			−1.25045
$415$		0			0
$416$	−89.5769	+	424.078i	−0.215329	+	1.01942i
$417$	37.8876	−	37.8876i	0.0908574	−	0.0908574i
$418$	−402.466	+	402.466i	−0.962838	+	0.962838i
$419$		−	572.404i		−	1.36612i	−0.730363	−	0.683060i	$-0.760649\pi$
$419$		−	572.404i		−	1.36612i	0.730363	−	0.683060i	$-0.239351\pi$
$420$		0			0
$421$		−	335.328i		−	0.796502i	−0.917276	−	0.398251i	$-0.869617\pi$
$421$		−	335.328i		−	0.796502i	0.917276	−	0.398251i	$-0.130383\pi$
$422$	−154.386	−	154.386i	−0.365845	−	0.365845i
$423$	−188.623	+	188.623i	−0.445917	+	0.445917i
$424$	−226.367			−0.533884
$425$		0			0
$426$	0.767558			0.00180178
$427$	−255.850	−	255.850i	−0.599181	−	0.599181i
$428$	−216.717	−	216.717i	−0.506347	−	0.506347i
$429$	62.0974	+	13.1167i	0.144749	+	0.0305750i
$430$		0			0
$431$		−	79.0478i		−	0.183406i	−0.995786	−	0.0917028i	$-0.970769\pi$
$431$		−	79.0478i		−	0.183406i	0.995786	−	0.0917028i	$-0.0292310\pi$
$432$	−152.011	+	152.011i	−0.351878	+	0.351878i
$433$	4.42481	+	4.42481i	0.0102190	+	0.0102190i	0.712198	−	0.701979i	$-0.247700\pi$
$433$	4.42481	+	4.42481i	0.0102190	+	0.0102190i	−0.701979	+	0.712198i	$0.747700\pi$
$434$	−105.722			−0.243600
$435$		0			0
$436$		−	271.458i		−	0.622610i
$437$	−478.878	−	478.878i	−1.09583	−	1.09583i
$438$	29.0964	+	29.0964i	0.0664302	+	0.0664302i
$439$		−	786.635i		−	1.79188i	−0.444176	−	0.895940i	$-0.646504\pi$
$439$		−	786.635i		−	1.79188i	0.444176	−	0.895940i	$-0.353496\pi$
$440$		0			0
$441$	125.141			0.283767
$442$	−106.620	−	163.724i	−0.241221	−	0.370415i
$443$	434.735	+	434.735i	0.981343	+	0.981343i	0.999829	−	0.0184863i	$-0.00588469\pi$
$443$	434.735	+	434.735i	0.981343	+	0.981343i	−0.0184863	+	0.999829i	$0.505885\pi$
$444$	−33.3282			−0.0750635
$445$		0			0
$446$	661.911			1.48411
$447$	−86.9776	−	86.9776i	−0.194581	−	0.194581i
$448$	−24.8347	+	24.8347i	−0.0554345	+	0.0554345i
$449$	−40.5436			−0.0902976			−0.0451488	−	0.998980i	$-0.514376\pi$
$449$	−40.5436			−0.0902976			−0.0451488	+	0.998980i	$0.514376\pi$
$450$		0			0
$451$	490.491			1.08756
$452$	158.606	−	158.606i	0.350899	−	0.350899i
$453$	122.523	−	122.523i	0.270469	−	0.270469i
$454$			124.401i			0.274012i
$455$		0			0
$456$	−72.8557			−0.159771
$457$	−142.776	−	142.776i	−0.312419	−	0.312419i	0.533427	−	0.845846i	$-0.320904\pi$
$457$	−142.776	−	142.776i	−0.312419	−	0.312419i	−0.845846	+	0.533427i	$0.820904\pi$
$458$	431.786	+	431.786i	0.942764	+	0.942764i
$459$		−	64.5331i		−	0.140595i
$460$		0			0
$461$		−	615.794i		−	1.33578i	−0.744260	−	0.667889i	$-0.767198\pi$
$461$		−	615.794i		−	1.33578i	0.744260	−	0.667889i	$-0.232802\pi$
$462$	69.2693	+	69.2693i	0.149934	+	0.149934i
$463$	476.235	−	476.235i	1.02859	−	1.02859i	0.0290068	−	0.999579i	$-0.490766\pi$
$463$	476.235	−	476.235i	1.02859	−	1.02859i	0.999579	−	0.0290068i	$-0.00923445\pi$
$464$			1008.60i			2.17370i
$465$		0			0
$466$			848.133i			1.82003i
$467$	164.188	−	164.188i	0.351580	−	0.351580i	−0.509117	−	0.860697i	$-0.670028\pi$
$467$	164.188	−	164.188i	0.351580	−	0.351580i	0.860697	+	0.509117i	$0.170028\pi$
$468$	143.115	+	219.766i	0.305802	+	0.469585i
$469$		−	256.864i		−	0.547685i
$470$		0			0
$471$	124.927			0.265238
$472$	37.9832	−	37.9832i	0.0804730	−	0.0804730i
$473$	−148.622	+	148.622i	−0.314211	+	0.314211i
$474$	−112.889			−0.238163
$475$		0			0
$476$		−	111.283i		−	0.233789i
$477$	−330.130	+	330.130i	−0.692097	+	0.692097i
$478$	−608.884	−	608.884i	−1.27382	−	1.27382i
$479$	366.297			0.764712			0.382356	−	0.924015i	$-0.375113\pi$
$479$	366.297			0.764712			0.382356	+	0.924015i	$0.375113\pi$
$480$		0			0
$481$	62.3970	−	295.402i	0.129724	−	0.614141i
$482$	−314.191	+	314.191i	−0.651849	+	0.651849i
$483$	−82.4206	+	82.4206i	−0.170643	+	0.170643i
$484$			134.887i			0.278693i
$485$		0			0
$486$			354.613i			0.729657i
$487$	480.523	+	480.523i	0.986701	+	0.986701i	0.999913	−	0.0132120i	$-0.00420562\pi$
$487$	480.523	+	480.523i	0.986701	+	0.986701i	−0.0132120	+	0.999913i	$0.504206\pi$
$488$	−134.235	+	134.235i	−0.275072	+	0.275072i
$489$	68.0397			0.139141
$490$		0			0
$491$	138.516			0.282110			0.141055	−	0.990002i	$-0.454951\pi$
$491$	138.516			0.282110			0.141055	+	0.990002i	$0.454951\pi$
$492$	−62.5378	−	62.5378i	−0.127109	−	0.127109i
$493$	−214.089	−	214.089i	−0.434258	−	0.434258i
$494$	−192.142	+	909.646i	−0.388952	+	1.84139i
$495$		0			0
$496$			104.771i			0.211232i
$497$	−2.80045	+	2.80045i	−0.00563472	+	0.00563472i
$498$	−109.419	−	109.419i	−0.219717	−	0.219717i
$499$	508.021			1.01808			0.509040	−	0.860743i	$-0.330001\pi$
$499$	508.021			1.01808			0.509040	+	0.860743i	$0.330001\pi$
$500$		0			0
$501$			108.697i			0.216960i
$502$	560.394	+	560.394i	1.11632	+	1.11632i
$503$	−415.356	−	415.356i	−0.825756	−	0.825756i	0.161170	−	0.986927i	$-0.448473\pi$
$503$	−415.356	−	415.356i	−0.825756	−	0.825756i	−0.986927	+	0.161170i	$0.948473\pi$
$504$		−	287.359i		−	0.570156i
$505$		0			0
$506$	477.762			0.944194
$507$	96.6907	−	37.3986i	0.190711	−	0.0737644i
$508$	299.771	+	299.771i	0.590099	+	0.590099i
$509$	−94.4082			−0.185478			−0.0927389	−	0.995690i	$-0.529562\pi$
$509$	−94.4082			−0.185478			−0.0927389	+	0.995690i	$0.529562\pi$
$510$		0			0
$511$	−212.318			−0.415495
$512$	233.636	+	233.636i	0.456320	+	0.456320i
$513$	−217.140	+	217.140i	−0.423275	+	0.423275i
$514$	49.1709			0.0956632
$515$		0			0
$516$	37.8987			0.0734471
$517$	174.076	−	174.076i	0.336704	−	0.336704i
$518$	329.519	−	329.519i	0.636137	−	0.636137i
$519$			125.444i			0.241703i
$520$		0			0
$521$	−782.708			−1.50232			−0.751159	−	0.660121i	$-0.770505\pi$
$521$	−782.708			−1.50232			−0.751159	+	0.660121i	$0.770505\pi$
$522$	778.745	+	778.745i	1.49185	+	1.49185i
$523$	617.667	+	617.667i	1.18101	+	1.18101i	0.979483	+	0.201525i	$0.0645896\pi$
$523$	617.667	+	617.667i	1.18101	+	1.18101i	0.201525	+	0.979483i	$0.435410\pi$
$524$		−	386.889i		−	0.738337i
$525$		0			0
$526$		−	387.796i		−	0.737255i
$527$	−22.2391	−	22.2391i	−0.0421995	−	0.0421995i
$528$	68.6461	−	68.6461i	0.130012	−	0.130012i
$529$			39.4690i			0.0746107i
$530$		0			0
$531$		−	110.789i		−	0.208641i
$532$	−374.445	+	374.445i	−0.703844	+	0.703844i
$533$	671.383	−	437.216i	1.25963	−	0.820293i
$534$			3.49785i			0.00655028i
$535$		0			0
$536$	−134.767			−0.251431
$537$	−6.11815	+	6.11815i	−0.0113932	+	0.0113932i
$538$	77.9863	−	77.9863i	0.144956	−	0.144956i
$539$	−115.490			−0.214267
$540$		0			0
$541$		−	381.768i		−	0.705671i	−0.935685	−	0.352835i	$-0.885218\pi$
$541$		−	381.768i		−	0.705671i	0.935685	−	0.352835i	$-0.114782\pi$
$542$	434.335	−	434.335i	0.801356	−	0.801356i
$543$	−64.8914	−	64.8914i	−0.119505	−	0.119505i
$544$	−199.019			−0.365844
$545$		0			0
$546$	156.561	+	33.0700i	0.286742	+	0.0605678i
$547$	1.21491	−	1.21491i	0.00222105	−	0.00222105i	−0.705995	−	0.708216i	$-0.749500\pi$
$547$	1.21491	−	1.21491i	0.00222105	−	0.00222105i	0.708216	+	0.705995i	$0.249500\pi$
$548$	−166.482	+	166.482i	−0.303800	+	0.303800i
$549$			391.533i			0.713175i
$550$		0			0
$551$			1440.73i			2.61475i
$552$	43.2430	+	43.2430i	0.0783387	+	0.0783387i
$553$	411.879	−	411.879i	0.744808	−	0.744808i
$554$	428.809			0.774023
$555$		0			0
$556$	−204.329			−0.367499
$557$	639.049	+	639.049i	1.14730	+	1.14730i	0.987081	+	0.160224i	$0.0512217\pi$
$557$	639.049	+	639.049i	1.14730	+	1.14730i	0.160224	+	0.987081i	$0.448778\pi$
$558$	80.8945	+	80.8945i	0.144972	+	0.144972i
$559$	−70.9540	+	335.913i	−0.126930	+	0.600917i
$560$		0			0
$561$			29.1422i			0.0519469i
$562$	−638.402	+	638.402i	−1.13595	+	1.13595i
$563$	−387.288	−	387.288i	−0.687901	−	0.687901i	0.273867	−	0.961768i	$-0.411697\pi$
$563$	−387.288	−	387.288i	−0.687901	−	0.687901i	−0.961768	+	0.273867i	$0.911697\pi$
$564$	−44.3894			−0.0787047
$565$		0			0
$566$		−	623.713i		−	1.10197i
$567$	−399.995	−	399.995i	−0.705458	−	0.705458i
$568$	1.46929	+	1.46929i	0.00258678	+	0.00258678i
$569$			661.698i			1.16291i	0.813577	+	0.581457i	$0.197517\pi$
$569$			661.698i			1.16291i	−0.813577	+	0.581457i	$0.802483\pi$
$570$		0			0
$571$	−545.786			−0.955843			−0.477921	−	0.878403i	$-0.658610\pi$
$571$	−545.786			−0.955843			−0.477921	+	0.878403i	$0.658610\pi$
$572$	−132.078	−	202.817i	−0.230905	−	0.354574i
$573$	87.6433	+	87.6433i	0.152955	+	0.152955i
$574$	1236.64			2.15442
$575$		0			0
$576$	38.0050			0.0659809
$577$	377.513	+	377.513i	0.654268	+	0.654268i	0.954018	−	0.299750i	$-0.0969032\pi$
$577$	377.513	+	377.513i	0.654268	+	0.654268i	−0.299750	+	0.954018i	$0.596903\pi$
$578$	−451.087	+	451.087i	−0.780427	+	0.780427i
$579$	104.875			0.181132
$580$		0			0
$581$	798.436			1.37424
$582$	131.629	−	131.629i	0.226167	−	0.226167i
$583$	304.670	−	304.670i	0.522589	−	0.522589i
$584$			111.395i			0.190745i
$585$		0			0
$586$	787.708			1.34421
$587$	80.0625	+	80.0625i	0.136393	+	0.136393i	0.772007	−	0.635614i	$-0.219253\pi$
$587$	80.0625	+	80.0625i	0.136393	+	0.136393i	−0.635614	+	0.772007i	$0.719253\pi$
$588$	14.7250	+	14.7250i	0.0250425	+	0.0250425i
$589$			149.660i			0.254091i
$590$		0			0
$591$			21.0905i			0.0356861i
$592$	−326.555	−	326.555i	−0.551613	−	0.551613i
$593$	−263.292	+	263.292i	−0.444000	+	0.444000i	−0.893354	−	0.449354i	$-0.851654\pi$
$593$	−263.292	+	263.292i	−0.444000	+	0.444000i	0.449354	+	0.893354i	$0.351654\pi$
$594$		−	216.634i		−	0.364704i
$595$		0			0
$596$			469.074i			0.787038i
$597$	−48.2501	+	48.2501i	−0.0808209	+	0.0808209i
$598$	653.959	−	425.870i	1.09358	−	0.712156i
$599$			386.253i			0.644830i	0.946598	+	0.322415i	$0.104495\pi$
$599$			386.253i			0.644830i	−0.946598	+	0.322415i	$0.895505\pi$
$600$		0			0
$601$	714.402			1.18869			0.594345	−	0.804210i	$-0.297411\pi$
$601$	714.402			1.18869			0.594345	+	0.804210i	$0.297411\pi$
$602$	−374.709	+	374.709i	−0.622439	+	0.622439i
$603$	−196.543	+	196.543i	−0.325941	+	0.325941i
$604$	−660.770			−1.09399
$605$		0			0
$606$			47.4095i			0.0782335i
$607$	−360.380	+	360.380i	−0.593706	+	0.593706i	−0.938631	−	0.344924i	$-0.887905\pi$
$607$	−360.380	+	360.380i	−0.593706	+	0.593706i	0.344924	+	0.938631i	$0.387905\pi$
$608$	669.656	+	669.656i	1.10141	+	1.10141i
$609$	247.966			0.407170
$610$		0			0
$611$	83.1059	−	393.443i	0.136016	−	0.643932i
$612$	−85.1497	+	85.1497i	−0.139134	+	0.139134i
$613$	−597.005	+	597.005i	−0.973906	+	0.973906i	−0.999668	−	0.0257619i	$-0.991799\pi$
$613$	−597.005	+	597.005i	−0.973906	+	0.973906i	0.0257619	+	0.999668i	$0.491799\pi$
$614$		−	7.61286i		−	0.0123988i
$615$		0			0
$616$			265.196i			0.430514i
$617$	−145.770	−	145.770i	−0.236256	−	0.236256i	0.579042	−	0.815298i	$-0.303427\pi$
$617$	−145.770	−	145.770i	−0.236256	−	0.236256i	−0.815298	+	0.579042i	$0.803427\pi$
$618$	−186.801	+	186.801i	−0.302266	+	0.302266i
$619$	−1024.63			−1.65530			−0.827648	−	0.561247i	$-0.810322\pi$
$619$	−1024.63			−1.65530			−0.827648	+	0.561247i	$0.810322\pi$
$620$		0			0
$621$	257.764			0.415079
$622$	−826.698	−	826.698i	−1.32910	−	1.32910i
$623$	−12.7620	−	12.7620i	−0.0204847	−	0.0204847i
$624$	32.7725	−	155.153i	0.0525200	−	0.248642i
$625$		0			0
$626$			104.574i			0.167052i
$627$	98.0572	−	98.0572i	0.156391	−	0.156391i
$628$	−336.869	−	336.869i	−0.536415	−	0.536415i
$629$	138.632			0.220400
$630$		0			0
$631$			680.647i			1.07868i	0.842088	+	0.539340i	$0.181326\pi$
$631$			680.647i			1.07868i	−0.842088	+	0.539340i	$0.818674\pi$
$632$	−216.097	−	216.097i	−0.341926	−	0.341926i
$633$	37.6149	+	37.6149i	0.0594232	+	0.0594232i
$634$			474.936i			0.749111i
$635$		0			0
$636$	−77.6910			−0.122156
$637$	−158.082	+	102.946i	−0.248166	+	0.161610i
$638$	−718.685	−	718.685i	−1.12647	−	1.12647i
$639$	4.28559			0.00670672
$640$		0			0
$641$	555.853			0.867165			0.433582	−	0.901114i	$-0.357249\pi$
$641$	555.853			0.867165			0.433582	+	0.901114i	$0.357249\pi$
$642$	143.085	+	143.085i	0.222874	+	0.222874i
$643$	545.418	−	545.418i	0.848240	−	0.848240i	−0.141673	−	0.989913i	$-0.545248\pi$
$643$	545.418	−	545.418i	0.848240	−	0.848240i	0.989913	+	0.141673i	$0.0452483\pi$
$644$	444.498			0.690215
$645$		0			0
$646$	−426.895			−0.660829
$647$	−248.574	+	248.574i	−0.384195	+	0.384195i	−0.872611	−	0.488416i	$-0.837575\pi$
$647$	−248.574	+	248.574i	−0.384195	+	0.384195i	0.488416	+	0.872611i	$0.337575\pi$
$648$	−209.862	+	209.862i	−0.323861	+	0.323861i
$649$			102.244i			0.157541i
$650$		0			0
$651$	25.7583			0.0395672
$652$	−183.471	−	183.471i	−0.281397	−	0.281397i
$653$	166.637	+	166.637i	0.255186	+	0.255186i	0.823093	−	0.567907i	$-0.192247\pi$
$653$	166.637	+	166.637i	0.255186	+	0.255186i	−0.567907	+	0.823093i	$0.692247\pi$
$654$			179.228i			0.274048i
$655$		0			0
$656$		−	1225.51i		−	1.86816i
$657$	162.457	+	162.457i	0.247271	+	0.247271i
$658$	438.883	−	438.883i	0.666995	−	0.666995i
$659$		−	1000.82i		−	1.51870i	−0.650685	−	0.759348i	$-0.725518\pi$
$659$		−	1000.82i		−	1.51870i	0.650685	−	0.759348i	$-0.274482\pi$
$660$		0			0
$661$			387.180i			0.585749i	0.956151	+	0.292874i	$0.0946118\pi$
$661$			387.180i			0.585749i	−0.956151	+	0.292874i	$0.905388\pi$
$662$	−149.483	+	149.483i	−0.225805	+	0.225805i
$663$	25.9769	+	39.8898i	0.0391808	+	0.0601655i
$664$		−	418.909i		−	0.630888i
$665$		0			0
$666$	−504.270			−0.757163
$667$	855.133	−	855.133i	1.28206	−	1.28206i
$668$	293.104	−	293.104i	0.438778	−	0.438778i
$669$	−161.269			−0.241059
$670$		0			0
$671$		−	361.337i		−	0.538505i
$672$	115.256	−	115.256i	0.171512	−	0.171512i
$673$	384.504	+	384.504i	0.571329	+	0.571329i	0.932500	−	0.361171i	$-0.117623\pi$
$673$	384.504	+	384.504i	0.571329	+	0.571329i	−0.361171	+	0.932500i	$0.617623\pi$
$674$	−329.656			−0.489103
$675$		0			0
$676$	−361.575	−	159.883i	−0.534874	−	0.236513i
$677$	−358.805	+	358.805i	−0.529993	+	0.529993i	−0.920570	−	0.390577i	$-0.872275\pi$
$677$	−358.805	+	358.805i	−0.529993	+	0.529993i	0.390577	+	0.920570i	$0.372275\pi$
$678$	−104.718	+	104.718i	−0.154452	+	0.154452i
$679$			960.506i			1.41459i
$680$		0			0
$681$		−	30.3093i		−	0.0445070i
$682$	−74.6556	−	74.6556i	−0.109466	−	0.109466i
$683$	−646.688	+	646.688i	−0.946835	+	0.946835i	−0.998656	−	0.0518212i	$-0.983497\pi$
$683$	−646.688	+	646.688i	−0.946835	+	0.946835i	0.0518212	+	0.998656i	$0.483497\pi$
$684$	573.021			0.837750
$685$		0			0
$686$	692.028			1.00879
$687$	−105.201	−	105.201i	−0.153131	−	0.153131i
$688$	371.338	+	371.338i	0.539735	+	0.539735i
$689$	145.453	−	688.608i	0.211107	−	0.999431i
$690$		0			0
$691$			363.653i			0.526270i	0.964759	+	0.263135i	$0.0847565\pi$
$691$			363.653i			0.526270i	−0.964759	+	0.263135i	$0.915244\pi$
$692$	338.262	−	338.262i	0.488818	−	0.488818i
$693$	386.759	+	386.759i	0.558094	+	0.558094i
$694$	939.186			1.35329
$695$		0			0
$696$		−	130.099i		−	0.186923i
$697$	260.132	+	260.132i	0.373216	+	0.373216i
$698$	853.393	+	853.393i	1.22263	+	1.22263i
$699$		−	206.640i		−	0.295622i
$700$		0			0
$701$	−743.139			−1.06011			−0.530056	−	0.847962i	$-0.677829\pi$
$701$	−743.139			−1.06011			−0.530056	+	0.847962i	$0.677829\pi$
$702$	−193.104	−	296.528i	−0.275077	−	0.422405i
$703$	−466.466	−	466.466i	−0.663536	−	0.663536i
$704$	−35.0739			−0.0498209
$705$		0			0
$706$	39.1338			0.0554303
$707$	−172.975	−	172.975i	−0.244660	−	0.244660i
$708$	13.0362	−	13.0362i	0.0184127	−	0.0184127i
$709$	−1179.60			−1.66376			−0.831879	−	0.554957i	$-0.812735\pi$
$709$	−1179.60			−1.66376			−0.831879	+	0.554957i	$0.812735\pi$
$710$		0			0
$711$	−630.307			−0.886508
$712$	−6.69573	+	6.69573i	−0.00940412	+	0.00940412i
$713$	88.8295	−	88.8295i	0.124586	−	0.124586i
$714$			73.4739i			0.102905i
$715$		0			0
$716$	32.9955			0.0460831
$717$	148.349	+	148.349i	0.206902	+	0.206902i
$718$	−703.023	−	703.023i	−0.979141	−	0.979141i
$719$			160.358i			0.223029i	0.993763	+	0.111514i	$0.0355702\pi$
$719$			160.358i			0.223029i	−0.993763	+	0.111514i	$0.964430\pi$
$720$		0			0
$721$		−	1363.09i		−	1.89056i
$722$	793.703	+	793.703i	1.09931	+	1.09931i
$723$	76.5498	−	76.5498i	0.105878	−	0.105878i
$724$			349.963i			0.483374i
$725$		0			0
$726$		−	89.0581i		−	0.122670i
$727$	−482.308	+	482.308i	−0.663422	+	0.663422i	−0.956185	−	0.292763i	$-0.905425\pi$
$727$	−482.308	+	482.308i	−0.663422	+	0.663422i	0.292763	+	0.956185i	$0.405425\pi$
$728$	236.392	+	363.000i	0.324714	+	0.498626i
$729$			552.433i			0.757796i
$730$		0			0
$731$	−157.643			−0.215654
$732$	−46.0706	+	46.0706i	−0.0629379	+	0.0629379i
$733$	−611.314	+	611.314i	−0.833989	+	0.833989i	−0.988060	−	0.154071i	$-0.950762\pi$
$733$	−611.314	+	611.314i	−0.833989	+	0.833989i	0.154071	+	0.988060i	$0.450762\pi$
$734$	116.657			0.158933
$735$		0			0
$736$		−	794.940i		−	1.08008i
$737$	181.384	−	181.384i	0.246112	−	0.246112i
$738$	−946.225	−	946.225i	−1.28215	−	1.28215i
$739$	−346.783			−0.469259			−0.234630	−	0.972085i	$-0.575388\pi$
$739$	−346.783			−0.469259			−0.234630	+	0.972085i	$0.575388\pi$
$740$		0			0
$741$	46.8137	−	221.627i	0.0631764	−	0.299092i
$742$	768.139	−	768.139i	1.03523	−	1.03523i
$743$	−551.121	+	551.121i	−0.741750	+	0.741750i	−0.972915	−	0.231164i	$-0.925747\pi$
$743$	−551.121	+	551.121i	−0.741750	+	0.741750i	0.231164	+	0.972915i	$0.425747\pi$
$744$		−	13.5144i		−	0.0181645i
$745$		0			0
$746$			153.030i			0.205133i
$747$	−610.932	−	610.932i	−0.817847	−	0.817847i
$748$	78.5827	−	78.5827i	0.105057	−	0.105057i
$749$	−1044.10			−1.39399
$750$		0			0
$751$	−714.986			−0.952045			−0.476023	−	0.879433i	$-0.657922\pi$
$751$	−714.986			−0.952045			−0.476023	+	0.879433i	$0.657922\pi$
$752$	−434.935	−	434.935i	−0.578370	−	0.578370i
$753$	−136.535	−	136.535i	−0.181321	−	0.181321i
$754$	−1624.36	−	343.109i	−2.15432	−	0.455052i
$755$		0			0
$756$		−	201.551i		−	0.266602i
$757$	−111.760	+	111.760i	−0.147636	+	0.147636i	−0.777061	−	0.629425i	$-0.783290\pi$
$757$	−111.760	+	111.760i	−0.147636	+	0.147636i	0.629425	+	0.777061i	$0.283290\pi$
$758$	880.486	+	880.486i	1.16159	+	1.16159i
$759$	−116.402			−0.153363
$760$		0			0
$761$			624.616i			0.820784i	0.911909	+	0.410392i	$0.134608\pi$
$761$			624.616i			0.820784i	−0.911909	+	0.410392i	$0.865392\pi$
$762$	−197.921	−	197.921i	−0.259738	−	0.259738i
$763$	−653.916	−	653.916i	−0.857032	−	0.857032i
$764$		−	472.665i		−	0.618671i
$765$		0			0
$766$	155.975			0.203623
$767$	91.1388	+	139.951i	0.118825	+	0.182466i
$768$	−141.181	−	141.181i	−0.183829	−	0.183829i
$769$	486.144			0.632177			0.316088	−	0.948730i	$-0.397630\pi$
$769$	486.144			0.632177			0.316088	+	0.948730i	$0.397630\pi$
$770$		0			0
$771$	−11.9800			−0.0155383
$772$	−282.798	−	282.798i	−0.366319	−	0.366319i
$773$	95.7264	−	95.7264i	0.123838	−	0.123838i	−0.642472	−	0.766309i	$-0.722091\pi$
$773$	95.7264	−	95.7264i	0.123838	−	0.123838i	0.766309	+	0.642472i	$0.222091\pi$
$774$	573.424			0.740858
$775$		0			0
$776$	503.941			0.649409
$777$	−80.2844	+	80.2844i	−0.103326	+	0.103326i
$778$	−608.774	+	608.774i	−0.782486	+	0.782486i
$779$		−	1750.58i		−	2.24721i
$780$		0			0
$781$	−3.95507			−0.00506411
$782$	253.381	+	253.381i	0.324017	+	0.324017i
$783$	−387.748	−	387.748i	−0.495208	−	0.495208i
$784$			288.556i			0.368056i
$785$		0			0
$786$			255.440i			0.324987i
$787$	−89.0150	−	89.0150i	−0.113107	−	0.113107i	0.648288	−	0.761395i	$-0.275485\pi$
$787$	−89.0150	−	89.0150i	−0.113107	−	0.113107i	−0.761395	+	0.648288i	$0.775485\pi$
$788$	56.8709	−	56.8709i	0.0721712	−	0.0721712i
$789$			94.4831i			0.119750i
$790$		0			0
$791$		−	764.135i		−	0.966037i
$792$	202.918	−	202.918i	0.256209	−	0.256209i
$793$	−322.090	−	494.596i	−0.406166	−	0.623703i
$794$		−	950.037i		−	1.19652i
$795$		0			0
$796$	260.215			0.326903
$797$	471.659	−	471.659i	0.591794	−	0.591794i	−0.346322	−	0.938116i	$-0.612570\pi$
$797$	471.659	−	471.659i	0.591794	−	0.591794i	0.938116	+	0.346322i	$0.112570\pi$
$798$	247.224	−	247.224i	0.309804	−	0.309804i
$799$	184.642			0.231091
$800$		0			0
$801$			19.5299i			0.0243819i
$802$	−461.567	+	461.567i	−0.575520	+	0.575520i
$803$	−149.928	−	149.928i	−0.186710	−	0.186710i
$804$	−46.2532			−0.0575288
$805$		0			0
$806$	−168.735	−	35.6415i	−0.209349	−	0.0442202i
$807$	−19.0007	+	19.0007i	−0.0235448	+	0.0235448i
$808$	−90.7532	+	90.7532i	−0.112318	+	0.112318i
$809$			148.398i			0.183434i	0.995785	+	0.0917168i	$0.0292355\pi$
$809$			148.398i			0.183434i	−0.995785	+	0.0917168i	$0.970765\pi$
$810$		0			0
$811$			1205.54i			1.48648i	0.669024	+	0.743241i	$0.266712\pi$
$811$			1205.54i			1.48648i	−0.669024	+	0.743241i	$0.733288\pi$
$812$	−668.647	−	668.647i	−0.823457	−	0.823457i
$813$	−105.822	+	105.822i	−0.130162	+	0.130162i
$814$	465.379			0.571719
$815$		0			0
$816$	72.8129			0.0892315
$817$	530.435	+	530.435i	0.649248	+	0.649248i
$818$	752.912	+	752.912i	0.920430	+	0.920430i
$819$	874.145	+	184.644i	1.06733	+	0.225450i
$820$		0			0
$821$			1294.13i			1.57629i	0.615491	+	0.788144i	$0.288958\pi$
$821$			1294.13i			1.57629i	−0.615491	+	0.788144i	$0.711042\pi$
$822$	109.918	−	109.918i	0.133721	−	0.133721i
$823$	709.426	+	709.426i	0.861999	+	0.861999i	0.991570	−	0.129571i	$-0.0413599\pi$
$823$	709.426	+	709.426i	0.861999	+	0.861999i	−0.129571	+	0.991570i	$0.541360\pi$
$824$	−715.163			−0.867917
$825$		0			0
$826$			257.780i			0.312082i
$827$	−578.353	−	578.353i	−0.699338	−	0.699338i	0.264930	−	0.964268i	$-0.414651\pi$
$827$	−578.353	−	578.353i	−0.699338	−	0.699338i	−0.964268	+	0.264930i	$0.914651\pi$
$828$	−340.113	−	340.113i	−0.410764	−	0.410764i
$829$			422.793i			0.510004i	0.966941	+	0.255002i	$0.0820761\pi$
$829$			422.793i			0.510004i	−0.966941	+	0.255002i	$0.917924\pi$
$830$		0			0
$831$	−104.475			−0.125722
$832$	−48.0090	+	31.2643i	−0.0577032	+	0.0375773i
$833$	−61.2500	−	61.2500i	−0.0735294	−	0.0735294i
$834$	134.907			0.161758
$835$		0			0
$836$	−528.827			−0.632569
$837$	−40.2785	−	40.2785i	−0.0481224	−	0.0481224i
$838$	1019.08	−	1019.08i	1.21609	−	1.21609i
$839$	651.223			0.776189			0.388095	−	0.921620i	$-0.373133\pi$
$839$	651.223			0.776189			0.388095	+	0.921620i	$0.373133\pi$
$840$		0			0
$841$	−1731.71			−2.05911
$842$	597.002	−	597.002i	0.709029	−	0.709029i
$843$	155.541	−	155.541i	0.184509	−	0.184509i
$844$		−	202.859i		−	0.240354i
$845$		0			0
$846$	−671.632			−0.793891
$847$	324.930	+	324.930i	0.383625	+	0.383625i
$848$	−761.228	−	761.228i	−0.897675	−	0.897675i
$849$			151.962i			0.178990i
$850$		0			0
$851$			553.735i			0.650687i
$852$	0.504273	+	0.504273i	0.000591870	+	0.000591870i
$853$	−266.180	+	266.180i	−0.312052	+	0.312052i	−0.845704	−	0.533652i	$-0.820819\pi$
$853$	−266.180	+	266.180i	−0.312052	+	0.312052i	0.533652	+	0.845704i	$0.320819\pi$
$854$		−	911.009i		−	1.06675i
$855$		0			0
$856$			547.799i			0.639952i
$857$	313.015	−	313.015i	0.365245	−	0.365245i	−0.500495	−	0.865740i	$-0.666848\pi$
$857$	313.015	−	313.015i	0.365245	−	0.365245i	0.865740	+	0.500495i	$0.166848\pi$
$858$	87.2031	+	133.908i	0.101635	+	0.156070i
$859$			515.308i			0.599892i	0.953956	+	0.299946i	$0.0969687\pi$
$859$			515.308i			0.599892i	−0.953956	+	0.299946i	$0.903031\pi$
$860$		0			0
$861$	−301.295			−0.349936
$862$	140.733	−	140.733i	0.163264	−	0.163264i
$863$	−324.876	+	324.876i	−0.376449	+	0.376449i	−0.869819	−	0.493370i	$-0.835765\pi$
$863$	−324.876	+	324.876i	−0.376449	+	0.376449i	0.493370	+	0.869819i	$0.335765\pi$
$864$	−360.454			−0.417192
$865$		0			0
$866$			15.7555i			0.0181934i
$867$	109.903	−	109.903i	0.126763	−	0.126763i
$868$	−69.4578	−	69.4578i	−0.0800205	−	0.0800205i
$869$	581.695			0.669385
$870$		0			0
$871$	86.5951	−	409.962i	0.0994204	−	0.470679i
$872$	−343.085	+	343.085i	−0.393446	+	0.393446i
$873$	734.941	−	734.941i	0.841857	−	0.841857i
$874$		−	1705.14i		−	1.95097i
$875$		0			0
$876$			38.2317i			0.0436435i
$877$	1176.18	+	1176.18i	1.34114	+	1.34114i	0.894922	+	0.446223i	$0.147231\pi$
$877$	1176.18	+	1176.18i	1.34114	+	1.34114i	0.446223	+	0.894922i	$0.352769\pi$
$878$	1400.49	−	1400.49i	1.59509	−	1.59509i
$879$	−191.918			−0.218337
$880$		0			0
$881$	−60.9585			−0.0691924			−0.0345962	−	0.999401i	$-0.511015\pi$
$881$	−60.9585			−0.0691924			−0.0345962	+	0.999401i	$0.511015\pi$
$882$	222.796	+	222.796i	0.252603	+	0.252603i
$883$	−452.293	−	452.293i	−0.512223	−	0.512223i	0.402984	−	0.915207i	$-0.367973\pi$
$883$	−452.293	−	452.293i	−0.512223	−	0.512223i	−0.915207	+	0.402984i	$0.867973\pi$
$884$	37.5163	−	177.611i	0.0424393	−	0.200917i
$885$		0			0
$886$			1547.96i			1.74714i
$887$	1048.86	−	1048.86i	1.18248	−	1.18248i	0.203376	−	0.979101i	$-0.434809\pi$
$887$	1048.86	−	1048.86i	1.18248	−	1.18248i	0.979101	−	0.203376i	$-0.0651913\pi$
$888$	42.1222	+	42.1222i	0.0474349	+	0.0474349i
$889$	1444.24			1.62456
$890$		0			0
$891$		−	564.912i		−	0.634020i
$892$	434.865	+	434.865i	0.487517	+	0.487517i
$893$	−621.280	−	621.280i	−0.695723	−	0.695723i
$894$		−	309.702i		−	0.346423i
$895$		0			0
$896$	974.407			1.08751
$897$	−159.331	+	103.759i	−0.177627	+	0.115674i
$898$	−72.1820	−	72.1820i	−0.0803809	−	0.0803809i
$899$	−267.248			−0.297272
$900$		0			0
$901$	323.163			0.358671
$902$	873.249	+	873.249i	0.968125	+	0.968125i
$903$	91.2943	−	91.2943i	0.101101	−	0.101101i
$904$	−400.913			−0.443488
$905$		0			0
$906$	436.267			0.481531
$907$	−490.097	+	490.097i	−0.540350	+	0.540350i	−0.923632	−	0.383282i	$-0.874794\pi$
$907$	−490.097	+	490.097i	−0.540350	+	0.540350i	0.383282	+	0.923632i	$0.374794\pi$
$908$	−81.7296	+	81.7296i	−0.0900106	+	0.0900106i
$909$			264.707i			0.291206i
$910$		0			0
$911$	487.918			0.535585			0.267793	−	0.963477i	$-0.413706\pi$
$911$	487.918			0.535585			0.267793	+	0.963477i	$0.413706\pi$
$912$	−245.000	−	245.000i	−0.268640	−	0.268640i
$913$	563.815	+	563.815i	0.617541	+	0.617541i
$914$		−	508.383i		−	0.556218i
$915$		0			0
$916$			567.353i			0.619381i
$917$	−931.978	−	931.978i	−1.01633	−	1.01633i
$918$	114.892	−	114.892i	0.125155	−	0.125155i
$919$		−	199.701i		−	0.217303i	−0.994080	−	0.108651i	$-0.965347\pi$
$919$		−	199.701i		−	0.217303i	0.994080	−	0.108651i	$-0.0346532\pi$
$920$		0			0
$921$			1.85481i			0.00201390i
$922$	1096.33	−	1096.33i	1.18908	−	1.18908i
$923$	−5.41369	+	3.52549i	−0.00586532	+	0.00381960i
$924$			91.0176i			0.0985039i
$925$		0			0
$926$	1695.74			1.83125
$927$	−1042.98	+	1042.98i	−1.12512	+	1.12512i
$928$	−1195.81	+	1195.81i	−1.28859	+	1.28859i
$929$	−617.232			−0.664405			−0.332202	−	0.943208i	$-0.607792\pi$
$929$	−617.232			−0.664405			−0.332202	+	0.943208i	$0.607792\pi$
$930$		0			0
$931$			412.186i			0.442734i
$932$	−557.209	+	557.209i	−0.597864	+	0.597864i
$933$	201.417	+	201.417i	0.215882	+	0.215882i
$934$	584.625			0.625937
$935$		0			0
$936$	96.8755	−	458.631i	0.103499	−	0.489990i
$937$	434.493	−	434.493i	0.463706	−	0.463706i	−0.436162	−	0.899868i	$-0.643662\pi$
$937$	434.493	−	434.493i	0.463706	−	0.463706i	0.899868	+	0.436162i	$0.143662\pi$
$938$	457.310	−	457.310i	0.487537	−	0.487537i
$939$		−	25.4786i		−	0.0271337i
$940$		0			0
$941$		−	1594.74i		−	1.69473i	−0.531008	−	0.847367i	$-0.678187\pi$
$941$		−	1594.74i		−	1.69473i	0.531008	−	0.847367i	$-0.321813\pi$
$942$	222.415	+	222.415i	0.236109	+	0.236109i
$943$	−1039.04	+	1039.04i	−1.10185	+	1.10185i
$944$	255.461			0.270615
$945$		0			0
$946$	−529.200			−0.559408
$947$	1127.45	+	1127.45i	1.19055	+	1.19055i	0.976913	+	0.213639i	$0.0685316\pi$
$947$	1127.45	+	1127.45i	1.19055	+	1.19055i	0.213639	+	0.976913i	$0.431468\pi$
$948$	−74.1664	−	74.1664i	−0.0782346	−	0.0782346i
$949$	−338.864	−	71.5774i	−0.357075	−	0.0754241i
$950$		0			0
$951$		−	115.714i		−	0.121676i
$952$	−140.647	+	140.647i	−0.147738	+	0.147738i
$953$	−976.109	−	976.109i	−1.02425	−	1.02425i	−0.999699	−	0.0245499i	$-0.992185\pi$
$953$	−976.109	−	976.109i	−1.02425	−	1.02425i	−0.0245499	−	0.999699i	$-0.507815\pi$
$954$	−1175.50			−1.23218
$955$		0			0
$956$		−	800.053i		−	0.836876i
$957$	175.101	+	175.101i	0.182969	+	0.182969i
$958$	652.139	+	652.139i	0.680729	+	0.680729i
$959$			802.079i			0.836370i
$960$		0			0
$961$	933.239			0.971112
$962$	637.009	−	414.831i	0.662172	−	0.431218i
$963$	798.903	+	798.903i	0.829598	+	0.829598i
$964$	−412.837			−0.428254
$965$		0			0
$966$	−293.476			−0.303805
$967$	23.8217	+	23.8217i	0.0246346	+	0.0246346i	0.719317	−	0.694682i	$-0.244455\pi$
$967$	23.8217	+	23.8217i	0.0246346	+	0.0246346i	−0.694682	+	0.719317i	$0.744455\pi$
$968$	170.479	−	170.479i	0.176114	−	0.176114i
$969$	104.009			0.107337
$970$		0			0
$971$	375.513			0.386728			0.193364	−	0.981127i	$-0.438060\pi$
$971$	375.513			0.386728			0.193364	+	0.981127i	$0.438060\pi$
$972$	−232.975	+	232.975i	−0.239686	+	0.239686i
$973$	−492.210	+	492.210i	−0.505868	+	0.505868i
$974$			1711.00i			1.75668i
$975$		0			0
$976$	−902.813			−0.925013
$977$	−90.3668	−	90.3668i	−0.0924942	−	0.0924942i	0.659346	−	0.751840i	$-0.270833\pi$
$977$	−90.3668	−	90.3668i	−0.0924942	−	0.0924942i	−0.751840	+	0.659346i	$0.770833\pi$
$978$	121.135	+	121.135i	0.123860	+	0.123860i
$979$		−	18.0237i		−	0.0184103i
$980$		0			0
$981$			1000.70i			1.02008i
$982$	246.608	+	246.608i	0.251128	+	0.251128i
$983$	792.321	−	792.321i	0.806024	−	0.806024i	−0.178006	−	0.984029i	$-0.556965\pi$
$983$	792.321	−	792.321i	0.806024	−	0.806024i	0.984029	+	0.178006i	$0.0569645\pi$
$984$			158.078i			0.160649i
$985$		0			0
$986$		−	762.309i		−	0.773133i
$987$	−106.930	+	106.930i	−0.108338	+	0.108338i
$988$	−723.857	+	471.388i	−0.732649	+	0.477114i
$989$		−	629.673i		−	0.636676i
$990$		0			0
$991$	−395.791			−0.399386			−0.199693	−	0.979859i	$-0.563994\pi$
$991$	−395.791			−0.399386			−0.199693	+	0.979859i	$0.563994\pi$
$992$	−124.218	+	124.218i	−0.125220	+	0.125220i
$993$	36.4201	−	36.4201i	0.0366769	−	0.0366769i
$994$	−9.97160			−0.0100318
$995$		0			0
$996$		−	143.773i		−	0.144351i
$997$	−151.445	+	151.445i	−0.151900	+	0.151900i	−0.778966	−	0.627066i	$-0.784256\pi$
$997$	−151.445	+	151.445i	−0.151900	+	0.151900i	0.627066	+	0.778966i	$0.284256\pi$
$998$	904.459	+	904.459i	0.906271	+	0.906271i
$999$	251.083			0.251334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.h.b.168.10		24
5.2	odd	4	inner	325.3.h.b.207.3		24
5.3	odd	4		65.3.h.a.12.10	yes	24
5.4	even	2		65.3.h.a.38.3	yes	24
13.12	even	2	inner	325.3.h.b.168.3		24
65.12	odd	4	inner	325.3.h.b.207.10		24
65.38	odd	4		65.3.h.a.12.3	✓	24
65.64	even	2		65.3.h.a.38.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.h.a.12.3	✓	24	65.38	odd	4
65.3.h.a.12.10	yes	24	5.3	odd	4
65.3.h.a.38.3	yes	24	5.4	even	2
65.3.h.a.38.10	yes	24	65.64	even	2
325.3.h.b.168.3		24	13.12	even	2	inner
325.3.h.b.168.10		24	1.1	even	1	trivial
325.3.h.b.207.3		24	5.2	odd	4	inner
325.3.h.b.207.10		24	65.12	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.78036 + 1.78036i) q^{2} +(-0.433767 - 0.433767i) q^{3} +2.33933i q^{4} -1.54452i q^{6} +(5.63522 + 5.63522i) q^{7} +(2.95658 - 2.95658i) q^{8} -8.62369i q^{9} +7.95860i q^{11} +(1.01472 - 1.01472i) q^{12} +(7.09417 + 10.8937i) q^{13} +20.0654i q^{14} +19.8849 q^{16} +(-4.22084 + 4.22084i) q^{17} +(15.3532 - 15.3532i) q^{18} +28.4044 q^{19} -4.88875i q^{21} +(-14.1691 + 14.1691i) q^{22} +(-16.8593 - 16.8593i) q^{23} -2.56494 q^{24} +(-6.76452 + 32.0248i) q^{26} +(-7.64458 + 7.64458i) q^{27} +(-13.1826 + 13.1826i) q^{28} +50.7219i q^{29} +5.26889i q^{31} +(23.5758 + 23.5758i) q^{32} +(3.45218 - 3.45218i) q^{33} -15.0292 q^{34} +20.1736 q^{36} +(-16.4223 - 16.4223i) q^{37} +(50.5700 + 50.5700i) q^{38} +(1.64811 - 7.80255i) q^{39} -61.6304i q^{41} +(8.70370 - 8.70370i) q^{42} +(18.6744 + 18.6744i) q^{43} -18.6178 q^{44} -60.0309i q^{46} +(-21.8727 - 21.8727i) q^{47} +(-8.62540 - 8.62540i) q^{48} +14.5113i q^{49} +3.66173 q^{51} +(-25.4840 + 16.5956i) q^{52} +(-38.2818 - 38.2818i) q^{53} -27.2201 q^{54} +33.3220 q^{56} +(-12.3209 - 12.3209i) q^{57} +(-90.3030 + 90.3030i) q^{58} +12.8470 q^{59} -45.4020 q^{61} +(-9.38049 + 9.38049i) q^{62} +(48.5964 - 48.5964i) q^{63} +4.40705i q^{64} +12.2922 q^{66} +(-22.7910 - 22.7910i) q^{67} +(-9.87393 - 9.87393i) q^{68} +14.6260i q^{69} +0.496956i q^{71} +(-25.4967 - 25.4967i) q^{72} +(-18.8385 + 18.8385i) q^{73} -58.4750i q^{74} +66.4473i q^{76} +(-44.8484 + 44.8484i) q^{77} +(16.8255 - 10.9571i) q^{78} -73.0902i q^{79} -70.9813 q^{81} +(109.724 - 109.724i) q^{82} +(70.8434 - 70.8434i) q^{83} +11.4364 q^{84} +66.4941i q^{86} +(22.0015 - 22.0015i) q^{87} +(23.5303 + 23.5303i) q^{88} -2.26468 q^{89} +(-21.4112 + 101.366i) q^{91} +(39.4393 - 39.4393i) q^{92} +(2.28547 - 2.28547i) q^{93} -77.8822i q^{94} -20.4528i q^{96} +(85.2235 + 85.2235i) q^{97} +(-25.8353 + 25.8353i) q^{98} +68.6325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 72 q^{12} + 36 q^{13} - 104 q^{16} + 48 q^{17} - 8 q^{22} + 104 q^{23} + 88 q^{26} - 56 q^{27} + 256 q^{36} - 124 q^{38} - 216 q^{42} - 8 q^{43} - 196 q^{48} - 296 q^{51} - 16 q^{52} - 220 q^{53}+ \cdots - 812 q^{92}+O(q^{100}) \) 24 * q + 4 * q^3 - 72 * q^12 + 36 * q^13 - 104 * q^16 + 48 * q^17 - 8 * q^22 + 104 * q^23 + 88 * q^26 - 56 * q^27 + 256 * q^36 - 124 * q^38 - 216 * q^42 - 8 * q^43 - 196 * q^48 - 296 * q^51 - 16 * q^52 - 220 * q^53 + 584 * q^56 - 8 * q^61 + 596 * q^62 - 360 * q^66 + 640 * q^68 - 388 * q^77 + 636 * q^78 - 224 * q^81 + 1004 * q^82 + 52 * q^87 - 780 * q^88 - 512 * q^91 - 812 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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