LMFDB - Embedded newform 644.2.bc.a.493.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.16
Character	$\chi$	$=$	644.493
Dual form			644.2.bc.a.145.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53184 + 2.97135i) q^{3} +(-0.875537 + 0.0836037i) q^{5} +(-0.805963 + 2.52000i) q^{7} +(-4.74221 + 6.65950i) q^{9} +O(q^{10})$	\(q+(1.53184 + 2.97135i) q^{3} +(-0.875537 + 0.0836037i) q^{5} +(-0.805963 + 2.52000i) q^{7} +(-4.74221 + 6.65950i) q^{9} +(1.55007 - 0.536483i) q^{11} +(-0.786153 - 2.67739i) q^{13} +(-1.58959 - 2.47346i) q^{15} +(1.00538 + 0.402492i) q^{17} +(-2.68784 + 1.07605i) q^{19} +(-8.72241 + 1.46544i) q^{21} +(3.52655 - 3.25015i) q^{23} +(-4.15007 + 0.799860i) q^{25} +(-17.1251 - 2.46222i) q^{27} +(0.643553 + 4.47601i) q^{29} +(9.78260 - 0.466003i) q^{31} +(3.96852 + 3.78398i) q^{33} +(0.494969 - 2.27374i) q^{35} +(3.36470 + 2.39599i) q^{37} +(6.75120 - 6.43726i) q^{39} +(1.91634 + 0.875165i) q^{41} +(1.30225 - 2.02633i) q^{43} +(3.59522 - 6.22711i) q^{45} +(-7.35927 + 4.24888i) q^{47} +(-5.70085 - 4.06206i) q^{49} +(0.344128 + 3.60387i) q^{51} +(5.79341 + 6.07595i) q^{53} +(-1.31229 + 0.599302i) q^{55} +(-7.31465 - 6.33818i) q^{57} +(-0.831057 - 0.201612i) q^{59} +(1.99360 + 1.02777i) q^{61} +(-12.9599 - 17.3177i) q^{63} +(0.912146 + 2.27843i) q^{65} +(-1.28327 - 6.65824i) q^{67} +(15.0594 + 5.49990i) q^{69} +(-0.354917 - 0.409596i) q^{71} +(-5.94181 + 7.55563i) q^{73} +(-8.73388 - 11.1060i) q^{75} +(0.102644 + 4.33856i) q^{77} +(10.8527 - 11.3820i) q^{79} +(-10.8950 - 31.4791i) q^{81} +(5.29810 + 11.6012i) q^{83} +(-0.913894 - 0.268343i) q^{85} +(-12.3140 + 8.76873i) q^{87} +(-0.737199 + 15.4757i) q^{89} +(7.38065 + 0.176768i) q^{91} +(16.3700 + 28.3536i) q^{93} +(2.26335 - 1.16684i) q^{95} +(-0.184659 + 0.404347i) q^{97} +(-3.77803 + 12.8668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.53184	+	2.97135i	0.884406	+	1.71551i	0.675198	+	0.737636i	$0.264058\pi$
$3$	1.53184	+	2.97135i	0.884406	+	1.71551i	0.209208	+	0.977871i	$0.432912\pi$
$4$		0			0
$5$	−0.875537	+	0.0836037i	−0.391552	+	0.0373887i	−0.288976	−	0.957336i	$-0.593315\pi$
$5$	−0.875537	+	0.0836037i	−0.391552	+	0.0373887i	−0.102576	+	0.994725i	$0.532709\pi$
$6$		0			0
$7$	−0.805963	+	2.52000i	−0.304625	+	0.952472i
$7$	−0.805963	+	2.52000i	−0.304625	+	0.952472i
$8$		0			0
$9$	−4.74221	+	6.65950i	−1.58074	+	2.21983i
$10$		0			0
$11$	1.55007	−	0.536483i	0.467362	−	0.161756i	−0.0832293	−	0.996530i	$-0.526523\pi$
$11$	1.55007	−	0.536483i	0.467362	−	0.161756i	0.550592	+	0.834775i	$0.314402\pi$
$12$		0			0
$13$	−0.786153	−	2.67739i	−0.218040	−	0.742575i	−0.993764	−	0.111503i	$-0.964433\pi$
$13$	−0.786153	−	2.67739i	−0.218040	−	0.742575i	0.775724	−	0.631072i	$-0.217385\pi$
$14$		0			0
$15$	−1.58959	−	2.47346i	−0.410432	−	0.638644i
$16$		0			0
$17$	1.00538	+	0.402492i	0.243839	+	0.0976186i	0.490363	−	0.871518i	$-0.336864\pi$
$17$	1.00538	+	0.402492i	0.243839	+	0.0976186i	−0.246524	+	0.969137i	$0.579288\pi$
$18$		0			0
$19$	−2.68784	+	1.07605i	−0.616634	+	0.246863i	−0.658885	−	0.752244i	$-0.728971\pi$
$19$	−2.68784	+	1.07605i	−0.616634	+	0.246863i	0.0422507	+	0.999107i	$0.486547\pi$
$20$		0			0
$21$	−8.72241	+	1.46544i	−1.90339	+	0.319785i
$22$		0			0
$23$	3.52655	−	3.25015i	0.735336	−	0.677703i
$23$	3.52655	−	3.25015i	0.735336	−	0.677703i
$24$		0			0
$25$	−4.15007	+	0.799860i	−0.830013	+	0.159972i
$26$		0			0
$27$	−17.1251	−	2.46222i	−3.29574	−	0.473855i
$28$		0			0
$29$	0.643553	+	4.47601i	0.119505	+	0.831174i	0.958103	+	0.286424i	$0.0924664\pi$
$29$	0.643553	+	4.47601i	0.119505	+	0.831174i	−0.838598	+	0.544750i	$0.816624\pi$
$30$		0			0
$31$	9.78260	−	0.466003i	1.75701	−	0.0836965i	0.855859	−	0.517209i	$-0.173029\pi$
$31$	9.78260	−	0.466003i	1.75701	−	0.0836965i	0.901147	+	0.433513i	$0.142726\pi$
$32$		0			0
$33$	3.96852	+	3.78398i	0.690831	+	0.658706i
$34$		0			0
$35$	0.494969	−	2.27374i	0.0836650	−	0.384332i
$36$		0			0
$37$	3.36470	+	2.39599i	0.553154	+	0.393899i	0.822175	−	0.569235i	$-0.192761\pi$
$37$	3.36470	+	2.39599i	0.553154	+	0.393899i	−0.269021	+	0.963134i	$0.586700\pi$
$38$		0			0
$39$	6.75120	−	6.43726i	1.08106	−	1.03079i
$40$		0			0
$41$	1.91634	+	0.875165i	0.299283	+	0.136678i	0.559397	−	0.828900i	$-0.311033\pi$
$41$	1.91634	+	0.875165i	0.299283	+	0.136678i	−0.260114	+	0.965578i	$0.583760\pi$
$42$		0			0
$43$	1.30225	−	2.02633i	0.198591	−	0.309013i	−0.727648	−	0.685951i	$-0.759387\pi$
$43$	1.30225	−	2.02633i	0.198591	−	0.309013i	0.926239	+	0.376938i	$0.123023\pi$
$44$		0			0
$45$	3.59522	−	6.22711i	0.535944	−	0.928282i
$46$		0			0
$47$	−7.35927	+	4.24888i	−1.07346	+	0.619763i	−0.929125	−	0.369766i	$-0.879438\pi$
$47$	−7.35927	+	4.24888i	−1.07346	+	0.619763i	−0.144335	+	0.989529i	$0.546104\pi$
$48$		0			0
$49$	−5.70085	−	4.06206i	−0.814407	−	0.580294i
$50$		0			0
$51$	0.344128	+	3.60387i	0.0481876	+	0.504643i
$52$		0			0
$53$	5.79341	+	6.07595i	0.795786	+	0.834596i	0.989208	−	0.146519i	$-0.0468071\pi$
$53$	5.79341	+	6.07595i	0.795786	+	0.834596i	−0.193422	+	0.981116i	$0.561959\pi$
$54$		0			0
$55$	−1.31229	+	0.599302i	−0.176949	+	0.0808099i
$56$		0			0
$57$	−7.31465	−	6.33818i	−0.968850	−	0.839513i
$58$		0			0
$59$	−0.831057	−	0.201612i	−0.108194	−	0.0262477i	0.181296	−	0.983429i	$-0.441971\pi$
$59$	−0.831057	−	0.201612i	−0.108194	−	0.0262477i	−0.289491	+	0.957181i	$0.593486\pi$
$60$		0			0
$61$	1.99360	+	1.02777i	0.255254	+	0.131593i	0.581105	−	0.813828i	$-0.302620\pi$
$61$	1.99360	+	1.02777i	0.255254	+	0.131593i	−0.325851	+	0.945421i	$0.605651\pi$
$62$		0			0
$63$	−12.9599	−	17.3177i	−1.63280	−	2.18182i
$64$		0			0
$65$	0.912146	+	2.27843i	0.113138	+	0.282605i
$66$		0			0
$67$	−1.28327	−	6.65824i	−0.156776	−	0.813433i	−0.972125	−	0.234463i	$-0.924667\pi$
$67$	−1.28327	−	6.65824i	−0.156776	−	0.813433i	0.815349	−	0.578970i	$-0.196545\pi$
$68$		0			0
$69$	15.0594	+	5.49990i	1.81294	+	0.662110i
$70$		0			0
$71$	−0.354917	−	0.409596i	−0.0421209	−	0.0486101i	0.734298	−	0.678827i	$-0.237511\pi$
$71$	−0.354917	−	0.409596i	−0.0421209	−	0.0486101i	−0.776419	+	0.630217i	$0.782966\pi$
$72$		0			0
$73$	−5.94181	+	7.55563i	−0.695436	+	0.884319i	−0.997622	−	0.0689300i	$-0.978042\pi$
$73$	−5.94181	+	7.55563i	−0.695436	+	0.884319i	0.302185	+	0.953249i	$0.402284\pi$
$74$		0			0
$75$	−8.73388	−	11.1060i	−1.00850	−	1.28241i
$76$		0			0
$77$	0.102644	+	4.33856i	0.0116974	+	0.494424i
$78$		0			0
$79$	10.8527	−	11.3820i	1.22102	−	1.28057i	0.273135	−	0.961976i	$-0.411940\pi$
$79$	10.8527	−	11.3820i	1.22102	−	1.28057i	0.947890	−	0.318598i	$-0.103212\pi$
$80$		0			0
$81$	−10.8950	−	31.4791i	−1.21056	−	3.49768i
$82$		0			0
$83$	5.29810	+	11.6012i	0.581542	+	1.27340i	0.940420	+	0.340016i	$0.110432\pi$
$83$	5.29810	+	11.6012i	0.581542	+	1.27340i	−0.358877	+	0.933385i	$0.616840\pi$
$84$		0			0
$85$	−0.913894	−	0.268343i	−0.0991257	−	0.0291059i
$86$		0			0
$87$	−12.3140	+	8.76873i	−1.32019	+	0.940106i
$88$		0			0
$89$	−0.737199	+	15.4757i	−0.0781430	+	1.64042i	0.531006	+	0.847368i	$0.321814\pi$
$89$	−0.737199	+	15.4757i	−0.0781430	+	1.64042i	−0.609149	+	0.793055i	$0.708489\pi$
$90$		0			0
$91$	7.38065	+	0.176768i	0.773703	+	0.0185304i
$92$		0			0
$93$	16.3700	+	28.3536i	1.69749	+	2.94014i
$94$		0			0
$95$	2.26335	−	1.16684i	0.232214	−	0.119715i
$96$		0			0
$97$	−0.184659	+	0.404347i	−0.0187493	+	0.0410552i	−0.918775	−	0.394782i	$-0.870820\pi$
$97$	−0.184659	+	0.404347i	−0.0187493	+	0.0410552i	0.900026	+	0.435837i	$0.143548\pi$
$98$		0			0
$99$	−3.77803	+	12.8668i	−0.379706	+	1.29316i
$100$		0			0
$101$	−0.389306	+	4.07699i	−0.0387374	+	0.405676i	0.955219	+	0.295900i	$0.0956195\pi$
$101$	−0.389306	+	4.07699i	−0.0387374	+	0.405676i	−0.993956	+	0.109776i	$0.964987\pi$
$102$		0			0
$103$	10.9893	+	2.11801i	1.08281	+	0.208694i	0.699289	−	0.714840i	$-0.253500\pi$
$103$	10.9893	+	2.11801i	1.08281	+	0.208694i	0.383518	+	0.923533i	$0.374712\pi$
$104$		0			0
$105$	7.51428	−	2.01227i	0.733319	−	0.196378i
$106$		0			0
$107$	−3.44905	+	6.69023i	−0.333432	+	0.646769i	−0.994636	−	0.103438i	$-0.967016\pi$
$107$	−3.44905	+	6.69023i	−0.333432	+	0.646769i	0.661203	+	0.750207i	$0.270046\pi$
$108$		0			0
$109$	7.01910	−	17.5329i	0.672308	−	1.67934i	−0.0598483	−	0.998207i	$-0.519062\pi$
$109$	7.01910	−	17.5329i	0.672308	−	1.67934i	0.732156	−	0.681137i	$-0.238514\pi$
$110$		0			0
$111$	−1.96516	+	13.6680i	−0.186524	+	1.29731i
$112$		0			0
$113$	14.1496	−	12.2607i	1.33108	−	1.15339i	0.355273	−	0.934763i	$-0.384388\pi$
$113$	14.1496	−	12.2607i	1.33108	−	1.15339i	0.975809	−	0.218626i	$-0.0701576\pi$
$114$		0			0
$115$	−2.81590	+	3.14046i	−0.262584	+	0.292849i
$116$		0			0
$117$	21.5582	+	7.46136i	1.99306	+	0.689803i
$118$		0			0
$119$	−1.82458	+	2.20916i	−0.167259	+	0.202513i
$120$		0			0
$121$	−6.53170	+	5.13658i	−0.593790	+	0.466962i
$122$		0			0
$123$	0.335106	+	7.03473i	0.0302155	+	0.634301i
$124$		0			0
$125$	7.78613	−	2.28622i	0.696413	−	0.204485i
$126$		0			0
$127$	−5.15003	+	5.94345i	−0.456991	+	0.527396i	−0.936748	−	0.350006i	$-0.886180\pi$
$127$	−5.15003	+	5.94345i	−0.456991	+	0.527396i	0.479756	+	0.877402i	$0.340725\pi$
$128$		0			0
$129$	8.01577	+	0.765413i	0.705749	+	0.0673909i
$130$		0			0
$131$	−7.90975	+	1.91889i	−0.691078	+	0.167654i	−0.565892	−	0.824479i	$-0.691468\pi$
$131$	−7.90975	+	1.91889i	−0.691078	+	0.167654i	−0.125186	+	0.992133i	$0.539953\pi$
$132$		0			0
$133$	−0.545350	−	7.64064i	−0.0472879	−	0.662527i
$134$		0			0
$135$	15.1996	+	0.724044i	1.30817	+	0.0623158i
$136$		0			0
$137$	3.50587	+	2.02411i	0.299526	+	0.172932i	0.642230	−	0.766512i	$-0.278009\pi$
$137$	3.50587	+	2.02411i	0.299526	+	0.172932i	−0.342704	+	0.939444i	$0.611343\pi$
$138$		0			0
$139$			2.56823i			0.217834i	0.994051	+	0.108917i	$0.0347383\pi$
$139$			2.56823i			0.217834i	−0.994051	+	0.108917i	$0.965262\pi$
$140$		0			0
$141$	−23.8981	−	15.3584i	−2.01258	−	1.29341i
$142$		0			0
$143$	−2.65496	−	3.72838i	−0.222019	−	0.311782i
$144$		0			0
$145$	−0.937665	−	3.86511i	−0.0778689	−	0.320980i
$146$		0			0
$147$	3.33703	−	23.1616i	0.275233	−	1.91034i
$148$		0			0
$149$	3.16795	−	16.4369i	0.259529	−	1.34656i	−0.584991	−	0.811040i	$-0.698902\pi$
$149$	3.16795	−	16.4369i	0.259529	−	1.34656i	0.844520	−	0.535524i	$-0.179886\pi$
$150$		0			0
$151$	−1.71805	+	7.08191i	−0.139813	+	0.576318i	0.858200	+	0.513315i	$0.171583\pi$
$151$	−1.71805	+	7.08191i	−0.139813	+	0.576318i	−0.998013	+	0.0630027i	$0.979932\pi$
$152$		0			0
$153$	−7.44810	+	4.78660i	−0.602143	+	0.386974i
$154$		0			0
$155$	−8.52607	+	1.22586i	−0.684830	+	0.0984637i
$156$		0			0
$157$	12.5425	+	9.86355i	1.00100	+	0.787197i	0.977157	−	0.212518i	$-0.0681665\pi$
$157$	12.5425	+	9.86355i	1.00100	+	0.787197i	0.0238457	+	0.999716i	$0.492409\pi$
$158$		0			0
$159$	−9.17921	+	26.5216i	−0.727959	+	2.10330i
$160$		0			0
$161$	5.34813	+	11.5064i	0.421491	+	0.906832i
$162$		0			0
$163$	7.05815	−	20.3932i	0.552837	−	1.59732i	−0.228727	−	0.973491i	$-0.573456\pi$
$163$	7.05815	−	20.3932i	0.552837	−	1.59732i	0.781563	−	0.623826i	$-0.214423\pi$
$164$		0			0
$165$	−3.79094	−	2.98123i	−0.295125	−	0.232088i
$166$		0			0
$167$	−4.82555	+	0.693810i	−0.373412	+	0.0536886i	−0.326466	−	0.945209i	$-0.605858\pi$
$167$	−4.82555	+	0.693810i	−0.373412	+	0.0536886i	−0.0469461	+	0.998897i	$0.514949\pi$
$168$		0			0
$169$	4.38590	−	2.81865i	0.337377	−	0.216819i
$170$		0			0
$171$	5.58036	−	23.0026i	0.426741	−	1.75905i
$172$		0			0
$173$	4.64296	−	24.0900i	0.352998	−	1.83153i	−0.177847	−	0.984058i	$-0.556913\pi$
$173$	4.64296	−	24.0900i	0.352998	−	1.83153i	0.530845	−	0.847469i	$-0.321875\pi$
$174$		0			0
$175$	1.32915	−	11.1028i	0.100474	−	0.839296i
$176$		0			0
$177$	−0.673982	−	2.77819i	−0.0506596	−	0.208822i
$178$		0			0
$179$	6.96605	+	9.78245i	0.520667	+	0.731175i	0.988262	−	0.152768i	$-0.0488188\pi$
$179$	6.96605	+	9.78245i	0.520667	+	0.731175i	−0.467595	+	0.883943i	$0.654879\pi$
$180$		0			0
$181$	0.534140	+	0.343271i	0.0397023	+	0.0255151i	0.560341	−	0.828262i	$-0.310670\pi$
$181$	0.534140	+	0.343271i	0.0397023	+	0.0255151i	−0.520639	+	0.853777i	$0.674306\pi$
$182$		0			0
$183$			7.49805i			0.554272i
$184$		0			0
$185$	−3.14624	−	1.81648i	−0.231316	−	0.133550i
$186$		0			0
$187$	1.77433	+	0.0845217i	0.129752	+	0.00618084i
$188$		0			0
$189$	20.0071	−	41.1710i	1.45530	−	2.99475i
$190$		0			0
$191$	1.40685	−	0.341298i	0.101796	−	0.0246955i	−0.184537	−	0.982826i	$-0.559079\pi$
$191$	1.40685	−	0.341298i	0.101796	−	0.0246955i	0.286333	+	0.958130i	$0.407563\pi$
$192$		0			0
$193$	13.2694	+	1.26707i	0.955151	+	0.0912059i	0.560978	−	0.827830i	$-0.310425\pi$
$193$	13.2694	+	1.26707i	0.955151	+	0.0912059i	0.394173	+	0.919036i	$0.371031\pi$
$194$		0			0
$195$	−5.37275	+	6.20049i	−0.384751	+	0.444026i
$196$		0			0
$197$	−21.6748	+	6.36431i	−1.54427	+	0.453438i	−0.939382	−	0.342873i	$-0.888600\pi$
$197$	−21.6748	+	6.36431i	−1.54427	+	0.453438i	−0.604887	+	0.796311i	$0.706782\pi$
$198$		0			0
$199$	−0.390973	−	8.20753i	−0.0277153	−	0.581816i	−0.969425	−	0.245389i	$-0.921084\pi$
$199$	−0.390973	−	8.20753i	−0.0277153	−	0.581816i	0.941709	−	0.336427i	$-0.109219\pi$
$200$		0			0
$201$	17.8182	−	14.0124i	1.25680	−	0.988356i
$202$		0			0
$203$	−11.7982	−	1.98574i	−0.828074	−	0.139372i
$204$		0			0
$205$	−1.75100	−	0.606026i	−0.122295	−	0.0423267i
$206$		0			0
$207$	4.92075	+	38.8979i	0.342016	+	2.70359i
$208$		0			0
$209$	−3.58905	+	3.10993i	−0.248260	+	0.215118i
$210$		0			0
$211$	2.45336	−	17.0635i	0.168896	−	1.17470i	−0.712275	−	0.701900i	$-0.752335\pi$
$211$	2.45336	−	17.0635i	0.168896	−	1.17470i	0.881171	−	0.472797i	$-0.156756\pi$
$212$		0			0
$213$	0.673377	−	1.68202i	0.0461391	−	0.115250i
$214$		0			0
$215$	−0.970756	+	1.88300i	−0.0662050	+	0.128420i
$216$		0			0
$217$	−6.71008	+	25.0278i	−0.455510	+	1.69900i
$218$		0			0
$219$	−31.5523	−	6.08120i	−2.13210	−	0.410929i
$220$		0			0
$221$	0.287249	−	3.00821i	0.0193224	−	0.202354i
$222$		0			0
$223$	4.74269	−	16.1521i	0.317594	−	1.08163i	−0.633761	−	0.773529i	$-0.718490\pi$
$223$	4.74269	−	16.1521i	0.317594	−	1.08163i	0.951355	−	0.308097i	$-0.0996920\pi$
$224$		0			0
$225$	14.3538	−	31.4305i	0.956921	−	2.09537i
$226$		0			0
$227$	14.3215	−	7.38326i	0.950553	−	0.490044i	0.0880612	−	0.996115i	$-0.471933\pi$
$227$	14.3215	−	7.38326i	0.950553	−	0.490044i	0.862492	+	0.506071i	$0.168903\pi$
$228$		0			0
$229$	−8.23785	−	14.2684i	−0.544373	−	0.942881i	−0.998646	−	0.0520187i	$-0.983434\pi$
$229$	−8.23785	−	14.2684i	−0.544373	−	0.942881i	0.454274	−	0.890862i	$-0.349899\pi$
$230$		0			0
$231$	−12.7341	+	6.95095i	−0.837844	+	0.457339i
$232$		0			0
$233$	−1.13158	+	23.7548i	−0.0741324	+	1.55623i	0.589250	+	0.807951i	$0.299423\pi$
$233$	−1.13158	+	23.7548i	−0.0741324	+	1.55623i	−0.663383	+	0.748280i	$0.730880\pi$
$234$		0			0
$235$	6.08810	−	4.33531i	0.397144	−	0.282805i
$236$		0			0
$237$	50.4444	+	14.8118i	3.27672	+	0.962130i
$238$		0			0
$239$	2.60293	+	5.69961i	0.168369	+	0.368677i	0.974943	−	0.222457i	$-0.0714076\pi$
$239$	2.60293	+	5.69961i	0.168369	+	0.368677i	−0.806573	+	0.591134i	$0.798680\pi$
$240$		0			0
$241$	1.40470	+	4.05861i	0.0904845	+	0.261438i	0.981158	−	0.193205i	$-0.0618882\pi$
$241$	1.40470	+	4.05861i	0.0904845	+	0.261438i	−0.890674	+	0.454643i	$0.849767\pi$
$242$		0			0
$243$	41.0283	−	43.0293i	2.63197	−	2.76033i
$244$		0			0
$245$	5.33091	+	3.07987i	0.340579	+	0.196766i
$246$		0			0
$247$	4.99407	+	6.35047i	0.317765	+	0.404071i
$248$		0			0
$249$	−26.3554	+	33.5137i	−1.67021	+	2.12384i
$250$		0			0
$251$	−18.8872	−	21.7970i	−1.19215	−	1.37582i	−0.909029	−	0.416732i	$-0.863175\pi$
$251$	−18.8872	−	21.7970i	−1.19215	−	1.37582i	−0.283122	−	0.959084i	$-0.591370\pi$
$252$		0			0
$253$	3.72273	−	6.92988i	0.234046	−	0.435678i
$254$		0			0
$255$	−0.602594	−	3.12655i	−0.0377359	−	0.195792i
$256$		0			0
$257$	4.21920	+	10.5391i	0.263187	+	0.657409i	0.999822	−	0.0188819i	$-0.00601065\pi$
$257$	4.21920	+	10.5391i	0.263187	+	0.657409i	−0.736635	+	0.676291i	$0.763586\pi$
$258$		0			0
$259$	−8.74974	+	6.54798i	−0.543682	+	0.406872i
$260$		0			0
$261$	−32.8598	−	16.9404i	−2.03397	−	1.04859i
$262$		0			0
$263$	−3.15055	−	0.764314i	−0.194271	−	0.0471296i	0.137443	−	0.990510i	$-0.456112\pi$
$263$	−3.15055	−	0.764314i	−0.194271	−	0.0471296i	−0.331714	+	0.943380i	$0.607627\pi$
$264$		0			0
$265$	−5.58032	−	4.83537i	−0.342796	−	0.297035i
$266$		0			0
$267$	−47.1130	+	21.5158i	−2.88327	+	1.31674i
$268$		0			0
$269$	13.6578	+	14.3239i	0.832730	+	0.873343i	0.993521	−	0.113646i	$-0.0362530\pi$
$269$	13.6578	+	14.3239i	0.832730	+	0.873343i	−0.160791	+	0.986988i	$0.551404\pi$
$270$		0			0
$271$	−2.03271	−	21.2875i	−0.123479	−	1.29313i	−0.818655	−	0.574286i	$-0.805280\pi$
$271$	−2.03271	−	21.2875i	−0.123479	−	1.29313i	0.695176	−	0.718840i	$-0.255326\pi$
$272$		0			0
$273$	10.7807	+	22.2013i	0.652478	+	1.34368i
$274$		0			0
$275$	−6.00376	+	3.46627i	−0.362041	+	0.209024i
$276$		0			0
$277$	4.04608	−	7.00801i	0.243105	−	0.421071i	−0.718492	−	0.695535i	$-0.755167\pi$
$277$	4.04608	−	7.00801i	0.243105	−	0.421071i	0.961597	+	0.274465i	$0.0885006\pi$
$278$		0			0
$279$	−43.2878	+	67.3571i	−2.59157	+	4.03256i
$280$		0			0
$281$	−23.1757	−	10.5840i	−1.38254	−	0.631387i	−0.421259	−	0.906941i	$-0.638412\pi$
$281$	−23.1757	−	10.5840i	−1.38254	−	0.631387i	−0.961286	+	0.275554i	$0.911139\pi$
$282$		0			0
$283$	−9.73638	+	9.28362i	−0.578767	+	0.551854i	−0.921897	−	0.387434i	$-0.873361\pi$
$283$	−9.73638	+	9.28362i	−0.578767	+	0.551854i	0.343130	+	0.939288i	$0.388513\pi$
$284$		0			0
$285$	6.93415	+	4.93779i	0.410744	+	0.292489i
$286$		0			0
$287$	−3.74992	+	4.12385i	−0.221351	+	0.243423i
$288$		0			0
$289$	−11.4547	−	10.9220i	−0.673806	−	0.642472i
$290$		0			0
$291$	−1.48432	+	0.0707069i	−0.0870125	+	0.00414491i
$292$		0			0
$293$	3.90132	+	27.1343i	0.227917	+	1.58520i	0.706859	+	0.707354i	$0.250111\pi$
$293$	3.90132	+	27.1343i	0.227917	+	1.58520i	−0.478942	+	0.877847i	$0.658980\pi$
$294$		0			0
$295$	0.744477	+	0.107040i	0.0433451	+	0.00623208i
$296$		0			0
$297$	−27.8660	+	5.37074i	−1.61695	+	0.311642i
$298$		0			0
$299$	−11.4743	−	6.88683i	−0.663578	−	0.398276i
$300$		0			0
$301$	4.05681	+	4.91482i	0.233831	+	0.283285i
$302$		0			0
$303$	−12.7105	+	5.08852i	−0.730200	+	0.292328i
$304$		0			0
$305$	−1.83140	−	0.733181i	−0.104865	−	0.0419818i
$306$		0			0
$307$	−11.6474	−	18.1237i	−0.664753	−	1.03438i	−0.995870	−	0.0907864i	$-0.971062\pi$
$307$	−11.6474	−	18.1237i	−0.664753	−	1.03438i	0.331117	−	0.943590i	$-0.392574\pi$
$308$		0			0
$309$	10.5404	+	35.8974i	0.599624	+	2.04213i
$310$		0			0
$311$	14.6279	−	5.06275i	0.829470	−	0.287082i	0.120848	−	0.992671i	$-0.461439\pi$
$311$	14.6279	−	5.06275i	0.829470	−	0.287082i	0.708622	+	0.705589i	$0.249317\pi$
$312$		0			0
$313$	2.58071	−	3.62409i	0.145870	−	0.204846i	−0.735176	−	0.677876i	$-0.762901\pi$
$313$	2.58071	−	3.62409i	0.145870	−	0.204846i	0.881046	+	0.473030i	$0.156840\pi$
$314$		0			0
$315$	12.7947	+	14.0788i	0.720901	+	0.793250i
$316$		0			0
$317$	−0.994809	+	0.0949927i	−0.0558740	+	0.00533532i	−0.122956	−	0.992412i	$-0.539237\pi$
$317$	−0.994809	+	0.0949927i	−0.0558740	+	0.00533532i	0.0670816	+	0.997747i	$0.478631\pi$
$318$		0			0
$319$	3.39885	+	6.59285i	0.190299	+	0.369129i
$320$		0			0
$321$	−25.1624			−1.40443
$322$		0			0
$323$	−3.13540			−0.174458
$324$		0			0
$325$	5.40413	+	10.4825i	0.299767	+	0.581467i
$326$		0			0
$327$	62.8483	−	6.00129i	3.47552	−	0.331872i
$328$		0			0
$329$	−4.77589	−	21.9698i	−0.263304	−	1.21124i
$330$		0			0
$331$	6.64315	−	9.32900i	0.365141	−	0.512768i	−0.590606	−	0.806960i	$-0.701111\pi$
$331$	6.64315	−	9.32900i	0.365141	−	0.512768i	0.955746	+	0.294192i	$0.0950506\pi$
$332$		0			0
$333$	−31.9122	+	11.0449i	−1.74878	+	0.605259i
$334$		0			0
$335$	1.68020	+	5.72225i	0.0917993	+	0.312640i
$336$		0			0
$337$	8.84769	+	13.7673i	0.481964	+	0.749951i	0.994043	−	0.108988i	$-0.0347609\pi$
$337$	8.84769	+	13.7673i	0.481964	+	0.749951i	−0.512079	+	0.858938i	$0.671124\pi$
$338$		0			0
$339$	58.1056	+	23.2620i	3.15586	+	1.26342i
$340$		0			0
$341$	14.9137	−	5.97053i	0.807620	−	0.323322i
$342$		0			0
$343$	14.8311	−	11.0923i	0.800803	−	0.598928i
$344$		0			0
$345$	−13.6449	−	3.55634i	−0.734616	−	0.191467i
$346$		0			0
$347$	29.5945	−	5.70388i	1.58872	−	0.306200i	0.683109	−	0.730316i	$-0.260627\pi$
$347$	29.5945	−	5.70388i	1.58872	−	0.306200i	0.905608	+	0.424116i	$0.139415\pi$
$348$		0			0
$349$	−16.4012	−	2.35813i	−0.877934	−	0.126228i	−0.311413	−	0.950275i	$-0.600802\pi$
$349$	−16.4012	−	2.35813i	−0.877934	−	0.126228i	−0.566522	+	0.824047i	$0.691711\pi$
$350$		0			0
$351$	6.87065	+	47.7864i	0.366728	+	2.55065i
$352$		0			0
$353$	−24.4845	+	1.16634i	−1.30318	+	0.0620780i	−0.687652	−	0.726040i	$-0.741359\pi$
$353$	−24.4845	+	1.16634i	−1.30318	+	0.0620780i	−0.615524	+	0.788118i	$0.711056\pi$
$354$		0			0
$355$	0.344987	+	0.328944i	0.0183100	+	0.0174586i
$356$		0			0
$357$	−9.35913	−	2.03738i	−0.495338	−	0.107830i
$358$		0			0
$359$	−23.0703	−	16.4283i	−1.21760	−	0.867052i	−0.223418	−	0.974723i	$-0.571722\pi$
$359$	−23.0703	−	16.4283i	−1.21760	−	0.867052i	−0.994187	+	0.107670i	$0.965661\pi$
$360$		0			0
$361$	−7.68432	+	7.32699i	−0.404438	+	0.385631i
$362$		0			0
$363$	−25.2680	−	11.5395i	−1.32623	−	0.605668i
$364$		0			0
$365$	4.57060	−	7.11199i	0.239236	−	0.372259i
$366$		0			0
$367$	−12.9378	+	22.4089i	−0.675346	+	1.16973i	0.301021	+	0.953617i	$0.402672\pi$
$367$	−12.9378	+	22.4089i	−0.675346	+	1.16973i	−0.976368	+	0.216116i	$0.930661\pi$
$368$		0			0
$369$	−14.9159	+	8.61168i	−0.776489	+	0.448306i
$370$		0			0
$371$	−19.9807	+	9.70243i	−1.03735	+	0.503725i
$372$		0			0
$373$	0.531085	+	5.56177i	0.0274985	+	0.287978i	0.998753	+	0.0499324i	$0.0159006\pi$
$373$	0.531085	+	5.56177i	0.0274985	+	0.287978i	−0.971254	+	0.238045i	$0.923493\pi$
$374$		0			0
$375$	18.7202	+	19.6332i	0.966708	+	1.01385i
$376$		0			0
$377$	11.4781	−	5.24187i	0.591152	−	0.269970i
$378$		0			0
$379$	−15.2881	−	13.2472i	−0.785297	−	0.680464i	0.166891	−	0.985975i	$-0.446627\pi$
$379$	−15.2881	−	13.2472i	−0.785297	−	0.680464i	−0.952188	+	0.305511i	$0.901173\pi$
$380$		0			0
$381$	−25.5491	−	6.19813i	−1.30892	−	0.317540i
$382$		0			0
$383$	17.8279	+	9.19095i	0.910966	+	0.469635i	0.848970	−	0.528441i	$-0.177223\pi$
$383$	17.8279	+	9.19095i	0.910966	+	0.469635i	0.0619956	+	0.998076i	$0.480254\pi$
$384$		0			0
$385$	−0.452588	−	3.78999i	−0.0230660	−	0.193156i
$386$		0			0
$387$	7.31885	+	18.2816i	0.372038	+	0.929306i
$388$		0			0
$389$	−0.409493	−	2.12465i	−0.0207621	−	0.107724i	0.970069	−	0.242828i	$-0.0780752\pi$
$389$	−0.409493	−	2.12465i	−0.0207621	−	0.107724i	−0.990831	+	0.135104i	$0.956863\pi$
$390$		0			0
$391$	4.85366	−	1.84822i	0.245460	−	0.0934683i
$392$		0			0
$393$	−17.8181	−	20.5632i	−0.898805	−	1.03728i
$394$		0			0
$395$	−8.55037	+	10.8727i	−0.430216	+	0.547064i
$396$		0			0
$397$	−18.1447	−	23.0729i	−0.910659	−	1.15800i	−0.986969	−	0.160913i	$-0.948556\pi$
$397$	−18.1447	−	23.0729i	−0.910659	−	1.15800i	0.0763098	−	0.997084i	$-0.475686\pi$
$398$		0			0
$399$	21.8676	−	13.3246i	1.09475	−	0.667066i
$400$		0			0
$401$	10.7268	−	11.2500i	0.535672	−	0.561797i	−0.399162	−	0.916880i	$-0.630699\pi$
$401$	10.7268	−	11.2500i	0.535672	−	0.561797i	0.934835	+	0.355083i	$0.115548\pi$
$402$		0			0
$403$	−8.93829	−	25.8255i	−0.445248	−	1.28646i
$404$		0			0
$405$	12.1708	+	26.6503i	0.604771	+	1.32426i
$406$		0			0
$407$	6.50092	+	1.90884i	0.322238	+	0.0946177i
$408$		0			0
$409$	−21.6339	+	15.4054i	−1.06973	+	0.761749i	−0.972357	−	0.233499i	$-0.924982\pi$
$409$	−21.6339	+	15.4054i	−1.06973	+	0.761749i	−0.0973699	+	0.995248i	$0.531043\pi$
$410$		0			0
$411$	−0.643930	+	13.5177i	−0.0317627	+	0.666781i
$412$		0			0
$413$	1.17786	−	1.93177i	0.0579589	−	0.0950564i
$414$		0			0
$415$	−5.60859	−	9.71437i	−0.275315	−	0.476860i
$416$		0			0
$417$	−7.63109	+	3.93410i	−0.373696	+	0.192654i
$418$		0			0
$419$	−4.34404	+	9.51212i	−0.212220	+	0.464697i	−0.985567	−	0.169286i	$-0.945854\pi$
$419$	−4.34404	+	9.51212i	−0.212220	+	0.464697i	0.773347	+	0.633983i	$0.218581\pi$
$420$		0			0
$421$	3.12858	−	10.6550i	0.152477	−	0.519291i	−0.847456	−	0.530866i	$-0.821867\pi$
$421$	3.12858	−	10.6550i	0.152477	−	0.519291i	0.999933	+	0.0115758i	$0.00368478\pi$
$422$		0			0
$423$	6.60380	−	69.1581i	0.321088	−	3.36258i
$424$		0			0
$425$	−4.49431	−	0.866208i	−0.218006	−	0.0420173i
$426$		0			0
$427$	−4.19676	+	4.19554i	−0.203095	+	0.203036i
$428$		0			0
$429$	7.01133	−	13.6001i	0.338510	−	0.656618i
$430$		0			0
$431$	6.01134	−	15.0156i	0.289556	−	0.723276i	−0.710257	−	0.703942i	$-0.751421\pi$
$431$	6.01134	−	15.0156i	0.289556	−	0.723276i	0.999813	−	0.0193337i	$-0.00615448\pi$
$432$		0			0
$433$	−1.83561	+	12.7669i	−0.0882137	+	0.613540i	0.896977	+	0.442077i	$0.145758\pi$
$433$	−1.83561	+	12.7669i	−0.0882137	+	0.613540i	−0.985191	+	0.171463i	$0.945151\pi$
$434$		0			0
$435$	10.0482	−	8.70684i	0.481776	−	0.417461i
$436$		0			0
$437$	−5.98148	+	12.5306i	−0.286133	+	0.599422i
$438$		0			0
$439$	−23.5449	−	8.14897i	−1.12374	−	0.388929i	−0.298891	−	0.954287i	$-0.596617\pi$
$439$	−23.5449	−	8.14897i	−1.12374	−	0.388929i	−0.824845	+	0.565358i	$0.808738\pi$
$440$		0			0
$441$	54.0859	−	18.7017i	2.57552	−	0.890555i
$442$		0			0
$443$	16.2964	−	12.8156i	0.774265	−	0.608889i	−0.150858	−	0.988555i	$-0.548204\pi$
$443$	16.2964	−	12.8156i	0.774265	−	0.608889i	0.925123	+	0.379666i	$0.123961\pi$
$444$		0			0
$445$	−0.648382	−	13.6112i	−0.0307362	−	0.645233i
$446$		0			0
$447$	53.6925	−	15.7655i	2.53957	−	0.745685i
$448$		0			0
$449$	−5.02519	+	5.79938i	−0.237153	+	0.273690i	−0.861834	−	0.507191i	$-0.830684\pi$
$449$	−5.02519	+	5.79938i	−0.237153	+	0.273690i	0.624680	+	0.780881i	$0.285229\pi$
$450$		0			0
$451$	3.43997	+	0.328477i	0.161982	+	0.0154674i
$452$		0			0
$453$	−23.6746	+	5.74339i	−1.11233	+	0.269848i
$454$		0			0
$455$	−6.47681	+	0.462282i	−0.303638	+	0.0216721i
$456$		0			0
$457$	−24.5379	−	1.16888i	−1.14783	−	0.0546781i	−0.534974	−	0.844869i	$-0.679679\pi$
$457$	−24.5379	−	1.16888i	−1.14783	−	0.0546781i	−0.612861	+	0.790191i	$0.709982\pi$
$458$		0			0
$459$	−16.2262	−	9.36819i	−0.757374	−	0.437270i
$460$		0			0
$461$		−	10.6294i		−	0.495059i	−0.968880	−	0.247530i	$-0.920381\pi$
$461$		−	10.6294i		−	0.495059i	0.968880	−	0.247530i	$-0.0796187\pi$
$462$		0			0
$463$	−26.1455	−	16.8027i	−1.21508	−	0.780887i	−0.233582	−	0.972337i	$-0.575045\pi$
$463$	−26.1455	−	16.8027i	−1.21508	−	0.780887i	−0.981502	+	0.191450i	$0.938681\pi$
$464$		0			0
$465$	−16.7030	−	23.4561i	−0.774583	−	1.08775i
$466$		0			0
$467$	2.54582	+	10.4940i	0.117807	+	0.485605i	0.999895	+	0.0145207i	$0.00462225\pi$
$467$	2.54582	+	10.4940i	0.117807	+	0.485605i	−0.882088	+	0.471085i	$0.843863\pi$
$468$		0			0
$469$	17.8131	+	2.13244i	0.822530	+	0.0984671i
$470$		0			0
$471$	−10.0949	+	52.3775i	−0.465150	+	2.41343i
$472$		0			0
$473$	0.931473	−	3.83958i	0.0428292	−	0.176544i
$474$		0			0
$475$	10.2940	−	6.61558i	0.472323	−	0.303544i
$476$		0			0
$477$	−67.9364	+	9.76777i	−3.11059	+	0.447236i
$478$		0			0
$479$	−11.8208	−	9.29598i	−0.540106	−	0.424744i	0.310480	−	0.950580i	$-0.399510\pi$
$479$	−11.8208	−	9.29598i	−0.540106	−	0.424744i	−0.850586	+	0.525836i	$0.823753\pi$
$480$		0			0
$481$	3.76984	−	10.8922i	0.171890	−	0.496644i
$482$		0			0
$483$	−25.9971	+	33.5171i	−1.18291	+	1.52508i
$484$		0			0
$485$	0.127871	−	0.369459i	0.00580632	−	0.0167763i
$486$		0			0
$487$	10.8237	+	8.51183i	0.490467	+	0.385708i	0.832539	−	0.553966i	$-0.186886\pi$
$487$	10.8237	+	8.51183i	0.490467	+	0.385708i	−0.342072	+	0.939674i	$0.611129\pi$
$488$		0			0
$489$	71.4071	−	10.2668i	3.22914	−	0.464280i
$490$		0			0
$491$	2.97562	−	1.91232i	0.134288	−	0.0863016i	−0.471772	−	0.881721i	$-0.656385\pi$
$491$	2.97562	−	1.91232i	0.134288	−	0.0863016i	0.606060	+	0.795419i	$0.292749\pi$
$492$		0			0
$493$	−1.15454	+	4.75909i	−0.0519980	+	0.214339i
$494$		0			0
$495$	2.23209	−	11.5812i	0.100325	−	0.520536i
$496$		0			0
$497$	1.31823	−	0.564273i	0.0591309	−	0.0253111i
$498$		0			0
$499$	−1.38033	−	5.68979i	−0.0617920	−	0.254710i	0.932535	−	0.361081i	$-0.117592\pi$
$499$	−1.38033	−	5.68979i	−0.0617920	−	0.254710i	−0.994327	+	0.106371i	$0.966077\pi$
$500$		0			0
$501$	−9.45350	−	13.2756i	−0.422351	−	0.593109i
$502$		0			0
$503$	−8.54077	−	5.48882i	−0.380814	−	0.244734i	0.336204	−	0.941789i	$-0.390857\pi$
$503$	−8.54077	−	5.48882i	−0.380814	−	0.244734i	−0.717018	+	0.697055i	$0.754493\pi$
$504$		0			0
$505$		−	3.60211i		−	0.160292i
$506$		0			0
$507$	15.0937	+	8.71433i	0.670333	+	0.387017i
$508$		0			0
$509$	13.4579	+	0.641080i	0.596512	+	0.0284154i	0.343667	−	0.939091i	$-0.388331\pi$
$509$	13.4579	+	0.641080i	0.596512	+	0.0284154i	0.252845	+	0.967507i	$0.418634\pi$
$510$		0			0
$511$	−14.2513	−	21.0629i	−0.630442	−	0.931770i
$512$		0			0
$513$	48.6792	−	11.8095i	2.14924	−	0.521400i
$514$		0			0
$515$	−9.79860	−	0.935653i	−0.431778	−	0.0412298i
$516$		0			0
$517$	−9.12790	+	10.5342i	−0.401445	+	0.463292i
$518$		0			0
$519$	78.6919	−	23.1060i	3.45419	−	1.01424i
$520$		0			0
$521$	1.44805	+	30.3984i	0.0634404	+	1.33178i	0.776252	+	0.630423i	$0.217118\pi$
$521$	1.44805	+	30.3984i	0.0634404	+	1.33178i	−0.712812	+	0.701355i	$0.752579\pi$
$522$		0			0
$523$	22.0589	−	17.3473i	0.964568	−	0.758545i	−0.00584815	−	0.999983i	$-0.501862\pi$
$523$	22.0589	−	17.3473i	0.964568	−	0.758545i	0.970416	+	0.241438i	$0.0776191\pi$
$524$		0			0
$525$	35.0264	−	13.0584i	1.52868	−	0.569914i
$526$		0			0
$527$	10.0227	+	3.46891i	0.436598	+	0.151108i
$528$		0			0
$529$	1.87306	−	22.9236i	0.0814373	−	0.996678i
$530$		0			0
$531$	5.28368	−	4.57833i	0.229292	−	0.198683i
$532$		0			0
$533$	0.836620	−	5.81882i	0.0362380	−	0.252041i
$534$		0			0
$535$	2.46045	−	6.14590i	0.106374	−	0.265710i
$536$		0			0
$537$	−18.3962	+	35.6837i	−0.793855	+	1.53986i
$538$		0			0
$539$	−11.0159	−	3.23805i	−0.474489	−	0.139473i
$540$		0			0
$541$	−2.66453	−	0.513545i	−0.114557	−	0.0220790i	0.131651	−	0.991296i	$-0.457972\pi$
$541$	−2.66453	−	0.513545i	−0.114557	−	0.0220790i	−0.246207	+	0.969217i	$0.579184\pi$
$542$		0			0
$543$	−0.201762	+	2.11295i	−0.00865844	+	0.0906753i
$544$		0			0
$545$	−4.67967	+	15.9375i	−0.200455	+	0.682688i
$546$		0			0
$547$	13.5223	−	29.6098i	0.578174	−	1.26602i	−0.364156	−	0.931338i	$-0.618643\pi$
$547$	13.5223	−	29.6098i	0.578174	−	1.26602i	0.942330	−	0.334686i	$-0.108630\pi$
$548$		0			0
$549$	−16.2985	+	8.40247i	−0.695604	+	0.358609i
$550$		0			0
$551$	−6.54618	−	11.3383i	−0.278877	−	0.483029i
$552$		0			0
$553$	19.9358	+	36.5223i	0.847756	+	1.55309i
$554$		0			0
$555$	0.577876	−	12.1311i	0.0245295	−	0.514937i
$556$		0			0
$557$	−5.95740	+	4.24225i	−0.252423	+	0.179750i	−0.699264	−	0.714864i	$-0.746489\pi$
$557$	−5.95740	+	4.24225i	−0.252423	+	0.179750i	0.446840	+	0.894614i	$0.352549\pi$
$558$		0			0
$559$	−6.44906	−	1.89361i	−0.272766	−	0.0800913i
$560$		0			0
$561$	2.46684	+	5.40162i	0.104150	+	0.228056i
$562$		0			0
$563$	1.75196	+	5.06196i	0.0738364	+	0.213336i	0.975880	−	0.218310i	$-0.0700542\pi$
$563$	1.75196	+	5.06196i	0.0738364	+	0.213336i	−0.902043	+	0.431646i	$0.857933\pi$
$564$		0			0
$565$	−11.3635	+	11.9177i	−0.478064	+	0.501379i
$566$		0			0
$567$	88.1086	−	2.08453i	3.70021	−	0.0875420i
$568$		0			0
$569$	−22.4546	−	28.5533i	−0.941344	−	1.19702i	−0.980248	−	0.197773i	$-0.936629\pi$
$569$	−22.4546	−	28.5533i	−0.941344	−	1.19702i	0.0389039	−	0.999243i	$-0.487613\pi$
$570$		0			0
$571$	12.5896	−	16.0090i	0.526860	−	0.669957i	−0.447674	−	0.894197i	$-0.647748\pi$
$571$	12.5896	−	16.0090i	0.526860	−	0.669957i	0.974534	+	0.224240i	$0.0719899\pi$
$572$		0			0
$573$	3.16918	+	3.65743i	0.132394	+	0.152791i
$574$		0			0
$575$	−12.0357	+	16.3091i	−0.501925	+	0.680136i
$576$		0			0
$577$	5.47279	+	28.3956i	0.227835	+	1.18212i	0.898029	+	0.439936i	$0.144999\pi$
$577$	5.47279	+	28.3956i	0.227835	+	1.18212i	−0.670194	+	0.742186i	$0.733789\pi$
$578$		0			0
$579$	16.5616	+	41.3689i	0.688277	+	1.71923i
$580$		0			0
$581$	−33.5052	+	4.00109i	−1.39003	+	0.165993i
$582$		0			0
$583$	12.2398	+	6.31006i	0.506921	+	0.261336i
$584$		0			0
$585$	−19.4988	−	4.73036i	−0.806176	−	0.195576i
$586$		0			0
$587$	−1.48788	−	1.28926i	−0.0614116	−	0.0532134i	0.623614	−	0.781732i	$-0.285664\pi$
$587$	−1.48788	−	1.28926i	−0.0614116	−	0.0532134i	−0.685026	+	0.728519i	$0.740209\pi$
$588$		0			0
$589$	−25.7927	+	11.7791i	−1.06277	+	0.485350i
$590$		0			0
$591$	−52.1129	−	54.6544i	−2.14364	−	2.24818i
$592$		0			0
$593$	2.04419	+	21.4077i	0.0839446	+	0.879108i	0.935145	+	0.354266i	$0.115269\pi$
$593$	2.04419	+	21.4077i	0.0839446	+	0.879108i	−0.851200	+	0.524842i	$0.824125\pi$
$594$		0			0
$595$	1.41279	−	2.08674i	0.0579188	−	0.0855481i
$596$		0			0
$597$	23.7885	−	13.7343i	0.973599	−	0.562108i
$598$		0			0
$599$	−2.27219	+	3.93555i	−0.0928391	+	0.160802i	−0.908705	−	0.417440i	$-0.862928\pi$
$599$	−2.27219	+	3.93555i	−0.0928391	+	0.160802i	0.815866	+	0.578242i	$0.196261\pi$
$600$		0			0
$601$	10.5239	−	16.3755i	0.429280	−	0.667972i	−0.557475	−	0.830194i	$-0.688230\pi$
$601$	10.5239	−	16.3755i	0.429280	−	0.667972i	0.986754	+	0.162222i	$0.0518660\pi$
$602$		0			0
$603$	50.4261	+	23.0288i	2.05351	+	0.937806i
$604$		0			0
$605$	5.28931	−	5.04334i	0.215041	−	0.205041i
$606$		0			0
$607$	−4.64570	−	3.30819i	−0.188563	−	0.134275i	0.481877	−	0.876239i	$-0.339955\pi$
$607$	−4.64570	−	3.30819i	−0.188563	−	0.134275i	−0.670440	+	0.741964i	$0.733895\pi$
$608$		0			0
$609$	−12.1726	−	38.0985i	−0.493260	−	1.54383i
$610$		0			0
$611$	17.1614	+	16.3634i	0.694277	+	0.661992i
$612$		0			0
$613$	−14.4908	+	0.690284i	−0.585279	+	0.0278803i	−0.338134	−	0.941098i	$-0.609796\pi$
$613$	−14.4908	+	0.690284i	−0.585279	+	0.0278803i	−0.247146	+	0.968978i	$0.579493\pi$
$614$		0			0
$615$	−0.881527	−	6.13116i	−0.0355466	−	0.247232i
$616$		0			0
$617$	5.77174	+	0.829850i	0.232361	+	0.0334085i	0.257512	−	0.966275i	$-0.417097\pi$
$617$	5.77174	+	0.829850i	0.232361	+	0.0334085i	−0.0251504	+	0.999684i	$0.508006\pi$
$618$		0			0
$619$	16.3422	−	3.14970i	0.656848	−	0.126597i	0.150073	−	0.988675i	$-0.452049\pi$
$619$	16.3422	−	3.14970i	0.656848	−	0.126597i	0.506776	+	0.862078i	$0.330837\pi$
$620$		0			0
$621$	−68.3952	+	46.9761i	−2.74461	+	1.88509i
$622$		0			0
$623$	−38.4047	−	14.3306i	−1.53865	−	0.574143i
$624$		0			0
$625$	12.9926	−	5.20144i	0.519703	−	0.208058i
$626$		0			0
$627$	−14.7385	−	5.90041i	−0.588600	−	0.235640i
$628$		0			0
$629$	2.41842	+	3.76314i	0.0964288	+	0.150046i
$630$		0			0
$631$	9.24998	+	31.5026i	0.368236	+	1.25410i	0.910367	+	0.413803i	$0.135800\pi$
$631$	9.24998	+	31.5026i	0.368236	+	1.25410i	−0.542131	+	0.840294i	$0.682382\pi$
$632$		0			0
$633$	54.4596	−	18.8487i	2.16458	−	0.749167i
$634$		0			0
$635$	4.01215	−	5.63428i	0.159217	−	0.223589i
$636$		0			0
$637$	−6.39399	+	18.4568i	−0.253339	+	0.731285i
$638$		0			0
$639$	4.41080	−	0.421180i	0.174488	−	0.0166616i
$640$		0			0
$641$	21.9269	+	42.5322i	0.866059	+	1.67992i	0.723710	+	0.690104i	$0.242435\pi$
$641$	21.9269	+	42.5322i	0.866059	+	1.67992i	0.142349	+	0.989817i	$0.454535\pi$
$642$		0			0
$643$	−3.06167			−0.120741			−0.0603703	−	0.998176i	$-0.519228\pi$
$643$	−3.06167			−0.120741			−0.0603703	+	0.998176i	$0.519228\pi$
$644$		0			0
$645$	−7.08210			−0.278857
$646$		0			0
$647$	3.08813	+	5.99013i	0.121407	+	0.235496i	0.941705	−	0.336440i	$-0.109223\pi$
$647$	3.08813	+	5.99013i	0.121407	+	0.235496i	−0.820298	+	0.571936i	$0.806193\pi$
$648$		0			0
$649$	−1.39635	+	0.133336i	−0.0548117	+	0.00523388i
$650$		0			0
$651$	−84.6449	+	18.4005i	−3.31750	+	0.721171i
$652$		0			0
$653$	−21.2043	+	29.7773i	−0.829788	+	1.16527i	0.154375	+	0.988012i	$0.450663\pi$
$653$	−21.2043	+	29.7773i	−0.829788	+	1.16527i	−0.984164	+	0.177262i	$0.943276\pi$
$654$		0			0
$655$	6.76486	−	2.34134i	0.264325	−	0.0914838i
$656$		0			0
$657$	−22.1394	−	75.3999i	−0.863740	−	2.94163i
$658$		0			0
$659$	−7.75867	−	12.0727i	−0.302235	−	0.470286i	0.656605	−	0.754235i	$-0.271992\pi$
$659$	−7.75867	−	12.0727i	−0.302235	−	0.470286i	−0.958840	+	0.283948i	$0.908356\pi$
$660$		0			0
$661$	13.7258	+	5.49498i	0.533871	+	0.213730i	0.622903	−	0.782299i	$-0.285953\pi$
$661$	13.7258	+	5.49498i	0.533871	+	0.213730i	−0.0890319	+	0.996029i	$0.528377\pi$
$662$		0			0
$663$	9.37844	−	3.75456i	0.364228	−	0.145815i
$664$		0			0
$665$	1.11626	+	6.64407i	0.0432867	+	0.257646i
$666$		0			0
$667$	16.8172	+	13.6932i	0.651165	+	0.530203i
$668$		0			0
$669$	55.2585	−	10.6502i	2.13642	−	0.411761i
$670$		0			0
$671$	3.64159	+	0.523582i	0.140582	+	0.0202127i
$672$		0			0
$673$	4.88705	+	33.9902i	0.188382	+	1.31022i	0.836198	+	0.548428i	$0.184773\pi$
$673$	4.88705	+	33.9902i	0.188382	+	1.31022i	−0.647816	+	0.761797i	$0.724318\pi$
$674$		0			0
$675$	73.0400	−	3.47932i	2.81131	−	0.133919i
$676$		0			0
$677$	−8.79347	−	8.38456i	−0.337961	−	0.322245i	0.502025	−	0.864853i	$-0.332588\pi$
$677$	−8.79347	−	8.38456i	−0.337961	−	0.322245i	−0.839986	+	0.542608i	$0.817437\pi$
$678$		0			0
$679$	−0.870127	−	0.791230i	−0.0333924	−	0.0303646i
$680$		0			0
$681$	43.8764	+	31.2443i	1.68135	+	1.19728i
$682$		0			0
$683$	19.1570	−	18.2662i	0.733022	−	0.698935i	−0.228537	−	0.973535i	$-0.573394\pi$
$683$	19.1570	−	18.2662i	0.733022	−	0.698935i	0.961558	+	0.274600i	$0.0885456\pi$
$684$		0			0
$685$	−3.23874	−	1.47908i	−0.123746	−	0.0565128i
$686$		0			0
$687$	29.7773	−	46.3343i	1.13607	−	1.76776i
$688$		0			0
$689$	11.7132	−	20.2879i	0.446237	−	0.772906i
$690$		0			0
$691$	2.74450	−	1.58454i	0.104406	−	0.0602787i	−0.446888	−	0.894590i	$-0.647468\pi$
$691$	2.74450	−	1.58454i	0.104406	−	0.0602787i	0.551294	+	0.834311i	$0.314134\pi$
$692$		0			0
$693$	−29.3794	−	19.8908i	−1.11603	−	0.755588i
$694$		0			0
$695$	−0.214713	−	2.24858i	−0.00814454	−	0.0852934i
$696$		0			0
$697$	1.57440	+	1.65118i	0.0596346	+	0.0625430i
$698$		0			0
$699$	−72.3173	+	33.0262i	−2.73529	+	1.24916i
$700$		0			0
$701$	5.82958	+	5.05136i	0.220180	+	0.190787i	0.757966	−	0.652294i	$-0.226193\pi$
$701$	5.82958	+	5.05136i	0.220180	+	0.190787i	−0.537785	+	0.843082i	$0.680739\pi$
$702$		0			0
$703$	−11.6220	−	2.81947i	−0.438332	−	0.106338i
$704$		0			0
$705$	22.2077	+	11.4489i	0.836390	+	0.431189i
$706$		0			0
$707$	−9.96028	−	4.26696i	−0.374595	−	0.160475i
$708$		0			0
$709$	0.531567	+	1.32779i	0.0199634	+	0.0498662i	0.938015	−	0.346595i	$-0.112662\pi$
$709$	0.531567	+	1.32779i	0.0199634	+	0.0498662i	−0.918051	+	0.396461i	$0.870238\pi$
$710$		0			0
$711$	24.3326	+	126.249i	0.912543	+	4.73472i
$712$		0			0
$713$	32.9842	−	33.4383i	1.23527	−	1.25227i
$714$		0			0
$715$	2.63623	+	3.04237i	0.0985893	+	0.113778i
$716$		0			0
$717$	−12.9483	+	16.4651i	−0.483562	+	0.614899i
$718$		0			0
$719$	14.9337	+	18.9897i	0.556932	+	0.708197i	0.980245	−	0.197787i	$-0.0633753\pi$
$719$	14.9337	+	18.9897i	0.556932	+	0.708197i	−0.423313	+	0.905984i	$0.639133\pi$
$720$		0			0
$721$	−14.1944	+	25.9860i	−0.528625	+	0.967770i
$722$		0			0
$723$	−9.90776	+	10.3910i	−0.368474	+	0.386444i
$724$		0			0
$725$	−6.25097	−	18.0610i	−0.232155	−	0.670768i
$726$		0			0
$727$	−1.33460	−	2.92236i	−0.0494974	−	0.108384i	0.883268	−	0.468869i	$-0.155338\pi$
$727$	−1.33460	−	2.92236i	−0.0494974	−	0.108384i	−0.932765	+	0.360485i	$0.882611\pi$
$728$		0			0
$729$	94.8179	+	27.8410i	3.51177	+	1.03115i
$730$		0			0
$731$	2.12483	−	1.51308i	0.0785897	−	0.0559634i
$732$		0			0
$733$	1.50839	−	31.6650i	0.0557136	−	1.16957i	−0.781934	−	0.623361i	$-0.785767\pi$
$733$	1.50839	−	31.6650i	0.0557136	−	1.16957i	0.837648	−	0.546211i	$-0.183930\pi$
$734$		0			0
$735$	−0.985295	+	20.5578i	−0.0363432	+	0.758287i
$736$		0			0
$737$	−5.56118	−	9.63225i	−0.204849	−	0.354808i
$738$		0			0
$739$	7.65594	−	3.94691i	0.281628	−	0.145190i	−0.311625	−	0.950205i	$-0.600873\pi$
$739$	7.65594	−	3.94691i	0.281628	−	0.145190i	0.593254	+	0.805016i	$0.297843\pi$
$740$		0			0
$741$	−11.2194	+	24.5670i	−0.412154	+	0.902491i
$742$		0			0
$743$	5.21864	−	17.7731i	0.191453	−	0.652031i	−0.806682	−	0.590986i	$-0.798739\pi$
$743$	5.21864	−	17.7731i	0.191453	−	0.652031i	0.998135	−	0.0610443i	$-0.0194431\pi$
$744$		0			0
$745$	−1.39948	+	14.6560i	−0.0512728	+	0.536953i
$746$		0			0
$747$	−102.383	−	19.7327i	−3.74600	−	0.721983i
$748$		0			0
$749$	−14.0796	−	14.0837i	−0.514457	−	0.514607i
$750$		0			0
$751$	9.86891	−	19.1430i	0.360122	−	0.698538i	−0.637276	−	0.770636i	$-0.719939\pi$
$751$	9.86891	−	19.1430i	0.360122	−	0.698538i	0.997398	+	0.0720973i	$0.0229692\pi$
$752$		0			0
$753$	35.8344	−	89.5100i	1.30588	−	3.26192i
$754$		0			0
$755$	0.912146	−	6.34411i	0.0331964	−	0.230886i
$756$		0			0
$757$	11.9086	−	10.3189i	0.432827	−	0.375047i	−0.411024	−	0.911625i	$-0.634829\pi$
$757$	11.9086	−	10.3189i	0.432827	−	0.375047i	0.843851	+	0.536578i	$0.180283\pi$
$758$		0			0
$759$	26.2937	+	0.446084i	0.954400	+	0.0161918i
$760$		0			0
$761$	−35.8844	−	12.4197i	−1.30081	−	0.450214i	−0.413127	−	0.910674i	$-0.635563\pi$
$761$	−35.8844	−	12.4197i	−1.30081	−	0.450214i	−0.887681	+	0.460460i	$0.847685\pi$
$762$		0			0
$763$	38.5258	+	31.8190i	1.39473	+	1.15193i
$764$		0			0
$765$	6.12091	−	4.81354i	0.221302	−	0.174034i
$766$		0			0
$767$	0.113543	+	2.38356i	0.00409980	+	0.0860655i
$768$		0			0
$769$	5.03238	−	1.47764i	0.181472	−	0.0532851i	−0.189734	−	0.981836i	$-0.560763\pi$
$769$	5.03238	−	1.47764i	0.181472	−	0.0532851i	0.371206	+	0.928551i	$0.378944\pi$
$770$		0			0
$771$	−24.8521	+	28.6808i	−0.895026	+	1.03291i
$772$		0			0
$773$	46.3777	+	4.42853i	1.66809	+	0.159283i	0.885937	−	0.463805i	$-0.153516\pi$
$773$	46.3777	+	4.42853i	1.66809	+	0.159283i	0.782152	+	0.623088i	$0.214122\pi$
$774$		0			0
$775$	−40.2257	+	9.75865i	−1.44495	+	0.350541i
$776$		0			0
$777$	−32.8595	−	15.9681i	−1.17883	−	0.572851i
$778$		0			0
$779$	−6.09256	−	0.290224i	−0.218289	−	0.0103984i
$780$		0			0
$781$	−0.769886	−	0.444494i	−0.0275487	−	0.0159052i
$782$		0			0
$783$		−	78.2369i		−	2.79596i
$784$		0			0
$785$	−11.8061	−	7.58731i	−0.421377	−	0.270803i
$786$		0			0
$787$	2.23240	+	3.13496i	0.0795764	+	0.111749i	0.852446	−	0.522816i	$-0.175119\pi$
$787$	2.23240	+	3.13496i	0.0795764	+	0.111749i	−0.772869	+	0.634565i	$0.781179\pi$
$788$		0			0
$789$	−2.55508	−	10.5322i	−0.0909631	−	0.374955i
$790$		0			0
$791$	19.4930	+	45.5387i	0.693090	+	1.61917i
$792$		0			0
$793$	1.18447	−	6.14564i	0.0420619	−	0.218238i
$794$		0			0
$795$	5.81944	−	23.9881i	0.206394	−	0.850769i
$796$		0			0
$797$	18.1884	−	11.6890i	0.644266	−	0.414044i	−0.177301	−	0.984157i	$-0.556737\pi$
$797$	18.1884	−	11.6890i	0.644266	−	0.414044i	0.821567	+	0.570112i	$0.193100\pi$
$798$		0			0
$799$	−9.10897	+	1.30967i	−0.322252	+	0.0463329i
$800$		0			0
$801$	−99.5646	−	78.2985i	−3.51794	−	2.76654i
$802$		0			0
$803$	−5.15673	+	14.8994i	−0.181977	+	0.525788i
$804$		0			0
$805$	−5.64446	−	9.62717i	−0.198941	−	0.339313i
$806$		0			0
$807$	−21.6397	+	62.5239i	−0.761754	+	2.20094i
$808$		0			0
$809$	19.2537	+	15.1413i	0.676923	+	0.532338i	0.896381	−	0.443283i	$-0.146186\pi$
$809$	19.2537	+	15.1413i	0.676923	+	0.532338i	−0.219458	+	0.975622i	$0.570429\pi$
$810$		0			0
$811$	23.2993	−	3.34994i	0.818150	−	0.117632i	0.279483	−	0.960151i	$-0.409837\pi$
$811$	23.2993	−	3.34994i	0.818150	−	0.117632i	0.538667	+	0.842519i	$0.318928\pi$
$812$		0			0
$813$	60.1389	−	38.6489i	2.10916	−	1.35548i
$814$		0			0
$815$	−4.47473	+	18.4451i	−0.156743	+	0.646103i
$816$		0			0
$817$	−1.31980	+	6.84775i	−0.0461738	+	0.239573i
$818$		0			0
$819$	−36.1778	+	48.3132i	−1.26415	+	1.68820i
$820$		0			0
$821$	1.24091	+	5.11511i	0.0433081	+	0.178518i	0.989358	−	0.145503i	$-0.0464801\pi$
$821$	1.24091	+	5.11511i	0.0433081	+	0.178518i	−0.946050	+	0.324022i	$0.894965\pi$
$822$		0			0
$823$	13.9402	+	19.5763i	0.485926	+	0.682388i	0.982639	−	0.185527i	$-0.0593992\pi$
$823$	13.9402	+	19.5763i	0.485926	+	0.682388i	−0.496713	+	0.867915i	$0.665460\pi$
$824$		0			0
$825$	−19.4963	−	12.5295i	−0.678773	−	0.436221i
$826$		0			0
$827$		−	52.3558i		−	1.82059i	−0.413961	−	0.910295i	$-0.635855\pi$
$827$		−	52.3558i		−	1.82059i	0.413961	−	0.910295i	$-0.364145\pi$
$828$		0			0
$829$	3.75027	+	2.16522i	0.130252	+	0.0752012i	0.563710	−	0.825973i	$-0.309373\pi$
$829$	3.75027	+	2.16522i	0.130252	+	0.0752012i	−0.433458	+	0.901174i	$0.642707\pi$
$830$		0			0
$831$	27.0212	+	1.28718i	0.937354	+	0.0446517i
$832$		0			0
$833$	−4.09655	−	6.37844i	−0.141937	−	0.221000i
$834$		0			0
$835$	4.16695	−	1.01089i	0.144203	−	0.0349833i
$836$		0			0
$837$	−168.676	−	16.1066i	−5.83029	−	0.556725i
$838$		0			0
$839$	9.93450	−	11.4650i	0.342977	−	0.395816i	−0.557888	−	0.829916i	$-0.688388\pi$
$839$	9.93450	−	11.4650i	0.342977	−	0.395816i	0.900865	+	0.434100i	$0.142934\pi$
$840$		0			0
$841$	8.20481	−	2.40915i	0.282924	−	0.0830741i
$842$		0			0
$843$	−4.05266	−	85.0758i	−0.139581	−	2.93017i
$844$		0			0
$845$	−3.60437	+	2.83451i	−0.123994	+	0.0975101i
$846$		0			0
$847$	−7.67991	−	20.5998i	−0.263885	−	0.707817i
$848$		0			0
$849$	−42.4994	−	14.7092i	−1.45857	−	0.504818i
$850$		0			0
$851$	19.6531	−	2.48620i	0.673700	−	0.0852259i
$852$		0			0
$853$	−7.73411	+	6.70165i	−0.264811	+	0.229460i	−0.777138	−	0.629331i	$-0.783329\pi$
$853$	−7.73411	+	6.70165i	−0.264811	+	0.229460i	0.512327	+	0.858791i	$0.328784\pi$
$854$		0			0
$855$	−2.96272	+	20.6061i	−0.101323	+	0.704715i
$856$		0			0
$857$	18.4979	−	46.2055i	0.631876	−	1.57835i	−0.173009	−	0.984920i	$-0.555349\pi$
$857$	18.4979	−	46.2055i	0.631876	−	1.57835i	0.804885	−	0.593431i	$-0.202227\pi$
$858$		0			0
$859$	−24.2008	+	46.9430i	−0.825720	+	1.60167i	−0.0272589	+	0.999628i	$0.508678\pi$
$859$	−24.2008	+	46.9430i	−0.825720	+	1.60167i	−0.798462	+	0.602046i	$0.794352\pi$
$860$		0			0
$861$	−17.9976	−	4.82527i	−0.613358	−	0.164445i
$862$		0			0
$863$	41.2260	+	7.94566i	1.40335	+	0.270473i	0.834064	−	0.551667i	$-0.186008\pi$
$863$	41.2260	+	7.94566i	1.40335	+	0.270473i	0.569285	+	0.822140i	$0.307220\pi$
$864$		0			0
$865$	−2.05108	+	21.4798i	−0.0697387	+	0.730337i
$866$		0			0
$867$	14.9064	−	50.7666i	0.506249	−	1.72413i
$868$		0			0
$869$	10.7162	−	23.4651i	0.363521	−	0.795999i
$870$		0			0
$871$	−16.8179	+	8.67021i	−0.569852	+	0.293779i
$872$		0			0
$873$	−1.81706	−	3.14723i	−0.0614980	−	0.106518i
$874$		0			0
$875$	−0.514061	+	21.4637i	−0.0173784	+	0.725605i
$876$		0			0
$877$	0.185135	−	3.88647i	0.00625157	−	0.131237i	−0.993584	−	0.113097i	$-0.963923\pi$
$877$	0.185135	−	3.88647i	0.00625157	−	0.131237i	0.999835	−	0.0181392i	$-0.00577420\pi$
$878$		0			0
$879$	−74.6491	+	53.1574i	−2.51785	+	1.79295i
$880$		0			0
$881$	−22.5625	−	6.62495i	−0.760150	−	0.223200i	−0.121389	−	0.992605i	$-0.538735\pi$
$881$	−22.5625	−	6.62495i	−0.760150	−	0.223200i	−0.638762	+	0.769405i	$0.720553\pi$
$882$		0			0
$883$	7.93600	+	17.3774i	0.267068	+	0.584797i	0.994890	−	0.100970i	$-0.0321945\pi$
$883$	7.93600	+	17.3774i	0.267068	+	0.584797i	−0.727822	+	0.685766i	$0.759467\pi$
$884$		0			0
$885$	0.822364	+	2.37606i	0.0276435	+	0.0798705i
$886$		0			0
$887$	−29.9476	+	31.4082i	−1.00554	+	1.05458i	−0.00703518	+	0.999975i	$0.502239\pi$
$887$	−29.9476	+	31.4082i	−1.00554	+	1.05458i	−0.998508	+	0.0546080i	$0.982609\pi$
$888$		0			0
$889$	−10.8268	−	17.7683i	−0.363119	−	0.595930i
$890$		0			0
$891$	−33.7760	−	42.9497i	−1.13154	−	1.43887i
$892$		0			0
$893$	15.2086	−	19.3393i	0.508935	−	0.647164i
$894$		0			0
$895$	−6.91689	−	7.98251i	−0.231206	−	0.266826i
$896$		0			0
$897$	2.88638	−	44.6437i	0.0963733	−	1.49061i
$898$		0			0
$899$	8.38145	+	43.4871i	0.279537	+	1.45038i
$900$		0			0
$901$	3.37903	+	8.44042i	0.112572	+	0.281191i
$902$		0			0
$903$	−8.38925	+	19.5829i	−0.279177	+	0.651677i
$904$		0			0
$905$	−0.496358	−	0.255890i	−0.0164995	−	0.00850608i
$906$		0			0
$907$	27.6575	+	6.70964i	0.918353	+	0.222790i	0.666958	−	0.745095i	$-0.267596\pi$
$907$	27.6575	+	6.70964i	0.918353	+	0.222790i	0.251394	+	0.967885i	$0.419111\pi$
$908$		0			0
$909$	−25.3046	−	21.9265i	−0.839299	−	0.727257i
$910$		0			0
$911$	17.6224	−	8.04788i	0.583856	−	0.266638i	−0.101513	−	0.994834i	$-0.532368\pi$
$911$	17.6224	−	8.04788i	0.583856	−	0.266638i	0.685369	+	0.728196i	$0.259641\pi$
$912$		0			0
$913$	14.4363	+	15.1403i	0.477771	+	0.501071i
$914$		0			0
$915$	−0.626865	−	6.56483i	−0.0207235	−	0.217026i
$916$		0			0
$917$	1.53937	−	21.4792i	0.0508344	−	0.709305i
$918$		0			0
$919$	45.5121	−	26.2764i	1.50131	−	0.866779i	0.501307	−	0.865270i	$-0.332853\pi$
$919$	45.5121	−	26.2764i	1.50131	−	0.866779i	0.999999	−	0.00150962i	$-0.000480528\pi$
$920$		0			0
$921$	36.0100	−	62.3711i	1.18657	−	2.05520i
$922$		0			0
$923$	−0.817630	+	1.27226i	−0.0269126	+	0.0418769i
$924$		0			0
$925$	−15.8802	−	7.25224i	−0.522138	−	0.238452i
$926$		0			0
$927$	−66.2184	+	63.1391i	−2.17490	+	2.07376i
$928$		0			0
$929$	27.3887	+	19.5034i	0.898595	+	0.639887i	0.933139	−	0.359516i	$-0.117058\pi$
$929$	27.3887	+	19.5034i	0.898595	+	0.639887i	−0.0345435	+	0.999403i	$0.510998\pi$
$930$		0			0
$931$	19.6940	+	4.78378i	0.645444	+	0.156782i
$932$		0			0
$933$	37.4507	+	35.7091i	1.22608	+	1.16906i
$934$		0			0
$935$	−1.56056	+	0.0743385i	−0.0510357	+	0.00243113i
$936$		0			0
$937$	1.70982	+	11.8921i	0.0558575	+	0.388497i	0.998503	+	0.0547013i	$0.0174206\pi$
$937$	1.70982	+	11.8921i	0.0558575	+	0.388497i	−0.942645	+	0.333796i	$0.891670\pi$
$938$		0			0
$939$	14.7217	+	2.11665i	0.480423	+	0.0690744i
$940$		0			0
$941$	−45.3898	+	8.74818i	−1.47967	+	0.285182i	−0.864267	−	0.503033i	$-0.832217\pi$
$941$	−45.3898	+	8.74818i	−1.47967	+	0.285182i	−0.615399	+	0.788215i	$0.711005\pi$
$942$		0			0
$943$	9.60250	−	3.14210i	0.312700	−	0.102321i
$944$		0			0
$945$	−14.0749	+	37.7194i	−0.457856	+	1.22701i
$946$		0			0
$947$	−19.0417	+	7.62317i	−0.618774	+	0.247720i	−0.659803	−	0.751438i	$-0.729360\pi$
$947$	−19.0417	+	7.62317i	−0.618774	+	0.247720i	0.0410297	+	0.999158i	$0.486936\pi$
$948$		0			0
$949$	24.9006	+	9.96868i	0.808306	+	0.323597i
$950$		0			0
$951$	−1.80614	−	2.81041i	−0.0585681	−	0.0911337i
$952$		0			0
$953$	7.46973	+	25.4396i	0.241968	+	0.824068i	0.987503	+	0.157601i	$0.0503761\pi$
$953$	7.46973	+	25.4396i	0.241968	+	0.824068i	−0.745535	+	0.666467i	$0.767806\pi$
$954$		0			0
$955$	−1.20322	+	0.416437i	−0.0389352	+	0.0134756i
$956$		0			0
$957$	−14.3832	+	20.1983i	−0.464942	+	0.652919i
$958$		0			0
$959$	−7.92637	+	7.20344i	−0.255956	+	0.232611i
$960$		0			0
$961$	64.6224	−	6.17069i	2.08459	−	0.199055i
$962$		0			0
$963$	−28.1974	−	54.6954i	−0.908650	−	1.76254i
$964$		0			0
$965$	−11.7238			−0.377402
$966$		0			0
$967$	−11.4522			−0.368279			−0.184140	−	0.982900i	$-0.558950\pi$
$967$	−11.4522			−0.368279			−0.184140	+	0.982900i	$0.558950\pi$
$968$		0			0
$969$	−4.80291	−	9.31635i	−0.154292	−	0.299284i
$970$		0			0
$971$	−9.64048	+	0.920555i	−0.309378	+	0.0295420i	−0.248590	−	0.968609i	$-0.579967\pi$
$971$	−9.64048	+	0.920555i	−0.309378	+	0.0295420i	−0.0607875	+	0.998151i	$0.519361\pi$
$972$		0			0
$973$	−6.47194	−	2.06990i	−0.207481	−	0.0663578i
$974$		0			0
$975$	−22.8690	+	32.1151i	−0.732395	+	1.02851i
$976$		0			0
$977$	−25.3259	+	8.76538i	−0.810248	+	0.280430i	−0.700612	−	0.713542i	$-0.747090\pi$
$977$	−25.3259	+	8.76538i	−0.810248	+	0.280430i	−0.109636	+	0.993972i	$0.534968\pi$
$978$		0			0
$979$	7.15975	+	24.3839i	0.228827	+	0.779312i
$980$		0			0
$981$	83.4741	+	129.888i	2.66512	+	4.14701i
$982$		0			0
$983$	11.6467	+	4.66265i	0.371473	+	0.148715i	0.549885	−	0.835241i	$-0.314672\pi$
$983$	11.6467	+	4.66265i	0.371473	+	0.148715i	−0.178412	+	0.983956i	$0.557096\pi$
$984$		0			0
$985$	18.4451	−	7.38429i	0.587708	−	0.235283i
$986$		0			0
$987$	57.9641	−	47.8450i	1.84502	−	1.52292i
$988$		0			0
$989$	−1.99346	−	11.3785i	−0.0633883	−	0.361814i
$990$		0			0
$991$	10.2616	−	1.97777i	0.325971	−	0.0628258i	−0.0236404	−	0.999721i	$-0.507526\pi$
$991$	10.2616	−	1.97777i	0.325971	−	0.0628258i	0.349612	+	0.936895i	$0.386314\pi$
$992$		0			0
$993$	37.8959	+	5.44861i	1.20259	+	0.172906i
$994$		0			0
$995$	1.02849	+	7.15331i	0.0326054	+	0.226775i
$996$		0			0
$997$	−3.44660	+	0.164182i	−0.109155	+	0.00519970i	−0.102088	−	0.994775i	$-0.532552\pi$
$997$	−3.44660	+	0.164182i	−0.109155	+	0.00519970i	−0.00706668	+	0.999975i	$0.502249\pi$
$998$		0			0
$999$	−51.7215	−	49.3164i	−1.63640	−	1.56030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.493.16	yes	320
7.5	odd	6	inner	644.2.bc.a.33.16	✓	320
23.7	odd	22	inner	644.2.bc.a.605.16	yes	320
161.145	even	66	inner	644.2.bc.a.145.16	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.16	✓	320	7.5	odd	6	inner
644.2.bc.a.145.16	yes	320	161.145	even	66	inner
644.2.bc.a.493.16	yes	320	1.1	even	1	trivial
644.2.bc.a.605.16	yes	320	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.53184 + 2.97135i) q^{3} +(-0.875537 + 0.0836037i) q^{5} +(-0.805963 + 2.52000i) q^{7} +(-4.74221 + 6.65950i) q^{9} +O(q^{10})\)	\(q+(1.53184 + 2.97135i) q^{3} +(-0.875537 + 0.0836037i) q^{5} +(-0.805963 + 2.52000i) q^{7} +(-4.74221 + 6.65950i) q^{9} +(1.55007 - 0.536483i) q^{11} +(-0.786153 - 2.67739i) q^{13} +(-1.58959 - 2.47346i) q^{15} +(1.00538 + 0.402492i) q^{17} +(-2.68784 + 1.07605i) q^{19} +(-8.72241 + 1.46544i) q^{21} +(3.52655 - 3.25015i) q^{23} +(-4.15007 + 0.799860i) q^{25} +(-17.1251 - 2.46222i) q^{27} +(0.643553 + 4.47601i) q^{29} +(9.78260 - 0.466003i) q^{31} +(3.96852 + 3.78398i) q^{33} +(0.494969 - 2.27374i) q^{35} +(3.36470 + 2.39599i) q^{37} +(6.75120 - 6.43726i) q^{39} +(1.91634 + 0.875165i) q^{41} +(1.30225 - 2.02633i) q^{43} +(3.59522 - 6.22711i) q^{45} +(-7.35927 + 4.24888i) q^{47} +(-5.70085 - 4.06206i) q^{49} +(0.344128 + 3.60387i) q^{51} +(5.79341 + 6.07595i) q^{53} +(-1.31229 + 0.599302i) q^{55} +(-7.31465 - 6.33818i) q^{57} +(-0.831057 - 0.201612i) q^{59} +(1.99360 + 1.02777i) q^{61} +(-12.9599 - 17.3177i) q^{63} +(0.912146 + 2.27843i) q^{65} +(-1.28327 - 6.65824i) q^{67} +(15.0594 + 5.49990i) q^{69} +(-0.354917 - 0.409596i) q^{71} +(-5.94181 + 7.55563i) q^{73} +(-8.73388 - 11.1060i) q^{75} +(0.102644 + 4.33856i) q^{77} +(10.8527 - 11.3820i) q^{79} +(-10.8950 - 31.4791i) q^{81} +(5.29810 + 11.6012i) q^{83} +(-0.913894 - 0.268343i) q^{85} +(-12.3140 + 8.76873i) q^{87} +(-0.737199 + 15.4757i) q^{89} +(7.38065 + 0.176768i) q^{91} +(16.3700 + 28.3536i) q^{93} +(2.26335 - 1.16684i) q^{95} +(-0.184659 + 0.404347i) q^{97} +(-3.77803 + 12.8668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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