LMFDB - Embedded newform 756.2.e.b.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(323,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("756.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.2
Character	$\chi$	$=$	756.323
Dual form			756.2.e.b.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40500 + 0.161188i) q^{2} +(1.94804 - 0.452937i) q^{4} +4.14952i q^{5} +1.00000i q^{7} +(-2.66398 + 0.950375i) q^{8} +O(q^{10})$	\(q+(-1.40500 + 0.161188i) q^{2} +(1.94804 - 0.452937i) q^{4} +4.14952i q^{5} +1.00000i q^{7} +(-2.66398 + 0.950375i) q^{8} +(-0.668852 - 5.83006i) q^{10} +3.98082 q^{11} +5.19698 q^{13} +(-0.161188 - 1.40500i) q^{14} +(3.58970 - 1.76468i) q^{16} -0.533690i q^{17} +1.00778i q^{19} +(1.87947 + 8.08341i) q^{20} +(-5.59304 + 0.641659i) q^{22} +2.52732 q^{23} -12.2185 q^{25} +(-7.30174 + 0.837689i) q^{26} +(0.452937 + 1.94804i) q^{28} +8.68221i q^{29} -5.49217i q^{31} +(-4.75907 + 3.05798i) q^{32} +(0.0860244 + 0.749834i) q^{34} -4.14952 q^{35} +2.40281 q^{37} +(-0.162442 - 1.41593i) q^{38} +(-3.94360 - 11.0542i) q^{40} -8.54069i q^{41} +10.7165i q^{43} +(7.75478 - 1.80306i) q^{44} +(-3.55088 + 0.407373i) q^{46} -9.11249 q^{47} -1.00000 q^{49} +(17.1670 - 1.96947i) q^{50} +(10.1239 - 2.35390i) q^{52} -7.18334i q^{53} +16.5185i q^{55} +(-0.950375 - 2.66398i) q^{56} +(-1.39947 - 12.1985i) q^{58} -6.12323 q^{59} +1.85588 q^{61} +(0.885271 + 7.71649i) q^{62} +(6.19357 - 5.06356i) q^{64} +21.5649i q^{65} +11.3389i q^{67} +(-0.241728 - 1.03965i) q^{68} +(5.83006 - 0.668852i) q^{70} +8.36943 q^{71} -1.90495 q^{73} +(-3.37594 + 0.387304i) q^{74} +(0.456462 + 1.96320i) q^{76} +3.98082i q^{77} +1.66368i q^{79} +(7.32255 + 14.8955i) q^{80} +(1.37666 + 11.9997i) q^{82} -10.2049 q^{83} +2.21456 q^{85} +(-1.72737 - 15.0567i) q^{86} +(-10.6048 + 3.78327i) q^{88} -3.43007i q^{89} +5.19698i q^{91} +(4.92331 - 1.14472i) q^{92} +(12.8030 - 1.46882i) q^{94} -4.18181 q^{95} +0.254738 q^{97} +(1.40500 - 0.161188i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4}+O(q^{10}) $ 24 * q + 4 * q^4	$ 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.40500	+	0.161188i	−0.993483	+	0.113977i
$2$	−1.40500	+	0.161188i	−0.993483	+	0.113977i
$3$		0			0
$3$		0			0
$4$	1.94804	−	0.452937i	0.974018	−	0.226468i
$5$			4.14952i			1.85572i	0.372928	+	0.927860i	$0.378354\pi$
$5$			4.14952i			1.85572i	−0.372928	+	0.927860i	$0.621646\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.66398	+	0.950375i	−0.941859	+	0.336008i
$9$		0			0
$10$	−0.668852	−	5.83006i	−0.211509	−	1.84363i
$11$	3.98082			1.20026			0.600131	−	0.799902i	$-0.295115\pi$
$11$	3.98082			1.20026			0.600131	+	0.799902i	$0.295115\pi$
$12$		0			0
$13$	5.19698			1.44138			0.720691	−	0.693257i	$-0.243825\pi$
$13$	5.19698			1.44138			0.720691	+	0.693257i	$0.243825\pi$
$14$	−0.161188	−	1.40500i	−0.0430792	−	0.375501i
$15$		0			0
$16$	3.58970	−	1.76468i	0.897424	−	0.441169i
$17$		−	0.533690i		−	0.129439i	−0.997903	−	0.0647195i	$-0.979385\pi$
$17$		−	0.533690i		−	0.129439i	0.997903	−	0.0647195i	$-0.0206153\pi$
$18$		0			0
$19$			1.00778i			0.231201i	0.993296	+	0.115601i	$0.0368793\pi$
$19$			1.00778i			0.231201i	−0.993296	+	0.115601i	$0.963121\pi$
$20$	1.87947	+	8.08341i	0.420262	+	1.80751i
$21$		0			0
$22$	−5.59304	+	0.641659i	−1.19244	+	0.136802i
$23$	2.52732			0.526982			0.263491	−	0.964662i	$-0.415126\pi$
$23$	2.52732			0.526982			0.263491	+	0.964662i	$0.415126\pi$
$24$		0			0
$25$	−12.2185			−2.44370
$26$	−7.30174	+	0.837689i	−1.43199	+	0.164284i
$27$		0			0
$28$	0.452937	+	1.94804i	0.0855970	+	0.368144i
$29$			8.68221i			1.61225i	0.591748	+	0.806123i	$0.298438\pi$
$29$			8.68221i			1.61225i	−0.591748	+	0.806123i	$0.701562\pi$
$30$		0			0
$31$		−	5.49217i		−	0.986423i	−0.869910	−	0.493211i	$-0.835823\pi$
$31$		−	5.49217i		−	0.986423i	0.869910	−	0.493211i	$-0.164177\pi$
$32$	−4.75907	+	3.05798i	−0.841293	+	0.540580i
$33$		0			0
$34$	0.0860244	+	0.749834i	0.0147531	+	0.128595i
$35$	−4.14952			−0.701396
$36$		0			0
$37$	2.40281			0.395020			0.197510	−	0.980301i	$-0.436715\pi$
$37$	2.40281			0.395020			0.197510	+	0.980301i	$0.436715\pi$
$38$	−0.162442	−	1.41593i	−0.0263516	−	0.229695i
$39$		0			0
$40$	−3.94360	−	11.0542i	−0.623538	−	1.74783i
$41$		−	8.54069i		−	1.33383i	−0.745133	−	0.666916i	$-0.767614\pi$
$41$		−	8.54069i		−	1.33383i	0.745133	−	0.666916i	$-0.232386\pi$
$42$		0			0
$43$			10.7165i			1.63426i	0.576457	+	0.817128i	$0.304435\pi$
$43$			10.7165i			1.63426i	−0.576457	+	0.817128i	$0.695565\pi$
$44$	7.75478	−	1.80306i	1.16908	−	0.271821i
$45$		0			0
$46$	−3.55088	+	0.407373i	−0.523548	+	0.0600639i
$47$	−9.11249			−1.32919			−0.664596	−	0.747203i	$-0.731396\pi$
$47$	−9.11249			−1.32919			−0.664596	+	0.747203i	$0.731396\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	17.1670	−	1.96947i	2.42777	−	0.278525i
$51$		0			0
$52$	10.1239	−	2.35390i	1.40393	−	0.326427i
$53$		−	7.18334i		−	0.986708i	−0.869829	−	0.493354i	$-0.835771\pi$
$53$		−	7.18334i		−	0.986708i	0.869829	−	0.493354i	$-0.164229\pi$
$54$		0			0
$55$			16.5185i			2.22735i
$56$	−0.950375	−	2.66398i	−0.126999	−	0.355989i
$57$		0			0
$58$	−1.39947	−	12.1985i	−0.183759	−	1.60174i
$59$	−6.12323			−0.797176			−0.398588	−	0.917130i	$-0.630500\pi$
$59$	−6.12323			−0.797176			−0.398588	+	0.917130i	$0.630500\pi$
$60$		0			0
$61$	1.85588			0.237621			0.118810	−	0.992917i	$-0.462092\pi$
$61$	1.85588			0.237621			0.118810	+	0.992917i	$0.462092\pi$
$62$	0.885271	+	7.71649i	0.112429	+	0.979995i
$63$		0			0
$64$	6.19357	−	5.06356i	0.774197	−	0.632945i
$65$			21.5649i			2.67480i
$66$		0			0
$67$			11.3389i			1.38527i	0.721289	+	0.692634i	$0.243550\pi$
$67$			11.3389i			1.38527i	−0.721289	+	0.692634i	$0.756450\pi$
$68$	−0.241728	−	1.03965i	−0.0293138	−	0.126076i
$69$		0			0
$70$	5.83006	−	0.668852i	0.696826	−	0.0799431i
$71$	8.36943			0.993269			0.496634	−	0.867960i	$-0.334569\pi$
$71$	8.36943			0.993269			0.496634	+	0.867960i	$0.334569\pi$
$72$		0			0
$73$	−1.90495			−0.222958			−0.111479	−	0.993767i	$-0.535559\pi$
$73$	−1.90495			−0.222958			−0.111479	+	0.993767i	$0.535559\pi$
$74$	−3.37594	+	0.387304i	−0.392445	+	0.0450231i
$75$		0			0
$76$	0.456462	+	1.96320i	0.0523598	+	0.225194i
$77$			3.98082i			0.453656i
$78$		0			0
$79$			1.66368i			0.187178i	0.995611	+	0.0935891i	$0.0298340\pi$
$79$			1.66368i			0.187178i	−0.995611	+	0.0935891i	$0.970166\pi$
$80$	7.32255	+	14.8955i	0.818686	+	1.66537i
$81$		0			0
$82$	1.37666	+	11.9997i	0.152026	+	1.32514i
$83$	−10.2049			−1.12013			−0.560066	−	0.828448i	$-0.689224\pi$
$83$	−10.2049			−1.12013			−0.560066	+	0.828448i	$0.689224\pi$
$84$		0			0
$85$	2.21456			0.240203
$86$	−1.72737	−	15.0567i	−0.186267	−	1.62361i
$87$		0			0
$88$	−10.6048	+	3.78327i	−1.13048	+	0.403298i
$89$		−	3.43007i		−	0.363587i	−0.983337	−	0.181793i	$-0.941810\pi$
$89$		−	3.43007i		−	0.363587i	0.983337	−	0.181793i	$-0.0581902\pi$
$90$		0			0
$91$			5.19698i			0.544791i
$92$	4.92331	−	1.14472i	0.513291	−	0.119345i
$93$		0			0
$94$	12.8030	−	1.46882i	1.32053	−	0.151497i
$95$	−4.18181			−0.429045
$96$		0			0
$97$	0.254738			0.0258648			0.0129324	−	0.999916i	$-0.495883\pi$
$97$	0.254738			0.0258648			0.0129324	+	0.999916i	$0.495883\pi$
$98$	1.40500	−	0.161188i	0.141926	−	0.0162824i
$99$		0			0
$100$	−23.8021	+	5.53421i	−2.38021	+	0.553421i
$101$		−	9.91460i		−	0.986540i	−0.869876	−	0.493270i	$-0.835802\pi$
$101$		−	9.91460i		−	0.986540i	0.869876	−	0.493270i	$-0.164198\pi$
$102$		0			0
$103$			1.30961i			0.129039i	0.997916	+	0.0645197i	$0.0205515\pi$
$103$			1.30961i			0.129039i	−0.997916	+	0.0645197i	$0.979448\pi$
$104$	−13.8446	+	4.93908i	−1.35758	+	0.484316i
$105$		0			0
$106$	1.15787	+	10.0926i	0.112462	+	0.980278i
$107$	−3.26311			−0.315457			−0.157728	−	0.987483i	$-0.550417\pi$
$107$	−3.26311			−0.315457			−0.157728	+	0.987483i	$0.550417\pi$
$108$		0			0
$109$	3.32451			0.318430			0.159215	−	0.987244i	$-0.449104\pi$
$109$	3.32451			0.318430			0.159215	+	0.987244i	$0.449104\pi$
$110$	−2.66258	−	23.2084i	−0.253867	−	2.21284i
$111$		0			0
$112$	1.76468	+	3.58970i	0.166746	+	0.339194i
$113$			9.83185i			0.924903i	0.886645	+	0.462451i	$0.153030\pi$
$113$			9.83185i			0.924903i	−0.886645	+	0.462451i	$0.846970\pi$
$114$		0			0
$115$			10.4872i			0.977932i
$116$	3.93249	+	16.9133i	0.365123	+	1.57036i
$117$		0			0
$118$	8.60312	−	0.986989i	0.791981	−	0.0908597i
$119$	0.533690			0.0489233
$120$		0			0
$121$	4.84691			0.440628
$122$	−2.60750	+	0.299145i	−0.236072	+	0.0270833i
$123$		0			0
$124$	−2.48761	−	10.6989i	−0.223394	−	0.960794i
$125$		−	29.9533i		−	2.67910i
$126$		0			0
$127$			4.41672i			0.391921i	0.980612	+	0.195960i	$0.0627824\pi$
$127$			4.41672i			0.391921i	−0.980612	+	0.195960i	$0.937218\pi$
$128$	−7.88577	+	8.11262i	−0.697010	+	0.717061i
$129$		0			0
$130$	−3.47600	−	30.2987i	−0.304866	−	2.65737i
$131$	8.00406			0.699318			0.349659	−	0.936877i	$-0.386297\pi$
$131$	8.00406			0.699318			0.349659	+	0.936877i	$0.386297\pi$
$132$		0			0
$133$	−1.00778			−0.0873858
$134$	−1.82769	−	15.9311i	−0.157889	−	1.37624i
$135$		0			0
$136$	0.507206	+	1.42174i	0.0434926	+	0.121913i
$137$		−	3.39675i		−	0.290204i	−0.989417	−	0.145102i	$-0.953649\pi$
$137$		−	3.39675i		−	0.290204i	0.989417	−	0.145102i	$-0.0463511\pi$
$138$		0			0
$139$		−	17.2693i		−	1.46477i	−0.680893	−	0.732383i	$-0.738408\pi$
$139$		−	17.2693i		−	1.46477i	0.680893	−	0.732383i	$-0.261592\pi$
$140$	−8.08341	+	1.87947i	−0.683173	+	0.158844i
$141$		0			0
$142$	−11.7590	+	1.34905i	−0.986796	+	0.113210i
$143$	20.6882			1.73004
$144$		0			0
$145$	−36.0270			−2.99188
$146$	2.67645	−	0.307055i	0.221505	−	0.0254120i
$147$		0			0
$148$	4.68076	−	1.08832i	0.384756	−	0.0894595i
$149$		−	8.81668i		−	0.722291i	−0.932510	−	0.361145i	$-0.882386\pi$
$149$		−	8.81668i		−	0.722291i	0.932510	−	0.361145i	$-0.117614\pi$
$150$		0			0
$151$		−	14.0421i		−	1.14273i	−0.820697	−	0.571363i	$-0.806415\pi$
$151$		−	14.0421i		−	1.14273i	0.820697	−	0.571363i	$-0.193585\pi$
$152$	−0.957772	−	2.68471i	−0.0776855	−	0.217759i
$153$		0			0
$154$	−0.641659	−	5.59304i	−0.0517064	−	0.450700i
$155$	22.7899			1.83053
$156$		0			0
$157$	3.06676			0.244754			0.122377	−	0.992484i	$-0.460948\pi$
$157$	3.06676			0.244754			0.122377	+	0.992484i	$0.460948\pi$
$158$	−0.268164	−	2.33746i	−0.0213340	−	0.185958i
$159$		0			0
$160$	−12.6891	−	19.7478i	−1.00316	−	1.56120i
$161$			2.52732i			0.199181i
$162$		0			0
$163$			4.07956i			0.319536i	0.987155	+	0.159768i	$0.0510746\pi$
$163$			4.07956i			0.319536i	−0.987155	+	0.159768i	$0.948925\pi$
$164$	−3.86840	−	16.6376i	−0.302071	−	1.29918i
$165$		0			0
$166$	14.3379	−	1.64490i	1.11283	−	0.127669i
$167$	14.8177			1.14663			0.573314	−	0.819336i	$-0.305657\pi$
$167$	14.8177			1.14663			0.573314	+	0.819336i	$0.305657\pi$
$168$		0			0
$169$	14.0086			1.07758
$170$	−3.11145	+	0.356960i	−0.238637	+	0.0273776i
$171$		0			0
$172$	4.85391	+	20.8762i	0.370107	+	1.59179i
$173$		−	7.12530i		−	0.541726i	−0.962618	−	0.270863i	$-0.912691\pi$
$173$		−	7.12530i		−	0.541726i	0.962618	−	0.270863i	$-0.0873091\pi$
$174$		0			0
$175$		−	12.2185i		−	0.923631i
$176$	14.2899	−	7.02485i	1.07714	−	0.529518i
$177$		0			0
$178$	0.552886	+	4.81924i	0.0414405	+	0.361217i
$179$	12.5172			0.935580			0.467790	−	0.883840i	$-0.345050\pi$
$179$	12.5172			0.935580			0.467790	+	0.883840i	$0.345050\pi$
$180$		0			0
$181$	19.0400			1.41524			0.707618	−	0.706596i	$-0.249770\pi$
$181$	19.0400			1.41524			0.707618	+	0.706596i	$0.249770\pi$
$182$	−0.837689	−	7.30174i	−0.0620936	−	0.541241i
$183$		0			0
$184$	−6.73273	+	2.40190i	−0.496343	+	0.177070i
$185$			9.97050i			0.733046i
$186$		0			0
$187$		−	2.12452i		−	0.155361i
$188$	−17.7515	+	4.12738i	−1.29466	+	0.301020i
$189$		0			0
$190$	5.87544	−	0.674057i	0.426249	−	0.0489012i
$191$	−6.31019			−0.456589			−0.228295	−	0.973592i	$-0.573315\pi$
$191$	−6.31019			−0.456589			−0.228295	+	0.973592i	$0.573315\pi$
$192$		0			0
$193$	−27.0112			−1.94431			−0.972155	−	0.234338i	$-0.924708\pi$
$193$	−27.0112			−1.94431			−0.972155	+	0.234338i	$0.924708\pi$
$194$	−0.357907	+	0.0410607i	−0.0256962	+	0.00294799i
$195$		0			0
$196$	−1.94804	+	0.452937i	−0.139145	+	0.0323526i
$197$		−	8.89344i		−	0.633631i	−0.948487	−	0.316816i	$-0.897386\pi$
$197$		−	8.89344i		−	0.633631i	0.948487	−	0.316816i	$-0.102614\pi$
$198$		0			0
$199$			20.0605i			1.42205i	0.703168	+	0.711024i	$0.251768\pi$
$199$			20.0605i			1.42205i	−0.703168	+	0.711024i	$0.748232\pi$
$200$	32.5498	−	11.6122i	2.30162	−	0.821103i
$201$		0			0
$202$	1.59811	+	13.9300i	0.112443	+	0.980111i
$203$	−8.68221			−0.609372
$204$		0			0
$205$	35.4398			2.47522
$206$	−0.211093	−	1.83999i	−0.0147075	−	0.128198i
$207$		0			0
$208$	18.6556	−	9.17098i	1.29353	−	0.635893i
$209$			4.01180i			0.277502i
$210$		0			0
$211$		−	22.9428i		−	1.57945i	−0.613462	−	0.789724i	$-0.710224\pi$
$211$		−	22.9428i		−	1.57945i	0.613462	−	0.789724i	$-0.289776\pi$
$212$	−3.25360	−	13.9934i	−0.223458	−	0.961072i
$213$		0			0
$214$	4.58466	−	0.525973i	0.313401	−	0.0359548i
$215$	−44.4684			−3.03272
$216$		0			0
$217$	5.49217			0.372833
$218$	−4.67092	+	0.535870i	−0.316355	+	0.0362937i
$219$		0			0
$220$	7.48183	+	32.1786i	0.504425	+	2.16948i
$221$		−	2.77358i		−	0.186571i
$222$		0			0
$223$			7.42461i			0.497188i	0.968608	+	0.248594i	$0.0799686\pi$
$223$			7.42461i			0.497188i	−0.968608	+	0.248594i	$0.920031\pi$
$224$	−3.05798	−	4.75907i	−0.204320	−	0.317979i
$225$		0			0
$226$	−1.58477	−	13.8137i	−0.105418	−	0.918875i
$227$	16.0055			1.06232			0.531162	−	0.847270i	$-0.321755\pi$
$227$	16.0055			1.06232			0.531162	+	0.847270i	$0.321755\pi$
$228$		0			0
$229$	−20.1281			−1.33010			−0.665050	−	0.746799i	$-0.731590\pi$
$229$	−20.1281			−1.33010			−0.665050	+	0.746799i	$0.731590\pi$
$230$	−1.69040	−	14.7344i	−0.111462	−	0.971559i
$231$		0			0
$232$	−8.25136	−	23.1292i	−0.541728	−	1.51851i
$233$		−	20.8221i		−	1.36410i	−0.731306	−	0.682050i	$-0.761089\pi$
$233$		−	20.8221i		−	1.36410i	0.731306	−	0.682050i	$-0.238911\pi$
$234$		0			0
$235$		−	37.8124i		−	2.46661i
$236$	−11.9283	+	2.77344i	−0.776464	+	0.180535i
$237$		0			0
$238$	−0.749834	+	0.0860244i	−0.0486045	+	0.00557613i
$239$	14.6579			0.948138			0.474069	−	0.880488i	$-0.342785\pi$
$239$	14.6579			0.948138			0.474069	+	0.880488i	$0.342785\pi$
$240$		0			0
$241$	−3.73980			−0.240902			−0.120451	−	0.992719i	$-0.538434\pi$
$241$	−3.73980			−0.240902			−0.120451	+	0.992719i	$0.538434\pi$
$242$	−6.80990	+	0.781263i	−0.437757	+	0.0502215i
$243$		0			0
$244$	3.61531	−	0.840595i	0.231447	−	0.0538136i
$245$		−	4.14952i		−	0.265103i
$246$		0			0
$247$			5.23742i			0.333249i
$248$	5.21962	+	14.6310i	0.331446	+	0.929071i
$249$		0			0
$250$	4.82810	+	42.0843i	0.305356	+	2.66164i
$251$	−14.6109			−0.922231			−0.461115	−	0.887340i	$-0.652551\pi$
$251$	−14.6109			−0.922231			−0.461115	+	0.887340i	$0.652551\pi$
$252$		0			0
$253$	10.0608			0.632517
$254$	−0.711921	−	6.20548i	−0.0446699	−	0.389367i
$255$		0			0
$256$	9.77184	−	12.6693i	0.610740	−	0.791831i
$257$			22.6331i			1.41182i	0.708303	+	0.705908i	$0.249461\pi$
$257$			22.6331i			1.41182i	−0.708303	+	0.705908i	$0.750539\pi$
$258$		0			0
$259$			2.40281i			0.149303i
$260$	9.76756	+	42.0093i	0.605758	+	2.60531i
$261$		0			0
$262$	−11.2457	+	1.29016i	−0.694761	+	0.0797061i
$263$	−10.2002			−0.628971			−0.314485	−	0.949262i	$-0.601832\pi$
$263$	−10.2002			−0.628971			−0.314485	+	0.949262i	$0.601832\pi$
$264$		0			0
$265$	29.8074			1.83105
$266$	1.41593	−	0.162442i	0.0868164	−	0.00995997i
$267$		0			0
$268$	5.13581	+	22.0886i	0.313720	+	1.34928i
$269$		−	4.39618i		−	0.268040i	−0.990979	−	0.134020i	$-0.957211\pi$
$269$		−	4.39618i		−	0.268040i	0.990979	−	0.134020i	$-0.0427886\pi$
$270$		0			0
$271$		−	27.4633i		−	1.66828i	−0.551555	−	0.834138i	$-0.685965\pi$
$271$		−	27.4633i		−	1.66828i	0.551555	−	0.834138i	$-0.314035\pi$
$272$	−0.941791	−	1.91579i	−0.0571044	−	0.116162i
$273$		0			0
$274$	0.547515	+	4.77243i	0.0330766	+	0.288313i
$275$	−48.6396			−2.93308
$276$		0			0
$277$	−8.98720			−0.539989			−0.269994	−	0.962862i	$-0.587022\pi$
$277$	−8.98720			−0.539989			−0.269994	+	0.962862i	$0.587022\pi$
$278$	2.78361	+	24.2634i	0.166950	+	1.45522i
$279$		0			0
$280$	11.0542	−	3.94360i	0.660617	−	0.235675i
$281$			13.5116i			0.806036i	0.915192	+	0.403018i	$0.132039\pi$
$281$			13.5116i			0.806036i	−0.915192	+	0.403018i	$0.867961\pi$
$282$		0			0
$283$		−	18.3476i		−	1.09065i	−0.838224	−	0.545327i	$-0.816406\pi$
$283$		−	18.3476i		−	1.09065i	0.838224	−	0.545327i	$-0.183594\pi$
$284$	16.3040	−	3.79082i	0.967462	−	0.224944i
$285$		0			0
$286$	−29.0669	+	3.33469i	−1.71876	+	0.197184i
$287$	8.54069			0.504141
$288$		0			0
$289$	16.7152			0.983246
$290$	50.6178	−	5.80711i	2.97238	−	0.341005i
$291$		0			0
$292$	−3.71092	+	0.862823i	−0.217165	+	0.0504929i
$293$			19.0563i			1.11328i	0.830753	+	0.556641i	$0.187910\pi$
$293$			19.0563i			1.11328i	−0.830753	+	0.556641i	$0.812090\pi$
$294$		0			0
$295$		−	25.4084i		−	1.47934i
$296$	−6.40104	+	2.28357i	−0.372053	+	0.132730i
$297$		0			0
$298$	1.42114	+	12.3874i	0.0823245	+	0.717584i
$299$	13.1344			0.759583
$300$		0			0
$301$	−10.7165			−0.617690
$302$	2.26341	+	19.7291i	0.130245	+	1.13528i
$303$		0			0
$304$	1.77841	+	3.61763i	0.101999	+	0.207486i
$305$			7.70099i			0.440957i
$306$		0			0
$307$		−	18.2341i		−	1.04067i	−0.853961	−	0.520337i	$-0.825806\pi$
$307$		−	18.2341i		−	1.04067i	0.853961	−	0.520337i	$-0.174194\pi$
$308$	1.80306	+	7.75478i	0.102739	+	0.441870i
$309$		0			0
$310$	−32.0197	+	3.67345i	−1.81860	+	0.208638i
$311$	13.3214			0.755386			0.377693	−	0.925931i	$-0.376717\pi$
$311$	13.3214			0.755386			0.377693	+	0.925931i	$0.376717\pi$
$312$		0			0
$313$	4.87372			0.275479			0.137740	−	0.990468i	$-0.456016\pi$
$313$	4.87372			0.275479			0.137740	+	0.990468i	$0.456016\pi$
$314$	−4.30879	+	0.494324i	−0.243159	+	0.0278963i
$315$		0			0
$316$	0.753540	+	3.24090i	0.0423900	+	0.182315i
$317$		−	4.95411i		−	0.278251i	−0.990275	−	0.139125i	$-0.955571\pi$
$317$		−	4.95411i		−	0.278251i	0.990275	−	0.139125i	$-0.0444291\pi$
$318$		0			0
$319$			34.5623i			1.93512i
$320$	21.0113	+	25.7003i	1.17457	+	1.43669i
$321$		0			0
$322$	−0.407373	−	3.55088i	−0.0227020	−	0.197883i
$323$	0.537844			0.0299264
$324$		0			0
$325$	−63.4992			−3.52230
$326$	−0.657575	−	5.73177i	−0.0364197	−	0.317453i
$327$		0			0
$328$	8.11686	+	22.7522i	0.448179	+	1.25628i
$329$		−	9.11249i		−	0.502388i
$330$		0			0
$331$			9.08569i			0.499395i	0.968324	+	0.249697i	$0.0803311\pi$
$331$			9.08569i			0.499395i	−0.968324	+	0.249697i	$0.919669\pi$
$332$	−19.8795	+	4.62217i	−1.09103	+	0.253675i
$333$		0			0
$334$	−20.8188	+	2.38843i	−1.13916	+	0.130689i
$335$	−47.0510			−2.57067
$336$		0			0
$337$	−4.16659			−0.226969			−0.113484	−	0.993540i	$-0.536201\pi$
$337$	−4.16659			−0.226969			−0.113484	+	0.993540i	$0.536201\pi$
$338$	−19.6820	+	2.25801i	−1.07056	+	0.122819i
$339$		0			0
$340$	4.31404	−	1.00306i	0.233962	−	0.0543983i
$341$		−	21.8633i		−	1.18397i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−10.1847	−	28.5486i	−0.549123	−	1.53924i
$345$		0			0
$346$	1.14851	+	10.0110i	0.0617443	+	0.538196i
$347$	−4.91923			−0.264078			−0.132039	−	0.991245i	$-0.542152\pi$
$347$	−4.91923			−0.264078			−0.132039	+	0.991245i	$0.542152\pi$
$348$		0			0
$349$	−20.0372			−1.07257			−0.536283	−	0.844038i	$-0.680172\pi$
$349$	−20.0372			−1.07257			−0.536283	+	0.844038i	$0.680172\pi$
$350$	1.96947	+	17.1670i	0.105273	+	0.917613i
$351$		0			0
$352$	−18.9450	+	12.1733i	−1.00977	+	0.648837i
$353$			25.0065i			1.33096i	0.746416	+	0.665480i	$0.231773\pi$
$353$			25.0065i			1.33096i	−0.746416	+	0.665480i	$0.768227\pi$
$354$		0			0
$355$			34.7291i			1.84323i
$356$	−1.55361	−	6.68190i	−0.0823409	−	0.354140i
$357$		0			0
$358$	−17.5867	+	2.01762i	−0.929484	+	0.106635i
$359$	17.3984			0.918255			0.459127	−	0.888370i	$-0.348162\pi$
$359$	17.3984			0.918255			0.459127	+	0.888370i	$0.348162\pi$
$360$		0			0
$361$	17.9844			0.946546
$362$	−26.7512	+	3.06902i	−1.40601	+	0.161304i
$363$		0			0
$364$	2.35390	+	10.1239i	0.123378	+	0.530637i
$365$		−	7.90463i		−	0.413747i
$366$		0			0
$367$		−	6.19921i		−	0.323596i	−0.986824	−	0.161798i	$-0.948271\pi$
$367$		−	6.19921i		−	0.323596i	0.986824	−	0.161798i	$-0.0517293\pi$
$368$	9.07231	−	4.45990i	0.472927	−	0.232488i
$369$		0			0
$370$	−1.60712	−	14.0085i	−0.0835504	−	0.728269i
$371$	7.18334			0.372941
$372$		0			0
$373$	25.3319			1.31163			0.655817	−	0.754920i	$-0.272324\pi$
$373$	25.3319			1.31163			0.655817	+	0.754920i	$0.272324\pi$
$374$	0.342447	+	2.98495i	0.0177075	+	0.154348i
$375$		0			0
$376$	24.2755	−	8.66028i	1.25191	−	0.446620i
$377$			45.1212i			2.32386i
$378$		0			0
$379$			31.8299i			1.63499i	0.575935	+	0.817495i	$0.304638\pi$
$379$			31.8299i			1.63499i	−0.575935	+	0.817495i	$0.695362\pi$
$380$	−8.14632	+	1.89410i	−0.417898	+	0.0971651i
$381$		0			0
$382$	8.86581	−	1.01713i	0.453614	−	0.0520407i
$383$	5.45690			0.278835			0.139417	−	0.990234i	$-0.455477\pi$
$383$	5.45690			0.278835			0.139417	+	0.990234i	$0.455477\pi$
$384$		0			0
$385$	−16.5185			−0.841859
$386$	37.9507	−	4.35388i	1.93164	−	0.221607i
$387$		0			0
$388$	0.496240	−	0.115380i	0.0251927	−	0.00585755i
$389$			12.9961i			0.658931i	0.944168	+	0.329465i	$0.106868\pi$
$389$			12.9961i			0.658931i	−0.944168	+	0.329465i	$0.893132\pi$
$390$		0			0
$391$		−	1.34881i		−	0.0682120i
$392$	2.66398	−	0.950375i	0.134551	−	0.0480012i
$393$		0			0
$394$	1.43351	+	12.4953i	0.0722194	+	0.629502i
$395$	−6.90345			−0.347350
$396$		0			0
$397$	34.8712			1.75014			0.875068	−	0.483999i	$-0.160816\pi$
$397$	34.8712			1.75014			0.875068	+	0.483999i	$0.160816\pi$
$398$	−3.23350	−	28.1849i	−0.162081	−	1.41278i
$399$		0			0
$400$	−43.8607	+	21.5617i	−2.19303	+	1.07808i
$401$		−	5.77725i		−	0.288502i	−0.989541	−	0.144251i	$-0.953923\pi$
$401$		−	5.77725i		−	0.288502i	0.989541	−	0.144251i	$-0.0460773\pi$
$402$		0			0
$403$		−	28.5427i		−	1.42181i
$404$	−4.49069	−	19.3140i	−0.223420	−	0.960908i
$405$		0			0
$406$	12.1985	−	1.39947i	0.605401	−	0.0694543i
$407$	9.56515			0.474127
$408$		0			0
$409$	−2.72140			−0.134564			−0.0672822	−	0.997734i	$-0.521433\pi$
$409$	−2.72140			−0.134564			−0.0672822	+	0.997734i	$0.521433\pi$
$410$	−49.7928	+	5.71246i	−2.45909	+	0.282118i
$411$		0			0
$412$	0.593169	+	2.55116i	0.0292233	+	0.125687i
$413$		−	6.12323i		−	0.301304i
$414$		0			0
$415$		−	42.3454i		−	2.07865i
$416$	−24.7328	+	15.8922i	−1.21262	+	0.779182i
$417$		0			0
$418$	−0.646653	−	5.63657i	−0.0316288	−	0.275694i
$419$	7.14516			0.349064			0.174532	−	0.984652i	$-0.444159\pi$
$419$	7.14516			0.349064			0.174532	+	0.984652i	$0.444159\pi$
$420$		0			0
$421$	−27.9761			−1.36347			−0.681735	−	0.731599i	$-0.738774\pi$
$421$	−27.9761			−1.36347			−0.681735	+	0.731599i	$0.738774\pi$
$422$	3.69810	+	32.2346i	0.180021	+	1.56916i
$423$		0			0
$424$	6.82687	+	19.1363i	0.331542	+	0.929340i
$425$			6.52089i			0.316310i
$426$		0			0
$427$			1.85588i			0.0898121i
$428$	−6.35665	+	1.47798i	−0.307260	+	0.0714410i
$429$		0			0
$430$	62.4780	−	7.16777i	3.01296	−	0.345660i
$431$	35.9456			1.73144			0.865719	−	0.500530i	$-0.166861\pi$
$431$	35.9456			1.73144			0.865719	+	0.500530i	$0.166861\pi$
$432$		0			0
$433$	19.8194			0.952461			0.476231	−	0.879320i	$-0.342003\pi$
$433$	19.8194			0.952461			0.476231	+	0.879320i	$0.342003\pi$
$434$	−7.71649	+	0.885271i	−0.370403	+	0.0424943i
$435$		0			0
$436$	6.47626	−	1.50579i	0.310157	−	0.0721144i
$437$			2.54699i			0.121839i
$438$		0			0
$439$		−	10.4492i		−	0.498714i	−0.968412	−	0.249357i	$-0.919781\pi$
$439$		−	10.4492i		−	0.498714i	0.968412	−	0.249357i	$-0.0802193\pi$
$440$	−15.6987	−	44.0049i	−0.748408	−	2.09785i
$441$		0			0
$442$	0.447067	+	3.89687i	0.0212648	+	0.185355i
$443$	36.0756			1.71400			0.857001	−	0.515315i	$-0.172325\pi$
$443$	36.0756			1.71400			0.857001	+	0.515315i	$0.172325\pi$
$444$		0			0
$445$	14.2331			0.674715
$446$	−1.19676	−	10.4316i	−0.0566680	−	0.493948i
$447$		0			0
$448$	5.06356	+	6.19357i	0.239231	+	0.292619i
$449$		−	12.0203i		−	0.567274i	−0.958932	−	0.283637i	$-0.908459\pi$
$449$		−	12.0203i		−	0.567274i	0.958932	−	0.283637i	$-0.0915410\pi$
$450$		0			0
$451$		−	33.9989i		−	1.60095i
$452$	4.45321	+	19.1528i	0.209461	+	0.900872i
$453$		0			0
$454$	−22.4877	+	2.57990i	−1.05540	+	0.121081i
$455$	−21.5649			−1.01098
$456$		0			0
$457$	18.6654			0.873129			0.436565	−	0.899673i	$-0.356195\pi$
$457$	18.6654			0.873129			0.436565	+	0.899673i	$0.356195\pi$
$458$	28.2799	−	3.24440i	1.32143	−	0.151601i
$459$		0			0
$460$	4.75002	+	20.4294i	0.221471	+	0.952524i
$461$			13.8439i			0.644776i	0.946608	+	0.322388i	$0.104486\pi$
$461$			13.8439i			0.644776i	−0.946608	+	0.322388i	$0.895514\pi$
$462$		0			0
$463$		−	16.3908i		−	0.761744i	−0.924628	−	0.380872i	$-0.875624\pi$
$463$		−	16.3908i		−	0.761744i	0.924628	−	0.380872i	$-0.124376\pi$
$464$	15.3213	+	31.1665i	0.711273	+	1.44687i
$465$		0			0
$466$	3.35627	+	29.2550i	0.155476	+	1.35521i
$467$	22.0851			1.02198			0.510989	−	0.859587i	$-0.329279\pi$
$467$	22.0851			1.02198			0.510989	+	0.859587i	$0.329279\pi$
$468$		0			0
$469$	−11.3389			−0.523582
$470$	6.09490	+	53.1264i	0.281137	+	2.45054i
$471$		0			0
$472$	16.3122	−	5.81936i	0.750828	−	0.267858i
$473$			42.6605i			1.96153i
$474$		0			0
$475$		−	12.3136i		−	0.564986i
$476$	1.03965	−	0.241728i	0.0476522	−	0.0110796i
$477$		0			0
$478$	−20.5943	+	2.36267i	−0.941960	+	0.108066i
$479$	−29.6410			−1.35433			−0.677167	−	0.735830i	$-0.736792\pi$
$479$	−29.6410			−1.35433			−0.677167	+	0.735830i	$0.736792\pi$
$480$		0			0
$481$	12.4873			0.569374
$482$	5.25441	−	0.602810i	0.239332	−	0.0274572i
$483$		0			0
$484$	9.44197	−	2.19535i	0.429180	−	0.0997885i
$485$			1.05704i			0.0479978i
$486$		0			0
$487$			19.1492i			0.867732i	0.900977	+	0.433866i	$0.142851\pi$
$487$			19.1492i			0.867732i	−0.900977	+	0.433866i	$0.857149\pi$
$488$	−4.94402	+	1.76378i	−0.223805	+	0.0798425i
$489$		0			0
$490$	0.668852	+	5.83006i	0.0302156	+	0.263375i
$491$	18.7147			0.844584			0.422292	−	0.906460i	$-0.361226\pi$
$491$	18.7147			0.844584			0.422292	+	0.906460i	$0.361226\pi$
$492$		0			0
$493$	4.63361			0.208687
$494$	−0.844208	−	7.35857i	−0.0379827	−	0.331078i
$495$		0			0
$496$	−9.69190	−	19.7152i	−0.435179	−	0.885239i
$497$			8.36943i			0.375420i
$498$		0			0
$499$			33.2654i			1.48916i	0.667531	+	0.744582i	$0.267351\pi$
$499$			33.2654i			1.48916i	−0.667531	+	0.744582i	$0.732649\pi$
$500$	−13.5669	−	58.3501i	−0.606732	−	2.60950i
$501$		0			0
$502$	20.5283	−	2.35510i	0.916221	−	0.105113i
$503$	18.8753			0.841607			0.420804	−	0.907152i	$-0.361748\pi$
$503$	18.8753			0.841607			0.420804	+	0.907152i	$0.361748\pi$
$504$		0			0
$505$	41.1408			1.83074
$506$	−14.1354	+	1.62168i	−0.628395	+	0.0720924i
$507$		0			0
$508$	2.00050	+	8.60393i	0.0887577	+	0.381738i
$509$		−	38.5296i		−	1.70780i	−0.520441	−	0.853898i	$-0.674232\pi$
$509$		−	38.5296i		−	1.70780i	0.520441	−	0.853898i	$-0.325768\pi$
$510$		0			0
$511$		−	1.90495i		−	0.0842701i
$512$	−11.6873	+	19.3754i	−0.516509	+	0.856282i
$513$		0			0
$514$	−3.64819	−	31.7995i	−0.160915	−	1.40262i
$515$	−5.43423			−0.239461
$516$		0			0
$517$	−36.2751			−1.59538
$518$	−0.387304	−	3.37594i	−0.0170171	−	0.148330i
$519$		0			0
$520$	−20.4948	−	57.4486i	−0.898756	−	2.51929i
$521$			9.20407i			0.403238i	0.979464	+	0.201619i	$0.0646202\pi$
$521$			9.20407i			0.403238i	−0.979464	+	0.201619i	$0.935380\pi$
$522$		0			0
$523$		−	21.4903i		−	0.939706i	−0.882745	−	0.469853i	$-0.844307\pi$
$523$		−	21.4903i		−	0.939706i	0.882745	−	0.469853i	$-0.155693\pi$
$524$	15.5922	−	3.62533i	0.681149	−	0.158373i
$525$		0			0
$526$	14.3312	−	1.64415i	0.624872	−	0.0716882i
$527$	−2.93112			−0.127682
$528$		0			0
$529$	−16.6127			−0.722290
$530$	−41.8793	+	4.80459i	−1.81912	+	0.208698i
$531$		0			0
$532$	−1.96320	+	0.456462i	−0.0851154	+	0.0197901i
$533$		−	44.3858i		−	1.92256i
$534$		0			0
$535$		−	13.5403i		−	0.585399i
$536$	−10.7762	−	30.2066i	−0.465462	−	1.30473i
$537$		0			0
$538$	0.708611	+	6.17663i	0.0305504	+	0.266293i
$539$	−3.98082			−0.171466
$540$		0			0
$541$	−7.69148			−0.330682			−0.165341	−	0.986236i	$-0.552873\pi$
$541$	−7.69148			−0.330682			−0.165341	+	0.986236i	$0.552873\pi$
$542$	4.42675	+	38.5859i	0.190145	+	1.65741i
$543$		0			0
$544$	1.63201	+	2.53987i	0.0699721	+	0.108896i
$545$			13.7951i			0.590917i
$546$		0			0
$547$			24.5636i			1.05026i	0.851021	+	0.525131i	$0.175984\pi$
$547$			24.5636i			1.05026i	−0.851021	+	0.525131i	$0.824016\pi$
$548$	−1.53852	−	6.61700i	−0.0657221	−	0.282664i
$549$		0			0
$550$	68.3385	−	7.84011i	2.91397	−	0.334303i
$551$	−8.74978			−0.372753
$552$		0			0
$553$	−1.66368			−0.0707467
$554$	12.6270	−	1.44863i	0.536470	−	0.0615463i
$555$		0			0
$556$	−7.82192	−	33.6413i	−0.331723	−	1.42671i
$557$			17.7138i			0.750556i	0.926912	+	0.375278i	$0.122453\pi$
$557$			17.7138i			0.750556i	−0.926912	+	0.375278i	$0.877547\pi$
$558$		0			0
$559$			55.6935i			2.35559i
$560$	−14.8955	+	7.32255i	−0.629450	+	0.309434i
$561$		0			0
$562$	−2.17791	−	18.9838i	−0.0918696	−	0.800784i
$563$	13.1471			0.554082			0.277041	−	0.960858i	$-0.410646\pi$
$563$	13.1471			0.554082			0.277041	+	0.960858i	$0.410646\pi$
$564$		0			0
$565$	−40.7974			−1.71636
$566$	2.95741	+	25.7784i	0.124309	+	1.08355i
$567$		0			0
$568$	−22.2960	+	7.95410i	−0.935519	+	0.333747i
$569$		−	31.3324i		−	1.31352i	−0.754099	−	0.656761i	$-0.771926\pi$
$569$		−	31.3324i		−	1.31352i	0.754099	−	0.656761i	$-0.228074\pi$
$570$		0			0
$571$			31.4655i			1.31679i	0.752672	+	0.658396i	$0.228765\pi$
$571$			31.4655i			1.31679i	−0.752672	+	0.658396i	$0.771235\pi$
$572$	40.3014	−	9.37046i	1.68509	−	0.391798i
$573$		0			0
$574$	−11.9997	+	1.37666i	−0.500856	+	0.0574605i
$575$	−30.8800			−1.28779
$576$		0			0
$577$	−34.5088			−1.43662			−0.718309	−	0.695724i	$-0.755084\pi$
$577$	−34.5088			−1.43662			−0.718309	+	0.695724i	$0.755084\pi$
$578$	−23.4848	+	2.69428i	−0.976838	+	0.112067i
$579$		0			0
$580$	−70.1819	+	16.3179i	−2.91414	+	0.677566i
$581$		−	10.2049i		−	0.423370i
$582$		0			0
$583$		−	28.5956i		−	1.18431i
$584$	5.07475	−	1.81042i	0.209995	−	0.0749156i
$585$		0			0
$586$	−3.07164	−	26.7741i	−0.126888	−	1.10603i
$587$	−22.5074			−0.928978			−0.464489	−	0.885579i	$-0.653762\pi$
$587$	−22.5074			−0.928978			−0.464489	+	0.885579i	$0.653762\pi$
$588$		0			0
$589$	5.53491			0.228062
$590$	4.09553	+	35.6988i	0.168610	+	1.46970i
$591$		0			0
$592$	8.62536	−	4.24018i	0.354500	−	0.174270i
$593$		−	16.9215i		−	0.694885i	−0.937701	−	0.347442i	$-0.887050\pi$
$593$		−	16.9215i		−	0.694885i	0.937701	−	0.347442i	$-0.112950\pi$
$594$		0			0
$595$			2.21456i			0.0907880i
$596$	−3.99340	−	17.1752i	−0.163576	−	0.703525i
$597$		0			0
$598$	−18.4538	+	2.11711i	−0.754633	+	0.0865749i
$599$	24.7753			1.01229			0.506146	−	0.862448i	$-0.331070\pi$
$599$	24.7753			1.01229			0.506146	+	0.862448i	$0.331070\pi$
$600$		0			0
$601$	30.2498			1.23392			0.616958	−	0.786996i	$-0.288365\pi$
$601$	30.2498			1.23392			0.616958	+	0.786996i	$0.288365\pi$
$602$	15.0567	−	1.72737i	0.613665	−	0.0704025i
$603$		0			0
$604$	−6.36017	−	27.3545i	−0.258792	−	1.11304i
$605$			20.1124i			0.817683i
$606$		0			0
$607$		−	17.1889i		−	0.697677i	−0.937183	−	0.348838i	$-0.886576\pi$
$607$		−	17.1889i		−	0.697677i	0.937183	−	0.348838i	$-0.113424\pi$
$608$	−3.08178	−	4.79611i	−0.124983	−	0.194508i
$609$		0			0
$610$	−1.24131	−	10.8199i	−0.0502590	−	0.438084i
$611$	−47.3574			−1.91587
$612$		0			0
$613$	−7.56051			−0.305366			−0.152683	−	0.988275i	$-0.548791\pi$
$613$	−7.56051			−0.305366			−0.152683	+	0.988275i	$0.548791\pi$
$614$	2.93911	+	25.6188i	0.118613	+	1.03389i
$615$		0			0
$616$	−3.78327	−	10.6048i	−0.152432	−	0.427280i
$617$		−	1.27971i		−	0.0515192i	−0.999668	−	0.0257596i	$-0.991800\pi$
$617$		−	1.27971i		−	0.0515192i	0.999668	−	0.0257596i	$-0.00820045\pi$
$618$		0			0
$619$		−	17.2766i		−	0.694407i	−0.937790	−	0.347203i	$-0.887131\pi$
$619$		−	17.2766i		−	0.694407i	0.937790	−	0.347203i	$-0.112869\pi$
$620$	44.3955	−	10.3224i	1.78297	−	0.414556i
$621$		0			0
$622$	−18.7165	+	2.14724i	−0.750464	+	0.0860966i
$623$	3.43007			0.137423
$624$		0			0
$625$	63.1992			2.52797
$626$	−6.84757	+	0.785585i	−0.273684	+	0.0313983i
$627$		0			0
$628$	5.97416	−	1.38905i	0.238395	−	0.0554291i
$629$		−	1.28236i		−	0.0511309i
$630$		0			0
$631$		−	21.5223i		−	0.856790i	−0.903592	−	0.428395i	$-0.859079\pi$
$631$		−	21.5223i		−	0.856790i	0.903592	−	0.428395i	$-0.140921\pi$
$632$	−1.58112	−	4.43200i	−0.0628934	−	0.176295i
$633$		0			0
$634$	0.798542	+	6.96052i	0.0317142	+	0.276437i
$635$	−18.3273			−0.727295
$636$		0			0
$637$	−5.19698			−0.205912
$638$	−5.57102	−	48.5599i	−0.220559	−	1.92251i
$639$		0			0
$640$	−33.6635	−	32.7222i	−1.33066	−	1.29346i
$641$			16.3691i			0.646541i	0.946307	+	0.323271i	$0.104782\pi$
$641$			16.3691i			0.646541i	−0.946307	+	0.323271i	$0.895218\pi$
$642$		0			0
$643$		−	25.7448i		−	1.01527i	−0.861571	−	0.507637i	$-0.830519\pi$
$643$		−	25.7448i		−	1.01527i	0.861571	−	0.507637i	$-0.169481\pi$
$644$	1.14472	+	4.92331i	0.0451081	+	0.194006i
$645$		0			0
$646$	−0.755670	+	0.0866939i	−0.0297314	+	0.00341093i
$647$	−29.9862			−1.17888			−0.589439	−	0.807813i	$-0.700651\pi$
$647$	−29.9862			−1.17888			−0.589439	+	0.807813i	$0.700651\pi$
$648$		0			0
$649$	−24.3755			−0.956820
$650$	89.2163	−	10.2353i	3.49935	−	0.401461i
$651$		0			0
$652$	1.84778	+	7.94713i	0.0723648	+	0.311234i
$653$		−	10.3759i		−	0.406041i	−0.979175	−	0.203020i	$-0.934924\pi$
$653$		−	10.3759i		−	0.406041i	0.979175	−	0.203020i	$-0.0650758\pi$
$654$		0			0
$655$			33.2130i			1.29774i
$656$	−15.0716	−	30.6585i	−0.588445	−	1.19701i
$657$		0			0
$658$	1.46882	+	12.8030i	0.0572606	+	0.499114i
$659$	−12.1897			−0.474844			−0.237422	−	0.971407i	$-0.576302\pi$
$659$	−12.1897			−0.474844			−0.237422	+	0.971407i	$0.576302\pi$
$660$		0			0
$661$	−9.68779			−0.376811			−0.188406	−	0.982091i	$-0.560332\pi$
$661$	−9.68779			−0.376811			−0.188406	+	0.982091i	$0.560332\pi$
$662$	−1.46450	−	12.7654i	−0.0569195	−	0.496140i
$663$		0			0
$664$	27.1856	−	9.69848i	1.05501	−	0.376374i
$665$		−	4.18181i		−	0.162164i
$666$		0			0
$667$			21.9427i			0.849625i
$668$	28.8654	−	6.71149i	1.11684	−	0.259675i
$669$		0			0
$670$	66.1066	−	7.58405i	2.55392	−	0.292997i
$671$	7.38790			0.285207
$672$		0			0
$673$	−14.5269			−0.559969			−0.279985	−	0.960004i	$-0.590329\pi$
$673$	−14.5269			−0.559969			−0.279985	+	0.960004i	$0.590329\pi$
$674$	5.85406	−	0.671604i	0.225490	−	0.0258692i
$675$		0			0
$676$	27.2892	−	6.34499i	1.04958	−	0.244038i
$677$			9.71184i			0.373257i	0.982431	+	0.186628i	$0.0597560\pi$
$677$			9.71184i			0.373257i	−0.982431	+	0.186628i	$0.940244\pi$
$678$		0			0
$679$			0.254738i			0.00977596i
$680$	−5.89954	+	2.10466i	−0.226237	+	0.0807100i
$681$		0			0
$682$	3.52410	+	30.7179i	0.134945	+	1.17625i
$683$	−46.7961			−1.79060			−0.895302	−	0.445459i	$-0.853040\pi$
$683$	−46.7961			−1.79060			−0.895302	+	0.445459i	$0.853040\pi$
$684$		0			0
$685$	14.0949			0.538538
$686$	0.161188	+	1.40500i	0.00615418	+	0.0536431i
$687$		0			0
$688$	18.9112	+	38.4691i	0.720983	+	1.46662i
$689$		−	37.3317i		−	1.42222i
$690$		0			0
$691$			8.55307i			0.325374i	0.986678	+	0.162687i	$0.0520161\pi$
$691$			8.55307i			0.325374i	−0.986678	+	0.162687i	$0.947984\pi$
$692$	−3.22731	−	13.8803i	−0.122684	−	0.527651i
$693$		0			0
$694$	6.91151	−	0.792920i	0.262357	−	0.0300988i
$695$	71.6594			2.71820
$696$		0			0
$697$	−4.55809			−0.172650
$698$	28.1522	−	3.22975i	1.06558	−	0.122248i
$699$		0			0
$700$	−5.53421	−	23.8021i	−0.209173	−	0.899634i
$701$			15.0026i			0.566640i	0.959025	+	0.283320i	$0.0914358\pi$
$701$			15.0026i			0.566640i	−0.959025	+	0.283320i	$0.908564\pi$
$702$		0			0
$703$			2.42151i			0.0913290i
$704$	24.6555	−	20.1571i	0.929239	−	0.759700i
$705$		0			0
$706$	−4.03074	−	35.1340i	−0.151699	−	1.32229i
$707$	9.91460			0.372877
$708$		0			0
$709$	40.8883			1.53559			0.767797	−	0.640693i	$-0.221353\pi$
$709$	40.8883			1.53559			0.767797	+	0.640693i	$0.221353\pi$
$710$	−5.59791	−	48.7943i	−0.210086	−	1.83122i
$711$		0			0
$712$	3.25985	+	9.13764i	0.122168	+	0.342447i
$713$		−	13.8805i		−	0.519827i
$714$		0			0
$715$			85.8461i			3.21046i
$716$	24.3840	−	5.66951i	0.911273	−	0.211879i
$717$		0			0
$718$	−24.4448	+	2.80442i	−0.912271	+	0.104660i
$719$	5.07004			0.189081			0.0945404	−	0.995521i	$-0.469862\pi$
$719$	5.07004			0.189081			0.0945404	+	0.995521i	$0.469862\pi$
$720$		0			0
$721$	−1.30961			−0.0487723
$722$	−25.2680	+	2.89886i	−0.940378	+	0.107884i
$723$		0			0
$724$	37.0907	−	8.62394i	1.37847	−	0.320506i
$725$		−	106.084i		−	3.93984i
$726$		0			0
$727$			24.6808i			0.915359i	0.889117	+	0.457680i	$0.151319\pi$
$727$			24.6808i			0.915359i	−0.889117	+	0.457680i	$0.848681\pi$
$728$	−4.93908	−	13.8446i	−0.183054	−	0.513116i
$729$		0			0
$730$	1.27413	+	11.1060i	0.0471577	+	0.411051i
$731$	5.71931			0.211536
$732$		0			0
$733$	−39.8279			−1.47108			−0.735539	−	0.677482i	$-0.763071\pi$
$733$	−39.8279			−1.47108			−0.735539	+	0.677482i	$0.763071\pi$
$734$	0.999236	+	8.70987i	0.0368825	+	0.321487i
$735$		0			0
$736$	−12.0277	+	7.72849i	−0.443347	+	0.284876i
$737$			45.1381i			1.66268i
$738$		0			0
$739$		−	1.24747i		−	0.0458890i	−0.999737	−	0.0229445i	$-0.992696\pi$
$739$		−	1.24747i		−	0.0458890i	0.999737	−	0.0229445i	$-0.00730409\pi$
$740$	4.51601	+	19.4229i	0.166012	+	0.714000i
$741$		0			0
$742$	−10.0926	+	1.15787i	−0.370510	+	0.0425066i
$743$	−8.49940			−0.311813			−0.155906	−	0.987772i	$-0.549830\pi$
$743$	−8.49940			−0.311813			−0.155906	+	0.987772i	$0.549830\pi$
$744$		0			0
$745$	36.5850			1.34037
$746$	−35.5912	+	4.08319i	−1.30309	+	0.149496i
$747$		0			0
$748$	−0.962276	−	4.13865i	−0.0351843	−	0.151324i
$749$		−	3.26311i		−	0.119231i
$750$		0			0
$751$		−	13.9330i		−	0.508423i	−0.967149	−	0.254211i	$-0.918184\pi$
$751$		−	13.9330i		−	0.508423i	0.967149	−	0.254211i	$-0.0818159\pi$
$752$	−32.7111	+	16.0806i	−1.19285	+	0.586399i
$753$		0			0
$754$	−7.27299	−	63.3952i	−0.264867	−	2.30872i
$755$	58.2678			2.12058
$756$		0			0
$757$	19.7441			0.717610			0.358805	−	0.933413i	$-0.383184\pi$
$757$	19.7441			0.717610			0.358805	+	0.933413i	$0.383184\pi$
$758$	−5.13059	−	44.7209i	−0.186351	−	1.62434i
$759$		0			0
$760$	11.1403	−	3.97429i	0.404100	−	0.144163i
$761$		−	0.477389i		−	0.0173054i	−0.999963	−	0.00865268i	$-0.997246\pi$
$761$		−	0.477389i		−	0.0173054i	0.999963	−	0.00865268i	$-0.00275427\pi$
$762$		0			0
$763$			3.32451i			0.120355i
$764$	−12.2925	+	2.85812i	−0.444727	+	0.103403i
$765$		0			0
$766$	−7.66694	+	0.879586i	−0.277018	+	0.0317807i
$767$	−31.8223			−1.14904
$768$		0			0
$769$	−23.1072			−0.833267			−0.416634	−	0.909074i	$-0.636790\pi$
$769$	−23.1072			−0.833267			−0.416634	+	0.909074i	$0.636790\pi$
$770$	23.2084	−	2.66258i	0.836373	−	0.0959526i
$771$		0			0
$772$	−52.6189	+	12.2344i	−1.89379	+	0.440325i
$773$		−	45.0472i		−	1.62024i	−0.586268	−	0.810118i	$-0.699403\pi$
$773$		−	45.0472i		−	1.62024i	0.586268	−	0.810118i	$-0.300597\pi$
$774$		0			0
$775$			67.1060i			2.41052i
$776$	−0.678618	+	0.242097i	−0.0243609	+	0.00869077i
$777$		0			0
$778$	−2.09482	−	18.2596i	−0.0751029	−	0.654637i
$779$	8.60716			0.308384
$780$		0			0
$781$	33.3172			1.19218
$782$	0.217411	+	1.89507i	0.00777460	+	0.0677675i
$783$		0			0
$784$	−3.58970	+	1.76468i	−0.128203	+	0.0630241i
$785$			12.7256i			0.454195i
$786$		0			0
$787$			38.1474i			1.35981i	0.733302	+	0.679903i	$0.237978\pi$
$787$			38.1474i			1.35981i	−0.733302	+	0.679903i	$0.762022\pi$
$788$	−4.02817	−	17.3247i	−0.143497	−	0.617169i
$789$		0			0
$790$	9.69934	−	1.11275i	0.345087	−	0.0395899i
$791$	−9.83185			−0.349580
$792$		0			0
$793$	9.64494			0.342502
$794$	−48.9940	+	5.62082i	−1.73873	+	0.199475i
$795$		0			0
$796$	9.08612	+	39.0785i	0.322049	+	1.38510i
$797$			19.2743i			0.682732i	0.939930	+	0.341366i	$0.110890\pi$
$797$			19.2743i			0.682732i	−0.939930	+	0.341366i	$0.889110\pi$
$798$		0			0
$799$			4.86325i			0.172049i
$800$	58.1487	−	37.3639i	2.05587	−	1.32101i
$801$		0			0
$802$	0.931221	+	8.11702i	0.0328826	+	0.286622i
$803$	−7.58327			−0.267608
$804$		0			0
$805$	−10.4872			−0.369624
$806$	4.60073	+	40.1024i	0.162054	+	1.41255i
$807$		0			0
$808$	9.42259	+	26.4123i	0.331486	+	0.929181i
$809$		−	29.0701i		−	1.02205i	−0.859566	−	0.511025i	$-0.829266\pi$
$809$		−	29.0701i		−	1.02205i	0.859566	−	0.511025i	$-0.170734\pi$
$810$		0			0
$811$		−	41.5526i		−	1.45911i	−0.683922	−	0.729555i	$-0.739727\pi$
$811$		−	41.5526i		−	1.45911i	0.683922	−	0.729555i	$-0.260273\pi$
$812$	−16.9133	+	3.93249i	−0.593539	+	0.138003i
$813$		0			0
$814$	−13.4390	+	1.54179i	−0.471037	+	0.0540395i
$815$	−16.9282			−0.592969
$816$		0			0
$817$	−10.7999			−0.377842
$818$	3.82356	−	0.438656i	0.133688	−	0.0153373i
$819$		0			0
$820$	69.0380	−	16.0520i	2.41091	−	0.560559i
$821$		−	45.4926i		−	1.58770i	−0.608112	−	0.793852i	$-0.708073\pi$
$821$		−	45.4926i		−	1.58770i	0.608112	−	0.793852i	$-0.291927\pi$
$822$		0			0
$823$		−	30.0184i		−	1.04638i	−0.852217	−	0.523188i	$-0.824742\pi$
$823$		−	30.0184i		−	1.04638i	0.852217	−	0.523188i	$-0.175258\pi$
$824$	−1.24462	−	3.48876i	−0.0433583	−	0.121537i
$825$		0			0
$826$	0.986989	+	8.60312i	0.0343418	+	0.299341i
$827$	−8.47824			−0.294817			−0.147409	−	0.989076i	$-0.547093\pi$
$827$	−8.47824			−0.294817			−0.147409	+	0.989076i	$0.547093\pi$
$828$		0			0
$829$	−49.6587			−1.72472			−0.862359	−	0.506298i	$-0.831014\pi$
$829$	−49.6587			−1.72472			−0.862359	+	0.506298i	$0.831014\pi$
$830$	6.82556	+	59.4952i	0.236919	+	2.06511i
$831$		0			0
$832$	32.1879	−	26.3152i	1.11591	−	0.912315i
$833$			0.533690i			0.0184913i
$834$		0			0
$835$			61.4863i			2.12782i
$836$	1.81709	+	7.81513i	0.0628455	+	0.270292i
$837$		0			0
$838$	−10.0389	+	1.15171i	−0.346789	+	0.0397852i
$839$	−2.53602			−0.0875532			−0.0437766	−	0.999041i	$-0.513939\pi$
$839$	−2.53602			−0.0875532			−0.0437766	+	0.999041i	$0.513939\pi$
$840$		0			0
$841$	−46.3807			−1.59934
$842$	39.3063	−	4.50940i	1.35458	−	0.155404i
$843$		0			0
$844$	−10.3916	−	44.6934i	−0.357695	−	1.53841i
$845$			58.1287i			1.99969i
$846$		0			0
$847$			4.84691i			0.166542i
$848$	−12.6763	−	25.7860i	−0.435305	−	0.885495i
$849$		0			0
$850$	−1.05109	−	9.16184i	−0.0360520	−	0.314249i
$851$	6.07267			0.208168
$852$		0			0
$853$	12.9593			0.443719			0.221860	−	0.975079i	$-0.428787\pi$
$853$	12.9593			0.443719			0.221860	+	0.975079i	$0.428787\pi$
$854$	−0.299145	−	2.60750i	−0.0102365	−	0.0892269i
$855$		0			0
$856$	8.69285	−	3.10118i	0.297116	−	0.105996i
$857$		−	31.2435i		−	1.06726i	−0.845719	−	0.533629i	$-0.820828\pi$
$857$		−	31.2435i		−	1.06726i	0.845719	−	0.533629i	$-0.179172\pi$
$858$		0			0
$859$			9.35430i			0.319164i	0.987185	+	0.159582i	$0.0510147\pi$
$859$			9.35430i			0.319164i	−0.987185	+	0.159582i	$0.948985\pi$
$860$	−86.6261	+	20.1414i	−2.95393	+	0.686816i
$861$		0			0
$862$	−50.5035	+	5.79399i	−1.72016	+	0.197344i
$863$	40.9621			1.39437			0.697184	−	0.716892i	$-0.254436\pi$
$863$	40.9621			1.39437			0.697184	+	0.716892i	$0.254436\pi$
$864$		0			0
$865$	29.5665			1.00529
$866$	−27.8463	+	3.19465i	−0.946254	+	0.108559i
$867$		0			0
$868$	10.6989	−	2.48761i	0.363146	−	0.0844349i
$869$			6.62279i			0.224663i
$870$		0			0
$871$			58.9280i			1.99670i
$872$	−8.85642	+	3.15953i	−0.299916	+	0.106995i
$873$		0			0
$874$	−0.410543	−	3.57851i	−0.0138868	−	0.121045i
$875$	29.9533			1.01261
$876$		0			0
$877$	−9.86549			−0.333134			−0.166567	−	0.986030i	$-0.553268\pi$
$877$	−9.86549			−0.333134			−0.166567	+	0.986030i	$0.553268\pi$
$878$	1.68429	+	14.6811i	0.0568419	+	0.495464i
$879$		0			0
$880$	29.1498	+	59.2963i	0.982638	+	1.99888i
$881$			8.83151i			0.297541i	0.988872	+	0.148771i	$0.0475316\pi$
$881$			8.83151i			0.297541i	−0.988872	+	0.148771i	$0.952468\pi$
$882$		0			0
$883$		−	43.2944i		−	1.45697i	−0.685061	−	0.728485i	$-0.740225\pi$
$883$		−	43.2944i		−	1.45697i	0.685061	−	0.728485i	$-0.259775\pi$
$884$	−1.25625	−	5.40303i	−0.0422524	−	0.181724i
$885$		0			0
$886$	−50.6861	+	5.81494i	−1.70283	+	0.195357i
$887$	10.0850			0.338622			0.169311	−	0.985563i	$-0.445846\pi$
$887$	10.0850			0.338622			0.169311	+	0.985563i	$0.445846\pi$
$888$		0			0
$889$	−4.41672			−0.148132
$890$	−19.9975	+	2.29421i	−0.670319	+	0.0769020i
$891$		0			0
$892$	3.36288	+	14.4634i	0.112597	+	0.484271i
$893$		−	9.18341i		−	0.307311i
$894$		0			0
$895$			51.9404i			1.73618i
$896$	−8.11262	−	7.88577i	−0.271024	−	0.263445i
$897$		0			0
$898$	1.93753	+	16.8885i	0.0646561	+	0.563577i
$899$	47.6842			1.59036
$900$		0			0
$901$	−3.83368			−0.127718
$902$	5.48022	+	47.7684i	0.182471	+	1.59052i
$903$		0			0
$904$	−9.34395	−	26.1918i	−0.310775	−	0.871128i
$905$			79.0070i			2.62628i
$906$		0			0
$907$			22.5872i			0.749996i	0.927026	+	0.374998i	$0.122357\pi$
$907$			22.5872i			0.749996i	−0.927026	+	0.374998i	$0.877643\pi$
$908$	31.1794	−	7.24950i	1.03472	−	0.240583i
$909$		0			0
$910$	30.2987	−	3.47600i	1.00439	−	0.115228i
$911$	38.1571			1.26420			0.632101	−	0.774886i	$-0.282193\pi$
$911$	38.1571			1.26420			0.632101	+	0.774886i	$0.282193\pi$
$912$		0			0
$913$	−40.6238			−1.34445
$914$	−26.2248	+	3.00863i	−0.867439	+	0.0995166i
$915$		0			0
$916$	−39.2102	+	9.11674i	−1.29554	+	0.301226i
$917$			8.00406i			0.264317i
$918$		0			0
$919$			53.4322i			1.76257i	0.472590	+	0.881283i	$0.343319\pi$
$919$			53.4322i			1.76257i	−0.472590	+	0.881283i	$0.656681\pi$
$920$	−9.96673	−	27.9376i	−0.328593	−	0.921074i
$921$		0			0
$922$	−2.23147	−	19.4507i	−0.0734896	−	0.640574i
$923$	43.4957			1.43168
$924$		0			0
$925$	−29.3587			−0.965309
$926$	2.64199	+	23.0290i	0.0868213	+	0.756780i
$927$		0			0
$928$	−26.5500	−	41.3192i	−0.871547	−	1.35637i
$929$			8.33847i			0.273576i	0.990600	+	0.136788i	$0.0436780\pi$
$929$			8.33847i			0.273576i	−0.990600	+	0.136788i	$0.956322\pi$
$930$		0			0
$931$		−	1.00778i		−	0.0330287i
$932$	−9.43109	−	40.5622i	−0.308926	−	1.32866i
$933$		0			0
$934$	−31.0296	+	3.55985i	−1.01532	+	0.116482i
$935$	8.81575			0.288306
$936$		0			0
$937$	−45.5957			−1.48955			−0.744773	−	0.667317i	$-0.767442\pi$
$937$	−45.5957			−1.48955			−0.744773	+	0.667317i	$0.767442\pi$
$938$	15.9311	−	1.82769i	0.520170	−	0.0596763i
$939$		0			0
$940$	−17.1266	−	73.6600i	−0.558609	−	2.40252i
$941$			4.57919i			0.149277i	0.997211	+	0.0746387i	$0.0237803\pi$
$941$			4.57919i			0.149277i	−0.997211	+	0.0746387i	$0.976220\pi$
$942$		0			0
$943$		−	21.5851i		−	0.702906i
$944$	−21.9805	+	10.8055i	−0.715405	+	0.351689i
$945$		0			0
$946$	−6.87636	−	59.9380i	−0.223570	−	1.94875i
$947$	−14.2142			−0.461900			−0.230950	−	0.972966i	$-0.574183\pi$
$947$	−14.2142			−0.461900			−0.230950	+	0.972966i	$0.574183\pi$
$948$		0			0
$949$	−9.89999			−0.321367
$950$	1.98480	+	17.3006i	0.0643954	+	0.561304i
$951$		0			0
$952$	−1.42174	+	0.507206i	−0.0460789	+	0.0164386i
$953$			35.4431i			1.14811i	0.818815	+	0.574057i	$0.194631\pi$
$953$			35.4431i			1.14811i	−0.818815	+	0.574057i	$0.805369\pi$
$954$		0			0
$955$		−	26.1843i		−	0.847303i
$956$	28.5541	−	6.63909i	0.923504	−	0.214723i
$957$		0			0
$958$	41.6456	−	4.77777i	1.34551	−	0.154363i
$959$	3.39675			0.109687
$960$		0			0
$961$	0.836077			0.0269702
$962$	−17.5447	+	2.01281i	−0.565663	+	0.0648955i
$963$		0			0
$964$	−7.28527	+	1.69389i	−0.234643	+	0.0545566i
$965$		−	112.084i		−	3.60810i
$966$		0			0
$967$		−	59.2999i		−	1.90696i	−0.301461	−	0.953479i	$-0.597474\pi$
$967$		−	59.2999i		−	1.90696i	0.301461	−	0.953479i	$-0.402526\pi$
$968$	−12.9121	+	4.60639i	−0.415010	+	0.148055i
$969$		0			0
$970$	−0.170382	−	1.48514i	−0.00547064	−	0.0476850i
$971$	0.0598654			0.00192117			0.000960586	−	1.00000i	$-0.499694\pi$
$971$	0.0598654			0.00192117			0.000960586		1.00000i	$0.499694\pi$
$972$		0			0
$973$	17.2693			0.553629
$974$	−3.08661	−	26.9046i	−0.0989015	−	0.862078i
$975$		0			0
$976$	6.66203	−	3.27502i	0.213246	−	0.104831i
$977$			48.2568i			1.54387i	0.635700	+	0.771936i	$0.280712\pi$
$977$			48.2568i			1.54387i	−0.635700	+	0.771936i	$0.719288\pi$
$978$		0			0
$979$		−	13.6545i		−	0.436399i
$980$	−1.87947	−	8.08341i	−0.0600375	−	0.258215i
$981$		0			0
$982$	−26.2941	+	3.01659i	−0.839080	+	0.0962631i
$983$	−46.2908			−1.47645			−0.738224	−	0.674556i	$-0.764335\pi$
$983$	−46.2908			−1.47645			−0.738224	+	0.674556i	$0.764335\pi$
$984$		0			0
$985$	36.9035			1.17584
$986$	−6.51021	+	0.746882i	−0.207327	+	0.0237856i
$987$		0			0
$988$	2.37222	+	10.2027i	0.0754704	+	0.324591i
$989$			27.0841i			0.861224i
$990$		0			0
$991$			29.3907i			0.933626i	0.884356	+	0.466813i	$0.154598\pi$
$991$			29.3907i			0.933626i	−0.884356	+	0.466813i	$0.845402\pi$
$992$	16.7949	+	26.1376i	0.533240	+	0.829870i
$993$		0			0
$994$	−1.34905	−	11.7590i	−0.0427893	−	0.372974i
$995$	−83.2412			−2.63892
$996$		0			0
$997$	15.2550			0.483132			0.241566	−	0.970384i	$-0.422339\pi$
$997$	15.2550			0.483132			0.241566	+	0.970384i	$0.422339\pi$
$998$	−5.36198	−	46.7378i	−0.169730	−	1.47946i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.b.323.2	yes	24
3.2	odd	2	inner	756.2.e.b.323.23	yes	24
4.3	odd	2	inner	756.2.e.b.323.24	yes	24
12.11	even	2	inner	756.2.e.b.323.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.b.323.1	✓	24	12.11	even	2	inner
756.2.e.b.323.2	yes	24	1.1	even	1	trivial
756.2.e.b.323.23	yes	24	3.2	odd	2	inner
756.2.e.b.323.24	yes	24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40500 + 0.161188i) q^{2} +(1.94804 - 0.452937i) q^{4} +4.14952i q^{5} +1.00000i q^{7} +(-2.66398 + 0.950375i) q^{8} +O(q^{10})\)	\(q+(-1.40500 + 0.161188i) q^{2} +(1.94804 - 0.452937i) q^{4} +4.14952i q^{5} +1.00000i q^{7} +(-2.66398 + 0.950375i) q^{8} +(-0.668852 - 5.83006i) q^{10} +3.98082 q^{11} +5.19698 q^{13} +(-0.161188 - 1.40500i) q^{14} +(3.58970 - 1.76468i) q^{16} -0.533690i q^{17} +1.00778i q^{19} +(1.87947 + 8.08341i) q^{20} +(-5.59304 + 0.641659i) q^{22} +2.52732 q^{23} -12.2185 q^{25} +(-7.30174 + 0.837689i) q^{26} +(0.452937 + 1.94804i) q^{28} +8.68221i q^{29} -5.49217i q^{31} +(-4.75907 + 3.05798i) q^{32} +(0.0860244 + 0.749834i) q^{34} -4.14952 q^{35} +2.40281 q^{37} +(-0.162442 - 1.41593i) q^{38} +(-3.94360 - 11.0542i) q^{40} -8.54069i q^{41} +10.7165i q^{43} +(7.75478 - 1.80306i) q^{44} +(-3.55088 + 0.407373i) q^{46} -9.11249 q^{47} -1.00000 q^{49} +(17.1670 - 1.96947i) q^{50} +(10.1239 - 2.35390i) q^{52} -7.18334i q^{53} +16.5185i q^{55} +(-0.950375 - 2.66398i) q^{56} +(-1.39947 - 12.1985i) q^{58} -6.12323 q^{59} +1.85588 q^{61} +(0.885271 + 7.71649i) q^{62} +(6.19357 - 5.06356i) q^{64} +21.5649i q^{65} +11.3389i q^{67} +(-0.241728 - 1.03965i) q^{68} +(5.83006 - 0.668852i) q^{70} +8.36943 q^{71} -1.90495 q^{73} +(-3.37594 + 0.387304i) q^{74} +(0.456462 + 1.96320i) q^{76} +3.98082i q^{77} +1.66368i q^{79} +(7.32255 + 14.8955i) q^{80} +(1.37666 + 11.9997i) q^{82} -10.2049 q^{83} +2.21456 q^{85} +(-1.72737 - 15.0567i) q^{86} +(-10.6048 + 3.78327i) q^{88} -3.43007i q^{89} +5.19698i q^{91} +(4.92331 - 1.14472i) q^{92} +(12.8030 - 1.46882i) q^{94} -4.18181 q^{95} +0.254738 q^{97} +(1.40500 - 0.161188i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4}+O(q^{10}) \) 24 * q + 4 * q^4	\( 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more