LMFDB - Embedded newform 756.2.e.b.323.16

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			323.16
Character	$\chi$	$=$	756.323
Dual form			756.2.e.b.323.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.492782 + 1.32558i) q^{2} +(-1.51433 + 1.30645i) q^{4} -3.62883i q^{5} +1.00000i q^{7} +(-2.47803 - 1.36358i) q^{8} +O(q^{10})$	\(q+(0.492782 + 1.32558i) q^{2} +(-1.51433 + 1.30645i) q^{4} -3.62883i q^{5} +1.00000i q^{7} +(-2.47803 - 1.36358i) q^{8} +(4.81031 - 1.78822i) q^{10} +0.830379 q^{11} -4.86954 q^{13} +(-1.32558 + 0.492782i) q^{14} +(0.586403 - 3.95678i) q^{16} -3.28257i q^{17} -6.45812i q^{19} +(4.74086 + 5.49525i) q^{20} +(0.409196 + 1.10073i) q^{22} +5.08897 q^{23} -8.16839 q^{25} +(-2.39962 - 6.45497i) q^{26} +(-1.30645 - 1.51433i) q^{28} -2.02968i q^{29} -7.12436i q^{31} +(5.53401 - 1.17251i) q^{32} +(4.35132 - 1.61759i) q^{34} +3.62883 q^{35} -4.68611 q^{37} +(8.56076 - 3.18244i) q^{38} +(-4.94819 + 8.99236i) q^{40} -2.95211i q^{41} +1.62825i q^{43} +(-1.25747 + 1.08484i) q^{44} +(2.50775 + 6.74585i) q^{46} +6.41454 q^{47} -1.00000 q^{49} +(-4.02523 - 10.8279i) q^{50} +(7.37410 - 6.36179i) q^{52} -4.22013i q^{53} -3.01330i q^{55} +(1.36358 - 2.47803i) q^{56} +(2.69051 - 1.00019i) q^{58} -8.31299 q^{59} -5.55733 q^{61} +(9.44392 - 3.51076i) q^{62} +(4.28131 + 6.75799i) q^{64} +17.6707i q^{65} +11.6216i q^{67} +(4.28850 + 4.97090i) q^{68} +(1.78822 + 4.81031i) q^{70} +7.15735 q^{71} +13.9537 q^{73} +(-2.30923 - 6.21181i) q^{74} +(8.43718 + 9.77974i) q^{76} +0.830379i q^{77} +10.0551i q^{79} +(-14.3585 - 2.12795i) q^{80} +(3.91327 - 1.45475i) q^{82} -16.5568 q^{83} -11.9119 q^{85} +(-2.15838 + 0.802373i) q^{86} +(-2.05771 - 1.13229i) q^{88} +15.9785i q^{89} -4.86954i q^{91} +(-7.70639 + 6.64846i) q^{92} +(3.16097 + 8.50299i) q^{94} -23.4354 q^{95} +8.59479 q^{97} +(-0.492782 - 1.32558i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.492782	+	1.32558i	0.348449	+	0.937328i
$2$	0.492782	+	1.32558i	0.348449	+	0.937328i
$3$		0			0
$3$		0			0
$4$	−1.51433	+	1.30645i	−0.757166	+	0.653223i
$5$		−	3.62883i		−	1.62286i	−0.584449	−	0.811431i	$-0.698689\pi$
$5$		−	3.62883i		−	1.62286i	0.584449	−	0.811431i	$-0.301311\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.47803	−	1.36358i	−0.876118	−	0.482098i
$9$		0			0
$10$	4.81031	−	1.78822i	1.52115	−	0.565485i
$11$	0.830379			0.250369			0.125184	−	0.992134i	$-0.460048\pi$
$11$	0.830379			0.250369			0.125184	+	0.992134i	$0.460048\pi$
$12$		0			0
$13$	−4.86954			−1.35057			−0.675284	−	0.737558i	$-0.735979\pi$
$13$	−4.86954			−1.35057			−0.675284	+	0.737558i	$0.735979\pi$
$14$	−1.32558	+	0.492782i	−0.354277	+	0.131702i
$15$		0			0
$16$	0.586403	−	3.95678i	0.146601	−	0.989196i
$17$		−	3.28257i		−	0.796140i	−0.917355	−	0.398070i	$-0.869680\pi$
$17$		−	3.28257i		−	0.796140i	0.917355	−	0.398070i	$-0.130320\pi$
$18$		0			0
$19$		−	6.45812i		−	1.48159i	−0.671729	−	0.740797i	$-0.734448\pi$
$19$		−	6.45812i		−	1.48159i	0.671729	−	0.740797i	$-0.265552\pi$
$20$	4.74086	+	5.49525i	1.06009	+	1.22878i
$21$		0			0
$22$	0.409196	+	1.10073i	0.0872408	+	0.234677i
$23$	5.08897			1.06112			0.530562	−	0.847646i	$-0.321981\pi$
$23$	5.08897			1.06112			0.530562	+	0.847646i	$0.321981\pi$
$24$		0			0
$25$	−8.16839			−1.63368
$26$	−2.39962	−	6.45497i	−0.470604	−	1.26592i
$27$		0			0
$28$	−1.30645	−	1.51433i	−0.246895	−	0.286182i
$29$		−	2.02968i		−	0.376902i	−0.982083	−	0.188451i	$-0.939653\pi$
$29$		−	2.02968i		−	0.376902i	0.982083	−	0.188451i	$-0.0603467\pi$
$30$		0			0
$31$		−	7.12436i		−	1.27957i	−0.768552	−	0.639787i	$-0.779023\pi$
$31$		−	7.12436i		−	1.27957i	0.768552	−	0.639787i	$-0.220977\pi$
$32$	5.53401	−	1.17251i	0.978283	−	0.207272i
$33$		0			0
$34$	4.35132	−	1.61759i	0.746244	−	0.277415i
$35$	3.62883			0.613384
$36$		0			0
$37$	−4.68611			−0.770391			−0.385195	−	0.922835i	$-0.625866\pi$
$37$	−4.68611			−0.770391			−0.385195	+	0.922835i	$0.625866\pi$
$38$	8.56076	−	3.18244i	1.38874	−	0.516261i
$39$		0			0
$40$	−4.94819	+	8.99236i	−0.782377	+	1.42182i
$41$		−	2.95211i		−	0.461043i	−0.973067	−	0.230521i	$-0.925957\pi$
$41$		−	2.95211i		−	0.461043i	0.973067	−	0.230521i	$-0.0740431\pi$
$42$		0			0
$43$			1.62825i			0.248306i	0.992263	+	0.124153i	$0.0396214\pi$
$43$			1.62825i			0.248306i	−0.992263	+	0.124153i	$0.960379\pi$
$44$	−1.25747	+	1.08484i	−0.189571	+	0.163546i
$45$		0			0
$46$	2.50775	+	6.74585i	0.369748	+	0.994621i
$47$	6.41454			0.935656			0.467828	−	0.883819i	$-0.345037\pi$
$47$	6.41454			0.935656			0.467828	+	0.883819i	$0.345037\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−4.02523	−	10.8279i	−0.569254	−	1.53129i
$51$		0			0
$52$	7.37410	−	6.36179i	1.02260	−	0.882221i
$53$		−	4.22013i		−	0.579679i	−0.957075	−	0.289840i	$-0.906398\pi$
$53$		−	4.22013i		−	0.579679i	0.957075	−	0.289840i	$-0.0936020\pi$
$54$		0			0
$55$		−	3.01330i		−	0.406314i
$56$	1.36358	−	2.47803i	0.182216	−	0.331141i
$57$		0			0
$58$	2.69051	−	1.00019i	0.353281	−	0.131331i
$59$	−8.31299			−1.08226			−0.541130	−	0.840939i	$-0.682003\pi$
$59$	−8.31299			−1.08226			−0.541130	+	0.840939i	$0.682003\pi$
$60$		0			0
$61$	−5.55733			−0.711543			−0.355771	−	0.934573i	$-0.615782\pi$
$61$	−5.55733			−0.711543			−0.355771	+	0.934573i	$0.615782\pi$
$62$	9.44392	−	3.51076i	1.19938	−	0.445867i
$63$		0			0
$64$	4.28131	+	6.75799i	0.535164	+	0.844748i
$65$			17.6707i			2.19178i
$66$		0			0
$67$			11.6216i			1.41981i	0.704298	+	0.709904i	$0.251262\pi$
$67$			11.6216i			1.41981i	−0.704298	+	0.709904i	$0.748738\pi$
$68$	4.28850	+	4.97090i	0.520057	+	0.602810i
$69$		0			0
$70$	1.78822	+	4.81031i	0.213733	+	0.574942i
$71$	7.15735			0.849422			0.424711	−	0.905329i	$-0.360376\pi$
$71$	7.15735			0.849422			0.424711	+	0.905329i	$0.360376\pi$
$72$		0			0
$73$	13.9537			1.63316			0.816579	−	0.577234i	$-0.195868\pi$
$73$	13.9537			1.63316			0.816579	+	0.577234i	$0.195868\pi$
$74$	−2.30923	−	6.21181i	−0.268442	−	0.722109i
$75$		0			0
$76$	8.43718	+	9.77974i	0.967811	+	1.12181i
$77$			0.830379i			0.0946305i
$78$		0			0
$79$			10.0551i			1.13129i	0.824649	+	0.565645i	$0.191373\pi$
$79$			10.0551i			1.13129i	−0.824649	+	0.565645i	$0.808627\pi$
$80$	−14.3585	−	2.12795i	−1.60533	−	0.237913i
$81$		0			0
$82$	3.91327	−	1.45475i	0.432148	−	0.160650i
$83$	−16.5568			−1.81735			−0.908674	−	0.417506i	$-0.862904\pi$
$83$	−16.5568			−1.81735			−0.908674	+	0.417506i	$0.862904\pi$
$84$		0			0
$85$	−11.9119			−1.29203
$86$	−2.15838	+	0.802373i	−0.232744	+	0.0865221i
$87$		0			0
$88$	−2.05771	−	1.13229i	−0.219352	−	0.120702i
$89$			15.9785i			1.69372i	0.531817	+	0.846860i	$0.321510\pi$
$89$			15.9785i			1.69372i	−0.531817	+	0.846860i	$0.678490\pi$
$90$		0			0
$91$		−	4.86954i		−	0.510466i
$92$	−7.70639	+	6.64846i	−0.803447	+	0.693150i
$93$		0			0
$94$	3.16097	+	8.50299i	0.326029	+	0.877016i
$95$	−23.4354			−2.40442
$96$		0			0
$97$	8.59479			0.872669			0.436334	−	0.899785i	$-0.356276\pi$
$97$	8.59479			0.872669			0.436334	+	0.899785i	$0.356276\pi$
$98$	−0.492782	−	1.32558i	−0.0497785	−	0.133904i
$99$		0			0
$100$	12.3697	−	10.6716i	1.23697	−	1.06716i
$101$		−	15.8624i		−	1.57837i	−0.614156	−	0.789185i	$-0.710503\pi$
$101$		−	15.8624i		−	1.57837i	0.614156	−	0.789185i	$-0.289497\pi$
$102$		0			0
$103$			3.04182i			0.299719i	0.988707	+	0.149860i	$0.0478822\pi$
$103$			3.04182i			0.299719i	−0.988707	+	0.149860i	$0.952118\pi$
$104$	12.0669	+	6.64000i	1.18326	+	0.651105i
$105$		0			0
$106$	5.59413	−	2.07960i	0.543349	−	0.201989i
$107$	19.1409			1.85042			0.925211	−	0.379452i	$-0.123888\pi$
$107$	19.1409			1.85042			0.925211	+	0.379452i	$0.123888\pi$
$108$		0			0
$109$	−19.3448			−1.85289			−0.926447	−	0.376425i	$-0.877153\pi$
$109$	−19.3448			−1.85289			−0.926447	+	0.376425i	$0.877153\pi$
$110$	3.99438	−	1.48490i	0.380849	−	0.141580i
$111$		0			0
$112$	3.95678	+	0.586403i	0.373881	+	0.0554099i
$113$		−	1.67488i		−	0.157559i	−0.996892	−	0.0787796i	$-0.974898\pi$
$113$		−	1.67488i		−	0.157559i	0.996892	−	0.0787796i	$-0.0251023\pi$
$114$		0			0
$115$		−	18.4670i		−	1.72206i
$116$	2.65167	+	3.07361i	0.246201	+	0.285378i
$117$		0			0
$118$	−4.09649	−	11.0195i	−0.377113	−	1.01443i
$119$	3.28257			0.300913
$120$		0			0
$121$	−10.3105			−0.937316
$122$	−2.73855	−	7.36669i	−0.247937	−	0.666949i
$123$		0			0
$124$	9.30759	+	10.7887i	0.835846	+	0.968850i
$125$			11.4975i			1.02837i
$126$		0			0
$127$		−	2.99779i		−	0.266011i	−0.991115	−	0.133006i	$-0.957537\pi$
$127$		−	2.99779i		−	0.266011i	0.991115	−	0.133006i	$-0.0424628\pi$
$128$	−6.84851	+	9.00544i	−0.605328	+	0.795976i
$129$		0			0
$130$	−23.4240	+	8.70781i	−2.05442	+	0.763726i
$131$	15.7213			1.37357			0.686786	−	0.726860i	$-0.259021\pi$
$131$	15.7213			1.37357			0.686786	+	0.726860i	$0.259021\pi$
$132$		0			0
$133$	6.45812			0.559990
$134$	−15.4054	+	5.72693i	−1.33083	+	0.494731i
$135$		0			0
$136$	−4.47604	+	8.13433i	−0.383817	+	0.697513i
$137$		−	14.6848i		−	1.25460i	−0.778776	−	0.627302i	$-0.784159\pi$
$137$		−	14.6848i		−	1.25460i	0.778776	−	0.627302i	$-0.215841\pi$
$138$		0			0
$139$			15.1324i			1.28351i	0.766909	+	0.641755i	$0.221794\pi$
$139$			15.1324i			1.28351i	−0.766909	+	0.641755i	$0.778206\pi$
$140$	−5.49525	+	4.74086i	−0.464433	+	0.400676i
$141$		0			0
$142$	3.52701	+	9.48765i	0.295980	+	0.796186i
$143$	−4.04356			−0.338140
$144$		0			0
$145$	−7.36536			−0.611660
$146$	6.87613	+	18.4968i	0.569073	+	1.53080i
$147$		0			0
$148$	7.09632	−	6.12214i	0.583314	−	0.503237i
$149$		−	8.68879i		−	0.711814i	−0.934521	−	0.355907i	$-0.884172\pi$
$149$		−	8.68879i		−	0.711814i	0.934521	−	0.355907i	$-0.115828\pi$
$150$		0			0
$151$		−	17.2323i		−	1.40234i	−0.712993	−	0.701171i	$-0.752661\pi$
$151$		−	17.2323i		−	1.40234i	0.712993	−	0.701171i	$-0.247339\pi$
$152$	−8.80615	+	16.0034i	−0.714273	+	1.29805i
$153$		0			0
$154$	−1.10073	+	0.409196i	−0.0886997	+	0.0329739i
$155$	−25.8531			−2.07657
$156$		0			0
$157$	−14.7386			−1.17626			−0.588132	−	0.808765i	$-0.700137\pi$
$157$	−14.7386			−1.17626			−0.588132	+	0.808765i	$0.700137\pi$
$158$	−13.3289	+	4.95498i	−1.06039	+	0.394197i
$159$		0			0
$160$	−4.25482	−	20.0820i	−0.336373	−	1.58762i
$161$			5.08897i			0.401067i
$162$		0			0
$163$			9.39469i			0.735849i	0.929856	+	0.367925i	$0.119932\pi$
$163$			9.39469i			0.735849i	−0.929856	+	0.367925i	$0.880068\pi$
$164$	3.85677	+	4.47048i	0.301163	+	0.349086i
$165$		0			0
$166$	−8.15891	−	21.9474i	−0.633254	−	1.70345i
$167$	1.79557			0.138945			0.0694725	−	0.997584i	$-0.477868\pi$
$167$	1.79557			0.138945			0.0694725	+	0.997584i	$0.477868\pi$
$168$		0			0
$169$	10.7124			0.824032
$170$	−5.86996	−	15.7902i	−0.450205	−	1.21105i
$171$		0			0
$172$	−2.12722	−	2.46571i	−0.162199	−	0.188009i
$173$			5.43851i			0.413483i	0.978396	+	0.206741i	$0.0662858\pi$
$173$			5.43851i			0.413483i	−0.978396	+	0.206741i	$0.933714\pi$
$174$		0			0
$175$		−	8.16839i		−	0.617472i
$176$	0.486936	−	3.28563i	0.0367042	−	0.247664i
$177$		0			0
$178$	−21.1808	+	7.87392i	−1.58757	+	0.590175i
$179$	11.1501			0.833401			0.416700	−	0.909044i	$-0.363186\pi$
$179$	11.1501			0.833401			0.416700	+	0.909044i	$0.363186\pi$
$180$		0			0
$181$	11.3584			0.844262			0.422131	−	0.906535i	$-0.361282\pi$
$181$	11.3584			0.844262			0.422131	+	0.906535i	$0.361282\pi$
$182$	6.45497	−	2.39962i	0.478474	−	0.177872i
$183$		0			0
$184$	−12.6107	−	6.93921i	−0.929670	−	0.511565i
$185$			17.0051i			1.25024i
$186$		0			0
$187$		−	2.72578i		−	0.199329i
$188$	−9.71374	+	8.38024i	−0.708447	+	0.611192i
$189$		0			0
$190$	−11.5485	−	31.0655i	−0.837819	−	2.25373i
$191$	−8.95001			−0.647600			−0.323800	−	0.946126i	$-0.604960\pi$
$191$	−8.95001			−0.647600			−0.323800	+	0.946126i	$0.604960\pi$
$192$		0			0
$193$	26.0046			1.87185			0.935925	−	0.352198i	$-0.114566\pi$
$193$	26.0046			1.87185			0.935925	+	0.352198i	$0.114566\pi$
$194$	4.23536	+	11.3931i	0.304081	+	0.817977i
$195$		0			0
$196$	1.51433	−	1.30645i	0.108167	−	0.0933175i
$197$		−	16.6421i		−	1.18570i	−0.805312	−	0.592851i	$-0.798002\pi$
$197$		−	16.6421i		−	1.18570i	0.805312	−	0.592851i	$-0.201998\pi$
$198$		0			0
$199$			8.92275i			0.632517i	0.948673	+	0.316259i	$0.102427\pi$
$199$			8.92275i			0.632517i	−0.948673	+	0.316259i	$0.897573\pi$
$200$	20.2416	+	11.1382i	1.43129	+	0.787592i
$201$		0			0
$202$	21.0269	−	7.81671i	1.47945	−	0.549982i
$203$	2.02968			0.142456
$204$		0			0
$205$	−10.7127			−0.748208
$206$	−4.03218	+	1.49895i	−0.280935	+	0.104437i
$207$		0			0
$208$	−2.85551	+	19.2677i	−0.197994	+	1.33598i
$209$		−	5.36269i		−	0.370945i
$210$		0			0
$211$		−	2.33852i		−	0.160991i	−0.996755	−	0.0804953i	$-0.974350\pi$
$211$		−	2.33852i		−	0.160991i	0.996755	−	0.0804953i	$-0.0256502\pi$
$212$	5.51337	+	6.39068i	0.378660	+	0.438914i
$213$		0			0
$214$	9.43230	+	25.3728i	0.644779	+	1.73445i
$215$	5.90865			0.402966
$216$		0			0
$217$	7.12436			0.483633
$218$	−9.53276	−	25.6431i	−0.645640	−	1.73677i
$219$		0			0
$220$	3.93671	+	4.56314i	0.265413	+	0.307647i
$221$			15.9846i			1.07524i
$222$		0			0
$223$		−	12.7557i		−	0.854188i	−0.904207	−	0.427094i	$-0.859537\pi$
$223$		−	12.7557i		−	0.854188i	0.904207	−	0.427094i	$-0.140463\pi$
$224$	1.17251	+	5.53401i	0.0783414	+	0.369756i
$225$		0			0
$226$	2.22019	−	0.825349i	0.147685	−	0.0549014i
$227$	−2.88882			−0.191738			−0.0958690	−	0.995394i	$-0.530563\pi$
$227$	−2.88882			−0.191738			−0.0958690	+	0.995394i	$0.530563\pi$
$228$		0			0
$229$	13.1532			0.869186			0.434593	−	0.900627i	$-0.356892\pi$
$229$	13.1532			0.869186			0.434593	+	0.900627i	$0.356892\pi$
$230$	24.4795	−	9.10021i	1.61413	−	0.600050i
$231$		0			0
$232$	−2.76763	+	5.02962i	−0.181704	+	0.330211i
$233$			3.37768i			0.221279i	0.993861	+	0.110640i	$0.0352900\pi$
$233$			3.37768i			0.221279i	−0.993861	+	0.110640i	$0.964710\pi$
$234$		0			0
$235$		−	23.2772i		−	1.51844i
$236$	12.5886	−	10.8605i	0.819450	−	0.706956i
$237$		0			0
$238$	1.61759	+	4.35132i	0.104853	+	0.282054i
$239$	−7.82300			−0.506028			−0.253014	−	0.967463i	$-0.581422\pi$
$239$	−7.82300			−0.506028			−0.253014	+	0.967463i	$0.581422\pi$
$240$		0			0
$241$	2.27086			0.146279			0.0731393	−	0.997322i	$-0.476698\pi$
$241$	2.27086			0.146279			0.0731393	+	0.997322i	$0.476698\pi$
$242$	−5.08081	−	13.6674i	−0.326607	−	0.878572i
$243$		0			0
$244$	8.41564	−	7.26034i	0.538756	−	0.464796i
$245$			3.62883i			0.231837i
$246$		0			0
$247$			31.4481i			2.00099i
$248$	−9.71462	+	17.6544i	−0.616879	+	1.12106i
$249$		0			0
$250$	−15.2409	+	5.66578i	−0.963921	+	0.358335i
$251$	13.5393			0.854592			0.427296	−	0.904112i	$-0.359466\pi$
$251$	13.5393			0.854592			0.427296	+	0.904112i	$0.359466\pi$
$252$		0			0
$253$	4.22578			0.265672
$254$	3.97382	−	1.47726i	0.249340	−	0.0926915i
$255$		0			0
$256$	−15.3123	−	4.64054i	−0.957016	−	0.290034i
$257$			1.12864i			0.0704028i	0.999380	+	0.0352014i	$0.0112073\pi$
$257$			1.12864i			0.0704028i	−0.999380	+	0.0352014i	$0.988793\pi$
$258$		0			0
$259$		−	4.68611i		−	0.291180i
$260$	−23.0858	−	26.7593i	−1.43172	−	1.65954i
$261$		0			0
$262$	7.74715	+	20.8398i	0.478620	+	1.28749i
$263$	−6.15279			−0.379397			−0.189699	−	0.981842i	$-0.560751\pi$
$263$	−6.15279			−0.379397			−0.189699	+	0.981842i	$0.560751\pi$
$264$		0			0
$265$	−15.3141			−0.940739
$266$	3.18244	+	8.56076i	0.195128	+	0.524894i
$267$		0			0
$268$	−15.1830	−	17.5990i	−0.927451	−	1.07503i
$269$			8.56481i			0.522206i	0.965311	+	0.261103i	$0.0840862\pi$
$269$			8.56481i			0.522206i	−0.965311	+	0.261103i	$0.915914\pi$
$270$		0			0
$271$			1.80089i			0.109396i	0.998503	+	0.0546980i	$0.0174196\pi$
$271$			1.80089i			0.109396i	−0.998503	+	0.0546980i	$0.982580\pi$
$272$	−12.9884	−	1.92491i	−0.787539	−	0.116715i
$273$		0			0
$274$	19.4659	−	7.23639i	1.17598	−	0.437166i
$275$	−6.78286			−0.409022
$276$		0			0
$277$	14.1332			0.849185			0.424592	−	0.905385i	$-0.360417\pi$
$277$	14.1332			0.849185			0.424592	+	0.905385i	$0.360417\pi$
$278$	−20.0592	+	7.45696i	−1.20307	+	0.447239i
$279$		0			0
$280$	−8.99236	−	4.94819i	−0.537396	−	0.295711i
$281$			3.04631i			0.181728i	0.995863	+	0.0908638i	$0.0289628\pi$
$281$			3.04631i			0.181728i	−0.995863	+	0.0908638i	$0.971037\pi$
$282$		0			0
$283$		−	1.52631i		−	0.0907298i	−0.998970	−	0.0453649i	$-0.985555\pi$
$283$		−	1.52631i		−	0.0907298i	0.998970	−	0.0453649i	$-0.0144450\pi$
$284$	−10.8386	+	9.35069i	−0.643153	+	0.554861i
$285$		0			0
$286$	−1.99259	−	5.36007i	−0.117825	−	0.316948i
$287$	2.95211			0.174258
$288$		0			0
$289$	6.22473			0.366160
$290$	−3.62952	−	9.76338i	−0.213133	−	0.573326i
$291$		0			0
$292$	−21.1305	+	18.2297i	−1.23657	+	1.06682i
$293$			9.41595i			0.550086i	0.961432	+	0.275043i	$0.0886920\pi$
$293$			9.41595i			0.550086i	−0.961432	+	0.275043i	$0.911308\pi$
$294$		0			0
$295$			30.1664i			1.75636i
$296$	11.6123	+	6.38987i	0.674953	+	0.371404i
$297$		0			0
$298$	11.5177	−	4.28168i	0.667203	−	0.248031i
$299$	−24.7810			−1.43312
$300$		0			0
$301$	−1.62825			−0.0938509
$302$	22.8428	−	8.49175i	1.31445	−	0.488646i
$303$		0			0
$304$	−25.5534	−	3.78706i	−1.46559	−	0.217203i
$305$			20.1666i			1.15473i
$306$		0			0
$307$			33.6663i			1.92144i	0.277520	+	0.960720i	$0.410488\pi$
$307$			33.6663i			1.92144i	−0.277520	+	0.960720i	$0.589512\pi$
$308$	−1.08484	−	1.25747i	−0.0618147	−	0.0716510i
$309$		0			0
$310$	−12.7399	−	34.2704i	−0.723580	−	1.94643i
$311$	−24.1439			−1.36908			−0.684539	−	0.728977i	$-0.739996\pi$
$311$	−24.1439			−1.36908			−0.684539	+	0.728977i	$0.739996\pi$
$312$		0			0
$313$	7.21126			0.407605			0.203802	−	0.979012i	$-0.434670\pi$
$313$	7.21126			0.407605			0.203802	+	0.979012i	$0.434670\pi$
$314$	−7.26289	−	19.5372i	−0.409869	−	1.10255i
$315$		0			0
$316$	−13.1365	−	15.2268i	−0.738984	−	0.856574i
$317$		−	11.2921i		−	0.634225i	−0.948388	−	0.317113i	$-0.897287\pi$
$317$		−	11.2921i		−	0.634225i	0.948388	−	0.317113i	$-0.102713\pi$
$318$		0			0
$319$		−	1.68540i		−	0.0943645i
$320$	24.5236	−	15.5361i	1.37091	−	0.868497i
$321$		0			0
$322$	−6.74585	+	2.50775i	−0.375931	+	0.139752i
$323$	−21.1992			−1.17956
$324$		0			0
$325$	39.7763			2.20639
$326$	−12.4534	+	4.62954i	−0.689732	+	0.256406i
$327$		0			0
$328$	−4.02544	+	7.31544i	−0.222268	+	0.403927i
$329$			6.41454i			0.353645i
$330$		0			0
$331$			21.5411i			1.18401i	0.805935	+	0.592004i	$0.201663\pi$
$331$			21.5411i			1.18401i	−0.805935	+	0.592004i	$0.798337\pi$
$332$	25.0725	−	21.6306i	1.37603	−	1.18713i
$333$		0			0
$334$	0.884823	+	2.38017i	0.0484153	+	0.130237i
$335$	42.1729			2.30415
$336$		0			0
$337$	24.9604			1.35968			0.679841	−	0.733360i	$-0.262049\pi$
$337$	24.9604			1.35968			0.679841	+	0.733360i	$0.262049\pi$
$338$	5.27889	+	14.2002i	0.287134	+	0.772388i
$339$		0			0
$340$	18.0385	−	15.5622i	0.978278	−	0.843980i
$341$		−	5.91592i		−	0.320365i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	2.22025	−	4.03487i	0.119708	−	0.217545i
$345$		0			0
$346$	−7.20919	+	2.68000i	−0.387569	+	0.144078i
$347$	17.4866			0.938731			0.469365	−	0.883004i	$-0.344483\pi$
$347$	17.4866			0.938731			0.469365	+	0.883004i	$0.344483\pi$
$348$		0			0
$349$	−5.82186			−0.311637			−0.155819	−	0.987786i	$-0.549802\pi$
$349$	−5.82186			−0.311637			−0.155819	+	0.987786i	$0.549802\pi$
$350$	10.8279	−	4.02523i	0.578774	−	0.215158i
$351$		0			0
$352$	4.59532	−	0.973625i	0.244931	−	0.0518944i
$353$		−	10.6711i		−	0.567966i	−0.958829	−	0.283983i	$-0.908344\pi$
$353$		−	10.6711i		−	0.567966i	0.958829	−	0.283983i	$-0.0916560\pi$
$354$		0			0
$355$		−	25.9728i		−	1.37849i
$356$	−20.8750	−	24.1968i	−1.10638	−	1.28243i
$357$		0			0
$358$	5.49459	+	14.7804i	0.290398	+	0.781169i
$359$	15.3833			0.811897			0.405949	−	0.913896i	$-0.366941\pi$
$359$	15.3833			0.811897			0.405949	+	0.913896i	$0.366941\pi$
$360$		0			0
$361$	−22.7073			−1.19512
$362$	5.59721	+	15.0565i	0.294183	+	0.791350i
$363$		0			0
$364$	6.36179	+	7.37410i	0.333448	+	0.386508i
$365$		−	50.6356i		−	2.65039i
$366$		0			0
$367$		−	11.6774i		−	0.609555i	−0.952424	−	0.304778i	$-0.901418\pi$
$367$		−	11.6774i		−	0.609555i	0.952424	−	0.304778i	$-0.0985821\pi$
$368$	2.98419	−	20.1360i	0.155562	−	1.04966i
$369$		0			0
$370$	−22.5416	+	8.37979i	−1.17188	+	0.435645i
$371$	4.22013			0.219098
$372$		0			0
$373$	17.0749			0.884103			0.442052	−	0.896990i	$-0.354251\pi$
$373$	17.0749			0.884103			0.442052	+	0.896990i	$0.354251\pi$
$374$	3.61324	−	1.34321i	0.186836	−	0.0694559i
$375$		0			0
$376$	−15.8954	−	8.74672i	−0.819745	−	0.451078i
$377$			9.88361i			0.509032i
$378$		0			0
$379$		−	16.9134i		−	0.868783i	−0.900724	−	0.434391i	$-0.856963\pi$
$379$		−	16.9134i		−	0.868783i	0.900724	−	0.434391i	$-0.143037\pi$
$380$	35.4890	−	30.6171i	1.82055	−	1.57062i
$381$		0			0
$382$	−4.41040	−	11.8640i	−0.225656	−	0.607013i
$383$	28.3777			1.45003			0.725017	−	0.688731i	$-0.241832\pi$
$383$	28.3777			1.45003			0.725017	+	0.688731i	$0.241832\pi$
$384$		0			0
$385$	3.01330			0.153572
$386$	12.8146	+	34.4712i	0.652245	+	1.75454i
$387$		0			0
$388$	−13.0154	+	11.2286i	−0.660755	+	0.570047i
$389$		−	28.7838i		−	1.45940i	−0.683770	−	0.729698i	$-0.739661\pi$
$389$		−	28.7838i		−	1.45940i	0.683770	−	0.729698i	$-0.260339\pi$
$390$		0			0
$391$		−	16.7049i		−	0.844804i
$392$	2.47803	+	1.36358i	0.125160	+	0.0688711i
$393$		0			0
$394$	22.0605	−	8.20093i	1.11139	−	0.413157i
$395$	36.4883			1.83593
$396$		0			0
$397$	23.8045			1.19472			0.597358	−	0.801975i	$-0.296217\pi$
$397$	23.8045			1.19472			0.597358	+	0.801975i	$0.296217\pi$
$398$	−11.8278	+	4.39697i	−0.592876	+	0.220400i
$399$		0			0
$400$	−4.78997	+	32.3205i	−0.239498	+	1.61603i
$401$		−	5.93299i		−	0.296279i	−0.988966	−	0.148140i	$-0.952671\pi$
$401$		−	5.93299i		−	0.296279i	0.988966	−	0.148140i	$-0.0473285\pi$
$402$		0			0
$403$			34.6924i			1.72815i
$404$	20.7234	+	24.0210i	1.03103	+	1.19509i
$405$		0			0
$406$	1.00019	+	2.69051i	0.0496386	+	0.133528i
$407$	−3.89124			−0.192882
$408$		0			0
$409$	−11.0387			−0.545827			−0.272913	−	0.962039i	$-0.587987\pi$
$409$	−11.0387			−0.545827			−0.272913	+	0.962039i	$0.587987\pi$
$410$	−5.27903	−	14.2006i	−0.260713	−	0.701316i
$411$		0			0
$412$	−3.97397	−	4.60633i	−0.195784	−	0.226937i
$413$		−	8.31299i		−	0.409056i
$414$		0			0
$415$			60.0819i			2.94930i
$416$	−26.9481	+	5.70957i	−1.32124	+	0.279935i
$417$		0			0
$418$	7.10868	−	2.64263i	0.347697	−	0.129255i
$419$	9.25932			0.452348			0.226174	−	0.974087i	$-0.427378\pi$
$419$	9.25932			0.452348			0.226174	+	0.974087i	$0.427378\pi$
$420$		0			0
$421$	16.9199			0.824625			0.412313	−	0.911042i	$-0.364721\pi$
$421$	16.9199			0.824625			0.412313	+	0.911042i	$0.364721\pi$
$422$	3.09990	−	1.15238i	0.150901	−	0.0560971i
$423$		0			0
$424$	−5.75448	+	10.4576i	−0.279462	+	0.507867i
$425$			26.8133i			1.30064i
$426$		0			0
$427$		−	5.55733i		−	0.268938i
$428$	−28.9857	+	25.0066i	−1.40108	+	1.20874i
$429$		0			0
$430$	2.91167	+	7.83239i	0.140413	+	0.377711i
$431$	12.5411			0.604086			0.302043	−	0.953294i	$-0.402331\pi$
$431$	12.5411			0.604086			0.302043	+	0.953294i	$0.402331\pi$
$432$		0			0
$433$	−6.35141			−0.305229			−0.152615	−	0.988286i	$-0.548769\pi$
$433$	−6.35141			−0.305229			−0.152615	+	0.988286i	$0.548769\pi$
$434$	3.51076	+	9.44392i	0.168522	+	0.453323i
$435$		0			0
$436$	29.2944	−	25.2729i	1.40295	−	1.21035i
$437$		−	32.8652i		−	1.57216i
$438$		0			0
$439$		−	27.6672i		−	1.32048i	−0.751054	−	0.660241i	$-0.770454\pi$
$439$		−	27.6672i		−	1.32048i	0.751054	−	0.660241i	$-0.229546\pi$
$440$	−4.10887	+	7.46707i	−0.195883	+	0.355978i
$441$		0			0
$442$	−21.1889	+	7.87693i	−1.00785	+	0.374667i
$443$	−21.7647			−1.03407			−0.517036	−	0.855963i	$-0.672965\pi$
$443$	−21.7647			−1.03407			−0.517036	+	0.855963i	$0.672965\pi$
$444$		0			0
$445$	57.9833			2.74867
$446$	16.9088	−	6.28580i	0.800654	−	0.297641i
$447$		0			0
$448$	−6.75799	+	4.28131i	−0.319285	+	0.202273i
$449$			7.05614i			0.333000i	0.986041	+	0.166500i	$0.0532466\pi$
$449$			7.05614i			0.333000i	−0.986041	+	0.166500i	$0.946753\pi$
$450$		0			0
$451$		−	2.45137i		−	0.115431i
$452$	2.18814	+	2.53632i	0.102921	+	0.119298i
$453$		0			0
$454$	−1.42356	−	3.82937i	−0.0668110	−	0.179721i
$455$	−17.6707			−0.828416
$456$		0			0
$457$	−31.5055			−1.47376			−0.736882	−	0.676022i	$-0.763703\pi$
$457$	−31.5055			−1.47376			−0.736882	+	0.676022i	$0.763703\pi$
$458$	6.48165	+	17.4356i	0.302867	+	0.814712i
$459$		0			0
$460$	24.1261	+	27.9652i	1.12489	+	1.30388i
$461$		−	34.0478i		−	1.58577i	−0.609374	−	0.792883i	$-0.708579\pi$
$461$		−	34.0478i		−	1.58577i	0.609374	−	0.792883i	$-0.291421\pi$
$462$		0			0
$463$			9.64882i			0.448419i	0.974541	+	0.224209i	$0.0719799\pi$
$463$			9.64882i			0.448419i	−0.974541	+	0.224209i	$0.928020\pi$
$464$	−8.03101	−	1.19021i	−0.372830	−	0.0552541i
$465$		0			0
$466$	−4.47739	+	1.66446i	−0.207411	+	0.0771047i
$467$	−0.206231			−0.00954322			−0.00477161	−	0.999989i	$-0.501519\pi$
$467$	−0.206231			−0.00954322			−0.00477161	+	0.999989i	$0.501519\pi$
$468$		0			0
$469$	−11.6216			−0.536637
$470$	30.8559	−	11.4706i	1.42328	−	0.529100i
$471$		0			0
$472$	20.5999	+	11.3354i	0.948186	+	0.521755i
$473$			1.35207i			0.0621681i
$474$		0			0
$475$			52.7524i			2.42045i
$476$	−4.97090	+	4.28850i	−0.227841	+	0.196563i
$477$		0			0
$478$	−3.85503	−	10.3700i	−0.176325	−	0.474314i
$479$	1.50202			0.0686292			0.0343146	−	0.999411i	$-0.489075\pi$
$479$	1.50202			0.0686292			0.0343146	+	0.999411i	$0.489075\pi$
$480$		0			0
$481$	22.8192			1.04046
$482$	1.11904	+	3.01020i	0.0509707	+	0.137111i
$483$		0			0
$484$	15.6135	−	13.4701i	0.709703	−	0.612276i
$485$		−	31.1890i		−	1.41622i
$486$		0			0
$487$		−	19.7258i		−	0.893863i	−0.894568	−	0.446931i	$-0.852517\pi$
$487$		−	19.7258i		−	0.893863i	0.894568	−	0.446931i	$-0.147483\pi$
$488$	13.7712	+	7.57785i	0.623395	+	0.343033i
$489$		0			0
$490$	−4.81031	+	1.78822i	−0.217307	+	0.0807836i
$491$	10.3729			0.468122			0.234061	−	0.972222i	$-0.424798\pi$
$491$	10.3729			0.468122			0.234061	+	0.972222i	$0.424798\pi$
$492$		0			0
$493$	−6.66257			−0.300067
$494$	−41.6870	+	15.4970i	−1.87559	+	0.697245i
$495$		0			0
$496$	−28.1896	−	4.17775i	−1.26575	−	0.187586i
$497$			7.15735i			0.321051i
$498$		0			0
$499$		−	20.2502i		−	0.906522i	−0.891378	−	0.453261i	$-0.850260\pi$
$499$		−	20.2502i		−	0.906522i	0.891378	−	0.453261i	$-0.149740\pi$
$500$	−15.0209	−	17.4111i	−0.671755	−	0.778648i
$501$		0			0
$502$	6.67192	+	17.9474i	0.297782	+	0.801033i
$503$	12.2134			0.544566			0.272283	−	0.962217i	$-0.412221\pi$
$503$	12.2134			0.544566			0.272283	+	0.962217i	$0.412221\pi$
$504$		0			0
$505$	−57.5620			−2.56147
$506$	2.08239	+	5.60161i	0.0925733	+	0.249022i
$507$		0			0
$508$	3.91645	+	4.53966i	0.173765	+	0.201415i
$509$		−	18.6047i		−	0.824639i	−0.911039	−	0.412319i	$-0.864719\pi$
$509$		−	18.6047i		−	0.824639i	0.911039	−	0.412319i	$-0.135281\pi$
$510$		0			0
$511$			13.9537i			0.617276i
$512$	−1.39420	−	22.5844i	−0.0616154	−	0.998100i
$513$		0			0
$514$	−1.49611	+	0.556174i	−0.0659904	+	0.0245318i
$515$	11.0382			0.486403
$516$		0			0
$517$	5.32650			0.234259
$518$	6.21181	−	2.30923i	0.272931	−	0.101462i
$519$		0			0
$520$	24.0954	−	43.7887i	1.05665	−	1.92026i
$521$		−	1.06091i		−	0.0464793i	−0.999730	−	0.0232396i	$-0.992602\pi$
$521$		−	1.06091i		−	0.0464793i	0.999730	−	0.0232396i	$-0.00739807\pi$
$522$		0			0
$523$		−	31.3612i		−	1.37133i	−0.727917	−	0.685665i	$-0.759511\pi$
$523$		−	31.3612i		−	1.37133i	0.727917	−	0.685665i	$-0.240489\pi$
$524$	−23.8072	+	20.5390i	−1.04002	+	0.897248i
$525$		0			0
$526$	−3.03199	−	8.15603i	−0.132201	−	0.355620i
$527$	−23.3862			−1.01872
$528$		0			0
$529$	2.89765			0.125985
$530$	−7.54652	−	20.3001i	−0.327800	−	0.881781i
$531$		0			0
$532$	−9.77974	+	8.43718i	−0.424005	+	0.365798i
$533$			14.3754i			0.622669i
$534$		0			0
$535$		−	69.4591i		−	3.00298i
$536$	15.8470	−	28.7988i	0.684486	−	1.24392i
$537$		0			0
$538$	−11.3534	+	4.22058i	−0.489478	+	0.181962i
$539$	−0.830379			−0.0357670
$540$		0			0
$541$	−9.50193			−0.408520			−0.204260	−	0.978917i	$-0.565479\pi$
$541$	−9.50193			−0.408520			−0.204260	+	0.978917i	$0.565479\pi$
$542$	−2.38722	+	0.887444i	−0.102540	+	0.0381190i
$543$		0			0
$544$	−3.84884	−	18.1658i	−0.165017	−	0.778851i
$545$			70.1989i			3.00699i
$546$		0			0
$547$			13.4987i			0.577164i	0.957455	+	0.288582i	$0.0931838\pi$
$547$			13.4987i			0.577164i	−0.957455	+	0.288582i	$0.906816\pi$
$548$	19.1848	+	22.2376i	0.819536	+	0.949944i
$549$		0			0
$550$	−3.34247	−	8.99123i	−0.142523	−	0.383387i
$551$	−13.1079			−0.558416
$552$		0			0
$553$	−10.0551			−0.427587
$554$	6.96461	+	18.7348i	0.295898	+	0.795964i
$555$		0			0
$556$	−19.7696	−	22.9154i	−0.838418	−	0.971831i
$557$		−	25.9931i		−	1.10136i	−0.834716	−	0.550681i	$-0.814368\pi$
$557$		−	25.9931i		−	1.10136i	0.834716	−	0.550681i	$-0.185632\pi$
$558$		0			0
$559$		−	7.92884i		−	0.335354i
$560$	2.12795	−	14.3585i	0.0899225	−	0.606757i
$561$		0			0
$562$	−4.03813	+	1.50117i	−0.170338	+	0.0633229i
$563$	11.4421			0.482228			0.241114	−	0.970497i	$-0.422487\pi$
$563$	11.4421			0.482228			0.241114	+	0.970497i	$0.422487\pi$
$564$		0			0
$565$	−6.07784			−0.255697
$566$	2.02325	−	0.752138i	0.0850435	−	0.0316147i
$567$		0			0
$568$	−17.7362	−	9.75961i	−0.744193	−	0.409504i
$569$			22.9126i			0.960545i	0.877119	+	0.480272i	$0.159462\pi$
$569$			22.9126i			0.960545i	−0.877119	+	0.480272i	$0.840538\pi$
$570$		0			0
$571$		−	15.1724i		−	0.634947i	−0.948267	−	0.317474i	$-0.897166\pi$
$571$		−	15.1724i		−	0.634947i	0.948267	−	0.317474i	$-0.102834\pi$
$572$	6.12330	−	5.28269i	0.256028	−	0.220880i
$573$		0			0
$574$	1.45475	+	3.91327i	0.0607200	+	0.163337i
$575$	−41.5687			−1.73354
$576$		0			0
$577$	13.9043			0.578845			0.289422	−	0.957202i	$-0.406537\pi$
$577$	13.9043			0.578845			0.289422	+	0.957202i	$0.406537\pi$
$578$	3.06743	+	8.25138i	0.127588	+	0.343212i
$579$		0			0
$580$	11.1536	−	9.62244i	0.463128	−	0.399550i
$581$		−	16.5568i		−	0.686893i
$582$		0			0
$583$		−	3.50431i		−	0.145134i
$584$	−34.5778	−	19.0270i	−1.43084	−	0.787341i
$585$		0			0
$586$	−12.4816	+	4.64001i	−0.515610	+	0.191677i
$587$	40.5217			1.67251			0.836256	−	0.548340i	$-0.184740\pi$
$587$	40.5217			1.67251			0.836256	+	0.548340i	$0.184740\pi$
$588$		0			0
$589$	−46.0100			−1.89581
$590$	−39.9880	+	14.8655i	−1.64628	+	0.612001i
$591$		0			0
$592$	−2.74795	+	18.5419i	−0.112940	+	0.762067i
$593$			3.71434i			0.152530i	0.997088	+	0.0762648i	$0.0242994\pi$
$593$			3.71434i			0.152530i	−0.997088	+	0.0762648i	$0.975701\pi$
$594$		0			0
$595$		−	11.9119i		−	0.488340i
$596$	11.3514	+	13.1577i	0.464973	+	0.538961i
$597$		0			0
$598$	−12.2116	−	32.8492i	−0.499370	−	1.34330i
$599$	−19.2075			−0.784797			−0.392398	−	0.919795i	$-0.628355\pi$
$599$	−19.2075			−0.784797			−0.392398	+	0.919795i	$0.628355\pi$
$600$		0			0
$601$	2.70359			0.110282			0.0551410	−	0.998479i	$-0.482439\pi$
$601$	2.70359			0.110282			0.0551410	+	0.998479i	$0.482439\pi$
$602$	−0.802373	−	2.15838i	−0.0327023	−	0.0879690i
$603$		0			0
$604$	22.5130	+	26.0954i	0.916042	+	1.06181i
$605$			37.4149i			1.52113i
$606$		0			0
$607$		−	16.7288i		−	0.679001i	−0.940606	−	0.339501i	$-0.889742\pi$
$607$		−	16.7288i		−	0.679001i	0.940606	−	0.339501i	$-0.110258\pi$
$608$	−7.57219	−	35.7393i	−0.307093	−	1.44942i
$609$		0			0
$610$	−26.7324	+	9.93772i	−1.08236	+	0.402367i
$611$	−31.2358			−1.26367
$612$		0			0
$613$	−2.25651			−0.0911395			−0.0455698	−	0.998961i	$-0.514510\pi$
$613$	−2.25651			−0.0911395			−0.0455698	+	0.998961i	$0.514510\pi$
$614$	−44.6275	+	16.5902i	−1.80102	+	0.669525i
$615$		0			0
$616$	1.13229	−	2.05771i	0.0456211	−	0.0829074i
$617$		−	7.73633i		−	0.311453i	−0.987800	−	0.155727i	$-0.950228\pi$
$617$		−	7.73633i		−	0.311453i	0.987800	−	0.155727i	$-0.0497719\pi$
$618$		0			0
$619$		−	7.22533i		−	0.290410i	−0.989402	−	0.145205i	$-0.953616\pi$
$619$		−	7.22533i		−	0.290410i	0.989402	−	0.145205i	$-0.0463842\pi$
$620$	39.1502	−	33.7756i	1.57231	−	1.35646i
$621$		0			0
$622$	−11.8977	−	32.0048i	−0.477054	−	1.28327i
$623$	−15.9785			−0.640166
$624$		0			0
$625$	0.880642			0.0352257
$626$	3.55358	+	9.55911i	0.142030	+	0.382059i
$627$		0			0
$628$	22.3191	−	19.2551i	0.890628	−	0.768363i
$629$			15.3825i			0.613339i
$630$		0			0
$631$			32.5190i			1.29456i	0.762251	+	0.647281i	$0.224094\pi$
$631$			32.5190i			1.29456i	−0.762251	+	0.647281i	$0.775906\pi$
$632$	13.7109	−	24.9169i	0.545392	−	0.991142i
$633$		0			0
$634$	14.9685	−	5.56452i	0.594477	−	0.220995i
$635$	−10.8785			−0.431699
$636$		0			0
$637$	4.86954			0.192938
$638$	2.23414	−	0.830536i	0.0884504	−	0.0328813i
$639$		0			0
$640$	32.6792	+	24.8521i	1.29176	+	0.982364i
$641$			47.9033i			1.89207i	0.324067	+	0.946034i	$0.394950\pi$
$641$			47.9033i			1.89207i	−0.324067	+	0.946034i	$0.605050\pi$
$642$		0			0
$643$			38.2215i			1.50731i	0.657270	+	0.753655i	$0.271711\pi$
$643$			38.2215i			1.50731i	−0.657270	+	0.753655i	$0.728289\pi$
$644$	−6.64846	−	7.70639i	−0.261986	−	0.303674i
$645$		0			0
$646$	−10.4466	−	28.1013i	−0.411016	−	1.10563i
$647$	−25.6193			−1.00720			−0.503599	−	0.863938i	$-0.667991\pi$
$647$	−25.6193			−1.00720			−0.503599	+	0.863938i	$0.667991\pi$
$648$		0			0
$649$	−6.90293			−0.270964
$650$	19.6010	+	52.7267i	0.768816	+	2.06811i
$651$		0			0
$652$	−12.2737	−	14.2267i	−0.480673	−	0.557160i
$653$			46.4500i			1.81773i	0.417093	+	0.908864i	$0.363049\pi$
$653$			46.4500i			1.81773i	−0.417093	+	0.908864i	$0.636951\pi$
$654$		0			0
$655$		−	57.0497i		−	2.22912i
$656$	−11.6809	−	1.73113i	−0.456061	−	0.0675892i
$657$		0			0
$658$	−8.50299	+	3.16097i	−0.331481	+	0.123227i
$659$	−7.60775			−0.296356			−0.148178	−	0.988961i	$-0.547341\pi$
$659$	−7.60775			−0.296356			−0.148178	+	0.988961i	$0.547341\pi$
$660$		0			0
$661$	0.148703			0.00578387			0.00289193	−	0.999996i	$-0.499079\pi$
$661$	0.148703			0.00578387			0.00289193	+	0.999996i	$0.499079\pi$
$662$	−28.5545	+	10.6151i	−1.10980	+	0.412567i
$663$		0			0
$664$	41.0284	+	22.5765i	1.59221	+	0.876139i
$665$		−	23.4354i		−	0.908786i
$666$		0			0
$667$		−	10.3290i		−	0.399940i
$668$	−2.71908	+	2.34581i	−0.105204	+	0.0907621i
$669$		0			0
$670$	20.7820	+	55.9036i	0.802880	+	2.15974i
$671$	−4.61469			−0.178148
$672$		0			0
$673$	−37.8555			−1.45922			−0.729611	−	0.683863i	$-0.760299\pi$
$673$	−37.8555			−1.45922			−0.729611	+	0.683863i	$0.760299\pi$
$674$	12.3001	+	33.0871i	0.473780	+	1.27447i
$675$		0			0
$676$	−16.2222	+	13.9952i	−0.623929	+	0.538276i
$677$		−	0.581474i		−	0.0223479i	−0.999938	−	0.0111739i	$-0.996443\pi$
$677$		−	0.581474i		−	0.0223479i	0.999938	−	0.0111739i	$-0.00355685\pi$
$678$		0			0
$679$			8.59479i			0.329838i
$680$	29.5181	+	16.2428i	1.13197	+	0.622882i
$681$		0			0
$682$	7.84203	−	2.91526i	0.300287	−	0.111631i
$683$	−17.4426			−0.667423			−0.333712	−	0.942675i	$-0.608301\pi$
$683$	−17.4426			−0.667423			−0.333712	+	0.942675i	$0.608301\pi$
$684$		0			0
$685$	−53.2885			−2.03605
$686$	1.32558	−	0.492782i	0.0506109	−	0.0188145i
$687$		0			0
$688$	6.44264	+	0.954812i	0.245623	+	0.0364019i
$689$			20.5501i			0.782896i
$690$		0			0
$691$		−	16.9008i		−	0.642939i	−0.946920	−	0.321469i	$-0.895823\pi$
$691$		−	16.9008i		−	0.642939i	0.946920	−	0.321469i	$-0.104177\pi$
$692$	−7.10512	−	8.23571i	−0.270096	−	0.313075i
$693$		0			0
$694$	8.61709	+	23.1799i	0.327100	+	0.879898i
$695$	54.9128			2.08296
$696$		0			0
$697$	−9.69052			−0.367055
$698$	−2.86891	−	7.71735i	−0.108590	−	0.292106i
$699$		0			0
$700$	10.6716	+	12.3697i	0.403347	+	0.467529i
$701$			27.8204i			1.05076i	0.850868	+	0.525380i	$0.176077\pi$
$701$			27.8204i			1.05076i	−0.850868	+	0.525380i	$0.823923\pi$
$702$		0			0
$703$			30.2634i			1.14141i
$704$	3.55511	+	5.61169i	0.133988	+	0.211498i
$705$		0			0
$706$	14.1454	−	5.25853i	0.532370	−	0.197908i
$707$	15.8624			0.596567
$708$		0			0
$709$	5.58359			0.209696			0.104848	−	0.994488i	$-0.466564\pi$
$709$	5.58359			0.209696			0.104848	+	0.994488i	$0.466564\pi$
$710$	34.4291	−	12.7989i	1.29210	−	0.480335i
$711$		0			0
$712$	21.7879	−	39.5953i	0.816538	−	1.48390i
$713$		−	36.2557i		−	1.35779i
$714$		0			0
$715$			14.6734i			0.548754i
$716$	−16.8850	+	14.5670i	−0.631023	+	0.544396i
$717$		0			0
$718$	7.58059	+	20.3918i	0.282905	+	0.761014i
$719$	−43.3477			−1.61660			−0.808299	−	0.588773i	$-0.799611\pi$
$719$	−43.3477			−1.61660			−0.808299	+	0.588773i	$0.799611\pi$
$720$		0			0
$721$	−3.04182			−0.113283
$722$	−11.1897	−	30.1004i	−0.416439	−	1.12022i
$723$		0			0
$724$	−17.2004	+	14.8391i	−0.639246	+	0.551491i
$725$			16.5792i			0.615737i
$726$		0			0
$727$			26.4800i			0.982087i	0.871135	+	0.491044i	$0.163384\pi$
$727$			26.4800i			0.982087i	−0.871135	+	0.491044i	$0.836616\pi$
$728$	−6.64000	+	12.0669i	−0.246095	+	0.447229i
$729$		0			0
$730$	67.1216	−	24.9523i	2.48428	−	0.923526i
$731$	5.34485			0.197687
$732$		0			0
$733$	8.11978			0.299911			0.149955	−	0.988693i	$-0.452087\pi$
$733$	8.11978			0.299911			0.149955	+	0.988693i	$0.452087\pi$
$734$	15.4793	−	5.75441i	0.571353	−	0.212399i
$735$		0			0
$736$	28.1624	−	5.96685i	1.03808	−	0.219941i
$737$			9.65036i			0.355475i
$738$		0			0
$739$		−	22.7938i		−	0.838484i	−0.907875	−	0.419242i	$-0.862296\pi$
$739$		−	22.7938i		−	0.838484i	0.907875	−	0.419242i	$-0.137704\pi$
$740$	−22.2162	−	25.7513i	−0.816683	−	0.946637i
$741$		0			0
$742$	2.07960	+	5.59413i	0.0763446	+	0.205367i
$743$	27.1485			0.995982			0.497991	−	0.867182i	$-0.334071\pi$
$743$	27.1485			0.995982			0.497991	+	0.867182i	$0.334071\pi$
$744$		0			0
$745$	−31.5301			−1.15517
$746$	8.41419	+	22.6341i	0.308065	+	0.828694i
$747$		0			0
$748$	3.56108	+	4.12773i	0.130206	+	0.150925i
$749$			19.1409i			0.699394i
$750$		0			0
$751$			42.9957i			1.56894i	0.620169	+	0.784469i	$0.287064\pi$
$751$			42.9957i			1.56894i	−0.620169	+	0.784469i	$0.712936\pi$
$752$	3.76150	−	25.3809i	0.137168	−	0.925547i
$753$		0			0
$754$	−13.1015	+	4.87046i	−0.477130	+	0.177372i
$755$	−62.5330			−2.27581
$756$		0			0
$757$	23.1826			0.842587			0.421294	−	0.906924i	$-0.361576\pi$
$757$	23.1826			0.842587			0.421294	+	0.906924i	$0.361576\pi$
$758$	22.4201	−	8.33461i	0.814334	−	0.302727i
$759$		0			0
$760$	58.0737	+	31.9560i	2.10656	+	1.15917i
$761$		−	44.4793i		−	1.61237i	−0.591661	−	0.806187i	$-0.701528\pi$
$761$		−	44.4793i		−	1.61237i	0.591661	−	0.806187i	$-0.298472\pi$
$762$		0			0
$763$		−	19.3448i		−	0.700328i
$764$	13.5533	−	11.6927i	0.490341	−	0.423027i
$765$		0			0
$766$	13.9840	+	37.6170i	0.505264	+	1.35916i
$767$	40.4804			1.46166
$768$		0			0
$769$	−41.5791			−1.49938			−0.749690	−	0.661790i	$-0.769797\pi$
$769$	−41.5791			−1.49938			−0.749690	+	0.661790i	$0.769797\pi$
$770$	1.48490	+	3.99438i	0.0535121	+	0.143947i
$771$		0			0
$772$	−39.3796	+	33.9736i	−1.41730	+	1.22274i
$773$		−	22.3930i		−	0.805419i	−0.915328	−	0.402710i	$-0.868068\pi$
$773$		−	22.3930i		−	0.805419i	0.915328	−	0.402710i	$-0.131932\pi$
$774$		0			0
$775$			58.1946i			2.09041i
$776$	−21.2982	−	11.7197i	−0.764561	−	0.420712i
$777$		0			0
$778$	38.1552	−	14.1841i	1.36793	−	0.508525i
$779$	−19.0651			−0.683078
$780$		0			0
$781$	5.94332			0.212669
$782$	22.1437	−	8.23188i	0.791858	−	0.294371i
$783$		0			0
$784$	−0.586403	+	3.95678i	−0.0209430	+	0.141314i
$785$			53.4837i			1.90891i
$786$		0			0
$787$		−	4.66218i		−	0.166189i	−0.996542	−	0.0830944i	$-0.973520\pi$
$787$		−	4.66218i		−	0.166189i	0.996542	−	0.0830944i	$-0.0264803\pi$
$788$	21.7420	+	25.2017i	0.774527	+	0.897773i
$789$		0			0
$790$	17.9808	+	48.3682i	0.639727	+	1.72086i
$791$	1.67488			0.0595518
$792$		0			0
$793$	27.0616			0.960986
$794$	11.7305	+	31.5549i	0.416298	+	1.11984i
$795$		0			0
$796$	−11.6571	−	13.5120i	−0.413174	−	0.478921i
$797$		−	12.3367i		−	0.436989i	−0.975838	−	0.218494i	$-0.929885\pi$
$797$		−	12.3367i		−	0.436989i	0.975838	−	0.218494i	$-0.0701145\pi$
$798$		0			0
$799$		−	21.0562i		−	0.744914i
$800$	−45.2039	+	9.57749i	−1.59820	+	0.338615i
$801$		0			0
$802$	7.86466	−	2.92367i	0.277711	−	0.103238i
$803$	11.5869			0.408892
$804$		0			0
$805$	18.4670			0.650876
$806$	−45.9876	+	17.0958i	−1.61984	+	0.602173i
$807$		0			0
$808$	−21.6296	+	39.3076i	−0.760928	+	1.38284i
$809$			9.09305i			0.319695i	0.987142	+	0.159847i	$0.0511002\pi$
$809$			9.09305i			0.319695i	−0.987142	+	0.159847i	$0.948900\pi$
$810$		0			0
$811$		−	32.0471i		−	1.12533i	−0.826686	−	0.562663i	$-0.809777\pi$
$811$		−	32.0471i		−	1.12533i	0.826686	−	0.562663i	$-0.190223\pi$
$812$	−3.07361	+	2.65167i	−0.107863	+	0.0930552i
$813$		0			0
$814$	−1.91753	−	5.15816i	−0.0672095	−	0.180793i
$815$	34.0917			1.19418
$816$		0			0
$817$	10.5154			0.367889
$818$	−5.43966	−	14.6327i	−0.190193	−	0.511619i
$819$		0			0
$820$	16.2226	−	13.9956i	0.566518	−	0.488746i
$821$			11.7754i			0.410966i	0.978661	+	0.205483i	$0.0658765\pi$
$821$			11.7754i			0.410966i	−0.978661	+	0.205483i	$0.934123\pi$
$822$		0			0
$823$		−	4.65294i		−	0.162191i	−0.996706	−	0.0810957i	$-0.974158\pi$
$823$		−	4.65294i		−	0.162191i	0.996706	−	0.0810957i	$-0.0258419\pi$
$824$	4.14776	−	7.53774i	0.144494	−	0.262589i
$825$		0			0
$826$	11.0195	−	4.09649i	0.383419	−	0.142535i
$827$	41.0263			1.42662			0.713312	−	0.700847i	$-0.247194\pi$
$827$	41.0263			1.42662			0.713312	+	0.700847i	$0.247194\pi$
$828$		0			0
$829$	0.541126			0.0187941			0.00939704	−	0.999956i	$-0.497009\pi$
$829$	0.541126			0.0187941			0.00939704	+	0.999956i	$0.497009\pi$
$830$	−79.6434	+	29.6073i	−2.76446	+	1.02768i
$831$		0			0
$832$	−20.8480	−	32.9083i	−0.722775	−	1.14089i
$833$			3.28257i			0.113734i
$834$		0			0
$835$		−	6.51580i		−	0.225489i
$836$	7.00605	+	8.12089i	0.242309	+	0.280867i
$837$		0			0
$838$	4.56283	+	12.2740i	0.157620	+	0.423998i
$839$	−32.6341			−1.12665			−0.563326	−	0.826234i	$-0.690479\pi$
$839$	−32.6341			−1.12665			−0.563326	+	0.826234i	$0.690479\pi$
$840$		0			0
$841$	24.8804			0.857945
$842$	8.33782	+	22.4287i	0.287340	+	0.772944i
$843$		0			0
$844$	3.05515	+	3.54130i	0.105163	+	0.121897i
$845$		−	38.8735i		−	1.33729i
$846$		0			0
$847$		−	10.3105i		−	0.354272i
$848$	−16.6981	−	2.47470i	−0.573416	−	0.0849814i
$849$		0			0
$850$	−35.5432	+	13.2131i	−1.21912	+	0.453206i
$851$	−23.8475			−0.817480
$852$		0			0
$853$	−12.0395			−0.412225			−0.206112	−	0.978528i	$-0.566081\pi$
$853$	−12.0395			−0.412225			−0.206112	+	0.978528i	$0.566081\pi$
$854$	7.36669	−	2.73855i	0.252083	−	0.0937112i
$855$		0			0
$856$	−47.4319	−	26.1001i	−1.62119	−	0.892084i
$857$		−	23.7723i		−	0.812046i	−0.913863	−	0.406023i	$-0.866915\pi$
$857$		−	23.7723i		−	0.812046i	0.913863	−	0.406023i	$-0.133085\pi$
$858$		0			0
$859$			25.4805i			0.869382i	0.900580	+	0.434691i	$0.143142\pi$
$859$			25.4805i			0.869382i	−0.900580	+	0.434691i	$0.856858\pi$
$860$	−8.94765	+	7.71932i	−0.305112	+	0.263227i
$861$		0			0
$862$	6.18005	+	16.6243i	0.210493	+	0.566226i
$863$	4.38551			0.149284			0.0746422	−	0.997210i	$-0.476219\pi$
$863$	4.38551			0.149284			0.0746422	+	0.997210i	$0.476219\pi$
$864$		0			0
$865$	19.7354			0.671025
$866$	−3.12986	−	8.41931i	−0.106357	−	0.286100i
$867$		0			0
$868$	−10.7887	+	9.30759i	−0.366191	+	0.315920i
$869$			8.34956i			0.283239i
$870$		0			0
$871$		−	56.5920i		−	1.91755i
$872$	47.9370	+	26.3781i	1.62335	+	0.893276i
$873$		0			0
$874$	43.5655	−	16.1954i	1.47362	−	0.547817i
$875$	−11.4975			−0.388688
$876$		0			0
$877$	−52.5847			−1.77566			−0.887829	−	0.460173i	$-0.847787\pi$
$877$	−52.5847			−1.77566			−0.887829	+	0.460173i	$0.847787\pi$
$878$	36.6751	−	13.6339i	1.23772	−	0.460121i
$879$		0			0
$880$	−11.9230	−	1.76701i	−0.401924	−	0.0595658i
$881$			6.08910i			0.205147i	0.994725	+	0.102573i	$0.0327077\pi$
$881$			6.08910i			0.205147i	−0.994725	+	0.102573i	$0.967292\pi$
$882$		0			0
$883$		−	26.9826i		−	0.908038i	−0.890992	−	0.454019i	$-0.849990\pi$
$883$		−	26.9826i		−	0.908038i	0.890992	−	0.454019i	$-0.150010\pi$
$884$	−20.8830	−	24.2060i	−0.702372	−	0.814136i
$885$		0			0
$886$	−10.7253	−	28.8509i	−0.360322	−	0.969265i
$887$	2.32111			0.0779354			0.0389677	−	0.999240i	$-0.487593\pi$
$887$	2.32111			0.0779354			0.0389677	+	0.999240i	$0.487593\pi$
$888$		0			0
$889$	2.99779			0.100543
$890$	28.5731	+	76.8615i	0.957773	+	2.57640i
$891$		0			0
$892$	16.6647	+	19.3164i	0.557975	+	0.646762i
$893$		−	41.4258i		−	1.38626i
$894$		0			0
$895$		−	40.4619i		−	1.35249i
$896$	−9.00544	−	6.84851i	−0.300851	−	0.228793i
$897$		0			0
$898$	−9.35349	+	3.47714i	−0.312130	+	0.116034i
$899$	−14.4602			−0.482274
$900$		0			0
$901$	−13.8529			−0.461506
$902$	3.24949	−	1.20799i	0.108196	−	0.0402217i
$903$		0			0
$904$	−2.28383	+	4.15040i	−0.0759589	+	0.138040i
$905$		−	41.2176i		−	1.37012i
$906$		0			0
$907$			40.0781i			1.33077i	0.746500	+	0.665385i	$0.231733\pi$
$907$			40.0781i			1.33077i	−0.746500	+	0.665385i	$0.768267\pi$
$908$	4.37464	−	3.77409i	0.145177	−	0.125248i
$909$		0			0
$910$	−8.70781	−	23.4240i	−0.288661	−	0.776497i
$911$	35.2588			1.16818			0.584089	−	0.811690i	$-0.301452\pi$
$911$	35.2588			1.16818			0.584089	+	0.811690i	$0.301452\pi$
$912$		0			0
$913$	−13.7484			−0.455007
$914$	−15.5253	−	41.7631i	−0.513532	−	1.38140i
$915$		0			0
$916$	−19.9183	+	17.1839i	−0.658118	+	0.567772i
$917$			15.7213i			0.519162i
$918$		0			0
$919$			19.4185i			0.640556i	0.947324	+	0.320278i	$0.103776\pi$
$919$			19.4185i			0.640556i	−0.947324	+	0.320278i	$0.896224\pi$
$920$	−25.1812	+	45.7619i	−0.830200	+	1.50872i
$921$		0			0
$922$	45.1332	−	16.7782i	1.48638	−	0.552559i
$923$	−34.8530			−1.14720
$924$		0			0
$925$	38.2779			1.25857
$926$	−12.7903	+	4.75476i	−0.420315	+	0.156251i
$927$		0			0
$928$	−2.37981	−	11.2323i	−0.0781212	−	0.368717i
$929$			14.8109i			0.485930i	0.970035	+	0.242965i	$0.0781200\pi$
$929$			14.8109i			0.485930i	−0.970035	+	0.242965i	$0.921880\pi$
$930$		0			0
$931$			6.45812i			0.211656i
$932$	−4.41276	−	5.11493i	−0.144545	−	0.167545i
$933$		0			0
$934$	−0.101627	−	0.273376i	−0.00332533	−	0.00894512i
$935$	−9.89138			−0.323483
$936$		0			0
$937$	−4.16694			−0.136128			−0.0680641	−	0.997681i	$-0.521682\pi$
$937$	−4.16694			−0.136128			−0.0680641	+	0.997681i	$0.521682\pi$
$938$	−5.72693	−	15.4054i	−0.186991	−	0.503005i
$939$		0			0
$940$	30.4104	+	35.2495i	0.991879	+	1.14971i
$941$			10.4690i			0.341280i	0.985333	+	0.170640i	$0.0545835\pi$
$941$			10.4690i			0.341280i	−0.985333	+	0.170640i	$0.945417\pi$
$942$		0			0
$943$		−	15.0232i		−	0.489223i
$944$	−4.87476	+	32.8927i	−0.158660	+	1.07057i
$945$		0			0
$946$	−1.79227	+	0.666274i	−0.0582719	+	0.0216624i
$947$	5.84942			0.190081			0.0950403	−	0.995473i	$-0.469702\pi$
$947$	5.84942			0.190081			0.0950403	+	0.995473i	$0.469702\pi$
$948$		0			0
$949$	−67.9481			−2.20569
$950$	−69.9276	+	25.9954i	−2.26875	+	0.843404i
$951$		0			0
$952$	−8.13433	−	4.47604i	−0.263635	−	0.145069i
$953$		−	31.5548i		−	1.02216i	−0.859533	−	0.511080i	$-0.829246\pi$
$953$		−	31.5548i		−	1.02216i	0.859533	−	0.511080i	$-0.170754\pi$
$954$		0			0
$955$			32.4780i			1.05096i
$956$	11.8466	−	10.2203i	0.383147	−	0.330549i
$957$		0			0
$958$	0.740170	+	1.99105i	0.0239138	+	0.0643280i
$959$	14.6848			0.474196
$960$		0			0
$961$	−19.7566			−0.637308
$962$	11.2449	+	30.2487i	0.362549	+	0.975256i
$963$		0			0
$964$	−3.43883	+	2.96675i	−0.110757	+	0.0955525i
$965$		−	94.3661i		−	3.03775i
$966$		0			0
$967$			28.7726i			0.925264i	0.886550	+	0.462632i	$0.153095\pi$
$967$			28.7726i			0.925264i	−0.886550	+	0.462632i	$0.846905\pi$
$968$	25.5497	+	14.0591i	0.821199	+	0.451878i
$969$		0			0
$970$	41.3436	−	15.3694i	1.32746	−	0.493481i
$971$	9.64706			0.309589			0.154794	−	0.987947i	$-0.450528\pi$
$971$	9.64706			0.309589			0.154794	+	0.987947i	$0.450528\pi$
$972$		0			0
$973$	−15.1324			−0.485121
$974$	26.1482	−	9.72054i	0.837842	−	0.311466i
$975$		0			0
$976$	−3.25883	+	21.9891i	−0.104313	+	0.703855i
$977$		−	14.7508i		−	0.471920i	−0.971763	−	0.235960i	$-0.924177\pi$
$977$		−	14.7508i		−	0.471920i	0.971763	−	0.235960i	$-0.0758234\pi$
$978$		0			0
$979$			13.2682i			0.424054i
$980$	−4.74086	−	5.49525i	−0.151441	−	0.175539i
$981$		0			0
$982$	5.11157	+	13.7501i	0.163117	+	0.438784i
$983$	−32.5463			−1.03807			−0.519033	−	0.854755i	$-0.673708\pi$
$983$	−32.5463			−1.03807			−0.519033	+	0.854755i	$0.673708\pi$
$984$		0			0
$985$	−60.3914			−1.92423
$986$	−3.28319	−	8.83178i	−0.104558	−	0.281261i
$987$		0			0
$988$	−41.0852	−	47.6228i	−1.30709	−	1.51508i
$989$			8.28613i			0.263484i
$990$		0			0
$991$		−	8.31633i		−	0.264177i	−0.991238	−	0.132088i	$-0.957832\pi$
$991$		−	8.31633i		−	0.264177i	0.991238	−	0.132088i	$-0.0421683\pi$
$992$	−8.35336	−	39.4263i	−0.265220	−	1.25179i
$993$		0			0
$994$	−9.48765	+	3.52701i	−0.300930	+	0.111870i
$995$	32.3791			1.02649
$996$		0			0
$997$	−39.4688			−1.24999			−0.624995	−	0.780629i	$-0.714899\pi$
$997$	−39.4688			−1.24999			−0.624995	+	0.780629i	$0.714899\pi$
$998$	26.8433	−	9.97892i	0.849709	−	0.315877i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.b.323.16	yes	24
3.2	odd	2	inner	756.2.e.b.323.9	✓	24
4.3	odd	2	inner	756.2.e.b.323.10	yes	24
12.11	even	2	inner	756.2.e.b.323.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.b.323.9	✓	24	3.2	odd	2	inner
756.2.e.b.323.10	yes	24	4.3	odd	2	inner
756.2.e.b.323.15	yes	24	12.11	even	2	inner
756.2.e.b.323.16	yes	24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.492782 + 1.32558i) q^{2} +(-1.51433 + 1.30645i) q^{4} -3.62883i q^{5} +1.00000i q^{7} +(-2.47803 - 1.36358i) q^{8} +O(q^{10})\)	\(q+(0.492782 + 1.32558i) q^{2} +(-1.51433 + 1.30645i) q^{4} -3.62883i q^{5} +1.00000i q^{7} +(-2.47803 - 1.36358i) q^{8} +(4.81031 - 1.78822i) q^{10} +0.830379 q^{11} -4.86954 q^{13} +(-1.32558 + 0.492782i) q^{14} +(0.586403 - 3.95678i) q^{16} -3.28257i q^{17} -6.45812i q^{19} +(4.74086 + 5.49525i) q^{20} +(0.409196 + 1.10073i) q^{22} +5.08897 q^{23} -8.16839 q^{25} +(-2.39962 - 6.45497i) q^{26} +(-1.30645 - 1.51433i) q^{28} -2.02968i q^{29} -7.12436i q^{31} +(5.53401 - 1.17251i) q^{32} +(4.35132 - 1.61759i) q^{34} +3.62883 q^{35} -4.68611 q^{37} +(8.56076 - 3.18244i) q^{38} +(-4.94819 + 8.99236i) q^{40} -2.95211i q^{41} +1.62825i q^{43} +(-1.25747 + 1.08484i) q^{44} +(2.50775 + 6.74585i) q^{46} +6.41454 q^{47} -1.00000 q^{49} +(-4.02523 - 10.8279i) q^{50} +(7.37410 - 6.36179i) q^{52} -4.22013i q^{53} -3.01330i q^{55} +(1.36358 - 2.47803i) q^{56} +(2.69051 - 1.00019i) q^{58} -8.31299 q^{59} -5.55733 q^{61} +(9.44392 - 3.51076i) q^{62} +(4.28131 + 6.75799i) q^{64} +17.6707i q^{65} +11.6216i q^{67} +(4.28850 + 4.97090i) q^{68} +(1.78822 + 4.81031i) q^{70} +7.15735 q^{71} +13.9537 q^{73} +(-2.30923 - 6.21181i) q^{74} +(8.43718 + 9.77974i) q^{76} +0.830379i q^{77} +10.0551i q^{79} +(-14.3585 - 2.12795i) q^{80} +(3.91327 - 1.45475i) q^{82} -16.5568 q^{83} -11.9119 q^{85} +(-2.15838 + 0.802373i) q^{86} +(-2.05771 - 1.13229i) q^{88} +15.9785i q^{89} -4.86954i q^{91} +(-7.70639 + 6.64846i) q^{92} +(3.16097 + 8.50299i) q^{94} -23.4354 q^{95} +8.59479 q^{97} +(-0.492782 - 1.32558i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4}+O(q^{10}) \) 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