LMFDB - Embedded newform 756.2.e.b.323.9

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			323.9
Character	$\chi$	$=$	756.323
Dual form			756.2.e.b.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.492782 - 1.32558i) q^{2} +(-1.51433 + 1.30645i) q^{4} +3.62883i q^{5} +1.00000i q^{7} +(2.47803 + 1.36358i) q^{8} +O(q^{10})$	\(q+(-0.492782 - 1.32558i) q^{2} +(-1.51433 + 1.30645i) q^{4} +3.62883i q^{5} +1.00000i q^{7} +(2.47803 + 1.36358i) q^{8} +(4.81031 - 1.78822i) q^{10} -0.830379 q^{11} -4.86954 q^{13} +(1.32558 - 0.492782i) q^{14} +(0.586403 - 3.95678i) q^{16} +3.28257i q^{17} -6.45812i q^{19} +(-4.74086 - 5.49525i) q^{20} +(0.409196 + 1.10073i) q^{22} -5.08897 q^{23} -8.16839 q^{25} +(2.39962 + 6.45497i) q^{26} +(-1.30645 - 1.51433i) q^{28} +2.02968i q^{29} -7.12436i q^{31} +(-5.53401 + 1.17251i) q^{32} +(4.35132 - 1.61759i) q^{34} -3.62883 q^{35} -4.68611 q^{37} +(-8.56076 + 3.18244i) q^{38} +(-4.94819 + 8.99236i) q^{40} +2.95211i q^{41} +1.62825i q^{43} +(1.25747 - 1.08484i) q^{44} +(2.50775 + 6.74585i) q^{46} -6.41454 q^{47} -1.00000 q^{49} +(4.02523 + 10.8279i) q^{50} +(7.37410 - 6.36179i) q^{52} +4.22013i q^{53} -3.01330i q^{55} +(-1.36358 + 2.47803i) q^{56} +(2.69051 - 1.00019i) q^{58} +8.31299 q^{59} -5.55733 q^{61} +(-9.44392 + 3.51076i) q^{62} +(4.28131 + 6.75799i) q^{64} -17.6707i q^{65} +11.6216i q^{67} +(-4.28850 - 4.97090i) q^{68} +(1.78822 + 4.81031i) q^{70} -7.15735 q^{71} +13.9537 q^{73} +(2.30923 + 6.21181i) q^{74} +(8.43718 + 9.77974i) q^{76} -0.830379i q^{77} +10.0551i q^{79} +(14.3585 + 2.12795i) q^{80} +(3.91327 - 1.45475i) q^{82} +16.5568 q^{83} -11.9119 q^{85} +(2.15838 - 0.802373i) q^{86} +(-2.05771 - 1.13229i) q^{88} -15.9785i q^{89} -4.86954i q^{91} +(7.70639 - 6.64846i) q^{92} +(3.16097 + 8.50299i) q^{94} +23.4354 q^{95} +8.59479 q^{97} +(0.492782 + 1.32558i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.301311\pi$
$5$			3.62883i			1.62286i	−0.584449	+	0.811431i	$0.698689\pi$
$6$		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	$-0.539952\pi$
$11$	−0.830379			−0.250369			−0.125184	+	0.992134i	$0.539952\pi$
$12$		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	$0.130320\pi$
$17$			3.28257i			0.796140i	−0.917355	+	0.398070i	$0.869680\pi$
$18$		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	$-0.678019\pi$
$23$	−5.08897			−1.06112			−0.530562	+	0.847646i	$0.678019\pi$
$24$		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	$0.0603467\pi$
$29$			2.02968i			0.376902i	−0.982083	+	0.188451i	$0.939653\pi$
$30$		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	$0.0740431\pi$
$41$			2.95211i			0.461043i	−0.973067	+	0.230521i	$0.925957\pi$
$42$		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	$-0.654963\pi$
$47$	−6.41454			−0.935656			−0.467828	+	0.883819i	$0.654963\pi$
$48$		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	$0.0936020\pi$
$53$			4.22013i			0.579679i	−0.957075	+	0.289840i	$0.906398\pi$
$54$		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	$-0.317997\pi$
$59$	8.31299			1.08226			0.541130	+	0.840939i	$0.317997\pi$
$60$		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	$-0.639624\pi$
$71$	−7.15735			−0.849422			−0.424711	+	0.905329i	$0.639624\pi$
$72$		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	$-0.137096\pi$
$83$	16.5568			1.81735			0.908674	+	0.417506i	$0.137096\pi$
$84$		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	$-0.678490\pi$
$89$		−	15.9785i		−	1.69372i	0.531817	−	0.846860i	$-0.321510\pi$
$90$		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	$0.289497\pi$
$101$			15.8624i			1.57837i	−0.614156	+	0.789185i	$0.710503\pi$
$102$		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	$-0.876112\pi$
$107$	−19.1409			−1.85042			−0.925211	+	0.379452i	$0.876112\pi$
$108$		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	$0.0251023\pi$
$113$			1.67488i			0.157559i	−0.996892	+	0.0787796i	$0.974898\pi$
$114$		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	$-0.740979\pi$
$131$	−15.7213			−1.37357			−0.686786	+	0.726860i	$0.740979\pi$
$132$		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	$0.215841\pi$
$137$			14.6848i			1.25460i	−0.778776	+	0.627302i	$0.784159\pi$
$138$		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	$0.115828\pi$
$149$			8.68879i			0.711814i	−0.934521	+	0.355907i	$0.884172\pi$
$150$		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	$-0.522132\pi$
$167$	−1.79557			−0.138945			−0.0694725	+	0.997584i	$0.522132\pi$
$168$		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	$-0.933714\pi$
$173$		−	5.43851i		−	0.413483i	0.978396	−	0.206741i	$-0.0662858\pi$
$174$		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	$-0.636814\pi$
$179$	−11.1501			−0.833401			−0.416700	+	0.909044i	$0.636814\pi$
$180$		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	$-0.395040\pi$
$191$	8.95001			0.647600			0.323800	+	0.946126i	$0.395040\pi$
$192$		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	$0.201998\pi$
$197$			16.6421i			1.18570i	−0.805312	+	0.592851i	$0.798002\pi$
$198$		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	$-0.469437\pi$
$227$	2.88882			0.191738			0.0958690	+	0.995394i	$0.469437\pi$
$228$		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	$-0.964710\pi$
$233$		−	3.37768i		−	0.221279i	0.993861	−	0.110640i	$-0.0352900\pi$
$234$		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	$-0.418578\pi$
$239$	7.82300			0.506028			0.253014	+	0.967463i	$0.418578\pi$
$240$		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	$-0.640534\pi$
$251$	−13.5393			−0.854592			−0.427296	+	0.904112i	$0.640534\pi$
$252$		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	$-0.988793\pi$
$257$		−	1.12864i		−	0.0704028i	0.999380	−	0.0352014i	$-0.0112073\pi$
$258$		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	$-0.439249\pi$
$263$	6.15279			0.379397			0.189699	+	0.981842i	$0.439249\pi$
$264$		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	$-0.915914\pi$
$269$		−	8.56481i		−	0.522206i	0.965311	−	0.261103i	$-0.0840862\pi$
$270$		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	$-0.971037\pi$
$281$		−	3.04631i		−	0.181728i	0.995863	−	0.0908638i	$-0.0289628\pi$
$282$		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	$-0.911308\pi$
$293$		−	9.41595i		−	0.550086i	0.961432	−	0.275043i	$-0.0886920\pi$
$294$		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	$-0.260004\pi$
$311$	24.1439			1.36908			0.684539	+	0.728977i	$0.260004\pi$
$312$		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	$0.102713\pi$
$317$			11.2921i			0.634225i	−0.948388	+	0.317113i	$0.897287\pi$
$318$		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	$-0.655517\pi$
$347$	−17.4866			−0.938731			−0.469365	+	0.883004i	$0.655517\pi$
$348$		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	$0.0916560\pi$
$353$			10.6711i			0.567966i	−0.958829	+	0.283983i	$0.908344\pi$
$354$		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	$-0.633059\pi$
$359$	−15.3833			−0.811897			−0.405949	+	0.913896i	$0.633059\pi$
$360$		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	$-0.758168\pi$
$383$	−28.3777			−1.45003			−0.725017	+	0.688731i	$0.758168\pi$
$384$		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	$0.260339\pi$
$389$			28.7838i			1.45940i	−0.683770	+	0.729698i	$0.739661\pi$
$390$		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	$0.0473285\pi$
$401$			5.93299i			0.296279i	−0.988966	+	0.148140i	$0.952671\pi$
$402$		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	$-0.572622\pi$
$419$	−9.25932			−0.452348			−0.226174	+	0.974087i	$0.572622\pi$
$420$		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	$-0.597669\pi$
$431$	−12.5411			−0.604086			−0.302043	+	0.953294i	$0.597669\pi$
$432$		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	$-0.327035\pi$
$443$	21.7647			1.03407			0.517036	+	0.855963i	$0.327035\pi$
$444$		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	$-0.946753\pi$
$449$		−	7.05614i		−	0.333000i	0.986041	−	0.166500i	$-0.0532466\pi$
$450$		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	$0.291421\pi$
$461$			34.0478i			1.58577i	−0.609374	+	0.792883i	$0.708579\pi$
$462$		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	$-0.498481\pi$
$467$	0.206231			0.00954322			0.00477161	+	0.999989i	$0.498481\pi$
$468$		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	$-0.510925\pi$
$479$	−1.50202			−0.0686292			−0.0343146	+	0.999411i	$0.510925\pi$
$480$		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	$-0.575202\pi$
$491$	−10.3729			−0.468122			−0.234061	+	0.972222i	$0.575202\pi$
$492$		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	$-0.587779\pi$
$503$	−12.2134			−0.544566			−0.272283	+	0.962217i	$0.587779\pi$
$504$		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	$0.135281\pi$
$509$			18.6047i			0.824639i	−0.911039	+	0.412319i	$0.864719\pi$
$510$		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	$0.00739807\pi$
$521$			1.06091i			0.0464793i	−0.999730	+	0.0232396i	$0.992602\pi$
$522$		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	$0.185632\pi$
$557$			25.9931i			1.10136i	−0.834716	+	0.550681i	$0.814368\pi$
$558$		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	$-0.577513\pi$
$563$	−11.4421			−0.482228			−0.241114	+	0.970497i	$0.577513\pi$
$564$		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	$-0.840538\pi$
$569$		−	22.9126i		−	0.960545i	0.877119	−	0.480272i	$-0.159462\pi$
$570$		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	$-0.815260\pi$
$587$	−40.5217			−1.67251			−0.836256	+	0.548340i	$0.815260\pi$
$588$		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	$-0.975701\pi$
$593$		−	3.71434i		−	0.152530i	0.997088	−	0.0762648i	$-0.0242994\pi$
$594$		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	$-0.371645\pi$
$599$	19.2075			0.784797			0.392398	+	0.919795i	$0.371645\pi$
$600$		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	$0.0497719\pi$
$617$			7.73633i			0.311453i	−0.987800	+	0.155727i	$0.950228\pi$
$618$		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	$-0.605050\pi$
$641$		−	47.9033i		−	1.89207i	0.324067	−	0.946034i	$-0.394950\pi$
$642$		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	$-0.332009\pi$
$647$	25.6193			1.00720			0.503599	+	0.863938i	$0.332009\pi$
$648$		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	$-0.636951\pi$
$653$		−	46.4500i		−	1.81773i	0.417093	−	0.908864i	$-0.363049\pi$
$654$		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	$-0.452659\pi$
$659$	7.60775			0.296356			0.148178	+	0.988961i	$0.452659\pi$
$660$		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	$0.00355685\pi$
$677$			0.581474i			0.0223479i	−0.999938	+	0.0111739i	$0.996443\pi$
$678$		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	$-0.391699\pi$
$683$	17.4426			0.667423			0.333712	+	0.942675i	$0.391699\pi$
$684$		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	$-0.823923\pi$
$701$		−	27.8204i		−	1.05076i	0.850868	−	0.525380i	$-0.176077\pi$
$702$		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	$-0.200389\pi$
$719$	43.3477			1.61660			0.808299	+	0.588773i	$0.200389\pi$
$720$		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	$-0.665929\pi$
$743$	−27.1485			−0.995982			−0.497991	+	0.867182i	$0.665929\pi$
$744$		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	$0.298472\pi$
$761$			44.4793i			1.61237i	−0.591661	+	0.806187i	$0.701528\pi$
$762$		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	$0.131932\pi$
$773$			22.3930i			0.805419i	−0.915328	+	0.402710i	$0.868068\pi$
$774$		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	$0.0701145\pi$
$797$			12.3367i			0.436989i	−0.975838	+	0.218494i	$0.929885\pi$
$798$		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	$-0.948900\pi$
$809$		−	9.09305i		−	0.319695i	0.987142	−	0.159847i	$-0.0511002\pi$
$810$		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	$-0.934123\pi$
$821$		−	11.7754i		−	0.410966i	0.978661	−	0.205483i	$-0.0658765\pi$
$822$		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	$-0.752806\pi$
$827$	−41.0263			−1.42662			−0.713312	+	0.700847i	$0.752806\pi$
$828$		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	$-0.309521\pi$
$839$	32.6341			1.12665			0.563326	+	0.826234i	$0.309521\pi$
$840$		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	$0.133085\pi$
$857$			23.7723i			0.812046i	−0.913863	+	0.406023i	$0.866915\pi$
$858$		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	$-0.523781\pi$
$863$	−4.38551			−0.149284			−0.0746422	+	0.997210i	$0.523781\pi$
$864$		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	$-0.967292\pi$
$881$		−	6.08910i		−	0.205147i	0.994725	−	0.102573i	$-0.0327077\pi$
$882$		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	$-0.512407\pi$
$887$	−2.32111			−0.0779354			−0.0389677	+	0.999240i	$0.512407\pi$
$888$		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	$-0.698548\pi$
$911$	−35.2588			−1.16818			−0.584089	+	0.811690i	$0.698548\pi$
$912$		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	$-0.921880\pi$
$929$		−	14.8109i		−	0.485930i	0.970035	−	0.242965i	$-0.0781200\pi$
$930$		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	$-0.945417\pi$
$941$		−	10.4690i		−	0.341280i	0.985333	−	0.170640i	$-0.0545835\pi$
$942$		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	$-0.530298\pi$
$947$	−5.84942			−0.190081			−0.0950403	+	0.995473i	$0.530298\pi$
$948$		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	$0.170754\pi$
$953$			31.5548i			1.02216i	−0.859533	+	0.511080i	$0.829246\pi$
$954$		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	$-0.549472\pi$
$971$	−9.64706			−0.309589			−0.154794	+	0.987947i	$0.549472\pi$
$972$		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	$0.0758234\pi$
$977$			14.7508i			0.471920i	−0.971763	+	0.235960i	$0.924177\pi$
$978$		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	$-0.326292\pi$
$983$	32.5463			1.03807			0.519033	+	0.854755i	$0.326292\pi$
$984$		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.323.9	✓	24
3.2	odd	2	inner	756.2.e.b.323.16	yes	24
4.3	odd	2	inner	756.2.e.b.323.15	yes	24
12.11	even	2	inner	756.2.e.b.323.10	yes	24

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

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

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