LMFDB - Embedded newform 1512.2.j.d.323.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.3
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37397 - 0.334962i) q^{2} +(1.77560 + 0.920458i) q^{4} +4.18263 q^{5} -1.00000i q^{7} +(-2.13131 - 1.85944i) q^{8} +O(q^{10})$	\(q+(-1.37397 - 0.334962i) q^{2} +(1.77560 + 0.920458i) q^{4} +4.18263 q^{5} -1.00000i q^{7} +(-2.13131 - 1.85944i) q^{8} +(-5.74682 - 1.40102i) q^{10} +1.86730i q^{11} -3.07604i q^{13} +(-0.334962 + 1.37397i) q^{14} +(2.30551 + 3.26873i) q^{16} -0.504885i q^{17} +3.05596 q^{19} +(7.42668 + 3.84993i) q^{20} +(0.625474 - 2.56561i) q^{22} -5.97229 q^{23} +12.4944 q^{25} +(-1.03036 + 4.22639i) q^{26} +(0.920458 - 1.77560i) q^{28} +3.52884 q^{29} -10.8980i q^{31} +(-2.07281 - 5.26341i) q^{32} +(-0.169117 + 0.693698i) q^{34} -4.18263i q^{35} -11.3660i q^{37} +(-4.19880 - 1.02363i) q^{38} +(-8.91447 - 7.77736i) q^{40} +7.26960i q^{41} +9.02120 q^{43} +(-1.71877 + 3.31557i) q^{44} +(8.20576 + 2.00049i) q^{46} +0.327367 q^{47} -1.00000 q^{49} +(-17.1669 - 4.18514i) q^{50} +(2.83136 - 5.46181i) q^{52} +8.32940 q^{53} +7.81021i q^{55} +(-1.85944 + 2.13131i) q^{56} +(-4.84853 - 1.18203i) q^{58} +5.98008i q^{59} +13.2783i q^{61} +(-3.65043 + 14.9736i) q^{62} +(1.08494 + 7.92609i) q^{64} -12.8659i q^{65} -9.21499 q^{67} +(0.464725 - 0.896474i) q^{68} +(-1.40102 + 5.74682i) q^{70} -9.02460 q^{71} +0.416491 q^{73} +(-3.80718 + 15.6166i) q^{74} +(5.42616 + 2.81288i) q^{76} +1.86730 q^{77} +6.00459i q^{79} +(9.64311 + 13.6719i) q^{80} +(2.43504 - 9.98822i) q^{82} -2.62368i q^{83} -2.11175i q^{85} +(-12.3949 - 3.02176i) q^{86} +(3.47213 - 3.97978i) q^{88} -5.69486i q^{89} -3.07604 q^{91} +(-10.6044 - 5.49724i) q^{92} +(-0.449793 - 0.109655i) q^{94} +12.7819 q^{95} +6.21289 q^{97} +(1.37397 + 0.334962i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.37397	−	0.334962i	−0.971545	−	0.236854i
$2$	−1.37397	−	0.334962i	−0.971545	−	0.236854i
$3$		0			0
$3$		0			0
$4$	1.77560	+	0.920458i	0.887800	+	0.460229i
$5$	4.18263			1.87053			0.935264	−	0.353951i	$-0.115162\pi$
$5$	4.18263			1.87053			0.935264	+	0.353951i	$0.115162\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.13131	−	1.85944i	−0.753531	−	0.657412i
$9$		0			0
$10$	−5.74682	−	1.40102i	−1.81730	−	0.443042i
$11$			1.86730i			0.563011i	0.959560	+	0.281506i	$0.0908338\pi$
$11$			1.86730i			0.563011i	−0.959560	+	0.281506i	$0.909166\pi$
$12$		0			0
$13$		−	3.07604i		−	0.853139i	−0.904455	−	0.426569i	$-0.859722\pi$
$13$		−	3.07604i		−	0.853139i	0.904455	−	0.426569i	$-0.140278\pi$
$14$	−0.334962	+	1.37397i	−0.0895224	+	0.367210i
$15$		0			0
$16$	2.30551	+	3.26873i	0.576379	+	0.817183i
$17$		−	0.504885i		−	0.122453i	−0.998124	−	0.0612263i	$-0.980499\pi$
$17$		−	0.504885i		−	0.122453i	0.998124	−	0.0612263i	$-0.0195011\pi$
$18$		0			0
$19$	3.05596			0.701085			0.350543	−	0.936547i	$-0.385997\pi$
$19$	3.05596			0.701085			0.350543	+	0.936547i	$0.385997\pi$
$20$	7.42668	+	3.84993i	1.66066	+	0.860871i
$21$		0			0
$22$	0.625474	−	2.56561i	0.133352	−	0.546991i
$23$	−5.97229			−1.24531			−0.622654	−	0.782497i	$-0.713946\pi$
$23$	−5.97229			−1.24531			−0.622654	+	0.782497i	$0.713946\pi$
$24$		0			0
$25$	12.4944			2.49887
$26$	−1.03036	+	4.22639i	−0.202069	+	0.828863i
$27$		0			0
$28$	0.920458	−	1.77560i	0.173950	−	0.335557i
$29$	3.52884			0.655289			0.327644	−	0.944801i	$-0.393745\pi$
$29$	3.52884			0.655289			0.327644	+	0.944801i	$0.393745\pi$
$30$		0			0
$31$		−	10.8980i		−	1.95734i	−0.205435	−	0.978671i	$-0.565861\pi$
$31$		−	10.8980i		−	1.95734i	0.205435	−	0.978671i	$-0.434139\pi$
$32$	−2.07281	−	5.26341i	−0.366425	−	0.930448i
$33$		0			0
$34$	−0.169117	+	0.693698i	−0.0290034	+	0.118968i
$35$		−	4.18263i		−	0.706993i
$36$		0			0
$37$		−	11.3660i		−	1.86856i	−0.356542	−	0.934279i	$-0.616044\pi$
$37$		−	11.3660i		−	1.86856i	0.356542	−	0.934279i	$-0.383956\pi$
$38$	−4.19880	−	1.02363i	−0.681136	−	0.166055i
$39$		0			0
$40$	−8.91447	−	7.77736i	−1.40950	−	1.22971i
$41$			7.26960i			1.13532i	0.823263	+	0.567660i	$0.192151\pi$
$41$			7.26960i			1.13532i	−0.823263	+	0.567660i	$0.807849\pi$
$42$		0			0
$43$	9.02120			1.37572			0.687860	−	0.725844i	$-0.258550\pi$
$43$	9.02120			1.37572			0.687860	+	0.725844i	$0.258550\pi$
$44$	−1.71877	+	3.31557i	−0.259114	+	0.499841i
$45$		0			0
$46$	8.20576	+	2.00049i	1.20987	+	0.294957i
$47$	0.327367			0.0477513			0.0238757	−	0.999715i	$-0.492399\pi$
$47$	0.327367			0.0477513			0.0238757	+	0.999715i	$0.492399\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−17.1669	−	4.18514i	−2.42777	−	0.591869i
$51$		0			0
$52$	2.83136	−	5.46181i	0.392639	−	0.757417i
$53$	8.32940			1.14413			0.572066	−	0.820208i	$-0.306142\pi$
$53$	8.32940			1.14413			0.572066	+	0.820208i	$0.306142\pi$
$54$		0			0
$55$			7.81021i			1.05313i
$56$	−1.85944	+	2.13131i	−0.248479	+	0.284808i
$57$		0			0
$58$	−4.84853	−	1.18203i	−0.636643	−	0.155208i
$59$			5.98008i			0.778540i	0.921124	+	0.389270i	$0.127273\pi$
$59$			5.98008i			0.778540i	−0.921124	+	0.389270i	$0.872727\pi$
$60$		0			0
$61$			13.2783i			1.70011i	0.526691	+	0.850057i	$0.323432\pi$
$61$			13.2783i			1.70011i	−0.526691	+	0.850057i	$0.676568\pi$
$62$	−3.65043	+	14.9736i	−0.463604	+	1.90165i
$63$		0			0
$64$	1.08494	+	7.92609i	0.135618	+	0.990761i
$65$		−	12.8659i		−	1.59582i
$66$		0			0
$67$	−9.21499			−1.12579			−0.562895	−	0.826528i	$-0.690312\pi$
$67$	−9.21499			−1.12579			−0.562895	+	0.826528i	$0.690312\pi$
$68$	0.464725	−	0.896474i	0.0563562	−	0.108713i
$69$		0			0
$70$	−1.40102	+	5.74682i	−0.167454	+	0.686876i
$71$	−9.02460			−1.07102			−0.535512	−	0.844528i	$-0.679881\pi$
$71$	−9.02460			−1.07102			−0.535512	+	0.844528i	$0.679881\pi$
$72$		0			0
$73$	0.416491			0.0487466			0.0243733	−	0.999703i	$-0.492241\pi$
$73$	0.416491			0.0487466			0.0243733	+	0.999703i	$0.492241\pi$
$74$	−3.80718	+	15.6166i	−0.442576	+	1.81539i
$75$		0			0
$76$	5.42616	+	2.81288i	0.622424	+	0.322660i
$77$	1.86730			0.212798
$78$		0			0
$79$			6.00459i			0.675569i	0.941224	+	0.337784i	$0.109677\pi$
$79$			6.00459i			0.675569i	−0.941224	+	0.337784i	$0.890323\pi$
$80$	9.64311	+	13.6719i	1.07813	+	1.52856i
$81$		0			0
$82$	2.43504	−	9.98822i	0.268905	−	1.10301i
$83$		−	2.62368i		−	0.287987i	−0.989579	−	0.143993i	$-0.954006\pi$
$83$		−	2.62368i		−	0.287987i	0.989579	−	0.143993i	$-0.0459944\pi$
$84$		0			0
$85$		−	2.11175i		−	0.229051i
$86$	−12.3949	−	3.02176i	−1.33657	−	0.325845i
$87$		0			0
$88$	3.47213	−	3.97978i	0.370131	−	0.424246i
$89$		−	5.69486i		−	0.603654i	−0.953363	−	0.301827i	$-0.902403\pi$
$89$		−	5.69486i		−	0.603654i	0.953363	−	0.301827i	$-0.0975966\pi$
$90$		0			0
$91$	−3.07604			−0.322456
$92$	−10.6044	−	5.49724i	−1.10559	−	0.573127i
$93$		0			0
$94$	−0.449793	−	0.109655i	−0.0463926	−	0.0113101i
$95$	12.7819			1.31140
$96$		0			0
$97$	6.21289			0.630824			0.315412	−	0.948955i	$-0.397857\pi$
$97$	6.21289			0.630824			0.315412	+	0.948955i	$0.397857\pi$
$98$	1.37397	+	0.334962i	0.138792	+	0.0338363i
$99$		0			0
$100$	22.1850	+	11.5005i	2.21850	+	1.15005i
$101$	−1.85216			−0.184296			−0.0921482	−	0.995745i	$-0.529373\pi$
$101$	−1.85216			−0.184296			−0.0921482	+	0.995745i	$0.529373\pi$
$102$		0			0
$103$			2.74001i			0.269982i	0.990847	+	0.134991i	$0.0431005\pi$
$103$			2.74001i			0.269982i	−0.990847	+	0.134991i	$0.956900\pi$
$104$	−5.71971	+	6.55598i	−0.560864	+	0.642867i
$105$		0			0
$106$	−11.4444	−	2.79004i	−1.11158	−	0.270992i
$107$			4.22506i			0.408452i	0.978924	+	0.204226i	$0.0654677\pi$
$107$			4.22506i			0.408452i	−0.978924	+	0.204226i	$0.934532\pi$
$108$		0			0
$109$		−	13.9420i		−	1.33540i	−0.744432	−	0.667698i	$-0.767280\pi$
$109$		−	13.9420i		−	1.33540i	0.744432	−	0.667698i	$-0.232720\pi$
$110$	2.61613	−	10.7310i	0.249438	−	1.02316i
$111$		0			0
$112$	3.26873	−	2.30551i	0.308866	−	0.217851i
$113$		−	7.49447i		−	0.705020i	−0.935808	−	0.352510i	$-0.885328\pi$
$113$		−	7.49447i		−	0.705020i	0.935808	−	0.352510i	$-0.114672\pi$
$114$		0			0
$115$	−24.9799			−2.32938
$116$	6.26581	+	3.24815i	0.581766	+	0.301583i
$117$		0			0
$118$	2.00310	−	8.21646i	0.184400	−	0.756387i
$119$	−0.504885			−0.0462827
$120$		0			0
$121$	7.51320			0.683018
$122$	4.44773	−	18.2440i	0.402679	−	1.65174i
$123$		0			0
$124$	10.0312	−	19.3505i	0.900825	−	1.73773i
$125$	31.3462			2.80369
$126$		0			0
$127$			18.0939i			1.60557i	0.596267	+	0.802787i	$0.296650\pi$
$127$			18.0939i			1.60557i	−0.596267	+	0.802787i	$0.703350\pi$
$128$	1.16426	−	11.2536i	0.102907	−	0.994691i
$129$		0			0
$130$	−4.30960	+	17.6774i	−0.377977	+	1.55041i
$131$			9.32625i			0.814839i	0.913241	+	0.407419i	$0.133571\pi$
$131$			9.32625i			0.814839i	−0.913241	+	0.407419i	$0.866429\pi$
$132$		0			0
$133$		−	3.05596i		−	0.264985i
$134$	12.6611	+	3.08667i	1.09376	+	0.266648i
$135$		0			0
$136$	−0.938805	+	1.07607i	−0.0805019	+	0.0922718i
$137$			6.53069i			0.557955i	0.960298	+	0.278977i	$0.0899954\pi$
$137$			6.53069i			0.557955i	−0.960298	+	0.278977i	$0.910005\pi$
$138$		0			0
$139$	−10.1589			−0.861664			−0.430832	−	0.902432i	$-0.641780\pi$
$139$	−10.1589			−0.861664			−0.430832	+	0.902432i	$0.641780\pi$
$140$	3.84993	−	7.42668i	0.325379	−	0.627669i
$141$		0			0
$142$	12.3996	+	3.02290i	1.04055	+	0.253676i
$143$	5.74387			0.480327
$144$		0			0
$145$	14.7598			1.22574
$146$	−0.572247	−	0.139509i	−0.0473595	−	0.0115458i
$147$		0			0
$148$	10.4619	−	20.1815i	0.859965	−	1.65891i
$149$	9.72516			0.796716			0.398358	−	0.917230i	$-0.369580\pi$
$149$	9.72516			0.796716			0.398358	+	0.917230i	$0.369580\pi$
$150$		0			0
$151$		−	12.4664i		−	1.01450i	−0.861800	−	0.507249i	$-0.830662\pi$
$151$		−	12.4664i		−	1.01450i	0.861800	−	0.507249i	$-0.169338\pi$
$152$	−6.51319	−	5.68238i	−0.528289	−	0.460902i
$153$		0			0
$154$	−2.56561	−	0.625474i	−0.206743	−	0.0504021i
$155$		−	45.5823i		−	3.66126i
$156$		0			0
$157$		−	11.3627i		−	0.906838i	−0.891297	−	0.453419i	$-0.850204\pi$
$157$		−	11.3627i		−	0.906838i	0.891297	−	0.453419i	$-0.149796\pi$
$158$	2.01131	−	8.25014i	0.160011	−	0.656346i
$159$		0			0
$160$	−8.66980	−	22.0149i	−0.685408	−	1.74043i
$161$			5.97229i			0.470682i
$162$		0			0
$163$	−3.59449			−0.281542			−0.140771	−	0.990042i	$-0.544958\pi$
$163$	−3.59449			−0.281542			−0.140771	+	0.990042i	$0.544958\pi$
$164$	−6.69136	+	12.9079i	−0.522507	+	1.00794i
$165$		0			0
$166$	−0.878835	+	3.60487i	−0.0682108	+	0.279792i
$167$	20.3801			1.57706			0.788531	−	0.614995i	$-0.210842\pi$
$167$	20.3801			1.57706			0.788531	+	0.614995i	$0.210842\pi$
$168$		0			0
$169$	3.53800			0.272154
$170$	−0.707355	+	2.90148i	−0.0542517	+	0.222533i
$171$		0			0
$172$	16.0180	+	8.30363i	1.22136	+	0.633146i
$173$	−4.49761			−0.341947			−0.170974	−	0.985276i	$-0.554691\pi$
$173$	−4.49761			−0.341947			−0.170974	+	0.985276i	$0.554691\pi$
$174$		0			0
$175$		−	12.4944i		−	0.944486i
$176$	−6.10369	+	4.30508i	−0.460083	+	0.324508i
$177$		0			0
$178$	−1.90756	+	7.82459i	−0.142978	+	0.586477i
$179$		−	2.63430i		−	0.196897i	−0.995142	−	0.0984485i	$-0.968612\pi$
$179$		−	2.63430i		−	0.196897i	0.995142	−	0.0984485i	$-0.0313880\pi$
$180$		0			0
$181$			10.3748i			0.771151i	0.922676	+	0.385576i	$0.125997\pi$
$181$			10.3748i			0.771151i	−0.922676	+	0.385576i	$0.874003\pi$
$182$	4.22639	+	1.03036i	0.313281	+	0.0763751i
$183$		0			0
$184$	12.7288	+	11.1051i	0.938379	+	0.818681i
$185$		−	47.5397i		−	3.49519i
$186$		0			0
$187$	0.942770			0.0689422
$188$	0.581272	+	0.301327i	0.0423936	+	0.0219765i
$189$		0			0
$190$	−17.5620	−	4.28147i	−1.27408	−	0.310610i
$191$	18.1707			1.31479			0.657395	−	0.753547i	$-0.271659\pi$
$191$	18.1707			1.31479			0.657395	+	0.753547i	$0.271659\pi$
$192$		0			0
$193$	−16.7704			−1.20716			−0.603578	−	0.797304i	$-0.706259\pi$
$193$	−16.7704			−1.20716			−0.603578	+	0.797304i	$0.706259\pi$
$194$	−8.53634	−	2.08109i	−0.612874	−	0.149413i
$195$		0			0
$196$	−1.77560	−	0.920458i	−0.126829	−	0.0657470i
$197$	−19.2240			−1.36965			−0.684826	−	0.728706i	$-0.740122\pi$
$197$	−19.2240			−1.36965			−0.684826	+	0.728706i	$0.740122\pi$
$198$		0			0
$199$		−	1.68931i		−	0.119752i	−0.998206	−	0.0598761i	$-0.980929\pi$
$199$		−	1.68931i		−	0.119752i	0.998206	−	0.0598761i	$-0.0190706\pi$
$200$	−26.6294	−	23.2326i	−1.88298	−	1.64279i
$201$		0			0
$202$	2.54481	+	0.620402i	0.179052	+	0.0436514i
$203$		−	3.52884i		−	0.247676i
$204$		0			0
$205$			30.4060i			2.12365i
$206$	0.917801	−	3.76470i	0.0639463	−	0.262299i
$207$		0			0
$208$	10.0547	−	7.09184i	0.697170	−	0.491731i
$209$			5.70638i			0.394719i
$210$		0			0
$211$	−14.1544			−0.974427			−0.487213	−	0.873283i	$-0.661987\pi$
$211$	−14.1544			−0.974427			−0.487213	+	0.873283i	$0.661987\pi$
$212$	14.7897	+	7.66687i	1.01576	+	0.526563i
$213$		0			0
$214$	1.41523	−	5.80511i	0.0967434	−	0.396829i
$215$	37.7323			2.57332
$216$		0			0
$217$	−10.8980			−0.739806
$218$	−4.67003	+	19.1559i	−0.316294	+	1.29740i
$219$		0			0
$220$	−7.18897	+	13.8678i	−0.484680	+	0.934967i
$221$	−1.55304			−0.104469
$222$		0			0
$223$		−	1.33032i		−	0.0890851i	−0.999007	−	0.0445425i	$-0.985817\pi$
$223$		−	1.33032i		−	0.0890851i	0.999007	−	0.0445425i	$-0.0141830\pi$
$224$	−5.26341	+	2.07281i	−0.351676	+	0.138496i
$225$		0			0
$226$	−2.51036	+	10.2972i	−0.166987	+	0.684959i
$227$			6.34646i			0.421229i	0.977569	+	0.210615i	$0.0675465\pi$
$227$			6.34646i			0.421229i	−0.977569	+	0.210615i	$0.932453\pi$
$228$		0			0
$229$			13.9920i			0.924619i	0.886719	+	0.462309i	$0.152979\pi$
$229$			13.9920i			0.924619i	−0.886719	+	0.462309i	$0.847021\pi$
$230$	34.3217	+	8.36732i	2.26310	+	0.551724i
$231$		0			0
$232$	−7.52104	−	6.56168i	−0.493781	−	0.430795i
$233$			14.0797i			0.922392i	0.887298	+	0.461196i	$0.152580\pi$
$233$			14.0797i			0.922392i	−0.887298	+	0.461196i	$0.847420\pi$
$234$		0			0
$235$	1.36925			0.0893202
$236$	−5.50441	+	10.6182i	−0.358307	+	0.691188i
$237$		0			0
$238$	0.693698	+	0.169117i	0.0449658	+	0.0109623i
$239$	−13.1737			−0.852134			−0.426067	−	0.904691i	$-0.640101\pi$
$239$	−13.1737			−0.852134			−0.426067	+	0.904691i	$0.640101\pi$
$240$		0			0
$241$	7.46846			0.481086			0.240543	−	0.970639i	$-0.422675\pi$
$241$	7.46846			0.481086			0.240543	+	0.970639i	$0.422675\pi$
$242$	−10.3229	−	2.51664i	−0.663583	−	0.161776i
$243$		0			0
$244$	−12.2221	+	23.5770i	−0.782442	+	1.50936i
$245$	−4.18263			−0.267218
$246$		0			0
$247$		−	9.40024i		−	0.598123i
$248$	−20.2642	+	23.2270i	−1.28678	+	1.47492i
$249$		0			0
$250$	−43.0688	−	10.4998i	−2.72391	−	0.664065i
$251$		−	16.3203i		−	1.03013i	−0.857151	−	0.515065i	$-0.827768\pi$
$251$		−	16.3203i		−	1.03013i	0.857151	−	0.515065i	$-0.172232\pi$
$252$		0			0
$253$		−	11.1520i		−	0.701123i
$254$	6.06077	−	24.8605i	0.380287	−	1.55989i
$255$		0			0
$256$	−5.36921	+	15.0722i	−0.335576	+	0.942013i
$257$			13.6939i			0.854205i	0.904203	+	0.427102i	$0.140466\pi$
$257$			13.6939i			0.854205i	−0.904203	+	0.427102i	$0.859534\pi$
$258$		0			0
$259$	−11.3660			−0.706249
$260$	11.8425	−	22.8447i	0.734443	−	1.41677i
$261$		0			0
$262$	3.12394	−	12.8140i	0.192998	−	0.791653i
$263$	−4.63480			−0.285794			−0.142897	−	0.989738i	$-0.545642\pi$
$263$	−4.63480			−0.285794			−0.142897	+	0.989738i	$0.545642\pi$
$264$		0			0
$265$	34.8388			2.14013
$266$	−1.02363	+	4.19880i	−0.0627629	+	0.257445i
$267$		0			0
$268$	−16.3621	−	8.48201i	−0.999477	−	0.518121i
$269$	−28.6544			−1.74709			−0.873545	−	0.486743i	$-0.838185\pi$
$269$	−28.6544			−1.74709			−0.873545	+	0.486743i	$0.838185\pi$
$270$		0			0
$271$			8.27458i			0.502645i	0.967903	+	0.251322i	$0.0808654\pi$
$271$			8.27458i			0.502645i	−0.967903	+	0.251322i	$0.919135\pi$
$272$	1.65033	−	1.16402i	0.100066	−	0.0705791i
$273$		0			0
$274$	2.18754	−	8.97299i	0.132154	−	0.542078i
$275$			23.3307i			1.40689i
$276$		0			0
$277$		−	12.5278i		−	0.752724i	−0.926473	−	0.376362i	$-0.877175\pi$
$277$		−	12.5278i		−	0.752724i	0.926473	−	0.376362i	$-0.122825\pi$
$278$	13.9580	+	3.40284i	0.837146	+	0.204089i
$279$		0			0
$280$	−7.77736	+	8.91447i	−0.464786	+	0.532741i
$281$			8.63112i			0.514889i	0.966293	+	0.257445i	$0.0828805\pi$
$281$			8.63112i			0.514889i	−0.966293	+	0.257445i	$0.917119\pi$
$282$		0			0
$283$	8.73498			0.519241			0.259620	−	0.965711i	$-0.416403\pi$
$283$	8.73498			0.519241			0.259620	+	0.965711i	$0.416403\pi$
$284$	−16.0241	−	8.30677i	−0.950855	−	0.492916i
$285$		0			0
$286$	−7.89192	−	1.92398i	−0.466659	−	0.113767i
$287$	7.26960			0.429111
$288$		0			0
$289$	16.7451			0.985005
$290$	−20.2796	−	4.94398i	−1.19086	−	0.290321i
$291$		0			0
$292$	0.739522	+	0.383362i	0.0432772	+	0.0224346i
$293$	−30.3572			−1.77348			−0.886742	−	0.462265i	$-0.847037\pi$
$293$	−30.3572			−1.77348			−0.886742	+	0.462265i	$0.847037\pi$
$294$		0			0
$295$			25.0124i			1.45628i
$296$	−21.1344	+	24.2244i	−1.22841	+	1.40802i
$297$		0			0
$298$	−13.3621	−	3.25756i	−0.774046	−	0.188706i
$299$			18.3710i			1.06242i
$300$		0			0
$301$		−	9.02120i		−	0.519973i
$302$	−4.17576	+	17.1284i	−0.240288	+	0.985630i
$303$		0			0
$304$	7.04556	+	9.98911i	0.404091	+	0.572915i
$305$			55.5382i			3.18011i
$306$		0			0
$307$	−29.1705			−1.66485			−0.832425	−	0.554138i	$-0.813048\pi$
$307$	−29.1705			−1.66485			−0.832425	+	0.554138i	$0.813048\pi$
$308$	3.31557	+	1.71877i	0.188922	+	0.0979359i
$309$		0			0
$310$	−15.2684	+	62.6289i	−0.867185	+	3.55708i
$311$	13.4778			0.764253			0.382127	−	0.924110i	$-0.375192\pi$
$311$	13.4778			0.764253			0.382127	+	0.924110i	$0.375192\pi$
$312$		0			0
$313$	20.7291			1.17168			0.585838	−	0.810428i	$-0.300765\pi$
$313$	20.7291			1.17168			0.585838	+	0.810428i	$0.300765\pi$
$314$	−3.80606	+	15.6120i	−0.214788	+	0.881034i
$315$		0			0
$316$	−5.52697	+	10.6617i	−0.310916	+	0.599770i
$317$	−0.453146			−0.0254512			−0.0127256	−	0.999919i	$-0.504051\pi$
$317$	−0.453146			−0.0254512			−0.0127256	+	0.999919i	$0.504051\pi$
$318$		0			0
$319$			6.58939i			0.368935i
$320$	4.53791	+	33.1519i	0.253677	+	1.85325i
$321$		0			0
$322$	2.00049	−	8.20576i	0.111483	−	0.457289i
$323$		−	1.54291i		−	0.0858497i
$324$		0			0
$325$		−	38.4331i		−	2.13189i
$326$	4.93873	+	1.20402i	0.273531	+	0.0666844i
$327$		0			0
$328$	13.5174	−	15.4937i	0.746374	−	0.855499i
$329$		−	0.327367i		−	0.0180483i
$330$		0			0
$331$	24.8798			1.36752			0.683759	−	0.729708i	$-0.260344\pi$
$331$	24.8798			1.36752			0.683759	+	0.729708i	$0.260344\pi$
$332$	2.41499	−	4.65861i	0.132540	−	0.255675i
$333$		0			0
$334$	−28.0018	−	6.82658i	−1.53219	−	0.373534i
$335$	−38.5429			−2.10582
$336$		0			0
$337$	21.8036			1.18772			0.593860	−	0.804568i	$-0.297603\pi$
$337$	21.8036			1.18772			0.593860	+	0.804568i	$0.297603\pi$
$338$	−4.86112	−	1.18510i	−0.264410	−	0.0644608i
$339$		0			0
$340$	1.94377	−	3.74962i	0.105416	−	0.203352i
$341$	20.3498			1.10201
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−19.2269	−	16.7744i	−1.03665	−	0.904415i
$345$		0			0
$346$	6.17960	+	1.50653i	0.332217	+	0.0809916i
$347$		−	20.7794i		−	1.11550i	−0.830010	−	0.557748i	$-0.811665\pi$
$347$		−	20.7794i		−	1.11550i	0.830010	−	0.557748i	$-0.188335\pi$
$348$		0			0
$349$			30.5928i			1.63760i	0.574081	+	0.818799i	$0.305360\pi$
$349$			30.5928i			1.63760i	−0.574081	+	0.818799i	$0.694640\pi$
$350$	−4.18514	+	17.1669i	−0.223705	+	0.917611i
$351$		0			0
$352$	9.82834	−	3.87055i	0.523852	−	0.206301i
$353$		−	19.5174i		−	1.03881i	−0.854529	−	0.519403i	$-0.826154\pi$
$353$		−	19.5174i		−	1.03881i	0.854529	−	0.519403i	$-0.173846\pi$
$354$		0			0
$355$	−37.7466			−2.00338
$356$	5.24188	−	10.1118i	0.277819	−	0.535924i
$357$		0			0
$358$	−0.882392	+	3.61946i	−0.0466358	+	0.191294i
$359$	20.3969			1.07651			0.538254	−	0.842783i	$-0.319084\pi$
$359$	20.3969			1.07651			0.538254	+	0.842783i	$0.319084\pi$
$360$		0			0
$361$	−9.66111			−0.508479
$362$	3.47516	−	14.2547i	0.182650	−	0.749208i
$363$		0			0
$364$	−5.46181	−	2.83136i	−0.286277	−	0.148404i
$365$	1.74203			0.0911818
$366$		0			0
$367$			25.6785i			1.34041i	0.742177	+	0.670203i	$0.233793\pi$
$367$			25.6785i			1.34041i	−0.742177	+	0.670203i	$0.766207\pi$
$368$	−13.7692	−	19.5218i	−0.717769	−	1.01764i
$369$		0			0
$370$	−15.9240	+	65.3183i	−0.827850	+	3.39574i
$371$		−	8.32940i		−	0.432441i
$372$		0			0
$373$			12.4313i			0.643669i	0.946796	+	0.321835i	$0.104300\pi$
$373$			12.4313i			0.643669i	−0.946796	+	0.321835i	$0.895700\pi$
$374$	−1.29534	−	0.315792i	−0.0669804	−	0.0163292i
$375$		0			0
$376$	−0.697719	−	0.608720i	−0.0359821	−	0.0313923i
$377$		−	10.8548i		−	0.559053i
$378$		0			0
$379$	−9.90048			−0.508553			−0.254277	−	0.967132i	$-0.581837\pi$
$379$	−9.90048			−0.508553			−0.254277	+	0.967132i	$0.581837\pi$
$380$	22.6956	+	11.7652i	1.16426	+	0.603544i
$381$		0			0
$382$	−24.9661	−	6.08652i	−1.27738	−	0.311413i
$383$	−23.6536			−1.20864			−0.604320	−	0.796741i	$-0.706555\pi$
$383$	−23.6536			−1.20864			−0.604320	+	0.796741i	$0.706555\pi$
$384$		0			0
$385$	7.81021			0.398045
$386$	23.0420	+	5.61744i	1.17281	+	0.285920i
$387$		0			0
$388$	11.0316	+	5.71871i	0.560045	+	0.290323i
$389$	3.14513			0.159465			0.0797323	−	0.996816i	$-0.474593\pi$
$389$	3.14513			0.159465			0.0797323	+	0.996816i	$0.474593\pi$
$390$		0			0
$391$			3.01532i			0.152491i
$392$	2.13131	+	1.85944i	0.107647	+	0.0939161i
$393$		0			0
$394$	26.4132	+	6.43931i	1.33068	+	0.324408i
$395$			25.1150i			1.26367i
$396$		0			0
$397$		−	12.2176i		−	0.613183i	−0.951841	−	0.306592i	$-0.900811\pi$
$397$		−	12.2176i		−	0.613183i	0.951841	−	0.306592i	$-0.0991886\pi$
$398$	−0.565856	+	2.32107i	−0.0283638	+	0.116345i
$399$		0			0
$400$	28.8060	+	40.8408i	1.44030	+	2.04204i
$401$		−	35.0797i		−	1.75180i	−0.482494	−	0.875899i	$-0.660269\pi$
$401$		−	35.0797i		−	1.75180i	0.482494	−	0.875899i	$-0.339731\pi$
$402$		0			0
$403$	−33.5227			−1.66988
$404$	−3.28869	−	1.70483i	−0.163618	−	0.0848186i
$405$		0			0
$406$	−1.18203	+	4.84853i	−0.0586631	+	0.240628i
$407$	21.2237			1.05202
$408$		0			0
$409$	−27.3489			−1.35231			−0.676157	−	0.736757i	$-0.736356\pi$
$409$	−27.3489			−1.35231			−0.676157	+	0.736757i	$0.736356\pi$
$410$	10.1849	−	41.7770i	0.502995	−	2.06322i
$411$		0			0
$412$	−2.52207	+	4.86517i	−0.124253	+	0.239690i
$413$	5.98008			0.294260
$414$		0			0
$415$		−	10.9739i		−	0.538687i
$416$	−16.1904	+	6.37604i	−0.793801	+	0.312611i
$417$		0			0
$418$	1.91142	−	7.84041i	0.0934908	−	0.383487i
$419$		−	14.6442i		−	0.715417i	−0.933833	−	0.357709i	$-0.883558\pi$
$419$		−	14.6442i		−	0.715417i	0.933833	−	0.357709i	$-0.116442\pi$
$420$		0			0
$421$			20.2168i			0.985305i	0.870226	+	0.492653i	$0.163973\pi$
$421$			20.2168i			0.985305i	−0.870226	+	0.492653i	$0.836027\pi$
$422$	19.4477	+	4.74118i	0.946700	+	0.230797i
$423$		0			0
$424$	−17.7525	−	15.4881i	−0.862139	−	0.752166i
$425$		−	6.30822i		−	0.305994i
$426$		0			0
$427$	13.2783			0.642583
$428$	−3.88899	+	7.50201i	−0.187981	+	0.362623i
$429$		0			0
$430$	−51.8431	−	12.6389i	−2.50010	−	0.609502i
$431$	−19.6656			−0.947260			−0.473630	−	0.880724i	$-0.657057\pi$
$431$	−19.6656			−0.947260			−0.473630	+	0.880724i	$0.657057\pi$
$432$		0			0
$433$	11.9996			0.576666			0.288333	−	0.957530i	$-0.406899\pi$
$433$	11.9996			0.576666			0.288333	+	0.957530i	$0.406899\pi$
$434$	14.9736	+	3.65043i	0.718755	+	0.175226i
$435$		0			0
$436$	12.8330	−	24.7553i	0.614588	−	1.18557i
$437$	−18.2511			−0.873068
$438$		0			0
$439$			7.82113i			0.373282i	0.982428	+	0.186641i	$0.0597601\pi$
$439$			7.82113i			0.373282i	−0.982428	+	0.186641i	$0.940240\pi$
$440$	14.5226	−	16.6460i	0.692340	−	0.793565i
$441$		0			0
$442$	2.13384	+	0.520211i	0.101496	+	0.0247439i
$443$			29.9854i			1.42465i	0.701850	+	0.712325i	$0.252358\pi$
$443$			29.9854i			1.42465i	−0.701850	+	0.712325i	$0.747642\pi$
$444$		0			0
$445$		−	23.8195i		−	1.12915i
$446$	−0.445608	+	1.82783i	−0.0211002	+	0.0865502i
$447$		0			0
$448$	7.92609	−	1.08494i	0.374473	−	0.0512587i
$449$			42.0892i			1.98631i	0.116797	+	0.993156i	$0.462737\pi$
$449$			42.0892i			1.98631i	−0.116797	+	0.993156i	$0.537263\pi$
$450$		0			0
$451$	−13.5745			−0.639198
$452$	6.89834	−	13.3072i	0.324471	−	0.625917i
$453$		0			0
$454$	2.12582	−	8.71986i	0.0997699	−	0.409243i
$455$	−12.8659			−0.603163
$456$		0			0
$457$	−12.1655			−0.569079			−0.284540	−	0.958664i	$-0.591841\pi$
$457$	−12.1655			−0.569079			−0.284540	+	0.958664i	$0.591841\pi$
$458$	4.68680	−	19.2247i	0.219000	−	0.898309i
$459$		0			0
$460$	−44.3543	−	22.9929i	−2.06803	−	1.07205i
$461$	−29.0054			−1.35091			−0.675457	−	0.737399i	$-0.736054\pi$
$461$	−29.0054			−1.35091			−0.675457	+	0.737399i	$0.736054\pi$
$462$		0			0
$463$			5.21317i			0.242277i	0.992636	+	0.121138i	$0.0386545\pi$
$463$			5.21317i			0.242277i	−0.992636	+	0.121138i	$0.961346\pi$
$464$	8.13579	+	11.5348i	0.377695	+	0.535491i
$465$		0			0
$466$	4.71617	−	19.3451i	0.218472	−	0.896146i
$467$		−	12.3061i		−	0.569460i	−0.958608	−	0.284730i	$-0.908096\pi$
$467$		−	12.3061i		−	0.569460i	0.958608	−	0.284730i	$-0.0919039\pi$
$468$		0			0
$469$			9.21499i			0.425509i
$470$	−1.88132	−	0.458648i	−0.0867786	−	0.0211559i
$471$		0			0
$472$	11.1196	−	12.7454i	0.511822	−	0.586654i
$473$			16.8452i			0.774545i
$474$		0			0
$475$	38.1823			1.75192
$476$	−0.896474	−	0.464725i	−0.0410898	−	0.0213007i
$477$		0			0
$478$	18.1003	+	4.41269i	0.827887	+	0.201832i
$479$	−19.9609			−0.912038			−0.456019	−	0.889970i	$-0.650725\pi$
$479$	−19.9609			−0.912038			−0.456019	+	0.889970i	$0.650725\pi$
$480$		0			0
$481$	−34.9622			−1.59414
$482$	−10.2615	−	2.50165i	−0.467396	−	0.113947i
$483$		0			0
$484$	13.3404	+	6.91559i	0.606384	+	0.314345i
$485$	25.9862			1.17997
$486$		0			0
$487$		−	5.61420i		−	0.254404i	−0.991877	−	0.127202i	$-0.959400\pi$
$487$		−	5.61420i		−	0.254404i	0.991877	−	0.127202i	$-0.0405996\pi$
$488$	24.6903	−	28.3002i	1.11768	−	1.28109i
$489$		0			0
$490$	5.74682	+	1.40102i	0.259615	+	0.0632918i
$491$			9.07131i			0.409382i	0.978827	+	0.204691i	$0.0656190\pi$
$491$			9.07131i			0.409382i	−0.978827	+	0.204691i	$0.934381\pi$
$492$		0			0
$493$		−	1.78166i		−	0.0802418i
$494$	−3.14873	+	12.9157i	−0.141668	+	0.581104i
$495$		0			0
$496$	35.6227	−	25.1255i	1.59951	−	1.12817i
$497$			9.02460i			0.404809i
$498$		0			0
$499$	−36.4346			−1.63103			−0.815517	−	0.578732i	$-0.803548\pi$
$499$	−36.4346			−1.63103			−0.815517	+	0.578732i	$0.803548\pi$
$500$	55.6583	+	28.8528i	2.48911	+	1.29034i
$501$		0			0
$502$	−5.46669	+	22.4237i	−0.243990	+	1.00082i
$503$	−4.10995			−0.183253			−0.0916267	−	0.995793i	$-0.529207\pi$
$503$	−4.10995			−0.183253			−0.0916267	+	0.995793i	$0.529207\pi$
$504$		0			0
$505$	−7.74688			−0.344732
$506$	−3.73551	+	15.3226i	−0.166064	+	0.681172i
$507$		0			0
$508$	−16.6547	+	32.1275i	−0.738931	+	1.42543i
$509$	−17.5175			−0.776450			−0.388225	−	0.921565i	$-0.626912\pi$
$509$	−17.5175			−0.776450			−0.388225	+	0.921565i	$0.626912\pi$
$510$		0			0
$511$		−	0.416491i		−	0.0184245i
$512$	12.4258	−	18.9103i	0.549147	−	0.835726i
$513$		0			0
$514$	4.58696	−	18.8151i	0.202322	−	0.829899i
$515$			11.4605i			0.505008i
$516$		0			0
$517$			0.611291i			0.0268845i
$518$	15.6166	+	3.80718i	0.686153	+	0.167278i
$519$		0			0
$520$	−23.9234	+	27.4212i	−1.04911	+	1.20250i
$521$		−	40.7567i		−	1.78558i	−0.450472	−	0.892791i	$-0.648744\pi$
$521$		−	40.7567i		−	1.78558i	0.450472	−	0.892791i	$-0.351256\pi$
$522$		0			0
$523$	7.03412			0.307581			0.153790	−	0.988103i	$-0.450852\pi$
$523$	7.03412			0.307581			0.153790	+	0.988103i	$0.450852\pi$
$524$	−8.58442	+	16.5597i	−0.375012	+	0.723414i
$525$		0			0
$526$	6.36808	+	1.55248i	0.277662	+	0.0676915i
$527$	−5.50225			−0.239682
$528$		0			0
$529$	12.6683			0.550794
$530$	−47.8675	−	11.6697i	−2.07923	−	0.506899i
$531$		0			0
$532$	2.81288	−	5.42616i	0.121954	−	0.235254i
$533$	22.3615			0.968586
$534$		0			0
$535$			17.6718i			0.764020i
$536$	19.6400	+	17.1347i	0.848318	+	0.740108i
$537$		0			0
$538$	39.3704	+	9.59815i	1.69738	+	0.413806i
$539$		−	1.86730i		−	0.0804302i
$540$		0			0
$541$			19.6764i			0.845953i	0.906141	+	0.422976i	$0.139015\pi$
$541$			19.6764i			0.845953i	−0.906141	+	0.422976i	$0.860985\pi$
$542$	2.77167	−	11.3690i	0.119053	−	0.488342i
$543$		0			0
$544$	−2.65742	+	1.04653i	−0.113936	+	0.0448697i
$545$		−	58.3140i		−	2.49790i
$546$		0			0
$547$	17.8078			0.761408			0.380704	−	0.924697i	$-0.375682\pi$
$547$	17.8078			0.761408			0.380704	+	0.924697i	$0.375682\pi$
$548$	−6.01123	+	11.5959i	−0.256787	+	0.495352i
$549$		0			0
$550$	7.81491	−	32.0557i	0.333229	−	1.36686i
$551$	10.7840			0.459413
$552$		0			0
$553$	6.00459			0.255341
$554$	−4.19635	+	17.2129i	−0.178286	+	0.731306i
$555$		0			0
$556$	−18.0381	−	9.35081i	−0.764986	−	0.396563i
$557$	5.99646			0.254078			0.127039	−	0.991898i	$-0.459453\pi$
$557$	5.99646			0.254078			0.127039	+	0.991898i	$0.459453\pi$
$558$		0			0
$559$		−	27.7495i		−	1.17368i
$560$	13.6719	−	9.64311i	0.577743	−	0.407496i
$561$		0			0
$562$	2.89110	−	11.8589i	0.121954	−	0.500238i
$563$			20.4848i			0.863333i	0.902033	+	0.431667i	$0.142074\pi$
$563$			20.4848i			0.863333i	−0.902033	+	0.431667i	$0.857926\pi$
$564$		0			0
$565$		−	31.3466i		−	1.31876i
$566$	−12.0016	−	2.92589i	−0.504466	−	0.122984i
$567$		0			0
$568$	19.2342	+	16.7807i	0.807049	+	0.704104i
$569$			38.1889i			1.60096i	0.599359	+	0.800480i	$0.295422\pi$
$569$			38.1889i			1.60096i	−0.599359	+	0.800480i	$0.704578\pi$
$570$		0			0
$571$	11.3551			0.475198			0.237599	−	0.971363i	$-0.423640\pi$
$571$	11.3551			0.475198			0.237599	+	0.971363i	$0.423640\pi$
$572$	10.1988	+	5.28699i	0.426434	+	0.221060i
$573$		0			0
$574$	−9.98822	−	2.43504i	−0.416900	−	0.101637i
$575$	−74.6200			−3.11187
$576$		0			0
$577$	−20.7869			−0.865371			−0.432685	−	0.901545i	$-0.642434\pi$
$577$	−20.7869			−0.865371			−0.432685	+	0.901545i	$0.642434\pi$
$578$	−23.0073	−	5.60897i	−0.956977	−	0.233303i
$579$		0			0
$580$	26.2075	+	13.5858i	1.08821	+	0.564119i
$581$	−2.62368			−0.108849
$582$		0			0
$583$			15.5535i			0.644159i
$584$	−0.887670	−	0.774441i	−0.0367321	−	0.0320466i
$585$		0			0
$586$	41.7099	+	10.1685i	1.72302	+	0.420057i
$587$		−	24.3849i		−	1.00647i	−0.864148	−	0.503237i	$-0.832142\pi$
$587$		−	24.3849i		−	1.00647i	0.864148	−	0.503237i	$-0.167858\pi$
$588$		0			0
$589$		−	33.3039i		−	1.37226i
$590$	8.37823	−	34.3664i	0.344926	−	1.41484i
$591$		0			0
$592$	37.1524	−	26.2045i	1.52695	−	1.07700i
$593$			32.5053i			1.33483i	0.744684	+	0.667417i	$0.232600\pi$
$593$			32.5053i			1.33483i	−0.744684	+	0.667417i	$0.767400\pi$
$594$		0			0
$595$	−2.11175			−0.0865731
$596$	17.2680	+	8.95160i	0.707325	+	0.366672i
$597$		0			0
$598$	6.15359	−	25.2412i	0.251639	−	1.03219i
$599$	10.4800			0.428200			0.214100	−	0.976812i	$-0.431318\pi$
$599$	10.4800			0.428200			0.214100	+	0.976812i	$0.431318\pi$
$600$		0			0
$601$	−22.4946			−0.917575			−0.458787	−	0.888546i	$-0.651716\pi$
$601$	−22.4946			−0.917575			−0.458787	+	0.888546i	$0.651716\pi$
$602$	−3.02176	+	12.3949i	−0.123158	+	0.505177i
$603$		0			0
$604$	11.4748	−	22.1353i	0.466901	−	0.900671i
$605$	31.4249			1.27761
$606$		0			0
$607$		−	32.3672i		−	1.31374i	−0.754002	−	0.656872i	$-0.771879\pi$
$607$		−	32.3672i		−	1.31374i	0.754002	−	0.656872i	$-0.228121\pi$
$608$	−6.33443	−	16.0848i	−0.256895	−	0.652323i
$609$		0			0
$610$	18.6032	−	76.3080i	0.753222	−	3.08962i
$611$		−	1.00699i		−	0.0407385i
$612$		0			0
$613$			34.8714i			1.40844i	0.709981	+	0.704220i	$0.248703\pi$
$613$			34.8714i			1.40844i	−0.709981	+	0.704220i	$0.751297\pi$
$614$	40.0795	+	9.77102i	1.61748	+	0.394326i
$615$		0			0
$616$	−3.97978	−	3.47213i	−0.160350	−	0.139896i
$617$		−	2.47324i		−	0.0995688i	−0.998760	−	0.0497844i	$-0.984147\pi$
$617$		−	2.47324i		−	0.0995688i	0.998760	−	0.0497844i	$-0.0158534\pi$
$618$		0			0
$619$	−15.2375			−0.612447			−0.306223	−	0.951960i	$-0.599065\pi$
$619$	−15.2375			−0.612447			−0.306223	+	0.951960i	$0.599065\pi$
$620$	41.9566	−	80.9360i	1.68502	−	3.25047i
$621$		0			0
$622$	−18.5181	−	4.51454i	−0.742507	−	0.181017i
$623$	−5.69486			−0.228160
$624$		0			0
$625$	68.6375			2.74550
$626$	−28.4812	−	6.94346i	−1.13834	−	0.277516i
$627$		0			0
$628$	10.4588	−	20.1755i	0.417353	−	0.805091i
$629$	−5.73852			−0.228810
$630$		0			0
$631$			23.2064i			0.923832i	0.886924	+	0.461916i	$0.152838\pi$
$631$			23.2064i			0.923832i	−0.886924	+	0.461916i	$0.847162\pi$
$632$	11.1652	−	12.7976i	0.444127	−	0.509062i
$633$		0			0
$634$	0.622610	+	0.151787i	0.0247270	+	0.00602823i
$635$			75.6800i			3.00327i
$636$		0			0
$637$			3.07604i			0.121877i
$638$	2.20720	−	9.05364i	0.0873838	−	0.358437i
$639$		0			0
$640$	4.86967	−	47.0698i	0.192491	−	1.86060i
$641$			29.5988i			1.16908i	0.811364	+	0.584541i	$0.198725\pi$
$641$			29.5988i			1.16908i	−0.811364	+	0.584541i	$0.801275\pi$
$642$		0			0
$643$	28.8060			1.13600			0.567999	−	0.823029i	$-0.307718\pi$
$643$	28.8060			1.13600			0.567999	+	0.823029i	$0.307718\pi$
$644$	−5.49724	+	10.6044i	−0.216622	+	0.417872i
$645$		0			0
$646$	−0.516816	+	2.11991i	−0.0203339	+	0.0834069i
$647$	−27.3622			−1.07572			−0.537860	−	0.843034i	$-0.680767\pi$
$647$	−27.3622			−1.07572			−0.537860	+	0.843034i	$0.680767\pi$
$648$		0			0
$649$	−11.1666			−0.438327
$650$	−12.8737	+	52.8061i	−0.504946	+	2.07123i
$651$		0			0
$652$	−6.38238	−	3.30858i	−0.249953	−	0.129574i
$653$	−39.9292			−1.56255			−0.781275	−	0.624187i	$-0.785430\pi$
$653$	−39.9292			−1.56255			−0.781275	+	0.624187i	$0.785430\pi$
$654$		0			0
$655$			39.0082i			1.52418i
$656$	−23.7624	+	16.7602i	−0.927764	+	0.654374i
$657$		0			0
$658$	−0.109655	+	0.449793i	−0.00427482	+	0.0175347i
$659$		−	14.9809i		−	0.583572i	−0.956484	−	0.291786i	$-0.905751\pi$
$659$		−	14.9809i		−	0.583572i	0.956484	−	0.291786i	$-0.0942495\pi$
$660$		0			0
$661$		−	33.0963i		−	1.28730i	−0.765322	−	0.643648i	$-0.777420\pi$
$661$		−	33.0963i		−	1.28730i	0.765322	−	0.643648i	$-0.222580\pi$
$662$	−34.1842	−	8.33380i	−1.32861	−	0.323902i
$663$		0			0
$664$	−4.87859	+	5.59187i	−0.189326	+	0.217007i
$665$		−	12.7819i		−	0.495662i
$666$		0			0
$667$	−21.0753			−0.816037
$668$	36.1870	+	18.7591i	1.40012	+	0.725810i
$669$		0			0
$670$	52.9568	+	12.9104i	2.04590	+	0.498773i
$671$	−24.7945			−0.957183
$672$		0			0
$673$	−12.1189			−0.467150			−0.233575	−	0.972339i	$-0.575043\pi$
$673$	−12.1189			−0.467150			−0.233575	+	0.972339i	$0.575043\pi$
$674$	−29.9576	−	7.30340i	−1.15392	−	0.281316i
$675$		0			0
$676$	6.28208	+	3.25658i	0.241618	+	0.125253i
$677$	27.7231			1.06549			0.532743	−	0.846277i	$-0.321161\pi$
$677$	27.7231			1.06549			0.532743	+	0.846277i	$0.321161\pi$
$678$		0			0
$679$		−	6.21289i		−	0.238429i
$680$	−3.92667	+	4.50078i	−0.150581	+	0.172597i
$681$		0			0
$682$	−27.9601	−	6.81643i	−1.07065	−	0.261014i
$683$			9.79813i			0.374915i	0.982273	+	0.187457i	$0.0600247\pi$
$683$			9.79813i			0.374915i	−0.982273	+	0.187457i	$0.939975\pi$
$684$		0			0
$685$			27.3155i			1.04367i
$686$	0.334962	−	1.37397i	0.0127889	−	0.0524585i
$687$		0			0
$688$	20.7985	+	29.4879i	0.792935	+	1.12421i
$689$		−	25.6215i		−	0.976103i
$690$		0			0
$691$	−37.4765			−1.42567			−0.712837	−	0.701330i	$-0.752590\pi$
$691$	−37.4765			−1.42567			−0.712837	+	0.701330i	$0.752590\pi$
$692$	−7.98597	−	4.13987i	−0.303581	−	0.157374i
$693$		0			0
$694$	−6.96032	+	28.5503i	−0.264210	+	1.08376i
$695$	−42.4908			−1.61177
$696$		0			0
$697$	3.67031			0.139023
$698$	10.2475	−	42.0337i	0.387872	−	1.59100i
$699$		0			0
$700$	11.5005	−	22.1850i	0.434680	−	0.838515i
$701$	−22.6525			−0.855575			−0.427787	−	0.903879i	$-0.640707\pi$
$701$	−22.6525			−0.855575			−0.427787	+	0.903879i	$0.640707\pi$
$702$		0			0
$703$		−	34.7340i		−	1.31002i
$704$	−14.8004	+	2.02591i	−0.557810	+	0.0763543i
$705$		0			0
$706$	−6.53759	+	26.8164i	−0.246045	+	1.00925i
$707$			1.85216i			0.0696575i
$708$		0			0
$709$			1.58535i			0.0595393i	0.999557	+	0.0297696i	$0.00947737\pi$
$709$			1.58535i			0.0595393i	−0.999557	+	0.0297696i	$0.990523\pi$
$710$	51.8627	+	12.6437i	1.94637	+	0.474509i
$711$		0			0
$712$	−10.5893	+	12.1375i	−0.396850	+	0.454872i
$713$			65.0861i			2.43749i
$714$		0			0
$715$	24.0245			0.898465
$716$	2.42476	−	4.67747i	0.0906177	−	0.174805i
$717$		0			0
$718$	−28.0248	−	6.83220i	−1.04588	−	0.254975i
$719$	−17.7228			−0.660948			−0.330474	−	0.943815i	$-0.607209\pi$
$719$	−17.7228			−0.660948			−0.330474	+	0.943815i	$0.607209\pi$
$720$		0			0
$721$	2.74001			0.102043
$722$	13.2741	+	3.23611i	0.494011	+	0.120435i
$723$		0			0
$724$	−9.54955	+	18.4215i	−0.354906	+	0.684628i
$725$	44.0906			1.63749
$726$		0			0
$727$		−	3.31812i		−	0.123062i	−0.998105	−	0.0615312i	$-0.980402\pi$
$727$		−	3.31812i		−	0.123062i	0.998105	−	0.0615312i	$-0.0195984\pi$
$728$	6.55598	+	5.71971i	0.242981	+	0.211987i
$729$		0			0
$730$	−2.39350	−	0.583513i	−0.0885873	−	0.0215968i
$731$		−	4.55467i		−	0.168460i
$732$		0			0
$733$			18.8547i			0.696414i	0.937418	+	0.348207i	$0.113209\pi$
$733$			18.8547i			0.696414i	−0.937418	+	0.348207i	$0.886791\pi$
$734$	8.60133	−	35.2816i	0.317481	−	1.30227i
$735$		0			0
$736$	12.3794	+	31.4346i	0.456312	+	1.15869i
$737$		−	17.2071i		−	0.633832i
$738$		0			0
$739$	−33.3560			−1.22702			−0.613510	−	0.789687i	$-0.710243\pi$
$739$	−33.3560			−1.22702			−0.613510	+	0.789687i	$0.710243\pi$
$740$	43.7583	−	84.4116i	1.60859	−	3.10303i
$741$		0			0
$742$	−2.79004	+	11.4444i	−0.102425	+	0.420136i
$743$	27.0826			0.993565			0.496783	−	0.867875i	$-0.334515\pi$
$743$	27.0826			0.993565			0.496783	+	0.867875i	$0.334515\pi$
$744$		0			0
$745$	40.6767			1.49028
$746$	4.16402	−	17.0803i	0.152456	−	0.625354i
$747$		0			0
$748$	1.67398	+	0.867780i	0.0612069	+	0.0317292i
$749$	4.22506			0.154380
$750$		0			0
$751$			44.3284i			1.61757i	0.588107	+	0.808783i	$0.299874\pi$
$751$			44.3284i			1.61757i	−0.588107	+	0.808783i	$0.700126\pi$
$752$	0.754748	+	1.07007i	0.0275228	+	0.0390216i
$753$		0			0
$754$	−3.63596	+	14.9142i	−0.132414	+	0.543145i
$755$		−	52.1421i		−	1.89765i
$756$		0			0
$757$		−	12.3093i		−	0.447391i	−0.974659	−	0.223695i	$-0.928188\pi$
$757$		−	12.3093i		−	0.447391i	0.974659	−	0.223695i	$-0.0718121\pi$
$758$	13.6030	+	3.31629i	0.494083	+	0.120453i
$759$		0			0
$760$	−27.2422	−	23.7673i	−0.988180	−	0.862130i
$761$		−	1.85054i		−	0.0670820i	−0.999437	−	0.0335410i	$-0.989322\pi$
$761$		−	1.85054i		−	0.0670820i	0.999437	−	0.0335410i	$-0.0106784\pi$
$762$		0			0
$763$	−13.9420			−0.504733
$764$	32.2640	+	16.7254i	1.16727	+	0.605104i
$765$		0			0
$766$	32.4993	+	7.92305i	1.17425	+	0.286272i
$767$	18.3949			0.664203
$768$		0			0
$769$	−31.2463			−1.12677			−0.563386	−	0.826194i	$-0.690502\pi$
$769$	−31.2463			−1.12677			−0.563386	+	0.826194i	$0.690502\pi$
$770$	−10.7310	−	2.61613i	−0.386719	−	0.0942786i
$771$		0			0
$772$	−29.7775	−	15.4364i	−1.07171	−	0.555569i
$773$	−44.4521			−1.59883			−0.799415	−	0.600779i	$-0.794857\pi$
$773$	−44.4521			−1.59883			−0.799415	+	0.600779i	$0.794857\pi$
$774$		0			0
$775$		−	136.164i		−	4.89115i
$776$	−13.2416	−	11.5525i	−0.475345	−	0.414711i
$777$		0			0
$778$	−4.32133	−	1.05350i	−0.154927	−	0.0377698i
$779$			22.2156i			0.795956i
$780$		0			0
$781$		−	16.8516i		−	0.602998i
$782$	1.01002	−	4.14297i	0.0361182	−	0.148152i
$783$		0			0
$784$	−2.30551	−	3.26873i	−0.0823398	−	0.116740i
$785$		−	47.5257i		−	1.69627i
$786$		0			0
$787$	28.0995			1.00164			0.500820	−	0.865551i	$-0.333032\pi$
$787$	28.0995			1.00164			0.500820	+	0.865551i	$0.333032\pi$
$788$	−34.1341	−	17.6949i	−1.21598	−	0.630354i
$789$		0			0
$790$	8.41256	−	34.5073i	0.299306	−	1.22771i
$791$	−7.49447			−0.266473
$792$		0			0
$793$	40.8446			1.45043
$794$	−4.09243	+	16.7866i	−0.145235	+	0.595735i
$795$		0			0
$796$	1.55494	−	2.99955i	0.0551135	−	0.106316i
$797$	42.9492			1.52134			0.760670	−	0.649139i	$-0.224871\pi$
$797$	42.9492			1.52134			0.760670	+	0.649139i	$0.224871\pi$
$798$		0			0
$799$		−	0.165282i		−	0.00584727i
$800$	−25.8985	−	65.7630i	−0.915649	−	2.32507i
$801$		0			0
$802$	−11.7504	+	48.1986i	−0.414921	+	1.70195i
$803$			0.777712i			0.0274449i
$804$		0			0
$805$			24.9799i			0.880425i
$806$	46.0593	+	11.2288i	1.62237	+	0.395519i
$807$		0			0
$808$	3.94751	+	3.44398i	0.138873	+	0.121159i
$809$		−	8.54301i		−	0.300356i	−0.988659	−	0.150178i	$-0.952015\pi$
$809$		−	8.54301i		−	0.300356i	0.988659	−	0.150178i	$-0.0479847\pi$
$810$		0			0
$811$	34.6880			1.21806			0.609030	−	0.793147i	$-0.291559\pi$
$811$	34.6880			1.21806			0.609030	+	0.793147i	$0.291559\pi$
$812$	3.24815	−	6.26581i	0.113988	−	0.219887i
$813$		0			0
$814$	−29.1608	−	7.10914i	−1.02208	−	0.249175i
$815$	−15.0344			−0.526632
$816$		0			0
$817$	27.5684			0.964497
$818$	37.5766	+	9.16084i	1.31383	+	0.320301i
$819$		0			0
$820$	−27.9875	+	53.9889i	−0.977364	+	1.88538i
$821$	−8.46951			−0.295588			−0.147794	−	0.989018i	$-0.547217\pi$
$821$	−8.46951			−0.295588			−0.147794	+	0.989018i	$0.547217\pi$
$822$		0			0
$823$		−	44.5109i		−	1.55155i	−0.631008	−	0.775777i	$-0.717358\pi$
$823$		−	44.5109i		−	1.55155i	0.631008	−	0.775777i	$-0.282642\pi$
$824$	5.09490	−	5.83981i	0.177489	−	0.203439i
$825$		0			0
$826$	−8.21646	−	2.00310i	−0.285887	−	0.0696968i
$827$		−	36.3895i		−	1.26539i	−0.774403	−	0.632693i	$-0.781949\pi$
$827$		−	36.3895i		−	1.26539i	0.774403	−	0.632693i	$-0.218051\pi$
$828$		0			0
$829$			39.2607i			1.36358i	0.731548	+	0.681790i	$0.238798\pi$
$829$			39.2607i			1.36358i	−0.731548	+	0.681790i	$0.761202\pi$
$830$	−3.67584	+	15.0778i	−0.127590	+	0.523359i
$831$		0			0
$832$	24.3809	−	3.33732i	0.845257	−	0.115701i
$833$			0.504885i			0.0174932i
$834$		0			0
$835$	85.2425			2.94994
$836$	−5.25249	+	10.1323i	−0.181661	+	0.350431i
$837$		0			0
$838$	−4.90527	+	20.1208i	−0.169450	+	0.695060i
$839$	−15.1101			−0.521659			−0.260830	−	0.965385i	$-0.583996\pi$
$839$	−15.1101			−0.521659			−0.260830	+	0.965385i	$0.583996\pi$
$840$		0			0
$841$	−16.5473			−0.570596
$842$	6.77186	−	27.7773i	0.233374	−	0.957268i
$843$		0			0
$844$	−25.1325	−	13.0285i	−0.865096	−	0.448459i
$845$	14.7981			0.509072
$846$		0			0
$847$		−	7.51320i		−	0.258157i
$848$	19.2036	+	27.2266i	0.659453	+	0.934965i
$849$		0			0
$850$	−2.11302	+	8.66732i	−0.0724759	+	0.297287i
$851$			67.8810i			2.32693i
$852$		0			0
$853$			23.4153i			0.801724i	0.916138	+	0.400862i	$0.131289\pi$
$853$			23.4153i			0.801724i	−0.916138	+	0.400862i	$0.868711\pi$
$854$	−18.2440	−	4.44773i	−0.624298	−	0.152198i
$855$		0			0
$856$	7.85625	−	9.00489i	0.268521	−	0.307781i
$857$		−	20.7800i		−	0.709833i	−0.934898	−	0.354916i	$-0.884509\pi$
$857$		−	20.7800i		−	0.709833i	0.934898	−	0.354916i	$-0.115491\pi$
$858$		0			0
$859$	12.0088			0.409735			0.204868	−	0.978790i	$-0.434324\pi$
$859$	12.0088			0.409735			0.204868	+	0.978790i	$0.434324\pi$
$860$	66.9975	+	34.7310i	2.28460	+	1.18432i
$861$		0			0
$862$	27.0200	+	6.58725i	0.920306	+	0.224363i
$863$	−11.5254			−0.392328			−0.196164	−	0.980571i	$-0.562849\pi$
$863$	−11.5254			−0.392328			−0.196164	+	0.980571i	$0.562849\pi$
$864$		0			0
$865$	−18.8118			−0.639622
$866$	−16.4872	−	4.01943i	−0.560257	−	0.136586i
$867$		0			0
$868$	−19.3505	−	10.0312i	−0.656800	−	0.340480i
$869$	−11.2123			−0.380353
$870$		0			0
$871$			28.3456i			0.960455i
$872$	−25.9243	+	29.7146i	−0.877906	+	1.00626i
$873$		0			0
$874$	25.0765	+	6.11342i	0.848225	+	0.206790i
$875$		−	31.3462i		−	1.05969i
$876$		0			0
$877$			7.25986i			0.245148i	0.992459	+	0.122574i	$0.0391149\pi$
$877$			7.25986i			0.245148i	−0.992459	+	0.122574i	$0.960885\pi$
$878$	2.61978	−	10.7460i	0.0884134	−	0.362660i
$879$		0			0
$880$	−25.5295	+	18.0065i	−0.860598	+	0.607000i
$881$		−	10.7411i		−	0.361876i	−0.983495	−	0.180938i	$-0.942087\pi$
$881$		−	10.7411i		−	0.361876i	0.983495	−	0.180938i	$-0.0579133\pi$
$882$		0			0
$883$	9.09009			0.305906			0.152953	−	0.988233i	$-0.451122\pi$
$883$	9.09009			0.305906			0.152953	+	0.988233i	$0.451122\pi$
$884$	−2.75759	−	1.42951i	−0.0927477	−	0.0480797i
$885$		0			0
$886$	10.0440	−	41.1991i	0.337434	−	1.38411i
$887$	29.0988			0.977041			0.488521	−	0.872552i	$-0.337537\pi$
$887$	29.0988			0.977041			0.488521	+	0.872552i	$0.337537\pi$
$888$		0			0
$889$	18.0939			0.606850
$890$	−7.97863	+	32.7273i	−0.267444	+	1.09702i
$891$		0			0
$892$	1.22451	−	2.36212i	0.0409995	−	0.0790898i
$893$	1.00042			0.0334778
$894$		0			0
$895$		−	11.0183i		−	0.368301i
$896$	−11.2536	−	1.16426i	−0.375958	−	0.0388952i
$897$		0			0
$898$	14.0983	−	57.8294i	0.470466	−	1.92979i
$899$		−	38.4574i		−	1.28262i
$900$		0			0
$901$		−	4.20539i		−	0.140102i
$902$	18.6510	+	4.54694i	0.621010	+	0.151397i
$903$		0			0
$904$	−13.9355	+	15.9730i	−0.463489	+	0.531254i
$905$			43.3938i			1.44246i
$906$		0			0
$907$	29.9962			0.996008			0.498004	−	0.867175i	$-0.334067\pi$
$907$	29.9962			0.996008			0.498004	+	0.867175i	$0.334067\pi$
$908$	−5.84165	+	11.2688i	−0.193862	+	0.373967i
$909$		0			0
$910$	17.6774	+	4.30960i	0.586000	+	0.142862i
$911$	43.3253			1.43543			0.717716	−	0.696336i	$-0.245188\pi$
$911$	43.3253			1.43543			0.717716	+	0.696336i	$0.245188\pi$
$912$		0			0
$913$	4.89919			0.162140
$914$	16.7151	+	4.07499i	0.552886	+	0.134789i
$915$		0			0
$916$	−12.8791	+	24.8442i	−0.425536	+	0.820877i
$917$	9.32625			0.307980
$918$		0			0
$919$			44.6079i			1.47148i	0.677264	+	0.735740i	$0.263165\pi$
$919$			44.6079i			1.47148i	−0.677264	+	0.735740i	$0.736835\pi$
$920$	53.2398	+	46.4486i	1.75526	+	1.53137i
$921$		0			0
$922$	39.8526	+	9.71570i	1.31247	+	0.319970i
$923$			27.7600i			0.913732i
$924$		0			0
$925$		−	142.011i		−	4.66929i
$926$	1.74622	−	7.16275i	0.0573842	−	0.235383i
$927$		0			0
$928$	−7.31462	−	18.5737i	−0.240114	−	0.609712i
$929$			7.73251i			0.253695i	0.991922	+	0.126848i	$0.0404860\pi$
$929$			7.73251i			0.253695i	−0.991922	+	0.126848i	$0.959514\pi$
$930$		0			0
$931$	−3.05596			−0.100155
$932$	−12.9598	+	24.9999i	−0.424512	+	0.818900i
$933$		0			0
$934$	−4.12209	+	16.9083i	−0.134879	+	0.553256i
$935$	3.94326			0.128958
$936$		0			0
$937$	25.6210			0.837002			0.418501	−	0.908216i	$-0.362556\pi$
$937$	25.6210			0.837002			0.418501	+	0.908216i	$0.362556\pi$
$938$	3.08667	−	12.6611i	0.100783	−	0.413401i
$939$		0			0
$940$	2.43125	+	1.26034i	0.0792985	+	0.0411077i
$941$	30.8529			1.00578			0.502888	−	0.864352i	$-0.332271\pi$
$941$	30.8529			1.00578			0.502888	+	0.864352i	$0.332271\pi$
$942$		0			0
$943$		−	43.4161i		−	1.41382i
$944$	−19.5473	+	13.7872i	−0.636209	+	0.448734i
$945$		0			0
$946$	5.64252	−	23.1449i	0.183454	−	0.752506i
$947$		−	39.5682i		−	1.28579i	−0.765953	−	0.642897i	$-0.777732\pi$
$947$		−	39.5682i		−	1.28579i	0.765953	−	0.642897i	$-0.222268\pi$
$948$		0			0
$949$		−	1.28114i		−	0.0415876i
$950$	−52.4614	−	12.7896i	−1.70207	−	0.414951i
$951$		0			0
$952$	1.07607	+	0.938805i	0.0348755	+	0.0304268i
$953$		−	4.36408i		−	0.141366i	−0.997499	−	0.0706832i	$-0.977482\pi$
$953$		−	4.36408i		−	0.141366i	0.997499	−	0.0706832i	$-0.0225179\pi$
$954$		0			0
$955$	76.0015			2.45935
$956$	−23.3912	−	12.1258i	−0.756525	−	0.392177i
$957$		0			0
$958$	27.4258	+	6.68616i	0.886086	+	0.216020i
$959$	6.53069			0.210887
$960$		0			0
$961$	−87.7668			−2.83119
$962$	48.0371	+	11.7110i	1.54878	+	0.377579i
$963$		0			0
$964$	13.2610	+	6.87440i	0.427108	+	0.221410i
$965$	−70.1442			−2.25802
$966$		0			0
$967$			51.1938i			1.64628i	0.567837	+	0.823141i	$0.307780\pi$
$967$			51.1938i			1.64628i	−0.567837	+	0.823141i	$0.692220\pi$
$968$	−16.0129	−	13.9704i	−0.514676	−	0.449025i
$969$		0			0
$970$	−35.7044	−	8.70440i	−1.14640	−	0.279482i
$971$		−	47.6773i		−	1.53004i	−0.644008	−	0.765019i	$-0.722730\pi$
$971$		−	47.6773i		−	1.53004i	0.644008	−	0.765019i	$-0.277270\pi$
$972$		0			0
$973$			10.1589i			0.325678i
$974$	−1.88055	+	7.71376i	−0.0602566	+	0.247165i
$975$		0			0
$976$	−43.4032	+	30.6133i	−1.38930	+	0.979909i
$977$			10.1656i			0.325225i	0.986690	+	0.162613i	$0.0519921\pi$
$977$			10.1656i			0.325225i	−0.986690	+	0.162613i	$0.948008\pi$
$978$		0			0
$979$	10.6340			0.339864
$980$	−7.42668	−	3.84993i	−0.237236	−	0.122982i
$981$		0			0
$982$	3.03855	−	12.4637i	0.0969639	−	0.397734i
$983$	7.35716			0.234657			0.117328	−	0.993093i	$-0.462567\pi$
$983$	7.35716			0.234657			0.117328	+	0.993093i	$0.462567\pi$
$984$		0			0
$985$	−80.4068			−2.56197
$986$	−0.596788	+	2.44795i	−0.0190056	+	0.0779586i
$987$		0			0
$988$	8.65253	−	16.6911i	0.275274	−	0.531014i
$989$	−53.8772			−1.71320
$990$		0			0
$991$			18.5907i			0.590552i	0.955412	+	0.295276i	$0.0954116\pi$
$991$			18.5907i			0.590552i	−0.955412	+	0.295276i	$0.904588\pi$
$992$	−57.3607	+	22.5895i	−1.82120	+	0.717218i
$993$		0			0
$994$	3.02290	−	12.3996i	0.0958806	−	0.393290i
$995$		−	7.06577i		−	0.224000i
$996$		0			0
$997$		−	4.19288i		−	0.132790i	−0.997793	−	0.0663950i	$-0.978850\pi$
$997$		−	4.19288i		−	0.132790i	0.997793	−	0.0663950i	$-0.0211497\pi$
$998$	50.0601	+	12.2042i	1.58462	+	0.386317i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.3	✓	48
3.2	odd	2	inner	1512.2.j.d.323.46	yes	48
4.3	odd	2		6048.2.j.d.5615.48		48
8.3	odd	2	inner	1512.2.j.d.323.45	yes	48
8.5	even	2		6048.2.j.d.5615.2		48
12.11	even	2		6048.2.j.d.5615.1		48
24.5	odd	2		6048.2.j.d.5615.47		48
24.11	even	2	inner	1512.2.j.d.323.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.3	✓	48	1.1	even	1	trivial
1512.2.j.d.323.4	yes	48	24.11	even	2	inner
1512.2.j.d.323.45	yes	48	8.3	odd	2	inner
1512.2.j.d.323.46	yes	48	3.2	odd	2	inner
6048.2.j.d.5615.1		48	12.11	even	2
6048.2.j.d.5615.2		48	8.5	even	2
6048.2.j.d.5615.47		48	24.5	odd	2
6048.2.j.d.5615.48		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37397 - 0.334962i) q^{2} +(1.77560 + 0.920458i) q^{4} +4.18263 q^{5} -1.00000i q^{7} +(-2.13131 - 1.85944i) q^{8} +O(q^{10})\)	\(q+(-1.37397 - 0.334962i) q^{2} +(1.77560 + 0.920458i) q^{4} +4.18263 q^{5} -1.00000i q^{7} +(-2.13131 - 1.85944i) q^{8} +(-5.74682 - 1.40102i) q^{10} +1.86730i q^{11} -3.07604i q^{13} +(-0.334962 + 1.37397i) q^{14} +(2.30551 + 3.26873i) q^{16} -0.504885i q^{17} +3.05596 q^{19} +(7.42668 + 3.84993i) q^{20} +(0.625474 - 2.56561i) q^{22} -5.97229 q^{23} +12.4944 q^{25} +(-1.03036 + 4.22639i) q^{26} +(0.920458 - 1.77560i) q^{28} +3.52884 q^{29} -10.8980i q^{31} +(-2.07281 - 5.26341i) q^{32} +(-0.169117 + 0.693698i) q^{34} -4.18263i q^{35} -11.3660i q^{37} +(-4.19880 - 1.02363i) q^{38} +(-8.91447 - 7.77736i) q^{40} +7.26960i q^{41} +9.02120 q^{43} +(-1.71877 + 3.31557i) q^{44} +(8.20576 + 2.00049i) q^{46} +0.327367 q^{47} -1.00000 q^{49} +(-17.1669 - 4.18514i) q^{50} +(2.83136 - 5.46181i) q^{52} +8.32940 q^{53} +7.81021i q^{55} +(-1.85944 + 2.13131i) q^{56} +(-4.84853 - 1.18203i) q^{58} +5.98008i q^{59} +13.2783i q^{61} +(-3.65043 + 14.9736i) q^{62} +(1.08494 + 7.92609i) q^{64} -12.8659i q^{65} -9.21499 q^{67} +(0.464725 - 0.896474i) q^{68} +(-1.40102 + 5.74682i) q^{70} -9.02460 q^{71} +0.416491 q^{73} +(-3.80718 + 15.6166i) q^{74} +(5.42616 + 2.81288i) q^{76} +1.86730 q^{77} +6.00459i q^{79} +(9.64311 + 13.6719i) q^{80} +(2.43504 - 9.98822i) q^{82} -2.62368i q^{83} -2.11175i q^{85} +(-12.3949 - 3.02176i) q^{86} +(3.47213 - 3.97978i) q^{88} -5.69486i q^{89} -3.07604 q^{91} +(-10.6044 - 5.49724i) q^{92} +(-0.449793 - 0.109655i) q^{94} +12.7819 q^{95} +6.21289 q^{97} +(1.37397 + 0.334962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more