LMFDB - Embedded newform 504.3.g.d.379.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(379,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.379"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.6
Character	$\chi$	$=$	504.379
Dual form			504.3.g.d.379.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.81394 + 0.842398i) q^{2} +(2.58073 - 3.05611i) q^{4} -5.94177i q^{5} +2.64575i q^{7} +(-2.10682 + 7.71760i) q^{8} +(5.00533 + 10.7780i) q^{10} -15.0849 q^{11} -11.2148i q^{13} +(-2.22877 - 4.79923i) q^{14} +(-2.67964 - 15.7740i) q^{16} +22.8244 q^{17} -33.0704 q^{19} +(-18.1587 - 15.3341i) q^{20} +(27.3631 - 12.7075i) q^{22} -1.69029i q^{23} -10.3046 q^{25} +(9.44732 + 20.3429i) q^{26} +(8.08571 + 6.82798i) q^{28} +28.9719i q^{29} +24.7233i q^{31} +(18.1487 + 26.3557i) q^{32} +(-41.4021 + 19.2272i) q^{34} +15.7204 q^{35} +53.7870i q^{37} +(59.9877 - 27.8584i) q^{38} +(45.8562 + 12.5183i) q^{40} -30.8925 q^{41} -44.2731 q^{43} +(-38.9301 + 46.1012i) q^{44} +(1.42389 + 3.06608i) q^{46} -37.2829i q^{47} -7.00000 q^{49} +(18.6919 - 8.68058i) q^{50} +(-34.2737 - 28.9424i) q^{52} +72.2354i q^{53} +89.6310i q^{55} +(-20.4188 - 5.57413i) q^{56} +(-24.4058 - 52.5532i) q^{58} -33.2212 q^{59} -96.8692i q^{61} +(-20.8269 - 44.8466i) q^{62} +(-55.1226 - 32.5192i) q^{64} -66.6357 q^{65} -86.0604 q^{67} +(58.9038 - 69.7540i) q^{68} +(-28.5159 + 13.2429i) q^{70} -40.4798i q^{71} +28.5905 q^{73} +(-45.3100 - 97.5662i) q^{74} +(-85.3459 + 101.067i) q^{76} -39.9109i q^{77} +80.5457i q^{79} +(-93.7255 + 15.9218i) q^{80} +(56.0370 - 26.0238i) q^{82} -36.2653 q^{83} -135.618i q^{85} +(80.3086 - 37.2955i) q^{86} +(31.7813 - 116.419i) q^{88} -13.9430 q^{89} +29.6716 q^{91} +(-5.16571 - 4.36218i) q^{92} +(31.4070 + 67.6288i) q^{94} +196.497i q^{95} -66.0297 q^{97} +(12.6976 - 5.89678i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 10 q^{4} - 10 q^{8} + 12 q^{10} - 32 q^{11} + 14 q^{14} + 66 q^{16} - 16 q^{17} - 64 q^{19} - 20 q^{20} + 12 q^{22} - 72 q^{25} - 100 q^{26} - 14 q^{28} - 98 q^{32} - 108 q^{34} + 72 q^{38}+ \cdots - 14 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 + 12 * q^10 - 32 * q^11 + 14 * q^14 + 66 * q^16 - 16 * q^17 - 64 * q^19 - 20 * q^20 + 12 * q^22 - 72 * q^25 - 100 * q^26 - 14 * q^28 - 98 * q^32 - 108 * q^34 + 72 * q^38 - 332 * q^40 + 80 * q^41 + 32 * q^43 + 292 * q^44 - 168 * q^49 - 46 * q^50 - 4 * q^52 - 98 * q^56 - 96 * q^58 + 16 * q^62 - 182 * q^64 + 192 * q^65 - 32 * q^67 - 188 * q^68 - 84 * q^70 - 240 * q^73 - 208 * q^74 + 8 * q^76 - 484 * q^80 - 372 * q^82 + 320 * q^83 + 604 * q^86 + 468 * q^88 - 400 * q^89 - 352 * q^92 - 72 * q^94 + 144 * q^97 - 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−1.81394	+	0.842398i	−0.906968	+	0.421199i
$2$	−1.81394	+	0.842398i	−0.906968	+	0.421199i
$3$		0			0
$3$		0			0
$4$	2.58073	−	3.05611i	0.645183	−	0.764028i
$5$		−	5.94177i		−	1.18835i	−0.804334	−	0.594177i	$-0.797478\pi$
$5$		−	5.94177i		−	1.18835i	0.804334	−	0.594177i	$-0.202522\pi$
$6$		0			0
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−2.10682	+	7.71760i	−0.263353	+	0.964700i
$9$		0			0
$10$	5.00533	+	10.7780i	0.500533	+	1.07780i
$11$	−15.0849			−1.37136			−0.685678	−	0.727905i	$-0.740494\pi$
$11$	−15.0849			−1.37136			−0.685678	+	0.727905i	$0.740494\pi$
$12$		0			0
$13$		−	11.2148i		−	0.862677i	−0.902190	−	0.431338i	$-0.858042\pi$
$13$		−	11.2148i		−	0.862677i	0.902190	−	0.431338i	$-0.141958\pi$
$14$	−2.22877	−	4.79923i	−0.159198	−	0.342802i
$15$		0			0
$16$	−2.67964	−	15.7740i	−0.167477	−	0.985876i
$17$	22.8244			1.34261			0.671307	−	0.741180i	$-0.265733\pi$
$17$	22.8244			1.34261			0.671307	+	0.741180i	$0.265733\pi$
$18$		0			0
$19$	−33.0704			−1.74055			−0.870274	−	0.492567i	$-0.836059\pi$
$19$	−33.0704			−1.74055			−0.870274	+	0.492567i	$0.836059\pi$
$20$	−18.1587	−	15.3341i	−0.907935	−	0.766706i
$21$		0			0
$22$	27.3631	−	12.7075i	1.24378	−	0.577613i
$23$		−	1.69029i		−	0.0734908i	−0.999325	−	0.0367454i	$-0.988301\pi$
$23$		−	1.69029i		−	0.0734908i	0.999325	−	0.0367454i	$-0.0116991\pi$
$24$		0			0
$25$	−10.3046			−0.412185
$26$	9.44732	+	20.3429i	0.363358	+	0.782420i
$27$		0			0
$28$	8.08571	+	6.82798i	0.288775	+	0.243856i
$29$			28.9719i			0.999030i	0.866305	+	0.499515i	$0.166488\pi$
$29$			28.9719i			0.999030i	−0.866305	+	0.499515i	$0.833512\pi$
$30$		0			0
$31$			24.7233i			0.797527i	0.917054	+	0.398764i	$0.130561\pi$
$31$			24.7233i			0.797527i	−0.917054	+	0.398764i	$0.869439\pi$
$32$	18.1487	+	26.3557i	0.567146	+	0.823617i
$33$		0			0
$34$	−41.4021	+	19.2272i	−1.21771	+	0.565507i
$35$	15.7204			0.449156
$36$		0			0
$37$			53.7870i			1.45370i	0.686795	+	0.726851i	$0.259017\pi$
$37$			53.7870i			1.45370i	−0.686795	+	0.726851i	$0.740983\pi$
$38$	59.9877	−	27.8584i	1.57862	−	0.733117i
$39$		0			0
$40$	45.8562	+	12.5183i	1.14640	+	0.312957i
$41$	−30.8925			−0.753476			−0.376738	−	0.926320i	$-0.622954\pi$
$41$	−30.8925			−0.753476			−0.376738	+	0.926320i	$0.622954\pi$
$42$		0			0
$43$	−44.2731			−1.02961			−0.514803	−	0.857308i	$-0.672135\pi$
$43$	−44.2731			−1.02961			−0.514803	+	0.857308i	$0.672135\pi$
$44$	−38.9301	+	46.1012i	−0.884775	+	1.04775i
$45$		0			0
$46$	1.42389	+	3.06608i	0.0309542	+	0.0666538i
$47$		−	37.2829i		−	0.793253i	−0.917980	−	0.396627i	$-0.870181\pi$
$47$		−	37.2829i		−	0.793253i	0.917980	−	0.396627i	$-0.129819\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	18.6919	−	8.68058i	0.373838	−	0.173612i
$51$		0			0
$52$	−34.2737	−	28.9424i	−0.659109	−	0.556584i
$53$			72.2354i			1.36293i	0.731850	+	0.681466i	$0.238657\pi$
$53$			72.2354i			1.36293i	−0.731850	+	0.681466i	$0.761343\pi$
$54$		0			0
$55$			89.6310i			1.62966i
$56$	−20.4188	−	5.57413i	−0.364622	−	0.0995381i
$57$		0			0
$58$	−24.4058	−	52.5532i	−0.420790	−	0.906089i
$59$	−33.2212			−0.563072			−0.281536	−	0.959551i	$-0.590844\pi$
$59$	−33.2212			−0.563072			−0.281536	+	0.959551i	$0.590844\pi$
$60$		0			0
$61$		−	96.8692i		−	1.58802i	−0.607905	−	0.794010i	$-0.707990\pi$
$61$		−	96.8692i		−	1.58802i	0.607905	−	0.794010i	$-0.292010\pi$
$62$	−20.8269	−	44.8466i	−0.335917	−	0.723332i
$63$		0			0
$64$	−55.1226	−	32.5192i	−0.861290	−	0.508113i
$65$	−66.6357			−1.02517
$66$		0			0
$67$	−86.0604			−1.28448			−0.642242	−	0.766502i	$-0.721995\pi$
$67$	−86.0604			−1.28448			−0.642242	+	0.766502i	$0.721995\pi$
$68$	58.9038	−	69.7540i	0.866232	−	1.02579i
$69$		0			0
$70$	−28.5159	+	13.2429i	−0.407370	+	0.189184i
$71$		−	40.4798i		−	0.570137i	−0.958507	−	0.285069i	$-0.907984\pi$
$71$		−	40.4798i		−	0.570137i	0.958507	−	0.285069i	$-0.0920164\pi$
$72$		0			0
$73$	28.5905			0.391651			0.195826	−	0.980639i	$-0.437261\pi$
$73$	28.5905			0.391651			0.195826	+	0.980639i	$0.437261\pi$
$74$	−45.3100	−	97.5662i	−0.612297	−	1.31846i
$75$		0			0
$76$	−85.3459	+	101.067i	−1.12297	+	1.32983i
$77$		−	39.9109i		−	0.518324i
$78$		0			0
$79$			80.5457i			1.01957i	0.860303	+	0.509783i	$0.170274\pi$
$79$			80.5457i			1.01957i	−0.860303	+	0.509783i	$0.829726\pi$
$80$	−93.7255	+	15.9218i	−1.17157	+	0.199022i
$81$		0			0
$82$	56.0370	−	26.0238i	0.683378	−	0.317363i
$83$	−36.2653			−0.436931			−0.218466	−	0.975845i	$-0.570105\pi$
$83$	−36.2653			−0.436931			−0.218466	+	0.975845i	$0.570105\pi$
$84$		0			0
$85$		−	135.618i		−	1.59550i
$86$	80.3086	−	37.2955i	0.933821	−	0.433669i
$87$		0			0
$88$	31.7813	−	116.419i	0.361151	−	1.32295i
$89$	−13.9430			−0.156663			−0.0783313	−	0.996927i	$-0.524959\pi$
$89$	−13.9430			−0.156663			−0.0783313	+	0.996927i	$0.524959\pi$
$90$		0			0
$91$	29.6716			0.326061
$92$	−5.16571	−	4.36218i	−0.0561490	−	0.0474150i
$93$		0			0
$94$	31.4070	+	67.6288i	0.334117	+	0.719456i
$95$			196.497i			2.06839i
$96$		0			0
$97$	−66.0297			−0.680718			−0.340359	−	0.940295i	$-0.610549\pi$
$97$	−66.0297			−0.680718			−0.340359	+	0.940295i	$0.610549\pi$
$98$	12.6976	−	5.89678i	0.129567	−	0.0601713i
$99$		0			0
$100$	−26.5935	+	31.4921i	−0.265935	+	0.314921i
$101$			158.436i			1.56867i	0.620336	+	0.784336i	$0.286996\pi$
$101$			158.436i			1.56867i	−0.620336	+	0.784336i	$0.713004\pi$
$102$		0			0
$103$			136.221i			1.32253i	0.750151	+	0.661266i	$0.229981\pi$
$103$			136.221i			1.32253i	−0.750151	+	0.661266i	$0.770019\pi$
$104$	86.5513	+	23.6276i	0.832224	+	0.227189i
$105$		0			0
$106$	−60.8509	−	131.030i	−0.574065	−	1.23614i
$107$	−164.556			−1.53790			−0.768951	−	0.639307i	$-0.779221\pi$
$107$	−164.556			−1.53790			−0.768951	+	0.639307i	$0.779221\pi$
$108$		0			0
$109$			18.6167i			0.170796i	0.996347	+	0.0853978i	$0.0272161\pi$
$109$			18.6167i			0.170796i	−0.996347	+	0.0853978i	$0.972784\pi$
$110$	−75.5050	−	162.585i	−0.686409	−	1.47805i
$111$		0			0
$112$	41.7341	−	7.08965i	0.372626	−	0.0633005i
$113$	−140.406			−1.24253			−0.621267	−	0.783599i	$-0.713382\pi$
$113$	−140.406			−1.24253			−0.621267	+	0.783599i	$0.713382\pi$
$114$		0			0
$115$	−10.0433			−0.0873331
$116$	88.5413	+	74.7687i	0.763287	+	0.644558i
$117$		0			0
$118$	60.2612	−	27.9855i	0.510688	−	0.237165i
$119$			60.3878i			0.507460i
$120$		0			0
$121$	106.554			0.880615
$122$	81.6024	+	175.715i	0.668872	+	1.44028i
$123$		0			0
$124$	75.5573	+	63.8043i	0.609333	+	0.514551i
$125$		−	87.3166i		−	0.698533i
$126$		0			0
$127$		−	191.983i		−	1.51168i	−0.654756	−	0.755840i	$-0.727229\pi$
$127$		−	191.983i		−	1.51168i	0.654756	−	0.755840i	$-0.272771\pi$
$128$	127.383	+	12.5527i	0.995180	+	0.0980682i
$129$		0			0
$130$	120.873	−	56.1338i	0.929792	−	0.431798i
$131$	−13.5685			−0.103576			−0.0517881	−	0.998658i	$-0.516492\pi$
$131$	−13.5685			−0.103576			−0.0517881	+	0.998658i	$0.516492\pi$
$132$		0			0
$133$		−	87.4961i		−	0.657866i
$134$	156.108	−	72.4971i	1.16499	−	0.541023i
$135$		0			0
$136$	−48.0871	+	176.150i	−0.353581	+	1.29522i
$137$	−75.2780			−0.549475			−0.274737	−	0.961519i	$-0.588591\pi$
$137$	−75.2780			−0.549475			−0.274737	+	0.961519i	$0.588591\pi$
$138$		0			0
$139$	222.721			1.60231			0.801153	−	0.598460i	$-0.204220\pi$
$139$	222.721			1.60231			0.801153	+	0.598460i	$0.204220\pi$
$140$	40.5703	−	48.0434i	0.289788	−	0.343167i
$141$		0			0
$142$	34.1000	+	73.4277i	0.240141	+	0.517097i
$143$			169.174i			1.18304i
$144$		0			0
$145$	172.144			1.18720
$146$	−51.8614	+	24.0846i	−0.355215	+	0.164963i
$147$		0			0
$148$	164.379	+	138.810i	1.11067	+	0.937904i
$149$		−	173.387i		−	1.16367i	−0.813307	−	0.581835i	$-0.802335\pi$
$149$		−	173.387i		−	1.16367i	0.813307	−	0.581835i	$-0.197665\pi$
$150$		0			0
$151$			84.9375i			0.562500i	0.959635	+	0.281250i	$0.0907490\pi$
$151$			84.9375i			0.562500i	−0.959635	+	0.281250i	$0.909251\pi$
$152$	69.6736	−	255.224i	0.458379	−	1.67911i
$153$		0			0
$154$	33.6209	+	72.3959i	0.218317	+	0.470103i
$155$	146.900			0.947744
$156$		0			0
$157$		−	57.6685i		−	0.367316i	−0.982990	−	0.183658i	$-0.941206\pi$
$157$		−	57.6685i		−	0.367316i	0.982990	−	0.183658i	$-0.0587938\pi$
$158$	−67.8515	−	146.105i	−0.429440	−	0.924714i
$159$		0			0
$160$	156.600	−	107.835i	0.978748	−	0.673971i
$161$	4.47208			0.0277769
$162$		0			0
$163$	10.8347			0.0664708			0.0332354	−	0.999448i	$-0.489419\pi$
$163$	10.8347			0.0664708			0.0332354	+	0.999448i	$0.489419\pi$
$164$	−79.7253	+	94.4109i	−0.486130	+	0.575676i
$165$		0			0
$166$	65.7829	−	30.5498i	0.396283	−	0.184035i
$167$		−	57.5843i		−	0.344816i	−0.985026	−	0.172408i	$-0.944845\pi$
$167$		−	57.5843i		−	0.344816i	0.985026	−	0.172408i	$-0.0551548\pi$
$168$		0			0
$169$	43.2283			0.255789
$170$	114.244	+	246.002i	0.672023	+	1.44707i
$171$		0			0
$172$	−114.257	+	135.304i	−0.664285	+	0.786648i
$173$		−	209.285i		−	1.20974i	−0.796323	−	0.604871i	$-0.793225\pi$
$173$		−	209.285i		−	1.20974i	0.796323	−	0.604871i	$-0.206775\pi$
$174$		0			0
$175$		−	27.2635i		−	0.155791i
$176$	40.4221	+	237.950i	0.229671	+	1.35199i
$177$		0			0
$178$	25.2917	−	11.7455i	0.142088	−	0.0659861i
$179$	228.951			1.27905			0.639527	−	0.768768i	$-0.279130\pi$
$179$	228.951			1.27905			0.639527	+	0.768768i	$0.279130\pi$
$180$		0			0
$181$		−	130.515i		−	0.721076i	−0.932744	−	0.360538i	$-0.882593\pi$
$181$		−	130.515i		−	0.721076i	0.932744	−	0.360538i	$-0.117407\pi$
$182$	−53.8223	+	24.9953i	−0.295727	+	0.137337i
$183$		0			0
$184$	13.0450	+	3.56114i	0.0708965	+	0.0193540i
$185$	319.590			1.72751
$186$		0			0
$187$	−344.304			−1.84120
$188$	−113.941	−	96.2172i	−0.606068	−	0.511794i
$189$		0			0
$190$	−165.528	−	356.433i	−0.871202	−	1.87596i
$191$			91.3000i			0.478010i	0.971018	+	0.239005i	$0.0768213\pi$
$191$			91.3000i			0.478010i	−0.971018	+	0.239005i	$0.923179\pi$
$192$		0			0
$193$	−125.665			−0.651115			−0.325557	−	0.945522i	$-0.605552\pi$
$193$	−125.665			−0.651115			−0.325557	+	0.945522i	$0.605552\pi$
$194$	119.774	−	55.6232i	0.617390	−	0.286718i
$195$		0			0
$196$	−18.0651	+	21.3928i	−0.0921690	+	0.109147i
$197$		−	74.5133i		−	0.378240i	−0.981954	−	0.189120i	$-0.939436\pi$
$197$		−	74.5133i		−	0.378240i	0.981954	−	0.189120i	$-0.0605635\pi$
$198$		0			0
$199$			77.2741i			0.388312i	0.980971	+	0.194156i	$0.0621968\pi$
$199$			77.2741i			0.388312i	−0.980971	+	0.194156i	$0.937803\pi$
$200$	21.7100	−	79.5269i	0.108550	−	0.397634i
$201$		0			0
$202$	−133.466	−	287.393i	−0.660723	−	1.42274i
$203$	−76.6524			−0.377598
$204$		0			0
$205$			183.556i			0.895395i
$206$	−114.752	−	247.096i	−0.557049	−	1.19950i
$207$		0			0
$208$	−176.902	+	30.0516i	−0.850492	+	0.144479i
$209$	498.864			2.38691
$210$		0			0
$211$	283.994			1.34594			0.672971	−	0.739669i	$-0.265018\pi$
$211$	283.994			1.34594			0.672971	+	0.739669i	$0.265018\pi$
$212$	220.759	+	186.420i	1.04132	+	0.879341i
$213$		0			0
$214$	298.493	−	138.621i	1.39483	−	0.647763i
$215$			263.060i			1.22354i
$216$		0			0
$217$	−65.4118			−0.301437
$218$	−15.6827	−	33.7696i	−0.0719389	−	0.154906i
$219$		0			0
$220$	273.922	+	231.314i	1.24510	+	1.05143i
$221$		−	255.971i		−	1.15824i
$222$		0			0
$223$			115.772i			0.519155i	0.965722	+	0.259577i	$0.0835833\pi$
$223$			115.772i			0.519155i	−0.965722	+	0.259577i	$0.916417\pi$
$224$	−69.7307	+	48.0169i	−0.311298	+	0.214361i
$225$		0			0
$226$	254.688	−	118.278i	1.12694	−	0.523354i
$227$	−6.83029			−0.0300894			−0.0150447	−	0.999887i	$-0.504789\pi$
$227$	−6.83029			−0.0300894			−0.0150447	+	0.999887i	$0.504789\pi$
$228$		0			0
$229$			217.138i			0.948203i	0.880470	+	0.474101i	$0.157227\pi$
$229$			217.138i			0.948203i	−0.880470	+	0.474101i	$0.842773\pi$
$230$	18.2179	−	8.46045i	0.0792083	−	0.0367846i
$231$		0			0
$232$	−223.593	−	61.0387i	−0.963764	−	0.263098i
$233$	−134.382			−0.576746			−0.288373	−	0.957518i	$-0.593114\pi$
$233$	−134.382			−0.576746			−0.288373	+	0.957518i	$0.593114\pi$
$234$		0			0
$235$	−221.526			−0.942665
$236$	−85.7352	+	101.528i	−0.363285	+	0.430203i
$237$		0			0
$238$	−50.8705	−	109.540i	−0.213742	−	0.460250i
$239$		−	408.424i		−	1.70889i	−0.519545	−	0.854443i	$-0.673899\pi$
$239$		−	408.424i		−	1.70889i	0.519545	−	0.854443i	$-0.326101\pi$
$240$		0			0
$241$	−237.295			−0.984629			−0.492314	−	0.870418i	$-0.663849\pi$
$241$	−237.295			−0.984629			−0.492314	+	0.870418i	$0.663849\pi$
$242$	−193.283	+	89.7612i	−0.798690	+	0.370914i
$243$		0			0
$244$	−296.043	−	249.993i	−1.21329	−	1.02456i
$245$			41.5924i			0.169765i
$246$		0			0
$247$			370.878i			1.50153i
$248$	−190.805	−	52.0877i	−0.769374	−	0.210031i
$249$		0			0
$250$	73.5553	+	158.387i	0.294221	+	0.633547i
$251$	−305.519			−1.21721			−0.608604	−	0.793474i	$-0.708270\pi$
$251$	−305.519			−1.21721			−0.608604	+	0.793474i	$0.708270\pi$
$252$		0			0
$253$			25.4978i			0.100782i
$254$	161.726	+	348.246i	0.636718	+	1.37105i
$255$		0			0
$256$	−241.639	+	84.5373i	−0.943903	+	0.330224i
$257$	212.323			0.826158			0.413079	−	0.910695i	$-0.364453\pi$
$257$	212.323			0.826158			0.413079	+	0.910695i	$0.364453\pi$
$258$		0			0
$259$	−142.307			−0.549448
$260$	−171.969	+	203.646i	−0.661419	+	0.783255i
$261$		0			0
$262$	24.6124	−	11.4301i	0.0939403	−	0.0436262i
$263$		−	55.8138i		−	0.212220i	−0.994354	−	0.106110i	$-0.966160\pi$
$263$		−	55.8138i		−	0.212220i	0.994354	−	0.106110i	$-0.0338396\pi$
$264$		0			0
$265$	429.206			1.61965
$266$	73.7065	+	158.712i	0.277092	+	0.596663i
$267$		0			0
$268$	−222.099	+	263.010i	−0.828727	+	0.981381i
$269$			392.637i			1.45962i	0.683651	+	0.729809i	$0.260391\pi$
$269$			392.637i			1.45962i	−0.683651	+	0.729809i	$0.739609\pi$
$270$		0			0
$271$		−	505.999i		−	1.86715i	−0.358377	−	0.933577i	$-0.616670\pi$
$271$		−	505.999i		−	1.86715i	0.358377	−	0.933577i	$-0.383330\pi$
$272$	−61.1612	−	360.033i	−0.224857	−	1.32365i
$273$		0			0
$274$	136.550	−	63.4140i	0.498356	−	0.231438i
$275$	155.444			0.565252
$276$		0			0
$277$		−	234.703i		−	0.847304i	−0.905825	−	0.423652i	$-0.860748\pi$
$277$		−	234.703i		−	0.847304i	0.905825	−	0.423652i	$-0.139252\pi$
$278$	−404.001	+	187.619i	−1.45324	+	0.674889i
$279$		0			0
$280$	−33.1202	+	121.324i	−0.118286	+	0.433300i
$281$	260.538			0.927182			0.463591	−	0.886049i	$-0.346561\pi$
$281$	260.538			0.927182			0.463591	+	0.886049i	$0.346561\pi$
$282$		0			0
$283$	314.398			1.11095			0.555474	−	0.831534i	$-0.312537\pi$
$283$	314.398			1.11095			0.555474	+	0.831534i	$0.312537\pi$
$284$	−123.711	−	104.467i	−0.435601	−	0.367843i
$285$		0			0
$286$	−142.512	−	306.871i	−0.498293	−	1.07298i
$287$		−	81.7339i		−	0.284787i
$288$		0			0
$289$	231.955			0.802612
$290$	−312.259	+	145.014i	−1.07675	+	0.500048i
$291$		0			0
$292$	73.7846	−	87.3759i	0.252687	−	0.299233i
$293$		−	54.0484i		−	0.184465i	−0.995737	−	0.0922327i	$-0.970600\pi$
$293$		−	54.0484i		−	0.184465i	0.995737	−	0.0922327i	$-0.0294004\pi$
$294$		0			0
$295$			197.393i			0.669129i
$296$	−415.106	−	113.320i	−1.40239	−	0.382837i
$297$		0			0
$298$	146.061	+	314.513i	0.490136	+	1.05541i
$299$	−18.9562			−0.0633988
$300$		0			0
$301$		−	117.136i		−	0.389155i
$302$	−71.5511	−	154.071i	−0.236924	−	0.510169i
$303$		0			0
$304$	88.6168	+	521.653i	0.291502	+	1.71597i
$305$	−575.574			−1.88713
$306$		0			0
$307$	−82.1306			−0.267526			−0.133763	−	0.991013i	$-0.542706\pi$
$307$	−82.1306			−0.267526			−0.133763	+	0.991013i	$0.542706\pi$
$308$	−121.972	−	102.999i	−0.396014	−	0.334414i
$309$		0			0
$310$	−266.468	+	123.749i	−0.859574	+	0.399189i
$311$		−	83.2457i		−	0.267671i	−0.991004	−	0.133835i	$-0.957271\pi$
$311$		−	83.2457i		−	0.267671i	0.991004	−	0.133835i	$-0.0427294\pi$
$312$		0			0
$313$	49.4110			0.157863			0.0789314	−	0.996880i	$-0.474849\pi$
$313$	49.4110			0.157863			0.0789314	+	0.996880i	$0.474849\pi$
$314$	48.5798	+	104.607i	0.154713	+	0.333144i
$315$		0			0
$316$	246.157	+	207.867i	0.778977	+	0.657807i
$317$		−	449.103i		−	1.41673i	−0.705847	−	0.708364i	$-0.749434\pi$
$317$		−	449.103i		−	1.41673i	0.705847	−	0.708364i	$-0.250566\pi$
$318$		0			0
$319$		−	437.038i		−	1.37003i
$320$	−193.222	+	327.526i	−0.603818	+	1.02352i
$321$		0			0
$322$	−8.11207	+	3.76727i	−0.0251928	+	0.0116996i
$323$	−754.814			−2.33688
$324$		0			0
$325$			115.564i			0.355582i
$326$	−19.6535	+	9.12716i	−0.0602869	+	0.0279974i
$327$		0			0
$328$	65.0851	−	238.416i	0.198430	−	0.726877i
$329$	98.6413			0.299822
$330$		0			0
$331$	−107.798			−0.325674			−0.162837	−	0.986653i	$-0.552064\pi$
$331$	−107.798			−0.325674			−0.162837	+	0.986653i	$0.552064\pi$
$332$	−93.5910	+	110.831i	−0.281901	+	0.333828i
$333$		0			0
$334$	48.5089	+	104.454i	0.145236	+	0.312737i
$335$			511.351i			1.52642i
$336$		0			0
$337$	−565.146			−1.67699			−0.838495	−	0.544909i	$-0.816564\pi$
$337$	−565.146			−1.67699			−0.838495	+	0.544909i	$0.816564\pi$
$338$	−78.4135	+	36.4154i	−0.231993	+	0.107738i
$339$		0			0
$340$	−414.462	−	349.993i	−1.21901	−	1.02939i
$341$		−	372.949i		−	1.09369i
$342$		0			0
$343$		−	18.5203i		−	0.0539949i
$344$	93.2756	−	341.682i	0.271150	−	0.993261i
$345$		0			0
$346$	176.302	+	379.630i	0.509542	+	1.09720i
$347$	617.119			1.77844			0.889221	−	0.457478i	$-0.151247\pi$
$347$	617.119			1.77844			0.889221	+	0.457478i	$0.151247\pi$
$348$		0			0
$349$		−	208.548i		−	0.597557i	−0.954322	−	0.298779i	$-0.903421\pi$
$349$		−	208.548i		−	0.597557i	0.954322	−	0.298779i	$-0.0965792\pi$
$350$	22.9667	+	49.4542i	0.0656190	+	0.141298i
$351$		0			0
$352$	−273.771	−	397.574i	−0.777759	−	1.12947i
$353$	−93.3007			−0.264308			−0.132154	−	0.991229i	$-0.542189\pi$
$353$	−93.3007			−0.264308			−0.132154	+	0.991229i	$0.542189\pi$
$354$		0			0
$355$	−240.521			−0.677525
$356$	−35.9831	+	42.6113i	−0.101076	+	0.119695i
$357$		0			0
$358$	−415.302	+	192.868i	−1.16006	+	0.538736i
$359$		−	319.598i		−	0.890246i	−0.895469	−	0.445123i	$-0.853160\pi$
$359$		−	319.598i		−	0.890246i	0.895469	−	0.445123i	$-0.146840\pi$
$360$		0			0
$361$	732.653			2.02951
$362$	109.945	+	236.746i	0.303716	+	0.653993i
$363$		0			0
$364$	76.5744	−	90.6796i	0.210369	−	0.249120i
$365$		−	169.878i		−	0.465420i
$366$		0			0
$367$			489.607i			1.33408i	0.745022	+	0.667040i	$0.232439\pi$
$367$			489.607i			1.33408i	−0.745022	+	0.667040i	$0.767561\pi$
$368$	−26.6626	+	4.52936i	−0.0724528	+	0.0123080i
$369$		0			0
$370$	−579.716	+	269.222i	−1.56680	+	0.727626i
$371$	−191.117			−0.515140
$372$		0			0
$373$		−	427.590i		−	1.14635i	−0.819432	−	0.573177i	$-0.805711\pi$
$373$		−	427.590i		−	1.14635i	0.819432	−	0.573177i	$-0.194289\pi$
$374$	624.547	−	290.041i	1.66991	−	0.775511i
$375$		0			0
$376$	287.734	+	78.5485i	0.765251	+	0.208906i
$377$	324.914			0.861840
$378$		0			0
$379$	−441.475			−1.16484			−0.582421	−	0.812887i	$-0.697894\pi$
$379$	−441.475			−1.16484			−0.582421	+	0.812887i	$0.697894\pi$
$380$	600.516	+	507.106i	1.58031	+	1.33449i
$381$		0			0
$382$	−76.9109	−	165.612i	−0.201337	−	0.433540i
$383$			392.842i			1.02570i	0.858479	+	0.512849i	$0.171410\pi$
$383$			392.842i			1.02570i	−0.858479	+	0.512849i	$0.828590\pi$
$384$		0			0
$385$	−237.141			−0.615952
$386$	227.949	−	105.860i	0.590540	−	0.274249i
$387$		0			0
$388$	−170.405	+	201.794i	−0.439188	+	0.520088i
$389$			539.166i			1.38603i	0.720923	+	0.693015i	$0.243718\pi$
$389$			539.166i			1.38603i	−0.720923	+	0.693015i	$0.756282\pi$
$390$		0			0
$391$		−	38.5799i		−	0.0986698i
$392$	14.7478	−	54.0232i	0.0376219	−	0.137814i
$393$		0			0
$394$	62.7698	+	135.162i	0.159314	+	0.343052i
$395$	478.584			1.21161
$396$		0			0
$397$		−	439.822i		−	1.10786i	−0.832562	−	0.553932i	$-0.813127\pi$
$397$		−	439.822i		−	1.10786i	0.832562	−	0.553932i	$-0.186873\pi$
$398$	−65.0955	−	140.170i	−0.163557	−	0.352187i
$399$		0			0
$400$	27.6126	+	162.545i	0.0690316	+	0.406363i
$401$	−256.316			−0.639191			−0.319596	−	0.947554i	$-0.603547\pi$
$401$	−256.316			−0.639191			−0.319596	+	0.947554i	$0.603547\pi$
$402$		0			0
$403$	277.267			0.688008
$404$	484.198	+	408.881i	1.19851	+	1.01208i
$405$		0			0
$406$	139.043	−	64.5718i	0.342469	−	0.159044i
$407$		−	811.371i		−	1.99354i
$408$		0			0
$409$	−401.361			−0.981322			−0.490661	−	0.871351i	$-0.663245\pi$
$409$	−401.361			−0.981322			−0.490661	+	0.871351i	$0.663245\pi$
$410$	−154.627	−	332.959i	−0.377139	−	0.812095i
$411$		0			0
$412$	416.306	+	351.550i	1.01045	+	0.853276i
$413$		−	87.8951i		−	0.212821i
$414$		0			0
$415$			215.480i			0.519229i
$416$	295.574	−	203.534i	0.710515	−	0.489264i
$417$		0			0
$418$	−904.908	+	420.242i	−2.16485	+	1.00536i
$419$	185.720			0.443247			0.221623	−	0.975132i	$-0.428864\pi$
$419$	185.720			0.443247			0.221623	+	0.975132i	$0.428864\pi$
$420$		0			0
$421$			361.664i			0.859060i	0.903053	+	0.429530i	$0.141321\pi$
$421$			361.664i			0.859060i	−0.903053	+	0.429530i	$0.858679\pi$
$422$	−515.147	+	239.236i	−1.22073	+	0.566909i
$423$		0			0
$424$	−557.484	−	152.187i	−1.31482	−	0.358932i
$425$	−235.197			−0.553405
$426$		0			0
$427$	256.292			0.600215
$428$	−424.674	+	502.900i	−0.992229	+	1.17500i
$429$		0			0
$430$	−221.601	−	477.175i	−0.515352	−	1.10971i
$431$			130.748i			0.303359i	0.988430	+	0.151679i	$0.0484681\pi$
$431$			130.748i			0.303359i	−0.988430	+	0.151679i	$0.951532\pi$
$432$		0			0
$433$	−450.084			−1.03945			−0.519727	−	0.854332i	$-0.673966\pi$
$433$	−450.084			−1.03945			−0.519727	+	0.854332i	$0.673966\pi$
$434$	118.653	−	55.1028i	0.273394	−	0.126965i
$435$		0			0
$436$	56.8948	+	48.0448i	0.130493	+	0.110194i
$437$			55.8986i			0.127914i
$438$		0			0
$439$		−	107.851i		−	0.245674i	−0.992427	−	0.122837i	$-0.960801\pi$
$439$		−	107.851i		−	0.245674i	0.992427	−	0.122837i	$-0.0391992\pi$
$440$	−691.736	−	188.837i	−1.57213	−	0.429175i
$441$		0			0
$442$	215.630	+	464.316i	0.487850	+	1.05049i
$443$	79.9983			0.180583			0.0902915	−	0.995915i	$-0.471220\pi$
$443$	79.9983			0.180583			0.0902915	+	0.995915i	$0.471220\pi$
$444$		0			0
$445$			82.8459i			0.186171i
$446$	−97.5256	−	210.002i	−0.218667	−	0.470857i
$447$		0			0
$448$	86.0378	−	145.841i	0.192049	−	0.325537i
$449$	−498.405			−1.11003			−0.555017	−	0.831839i	$-0.687288\pi$
$449$	−498.405			−1.11003			−0.555017	+	0.831839i	$0.687288\pi$
$450$		0			0
$451$	466.010			1.03328
$452$	−362.352	+	429.098i	−0.801663	+	0.949331i
$453$		0			0
$454$	12.3897	−	5.75382i	0.0272901	−	0.0126736i
$455$		−	176.302i		−	0.387476i
$456$		0			0
$457$	−469.124			−1.02653			−0.513264	−	0.858231i	$-0.671564\pi$
$457$	−469.124			−1.02653			−0.513264	+	0.858231i	$0.671564\pi$
$458$	−182.917	−	393.875i	−0.399382	−	0.859990i
$459$		0			0
$460$	−25.9191	+	30.6935i	−0.0563458	+	0.0667249i
$461$			729.055i			1.58146i	0.612162	+	0.790732i	$0.290300\pi$
$461$			729.055i			1.58146i	−0.612162	+	0.790732i	$0.709700\pi$
$462$		0			0
$463$		−	602.290i		−	1.30084i	−0.759574	−	0.650421i	$-0.774593\pi$
$463$		−	602.290i		−	1.30084i	0.759574	−	0.650421i	$-0.225407\pi$
$464$	457.003	−	77.6341i	0.984920	−	0.167315i
$465$		0			0
$466$	243.760	−	113.203i	0.523090	−	0.242925i
$467$	356.045			0.762409			0.381204	−	0.924491i	$-0.375509\pi$
$467$	356.045			0.762409			0.381204	+	0.924491i	$0.375509\pi$
$468$		0			0
$469$		−	227.694i		−	0.485489i
$470$	401.835	−	186.613i	0.854968	−	0.397050i
$471$		0			0
$472$	69.9913	−	256.388i	0.148287	−	0.543195i
$473$	667.855			1.41196
$474$		0			0
$475$	340.778			0.717427
$476$	184.552	+	155.845i	0.387714	+	0.327405i
$477$		0			0
$478$	344.055	+	740.855i	0.719781	+	1.54991i
$479$		−	201.862i		−	0.421424i	−0.977548	−	0.210712i	$-0.932422\pi$
$479$		−	201.862i		−	0.421424i	0.977548	−	0.210712i	$-0.0675782\pi$
$480$		0			0
$481$	603.210			1.25407
$482$	430.439	−	199.897i	0.893027	−	0.414724i
$483$		0			0
$484$	274.988	−	325.642i	0.568158	−	0.672815i
$485$			392.333i			0.808934i
$486$		0			0
$487$		−	343.994i		−	0.706353i	−0.935557	−	0.353177i	$-0.885102\pi$
$487$		−	343.994i		−	0.706353i	0.935557	−	0.353177i	$-0.114898\pi$
$488$	747.597	+	204.086i	1.53196	+	0.418210i
$489$		0			0
$490$	−35.0373	−	75.4459i	−0.0715047	−	0.153971i
$491$	−178.510			−0.363564			−0.181782	−	0.983339i	$-0.558187\pi$
$491$	−178.510			−0.363564			−0.181782	+	0.983339i	$0.558187\pi$
$492$		0			0
$493$			661.267i			1.34131i
$494$	−312.427	−	672.749i	−0.632443	−	1.36184i
$495$		0			0
$496$	389.986	−	66.2496i	0.786263	−	0.133568i
$497$	107.099			0.215492
$498$		0			0
$499$	548.499			1.09920			0.549598	−	0.835429i	$-0.314781\pi$
$499$	548.499			1.09920			0.549598	+	0.835429i	$0.314781\pi$
$500$	−266.849	−	225.341i	−0.533698	−	0.450681i
$501$		0			0
$502$	554.193	−	257.369i	1.10397	−	0.512687i
$503$		−	394.287i		−	0.783872i	−0.919993	−	0.391936i	$-0.871806\pi$
$503$		−	394.287i		−	0.783872i	0.919993	−	0.391936i	$-0.128194\pi$
$504$		0			0
$505$	941.389			1.86414
$506$	−21.4793	−	46.2515i	−0.0424492	−	0.0914061i
$507$		0			0
$508$	−586.723	−	495.458i	−1.15497	−	0.975310i
$509$			863.631i			1.69672i	0.529419	+	0.848360i	$0.322410\pi$
$509$			863.631i			1.69672i	−0.529419	+	0.848360i	$0.677590\pi$
$510$		0			0
$511$			75.6435i			0.148030i
$512$	367.104	−	356.901i	0.717000	−	0.697073i
$513$		0			0
$514$	−385.140	+	178.860i	−0.749299	+	0.347977i
$515$	809.393			1.57164
$516$		0			0
$517$			562.409i			1.08783i
$518$	258.136	−	119.879i	0.498332	−	0.231427i
$519$		0			0
$520$	140.390	−	514.268i	0.269980	−	0.988976i
$521$	−499.986			−0.959666			−0.479833	−	0.877360i	$-0.659303\pi$
$521$	−499.986			−0.959666			−0.479833	+	0.877360i	$0.659303\pi$
$522$		0			0
$523$	−80.9144			−0.154712			−0.0773561	−	0.997004i	$-0.524648\pi$
$523$	−80.9144			−0.154712			−0.0773561	+	0.997004i	$0.524648\pi$
$524$	−35.0166	+	41.4668i	−0.0668256	+	0.0791351i
$525$		0			0
$526$	47.0174	+	101.243i	0.0893868	+	0.192477i
$527$			564.296i			1.07077i
$528$		0			0
$529$	526.143			0.994599
$530$	−778.552	+	361.562i	−1.46897	+	0.682193i
$531$		0			0
$532$	−267.398	−	225.804i	−0.502628	−	0.424444i
$533$			346.453i			0.650006i
$534$		0			0
$535$			977.751i			1.82757i
$536$	181.314	−	664.179i	0.338273	−	1.23914i
$537$		0			0
$538$	−330.757	−	712.219i	−0.614789	−	1.32383i
$539$	105.594			0.195908
$540$		0			0
$541$		−	552.750i		−	1.02172i	−0.859664	−	0.510860i	$-0.829327\pi$
$541$		−	552.750i		−	1.02172i	0.859664	−	0.510860i	$-0.170673\pi$
$542$	426.252	+	917.850i	0.786443	+	1.69345i
$543$		0			0
$544$	414.233	+	601.555i	0.761459	+	1.10580i
$545$	110.616			0.202966
$546$		0			0
$547$	−570.865			−1.04363			−0.521814	−	0.853059i	$-0.674745\pi$
$547$	−570.865			−1.04363			−0.521814	+	0.853059i	$0.674745\pi$
$548$	−194.272	+	230.058i	−0.354512	+	0.419814i
$549$		0			0
$550$	−281.966	+	130.946i	−0.512665	+	0.238083i
$551$		−	958.112i		−	1.73886i
$552$		0			0
$553$	−213.104			−0.385360
$554$	197.713	+	425.737i	0.356883	+	0.768478i
$555$		0			0
$556$	574.782	−	680.659i	1.03378	−	1.22421i
$557$		−	1107.30i		−	1.98797i	−0.109496	−	0.993987i	$-0.534924\pi$
$557$		−	1107.30i		−	1.98797i	0.109496	−	0.993987i	$-0.465076\pi$
$558$		0			0
$559$			496.514i			0.888218i
$560$	−42.1251	−	247.974i	−0.0752234	−	0.442812i
$561$		0			0
$562$	−472.600	+	219.477i	−0.840924	+	0.390528i
$563$	−32.2930			−0.0573587			−0.0286794	−	0.999589i	$-0.509130\pi$
$563$	−32.2930			−0.0573587			−0.0286794	+	0.999589i	$0.509130\pi$
$564$		0			0
$565$			834.263i			1.47657i
$566$	−570.298	+	264.848i	−1.00759	+	0.467930i
$567$		0			0
$568$	312.406	+	85.2837i	0.550011	+	0.150147i
$569$	−838.069			−1.47288			−0.736440	−	0.676503i	$-0.763495\pi$
$569$	−838.069			−1.47288			−0.736440	+	0.676503i	$0.763495\pi$
$570$		0			0
$571$	−590.149			−1.03354			−0.516768	−	0.856126i	$-0.672865\pi$
$571$	−590.149			−1.03354			−0.516768	+	0.856126i	$0.672865\pi$
$572$	517.015	+	436.593i	0.903873	+	0.763275i
$573$		0			0
$574$	68.8524	+	148.260i	0.119952	+	0.258293i
$575$			17.4178i			0.0302918i
$576$		0			0
$577$	376.385			0.652314			0.326157	−	0.945316i	$-0.394246\pi$
$577$	376.385			0.652314			0.326157	+	0.945316i	$0.394246\pi$
$578$	−420.751	+	195.398i	−0.727943	+	0.338059i
$579$		0			0
$580$	444.258	−	526.092i	0.765962	−	0.907055i
$581$		−	95.9489i		−	0.165144i
$582$		0			0
$583$		−	1089.66i		−	1.86906i
$584$	−60.2353	+	220.650i	−0.103143	+	0.377826i
$585$		0			0
$586$	45.5302	+	98.0404i	0.0776966	+	0.167304i
$587$	489.154			0.833311			0.416656	−	0.909064i	$-0.363202\pi$
$587$	489.154			0.833311			0.416656	+	0.909064i	$0.363202\pi$
$588$		0			0
$589$		−	817.611i		−	1.38813i
$590$	−166.283	−	358.058i	−0.281836	−	0.606879i
$591$		0			0
$592$	848.436	−	144.130i	1.43317	−	0.243462i
$593$	−180.522			−0.304421			−0.152211	−	0.988348i	$-0.548639\pi$
$593$	−180.522			−0.304421			−0.152211	+	0.988348i	$0.548639\pi$
$594$		0			0
$595$	358.810			0.603042
$596$	−529.889	−	447.465i	−0.889076	−	0.750780i
$597$		0			0
$598$	34.3854	−	15.9687i	0.0575007	−	0.0267035i
$599$		−	16.6365i		−	0.0277738i	−0.999904	−	0.0138869i	$-0.995580\pi$
$599$		−	16.6365i		−	0.0277738i	0.999904	−	0.0138869i	$-0.00442048\pi$
$600$		0			0
$601$	−763.074			−1.26967			−0.634837	−	0.772646i	$-0.718933\pi$
$601$	−763.074			−1.26967			−0.634837	+	0.772646i	$0.718933\pi$
$602$	98.6747	+	212.477i	0.163912	+	0.352951i
$603$		0			0
$604$	259.578	+	219.201i	0.429765	+	0.362915i
$605$		−	633.122i		−	1.04648i
$606$		0			0
$607$			82.3314i			0.135637i	0.997698	+	0.0678183i	$0.0216038\pi$
$607$			82.3314i			0.135637i	−0.997698	+	0.0678183i	$0.978396\pi$
$608$	−600.185	−	871.596i	−0.987146	−	1.43355i
$609$		0			0
$610$	1044.06	−	484.862i	1.71157	−	0.794856i
$611$	−418.120			−0.684321
$612$		0			0
$613$			522.712i			0.852712i	0.904556	+	0.426356i	$0.140203\pi$
$613$			522.712i			0.852712i	−0.904556	+	0.426356i	$0.859797\pi$
$614$	148.980	−	69.1866i	0.242638	−	0.112682i
$615$		0			0
$616$	308.016	+	84.0853i	0.500026	+	0.136502i
$617$	1005.31			1.62935			0.814674	−	0.579920i	$-0.196916\pi$
$617$	1005.31			1.62935			0.814674	+	0.579920i	$0.196916\pi$
$618$		0			0
$619$	519.176			0.838734			0.419367	−	0.907817i	$-0.362252\pi$
$619$	519.176			0.838734			0.419367	+	0.907817i	$0.362252\pi$
$620$	379.111	−	448.944i	0.611469	−	0.724103i
$621$		0			0
$622$	70.1259	+	151.002i	0.112743	+	0.242769i
$623$		−	36.8896i		−	0.0592129i
$624$		0			0
$625$	−776.430			−1.24229
$626$	−89.6285	+	41.6237i	−0.143177	+	0.0664916i
$627$		0			0
$628$	−176.241	−	148.827i	−0.280639	−	0.236986i
$629$			1227.66i			1.95176i
$630$		0			0
$631$			62.6700i			0.0993185i	0.998766	+	0.0496592i	$0.0158135\pi$
$631$			62.6700i			0.0993185i	−0.998766	+	0.0496592i	$0.984186\pi$
$632$	−621.619	−	169.696i	−0.983575	−	0.268506i
$633$		0			0
$634$	378.323	+	814.644i	0.596724	+	1.28493i
$635$	−1140.72			−1.79641
$636$		0			0
$637$			78.5036i			0.123240i
$638$	368.160	+	792.759i	0.577053	+	1.24257i
$639$		0			0
$640$	74.5854	−	756.880i	0.116540	−	1.18263i
$641$	−800.473			−1.24879			−0.624394	−	0.781110i	$-0.714654\pi$
$641$	−800.473			−1.24879			−0.624394	+	0.781110i	$0.714654\pi$
$642$		0			0
$643$	−818.686			−1.27323			−0.636614	−	0.771183i	$-0.719666\pi$
$643$	−818.686			−1.27323			−0.636614	+	0.771183i	$0.719666\pi$
$644$	11.5412	−	13.6672i	0.0179212	−	0.0212223i
$645$		0			0
$646$	1369.18	−	635.853i	2.11948	−	0.984293i
$647$			509.102i			0.786866i	0.919353	+	0.393433i	$0.128713\pi$
$647$			509.102i			0.786866i	−0.919353	+	0.393433i	$0.871287\pi$
$648$		0			0
$649$	501.139			0.772172
$650$	−97.3510	−	209.626i	−0.149771	−	0.322502i
$651$		0			0
$652$	27.9616	−	33.1122i	0.0428859	−	0.0507856i
$653$		−	997.554i		−	1.52765i	−0.645424	−	0.763824i	$-0.723319\pi$
$653$		−	997.554i		−	1.52765i	0.645424	−	0.763824i	$-0.276681\pi$
$654$		0			0
$655$			80.6208i			0.123085i
$656$	82.7807	+	487.299i	0.126190	+	0.742833i
$657$		0			0
$658$	−178.929	+	83.0952i	−0.271929	+	0.126284i
$659$	−179.635			−0.272588			−0.136294	−	0.990668i	$-0.543519\pi$
$659$	−179.635			−0.272588			−0.136294	+	0.990668i	$0.543519\pi$
$660$		0			0
$661$			155.299i			0.234946i	0.993076	+	0.117473i	$0.0374793\pi$
$661$			155.299i			0.234946i	−0.993076	+	0.117473i	$0.962521\pi$
$662$	195.539	−	90.8088i	0.295376	−	0.137173i
$663$		0			0
$664$	76.4046	−	279.881i	0.115067	−	0.421507i
$665$	−519.882			−0.781777
$666$		0			0
$667$	48.9708			0.0734195
$668$	−175.984	−	148.610i	−0.263449	−	0.222470i
$669$		0			0
$670$	−430.761	−	927.558i	−0.642927	−	1.38442i
$671$			1461.26i			2.17774i
$672$		0			0
$673$	−1066.49			−1.58469			−0.792343	−	0.610076i	$-0.791139\pi$
$673$	−1066.49			−1.58469			−0.792343	+	0.610076i	$0.791139\pi$
$674$	1025.14	−	476.077i	1.52098	−	0.706346i
$675$		0			0
$676$	111.561	−	132.111i	0.165031	−	0.195430i
$677$			248.880i			0.367622i	0.982962	+	0.183811i	$0.0588434\pi$
$677$			248.880i			0.367622i	−0.982962	+	0.183811i	$0.941157\pi$
$678$		0			0
$679$		−	174.698i		−	0.257287i
$680$	1046.64	+	285.722i	1.53918	+	0.420180i
$681$		0			0
$682$	314.172	+	676.506i	0.460662	+	0.991945i
$683$	−465.842			−0.682053			−0.341026	−	0.940054i	$-0.610775\pi$
$683$	−465.842			−0.682053			−0.341026	+	0.940054i	$0.610775\pi$
$684$		0			0
$685$			447.285i			0.652970i
$686$	15.6014	+	33.5946i	0.0227426	+	0.0489717i
$687$		0			0
$688$	118.636	+	698.364i	0.172436	+	1.01506i
$689$	810.105			1.17577
$690$		0			0
$691$	−854.073			−1.23600			−0.617998	−	0.786180i	$-0.712056\pi$
$691$	−854.073			−1.23600			−0.617998	+	0.786180i	$0.712056\pi$
$692$	−639.600	−	540.110i	−0.924277	−	0.780505i
$693$		0			0
$694$	−1119.42	+	519.860i	−1.61299	+	0.749077i
$695$		−	1323.35i		−	1.90411i
$696$		0			0
$697$	−705.104			−1.01163
$698$	175.680	+	378.292i	0.251690	+	0.541966i
$699$		0			0
$700$	−83.3202	−	70.3597i	−0.119029	−	0.100514i
$701$			746.975i			1.06559i	0.846246	+	0.532793i	$0.178857\pi$
$701$			746.975i			1.06559i	−0.846246	+	0.532793i	$0.821143\pi$
$702$		0			0
$703$		−	1778.76i		−	2.53024i
$704$	831.519	+	490.550i	1.18113	+	0.696804i
$705$		0			0
$706$	169.241	−	78.5962i	0.239719	−	0.111326i
$707$	−419.182			−0.592902
$708$		0			0
$709$			939.270i			1.32478i	0.749158	+	0.662391i	$0.230458\pi$
$709$			939.270i			1.32478i	−0.749158	+	0.662391i	$0.769542\pi$
$710$	436.290	−	202.615i	0.614494	−	0.285373i
$711$		0			0
$712$	29.3754	−	107.606i	0.0412576	−	0.151132i
$713$	41.7896			0.0586109
$714$		0			0
$715$	1005.19			1.40587
$716$	590.861	−	699.699i	0.825224	−	0.977233i
$717$		0			0
$718$	269.229	+	579.731i	0.374971	+	0.807425i
$719$		−	683.284i		−	0.950325i	−0.879898	−	0.475163i	$-0.842389\pi$
$719$		−	683.284i		−	0.950325i	0.879898	−	0.475163i	$-0.157611\pi$
$720$		0			0
$721$	−360.407			−0.499870
$722$	−1328.99	+	617.185i	−1.84070	+	0.854827i
$723$		0			0
$724$	−398.868	−	336.824i	−0.550922	−	0.465226i
$725$		−	298.544i		−	0.411785i
$726$		0			0
$727$		−	77.6493i		−	0.106808i	−0.998573	−	0.0534039i	$-0.982993\pi$
$727$		−	77.6493i		−	0.106808i	0.998573	−	0.0534039i	$-0.0170071\pi$
$728$	−62.5128	+	228.993i	−0.0858692	+	0.314551i
$729$		0			0
$730$	143.105	+	308.149i	0.196034	+	0.422121i
$731$	−1010.51			−1.38236
$732$		0			0
$733$			829.362i			1.13146i	0.824590	+	0.565731i	$0.191406\pi$
$733$			829.362i			1.13146i	−0.824590	+	0.565731i	$0.808594\pi$
$734$	−412.444	−	888.116i	−0.561913	−	1.20997i
$735$		0			0
$736$	44.5488	−	30.6765i	0.0605283	−	0.0416800i
$737$	1298.21			1.76148
$738$		0			0
$739$	961.998			1.30176			0.650878	−	0.759182i	$-0.274401\pi$
$739$	961.998			1.30176			0.650878	+	0.759182i	$0.274401\pi$
$740$	824.776	−	976.702i	1.11456	−	1.31987i
$741$		0			0
$742$	346.674	−	160.996i	0.467216	−	0.216976i
$743$			1037.64i			1.39656i	0.715826	+	0.698279i	$0.246051\pi$
$743$			1037.64i			1.39656i	−0.715826	+	0.698279i	$0.753949\pi$
$744$		0			0
$745$	−1030.22			−1.38285
$746$	360.201	+	775.621i	0.482843	+	1.03971i
$747$		0			0
$748$	−888.558	+	1052.23i	−1.18791	+	1.40673i
$749$		−	435.373i		−	0.581273i
$750$		0			0
$751$		−	988.651i		−	1.31645i	−0.752823	−	0.658223i	$-0.771308\pi$
$751$		−	988.651i		−	1.31645i	0.752823	−	0.658223i	$-0.228692\pi$
$752$	−588.101	+	99.9047i	−0.782049	+	0.132852i
$753$		0			0
$754$	−589.373	+	273.707i	−0.781662	+	0.363006i
$755$	504.679			0.668449
$756$		0			0
$757$			398.170i			0.525984i	0.964798	+	0.262992i	$0.0847093\pi$
$757$			398.170i			0.525984i	−0.964798	+	0.262992i	$0.915291\pi$
$758$	800.808	−	371.898i	1.05647	−	0.490630i
$759$		0			0
$760$	−1516.48	−	413.984i	−1.99537	−	0.544716i
$761$	−573.007			−0.752966			−0.376483	−	0.926424i	$-0.622867\pi$
$761$	−573.007			−0.752966			−0.376483	+	0.926424i	$0.622867\pi$
$762$		0			0
$763$	−49.2552			−0.0645547
$764$	279.023	+	235.621i	0.365213	+	0.308404i
$765$		0			0
$766$	−330.929	−	712.591i	−0.432023	−	0.930275i
$767$			372.569i			0.485749i
$768$		0			0
$769$	1317.67			1.71349			0.856743	−	0.515743i	$-0.172484\pi$
$769$	1317.67			1.71349			0.856743	+	0.515743i	$0.172484\pi$
$770$	430.160	−	199.767i	0.558649	−	0.259438i
$771$		0			0
$772$	−324.308	+	384.047i	−0.420088	+	0.497470i
$773$			753.284i			0.974495i	0.873264	+	0.487247i	$0.161999\pi$
$773$			753.284i			0.974495i	−0.873264	+	0.487247i	$0.838001\pi$
$774$		0			0
$775$		−	254.765i		−	0.328728i
$776$	139.113	−	509.590i	0.179269	−	0.656689i
$777$		0			0
$778$	−454.192	−	978.013i	−0.583794	−	1.25709i
$779$	1021.63			1.31146
$780$		0			0
$781$			610.633i			0.781861i
$782$	32.4996	+	69.9814i	0.0415596	+	0.0894903i
$783$		0			0
$784$	18.7575	+	110.418i	0.0239253	+	0.140839i
$785$	−342.653			−0.436501
$786$		0			0
$787$	−77.2279			−0.0981295			−0.0490648	−	0.998796i	$-0.515624\pi$
$787$	−77.2279			−0.0981295			−0.0490648	+	0.998796i	$0.515624\pi$
$788$	−227.721	−	192.299i	−0.288986	−	0.244034i
$789$		0			0
$790$	−868.121	+	403.158i	−1.09889	+	0.510327i
$791$		−	371.481i		−	0.469634i
$792$		0			0
$793$	−1086.37			−1.36995
$794$	370.505	+	797.809i	0.466631	+	1.00480i
$795$		0			0
$796$	236.158	+	199.424i	0.296681	+	0.250532i
$797$			509.008i			0.638655i	0.947644	+	0.319327i	$0.103457\pi$
$797$			509.008i			0.638655i	−0.947644	+	0.319327i	$0.896543\pi$
$798$		0			0
$799$		−	850.961i		−	1.06503i
$800$	−187.015	−	271.586i	−0.233769	−	0.339482i
$801$		0			0
$802$	464.940	−	215.920i	0.579726	−	0.269227i
$803$	−431.286			−0.537093
$804$		0			0
$805$		−	26.5721i		−	0.0330088i
$806$	−502.945	+	233.569i	−0.624002	+	0.289788i
$807$		0			0
$808$	−1222.74	−	333.797i	−1.51330	−	0.413115i
$809$	−692.461			−0.855946			−0.427973	−	0.903791i	$-0.640772\pi$
$809$	−692.461			−0.855946			−0.427973	+	0.903791i	$0.640772\pi$
$810$		0			0
$811$	1496.99			1.84585			0.922926	−	0.384978i	$-0.125791\pi$
$811$	1496.99			1.84585			0.922926	+	0.384978i	$0.125791\pi$
$812$	−197.819	+	234.258i	−0.243620	+	0.288495i
$813$		0			0
$814$	683.497	+	1471.78i	0.839677	+	1.80808i
$815$		−	64.3775i		−	0.0789909i
$816$		0			0
$817$	1464.13			1.79208
$818$	728.043	−	338.105i	0.890028	−	0.413332i
$819$		0			0
$820$	560.968	+	473.709i	0.684107	+	0.577694i
$821$			1081.65i			1.31748i	0.752371	+	0.658740i	$0.228910\pi$
$821$			1081.65i			1.31748i	−0.752371	+	0.658740i	$0.771090\pi$
$822$		0			0
$823$			684.571i			0.831799i	0.909410	+	0.415900i	$0.136533\pi$
$823$			684.571i			0.831799i	−0.909410	+	0.415900i	$0.863467\pi$
$824$	−1051.30	−	286.993i	−1.27585	−	0.348293i
$825$		0			0
$826$	74.0427	+	159.436i	0.0896400	+	0.193022i
$827$	−526.172			−0.636242			−0.318121	−	0.948050i	$-0.603052\pi$
$827$	−526.172			−0.636242			−0.318121	+	0.948050i	$0.603052\pi$
$828$		0			0
$829$		−	1255.76i		−	1.51479i	−0.652959	−	0.757393i	$-0.726473\pi$
$829$		−	1255.76i		−	1.51479i	0.652959	−	0.757393i	$-0.273527\pi$
$830$	−181.520	−	390.867i	−0.218699	−	0.470924i
$831$		0			0
$832$	−364.697	+	618.189i	−0.438337	+	0.743015i
$833$	−159.771			−0.191802
$834$		0			0
$835$	−342.153			−0.409764
$836$	1287.44	−	1524.59i	1.53999	−	1.82367i
$837$		0			0
$838$	−336.885	+	156.450i	−0.402011	+	0.186695i
$839$			93.1019i			0.110968i	0.998460	+	0.0554839i	$0.0176701\pi$
$839$			93.1019i			0.110968i	−0.998460	+	0.0554839i	$0.982330\pi$
$840$		0			0
$841$	1.63019			0.00193840
$842$	−304.665	−	656.036i	−0.361835	−	0.779141i
$843$		0			0
$844$	732.912	−	867.917i	0.868379	−	1.02834i
$845$		−	256.853i		−	0.303968i
$846$		0			0
$847$			281.917i			0.332841i
$848$	1139.44	−	193.565i	1.34368	−	0.228260i
$849$		0			0
$850$	426.633	−	198.129i	0.501921	−	0.233093i
$851$	90.9155			0.106834
$852$		0			0
$853$			1226.85i			1.43828i	0.694867	+	0.719138i	$0.255463\pi$
$853$			1226.85i			1.43828i	−0.694867	+	0.719138i	$0.744537\pi$
$854$	−464.897	+	215.900i	−0.544376	+	0.252810i
$855$		0			0
$856$	346.690	−	1269.97i	0.405011	−	1.48361i
$857$	−201.847			−0.235528			−0.117764	−	0.993042i	$-0.537573\pi$
$857$	−201.847			−0.235528			−0.117764	+	0.993042i	$0.537573\pi$
$858$		0			0
$859$	−1493.93			−1.73915			−0.869574	−	0.493802i	$-0.835607\pi$
$859$	−1493.93			−1.73915			−0.869574	+	0.493802i	$0.835607\pi$
$860$	803.942	+	678.889i	0.934816	+	0.789405i
$861$		0			0
$862$	−110.141	−	237.168i	−0.127774	−	0.275137i
$863$			453.506i			0.525499i	0.964864	+	0.262750i	$0.0846294\pi$
$863$			453.506i			0.525499i	−0.964864	+	0.262750i	$0.915371\pi$
$864$		0			0
$865$	−1243.53			−1.43760
$866$	816.424	−	379.150i	0.942753	−	0.437817i
$867$		0			0
$868$	−168.810	+	199.906i	−0.194482	+	0.230306i
$869$		−	1215.02i		−	1.39819i
$870$		0			0
$871$			965.150i			1.10809i
$872$	−143.676	−	39.2222i	−0.164766	−	0.0449796i
$873$		0			0
$874$	−47.0888	−	101.396i	−0.0538774	−	0.116014i
$875$	231.018			0.264020
$876$		0			0
$877$			75.4930i			0.0860809i	0.999073	+	0.0430405i	$0.0137044\pi$
$877$			75.4930i			0.0860809i	−0.999073	+	0.0430405i	$0.986296\pi$
$878$	90.8533	+	195.635i	0.103478	+	0.222819i
$879$		0			0
$880$	1413.84	−	240.179i	1.60664	−	0.272930i
$881$	1065.89			1.20986			0.604931	−	0.796278i	$-0.293201\pi$
$881$	1065.89			1.20986			0.604931	+	0.796278i	$0.293201\pi$
$882$		0			0
$883$	−956.369			−1.08309			−0.541545	−	0.840672i	$-0.682161\pi$
$883$	−956.369			−1.08309			−0.541545	+	0.840672i	$0.682161\pi$
$884$	−782.277	−	660.594i	−0.884929	−	0.747278i
$885$		0			0
$886$	−145.112	+	67.3904i	−0.163783	+	0.0760614i
$887$			158.851i			0.179088i	0.995983	+	0.0895440i	$0.0285410\pi$
$887$			158.851i			0.179088i	−0.995983	+	0.0895440i	$0.971459\pi$
$888$		0			0
$889$	507.940			0.571361
$890$	−69.7892	−	150.277i	−0.0784148	−	0.168851i
$891$		0			0
$892$	353.811	+	298.775i	0.396649	+	0.334950i
$893$			1232.96i			1.38070i
$894$		0			0
$895$		−	1360.37i		−	1.51997i
$896$	−33.2114	+	337.024i	−0.0370663	+	0.376143i
$897$		0			0
$898$	904.075	−	419.855i	1.00676	−	0.467545i
$899$	−716.282			−0.796754
$900$		0			0
$901$			1648.73i			1.82989i
$902$	−845.313	+	392.566i	−0.937155	+	0.435217i
$903$		0			0
$904$	295.812	−	1083.60i	0.327225	−	1.19867i
$905$	−775.489			−0.856894
$906$		0			0
$907$	1106.62			1.22008			0.610042	−	0.792369i	$-0.291152\pi$
$907$	1106.62			1.22008			0.610042	+	0.792369i	$0.291152\pi$
$908$	−17.6271	+	20.8741i	−0.0194132	+	0.0229891i
$909$		0			0
$910$	148.516	+	319.800i	0.163204	+	0.351428i
$911$			950.439i			1.04329i	0.853162	+	0.521646i	$0.174682\pi$
$911$			950.439i			1.04329i	−0.853162	+	0.521646i	$0.825318\pi$
$912$		0			0
$913$	547.059			0.599188
$914$	850.961	−	395.189i	0.931029	−	0.432373i
$915$		0			0
$916$	663.599	+	560.376i	0.724453	+	0.611764i
$917$		−	35.8988i		−	0.0391481i
$918$		0			0
$919$		−	609.662i		−	0.663397i	−0.943385	−	0.331698i	$-0.892378\pi$
$919$		−	609.662i		−	0.663397i	0.943385	−	0.331698i	$-0.107622\pi$
$920$	21.1595	−	77.5101i	0.0229994	−	0.0842502i
$921$		0			0
$922$	−614.154	−	1322.46i	−0.666111	−	1.43434i
$923$	−453.972			−0.491844
$924$		0			0
$925$		−	554.254i		−	0.599194i
$926$	507.367	+	1092.52i	0.547913	+	1.17982i
$927$		0			0
$928$	−763.575	+	525.801i	−0.822818	+	0.566596i
$929$	306.485			0.329909			0.164954	−	0.986301i	$-0.447252\pi$
$929$	306.485			0.329909			0.164954	+	0.986301i	$0.447252\pi$
$930$		0			0
$931$	231.493			0.248650
$932$	−346.804	+	410.686i	−0.372107	+	0.440650i
$933$		0			0
$934$	−645.843	+	299.931i	−0.691481	+	0.321126i
$935$			2045.78i			2.18800i
$936$		0			0
$937$	885.867			0.945429			0.472715	−	0.881216i	$-0.343274\pi$
$937$	885.867			0.945429			0.472715	+	0.881216i	$0.343274\pi$
$938$	191.809	+	413.023i	0.204487	+	0.440323i
$939$		0			0
$940$	−571.700	+	677.009i	−0.608192	+	0.720223i
$941$		−	1527.11i		−	1.62285i	−0.584454	−	0.811427i	$-0.698691\pi$
$941$		−	1527.11i		−	1.62285i	0.584454	−	0.811427i	$-0.301309\pi$
$942$		0			0
$943$			52.2172i			0.0553735i
$944$	89.0209	+	524.032i	0.0943018	+	0.555119i
$945$		0			0
$946$	−1211.45	+	562.600i	−1.28060	+	0.594714i
$947$	43.0382			0.0454468			0.0227234	−	0.999742i	$-0.492766\pi$
$947$	43.0382			0.0454468			0.0227234	+	0.999742i	$0.492766\pi$
$948$		0			0
$949$		−	320.637i		−	0.337868i
$950$	−618.150	+	287.071i	−0.650684	+	0.302180i
$951$		0			0
$952$	−466.048	−	127.226i	−0.489547	−	0.133641i
$953$	−701.454			−0.736048			−0.368024	−	0.929816i	$-0.619966\pi$
$953$	−701.454			−0.736048			−0.368024	+	0.929816i	$0.619966\pi$
$954$		0			0
$955$	542.483			0.568045
$956$	−1248.19	−	1054.03i	−1.30564	−	1.10254i
$957$		0			0
$958$	170.048	+	366.165i	0.177503	+	0.382218i
$959$		−	199.167i		−	0.207682i
$960$		0			0
$961$	349.756			0.363950
$962$	−1094.18	+	508.143i	−1.13741	+	0.528215i
$963$		0			0
$964$	−612.396	+	725.202i	−0.635266	+	0.752284i
$965$			746.673i			0.773755i
$966$		0			0
$967$			1078.20i			1.11500i	0.830178	+	0.557499i	$0.188239\pi$
$967$			1078.20i			1.11500i	−0.830178	+	0.557499i	$0.811761\pi$
$968$	−224.491	+	822.344i	−0.231913	+	0.849529i
$969$		0			0
$970$	−330.500	−	711.668i	−0.340722	−	0.733678i
$971$	−68.6986			−0.0707504			−0.0353752	−	0.999374i	$-0.511263\pi$
$971$	−68.6986			−0.0707504			−0.0353752	+	0.999374i	$0.511263\pi$
$972$		0			0
$973$			589.263i			0.605615i
$974$	289.780	+	623.983i	0.297515	+	0.640640i
$975$		0			0
$976$	−1528.02	+	259.574i	−1.56559	+	0.265957i
$977$	−785.845			−0.804345			−0.402172	−	0.915564i	$-0.631745\pi$
$977$	−785.845			−0.804345			−0.402172	+	0.915564i	$0.631745\pi$
$978$		0			0
$979$	210.328			0.214840
$980$	127.111	+	107.339i	0.129705	+	0.109529i
$981$		0			0
$982$	323.806	−	150.376i	0.329741	−	0.153133i
$983$		−	14.8697i		−	0.0151269i	−0.999971	−	0.00756345i	$-0.997592\pi$
$983$		−	14.8697i		−	0.0151269i	0.999971	−	0.00756345i	$-0.00240754\pi$
$984$		0			0
$985$	−442.741			−0.449483
$986$	−557.049	−	1199.50i	−0.564959	−	1.21653i
$987$		0			0
$988$	1133.44	+	957.137i	1.14721	+	0.968762i
$989$			74.8343i			0.0756666i
$990$		0			0
$991$			1163.67i			1.17424i	0.809499	+	0.587121i	$0.199739\pi$
$991$			1163.67i			1.17424i	−0.809499	+	0.587121i	$0.800261\pi$
$992$	−651.602	+	448.696i	−0.656857	+	0.452315i
$993$		0			0
$994$	−194.271	+	90.2202i	−0.195444	+	0.0907648i
$995$	459.145			0.461452
$996$		0			0
$997$		−	1235.53i		−	1.23925i	−0.784898	−	0.619625i	$-0.787285\pi$
$997$		−	1235.53i		−	1.23925i	0.784898	−	0.619625i	$-0.212715\pi$
$998$	−994.942	+	462.054i	−0.996936	+	0.462980i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.d.379.6		24
3.2	odd	2		168.3.g.a.43.19	✓	24
4.3	odd	2		2016.3.g.d.1135.5		24
8.3	odd	2	inner	504.3.g.d.379.5		24
8.5	even	2		2016.3.g.d.1135.20		24
12.11	even	2		672.3.g.a.463.9		24
24.5	odd	2		672.3.g.a.463.4		24
24.11	even	2		168.3.g.a.43.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.g.a.43.19	✓	24	3.2	odd	2
168.3.g.a.43.20	yes	24	24.11	even	2
504.3.g.d.379.5		24	8.3	odd	2	inner
504.3.g.d.379.6		24	1.1	even	1	trivial
672.3.g.a.463.4		24	24.5	odd	2
672.3.g.a.463.9		24	12.11	even	2
2016.3.g.d.1135.5		24	4.3	odd	2
2016.3.g.d.1135.20		24	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.81394 + 0.842398i) q^{2} +(2.58073 - 3.05611i) q^{4} -5.94177i q^{5} +2.64575i q^{7} +(-2.10682 + 7.71760i) q^{8} +(5.00533 + 10.7780i) q^{10} -15.0849 q^{11} -11.2148i q^{13} +(-2.22877 - 4.79923i) q^{14} +(-2.67964 - 15.7740i) q^{16} +22.8244 q^{17} -33.0704 q^{19} +(-18.1587 - 15.3341i) q^{20} +(27.3631 - 12.7075i) q^{22} -1.69029i q^{23} -10.3046 q^{25} +(9.44732 + 20.3429i) q^{26} +(8.08571 + 6.82798i) q^{28} +28.9719i q^{29} +24.7233i q^{31} +(18.1487 + 26.3557i) q^{32} +(-41.4021 + 19.2272i) q^{34} +15.7204 q^{35} +53.7870i q^{37} +(59.9877 - 27.8584i) q^{38} +(45.8562 + 12.5183i) q^{40} -30.8925 q^{41} -44.2731 q^{43} +(-38.9301 + 46.1012i) q^{44} +(1.42389 + 3.06608i) q^{46} -37.2829i q^{47} -7.00000 q^{49} +(18.6919 - 8.68058i) q^{50} +(-34.2737 - 28.9424i) q^{52} +72.2354i q^{53} +89.6310i q^{55} +(-20.4188 - 5.57413i) q^{56} +(-24.4058 - 52.5532i) q^{58} -33.2212 q^{59} -96.8692i q^{61} +(-20.8269 - 44.8466i) q^{62} +(-55.1226 - 32.5192i) q^{64} -66.6357 q^{65} -86.0604 q^{67} +(58.9038 - 69.7540i) q^{68} +(-28.5159 + 13.2429i) q^{70} -40.4798i q^{71} +28.5905 q^{73} +(-45.3100 - 97.5662i) q^{74} +(-85.3459 + 101.067i) q^{76} -39.9109i q^{77} +80.5457i q^{79} +(-93.7255 + 15.9218i) q^{80} +(56.0370 - 26.0238i) q^{82} -36.2653 q^{83} -135.618i q^{85} +(80.3086 - 37.2955i) q^{86} +(31.7813 - 116.419i) q^{88} -13.9430 q^{89} +29.6716 q^{91} +(-5.16571 - 4.36218i) q^{92} +(31.4070 + 67.6288i) q^{94} +196.497i q^{95} -66.0297 q^{97} +(12.6976 - 5.89678i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 10 q^{4} - 10 q^{8} + 12 q^{10} - 32 q^{11} + 14 q^{14} + 66 q^{16} - 16 q^{17} - 64 q^{19} - 20 q^{20} + 12 q^{22} - 72 q^{25} - 100 q^{26} - 14 q^{28} - 98 q^{32} - 108 q^{34} + 72 q^{38}+ \cdots - 14 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 + 12 * q^10 - 32 * q^11 + 14 * q^14 + 66 * q^16 - 16 * q^17 - 64 * q^19 - 20 * q^20 + 12 * q^22 - 72 * q^25 - 100 * q^26 - 14 * q^28 - 98 * q^32 - 108 * q^34 + 72 * q^38 - 332 * q^40 + 80 * q^41 + 32 * q^43 + 292 * q^44 - 168 * q^49 - 46 * q^50 - 4 * q^52 - 98 * q^56 - 96 * q^58 + 16 * q^62 - 182 * q^64 + 192 * q^65 - 32 * q^67 - 188 * q^68 - 84 * q^70 - 240 * q^73 - 208 * q^74 + 8 * q^76 - 484 * q^80 - 372 * q^82 + 320 * q^83 + 604 * q^86 + 468 * q^88 - 400 * q^89 - 352 * q^92 - 72 * q^94 + 144 * q^97 - 14 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more