LMFDB - Embedded newform 287.3.d.d.286.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(286,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("287.286");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.d (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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			286.17
Character	$\chi$	$=$	287.286
Dual form			287.3.d.d.286.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.16717 q^{2} -4.43412 q^{3} -2.63772 q^{4} -9.05049i q^{5} -5.17535 q^{6} +(6.69015 - 2.05957i) q^{7} -7.74732 q^{8} +10.6614 q^{9} +O(q^{10})$	\(q+1.16717 q^{2} -4.43412 q^{3} -2.63772 q^{4} -9.05049i q^{5} -5.17535 q^{6} +(6.69015 - 2.05957i) q^{7} -7.74732 q^{8} +10.6614 q^{9} -10.5634i q^{10} +15.2851i q^{11} +11.6960 q^{12} -11.9347 q^{13} +(7.80852 - 2.40386i) q^{14} +40.1310i q^{15} +1.50849 q^{16} -17.3346 q^{17} +12.4437 q^{18} +0.333198 q^{19} +23.8727i q^{20} +(-29.6650 + 9.13239i) q^{21} +17.8403i q^{22} +14.2064 q^{23} +34.3526 q^{24} -56.9114 q^{25} -13.9298 q^{26} -7.36701 q^{27} +(-17.6468 + 5.43258i) q^{28} +9.15119i q^{29} +46.8395i q^{30} +50.9978i q^{31} +32.7499 q^{32} -67.7760i q^{33} -20.2324 q^{34} +(-18.6401 - 60.5492i) q^{35} -28.1219 q^{36} +16.3960 q^{37} +0.388897 q^{38} +52.9199 q^{39} +70.1171i q^{40} +(8.37067 + 40.1364i) q^{41} +(-34.6239 + 10.6590i) q^{42} -38.9612 q^{43} -40.3179i q^{44} -96.4912i q^{45} +16.5812 q^{46} -79.8303 q^{47} -6.68881 q^{48} +(40.5163 - 27.5577i) q^{49} -66.4250 q^{50} +76.8638 q^{51} +31.4805 q^{52} +28.3291i q^{53} -8.59852 q^{54} +138.338 q^{55} +(-51.8308 + 15.9562i) q^{56} -1.47744 q^{57} +10.6810i q^{58} -89.3467i q^{59} -105.854i q^{60} +35.2643i q^{61} +59.5229i q^{62} +(71.3266 - 21.9580i) q^{63} +32.1907 q^{64} +108.015i q^{65} -79.1059i q^{66} -62.8702i q^{67} +45.7240 q^{68} -62.9929 q^{69} +(-21.7561 - 70.6709i) q^{70} -30.5308i q^{71} -82.5976 q^{72} +19.9599i q^{73} +19.1369 q^{74} +252.352 q^{75} -0.878884 q^{76} +(31.4808 + 102.260i) q^{77} +61.7663 q^{78} +38.5638i q^{79} -13.6525i q^{80} -63.2867 q^{81} +(9.76995 + 46.8458i) q^{82} -113.184i q^{83} +(78.2480 - 24.0887i) q^{84} +156.887i q^{85} -45.4742 q^{86} -40.5775i q^{87} -118.419i q^{88} -141.916 q^{89} -112.621i q^{90} +(-79.8450 + 24.5804i) q^{91} -37.4725 q^{92} -226.130i q^{93} -93.1752 q^{94} -3.01560i q^{95} -145.217 q^{96} -86.9985 q^{97} +(47.2893 - 32.1644i) q^{98} +162.961i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9	$ 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9} - 92 q^{16} - 48 q^{18} - 72 q^{21} + 140 q^{23} - 500 q^{25} + 92 q^{32} - 284 q^{36} + 312 q^{37} + 140 q^{39} + 8 q^{42} - 120 q^{43} - 344 q^{46} - 552 q^{49} + 416 q^{50} - 364 q^{51} - 316 q^{57} - 320 q^{64} + 972 q^{72} + 680 q^{74} + 428 q^{77} + 1144 q^{78} - 240 q^{81} + 640 q^{84} + 260 q^{86} - 160 q^{91} + 676 q^{92} + 532 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9 - 92 * q^16 - 48 * q^18 - 72 * q^21 + 140 * q^23 - 500 * q^25 + 92 * q^32 - 284 * q^36 + 312 * q^37 + 140 * q^39 + 8 * q^42 - 120 * q^43 - 344 * q^46 - 552 * q^49 + 416 * q^50 - 364 * q^51 - 316 * q^57 - 320 * q^64 + 972 * q^72 + 680 * q^74 + 428 * q^77 + 1144 * q^78 - 240 * q^81 + 640 * q^84 + 260 * q^86 - 160 * q^91 + 676 * q^92 + 532 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.16717			0.583583			0.291791	−	0.956482i	$-0.405749\pi$
$2$	1.16717			0.583583			0.291791	+	0.956482i	$0.405749\pi$
$3$	−4.43412			−1.47804			−0.739020	−	0.673683i	$-0.764711\pi$
$3$	−4.43412			−1.47804			−0.739020	+	0.673683i	$0.764711\pi$
$4$	−2.63772			−0.659431
$5$		−	9.05049i		−	1.81010i	−0.425307	−	0.905049i	$-0.639834\pi$
$5$		−	9.05049i		−	1.81010i	0.425307	−	0.905049i	$-0.360166\pi$
$6$	−5.17535			−0.862559
$7$	6.69015	−	2.05957i	0.955736	−	0.294225i
$7$	6.69015	−	2.05957i	0.955736	−	0.294225i
$8$	−7.74732			−0.968416
$9$	10.6614			1.18460
$10$		−	10.5634i		−	1.05634i
$11$			15.2851i			1.38956i	0.719225	+	0.694778i	$0.244497\pi$
$11$			15.2851i			1.38956i	−0.719225	+	0.694778i	$0.755503\pi$
$12$	11.6960			0.974666
$13$	−11.9347			−0.918054			−0.459027	−	0.888422i	$-0.651802\pi$
$13$	−11.9347			−0.918054			−0.459027	+	0.888422i	$0.651802\pi$
$14$	7.80852	−	2.40386i	0.557751	−	0.171704i
$15$			40.1310i			2.67540i
$16$	1.50849			0.0942804
$17$	−17.3346			−1.01968			−0.509842	−	0.860268i	$-0.670296\pi$
$17$	−17.3346			−1.01968			−0.509842	+	0.860268i	$0.670296\pi$
$18$	12.4437			0.691315
$19$	0.333198			0.0175367			0.00876836	−	0.999962i	$-0.497209\pi$
$19$	0.333198			0.0175367			0.00876836	+	0.999962i	$0.497209\pi$
$20$			23.8727i			1.19364i
$21$	−29.6650	+	9.13239i	−1.41262	+	0.434876i
$22$			17.8403i			0.810921i
$23$	14.2064			0.617669			0.308835	−	0.951116i	$-0.400061\pi$
$23$	14.2064			0.617669			0.308835	+	0.951116i	$0.400061\pi$
$24$	34.3526			1.43136
$25$	−56.9114			−2.27646
$26$	−13.9298			−0.535761
$27$	−7.36701			−0.272852
$28$	−17.6468	+	5.43258i	−0.630242	+	0.194021i
$29$			9.15119i			0.315558i	0.987474	+	0.157779i	$0.0504334\pi$
$29$			9.15119i			0.315558i	−0.987474	+	0.157779i	$0.949567\pi$
$30$			46.8395i			1.56132i
$31$			50.9978i			1.64509i	0.568700	+	0.822545i	$0.307446\pi$
$31$			50.9978i			1.64509i	−0.568700	+	0.822545i	$0.692554\pi$
$32$	32.7499			1.02344
$33$		−	67.7760i		−	2.05382i
$34$	−20.2324			−0.595070
$35$	−18.6401	−	60.5492i	−0.532575	−	1.72998i
$36$	−28.1219			−0.781165
$37$	16.3960			0.443135			0.221568	−	0.975145i	$-0.428883\pi$
$37$	16.3960			0.443135			0.221568	+	0.975145i	$0.428883\pi$
$38$	0.388897			0.0102341
$39$	52.9199			1.35692
$40$			70.1171i			1.75293i
$41$	8.37067	+	40.1364i	0.204163	+	0.978937i
$41$	8.37067	+	40.1364i	0.204163	+	0.978937i
$42$	−34.6239	+	10.6590i	−0.824379	+	0.253786i
$43$	−38.9612			−0.906075			−0.453037	−	0.891492i	$-0.649660\pi$
$43$	−38.9612			−0.906075			−0.453037	+	0.891492i	$0.649660\pi$
$44$		−	40.3179i		−	0.916316i
$45$		−	96.4912i		−	2.14425i
$46$	16.5812			0.360461
$47$	−79.8303			−1.69852			−0.849259	−	0.527977i	$-0.822951\pi$
$47$	−79.8303			−1.69852			−0.849259	+	0.527977i	$0.822951\pi$
$48$	−6.68881			−0.139350
$49$	40.5163	−	27.5577i	0.826864	−	0.562402i
$50$	−66.4250			−1.32850
$51$	76.8638			1.50713
$52$	31.4805			0.605394
$53$			28.3291i			0.534511i	0.963626	+	0.267256i	$0.0861168\pi$
$53$			28.3291i			0.534511i	−0.963626	+	0.267256i	$0.913883\pi$
$54$	−8.59852			−0.159232
$55$	138.338			2.51523
$56$	−51.8308	+	15.9562i	−0.925550	+	0.284932i
$57$	−1.47744			−0.0259200
$58$			10.6810i			0.184154i
$59$		−	89.3467i		−	1.51435i	−0.653211	−	0.757176i	$-0.726579\pi$
$59$		−	89.3467i		−	1.51435i	0.653211	−	0.757176i	$-0.273421\pi$
$60$		−	105.854i		−	1.76424i
$61$			35.2643i			0.578102i	0.957314	+	0.289051i	$0.0933398\pi$
$61$			35.2643i			0.578102i	−0.957314	+	0.289051i	$0.906660\pi$
$62$			59.5229i			0.960046i
$63$	71.3266	−	21.9580i	1.13217	−	0.348540i
$64$	32.1907			0.502979
$65$			108.015i			1.66177i
$66$		−	79.1059i		−	1.19857i
$67$		−	62.8702i		−	0.938362i	−0.883102	−	0.469181i	$-0.844549\pi$
$67$		−	62.8702i		−	0.938362i	0.883102	−	0.469181i	$-0.155451\pi$
$68$	45.7240			0.672411
$69$	−62.9929			−0.912940
$70$	−21.7561	−	70.6709i	−0.310802	−	1.00958i
$71$		−	30.5308i		−	0.430011i	−0.976613	−	0.215006i	$-0.931023\pi$
$71$		−	30.5308i		−	0.430011i	0.976613	−	0.215006i	$-0.0689770\pi$
$72$	−82.5976			−1.14719
$73$			19.9599i			0.273423i	0.990611	+	0.136711i	$0.0436533\pi$
$73$			19.9599i			0.273423i	−0.990611	+	0.136711i	$0.956347\pi$
$74$	19.1369			0.258606
$75$	252.352			3.36469
$76$	−0.878884			−0.0115643
$77$	31.4808	+	102.260i	0.408841	+	1.32805i
$78$	61.7663			0.791876
$79$			38.5638i			0.488149i	0.969756	+	0.244075i	$0.0784842\pi$
$79$			38.5638i			0.488149i	−0.969756	+	0.244075i	$0.921516\pi$
$80$		−	13.6525i		−	0.170657i
$81$	−63.2867			−0.781318
$82$	9.76995	+	46.8458i	0.119146	+	0.571291i
$83$		−	113.184i		−	1.36367i	−0.731508	−	0.681833i	$-0.761183\pi$
$83$		−	113.184i		−	1.36367i	0.731508	−	0.681833i	$-0.238817\pi$
$84$	78.2480	−	24.0887i	0.931524	−	0.286771i
$85$			156.887i			1.84573i
$86$	−45.4742			−0.528770
$87$		−	40.5775i		−	0.466408i
$88$		−	118.419i		−	1.34567i
$89$	−141.916			−1.59456			−0.797281	−	0.603609i	$-0.793729\pi$
$89$	−141.916			−1.59456			−0.797281	+	0.603609i	$0.793729\pi$
$90$		−	112.621i		−	1.25135i
$91$	−79.8450	+	24.5804i	−0.877418	+	0.270114i
$92$	−37.4725			−0.407310
$93$		−	226.130i		−	2.43151i
$94$	−93.1752			−0.991226
$95$		−	3.01560i		−	0.0317432i
$96$	−145.217			−1.51268
$97$	−86.9985			−0.896892			−0.448446	−	0.893810i	$-0.648022\pi$
$97$	−86.9985			−0.896892			−0.448446	+	0.893810i	$0.648022\pi$
$98$	47.2893	−	32.1644i	0.482544	−	0.328208i
$99$			162.961i			1.64607i
$100$	150.117			1.50117
$101$	−54.1701			−0.536338			−0.268169	−	0.963372i	$-0.586419\pi$
$101$	−54.1701			−0.536338			−0.268169	+	0.963372i	$0.586419\pi$
$102$	89.7128			0.879538
$103$			132.145i			1.28296i	0.767140	+	0.641480i	$0.221679\pi$
$103$			132.145i			1.28296i	−0.767140	+	0.641480i	$0.778321\pi$
$104$	92.4620			0.889058
$105$	82.6526	+	268.482i	0.787168	+	2.55698i
$106$			33.0647i			0.311932i
$107$	−182.443			−1.70507			−0.852536	−	0.522668i	$-0.824937\pi$
$107$	−182.443			−1.70507			−0.852536	+	0.522668i	$0.824937\pi$
$108$	19.4321			0.179927
$109$			10.7582i			0.0986987i	0.998782	+	0.0493494i	$0.0157148\pi$
$109$			10.7582i			0.0986987i	−0.998782	+	0.0493494i	$0.984285\pi$
$110$	161.463			1.46785
$111$	−72.7019			−0.654972
$112$	10.0920	−	3.10684i	0.0901072	−	0.0277396i
$113$	70.0377			0.619803			0.309901	−	0.950769i	$-0.399704\pi$
$113$	70.0377			0.619803			0.309901	+	0.950769i	$0.399704\pi$
$114$	−1.72442			−0.0151265
$115$		−	128.575i		−	1.11804i
$116$		−	24.1383i		−	0.208089i
$117$	−127.241			−1.08753
$118$		−	104.282i		−	0.883750i
$119$	−115.971	+	35.7019i	−0.974549	+	0.300016i
$120$		−	310.908i		−	2.59090i
$121$	−112.635			−0.930864
$122$			41.1592i			0.337371i
$123$	−37.1165	−	177.970i	−0.301761	−	1.44691i
$124$		−	134.518i		−	1.08482i
$125$			288.814i			2.31051i
$126$	83.2500	−	25.6286i	0.660714	−	0.203402i
$127$	−105.378			−0.829747			−0.414873	−	0.909879i	$-0.636174\pi$
$127$	−105.378			−0.829747			−0.414873	+	0.909879i	$0.636174\pi$
$128$	−93.4279			−0.729906
$129$	172.759			1.33922
$130$			126.071i			0.969780i
$131$			132.914i			1.01461i	0.861766	+	0.507306i	$0.169359\pi$
$131$			132.914i			1.01461i	−0.861766	+	0.507306i	$0.830641\pi$
$132$			178.774i			1.35435i
$133$	2.22914	−	0.686245i	0.0167605	−	0.00515973i
$134$		−	73.3800i		−	0.547612i
$135$			66.6750i			0.493889i
$136$	134.297			0.987478
$137$			28.4370i			0.207569i	0.994600	+	0.103785i	$0.0330953\pi$
$137$			28.4370i			0.207569i	−0.994600	+	0.103785i	$0.966905\pi$
$138$	−73.5231			−0.532776
$139$		−	2.50637i		−	0.0180314i	−0.999959	−	0.00901571i	$-0.997130\pi$
$139$		−	2.50637i		−	0.0180314i	0.999959	−	0.00901571i	$-0.00286983\pi$
$140$	49.1675	+	159.712i	0.351197	+	1.14080i
$141$	353.977			2.51048
$142$		−	35.6345i		−	0.250947i
$143$		−	182.423i		−	1.27569i
$144$	16.0826			0.111685
$145$	82.8228			0.571192
$146$			23.2965i			0.159565i
$147$	−179.654	+	122.194i	−1.22214	+	0.831253i
$148$	−43.2481			−0.292217
$149$		−	246.154i		−	1.65204i	−0.563643	−	0.826019i	$-0.690601\pi$
$149$		−	246.154i		−	1.65204i	0.563643	−	0.826019i	$-0.309399\pi$
$150$	294.537			1.96358
$151$			140.536i			0.930705i	0.885126	+	0.465352i	$0.154072\pi$
$151$			140.536i			0.930705i	−0.885126	+	0.465352i	$0.845928\pi$
$152$	−2.58139			−0.0169828
$153$	−184.812			−1.20792
$154$	36.7433	+	119.354i	0.238593	+	0.775026i
$155$	461.555			2.97777
$156$	−139.588			−0.894796
$157$	−26.0425			−0.165876			−0.0829378	−	0.996555i	$-0.526430\pi$
$157$	−26.0425			−0.165876			−0.0829378	+	0.996555i	$0.526430\pi$
$158$			45.0104i			0.284876i
$159$		−	125.615i		−	0.790029i
$160$		−	296.403i		−	1.85252i
$161$	95.0429	−	29.2591i	0.590329	−	0.181733i
$162$	−73.8661			−0.455963
$163$	93.4220			0.573141			0.286571	−	0.958059i	$-0.407485\pi$
$163$	93.4220			0.573141			0.286571	+	0.958059i	$0.407485\pi$
$164$	−22.0795	−	105.869i	−0.134631	−	0.645541i
$165$	−613.406			−3.71761
$166$		−	132.105i		−	0.795812i
$167$	235.762			1.41175			0.705875	−	0.708336i	$-0.250554\pi$
$167$	235.762			1.41175			0.705875	+	0.708336i	$0.250554\pi$
$168$	229.824	−	70.7516i	1.36800	−	0.421141i
$169$	−26.5628			−0.157176
$170$			183.113i			1.07714i
$171$	3.55237			0.0207741
$172$	102.769			0.597494
$173$		−	226.574i		−	1.30968i	−0.755769	−	0.654838i	$-0.772737\pi$
$173$		−	226.574i		−	1.30968i	0.755769	−	0.654838i	$-0.227263\pi$
$174$		−	47.3607i		−	0.272188i
$175$	−380.746	+	117.213i	−2.17569	+	0.669789i
$176$			23.0574i			0.131008i
$177$			396.174i			2.23827i
$178$	−165.639			−0.930559
$179$			274.692i			1.53459i	0.641294	+	0.767295i	$0.278398\pi$
$179$			274.692i			1.53459i	−0.641294	+	0.767295i	$0.721602\pi$
$180$			254.517i			1.41398i
$181$	−98.0863			−0.541913			−0.270957	−	0.962592i	$-0.587340\pi$
$181$	−98.0863			−0.541913			−0.270957	+	0.962592i	$0.587340\pi$
$182$	−93.1924	+	28.6894i	−0.512046	+	0.157634i
$183$		−	156.366i		−	0.854459i
$184$	−110.061			−0.598160
$185$		−	148.392i		−	0.802118i
$186$		−	263.932i		−	1.41899i
$187$		−	264.962i		−	1.41691i
$188$	210.570			1.12006
$189$	−49.2864	+	15.1729i	−0.260775	+	0.0802798i
$190$		−	3.51971i		−	0.0185248i
$191$		−	291.856i		−	1.52804i	−0.645191	−	0.764022i	$-0.723222\pi$
$191$		−	291.856i		−	1.52804i	0.645191	−	0.764022i	$-0.276778\pi$
$192$	−142.737			−0.743424
$193$			186.353i			0.965559i	0.875742	+	0.482780i	$0.160373\pi$
$193$			186.353i			0.965559i	−0.875742	+	0.482780i	$0.839627\pi$
$194$	−101.542			−0.523411
$195$		−	478.951i		−	2.45616i
$196$	−106.871	+	72.6896i	−0.545260	+	0.370866i
$197$	−189.225			−0.960531			−0.480266	−	0.877123i	$-0.659460\pi$
$197$	−189.225			−0.960531			−0.480266	+	0.877123i	$0.659460\pi$
$198$			190.203i			0.960620i
$199$	−17.2404			−0.0866351			−0.0433176	−	0.999061i	$-0.513793\pi$
$199$	−17.2404			−0.0866351			−0.0433176	+	0.999061i	$0.513793\pi$
$200$	440.911			2.20455
$201$			278.774i			1.38694i
$202$	−63.2255			−0.312997
$203$	18.8475	+	61.2229i	0.0928450	+	0.301591i
$204$	−202.746			−0.993851
$205$	363.254	−	75.7586i	1.77197	−	0.369554i
$206$			154.235i			0.748713i
$207$	151.460			0.731693
$208$	−18.0033			−0.0865545
$209$			5.09296i			0.0243682i
$210$	96.4693	+	313.363i	0.459378	+	1.49221i
$211$		−	74.0767i		−	0.351074i	−0.984473	−	0.175537i	$-0.943834\pi$
$211$		−	74.0767i		−	0.351074i	0.984473	−	0.175537i	$-0.0561662\pi$
$212$		−	74.7243i		−	0.352473i
$213$			135.377i			0.635574i
$214$	−212.941			−0.995051
$215$			352.618i			1.64008i
$216$	57.0746			0.264234
$217$	105.034	+	341.183i	0.484026	+	1.57227i
$218$			12.5566i			0.0575989i
$219$		−	88.5045i		−	0.404130i
$220$	−364.897			−1.65862
$221$	206.884			0.936125
$222$	−84.8551			−0.382230
$223$			420.599i			1.88609i	0.332662	+	0.943046i	$0.392053\pi$
$223$			420.599i			1.88609i	−0.332662	+	0.943046i	$0.607947\pi$
$224$	219.102	−	67.4509i	0.978135	−	0.301120i
$225$	−606.757			−2.69670
$226$	81.7456			0.361706
$227$	84.3164			0.371438			0.185719	−	0.982603i	$-0.440539\pi$
$227$	84.3164			0.371438			0.185719	+	0.982603i	$0.440539\pi$
$228$	3.89708			0.0170924
$229$	−141.115			−0.616224			−0.308112	−	0.951350i	$-0.599697\pi$
$229$	−141.115			−0.616224			−0.308112	+	0.951350i	$0.599697\pi$
$230$		−	150.068i		−	0.652470i
$231$	−139.590	−	453.432i	−0.604284	−	1.96291i
$232$		−	70.8973i		−	0.305592i
$233$			199.548i			0.856428i	0.903677	+	0.428214i	$0.140857\pi$
$233$			199.548i			0.856428i	−0.903677	+	0.428214i	$0.859143\pi$
$234$	−148.511			−0.634664
$235$			722.504i			3.07448i
$236$			235.672i			0.998610i
$237$		−	170.997i		−	0.721505i
$238$	−135.358	+	41.6700i	−0.568730	+	0.175084i
$239$			61.1830i			0.255996i	0.991774	+	0.127998i	$0.0408551\pi$
$239$			61.1830i			0.255996i	−0.991774	+	0.127998i	$0.959145\pi$
$240$			60.5370i			0.252238i
$241$			209.187i			0.867996i	0.900914	+	0.433998i	$0.142898\pi$
$241$			209.187i			0.867996i	−0.900914	+	0.433998i	$0.857102\pi$
$242$	−131.463			−0.543236
$243$	346.924			1.42767
$244$		−	93.0174i		−	0.381219i
$245$	−249.411	−	366.693i	−1.01800	−	1.49670i
$246$	−43.3212	−	207.720i	−0.176102	−	0.844391i
$247$	−3.97662			−0.0160997
$248$		−	395.096i		−	1.59313i
$249$			501.873i			2.01555i
$250$			337.094i			1.34837i
$251$			6.07084i			0.0241866i	0.999927	+	0.0120933i	$0.00384952\pi$
$251$			6.07084i			0.0241866i	−0.999927	+	0.0120933i	$0.996150\pi$
$252$	−188.140	+	57.9191i	−0.746587	+	0.229838i
$253$			217.146i			0.858285i
$254$	−122.993			−0.484226
$255$		−	695.655i		−	2.72806i
$256$	−237.809			−0.928940
$257$	96.9712			0.377320			0.188660	−	0.982042i	$-0.439586\pi$
$257$	96.9712			0.377320			0.188660	+	0.982042i	$0.439586\pi$
$258$	201.638			0.781543
$259$	109.692	−	33.7688i	0.423520	−	0.130381i
$260$		−	284.914i		−	1.09582i
$261$			97.5648i			0.373812i
$262$			155.133i			0.592110i
$263$		−	246.414i		−	0.936935i	−0.883481	−	0.468467i	$-0.844806\pi$
$263$		−	246.414i		−	0.936935i	0.883481	−	0.468467i	$-0.155194\pi$
$264$			525.083i			1.98895i
$265$	256.392			0.967518
$266$	2.60178	−	0.800961i	0.00978113	−	0.00301113i
$267$	629.273			2.35683
$268$			165.834i			0.618785i
$269$		−	65.0432i		−	0.241796i	−0.992665	−	0.120898i	$-0.961423\pi$
$269$		−	65.0432i		−	0.241796i	0.992665	−	0.120898i	$-0.0385775\pi$
$270$			77.8208i			0.288225i
$271$			259.763i			0.958536i	0.877669	+	0.479268i	$0.159098\pi$
$271$			259.763i			0.958536i	−0.877669	+	0.479268i	$0.840902\pi$
$272$	−26.1490			−0.0961362
$273$	354.043	−	108.992i	1.29686	−	0.399240i
$274$			33.1907i			0.121134i
$275$		−	869.897i		−	3.16326i
$276$	166.158			0.602021
$277$	−18.1476			−0.0655146			−0.0327573	−	0.999463i	$-0.510429\pi$
$277$	−18.1476			−0.0655146			−0.0327573	+	0.999463i	$0.510429\pi$
$278$		−	2.92535i		−	0.0105228i
$279$			543.709i			1.94878i
$280$	144.411	+	469.094i	0.515754	+	1.67534i
$281$		−	196.222i		−	0.698297i	−0.937067	−	0.349149i	$-0.886471\pi$
$281$		−	196.222i		−	0.698297i	0.937067	−	0.349149i	$-0.113529\pi$
$282$	413.150			1.46507
$283$		−	304.726i		−	1.07677i	−0.842698	−	0.538386i	$-0.819034\pi$
$283$		−	304.726i		−	1.07677i	0.842698	−	0.538386i	$-0.180966\pi$
$284$			80.5318i			0.283563i
$285$			13.3715i			0.0469177i
$286$		−	212.918i		−	0.744469i
$287$	138.665	+	251.279i	0.483153	+	0.875536i
$288$	349.161			1.21237
$289$	11.4892			0.0397550
$290$	96.6679			0.333338
$291$	385.762			1.32564
$292$		−	52.6486i		−	0.180304i
$293$	−528.537			−1.80388			−0.901940	−	0.431862i	$-0.857857\pi$
$293$	−528.537			−1.80388			−0.901940	+	0.431862i	$0.857857\pi$
$294$	−209.686	+	142.621i	−0.713219	+	0.485105i
$295$	−808.632			−2.74112
$296$	−127.025			−0.429139
$297$		−	112.605i		−	0.379143i
$298$		−	287.302i		−	0.964101i
$299$	−169.549			−0.567054
$300$	−665.635			−2.21878
$301$	−260.656	+	80.2434i	−0.865968	+	0.266589i
$302$			164.029i			0.543143i
$303$	240.197			0.792729
$304$	0.502624			0.00165337
$305$	319.159			1.04642
$306$	−215.706			−0.704922
$307$		−	385.509i		−	1.25573i	−0.778323	−	0.627865i	$-0.783929\pi$
$307$		−	385.509i		−	1.25573i	0.778323	−	0.627865i	$-0.216071\pi$
$308$	−83.0376	−	269.733i	−0.269603	−	0.875756i
$309$		−	585.946i		−	1.89627i
$310$	538.711			1.73778
$311$	370.453			1.19117			0.595584	−	0.803293i	$-0.296921\pi$
$311$	370.453			1.19117			0.595584	+	0.803293i	$0.296921\pi$
$312$	−409.988			−1.31406
$313$	−25.9563			−0.0829275			−0.0414638	−	0.999140i	$-0.513202\pi$
$313$	−25.9563			−0.0829275			−0.0414638	+	0.999140i	$0.513202\pi$
$314$	−30.3959			−0.0968022
$315$	−198.731	−	645.541i	−0.630891	−	2.04934i
$316$		−	101.721i		−	0.321901i
$317$		−	481.625i		−	1.51932i	−0.650320	−	0.759661i	$-0.725365\pi$
$317$		−	481.625i		−	1.51932i	0.650320	−	0.759661i	$-0.274635\pi$
$318$		−	146.613i		−	0.461047i
$319$	−139.877			−0.438486
$320$		−	291.341i		−	0.910442i
$321$	808.973			2.52017
$322$	110.931	−	34.1502i	0.344506	−	0.106057i
$323$	−5.77586			−0.0178819
$324$	166.933			0.515225
$325$	679.221			2.08991
$326$	109.039			0.334475
$327$		−	47.7030i		−	0.145881i
$328$	−64.8503	−	310.950i	−0.197714	−	0.948018i
$329$	−534.077	+	164.416i	−1.62334	+	0.499746i
$330$	−715.947			−2.16954
$331$		−	213.502i		−	0.645021i	−0.946566	−	0.322510i	$-0.895473\pi$
$331$		−	213.502i		−	0.645021i	0.946566	−	0.322510i	$-0.104527\pi$
$332$			298.549i			0.899243i
$333$	174.805			0.524940
$334$	275.174			0.823873
$335$	−569.007			−1.69853
$336$	−44.7492	+	13.7761i	−0.133182	+	0.0410003i
$337$	144.101			0.427600			0.213800	−	0.976877i	$-0.431416\pi$
$337$	144.101			0.427600			0.213800	+	0.976877i	$0.431416\pi$
$338$	−31.0032			−0.0917254
$339$	−310.556			−0.916094
$340$		−	413.824i		−	1.21713i
$341$	−779.507			−2.28594
$342$	4.14620			0.0121234
$343$	214.303	−	267.812i	0.624791	−	0.780792i
$344$	301.845			0.877457
$345$			570.116i			1.65251i
$346$		−	264.449i		−	0.764305i
$347$		−	365.274i		−	1.05266i	−0.850279	−	0.526332i	$-0.823567\pi$
$347$		−	365.274i		−	1.05266i	0.850279	−	0.526332i	$-0.176433\pi$
$348$			107.032i			0.307564i
$349$			161.384i			0.462417i	0.972904	+	0.231209i	$0.0742680\pi$
$349$			161.384i			0.462417i	−0.972904	+	0.231209i	$0.925732\pi$
$350$	−444.394	+	136.807i	−1.26970	+	0.390877i
$351$	87.9230			0.250493
$352$			500.587i			1.42212i
$353$		−	215.147i		−	0.609481i	−0.952435	−	0.304740i	$-0.901430\pi$
$353$		−	215.147i		−	0.609481i	0.952435	−	0.304740i	$-0.0985697\pi$
$354$			462.401i			1.30622i
$355$	−276.319			−0.778362
$356$	374.335			1.05150
$357$	514.231	−	158.307i	1.44042	−	0.443436i
$358$			320.611i			0.895561i
$359$	68.7380			0.191471			0.0957354	−	0.995407i	$-0.469480\pi$
$359$	68.7380			0.191471			0.0957354	+	0.995407i	$0.469480\pi$
$360$			747.549i			2.07652i
$361$	−360.889			−0.999692
$362$	−114.483			−0.316251
$363$	499.435			1.37585
$364$	210.609	−	64.8363i	0.578597	−	0.178122i
$365$	180.647			0.494922
$366$		−	182.505i		−	0.498648i
$367$			255.033i			0.694912i	0.937696	+	0.347456i	$0.112954\pi$
$367$			255.033i			0.694912i	−0.937696	+	0.347456i	$0.887046\pi$
$368$	21.4301			0.0582341
$369$	89.2433	+	427.912i	0.241852	+	1.15965i
$370$		−	173.198i		−	0.468102i
$371$	58.3458	+	189.526i	0.157266	+	0.510852i
$372$			596.469i			1.60341i
$373$	317.831			0.852095			0.426048	−	0.904701i	$-0.359906\pi$
$373$	317.831			0.852095			0.426048	+	0.904701i	$0.359906\pi$
$374$		−	309.254i		−	0.826883i
$375$		−	1280.64i		−	3.41503i
$376$	618.471			1.64487
$377$		−	109.217i		−	0.289700i
$378$	−57.5254	+	17.7093i	−0.152184	+	0.0468499i
$379$	567.422			1.49716			0.748578	−	0.663047i	$-0.230737\pi$
$379$	567.422			1.49716			0.748578	+	0.663047i	$0.230737\pi$
$380$			7.95433i			0.0209324i
$381$	467.258			1.22640
$382$		−	340.645i		−	0.891740i
$383$	363.473			0.949016			0.474508	−	0.880251i	$-0.342626\pi$
$383$	363.473			0.949016			0.474508	+	0.880251i	$0.342626\pi$
$384$	414.271			1.07883
$385$	925.501	−	284.917i	2.40390	−	0.740043i
$386$			217.505i			0.563484i
$387$	−415.382			−1.07334
$388$	229.478			0.591438
$389$	0.303045			0.000779037			0.000389519	−	1.00000i	$-0.499876\pi$
$389$	0.303045			0.000779037			0.000389519		1.00000i	$0.499876\pi$
$390$		−	559.016i		−	1.43337i
$391$	−246.262			−0.629827
$392$	−313.893	+	213.499i	−0.800748	+	0.544639i
$393$		−	589.358i		−	1.49964i
$394$	−220.857			−0.560550
$395$	349.021			0.883599
$396$		−	429.847i		−	1.08547i
$397$	−373.212			−0.940081			−0.470041	−	0.882645i	$-0.655761\pi$
$397$	−373.212			−0.940081			−0.470041	+	0.882645i	$0.655761\pi$
$398$	−20.1224			−0.0505588
$399$	−9.88429	+	3.04289i	−0.0247727	+	0.00762630i
$400$	−85.8500			−0.214625
$401$	172.196			0.429417			0.214709	−	0.976678i	$-0.431120\pi$
$401$	172.196			0.429417			0.214709	+	0.976678i	$0.431120\pi$
$402$			325.376i			0.809393i
$403$		−	608.643i		−	1.51028i
$404$	142.886			0.353678
$405$			572.776i			1.41426i
$406$	21.9982	+	71.4573i	0.0541828	+	0.176003i
$407$			250.615i			0.615761i
$408$	−595.489			−1.45953
$409$		−	132.063i		−	0.322893i	−0.986881	−	0.161446i	$-0.948384\pi$
$409$		−	132.063i		−	0.322893i	0.986881	−	0.161446i	$-0.0516159\pi$
$410$	423.978	−	88.4229i	1.03409	−	0.215666i
$411$		−	126.093i		−	0.306796i
$412$		−	348.562i		−	0.846023i
$413$	−184.016	−	597.743i	−0.445559	−	1.44732i
$414$	176.779			0.427004
$415$	−1024.37			−2.46837
$416$	−390.861			−0.939570
$417$			11.1135i			0.0266512i
$418$			5.94433i			0.0142209i
$419$			585.115i			1.39646i	0.715875	+	0.698228i	$0.246028\pi$
$419$			585.115i			1.39646i	−0.715875	+	0.698228i	$0.753972\pi$
$420$	−218.015	−	708.183i	−0.519083	−	1.68615i
$421$			436.655i			1.03718i	0.855022	+	0.518592i	$0.173544\pi$
$421$			436.655i			1.03718i	−0.855022	+	0.518592i	$0.826456\pi$
$422$		−	86.4598i		−	0.204881i
$423$	−851.106			−2.01207
$424$		−	219.475i		−	0.517629i
$425$	986.538			2.32126
$426$			158.008i			0.370910i
$427$	72.6293	+	235.923i	0.170092	+	0.552514i
$428$	481.234			1.12438
$429$			808.887i			1.88552i
$430$			411.564i			0.957125i
$431$	−110.451			−0.256268			−0.128134	−	0.991757i	$-0.540899\pi$
$431$	−110.451			−0.256268			−0.128134	+	0.991757i	$0.540899\pi$
$432$	−11.1130			−0.0257246
$433$			70.1227i			0.161946i	0.996716	+	0.0809731i	$0.0258028\pi$
$433$			70.1227i			0.161946i	−0.996716	+	0.0809731i	$0.974197\pi$
$434$	122.592	+	398.217i	0.282469	+	0.917551i
$435$	−367.246			−0.844244
$436$		−	28.3771i		−	0.0650850i
$437$	4.73354			0.0108319
$438$		−	103.299i		−	0.235843i
$439$	−640.138			−1.45817			−0.729086	−	0.684422i	$-0.760055\pi$
$439$	−640.138			−1.45817			−0.729086	+	0.684422i	$0.760055\pi$
$440$	−1071.75			−2.43579
$441$	431.962	−	293.805i	0.979506	−	0.666224i
$442$	241.467			0.546307
$443$	−122.631			−0.276820			−0.138410	−	0.990375i	$-0.544199\pi$
$443$	−122.631			−0.276820			−0.138410	+	0.990375i	$0.544199\pi$
$444$	191.768			0.431909
$445$			1284.41i			2.88631i
$446$			490.908i			1.10069i
$447$			1091.47i			2.44178i
$448$	215.361	−	66.2990i	0.480716	−	0.147989i
$449$	−201.374			−0.448494			−0.224247	−	0.974532i	$-0.571992\pi$
$449$	−201.374			−0.448494			−0.224247	+	0.974532i	$0.571992\pi$
$450$	−708.186			−1.57375
$451$	−613.489	+	127.947i	−1.36029	+	0.283695i
$452$	−184.740			−0.408717
$453$		−	623.155i		−	1.37562i
$454$	98.4112			0.216765
$455$	222.465	+	722.637i	0.488933	+	1.58821i
$456$	11.4462			0.0251013
$457$			3.62254i			0.00792678i	0.999992	+	0.00396339i	$0.00126159\pi$
$457$			3.62254i			0.00792678i	−0.999992	+	0.00396339i	$0.998738\pi$
$458$	−164.705			−0.359618
$459$	127.704			0.278223
$460$			339.145i			0.737271i
$461$			178.971i			0.388223i	0.980979	+	0.194112i	$0.0621824\pi$
$461$			178.971i			0.388223i	−0.980979	+	0.194112i	$0.937818\pi$
$462$	−162.924	−	529.230i	−0.352650	−	1.14552i
$463$		−	291.968i		−	0.630600i	−0.948992	−	0.315300i	$-0.897895\pi$
$463$		−	291.968i		−	0.630600i	0.948992	−	0.315300i	$-0.102105\pi$
$464$			13.8044i			0.0297510i
$465$	−2046.59			−4.40127
$466$			232.905i			0.499797i
$467$		−	627.934i		−	1.34461i	−0.740273	−	0.672306i	$-0.765304\pi$
$467$		−	627.934i		−	1.34461i	0.740273	−	0.672306i	$-0.234696\pi$
$468$	335.627			0.717151
$469$	−129.486	−	420.612i	−0.276089	−	0.896827i
$470$			843.282i			1.79422i
$471$	115.476			0.245171
$472$			692.198i			1.46652i
$473$		−	595.526i		−	1.25904i
$474$		−	199.581i		−	0.421058i
$475$	−18.9627			−0.0399216
$476$	305.900	−	94.1718i	0.642648	−	0.197840i
$477$			302.029i			0.633184i
$478$			71.4107i			0.149395i
$479$	301.484			0.629404			0.314702	−	0.949191i	$-0.398095\pi$
$479$	301.484			0.629404			0.314702	+	0.949191i	$0.398095\pi$
$480$			1314.29i			2.73810i
$481$	−195.681			−0.406822
$482$			244.156i			0.506548i
$483$	−421.432	+	129.738i	−0.872530	+	0.268609i
$484$	297.099			0.613841
$485$			787.379i			1.62346i
$486$	404.918			0.833164
$487$	10.6678			0.0219051			0.0109526	−	0.999940i	$-0.496514\pi$
$487$	10.6678			0.0219051			0.0109526	+	0.999940i	$0.496514\pi$
$488$		−	273.204i		−	0.559843i
$489$	−414.244			−0.847126
$490$	−291.104	−	427.991i	−0.594089	−	0.873451i
$491$	−793.174			−1.61543			−0.807713	−	0.589576i	$-0.799295\pi$
$491$	−793.174			−1.61543			−0.807713	+	0.589576i	$0.799295\pi$
$492$	97.9032	+	469.435i	0.198990	+	0.954136i
$493$		−	158.632i		−	0.321770i
$494$	−4.64137			−0.00939549
$495$	1474.88			2.97955
$496$			76.9294i			0.155100i
$497$	−62.8804	−	204.256i	−0.126520	−	0.410977i
$498$			585.769i			1.17624i
$499$		−	330.798i		−	0.662922i	−0.943469	−	0.331461i	$-0.892459\pi$
$499$		−	330.798i		−	0.662922i	0.943469	−	0.331461i	$-0.107541\pi$
$500$		−	761.811i		−	1.52362i
$501$	−1045.40			−2.08662
$502$			7.08568i			0.0141149i
$503$	543.482			1.08048			0.540241	−	0.841510i	$-0.318333\pi$
$503$	543.482			1.08048			0.540241	+	0.841510i	$0.318333\pi$
$504$	−552.591	+	170.116i	−1.09641	+	0.337531i
$505$			490.266i			0.970824i
$506$			253.446i			0.500881i
$507$	117.783			0.232313
$508$	277.958			0.547161
$509$	−371.445			−0.729755			−0.364878	−	0.931056i	$-0.618889\pi$
$509$	−371.445			−0.729755			−0.364878	+	0.931056i	$0.618889\pi$
$510$		−	811.945i		−	1.59205i
$511$	41.1088	+	133.535i	0.0804477	+	0.261320i
$512$	96.1498			0.187793
$513$	−2.45467			−0.00478493
$514$	113.182			0.220197
$515$	1195.98			2.32228
$516$	−455.690			−0.883120
$517$		−	1220.22i		−	2.36018i
$518$	128.028	−	39.4137i	0.247159	−	0.0760883i
$519$			1004.66i			1.93575i
$520$		−	836.827i		−	1.60928i
$521$	−121.091			−0.232421			−0.116210	−	0.993225i	$-0.537075\pi$
$521$	−121.091			−0.232421			−0.116210	+	0.993225i	$0.537075\pi$
$522$			113.874i			0.218150i
$523$			189.011i			0.361398i	0.983538	+	0.180699i	$0.0578360\pi$
$523$			189.011i			0.361398i	−0.983538	+	0.180699i	$0.942164\pi$
$524$		−	350.591i		−	0.669067i
$525$	1688.27	−	519.737i	3.21576	−	0.989976i
$526$		−	287.606i		−	0.546779i
$527$		−	884.027i		−	1.67747i
$528$		−	102.239i		−	0.193635i
$529$	−327.179			−0.618485
$530$	299.252			0.564627
$531$		−	952.564i		−	1.79391i
$532$	−5.87987	+	1.81012i	−0.0110524	+	0.00340249i
$533$	−99.9014	−	479.016i	−0.187432	−	0.898717i
$534$	734.466			1.37540
$535$			1651.20i			3.08635i
$536$			487.076i			0.908724i
$537$		−	1218.02i		−	2.26819i
$538$		−	75.9162i		−	0.141108i
$539$	421.223	+	619.296i	0.781489	+	1.14897i
$540$		−	175.870i		−	0.325686i
$541$	−543.204			−1.00407			−0.502037	−	0.864846i	$-0.667416\pi$
$541$	−543.204			−1.00407			−0.502037	+	0.864846i	$0.667416\pi$
$542$			303.187i			0.559385i
$543$	434.927			0.800970
$544$	−567.708			−1.04358
$545$	97.3667			0.178654
$546$	413.226	−	127.212i	0.756825	−	0.232989i
$547$		−	389.951i		−	0.712890i	−0.934316	−	0.356445i	$-0.883989\pi$
$547$		−	389.951i		−	0.712890i	0.934316	−	0.356445i	$-0.116011\pi$
$548$		−	75.0089i		−	0.136878i
$549$			375.968i			0.684822i
$550$		−	1015.31i		−	1.84602i
$551$			3.04916i			0.00553386i
$552$	488.026			0.884105
$553$	79.4249	+	257.998i	0.143626	+	0.466542i
$554$	−21.1812			−0.0382332
$555$			657.988i			1.18556i
$556$			6.61111i			0.0118905i
$557$		−	871.683i		−	1.56496i	−0.622675	−	0.782480i	$-0.713954\pi$
$557$		−	871.683i		−	1.56496i	0.622675	−	0.782480i	$-0.286046\pi$
$558$			634.599i			1.13727i
$559$	464.991			0.831826
$560$	−28.1184	−	91.3376i	−0.0502114	−	0.163103i
$561$			1174.87i			2.09425i
$562$		−	229.023i		−	0.407514i
$563$	869.717			1.54479			0.772396	−	0.635142i	$-0.219058\pi$
$563$	869.717			1.54479			0.772396	+	0.635142i	$0.219058\pi$
$564$	−933.695			−1.65549
$565$		−	633.876i		−	1.12190i
$566$		−	355.666i		−	0.628386i
$567$	−423.398	+	130.344i	−0.746734	+	0.229883i
$568$			236.532i			0.416429i
$569$	−703.517			−1.23641			−0.618205	−	0.786017i	$-0.712140\pi$
$569$	−703.517			−1.23641			−0.618205	+	0.786017i	$0.712140\pi$
$570$			15.6068i			0.0273804i
$571$			599.351i			1.04965i	0.851210	+	0.524826i	$0.175870\pi$
$571$			599.351i			1.04965i	−0.851210	+	0.524826i	$0.824130\pi$
$572$			481.182i			0.841228i
$573$			1294.13i			2.25851i
$574$	161.845	+	293.284i	0.281960	+	0.510948i
$575$	−808.505			−1.40610
$576$	343.199			0.595831
$577$	344.447			0.596962			0.298481	−	0.954416i	$-0.403520\pi$
$577$	344.447			0.596962			0.298481	+	0.954416i	$0.403520\pi$
$578$	13.4098			0.0232003
$579$		−	826.311i		−	1.42714i
$580$	−218.464			−0.376662
$581$	−233.111	−	757.220i	−0.401224	−	1.30330i
$582$	450.248			0.773622
$583$	−433.013			−0.742733
$584$		−	154.636i		−	0.264787i
$585$			1151.59i			1.96854i
$586$	−616.890			−1.05271
$587$	−14.3452			−0.0244382			−0.0122191	−	0.999925i	$-0.503890\pi$
$587$	−14.3452			−0.0244382			−0.0122191	+	0.999925i	$0.503890\pi$
$588$	473.879	−	322.315i	0.805916	−	0.548154i
$589$			16.9923i			0.0288495i
$590$	−943.807			−1.59967
$591$	839.045			1.41970
$592$	24.7331			0.0417790
$593$	835.017			1.40812			0.704061	−	0.710139i	$-0.251368\pi$
$593$	835.017			1.40812			0.704061	+	0.710139i	$0.251368\pi$
$594$		−	131.429i		−	0.221261i
$595$	323.120	+	1049.60i	0.543058	+	1.76403i
$596$			649.285i			1.08940i
$597$	76.4460			0.128050
$598$	−197.892			−0.330923
$599$	527.043			0.879872			0.439936	−	0.898029i	$-0.355001\pi$
$599$	527.043			0.879872			0.439936	+	0.898029i	$0.355001\pi$
$600$	−1955.05			−3.25842
$601$	89.1917			0.148405			0.0742027	−	0.997243i	$-0.476359\pi$
$601$	89.1917			0.148405			0.0742027	+	0.997243i	$0.476359\pi$
$602$	−304.229	+	93.6574i	−0.505364	+	0.155577i
$603$		−	670.287i		−	1.11159i
$604$		−	370.696i		−	0.613735i
$605$			1019.40i			1.68495i
$606$	280.350			0.462623
$607$			151.022i			0.248801i	0.992232	+	0.124401i	$0.0397008\pi$
$607$			151.022i			0.248801i	−0.992232	+	0.124401i	$0.960299\pi$
$608$	10.9122			0.0179477
$609$	−83.5723	−	271.470i	−0.137229	−	0.445763i
$610$	372.511			0.610674
$611$	952.751			1.55933
$612$	487.483			0.796541
$613$	−799.097			−1.30358			−0.651792	−	0.758397i	$-0.725983\pi$
$613$	−799.097			−1.30358			−0.651792	+	0.758397i	$0.725983\pi$
$614$		−	449.953i		−	0.732822i
$615$	−1610.71	+	335.923i	−2.61905	+	0.546216i
$616$	−243.892	−	792.239i	−0.395928	−	1.28610i
$617$	−29.0725			−0.0471192			−0.0235596	−	0.999722i	$-0.507500\pi$
$617$	−29.0725			−0.0471192			−0.0235596	+	0.999722i	$0.507500\pi$
$618$		−	683.896i		−	1.10663i
$619$			467.755i			0.755662i	0.925875	+	0.377831i	$0.123330\pi$
$619$			467.755i			0.755662i	−0.925875	+	0.377831i	$0.876670\pi$
$620$	−1217.45			−1.96364
$621$	−104.659			−0.168532
$622$	432.380			0.695145
$623$	−949.440	+	292.286i	−1.52398	+	0.469159i
$624$	79.8290			0.127931
$625$	1191.12			1.90579
$626$	−30.2953			−0.0483951
$627$		−	22.5828i		−	0.0360172i
$628$	68.6929			0.109384
$629$	−284.219			−0.451858
$630$	−231.952	−	753.453i	−0.368177	−	1.19596i
$631$	330.433			0.523666			0.261833	−	0.965113i	$-0.415673\pi$
$631$	330.433			0.523666			0.261833	+	0.965113i	$0.415673\pi$
$632$		−	298.766i		−	0.472732i
$633$			328.465i			0.518902i
$634$		−	562.136i		−	0.886650i
$635$			953.721i			1.50192i
$636$			331.337i			0.520970i
$637$	−483.550	+	328.893i	−0.759106	+	0.516316i
$638$	−163.260			−0.255893
$639$		−	325.502i		−	0.509393i
$640$			845.569i			1.32120i
$641$			603.751i			0.941889i	0.882163	+	0.470944i	$0.156087\pi$
$641$			603.751i			0.941889i	−0.882163	+	0.470944i	$0.843913\pi$
$642$	944.206			1.47073
$643$	−841.198			−1.30824			−0.654120	−	0.756391i	$-0.726961\pi$
$643$	−841.198			−1.30824			−0.654120	+	0.756391i	$0.726961\pi$
$644$	−250.697	+	77.1774i	−0.389281	+	0.119841i
$645$		−	1563.55i		−	2.42411i
$646$	−6.74138			−0.0104356
$647$			87.5245i			0.135277i	0.997710	+	0.0676387i	$0.0215465\pi$
$647$			87.5245i			0.135277i	−0.997710	+	0.0676387i	$0.978453\pi$
$648$	490.303			0.756640
$649$	1365.67			2.10427
$650$	792.763			1.21964
$651$	−465.732	−	1512.85i	−0.715410	−	2.32388i
$652$	−246.421			−0.377947
$653$			941.438i			1.44171i	0.693085	+	0.720856i	$0.256251\pi$
$653$			941.438i			1.44171i	−0.693085	+	0.720856i	$0.743749\pi$
$654$		−	55.6773i		−	0.0851335i
$655$	1202.94			1.83655
$656$	12.6270	+	60.5452i	0.0192485	+	0.0922946i
$657$			212.801i			0.323898i
$658$	−623.357	+	191.901i	−0.947350	+	0.291643i
$659$			727.209i			1.10350i	0.834008	+	0.551752i	$0.186040\pi$
$659$			727.209i			1.10350i	−0.834008	+	0.551752i	$0.813960\pi$
$660$	1618.00			2.45151
$661$		−	1035.36i		−	1.56635i	−0.621798	−	0.783177i	$-0.713598\pi$
$661$		−	1035.36i		−	1.56635i	0.621798	−	0.783177i	$-0.286402\pi$
$662$		−	249.192i		−	0.376423i
$663$	−917.347			−1.38363
$664$			876.875i			1.32059i
$665$	−6.21085	−	20.1748i	−0.00933963	−	0.0303381i
$666$	204.026			0.306346
$667$			130.005i			0.194911i
$668$	−621.876			−0.930952
$669$		−	1864.99i		−	2.78772i
$670$	−664.125			−0.991231
$671$	−539.018			−0.803305
$672$	−971.526	+	299.085i	−1.44572	+	0.445068i
$673$		−	1029.20i		−	1.52927i	−0.644462	−	0.764636i	$-0.722919\pi$
$673$		−	1029.20i		−	1.52927i	0.644462	−	0.764636i	$-0.277081\pi$
$674$	168.190			0.249540
$675$	419.267			0.621136
$676$	70.0654			0.103647
$677$		−	351.751i		−	0.519574i	−0.965666	−	0.259787i	$-0.916348\pi$
$677$		−	351.751i		−	0.519574i	0.965666	−	0.259787i	$-0.0836523\pi$
$678$	−362.470			−0.534617
$679$	−582.033	+	179.180i	−0.857192	+	0.263888i
$680$		−	1215.45i		−	1.78743i
$681$	−373.869			−0.549000
$682$	−909.813			−1.33404
$683$			942.056i			1.37929i	0.724147	+	0.689646i	$0.242234\pi$
$683$			942.056i			1.37929i	−0.724147	+	0.689646i	$0.757766\pi$
$684$	−9.37016			−0.0136991
$685$	257.369			0.375721
$686$	250.128	−	312.581i	0.364617	−	0.455657i
$687$	625.722			0.910804
$688$	−58.7724			−0.0854251
$689$		−	338.099i		−	0.490710i
$690$			665.420i			0.964377i
$691$	546.729			0.791214			0.395607	−	0.918420i	$-0.370534\pi$
$691$	546.729			0.791214			0.395607	+	0.918420i	$0.370534\pi$
$692$			597.640i			0.863641i
$693$	335.630	+	1090.24i	0.484315	+	1.57321i
$694$		−	426.336i		−	0.614317i
$695$	−22.6839			−0.0326386
$696$			314.367i			0.451677i
$697$	−145.102	−	695.750i	−0.208181	−	0.998206i
$698$			188.361i			0.269859i
$699$		−	884.819i		−	1.26584i
$700$	1004.30	−	309.176i	1.43472	−	0.441680i
$701$	160.450			0.228888			0.114444	−	0.993430i	$-0.463491\pi$
$701$	160.450			0.228888			0.114444	+	0.993430i	$0.463491\pi$
$702$	102.621			0.146183
$703$	5.46311			0.00777114
$704$			492.038i			0.698917i
$705$		−	3203.67i		−	4.54421i
$706$		−	251.112i		−	0.355682i
$707$	−362.406	+	111.567i	−0.512597	+	0.157804i
$708$		−	1045.00i		−	1.47599i
$709$			774.322i			1.09213i	0.837742	+	0.546067i	$0.183875\pi$
$709$			774.322i			1.09213i	−0.837742	+	0.546067i	$0.816125\pi$
$710$	−322.510			−0.454239
$711$			411.146i			0.578264i
$712$	1099.47			1.54420
$713$			724.494i			1.01612i
$714$	600.193	−	184.770i	0.840606	−	0.258782i
$715$	−1651.02			−2.30912
$716$		−	724.561i		−	1.01196i
$717$		−	271.293i		−	0.378372i
$718$	80.2286			0.111739
$719$	591.145			0.822176			0.411088	−	0.911596i	$-0.365149\pi$
$719$	591.145			0.822176			0.411088	+	0.911596i	$0.365149\pi$
$720$		−	145.556i		−	0.202161i
$721$	272.162	+	884.069i	0.377478	+	1.22617i
$722$	−421.217			−0.583403
$723$		−	927.561i		−	1.28293i
$724$	258.725			0.357355
$725$		−	520.807i		−	0.718355i
$726$	582.924			0.802925
$727$	−19.6607			−0.0270436			−0.0135218	−	0.999909i	$-0.504304\pi$
$727$	−19.6607			−0.0270436			−0.0135218	+	0.999909i	$0.504304\pi$
$728$	618.585	−	190.432i	0.849705	−	0.261583i
$729$	−968.723			−1.32884
$730$	210.845			0.288828
$731$	675.378			0.923910
$732$			412.450i			0.563457i
$733$			284.356i			0.387935i	0.981008	+	0.193967i	$0.0621356\pi$
$733$			284.356i			0.387935i	−0.981008	+	0.193967i	$0.937864\pi$
$734$			297.665i			0.405539i
$735$	1105.92	+	1625.96i	1.50465	+	2.21219i
$736$	465.259			0.632145
$737$	960.979			1.30391
$738$	104.162	+	499.444i	0.141141	+	0.676753i
$739$	105.738			0.143083			0.0715416	−	0.997438i	$-0.477208\pi$
$739$	105.738			0.143083			0.0715416	+	0.997438i	$0.477208\pi$
$740$			391.417i			0.528942i
$741$	17.6328			0.0237960
$742$	68.0992	+	221.208i	0.0917779	+	0.298124i
$743$	1098.00			1.47779			0.738894	−	0.673822i	$-0.235348\pi$
$743$	1098.00			1.47779			0.738894	+	0.673822i	$0.235348\pi$
$744$			1751.91i			2.35471i
$745$	−2227.81			−2.99035
$746$	370.962			0.497268
$747$		−	1206.71i		−	1.61540i
$748$			698.896i			0.934352i
$749$	−1220.57	+	375.754i	−1.62960	+	0.501674i
$750$		−	1494.71i		−	1.99295i
$751$		−	1238.52i		−	1.64916i	−0.565748	−	0.824578i	$-0.691412\pi$
$751$		−	1238.52i		−	1.64916i	0.565748	−	0.824578i	$-0.308588\pi$
$752$	−120.423			−0.160137
$753$		−	26.9189i		−	0.0357488i
$754$		−	127.474i		−	0.169064i
$755$	1271.92			1.68467
$756$	130.004	−	40.0219i	0.171963	−	0.0529390i
$757$			824.856i			1.08964i	0.838554	+	0.544819i	$0.183402\pi$
$757$			824.856i			1.08964i	−0.838554	+	0.544819i	$0.816598\pi$
$758$	662.275			0.873714
$759$		−	962.853i		−	1.26858i
$760$			23.3628i			0.0307406i
$761$			214.329i			0.281642i	0.990035	+	0.140821i	$0.0449741\pi$
$761$			214.329i			0.281642i	−0.990035	+	0.140821i	$0.955026\pi$
$762$	545.368			0.715706
$763$	22.1572	+	71.9738i	0.0290396	+	0.0943300i
$764$			769.836i			1.00764i
$765$			1672.64i			2.18646i
$766$	424.234			0.553830
$767$			1066.33i			1.39026i
$768$	1054.47			1.37301
$769$		−	74.1441i		−	0.0964163i	−0.998837	−	0.0482081i	$-0.984649\pi$
$769$		−	74.1441i		−	0.0964163i	0.998837	−	0.0482081i	$-0.0153511\pi$
$770$	1080.21	−	332.545i	1.40287	−	0.431876i
$771$	−429.982			−0.557694
$772$		−	491.548i		−	0.636720i
$773$	−389.758			−0.504215			−0.252108	−	0.967699i	$-0.581124\pi$
$773$	−389.758			−0.504215			−0.252108	+	0.967699i	$0.581124\pi$
$774$	−484.820			−0.626383
$775$		−	2902.35i		−	3.74497i
$776$	674.006			0.868564
$777$	−486.387	+	149.735i	−0.625980	+	0.192709i
$778$	0.353704			0.000454633
$779$	2.78909	+	13.3734i	0.00358034	+	0.0171673i
$780$			1263.34i			1.61967i
$781$	466.666			0.597524
$782$	−287.429			−0.367556
$783$		−	67.4169i		−	0.0861007i
$784$	61.1183	−	41.5704i	0.0779570	−	0.0530235i
$785$			235.697i			0.300251i
$786$		−	687.878i		−	0.875163i
$787$			939.917i			1.19430i	0.802128	+	0.597152i	$0.203701\pi$
$787$			939.917i			1.19430i	−0.802128	+	0.597152i	$0.796299\pi$
$788$	499.123			0.633404
$789$			1092.63i			1.38483i
$790$	407.366			0.515653
$791$	468.563	−	144.248i	0.592368	−	0.182361i
$792$		−	1262.51i		−	1.59408i
$793$		−	420.868i		−	0.530729i
$794$	−435.601			−0.548615
$795$	−1136.87			−1.43003
$796$	45.4754			0.0571299
$797$		−	1061.91i		−	1.33238i	−0.745781	−	0.666191i	$-0.767924\pi$
$797$		−	1061.91i		−	1.33238i	0.745781	−	0.666191i	$-0.232076\pi$
$798$	−11.5366	+	3.55156i	−0.0144569	+	0.00445058i
$799$	1383.83			1.73195
$800$	−1863.85			−2.32981
$801$	−1513.03			−1.88892
$802$	200.982			0.250600
$803$	−305.089			−0.379936
$804$		−	735.330i		−	0.914589i
$805$	−264.809	−	860.185i	−0.328955	−	1.06855i
$806$		−	710.388i		−	0.881374i
$807$			288.410i			0.357385i
$808$	419.673			0.519398
$809$			527.236i			0.651714i	0.945419	+	0.325857i	$0.105653\pi$
$809$			527.236i			0.651714i	−0.945419	+	0.325857i	$0.894347\pi$
$810$			668.524i			0.825339i
$811$			98.1048i			0.120968i	0.998169	+	0.0604838i	$0.0192644\pi$
$811$			98.1048i			0.120968i	−0.998169	+	0.0604838i	$0.980736\pi$
$812$	−49.7146	−	161.489i	−0.0612249	−	0.198878i
$813$		−	1151.82i		−	1.41676i
$814$			292.509i			0.359348i
$815$		−	845.515i		−	1.03744i
$816$	115.948			0.142093
$817$	−12.9818			−0.0158896
$818$		−	154.140i		−	0.188435i
$819$	−851.262	+	262.062i	−1.03939	+	0.319978i
$820$	−958.165	+	199.830i	−1.16849	+	0.243696i
$821$	1035.05			1.26072			0.630358	−	0.776304i	$-0.282908\pi$
$821$	1035.05			1.26072			0.630358	+	0.776304i	$0.282908\pi$
$822$		−	147.171i		−	0.179041i
$823$		−	1117.99i		−	1.35843i	−0.733939	−	0.679216i	$-0.762320\pi$
$823$		−	1117.99i		−	1.35843i	0.733939	−	0.679216i	$-0.237680\pi$
$824$		−	1023.77i		−	1.24244i
$825$			3857.23i			4.67543i
$826$	−214.777	−	697.666i	−0.260021	−	0.844631i
$827$		−	1053.80i		−	1.27425i	−0.770760	−	0.637125i	$-0.780123\pi$
$827$		−	1053.80i		−	1.27425i	0.770760	−	0.637125i	$-0.219877\pi$
$828$	−399.511			−0.482501
$829$			317.668i			0.383194i	0.981474	+	0.191597i	$0.0613666\pi$
$829$			317.668i			0.383194i	−0.981474	+	0.191597i	$0.938633\pi$
$830$	−1195.61			−1.44050
$831$	80.4685			0.0968333
$832$	−384.186			−0.461762
$833$	−702.335	+	477.703i	−0.843140	+	0.573472i
$834$			12.9713i			0.0155532i
$835$		−	2133.77i		−	2.55541i
$836$		−	13.4338i		−	0.0160692i
$837$		−	375.701i		−	0.448866i
$838$			682.927i			0.814948i
$839$	−1629.21			−1.94185			−0.970925	−	0.239382i	$-0.923055\pi$
$839$	−1629.21			−1.94185			−0.970925	+	0.239382i	$0.923055\pi$
$840$	−640.337	−	2080.02i	−0.762306	−	2.47621i
$841$	757.256			0.900423
$842$			509.648i			0.605283i
$843$			870.070i			1.03211i
$844$			195.394i			0.231509i
$845$			240.406i			0.284505i
$846$	−993.382			−1.17421
$847$	−753.542	+	231.979i	−0.889660	+	0.273883i
$848$			42.7340i			0.0503939i
$849$			1351.19i			1.59151i
$850$	1151.45			1.35465
$851$	232.928			0.273711
$852$		−	357.088i		−	0.419117i
$853$			937.070i			1.09856i	0.835639	+	0.549279i	$0.185098\pi$
$853$			937.070i			1.09856i	−0.835639	+	0.549279i	$0.814902\pi$
$854$	84.7704	+	275.362i	0.0992627	+	0.322437i
$855$		−	32.1507i		−	0.0376031i
$856$	1413.44			1.65122
$857$		−	497.757i		−	0.580813i	−0.956903	−	0.290407i	$-0.906209\pi$
$857$		−	497.757i		−	0.580813i	0.956903	−	0.290407i	$-0.0937905\pi$
$858$			944.105i			1.10036i
$859$		−	450.744i		−	0.524731i	−0.964969	−	0.262365i	$-0.915497\pi$
$859$		−	450.744i		−	0.524731i	0.964969	−	0.262365i	$-0.0845026\pi$
$860$		−	930.109i		−	1.08152i
$861$	−614.857	−	1114.20i	−0.714120	−	1.29408i
$862$	−128.915			−0.149554
$863$	1035.10			1.19942			0.599710	−	0.800218i	$-0.295283\pi$
$863$	1035.10			1.19942			0.599710	+	0.800218i	$0.295283\pi$
$864$	−241.269			−0.279247
$865$	−2050.61			−2.37064
$866$			81.8448i			0.0945090i
$867$	−50.9445			−0.0587595
$868$	−277.050	−	899.947i	−0.319182	−	1.03680i
$869$	−589.452			−0.678311
$870$	−428.637			−0.492687
$871$			750.338i			0.861467i
$872$		−	83.3470i		−	0.0955814i
$873$	−927.529			−1.06246
$874$	5.52482			0.00632130
$875$	594.833	+	1932.21i	0.679809	+	2.20824i
$876$			233.450i			0.266496i
$877$	207.891			0.237048			0.118524	−	0.992951i	$-0.462184\pi$
$877$	207.891			0.237048			0.118524	+	0.992951i	$0.462184\pi$
$878$	−747.147			−0.850965
$879$	2343.60			2.66621
$880$	208.681			0.237137
$881$		−	440.754i		−	0.500288i	−0.968209	−	0.250144i	$-0.919522\pi$
$881$		−	440.754i		−	0.500288i	0.968209	−	0.250144i	$-0.0804780\pi$
$882$	504.171	−	342.919i	0.571623	−	0.388797i
$883$			377.705i			0.427752i	0.976861	+	0.213876i	$0.0686089\pi$
$883$			377.705i			0.427752i	−0.976861	+	0.213876i	$0.931391\pi$
$884$	−545.702			−0.617310
$885$	3585.57			4.05149
$886$	−143.131			−0.161547
$887$	−1273.12			−1.43531			−0.717655	−	0.696399i	$-0.754784\pi$
$887$	−1273.12			−1.43531			−0.717655	+	0.696399i	$0.754784\pi$
$888$	563.245			0.634285
$889$	−704.994	+	217.033i	−0.793019	+	0.244132i
$890$			1499.12i			1.68440i
$891$		−	967.344i		−	1.08568i
$892$		−	1109.42i		−	1.24375i
$893$	−26.5993			−0.0297864
$894$			1273.93i			1.42498i
$895$	2486.09			2.77776
$896$	−625.047	+	192.422i	−0.697598	+	0.214756i
$897$	751.801			0.838128
$898$	−235.037			−0.261733
$899$	−466.690			−0.519122
$900$	1600.46			1.77829
$901$		−	491.074i		−	0.545032i
$902$	−716.044	+	149.335i	−0.793840	+	0.165560i
$903$	1155.78	−	355.809i	1.27994	−	0.394030i
$904$	−542.605			−0.600227
$905$			887.730i			0.980917i
$906$		−	727.326i		−	0.802788i
$907$	1470.59			1.62138			0.810689	−	0.585477i	$-0.199093\pi$
$907$	1470.59			1.62138			0.810689	+	0.585477i	$0.199093\pi$
$908$	−222.403			−0.244938
$909$	−577.531			−0.635348
$910$	259.653	+	843.437i	0.285333	+	0.926854i
$911$	−277.146			−0.304222			−0.152111	−	0.988363i	$-0.548607\pi$
$911$	−277.146			−0.304222			−0.152111	+	0.988363i	$0.548607\pi$
$912$	−2.22870			−0.00244375
$913$	1730.03			1.89489
$914$			4.22810i			0.00462594i
$915$	−1415.19			−1.54665
$916$	372.223			0.406357
$917$	273.746	+	889.216i	0.298524	+	0.969702i
$918$	149.052			0.162366
$919$			1173.84i			1.27730i	0.769496	+	0.638651i	$0.220507\pi$
$919$			1173.84i			1.27730i	−0.769496	+	0.638651i	$0.779493\pi$
$920$			996.111i			1.08273i
$921$			1709.39i			1.85602i
$922$			208.889i			0.226560i
$923$			364.376i			0.394773i
$924$	368.199	+	1196.03i	0.398484	+	1.29440i
$925$	−933.119			−1.00878
$926$		−	340.775i		−	0.368007i
$927$			1408.85i			1.51980i
$928$			299.701i			0.322954i
$929$	−55.5029			−0.0597448			−0.0298724	−	0.999554i	$-0.509510\pi$
$929$	−55.5029			−0.0597448			−0.0298724	+	0.999554i	$0.509510\pi$
$930$	−2388.71			−2.56851
$931$	13.4999	−	9.18216i	0.0145005	−	0.00986269i
$932$		−	526.352i		−	0.564755i
$933$	−1642.63			−1.76059
$934$		−	732.903i		−	0.784693i
$935$	−2398.03			−2.56474
$936$	985.778			1.05318
$937$	420.521			0.448795			0.224398	−	0.974498i	$-0.427959\pi$
$937$	420.521			0.448795			0.224398	+	0.974498i	$0.427959\pi$
$938$	−151.131	−	490.923i	−0.161121	−	0.523373i
$939$	115.093			0.122570
$940$		−	1905.77i		−	2.02741i
$941$			1591.40i			1.69118i	0.533834	+	0.845589i	$0.320751\pi$
$941$			1591.40i			1.69118i	−0.533834	+	0.845589i	$0.679249\pi$
$942$	134.779			0.143078
$943$	118.917	+	570.194i	0.126105	+	0.604659i
$944$		−	134.778i		−	0.142774i
$945$	137.322	+	446.066i	0.145314	+	0.472028i
$946$		−	695.078i		−	0.734755i
$947$	−742.202			−0.783740			−0.391870	−	0.920021i	$-0.628172\pi$
$947$	−742.202			−0.783740			−0.391870	+	0.920021i	$0.628172\pi$
$948$			451.042i			0.475783i
$949$		−	238.215i		−	0.251017i
$950$	−22.1327			−0.0232975
$951$			2135.58i			2.24562i
$952$	898.467	−	276.594i	0.943768	−	0.290540i
$953$	−721.199			−0.756767			−0.378384	−	0.925649i	$-0.623520\pi$
$953$	−721.199			−0.756767			−0.378384	+	0.925649i	$0.623520\pi$
$954$			352.518i			0.369515i
$955$	−2641.44			−2.76591
$956$		−	161.384i		−	0.168812i
$957$	620.231			0.648100
$958$	351.882			0.367309
$959$	58.5680	+	190.248i	0.0610720	+	0.198381i
$960$			1291.84i			1.34567i
$961$	−1639.77			−1.70632
$962$	−228.393			−0.237414
$963$	−1945.10			−2.01984
$964$		−	551.778i		−	0.572384i
$965$	1686.59			1.74776
$966$	−491.881	+	151.426i	−0.509193	+	0.156756i
$967$			1694.31i			1.75213i	0.482189	+	0.876067i	$0.339842\pi$
$967$			1694.31i			1.75213i	−0.482189	+	0.876067i	$0.660158\pi$
$968$	872.616			0.901463
$969$	25.6108			0.0264302
$970$			919.002i			0.947425i
$971$	−833.947			−0.858854			−0.429427	−	0.903102i	$-0.641284\pi$
$971$	−833.947			−0.858854			−0.429427	+	0.903102i	$0.641284\pi$
$972$	−915.090			−0.941451
$973$	−5.16204	−	16.7680i	−0.00530529	−	0.0172333i
$974$	12.4511			0.0127835
$975$	−3011.75			−3.08897
$976$			53.1956i			0.0545037i
$977$		−	1051.47i		−	1.07623i	−0.842872	−	0.538114i	$-0.819137\pi$
$977$		−	1051.47i		−	1.07623i	0.842872	−	0.538114i	$-0.180863\pi$
$978$	−483.492			−0.494368
$979$		−	2169.20i		−	2.21573i
$980$	657.877	+	967.234i	0.671303	+	0.986974i
$981$			114.697i			0.116919i
$982$	−925.766			−0.942735
$983$		−	983.670i		−	1.00068i	−0.865829	−	0.500341i	$-0.833208\pi$
$983$		−	983.670i		−	1.00068i	0.865829	−	0.500341i	$-0.166792\pi$
$984$	287.554	+	1378.79i	0.292230	+	1.40121i
$985$			1712.58i			1.73866i
$986$		−	185.150i		−	0.187779i
$987$	2368.16	−	729.042i	2.39935	−	0.738644i
$988$	10.4892			0.0106166
$989$	−553.498			−0.559654
$990$	1721.43			1.73882
$991$		−	1010.76i		−	1.01994i	−0.860192	−	0.509970i	$-0.829657\pi$
$991$		−	1010.76i		−	1.01994i	0.860192	−	0.509970i	$-0.170343\pi$
$992$			1670.17i			1.68364i
$993$			946.694i			0.953367i
$994$	−73.3918	−	238.400i	−0.0738348	−	0.239839i
$995$			156.034i			0.156818i
$996$		−	1323.80i		−	1.32912i
$997$	1395.18			1.39938			0.699691	−	0.714445i	$-0.253321\pi$
$997$	1395.18			1.39938			0.699691	+	0.714445i	$0.253321\pi$
$998$		−	386.096i		−	0.386870i
$999$	−120.789			−0.120910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.d.286.17	✓	32
7.6	odd	2	inner	287.3.d.d.286.20	yes	32
41.40	even	2	inner	287.3.d.d.286.19	yes	32
287.286	odd	2	inner	287.3.d.d.286.18	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.d.286.17	✓	32	1.1	even	1	trivial
287.3.d.d.286.18	yes	32	287.286	odd	2	inner
287.3.d.d.286.19	yes	32	41.40	even	2	inner
287.3.d.d.286.20	yes	32	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.16717 q^{2} -4.43412 q^{3} -2.63772 q^{4} -9.05049i q^{5} -5.17535 q^{6} +(6.69015 - 2.05957i) q^{7} -7.74732 q^{8} +10.6614 q^{9} +O(q^{10})\)	\(q+1.16717 q^{2} -4.43412 q^{3} -2.63772 q^{4} -9.05049i q^{5} -5.17535 q^{6} +(6.69015 - 2.05957i) q^{7} -7.74732 q^{8} +10.6614 q^{9} -10.5634i q^{10} +15.2851i q^{11} +11.6960 q^{12} -11.9347 q^{13} +(7.80852 - 2.40386i) q^{14} +40.1310i q^{15} +1.50849 q^{16} -17.3346 q^{17} +12.4437 q^{18} +0.333198 q^{19} +23.8727i q^{20} +(-29.6650 + 9.13239i) q^{21} +17.8403i q^{22} +14.2064 q^{23} +34.3526 q^{24} -56.9114 q^{25} -13.9298 q^{26} -7.36701 q^{27} +(-17.6468 + 5.43258i) q^{28} +9.15119i q^{29} +46.8395i q^{30} +50.9978i q^{31} +32.7499 q^{32} -67.7760i q^{33} -20.2324 q^{34} +(-18.6401 - 60.5492i) q^{35} -28.1219 q^{36} +16.3960 q^{37} +0.388897 q^{38} +52.9199 q^{39} +70.1171i q^{40} +(8.37067 + 40.1364i) q^{41} +(-34.6239 + 10.6590i) q^{42} -38.9612 q^{43} -40.3179i q^{44} -96.4912i q^{45} +16.5812 q^{46} -79.8303 q^{47} -6.68881 q^{48} +(40.5163 - 27.5577i) q^{49} -66.4250 q^{50} +76.8638 q^{51} +31.4805 q^{52} +28.3291i q^{53} -8.59852 q^{54} +138.338 q^{55} +(-51.8308 + 15.9562i) q^{56} -1.47744 q^{57} +10.6810i q^{58} -89.3467i q^{59} -105.854i q^{60} +35.2643i q^{61} +59.5229i q^{62} +(71.3266 - 21.9580i) q^{63} +32.1907 q^{64} +108.015i q^{65} -79.1059i q^{66} -62.8702i q^{67} +45.7240 q^{68} -62.9929 q^{69} +(-21.7561 - 70.6709i) q^{70} -30.5308i q^{71} -82.5976 q^{72} +19.9599i q^{73} +19.1369 q^{74} +252.352 q^{75} -0.878884 q^{76} +(31.4808 + 102.260i) q^{77} +61.7663 q^{78} +38.5638i q^{79} -13.6525i q^{80} -63.2867 q^{81} +(9.76995 + 46.8458i) q^{82} -113.184i q^{83} +(78.2480 - 24.0887i) q^{84} +156.887i q^{85} -45.4742 q^{86} -40.5775i q^{87} -118.419i q^{88} -141.916 q^{89} -112.621i q^{90} +(-79.8450 + 24.5804i) q^{91} -37.4725 q^{92} -226.130i q^{93} -93.1752 q^{94} -3.01560i q^{95} -145.217 q^{96} -86.9985 q^{97} +(47.2893 - 32.1644i) q^{98} +162.961i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9	\( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9} - 92 q^{16} - 48 q^{18} - 72 q^{21} + 140 q^{23} - 500 q^{25} + 92 q^{32} - 284 q^{36} + 312 q^{37} + 140 q^{39} + 8 q^{42} - 120 q^{43} - 344 q^{46} - 552 q^{49} + 416 q^{50} - 364 q^{51} - 316 q^{57} - 320 q^{64} + 972 q^{72} + 680 q^{74} + 428 q^{77} + 1144 q^{78} - 240 q^{81} + 640 q^{84} + 260 q^{86} - 160 q^{91} + 676 q^{92} + 532 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9 - 92 * q^16 - 48 * q^18 - 72 * q^21 + 140 * q^23 - 500 * q^25 + 92 * q^32 - 284 * q^36 + 312 * q^37 + 140 * q^39 + 8 * q^42 - 120 * q^43 - 344 * q^46 - 552 * q^49 + 416 * q^50 - 364 * q^51 - 316 * q^57 - 320 * q^64 + 972 * q^72 + 680 * q^74 + 428 * q^77 + 1144 * q^78 - 240 * q^81 + 640 * q^84 + 260 * q^86 - 160 * q^91 + 676 * q^92 + 532 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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