LMFDB - Embedded newform 483.3.b.a.323.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(323,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("483.323");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.b (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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.16
Character	$\chi$	$=$	483.323
Dual form			483.3.b.a.323.73

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.84584i q^{2} +(-0.677666 + 2.92246i) q^{3} -4.09879 q^{4} -7.26917i q^{5} +(8.31684 + 1.92853i) q^{6} +2.64575 q^{7} +0.281139i q^{8} +(-8.08154 - 3.96090i) q^{9} -20.6869 q^{10} -5.51617i q^{11} +(2.77761 - 11.9785i) q^{12} +17.3116 q^{13} -7.52938i q^{14} +(21.2438 + 4.92607i) q^{15} -15.5951 q^{16} +6.88093i q^{17} +(-11.2721 + 22.9987i) q^{18} -3.01757 q^{19} +29.7948i q^{20} +(-1.79294 + 7.73210i) q^{21} -15.6981 q^{22} +4.79583i q^{23} +(-0.821618 - 0.190519i) q^{24} -27.8408 q^{25} -49.2661i q^{26} +(17.0522 - 20.9338i) q^{27} -10.8444 q^{28} -56.0064i q^{29} +(14.0188 - 60.4565i) q^{30} -56.7937 q^{31} +45.5056i q^{32} +(16.1208 + 3.73812i) q^{33} +19.5820 q^{34} -19.2324i q^{35} +(33.1245 + 16.2349i) q^{36} -20.7015 q^{37} +8.58751i q^{38} +(-11.7315 + 50.5925i) q^{39} +2.04365 q^{40} -25.4386i q^{41} +(22.0043 + 5.10241i) q^{42} -60.2734 q^{43} +22.6096i q^{44} +(-28.7925 + 58.7460i) q^{45} +13.6482 q^{46} +70.4723i q^{47} +(10.5683 - 45.5760i) q^{48} +7.00000 q^{49} +79.2304i q^{50} +(-20.1092 - 4.66298i) q^{51} -70.9567 q^{52} -12.5579i q^{53} +(-59.5742 - 48.5277i) q^{54} -40.0980 q^{55} +0.743825i q^{56} +(2.04491 - 8.81873i) q^{57} -159.385 q^{58} -113.353i q^{59} +(-87.0741 - 20.1909i) q^{60} +10.7676 q^{61} +161.626i q^{62} +(-21.3817 - 10.4796i) q^{63} +67.1213 q^{64} -125.841i q^{65} +(10.6381 - 45.8771i) q^{66} -17.2382 q^{67} -28.2035i q^{68} +(-14.0156 - 3.24997i) q^{69} -54.7323 q^{70} +118.800i q^{71} +(1.11357 - 2.27204i) q^{72} +6.64155 q^{73} +58.9131i q^{74} +(18.8668 - 81.3636i) q^{75} +12.3684 q^{76} -14.5944i q^{77} +(143.978 + 33.3860i) q^{78} +104.213 q^{79} +113.363i q^{80} +(49.6225 + 64.0204i) q^{81} -72.3940 q^{82} -54.8590i q^{83} +(7.34887 - 31.6923i) q^{84} +50.0187 q^{85} +171.528i q^{86} +(163.676 + 37.9536i) q^{87} +1.55081 q^{88} -119.578i q^{89} +(167.182 + 81.9387i) q^{90} +45.8023 q^{91} -19.6571i q^{92} +(38.4872 - 165.977i) q^{93} +200.553 q^{94} +21.9352i q^{95} +(-132.988 - 30.8376i) q^{96} +92.4684 q^{97} -19.9209i q^{98} +(-21.8490 + 44.5791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30}+ \cdots - 248 q^{99}+O(q^{100}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	2.84584i		−	1.42292i	−0.702727	−	0.711459i	$-0.748035\pi$
$2$		−	2.84584i		−	1.42292i	0.702727	−	0.711459i	$-0.251965\pi$
$3$	−0.677666	+	2.92246i	−0.225889	+	0.974153i
$3$	−0.677666	+	2.92246i	−0.225889	+	0.974153i
$4$	−4.09879			−1.02470
$5$		−	7.26917i		−	1.45383i	−0.686726	−	0.726917i	$-0.740953\pi$
$5$		−	7.26917i		−	1.45383i	0.686726	−	0.726917i	$-0.259047\pi$
$6$	8.31684	+	1.92853i	1.38614	+	0.321421i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$			0.281139i			0.0351424i
$9$	−8.08154	−	3.96090i	−0.897949	−	0.440101i
$10$	−20.6869			−2.06869
$11$		−	5.51617i		−	0.501470i	−0.968056	−	0.250735i	$-0.919328\pi$
$11$		−	5.51617i		−	0.501470i	0.968056	−	0.250735i	$-0.0806723\pi$
$12$	2.77761	−	11.9785i	0.231468	−	0.998212i
$13$	17.3116			1.33166			0.665832	−	0.746102i	$-0.268077\pi$
$13$	17.3116			1.33166			0.665832	+	0.746102i	$0.268077\pi$
$14$		−	7.52938i		−	0.537813i
$15$	21.2438	+	4.92607i	1.41626	+	0.328405i
$16$	−15.5951			−0.974693
$17$			6.88093i			0.404761i	0.979307	+	0.202380i	$0.0648677\pi$
$17$			6.88093i			0.404761i	−0.979307	+	0.202380i	$0.935132\pi$
$18$	−11.2721	+	22.9987i	−0.626227	+	1.27771i
$19$	−3.01757			−0.158819			−0.0794097	−	0.996842i	$-0.525304\pi$
$19$	−3.01757			−0.158819			−0.0794097	+	0.996842i	$0.525304\pi$
$20$			29.7948i			1.48974i
$21$	−1.79294	+	7.73210i	−0.0853779	+	0.368195i
$22$	−15.6981			−0.713551
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	−0.821618	−	0.190519i	−0.0342341	−	0.00793828i
$25$	−27.8408			−1.11363
$26$		−	49.2661i		−	1.89485i
$27$	17.0522	−	20.9338i	0.631562	−	0.775326i
$28$	−10.8444			−0.387299
$29$		−	56.0064i		−	1.93125i	−0.259931	−	0.965627i	$-0.583700\pi$
$29$		−	56.0064i		−	1.93125i	0.259931	−	0.965627i	$-0.416300\pi$
$30$	14.0188	−	60.4565i	0.467293	−	2.01522i
$31$	−56.7937			−1.83206			−0.916028	−	0.401115i	$-0.868623\pi$
$31$	−56.7937			−1.83206			−0.916028	+	0.401115i	$0.868623\pi$
$32$			45.5056i			1.42205i
$33$	16.1208	+	3.73812i	0.488508	+	0.113276i
$34$	19.5820			0.575942
$35$		−	19.2324i		−	0.549497i
$36$	33.1245	+	16.2349i	0.920126	+	0.450970i
$37$	−20.7015			−0.559500			−0.279750	−	0.960073i	$-0.590252\pi$
$37$	−20.7015			−0.559500			−0.279750	+	0.960073i	$0.590252\pi$
$38$			8.58751i			0.225987i
$39$	−11.7315	+	50.5925i	−0.300808	+	1.29724i
$40$	2.04365			0.0510912
$41$		−	25.4386i		−	0.620453i	−0.950663	−	0.310226i	$-0.899595\pi$
$41$		−	25.4386i		−	0.620453i	0.950663	−	0.310226i	$-0.100405\pi$
$42$	22.0043	+	5.10241i	0.523912	+	0.121486i
$43$	−60.2734			−1.40171			−0.700854	−	0.713305i	$-0.747197\pi$
$43$	−60.2734			−1.40171			−0.700854	+	0.713305i	$0.747197\pi$
$44$			22.6096i			0.513855i
$45$	−28.7925	+	58.7460i	−0.639833	+	1.30547i
$46$	13.6482			0.296699
$47$			70.4723i			1.49941i	0.661771	+	0.749706i	$0.269805\pi$
$47$			70.4723i			1.49941i	−0.661771	+	0.749706i	$0.730195\pi$
$48$	10.5683	−	45.5760i	0.220172	−	0.949500i
$49$	7.00000			0.142857
$50$			79.2304i			1.58461i
$51$	−20.1092	−	4.66298i	−0.394299	−	0.0914309i
$52$	−70.9567			−1.36455
$53$		−	12.5579i		−	0.236942i	−0.992957	−	0.118471i	$-0.962201\pi$
$53$		−	12.5579i		−	0.236942i	0.992957	−	0.118471i	$-0.0377993\pi$
$54$	−59.5742	−	48.5277i	−1.10323	−	0.898661i
$55$	−40.0980			−0.729054
$56$			0.743825i			0.0132826i
$57$	2.04491	−	8.81873i	0.0358755	−	0.154715i
$58$	−159.385			−2.74802
$59$		−	113.353i		−	1.92123i	−0.277876	−	0.960617i	$-0.589630\pi$
$59$		−	113.353i		−	1.92123i	0.277876	−	0.960617i	$-0.410370\pi$
$60$	−87.0741	−	20.1909i	−1.45123	−	0.336515i
$61$	10.7676			0.176518			0.0882589	−	0.996098i	$-0.471870\pi$
$61$	10.7676			0.176518			0.0882589	+	0.996098i	$0.471870\pi$
$62$			161.626i			2.60687i
$63$	−21.3817	−	10.4796i	−0.339393	−	0.166342i
$64$	67.1213			1.04877
$65$		−	125.841i		−	1.93602i
$66$	10.6381	−	45.8771i	0.161183	−	0.695108i
$67$	−17.2382			−0.257286			−0.128643	−	0.991691i	$-0.541062\pi$
$67$	−17.2382			−0.257286			−0.128643	+	0.991691i	$0.541062\pi$
$68$		−	28.2035i		−	0.414757i
$69$	−14.0156	−	3.24997i	−0.203125	−	0.0471011i
$70$	−54.7323			−0.781890
$71$			118.800i			1.67324i	0.547785	+	0.836619i	$0.315471\pi$
$71$			118.800i			1.67324i	−0.547785	+	0.836619i	$0.684529\pi$
$72$	1.11357	−	2.27204i	0.0154662	−	0.0315561i
$73$	6.64155			0.0909801			0.0454901	−	0.998965i	$-0.485515\pi$
$73$	6.64155			0.0909801			0.0454901	+	0.998965i	$0.485515\pi$
$74$			58.9131i			0.796122i
$75$	18.8668	−	81.3636i	0.251557	−	1.08485i
$76$	12.3684			0.162742
$77$		−	14.5944i		−	0.189538i
$78$	143.978	+	33.3860i	1.84587	+	0.428025i
$79$	104.213			1.31915			0.659574	−	0.751640i	$-0.270737\pi$
$79$	104.213			1.31915			0.659574	+	0.751640i	$0.270737\pi$
$80$			113.363i			1.41704i
$81$	49.6225	+	64.0204i	0.612623	+	0.790375i
$82$	−72.3940			−0.882854
$83$		−	54.8590i		−	0.660952i	−0.943814	−	0.330476i	$-0.892791\pi$
$83$		−	54.8590i		−	0.660952i	0.943814	−	0.330476i	$-0.107209\pi$
$84$	7.34887	−	31.6923i	0.0874865	−	0.377289i
$85$	50.0187			0.588455
$86$			171.528i			1.99452i
$87$	163.676	+	37.9536i	1.88134	+	0.436249i
$88$	1.55081			0.0176229
$89$		−	119.578i		−	1.34357i	−0.740745	−	0.671786i	$-0.765527\pi$
$89$		−	119.578i		−	1.34357i	0.740745	−	0.671786i	$-0.234473\pi$
$90$	167.182	+	81.9387i	1.85757	+	0.910430i
$91$	45.8023			0.503322
$92$		−	19.6571i		−	0.213664i
$93$	38.4872	−	165.977i	0.413841	−	1.78470i
$94$	200.553			2.13354
$95$			21.9352i			0.230897i
$96$	−132.988	−	30.8376i	−1.38530	−	0.321225i
$97$	92.4684			0.953282			0.476641	−	0.879098i	$-0.341854\pi$
$97$	92.4684			0.953282			0.476641	+	0.879098i	$0.341854\pi$
$98$		−	19.9209i		−	0.203274i
$99$	−21.8490	+	44.5791i	−0.220697	+	0.450294i
$100$	114.114			1.14114
$101$		−	21.3996i		−	0.211878i	−0.994373	−	0.105939i	$-0.966215\pi$
$101$		−	21.3996i		−	0.211878i	0.994373	−	0.105939i	$-0.0337848\pi$
$102$	−13.2701	+	57.2276i	−0.130099	+	0.561055i
$103$	57.7628			0.560804			0.280402	−	0.959883i	$-0.409532\pi$
$103$	57.7628			0.560804			0.280402	+	0.959883i	$0.409532\pi$
$104$			4.86698i			0.0467979i
$105$	56.2059	+	13.0332i	0.535295	+	0.124125i
$106$	−35.7379			−0.337150
$107$			59.9692i			0.560460i	0.959933	+	0.280230i	$0.0904107\pi$
$107$			59.9692i			0.560460i	−0.959933	+	0.280230i	$0.909589\pi$
$108$	−69.8932	+	85.8032i	−0.647160	+	0.794474i
$109$	−69.0522			−0.633506			−0.316753	−	0.948508i	$-0.602593\pi$
$109$	−69.0522			−0.633506			−0.316753	+	0.948508i	$0.602593\pi$
$110$			114.112i			1.03738i
$111$	14.0287	−	60.4992i	0.126385	−	0.545038i
$112$	−41.2607			−0.368399
$113$			186.025i			1.64624i	0.567866	+	0.823121i	$0.307769\pi$
$113$			186.025i			1.64624i	−0.567866	+	0.823121i	$0.692231\pi$
$114$	−25.0967	−	5.81947i	−0.220146	−	0.0510480i
$115$	34.8617			0.303145
$116$			229.558i			1.97895i
$117$	−139.905	−	68.5697i	−1.19577	−	0.586066i
$118$	−322.584			−2.73376
$119$			18.2052i			0.152985i
$120$	−1.38491	+	5.97248i	−0.0115409	+	0.0497707i
$121$	90.5719			0.748528
$122$		−	30.6428i		−	0.251171i
$123$	74.3432	+	17.2389i	0.604416	+	0.140153i
$124$	232.785			1.87730
$125$			20.6503i			0.165202i
$126$	−29.8231	+	60.8489i	−0.236692	+	0.482928i
$127$	64.0779			0.504550			0.252275	−	0.967656i	$-0.418821\pi$
$127$	64.0779			0.504550			0.252275	+	0.967656i	$0.418821\pi$
$128$		−	8.99372i		−	0.0702634i
$129$	40.8453	−	176.147i	0.316630	−	1.36548i
$130$	−358.123			−2.75480
$131$			43.2540i			0.330183i	0.986278	+	0.165092i	$0.0527920\pi$
$131$			43.2540i			0.330183i	−0.986278	+	0.165092i	$0.947208\pi$
$132$	−66.0757	−	15.3218i	−0.500573	−	0.116074i
$133$	−7.98374			−0.0600281
$134$			49.0570i			0.366097i
$135$	−152.171	−	123.955i	−1.12719	−	0.918186i
$136$	−1.93450			−0.0142243
$137$		−	183.776i		−	1.34143i	−0.741716	−	0.670714i	$-0.765988\pi$
$137$		−	183.776i		−	1.34143i	0.741716	−	0.670714i	$-0.234012\pi$
$138$	−9.24890	+	39.8862i	−0.0670210	+	0.289030i
$139$	81.4323			0.585844			0.292922	−	0.956136i	$-0.405372\pi$
$139$	81.4323			0.585844			0.292922	+	0.956136i	$0.405372\pi$
$140$			78.8296i			0.563069i
$141$	−205.953	−	47.7567i	−1.46066	−	0.338700i
$142$	338.085			2.38088
$143$		−	95.4939i		−	0.667789i
$144$	126.032	+	61.7706i	0.875224	+	0.428963i
$145$	−407.120			−2.80772
$146$		−	18.9008i		−	0.129457i
$147$	−4.74366	+	20.4572i	−0.0322698	+	0.139165i
$148$	84.8510			0.573318
$149$		−	223.941i		−	1.50296i	−0.659755	−	0.751481i	$-0.729340\pi$
$149$		−	223.941i		−	1.50296i	0.659755	−	0.751481i	$-0.270660\pi$
$150$	−231.548	−	53.6918i	−1.54365	−	0.357945i
$151$	107.497			0.711900			0.355950	−	0.934505i	$-0.384157\pi$
$151$	107.497			0.711900			0.355950	+	0.934505i	$0.384157\pi$
$152$		−	0.848358i		−	0.00558130i
$153$	27.2547	−	55.6085i	0.178135	−	0.363454i
$154$	−41.5333			−0.269697
$155$			412.843i			2.66350i
$156$	48.0850	−	207.368i	0.308237	−	1.32928i
$157$	130.700			0.832486			0.416243	−	0.909253i	$-0.363346\pi$
$157$	130.700			0.832486			0.416243	+	0.909253i	$0.363346\pi$
$158$		−	296.572i		−	1.87704i
$159$	36.7001	+	8.51010i	0.230818	+	0.0535226i
$160$	330.788			2.06743
$161$			12.6886i			0.0788110i
$162$	182.192	−	141.217i	1.12464	−	0.871713i
$163$	96.1763			0.590039			0.295019	−	0.955491i	$-0.404674\pi$
$163$	96.1763			0.590039			0.295019	+	0.955491i	$0.404674\pi$
$164$			104.267i			0.635776i
$165$	27.1730	−	117.185i	0.164685	−	0.710210i
$166$	−156.120			−0.940481
$167$		−	172.512i		−	1.03301i	−0.856285	−	0.516503i	$-0.827233\pi$
$167$		−	172.512i		−	1.03301i	0.856285	−	0.516503i	$-0.172767\pi$
$168$	−2.17380	−	0.504065i	−0.0129393	−	0.00300039i
$169$	130.693			0.773329
$170$		−	142.345i		−	0.837323i
$171$	24.3866	+	11.9523i	0.142612	+	0.0698965i
$172$	247.048			1.43633
$173$		−	185.842i		−	1.07423i	−0.843508	−	0.537116i	$-0.819514\pi$
$173$		−	185.842i		−	1.07423i	0.843508	−	0.537116i	$-0.180486\pi$
$174$	108.010	−	465.796i	0.620746	−	2.67699i
$175$	−73.6598			−0.420913
$176$			86.0251i			0.488779i
$177$	331.269	+	76.8154i	1.87158	+	0.433985i
$178$	−340.299			−1.91179
$179$			208.522i			1.16493i	0.812857	+	0.582463i	$0.197911\pi$
$179$			208.522i			1.16493i	−0.812857	+	0.582463i	$0.802089\pi$
$180$	118.014	−	240.788i	0.655635	−	1.33771i
$181$	−239.472			−1.32305			−0.661525	−	0.749923i	$-0.730090\pi$
$181$	−239.472			−1.32305			−0.661525	+	0.749923i	$0.730090\pi$
$182$		−	130.346i		−	0.716186i
$183$	−7.29683	+	31.4678i	−0.0398734	+	0.171955i
$184$	−1.34830			−0.00732770
$185$			150.483i			0.813419i
$186$	−472.344	−	109.528i	−2.53949	−	0.588862i
$187$	37.9564			0.202975
$188$		−	288.851i		−	1.53644i
$189$	45.1158	−	55.3856i	0.238708	−	0.293046i
$190$	62.4241			0.328548
$191$		−	7.48693i		−	0.0391986i	−0.999808	−	0.0195993i	$-0.993761\pi$
$191$		−	7.48693i		−	0.0391986i	0.999808	−	0.0195993i	$-0.00623905\pi$
$192$	−45.4858	+	196.159i	−0.236905	+	1.02166i
$193$	278.704			1.44406			0.722030	−	0.691862i	$-0.243209\pi$
$193$	278.704			1.44406			0.722030	+	0.691862i	$0.243209\pi$
$194$		−	263.150i		−	1.35644i
$195$	367.766	+	85.2783i	1.88598	+	0.437325i
$196$	−28.6915			−0.146385
$197$		−	41.0263i		−	0.208255i	−0.994564	−	0.104128i	$-0.966795\pi$
$197$		−	41.0263i		−	0.208255i	0.994564	−	0.104128i	$-0.0332051\pi$
$198$	126.865	+	62.1787i	0.640732	+	0.314034i
$199$	−161.972			−0.813930			−0.406965	−	0.913444i	$-0.633413\pi$
$199$	−161.972			−0.813930			−0.406965	+	0.913444i	$0.633413\pi$
$200$		−	7.82715i		−	0.0391357i
$201$	11.6817	−	50.3778i	0.0581180	−	0.250636i
$202$	−60.8999			−0.301485
$203$		−	148.179i		−	0.729945i
$204$	82.4236	+	19.1126i	0.404037	+	0.0936890i
$205$	−184.917			−0.902035
$206$		−	164.383i		−	0.797978i
$207$	18.9958	−	38.7577i	0.0917673	−	0.187235i
$208$	−269.976			−1.29796
$209$			16.6454i			0.0796432i
$210$	37.0902	−	159.953i	0.176620	−	0.761681i
$211$	−54.1378			−0.256577			−0.128289	−	0.991737i	$-0.540948\pi$
$211$	−54.1378			−0.256577			−0.128289	+	0.991737i	$0.540948\pi$
$212$			51.4724i			0.242794i
$213$	−347.188	−	80.5067i	−1.62999	−	0.377966i
$214$	170.662			0.797488
$215$			438.138i			2.03785i
$216$	5.88531	+	4.79404i	0.0272468	+	0.0221946i
$217$	−150.262			−0.692452
$218$			196.511i			0.901428i
$219$	−4.50076	+	19.4097i	−0.0205514	+	0.0886286i
$220$	164.353			0.747059
$221$			119.120i			0.539005i
$222$	−172.171	−	39.9234i	−0.775545	−	0.179835i
$223$	29.8726			0.133958			0.0669790	−	0.997754i	$-0.478664\pi$
$223$	29.8726			0.133958			0.0669790	+	0.997754i	$0.478664\pi$
$224$			120.397i			0.537485i
$225$	224.996	+	110.275i	0.999984	+	0.490110i
$226$	529.398			2.34247
$227$		−	320.197i		−	1.41056i	−0.708930	−	0.705279i	$-0.750822\pi$
$227$		−	320.197i		−	1.41056i	0.708930	−	0.705279i	$-0.249178\pi$
$228$	−8.38164	+	36.1461i	−0.0367616	+	0.158536i
$229$	365.242			1.59494			0.797471	−	0.603357i	$-0.206170\pi$
$229$	365.242			1.59494			0.797471	+	0.603357i	$0.206170\pi$
$230$		−	99.2107i		−	0.431351i
$231$	42.6516	+	9.89014i	0.184639	+	0.0428145i
$232$	15.7456			0.0678690
$233$		−	126.020i		−	0.540859i	−0.962740	−	0.270429i	$-0.912834\pi$
$233$		−	126.020i		−	0.540859i	0.962740	−	0.270429i	$-0.0871657\pi$
$234$	−195.138	+	398.146i	−0.833924	+	1.70148i
$235$	512.275			2.17990
$236$			464.609i			1.96868i
$237$	−70.6214	+	304.557i	−0.297981	+	1.28505i
$238$	51.8091			0.217685
$239$			102.250i			0.427826i	0.976853	+	0.213913i	$0.0686209\pi$
$239$			102.250i			0.427826i	−0.976853	+	0.213913i	$0.931379\pi$
$240$	−331.300	−	76.8225i	−1.38041	−	0.320094i
$241$	−302.768			−1.25630			−0.628149	−	0.778093i	$-0.716187\pi$
$241$	−302.768			−1.25630			−0.628149	+	0.778093i	$0.716187\pi$
$242$		−	257.753i		−	1.06509i
$243$	−220.724	+	101.635i	−0.908331	+	0.418252i
$244$	−44.1341			−0.180877
$245$		−	50.8842i		−	0.207691i
$246$	49.0590	−	211.569i	0.199427	−	0.860035i
$247$	−52.2391			−0.211494
$248$		−	15.9669i		−	0.0643829i
$249$	160.323	+	37.1761i	0.643868	+	0.149302i
$250$	58.7674			0.235069
$251$		−	152.888i		−	0.609115i	−0.952494	−	0.304558i	$-0.901491\pi$
$251$		−	152.888i		−	0.609115i	0.952494	−	0.304558i	$-0.0985086\pi$
$252$	87.6392	+	42.9535i	0.347775	+	0.170451i
$253$	26.4546			0.104564
$254$		−	182.355i		−	0.717934i
$255$	−33.8960	+	146.177i	−0.132925	+	0.573245i
$256$	242.890			0.948791
$257$			279.820i			1.08879i	0.838828	+	0.544397i	$0.183241\pi$
$257$			279.820i			1.08879i	−0.838828	+	0.544397i	$0.816759\pi$
$258$	−501.285	−	116.239i	−1.94296	−	0.450539i
$259$	−54.7710			−0.211471
$260$			515.796i			1.98383i
$261$	−221.836	+	452.618i	−0.849946	+	1.73417i
$262$	123.094			0.469824
$263$			248.447i			0.944665i	0.881420	+	0.472333i	$0.156588\pi$
$263$			248.447i			0.944665i	−0.881420	+	0.472333i	$0.843412\pi$
$264$	−1.05093	+	4.53219i	−0.00398081	+	0.0171674i
$265$	−91.2858			−0.344475
$266$			22.7204i			0.0854151i
$267$	349.462	+	81.0339i	1.30885	+	0.303498i
$268$	70.6556			0.263640
$269$		−	140.499i		−	0.522299i	−0.965298	−	0.261150i	$-0.915898\pi$
$269$		−	140.499i		−	0.522299i	0.965298	−	0.261150i	$-0.0841016\pi$
$270$	−352.756	+	433.055i	−1.30650	+	1.60391i
$271$	−17.7583			−0.0655289			−0.0327644	−	0.999463i	$-0.510431\pi$
$271$	−17.7583			−0.0655289			−0.0327644	+	0.999463i	$0.510431\pi$
$272$		−	107.309i		−	0.394517i
$273$	−31.0387	+	133.855i	−0.113695	+	0.490312i
$274$	−522.995			−1.90874
$275$			153.575i			0.558453i
$276$	57.4471	+	13.3210i	0.208142	+	0.0482643i
$277$	134.723			0.486365			0.243183	−	0.969981i	$-0.421809\pi$
$277$	134.723			0.486365			0.243183	+	0.969981i	$0.421809\pi$
$278$		−	231.743i		−	0.833608i
$279$	458.980	+	224.954i	1.64509	+	0.806288i
$280$	5.40699			0.0193107
$281$			187.477i			0.667178i	0.942719	+	0.333589i	$0.108260\pi$
$281$			187.477i			0.667178i	−0.942719	+	0.333589i	$0.891740\pi$
$282$	−135.908	+	586.107i	−0.481943	+	2.07840i
$283$	462.915			1.63574			0.817871	−	0.575401i	$-0.195154\pi$
$283$	462.915			1.63574			0.817871	+	0.575401i	$0.195154\pi$
$284$		−	486.936i		−	1.71456i
$285$	−64.1048	−	14.8648i	−0.224929	−	0.0521571i
$286$	−271.760			−0.950210
$287$		−	67.3041i		−	0.234509i
$288$	180.243	−	367.755i	0.625845	−	1.27693i
$289$	241.653			0.836169
$290$			1158.60i			3.99516i
$291$	−62.6627	+	270.235i	−0.215336	+	0.928643i
$292$	−27.2223			−0.0932271
$293$		−	506.281i		−	1.72792i	−0.503561	−	0.863960i	$-0.667977\pi$
$293$		−	506.281i		−	1.72792i	0.503561	−	0.863960i	$-0.332023\pi$
$294$	58.2179	+	13.4997i	0.198020	+	0.0459173i
$295$	−823.981			−2.79315
$296$		−	5.82000i		−	0.0196622i
$297$	−115.474	−	94.0626i	−0.388802	−	0.316709i
$298$	−637.300			−2.13859
$299$			83.0237i			0.277671i
$300$	−77.3309	+	333.492i	−0.257770	+	1.11164i
$301$	−159.468			−0.529796
$302$		−	305.919i		−	1.01298i
$303$	62.5396	+	14.5018i	0.206401	+	0.0478608i
$304$	47.0593			0.154800
$305$		−	78.2714i		−	0.256628i
$306$	−158.253	−	77.5625i	−0.517166	−	0.253472i
$307$	114.144			0.371804			0.185902	−	0.982568i	$-0.440479\pi$
$307$	114.144			0.371804			0.185902	+	0.982568i	$0.440479\pi$
$308$			59.8194i			0.194219i
$309$	−39.1439	+	168.809i	−0.126679	+	0.546309i
$310$	1174.88			3.78995
$311$			184.421i			0.592993i	0.955034	+	0.296497i	$0.0958184\pi$
$311$			184.421i			0.592993i	−0.955034	+	0.296497i	$0.904182\pi$
$312$	−14.2236	−	3.29819i	−0.0455883	−	0.0105711i
$313$	231.901			0.740899			0.370449	−	0.928853i	$-0.379204\pi$
$313$	231.901			0.740899			0.370449	+	0.928853i	$0.379204\pi$
$314$		−	371.952i		−	1.18456i
$315$	−76.1777	+	155.427i	−0.241834	+	0.493420i
$316$	−427.146			−1.35173
$317$			466.836i			1.47267i	0.676617	+	0.736335i	$0.263445\pi$
$317$			466.836i			1.47267i	−0.676617	+	0.736335i	$0.736555\pi$
$318$	24.2184	−	104.442i	0.0761583	−	0.328435i
$319$	−308.941			−0.968466
$320$		−	487.916i		−	1.52474i
$321$	−175.257	−	40.6391i	−0.545973	−	0.126602i
$322$	36.1096			0.112142
$323$		−	20.7637i		−	0.0642839i
$324$	−203.392	−	262.406i	−0.627753	−	0.809895i
$325$	−481.970			−1.48298
$326$		−	273.702i		−	0.839577i
$327$	46.7944	−	201.802i	0.143102	−	0.617132i
$328$	7.15178			0.0218042
$329$			186.452i			0.566724i
$330$	−333.488	−	77.3300i	−1.01057	−	0.234333i
$331$	205.183			0.619887			0.309943	−	0.950755i	$-0.399690\pi$
$331$	205.183			0.619887			0.309943	+	0.950755i	$0.399690\pi$
$332$			224.856i			0.677276i
$333$	167.300	+	81.9966i	0.502402	+	0.246236i
$334$	−490.941			−1.46988
$335$			125.307i			0.374051i
$336$	27.9610	−	120.583i	0.0832172	−	0.358877i
$337$	153.440			0.455311			0.227655	−	0.973742i	$-0.426894\pi$
$337$	153.440			0.455311			0.227655	+	0.973742i	$0.426894\pi$
$338$		−	371.930i		−	1.10038i
$339$	−543.652	−	126.063i	−1.60369	−	0.371868i
$340$	−205.016			−0.602988
$341$			313.284i			0.918720i
$342$	34.0143	−	69.4003i	0.0994571	−	0.202925i
$343$	18.5203			0.0539949
$344$		−	16.9452i		−	0.0492594i
$345$	−23.6246	+	101.882i	−0.0684771	+	0.295310i
$346$	−528.876			−1.52854
$347$		−	58.2790i		−	0.167951i	−0.996468	−	0.0839754i	$-0.973238\pi$
$347$		−	58.2790i		−	0.167951i	0.996468	−	0.0839754i	$-0.0267617\pi$
$348$	−670.875	−	155.564i	−1.92780	−	0.447023i
$349$	−141.335			−0.404972			−0.202486	−	0.979285i	$-0.564902\pi$
$349$	−141.335			−0.404972			−0.202486	+	0.979285i	$0.564902\pi$
$350$			209.624i			0.598926i
$351$	295.201	−	362.398i	0.841028	−	1.03247i
$352$	251.017			0.713116
$353$			360.384i			1.02092i	0.859902	+	0.510459i	$0.170525\pi$
$353$			360.384i			1.02092i	−0.859902	+	0.510459i	$0.829475\pi$
$354$	218.604	−	942.738i	0.617526	−	2.66310i
$355$	863.576			2.43261
$356$			490.125i			1.37676i
$357$	−53.2041	−	12.3371i	−0.149031	−	0.0345576i
$358$	593.419			1.65760
$359$		−	480.536i		−	1.33854i	−0.743019	−	0.669270i	$-0.766607\pi$
$359$		−	480.536i		−	1.33854i	0.743019	−	0.669270i	$-0.233393\pi$
$360$	−16.5158	−	8.09470i	−0.0458773	−	0.0224853i
$361$	−351.894			−0.974776
$362$			681.498i			1.88259i
$363$	−61.3775	+	264.693i	−0.169084	+	0.729181i
$364$	−187.734			−0.515752
$365$		−	48.2785i		−	0.132270i
$366$	89.5524	+	20.7656i	0.244679	+	0.0567366i
$367$	644.449			1.75599			0.877996	−	0.478668i	$-0.158880\pi$
$367$	644.449			1.75599			0.877996	+	0.478668i	$0.158880\pi$
$368$		−	74.7914i		−	0.203237i
$369$	−100.760	+	205.583i	−0.273062	+	0.557135i
$370$	428.249			1.15743
$371$		−	33.2252i		−	0.0895558i
$372$	−157.751	+	680.306i	−0.424062	+	1.82878i
$373$	−235.497			−0.631359			−0.315679	−	0.948866i	$-0.602232\pi$
$373$	−235.497			−0.631359			−0.315679	+	0.948866i	$0.602232\pi$
$374$		−	108.018i		−	0.288817i
$375$	−60.3496	−	13.9940i	−0.160932	−	0.0373173i
$376$	−19.8126			−0.0526930
$377$		−	969.562i		−	2.57178i
$378$	−157.618	−	128.392i	−0.416980	−	0.339662i
$379$	189.548			0.500126			0.250063	−	0.968230i	$-0.419549\pi$
$379$	189.548			0.500126			0.250063	+	0.968230i	$0.419549\pi$
$380$		−	89.9079i		−	0.236600i
$381$	−43.4234	+	187.265i	−0.113972	+	0.491509i
$382$	−21.3066			−0.0557764
$383$			54.6498i			0.142689i	0.997452	+	0.0713444i	$0.0227289\pi$
$383$			54.6498i			0.142689i	−0.997452	+	0.0713444i	$0.977271\pi$
$384$	26.2838	+	6.09474i	0.0684473	+	0.0158717i
$385$	−106.089			−0.275556
$386$		−	793.145i		−	2.05478i
$387$	487.102	+	238.737i	1.25866	+	0.616892i
$388$	−379.008			−0.976826
$389$			310.164i			0.797337i	0.917095	+	0.398669i	$0.130528\pi$
$389$			310.164i			0.797337i	−0.917095	+	0.398669i	$0.869472\pi$
$390$	242.688	−	1046.60i	0.622277	−	2.68359i
$391$	−32.9998			−0.0843985
$392$			1.96798i			0.00502035i
$393$	−126.408	−	29.3118i	−0.321649	−	0.0745847i
$394$	−116.754			−0.296331
$395$		−	757.539i		−	1.91782i
$396$	89.5545	−	182.720i	0.226148	−	0.461415i
$397$	−8.12560			−0.0204675			−0.0102338	−	0.999948i	$-0.503258\pi$
$397$	−8.12560			−0.0204675			−0.0102338	+	0.999948i	$0.503258\pi$
$398$			460.946i			1.15816i
$399$	5.41031	−	23.3322i	0.0135597	−	0.0584766i
$400$	434.180			1.08545
$401$		−	383.406i		−	0.956123i	−0.878326	−	0.478062i	$-0.841340\pi$
$401$		−	383.406i		−	0.956123i	0.878326	−	0.478062i	$-0.158660\pi$
$402$	−143.367	−	33.2443i	−0.356635	−	0.0826972i
$403$	−983.192			−2.43968
$404$			87.7126i			0.217111i
$405$	465.375	−	360.714i	1.14907	−	0.890652i
$406$	−421.693			−1.03865
$407$			114.193i			0.280572i
$408$	1.31095	−	5.65350i	0.00321310	−	0.0138566i
$409$	66.9417			0.163672			0.0818358	−	0.996646i	$-0.473922\pi$
$409$	66.9417			0.163672			0.0818358	+	0.996646i	$0.473922\pi$
$410$			526.244i			1.28352i
$411$	537.077	+	124.539i	1.30676	+	0.303013i
$412$	−236.757			−0.574654
$413$		−	299.903i		−	0.726158i
$414$	−110.298	−	54.0590i	−0.266420	−	0.130577i
$415$	−398.779			−0.960914
$416$			787.777i			1.89369i
$417$	−55.1839	+	237.983i	−0.132336	+	0.570702i
$418$	47.3702			0.113326
$419$			420.328i			1.00317i	0.865109	+	0.501585i	$0.167249\pi$
$419$			420.328i			1.00317i	−0.865109	+	0.501585i	$0.832751\pi$
$420$	−230.376	−	53.4202i	−0.548515	−	0.127191i
$421$	−609.902			−1.44870			−0.724349	−	0.689433i	$-0.757860\pi$
$421$	−609.902			−1.44870			−0.724349	+	0.689433i	$0.757860\pi$
$422$			154.067i			0.365088i
$423$	279.134	−	569.525i	0.659892	−	1.34639i
$424$	3.53053			0.00832673
$425$		−	191.571i		−	0.450755i
$426$	−229.109	+	988.040i	−0.537814	+	2.31934i
$427$	28.4884			0.0667175
$428$		−	245.801i		−	0.574301i
$429$	279.077	+	64.7130i	0.650529	+	0.150846i
$430$	1246.87			2.89969
$431$		−	175.224i		−	0.406552i	−0.979122	−	0.203276i	$-0.934841\pi$
$431$		−	175.224i		−	0.406552i	0.979122	−	0.203276i	$-0.0651588\pi$
$432$	−265.930	+	326.464i	−0.615579	+	0.755704i
$433$	345.608			0.798170			0.399085	−	0.916914i	$-0.369328\pi$
$433$	345.608			0.798170			0.399085	+	0.916914i	$0.369328\pi$
$434$			427.621i			0.985303i
$435$	275.891	−	1189.79i	0.634233	−	2.73515i
$436$	283.030			0.649152
$437$		−	14.4718i		−	0.0331162i
$438$	55.2367	+	12.8084i	0.126111	+	0.0292430i
$439$	88.8618			0.202419			0.101209	−	0.994865i	$-0.467729\pi$
$439$	88.8618			0.202419			0.101209	+	0.994865i	$0.467729\pi$
$440$		−	11.2731i		−	0.0256207i
$441$	−56.5708	−	27.7263i	−0.128278	−	0.0628715i
$442$	338.997			0.766961
$443$		−	131.959i		−	0.297876i	−0.988847	−	0.148938i	$-0.952415\pi$
$443$		−	131.959i		−	0.297876i	0.988847	−	0.148938i	$-0.0475855\pi$
$444$	−57.5007	+	247.974i	−0.129506	+	0.558499i
$445$	−869.232			−1.95333
$446$		−	85.0126i		−	0.190611i
$447$	654.459	+	151.757i	1.46411	+	0.339502i
$448$	177.586			0.396398
$449$		−	528.046i		−	1.17605i	−0.808843	−	0.588025i	$-0.799906\pi$
$449$		−	528.046i		−	1.17605i	0.808843	−	0.588025i	$-0.200094\pi$
$450$	313.824	−	640.303i	0.697387	−	1.42290i
$451$	−140.323			−0.311138
$452$		−	762.479i		−	1.68690i
$453$	−72.8470	+	314.155i	−0.160810	+	0.693500i
$454$	−911.228			−2.00711
$455$		−	332.944i		−	0.731746i
$456$	2.47929	+	0.574904i	0.00543704	+	0.00126075i
$457$	−339.079			−0.741968			−0.370984	−	0.928639i	$-0.620979\pi$
$457$	−339.079			−0.741968			−0.370984	+	0.928639i	$0.620979\pi$
$458$		−	1039.42i		−	2.26947i
$459$	144.044	+	117.335i	0.313821	+	0.255631i
$460$	−142.891			−0.310632
$461$			111.834i			0.242589i	0.992617	+	0.121295i	$0.0387046\pi$
$461$			111.834i			0.242589i	−0.992617	+	0.121295i	$0.961295\pi$
$462$	28.1457	−	121.379i	0.0609215	−	0.262726i
$463$	−726.379			−1.56885			−0.784427	−	0.620221i	$-0.787043\pi$
$463$	−726.379			−1.56885			−0.784427	+	0.620221i	$0.787043\pi$
$464$			873.424i			1.88238i
$465$	−1206.52	−	279.770i	−2.59466	−	0.601656i
$466$	−358.633			−0.769598
$467$			203.969i			0.436764i	0.975863	+	0.218382i	$0.0700779\pi$
$467$			203.969i			0.436764i	−0.975863	+	0.218382i	$0.929922\pi$
$468$	573.439	+	281.053i	1.22530	+	0.600540i
$469$	−45.6079			−0.0972450
$470$		−	1457.85i		−	3.10181i
$471$	−88.5712	+	381.967i	−0.188049	+	0.810969i
$472$	31.8679			0.0675168
$473$			332.478i			0.702914i
$474$	866.720	+	200.977i	1.82852	+	0.424002i
$475$	84.0116			0.176867
$476$		−	74.6194i		−	0.156764i
$477$	−49.7408	+	101.488i	−0.104278	+	0.212762i
$478$	290.988			0.608761
$479$		−	496.057i		−	1.03561i	−0.855499	−	0.517805i	$-0.826749\pi$
$479$		−	496.057i		−	1.03561i	0.855499	−	0.517805i	$-0.173251\pi$
$480$	−224.164	+	966.715i	−0.467008	+	2.01399i
$481$	−358.376			−0.745065
$482$			861.628i			1.78761i
$483$	−37.0819	−	8.59862i	−0.0767740	−	0.0178025i
$484$	−371.235			−0.767015
$485$		−	672.168i		−	1.38591i
$486$	289.237	+	628.146i	0.595138	+	1.29248i
$487$	−823.419			−1.69080			−0.845399	−	0.534135i	$-0.820637\pi$
$487$	−823.419			−1.69080			−0.845399	+	0.534135i	$0.820637\pi$
$488$			3.02719i			0.00620327i
$489$	−65.1754	+	281.071i	−0.133283	+	0.574788i
$490$	−144.808			−0.295527
$491$		−	828.069i		−	1.68649i	−0.537526	−	0.843247i	$-0.680641\pi$
$491$		−	828.069i		−	1.68649i	0.537526	−	0.843247i	$-0.319359\pi$
$492$	−304.717	−	70.6585i	−0.619344	−	0.143615i
$493$	385.376			0.781696
$494$			148.664i			0.300939i
$495$	324.053	+	158.824i	0.654653	+	0.320857i
$496$	885.703			1.78569
$497$			314.315i			0.632424i
$498$	105.797	−	456.254i	0.212444	−	0.916172i
$499$	−164.156			−0.328970			−0.164485	−	0.986380i	$-0.552596\pi$
$499$	−164.156			−0.328970			−0.164485	+	0.986380i	$0.552596\pi$
$500$		−	84.6412i		−	0.169282i
$501$	504.160	+	116.906i	1.00631	+	0.233345i
$502$	−435.094			−0.866721
$503$		−	791.160i		−	1.57288i	−0.617664	−	0.786442i	$-0.711921\pi$
$503$		−	791.160i		−	1.57288i	0.617664	−	0.786442i	$-0.288079\pi$
$504$	2.94622	−	6.01125i	0.00584567	−	0.0119271i
$505$	−155.558			−0.308035
$506$		−	75.2855i		−	0.148786i
$507$	−88.5660	+	381.944i	−0.174686	+	0.753341i
$508$	−262.642			−0.517011
$509$			56.4471i			0.110898i	0.998462	+	0.0554490i	$0.0176590\pi$
$509$			56.4471i			0.110898i	−0.998462	+	0.0554490i	$0.982341\pi$
$510$	415.997	+	96.4624i	0.815681	+	0.189142i
$511$	17.5719			0.0343873
$512$		−	727.201i		−	1.42032i
$513$	−51.4561	+	63.1692i	−0.100304	+	0.123137i
$514$	796.322			1.54926
$515$		−	419.887i		−	0.815315i
$516$	−167.416	+	721.988i	−0.324450	+	1.39920i
$517$	388.737			0.751910
$518$			155.869i			0.300906i
$519$	543.116	+	125.939i	1.04647	+	0.242657i
$520$	35.3789			0.0680364
$521$			956.062i			1.83505i	0.397677	+	0.917525i	$0.369816\pi$
$521$			956.062i			1.83505i	−0.397677	+	0.917525i	$0.630184\pi$
$522$	1288.08	+	631.309i	2.46758	+	1.20940i
$523$	134.025			0.256262			0.128131	−	0.991757i	$-0.459102\pi$
$523$	134.025			0.256262			0.128131	+	0.991757i	$0.459102\pi$
$524$		−	177.289i		−	0.338338i
$525$	49.9168	−	215.268i	0.0950796	−	0.410034i
$526$	707.040			1.34418
$527$		−	390.794i		−	0.741544i
$528$	−251.405	−	58.2963i	−0.476146	−	0.110410i
$529$	−23.0000			−0.0434783
$530$			259.785i			0.490160i
$531$	−448.980	+	916.065i	−0.845536	+	1.72517i
$532$	32.7237			0.0615107
$533$		−	440.383i		−	0.826235i
$534$	230.609	−	994.511i	0.431853	−	1.86238i
$535$	435.926			0.814815
$536$		−	4.84633i		−	0.00904165i
$537$	−609.397	−	141.308i	−1.13482	−	0.263144i
$538$	−399.836			−0.743189
$539$		−	38.6132i		−	0.0716385i
$540$	623.718	+	508.066i	1.15503	+	0.940863i
$541$	−31.9013			−0.0589672			−0.0294836	−	0.999565i	$-0.509386\pi$
$541$	−31.9013			−0.0589672			−0.0294836	+	0.999565i	$0.509386\pi$
$542$			50.5373i			0.0932423i
$543$	162.282	−	699.847i	0.298862	−	1.28885i
$544$	−313.121			−0.575590
$545$			501.952i			0.921013i
$546$	380.930	+	88.3310i	0.697675	+	0.161778i
$547$	−425.710			−0.778263			−0.389131	−	0.921182i	$-0.627225\pi$
$547$	−425.710			−0.778263			−0.389131	+	0.921182i	$0.627225\pi$
$548$			753.257i			1.37456i
$549$	−87.0187	−	42.6494i	−0.158504	−	0.0776856i
$550$	437.048			0.794633
$551$			169.003i			0.306721i
$552$	0.913696	−	3.94034i	0.00165525	−	0.00713830i
$553$	275.721			0.498591
$554$		−	383.400i		−	0.692058i
$555$	−439.779	−	101.977i	−0.792395	−	0.183742i
$556$	−333.774			−0.600313
$557$		−	91.2622i		−	0.163846i	−0.996639	−	0.0819230i	$-0.973894\pi$
$557$		−	91.2622i		−	0.163846i	0.996639	−	0.0819230i	$-0.0261061\pi$
$558$	640.184	−	1306.18i	1.14728	−	2.34083i
$559$	−1043.43			−1.86660
$560$			299.931i			0.535591i
$561$	−25.7218	+	110.926i	−0.0458498	+	0.197729i
$562$	533.529			0.949340
$563$		−	972.604i		−	1.72754i	−0.503888	−	0.863769i	$-0.668098\pi$
$563$		−	972.604i		−	1.72754i	0.503888	−	0.863769i	$-0.331902\pi$
$564$	844.156	+	195.745i	1.49673	+	0.347065i
$565$	1352.25			2.39336
$566$		−	1317.38i		−	2.32753i
$567$	131.289	+	169.382i	0.231550	+	0.298734i
$568$	−33.3993			−0.0588016
$569$			679.718i			1.19458i	0.802024	+	0.597291i	$0.203756\pi$
$569$			679.718i			1.19458i	−0.802024	+	0.597291i	$0.796244\pi$
$570$	−42.3027	+	182.432i	−0.0742153	+	0.320056i
$571$	417.234			0.730707			0.365354	−	0.930869i	$-0.380948\pi$
$571$	417.234			0.730707			0.365354	+	0.930869i	$0.380948\pi$
$572$			391.409i			0.684282i
$573$	21.8802	+	5.07364i	0.0381854	+	0.00885452i
$574$	−191.537			−0.333687
$575$		−	133.520i		−	0.232208i
$576$	−542.443	−	265.861i	−0.941741	−	0.461564i
$577$	−471.969			−0.817970			−0.408985	−	0.912541i	$-0.634117\pi$
$577$	−471.969			−0.817970			−0.408985	+	0.912541i	$0.634117\pi$
$578$		−	687.704i		−	1.18980i
$579$	−188.868	+	814.500i	−0.326197	+	1.40674i
$580$	1668.70			2.87707
$581$		−	145.143i		−	0.249816i
$582$	769.045	+	178.328i	1.32138	+	0.306405i
$583$	−69.2717			−0.118819
$584$			1.86720i			0.00319726i
$585$	−498.445	+	1016.99i	−0.852042	+	1.73844i
$586$	−1440.79			−2.45869
$587$			412.629i			0.702946i	0.936198	+	0.351473i	$0.114319\pi$
$587$			412.629i			0.702946i	−0.936198	+	0.351473i	$0.885681\pi$
$588$	19.4433	−	83.8498i	0.0330668	−	0.142602i
$589$	171.379			0.290966
$590$			2344.91i			3.97443i
$591$	119.898	+	27.8022i	0.202873	+	0.0470426i
$592$	322.841			0.545340
$593$			165.937i			0.279826i	0.990164	+	0.139913i	$0.0446822\pi$
$593$			165.937i			0.279826i	−0.990164	+	0.139913i	$0.955318\pi$
$594$	−267.687	+	328.621i	−0.450651	+	0.553234i
$595$	132.337			0.222415
$596$			917.888i			1.54008i
$597$	109.763	−	473.357i	0.183858	−	0.792892i
$598$	236.272			0.395103
$599$			1115.97i			1.86305i	0.363671	+	0.931527i	$0.381523\pi$
$599$			1115.97i			1.86305i	−0.363671	+	0.931527i	$0.618477\pi$
$600$	22.8745	+	5.30419i	0.0381242	+	0.00884032i
$601$	733.764			1.22091			0.610453	−	0.792053i	$-0.290987\pi$
$601$	733.764			1.22091			0.610453	+	0.792053i	$0.290987\pi$
$602$			453.821i			0.753856i
$603$	139.311	+	68.2787i	0.231030	+	0.113232i
$604$	−440.607			−0.729482
$605$		−	658.382i		−	1.08824i
$606$	41.2698	−	177.977i	0.0681020	−	0.293692i
$607$	−928.470			−1.52961			−0.764803	−	0.644265i	$-0.777164\pi$
$607$	−928.470			−1.52961			−0.764803	+	0.644265i	$0.777164\pi$
$608$		−	137.316i		−	0.225849i
$609$	433.047	+	100.416i	0.711079	+	0.164886i
$610$	−222.748			−0.365160
$611$			1219.99i			1.99671i
$612$	−111.711	+	227.928i	−0.182535	+	0.372431i
$613$	−531.050			−0.866314			−0.433157	−	0.901319i	$-0.642600\pi$
$613$	−531.050			−0.866314			−0.433157	+	0.901319i	$0.642600\pi$
$614$		−	324.835i		−	0.529047i
$615$	125.312	−	540.413i	0.203760	−	0.878720i
$616$	4.10306			0.00666082
$617$			1156.56i			1.87449i	0.348666	+	0.937247i	$0.386635\pi$
$617$			1156.56i			1.87449i	−0.348666	+	0.937247i	$0.613365\pi$
$618$	480.404	+	111.397i	0.777353	+	0.180254i
$619$	−168.777			−0.272660			−0.136330	−	0.990663i	$-0.543531\pi$
$619$	−168.777			−0.272660			−0.136330	+	0.990663i	$0.543531\pi$
$620$		−	1692.16i		−	2.72929i
$621$	100.395	+	81.7793i	0.161667	+	0.131690i
$622$	524.832			0.843781
$623$		−	316.373i		−	0.507823i
$624$	182.954	−	788.995i	0.293195	−	1.26441i
$625$	−545.910			−0.873456
$626$		−	659.953i		−	1.05424i
$627$	−48.6456	−	11.2800i	−0.0775847	−	0.0179905i
$628$	−535.713			−0.853047
$629$		−	142.446i		−	0.226463i
$630$	442.321	+	216.789i	0.702097	+	0.344110i
$631$	494.393			0.783507			0.391753	−	0.920070i	$-0.371869\pi$
$631$	494.393			0.783507			0.391753	+	0.920070i	$0.371869\pi$
$632$			29.2983i			0.0463580i
$633$	36.6873	−	158.215i	0.0579579	−	0.249945i
$634$	1328.54			2.09549
$635$		−	465.793i		−	0.733532i
$636$	−150.426	−	34.8811i	−0.236519	−	0.0548445i
$637$	121.181			0.190238
$638$			879.195i			1.37805i
$639$	470.555	−	960.086i	0.736393	−	1.50248i
$640$	−65.3768			−0.102151
$641$		−	247.425i		−	0.385998i	−0.981199	−	0.192999i	$-0.938179\pi$
$641$		−	247.425i		−	0.385998i	0.981199	−	0.192999i	$-0.0618215\pi$
$642$	−115.652	+	498.754i	−0.180144	+	0.776876i
$643$	90.7041			0.141064			0.0705320	−	0.997510i	$-0.477530\pi$
$643$	90.7041			0.141064			0.0705320	+	0.997510i	$0.477530\pi$
$644$		−	52.0078i		−	0.0807575i
$645$	−1280.44	−	296.911i	−1.98518	−	0.460327i
$646$	−59.0901			−0.0914708
$647$		−	40.2237i		−	0.0621695i	−0.999517	−	0.0310848i	$-0.990104\pi$
$647$		−	40.2237i		−	0.0621695i	0.999517	−	0.0310848i	$-0.00989618\pi$
$648$	−17.9987	+	13.9508i	−0.0277757	+	0.0215291i
$649$	−625.273			−0.963441
$650$			1371.61i			2.11017i
$651$	101.828	−	439.135i	0.156417	−	0.674554i
$652$	−394.206			−0.604611
$653$			514.096i			0.787283i	0.919264	+	0.393641i	$0.128785\pi$
$653$			514.096i			0.787283i	−0.919264	+	0.393641i	$0.871215\pi$
$654$	−574.296	−	133.169i	−0.878129	−	0.203623i
$655$	314.421			0.480031
$656$			396.717i			0.604751i
$657$	−53.6739	−	26.3065i	−0.0816955	−	0.0400404i
$658$	530.613			0.806403
$659$			685.333i			1.03996i	0.854179	+	0.519979i	$0.174060\pi$
$659$			685.333i			1.03996i	−0.854179	+	0.519979i	$0.825940\pi$
$660$	−111.377	+	480.315i	−0.168752	+	0.727750i
$661$	265.124			0.401096			0.200548	−	0.979684i	$-0.435728\pi$
$661$	265.124			0.401096			0.200548	+	0.979684i	$0.435728\pi$
$662$		−	583.916i		−	0.882049i
$663$	−348.124	−	80.7237i	−0.525074	−	0.121755i
$664$	15.4230			0.0232274
$665$			58.0352i			0.0872709i
$666$	233.349	−	476.108i	0.350374	−	0.714877i
$667$	268.597			0.402694
$668$			707.091i			1.05852i
$669$	−20.2437	+	87.3015i	−0.0302596	+	0.130496i
$670$	356.604			0.532244
$671$		−	59.3958i		−	0.0885184i
$672$	−351.854	−	81.5887i	−0.523592	−	0.121412i
$673$	1051.70			1.56270			0.781351	−	0.624092i	$-0.214531\pi$
$673$	1051.70			1.56270			0.781351	+	0.624092i	$0.214531\pi$
$674$		−	436.664i		−	0.647870i
$675$	−474.746	+	582.814i	−0.703328	+	0.863427i
$676$	−535.681			−0.792428
$677$		−	767.206i		−	1.13324i	−0.823978	−	0.566622i	$-0.808250\pi$
$677$		−	767.206i		−	1.13324i	0.823978	−	0.566622i	$-0.191750\pi$
$678$	−358.755	+	1547.14i	−0.529138	+	2.28192i
$679$	244.648			0.360307
$680$			14.0622i			0.0206797i
$681$	935.762	+	216.987i	1.37410	+	0.318629i
$682$	891.554			1.30726
$683$			113.372i			0.165991i	0.996550	+	0.0829954i	$0.0264487\pi$
$683$			113.372i			0.165991i	−0.996550	+	0.0829954i	$0.973551\pi$
$684$	−99.9556	−	48.9900i	−0.146134	−	0.0716228i
$685$	−1335.90			−1.95021
$686$		−	52.7056i		−	0.0768304i
$687$	−247.512	+	1067.40i	−0.360280	+	1.55372i
$688$	939.969			1.36623
$689$		−	217.399i		−	0.315528i
$690$	289.939	+	67.2318i	0.420202	+	0.0974374i
$691$	945.327			1.36806			0.684028	−	0.729456i	$-0.260227\pi$
$691$	945.327			1.36806			0.684028	+	0.729456i	$0.260227\pi$
$692$			761.728i			1.10076i
$693$	−57.8071	+	117.945i	−0.0834157	+	0.170195i
$694$	−165.852			−0.238980
$695$		−	591.945i		−	0.851719i
$696$	−10.6703	+	46.0159i	−0.0153308	+	0.0661147i
$697$	175.041			0.251135
$698$			402.218i			0.576243i
$699$	368.289	+	85.3996i	0.526879	+	0.122174i
$700$	301.916			0.431309
$701$		−	29.3523i		−	0.0418721i	−0.999781	−	0.0209360i	$-0.993335\pi$
$701$		−	29.3523i		−	0.0418721i	0.999781	−	0.0209360i	$-0.00666463\pi$
$702$	−1031.33	−	840.094i	−1.46913	−	1.19671i
$703$	62.4682			0.0888594
$704$		−	370.252i		−	0.525926i
$705$	−347.152	+	1497.10i	−0.492414	+	2.12355i
$706$	1025.59			1.45268
$707$		−	56.6181i		−	0.0800822i
$708$	−1357.80	−	314.850i	−1.91780	−	0.444703i
$709$	303.215			0.427665			0.213833	−	0.976870i	$-0.431405\pi$
$709$	303.215			0.427665			0.213833	+	0.976870i	$0.431405\pi$
$710$		−	2457.60i		−	3.46140i
$711$	−842.199	−	412.776i	−1.18453	−	0.580558i
$712$	33.6181			0.0472164
$713$		−	272.373i		−	0.382010i
$714$	−35.1093	+	151.410i	−0.0491727	+	0.212059i
$715$	−694.161			−0.970855
$716$		−	854.687i		−	1.19370i
$717$	−298.822	−	69.2916i	−0.416768	−	0.0966410i
$718$	−1367.53			−1.90463
$719$			956.271i			1.33000i	0.746843	+	0.665001i	$0.231569\pi$
$719$			956.271i			1.33000i	−0.746843	+	0.665001i	$0.768431\pi$
$720$	449.021	−	916.149i	0.623640	−	1.27243i
$721$	152.826			0.211964
$722$			1001.43i			1.38703i
$723$	205.176	−	884.827i	0.283784	−	1.22383i
$724$	981.546			1.35573
$725$			1559.26i			2.15071i
$726$	753.272	+	174.670i	1.03757	+	0.240593i
$727$	232.907			0.320367			0.160184	−	0.987087i	$-0.448791\pi$
$727$	232.907			0.320367			0.160184	+	0.987087i	$0.448791\pi$
$728$			12.8768i			0.0176879i
$729$	−147.447	−	713.933i	−0.202259	−	0.979332i
$730$	−137.393			−0.188209
$731$		−	414.737i		−	0.567356i
$732$	29.9082	−	128.980i	0.0408582	−	0.176202i
$733$	1111.04			1.51574			0.757871	−	0.652405i	$-0.226240\pi$
$733$	1111.04			1.51574			0.757871	+	0.652405i	$0.226240\pi$
$734$		−	1834.00i		−	2.49863i
$735$	148.707	+	34.4825i	0.202322	+	0.0469150i
$736$	−218.237			−0.296518
$737$			95.0886i			0.129021i
$738$	585.055	+	286.746i	0.792757	+	0.388544i
$739$	−967.998			−1.30988			−0.654938	−	0.755683i	$-0.727305\pi$
$739$	−967.998			−1.30988			−0.654938	+	0.755683i	$0.727305\pi$
$740$		−	616.796i		−	0.833509i
$741$	35.4007	−	152.667i	0.0477742	−	0.206028i
$742$	−94.5535			−0.127431
$743$		−	1150.94i		−	1.54905i	−0.632544	−	0.774524i	$-0.717989\pi$
$743$		−	1150.94i		−	1.54905i	0.632544	−	0.774524i	$-0.282011\pi$
$744$	46.6628	+	10.8203i	0.0627188	+	0.0145434i
$745$	−1627.87			−2.18506
$746$			670.186i			0.898372i
$747$	−217.291	+	443.345i	−0.290885	+	0.593501i
$748$	−155.575			−0.207988
$749$			158.664i			0.211834i
$750$	−39.8247	+	171.745i	−0.0530995	+	0.228994i
$751$	1100.29			1.46511			0.732553	−	0.680710i	$-0.238329\pi$
$751$	1100.29			1.46511			0.732553	+	0.680710i	$0.238329\pi$
$752$		−	1099.02i		−	1.46147i
$753$	446.809	+	103.607i	0.593371	+	0.137592i
$754$	−2759.21			−3.65944
$755$		−	781.413i		−	1.03498i
$756$	−184.920	+	227.014i	−0.244603	+	0.300283i
$757$	244.526			0.323020			0.161510	−	0.986871i	$-0.448364\pi$
$757$	244.526			0.323020			0.161510	+	0.986871i	$0.448364\pi$
$758$		−	539.422i		−	0.711638i
$759$	−17.9274	+	77.3125i	−0.0236198	+	0.101861i
$760$	−6.16686			−0.00811428
$761$		−	22.8281i		−	0.0299975i	−0.999888	−	0.0149987i	$-0.995226\pi$
$761$		−	22.8281i		−	0.0299975i	0.999888	−	0.0149987i	$-0.00477442\pi$
$762$	532.926	+	123.576i	0.699378	+	0.162173i
$763$	−182.695			−0.239443
$764$			30.6873i			0.0401667i
$765$	−404.228	−	198.119i	−0.528402	−	0.258979i
$766$	155.524			0.203034
$767$		−	1962.32i		−	2.55844i
$768$	−164.599	+	709.837i	−0.214321	+	0.924267i
$769$	789.173			1.02623			0.513117	−	0.858319i	$-0.328491\pi$
$769$	789.173			1.02623			0.513117	+	0.858319i	$0.328491\pi$
$770$			301.913i			0.392094i
$771$	−817.762	−	189.625i	−1.06065	−	0.245946i
$772$	−1142.35			−1.47972
$773$		−	263.077i		−	0.340332i	−0.985415	−	0.170166i	$-0.945570\pi$
$773$		−	263.077i		−	0.340332i	0.985415	−	0.170166i	$-0.0544304\pi$
$774$	679.407	−	1386.21i	0.877787	−	1.79097i
$775$	1581.18			2.04024
$776$			25.9965i			0.0335007i
$777$	37.1164	−	160.066i	0.0477689	−	0.206005i
$778$	882.677			1.13455
$779$			76.7627i			0.0985400i
$780$	−1507.39	−	349.538i	−1.93256	−	0.448126i
$781$	655.320			0.839078
$782$			93.9120i			0.120092i
$783$	−1172.43	−	955.030i	−1.49735	−	1.21971i
$784$	−109.166			−0.139242
$785$		−	950.083i		−	1.21030i
$786$	−83.4166	+	359.737i	−0.106128	+	0.457680i
$787$	810.866			1.03032			0.515162	−	0.857093i	$-0.327732\pi$
$787$	810.866			1.03032			0.515162	+	0.857093i	$0.327732\pi$
$788$			168.158i			0.213399i
$789$	−726.076	−	168.364i	−0.920249	−	0.213389i
$790$	−2155.83			−2.72890
$791$			492.177i			0.622221i
$792$	−12.5329	−	6.14262i	−0.0158244	−	0.00775583i
$793$	186.405			0.235063
$794$			23.1241i			0.0291236i
$795$	61.8613	−	266.779i	0.0778130	−	0.335571i
$796$	663.889			0.834032
$797$		−	856.466i		−	1.07461i	−0.843387	−	0.537306i	$-0.819442\pi$
$797$		−	856.466i		−	1.07461i	0.843387	−	0.537306i	$-0.180558\pi$
$798$	−66.3995	−	15.3969i	−0.0832074	−	0.0192943i
$799$	−484.915			−0.606903
$800$		−	1266.91i		−	1.58364i
$801$	−473.637	+	966.373i	−0.591307	+	1.20646i
$802$	−1091.11			−1.36049
$803$		−	36.6359i		−	0.0456238i
$804$	−47.8809	+	206.488i	−0.0595534	+	0.256826i
$805$	92.2354			0.114578
$806$			2798.00i			3.47147i
$807$	410.601	+	95.2111i	0.508800	+	0.117982i
$808$	6.01628			0.00744589
$809$			190.452i			0.235416i	0.993048	+	0.117708i	$0.0375548\pi$
$809$			190.452i			0.235416i	−0.993048	+	0.117708i	$0.962445\pi$
$810$	−1026.53	−	1324.38i	−1.26733	−	1.63504i
$811$	−1132.47			−1.39639			−0.698193	−	0.715909i	$-0.746012\pi$
$811$	−1132.47			−1.39639			−0.698193	+	0.715909i	$0.746012\pi$
$812$			607.354i			0.747973i
$813$	12.0342	−	51.8980i	0.0148022	−	0.0638352i
$814$	324.974			0.399231
$815$		−	699.122i		−	0.857818i
$816$	313.605	+	72.7195i	0.384320	+	0.0891170i
$817$	181.879			0.222618
$818$		−	190.505i		−	0.232891i
$819$	−370.153	−	181.418i	−0.451957	−	0.221512i
$820$	757.937			0.924313
$821$			895.125i			1.09029i	0.838343	+	0.545143i	$0.183525\pi$
$821$			895.125i			1.09029i	−0.838343	+	0.545143i	$0.816475\pi$
$822$	354.416	−	1528.43i	0.431163	−	1.85941i
$823$	416.341			0.505882			0.252941	−	0.967482i	$-0.418602\pi$
$823$	416.341			0.505882			0.252941	+	0.967482i	$0.418602\pi$
$824$			16.2394i			0.0197080i
$825$	−448.815	−	104.072i	−0.544019	−	0.126148i
$826$	−853.476			−1.03326
$827$		−	229.621i		−	0.277656i	−0.990317	−	0.138828i	$-0.955666\pi$
$827$		−	229.621i		−	0.277656i	0.990317	−	0.138828i	$-0.0443335\pi$
$828$	−77.8599	+	158.860i	−0.0940337	+	0.191859i
$829$	1247.07			1.50431			0.752153	−	0.658988i	$-0.229015\pi$
$829$	1247.07			1.50431			0.752153	+	0.658988i	$0.229015\pi$
$830$			1134.86i			1.36730i
$831$	−91.2974	+	393.723i	−0.109864	+	0.473794i
$832$	1161.98			1.39661
$833$			48.1665i			0.0578230i
$834$	677.260	+	157.044i	0.812062	+	0.188303i
$835$	−1254.02			−1.50182
$836$		−	68.2261i		−	0.0816102i
$837$	−968.456	+	1188.91i	−1.15706	+	1.42044i
$838$	1196.18			1.42743
$839$			831.736i			0.991342i	0.868510	+	0.495671i	$0.165078\pi$
$839$			831.736i			0.991342i	−0.868510	+	0.495671i	$0.834922\pi$
$840$	−3.66413	+	15.8017i	−0.00436206	+	0.0188116i
$841$	−2295.71			−2.72974
$842$			1735.68i			2.06138i
$843$	−547.894	−	127.047i	−0.649933	−	0.150708i
$844$	221.899			0.262914
$845$		−	950.026i		−	1.12429i
$846$	−1620.78	−	794.371i	−1.91581	−	0.938972i
$847$	239.631			0.282917
$848$			195.842i			0.230946i
$849$	−313.702	+	1352.85i	−0.369496	+	1.59346i
$850$	−545.179			−0.641387
$851$		−	99.2808i		−	0.116664i
$852$	1423.05	+	329.980i	1.67025	+	0.387300i
$853$	−878.370			−1.02974			−0.514871	−	0.857268i	$-0.672160\pi$
$853$	−878.370			−1.02974			−0.514871	+	0.857268i	$0.672160\pi$
$854$		−	81.0733i		−	0.0949336i
$855$	86.8833	−	177.270i	0.101618	−	0.207334i
$856$	−16.8597			−0.0196959
$857$			757.697i			0.884127i	0.896984	+	0.442064i	$0.145754\pi$
$857$			757.697i			0.884127i	−0.896984	+	0.442064i	$0.854246\pi$
$858$	184.163	−	794.208i	0.214642	−	0.925650i
$859$	616.704			0.717933			0.358966	−	0.933350i	$-0.383129\pi$
$859$	616.704			0.717933			0.358966	+	0.933350i	$0.383129\pi$
$860$		−	1795.83i		−	2.08818i
$861$	196.694	+	45.6097i	0.228448	+	0.0529730i
$862$	−498.658			−0.578490
$863$			11.0011i			0.0127476i	0.999980	+	0.00637378i	$0.00202885\pi$
$863$			11.0011i			0.0127476i	−0.999980	+	0.00637378i	$0.997971\pi$
$864$	952.605	+	775.970i	1.10255	+	0.898113i
$865$	−1350.92			−1.56175
$866$		−	983.543i		−	1.13573i
$867$	−163.760	+	706.220i	−0.188881	+	0.814556i
$868$	615.893			0.709554
$869$		−	574.855i		−	0.661513i
$870$	−3385.95	−	785.142i	−3.89190	−	0.902462i
$871$	−298.421			−0.342619
$872$		−	19.4133i		−	0.0222630i
$873$	−747.287	−	366.258i	−0.855998	−	0.419540i
$874$	−41.1843			−0.0471216
$875$			54.6355i			0.0624406i
$876$	18.4476	−	79.5561i	0.0210590	−	0.0908175i
$877$	205.495			0.234315			0.117158	−	0.993113i	$-0.462622\pi$
$877$	205.495			0.234315			0.117158	+	0.993113i	$0.462622\pi$
$878$		−	252.886i		−	0.288025i
$879$	1479.58	+	343.089i	1.68326	+	0.390318i
$880$	625.331			0.710603
$881$		−	1253.96i		−	1.42333i	−0.702517	−	0.711667i	$-0.747940\pi$
$881$		−	1253.96i		−	1.42333i	0.702517	−	0.711667i	$-0.252060\pi$
$882$	−78.9046	+	160.991i	−0.0894610	+	0.182530i
$883$	−98.8845			−0.111987			−0.0559935	−	0.998431i	$-0.517833\pi$
$883$	−98.8845			−0.111987			−0.0559935	+	0.998431i	$0.517833\pi$
$884$		−	488.249i		−	0.552317i
$885$	558.384	−	2408.05i	0.630942	−	2.72096i
$886$	−375.534			−0.423853
$887$			316.638i			0.356977i	0.983942	+	0.178488i	$0.0571207\pi$
$887$			316.638i			0.356977i	−0.983942	+	0.178488i	$0.942879\pi$
$888$	17.0087	+	3.94402i	0.0191540	+	0.00444146i
$889$	169.534			0.190702
$890$			2473.69i			2.77943i
$891$	353.147	−	273.726i	0.396349	−	0.307212i
$892$	−122.442			−0.137266
$893$		−	212.655i		−	0.238136i
$894$	431.877	−	1862.48i	0.483084	−	2.08332i
$895$	1515.78			1.69361
$896$		−	23.7951i		−	0.0265571i
$897$	−242.633	−	56.2623i	−0.270494	−	0.0627228i
$898$	−1502.73			−1.67342
$899$			3180.81i			3.53816i
$900$	−922.213	−	451.993i	−1.02468	−	0.502215i
$901$	86.4104			0.0959050
$902$			399.338i			0.442725i
$903$	108.066	−	466.040i	0.119675	−	0.516102i
$904$	−52.2991			−0.0578530
$905$			1740.76i			1.92349i
$906$	894.035	+	207.311i	0.986794	+	0.228820i
$907$	1788.39			1.97177			0.985883	−	0.167435i	$-0.0535485\pi$
$907$	1788.39			1.97177			0.985883	+	0.167435i	$0.0535485\pi$
$908$			1312.42i			1.44540i
$909$	−84.7620	+	172.942i	−0.0932475	+	0.190255i
$910$	−947.506			−1.04121
$911$			186.043i			0.204218i	0.994773	+	0.102109i	$0.0325591\pi$
$911$			186.043i			0.204218i	−0.994773	+	0.102109i	$0.967441\pi$
$912$	−31.8905	+	137.529i	−0.0349676	+	0.150799i
$913$	−302.611			−0.331447
$914$			964.964i			1.05576i
$915$	228.745	+	53.0419i	0.249995	+	0.0579693i
$916$	−1497.05			−1.63433
$917$			114.439i			0.124798i
$918$	333.916	−	409.926i	0.363743	−	0.446542i
$919$	−152.036			−0.165437			−0.0827184	−	0.996573i	$-0.526360\pi$
$919$	−152.036			−0.165437			−0.0827184	+	0.996573i	$0.526360\pi$
$920$			9.80100i			0.0106533i
$921$	−77.3514	+	333.581i	−0.0839863	+	0.362194i
$922$	318.261			0.345185
$923$			2056.62i			2.22819i
$924$	−174.820	−	40.5376i	−0.189199	−	0.0438719i
$925$	576.346			0.623077
$926$			2067.16i			2.23235i
$927$	−466.812	−	228.793i	−0.503573	−	0.246810i
$928$	2548.60			2.74634
$929$			210.124i			0.226183i	0.993585	+	0.113092i	$0.0360753\pi$
$929$			210.124i			0.226183i	−0.993585	+	0.113092i	$0.963925\pi$
$930$	−796.179	+	3433.55i	−0.856107	+	3.69199i
$931$	−21.1230			−0.0226885
$932$			516.530i			0.554217i
$933$	−538.963	−	124.976i	−0.577666	−	0.133951i
$934$	580.462			0.621480
$935$		−	275.911i		−	0.295092i
$936$	19.2776	−	39.3327i	0.0205958	−	0.0420221i
$937$	−645.838			−0.689262			−0.344631	−	0.938738i	$-0.611996\pi$
$937$	−645.838			−0.689262			−0.344631	+	0.938738i	$0.611996\pi$
$938$			129.793i			0.138372i
$939$	−157.152	+	677.722i	−0.167361	+	0.721749i
$940$	−2099.71			−2.23373
$941$			295.988i			0.314546i	0.987555	+	0.157273i	$0.0502703\pi$
$941$			295.988i			0.314546i	−0.987555	+	0.157273i	$0.949730\pi$
$942$	1087.01	+	252.059i	1.15394	+	0.267579i
$943$	121.999			0.129373
$944$			1767.75i			1.87261i
$945$	−402.607	−	327.954i	−0.426039	−	0.347042i
$946$	946.179			1.00019
$947$			171.823i			0.181440i	0.995876	+	0.0907198i	$0.0289168\pi$
$947$			171.823i			0.181440i	−0.995876	+	0.0907198i	$0.971083\pi$
$948$	289.462	−	1248.32i	0.305340	−	1.31679i
$949$	114.976			0.121155
$950$		−	239.083i		−	0.251667i
$951$	−1364.31	−	316.359i	−1.43461	−	0.332660i
$952$	−5.11821			−0.00537627
$953$		−	1722.85i		−	1.80782i	−0.427721	−	0.903911i	$-0.640683\pi$
$953$		−	1722.85i		−	1.80782i	0.427721	−	0.903911i	$-0.359317\pi$
$954$	288.817	+	141.554i	0.302743	+	0.148380i
$955$	−54.4237			−0.0569882
$956$		−	419.103i		−	0.438392i
$957$	209.359	−	902.866i	0.218766	−	0.943434i
$958$	−1411.70			−1.47359
$959$		−	486.225i		−	0.507012i
$960$	1425.91	+	330.644i	1.48533	+	0.344421i
$961$	2264.53			2.35643
$962$			1019.88i			1.06017i
$963$	237.532	−	484.643i	0.246659	−	0.503264i
$964$	1240.98			1.28733
$965$		−	2025.94i		−	2.09942i
$966$	−24.4703	+	105.529i	−0.0253316	+	0.109243i
$967$	1006.28			1.04062			0.520310	−	0.853978i	$-0.325817\pi$
$967$	1006.28			1.04062			0.520310	+	0.853978i	$0.325817\pi$
$968$			25.4633i			0.0263051i
$969$	60.6811	+	14.0709i	0.0626224	+	0.0145210i
$970$	−1912.88			−1.97204
$971$		−	1294.27i		−	1.33292i	−0.745540	−	0.666461i	$-0.767808\pi$
$971$		−	1294.27i		−	1.33292i	0.745540	−	0.666461i	$-0.232192\pi$
$972$	904.703	−	416.581i	0.930765	−	0.428582i
$973$	215.450			0.221428
$974$			2343.32i			2.40587i
$975$	326.615	−	1408.54i	0.334989	−	1.44465i
$976$	−167.921			−0.172051
$977$			1120.68i			1.14706i	0.819184	+	0.573531i	$0.194427\pi$
$977$			1120.68i			1.14706i	−0.819184	+	0.573531i	$0.805573\pi$
$978$	799.883	+	185.479i	0.817876	+	0.189651i
$979$	−659.612			−0.673761
$980$			208.564i			0.212820i
$981$	558.048	+	273.509i	0.568856	+	0.278807i
$982$	−2356.55			−2.39974
$983$			574.248i			0.584179i	0.956391	+	0.292089i	$0.0943505\pi$
$983$			574.248i			0.584179i	−0.956391	+	0.292089i	$0.905650\pi$
$984$	−4.84652	+	20.9008i	−0.00492533	+	0.0212406i
$985$	−298.227			−0.302769
$986$		−	1096.72i		−	1.11229i
$987$	−544.899	−	126.352i	−0.552076	−	0.128017i
$988$	214.117			0.216718
$989$		−	289.061i		−	0.292276i
$990$	451.988	−	922.202i	0.456553	−	0.931518i
$991$	756.387			0.763257			0.381628	−	0.924316i	$-0.375363\pi$
$991$	756.387			0.763257			0.381628	+	0.924316i	$0.375363\pi$
$992$		−	2584.43i		−	2.60528i
$993$	−139.045	+	599.638i	−0.140026	+	0.603865i
$994$	894.489			0.899888
$995$			1177.40i			1.18332i
$996$	−657.131	−	152.377i	−0.659770	−	0.152989i
$997$	1058.99			1.06218			0.531089	−	0.847316i	$-0.321783\pi$
$997$	1058.99			1.06218			0.531089	+	0.847316i	$0.321783\pi$
$998$			467.161i			0.468097i
$999$	−353.005	+	433.361i	−0.353359	+	0.433794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.b.a.323.16	✓	88
3.2	odd	2	inner	483.3.b.a.323.73	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.b.a.323.16	✓	88	1.1	even	1	trivial
483.3.b.a.323.73	yes	88	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.84584i q^{2} +(-0.677666 + 2.92246i) q^{3} -4.09879 q^{4} -7.26917i q^{5} +(8.31684 + 1.92853i) q^{6} +2.64575 q^{7} +0.281139i q^{8} +(-8.08154 - 3.96090i) q^{9} -20.6869 q^{10} -5.51617i q^{11} +(2.77761 - 11.9785i) q^{12} +17.3116 q^{13} -7.52938i q^{14} +(21.2438 + 4.92607i) q^{15} -15.5951 q^{16} +6.88093i q^{17} +(-11.2721 + 22.9987i) q^{18} -3.01757 q^{19} +29.7948i q^{20} +(-1.79294 + 7.73210i) q^{21} -15.6981 q^{22} +4.79583i q^{23} +(-0.821618 - 0.190519i) q^{24} -27.8408 q^{25} -49.2661i q^{26} +(17.0522 - 20.9338i) q^{27} -10.8444 q^{28} -56.0064i q^{29} +(14.0188 - 60.4565i) q^{30} -56.7937 q^{31} +45.5056i q^{32} +(16.1208 + 3.73812i) q^{33} +19.5820 q^{34} -19.2324i q^{35} +(33.1245 + 16.2349i) q^{36} -20.7015 q^{37} +8.58751i q^{38} +(-11.7315 + 50.5925i) q^{39} +2.04365 q^{40} -25.4386i q^{41} +(22.0043 + 5.10241i) q^{42} -60.2734 q^{43} +22.6096i q^{44} +(-28.7925 + 58.7460i) q^{45} +13.6482 q^{46} +70.4723i q^{47} +(10.5683 - 45.5760i) q^{48} +7.00000 q^{49} +79.2304i q^{50} +(-20.1092 - 4.66298i) q^{51} -70.9567 q^{52} -12.5579i q^{53} +(-59.5742 - 48.5277i) q^{54} -40.0980 q^{55} +0.743825i q^{56} +(2.04491 - 8.81873i) q^{57} -159.385 q^{58} -113.353i q^{59} +(-87.0741 - 20.1909i) q^{60} +10.7676 q^{61} +161.626i q^{62} +(-21.3817 - 10.4796i) q^{63} +67.1213 q^{64} -125.841i q^{65} +(10.6381 - 45.8771i) q^{66} -17.2382 q^{67} -28.2035i q^{68} +(-14.0156 - 3.24997i) q^{69} -54.7323 q^{70} +118.800i q^{71} +(1.11357 - 2.27204i) q^{72} +6.64155 q^{73} +58.9131i q^{74} +(18.8668 - 81.3636i) q^{75} +12.3684 q^{76} -14.5944i q^{77} +(143.978 + 33.3860i) q^{78} +104.213 q^{79} +113.363i q^{80} +(49.6225 + 64.0204i) q^{81} -72.3940 q^{82} -54.8590i q^{83} +(7.34887 - 31.6923i) q^{84} +50.0187 q^{85} +171.528i q^{86} +(163.676 + 37.9536i) q^{87} +1.55081 q^{88} -119.578i q^{89} +(167.182 + 81.9387i) q^{90} +45.8023 q^{91} -19.6571i q^{92} +(38.4872 - 165.977i) q^{93} +200.553 q^{94} +21.9352i q^{95} +(-132.988 - 30.8376i) q^{96} +92.4684 q^{97} -19.9209i q^{98} +(-21.8490 + 44.5791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30}+ \cdots - 248 q^{99}+O(q^{100}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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