LMFDB - Embedded newform 253.3.c.a.208.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,3,Mod(208,253)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("253.208"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(253, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	253.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89375068832$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			208.26
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.919935i q^{2} +4.75301 q^{3} +3.15372 q^{4} +0.241391 q^{5} +4.37246i q^{6} -3.10005i q^{7} +6.58096i q^{8} +13.5911 q^{9} +0.222064i q^{10} +(-9.14341 + 6.11540i) q^{11} +14.9897 q^{12} -4.95337i q^{13} +2.85185 q^{14} +1.14733 q^{15} +6.56082 q^{16} +23.5594i q^{17} +12.5030i q^{18} -32.7967i q^{19} +0.761278 q^{20} -14.7346i q^{21} +(-5.62577 - 8.41134i) q^{22} -4.79583 q^{23} +31.2794i q^{24} -24.9417 q^{25} +4.55677 q^{26} +21.8217 q^{27} -9.77670i q^{28} -47.1256i q^{29} +1.05547i q^{30} +25.6526 q^{31} +32.3594i q^{32} +(-43.4587 + 29.0666i) q^{33} -21.6731 q^{34} -0.748324i q^{35} +42.8626 q^{36} -50.3573 q^{37} +30.1708 q^{38} -23.5434i q^{39} +1.58858i q^{40} +13.0072i q^{41} +13.5549 q^{42} +48.3618i q^{43} +(-28.8357 + 19.2863i) q^{44} +3.28077 q^{45} -4.41185i q^{46} +30.1624 q^{47} +31.1837 q^{48} +39.3897 q^{49} -22.9448i q^{50} +111.978i q^{51} -15.6215i q^{52} +5.53710 q^{53} +20.0745i q^{54} +(-2.20713 + 1.47620i) q^{55} +20.4013 q^{56} -155.883i q^{57} +43.3525 q^{58} -32.5864 q^{59} +3.61836 q^{60} +83.2209i q^{61} +23.5988i q^{62} -42.1332i q^{63} -3.52523 q^{64} -1.19570i q^{65} +(-26.7394 - 39.9792i) q^{66} -127.307 q^{67} +74.2997i q^{68} -22.7946 q^{69} +0.688409 q^{70} +40.3863 q^{71} +89.4426i q^{72} -57.4513i q^{73} -46.3254i q^{74} -118.548 q^{75} -103.431i q^{76} +(18.9581 + 28.3450i) q^{77} +21.6584 q^{78} -76.1879i q^{79} +1.58372 q^{80} -18.6015 q^{81} -11.9657 q^{82} -115.062i q^{83} -46.4688i q^{84} +5.68701i q^{85} -44.4897 q^{86} -223.989i q^{87} +(-40.2452 - 60.1724i) q^{88} -46.9157 q^{89} +3.01809i q^{90} -15.3557 q^{91} -15.1247 q^{92} +121.927 q^{93} +27.7475i q^{94} -7.91681i q^{95} +153.804i q^{96} -14.0830 q^{97} +36.2359i q^{98} +(-124.269 + 83.1152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) $ 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.919935i			0.459968i	0.973194	+	0.229984i	$0.0738673\pi$
$2$			0.919935i			0.459968i	−0.973194	+	0.229984i	$0.926133\pi$
$3$	4.75301			1.58434			0.792169	−	0.610302i	$-0.208952\pi$
$3$	4.75301			1.58434			0.792169	+	0.610302i	$0.208952\pi$
$4$	3.15372			0.788430
$5$	0.241391			0.0482781			0.0241391	−	0.999709i	$-0.492316\pi$
$5$	0.241391			0.0482781			0.0241391	+	0.999709i	$0.492316\pi$
$6$			4.37246i			0.728744i
$7$		−	3.10005i		−	0.442865i	−0.975176	−	0.221432i	$-0.928927\pi$
$7$		−	3.10005i		−	0.442865i	0.975176	−	0.221432i	$-0.0710732\pi$
$8$			6.58096i			0.822620i
$9$	13.5911			1.51012
$10$			0.222064i			0.0222064i
$11$	−9.14341	+	6.11540i	−0.831219	+	0.555946i
$11$	−9.14341	+	6.11540i	−0.831219	+	0.555946i
$12$	14.9897			1.24914
$13$		−	4.95337i		−	0.381028i	−0.981684	−	0.190514i	$-0.938985\pi$
$13$		−	4.95337i		−	0.381028i	0.981684	−	0.190514i	$-0.0610155\pi$
$14$	2.85185			0.203703
$15$	1.14733			0.0764888
$16$	6.56082			0.410051
$17$			23.5594i			1.38585i	0.721012	+	0.692923i	$0.243677\pi$
$17$			23.5594i			1.38585i	−0.721012	+	0.692923i	$0.756323\pi$
$18$			12.5030i			0.694608i
$19$		−	32.7967i		−	1.72614i	−0.505084	−	0.863070i	$-0.668538\pi$
$19$		−	32.7967i		−	1.72614i	0.505084	−	0.863070i	$-0.331462\pi$
$20$	0.761278			0.0380639
$21$		−	14.7346i		−	0.701647i
$22$	−5.62577	−	8.41134i	−0.255717	−	0.382334i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$			31.2794i			1.30331i
$25$	−24.9417			−0.997669
$26$	4.55677			0.175261
$27$	21.8217			0.808209
$28$		−	9.77670i		−	0.349168i
$29$		−	47.1256i		−	1.62502i	−0.582946	−	0.812511i	$-0.698100\pi$
$29$		−	47.1256i		−	1.62502i	0.582946	−	0.812511i	$-0.301900\pi$
$30$			1.05547i			0.0351824i
$31$	25.6526			0.827504			0.413752	−	0.910390i	$-0.364218\pi$
$31$	25.6526			0.827504			0.413752	+	0.910390i	$0.364218\pi$
$32$			32.3594i			1.01123i
$33$	−43.4587	+	29.0666i	−1.31693	+	0.880805i
$34$	−21.6731			−0.637444
$35$		−	0.748324i		−	0.0213807i
$36$	42.8626			1.19063
$37$	−50.3573			−1.36101			−0.680503	−	0.732745i	$-0.738239\pi$
$37$	−50.3573			−1.36101			−0.680503	+	0.732745i	$0.738239\pi$
$38$	30.1708			0.793969
$39$		−	23.5434i		−	0.603677i
$40$			1.58858i			0.0397145i
$41$			13.0072i			0.317248i	0.987339	+	0.158624i	$0.0507057\pi$
$41$			13.0072i			0.317248i	−0.987339	+	0.158624i	$0.949294\pi$
$42$	13.5549			0.322735
$43$			48.3618i			1.12469i	0.826901	+	0.562347i	$0.190101\pi$
$43$			48.3618i			1.12469i	−0.826901	+	0.562347i	$0.809899\pi$
$44$	−28.8357	+	19.2863i	−0.655358	+	0.438324i
$45$	3.28077			0.0729060
$46$		−	4.41185i		−	0.0959099i
$47$	30.1624			0.641754			0.320877	−	0.947121i	$-0.396022\pi$
$47$	30.1624			0.641754			0.320877	+	0.947121i	$0.396022\pi$
$48$	31.1837			0.649660
$49$	39.3897			0.803871
$50$		−	22.9448i		−	0.458896i
$51$			111.978i			2.19565i
$52$		−	15.6215i		−	0.300414i
$53$	5.53710			0.104474			0.0522368	−	0.998635i	$-0.483365\pi$
$53$	5.53710			0.104474			0.0522368	+	0.998635i	$0.483365\pi$
$54$			20.0745i			0.371750i
$55$	−2.20713	+	1.47620i	−0.0401297	+	0.0268400i
$56$	20.4013			0.364309
$57$		−	155.883i		−	2.73479i
$58$	43.3525			0.747457
$59$	−32.5864			−0.552312			−0.276156	−	0.961113i	$-0.589061\pi$
$59$	−32.5864			−0.552312			−0.276156	+	0.961113i	$0.589061\pi$
$60$	3.61836			0.0603061
$61$			83.2209i			1.36428i	0.731223	+	0.682139i	$0.238950\pi$
$61$			83.2209i			1.36428i	−0.731223	+	0.682139i	$0.761050\pi$
$62$			23.5988i			0.380625i
$63$		−	42.1332i		−	0.668781i
$64$	−3.52523			−0.0550817
$65$		−	1.19570i		−	0.0183953i
$66$	−26.7394	−	39.9792i	−0.405142	−	0.605745i
$67$	−127.307			−1.90011			−0.950053	−	0.312090i	$-0.898971\pi$
$67$	−127.307			−1.90011			−0.950053	+	0.312090i	$0.898971\pi$
$68$			74.2997i			1.09264i
$69$	−22.7946			−0.330357
$70$	0.688409			0.00983442
$71$	40.3863			0.568821			0.284410	−	0.958703i	$-0.408202\pi$
$71$	40.3863			0.568821			0.284410	+	0.958703i	$0.408202\pi$
$72$			89.4426i			1.24226i
$73$		−	57.4513i		−	0.787004i	−0.919324	−	0.393502i	$-0.871263\pi$
$73$		−	57.4513i		−	0.787004i	0.919324	−	0.393502i	$-0.128737\pi$
$74$		−	46.3254i		−	0.626019i
$75$	−118.548			−1.58064
$76$		−	103.431i		−	1.36094i
$77$	18.9581	+	28.3450i	0.246209	+	0.368117i
$78$	21.6584			0.277672
$79$		−	76.1879i		−	0.964404i	−0.876060	−	0.482202i	$-0.839837\pi$
$79$		−	76.1879i		−	0.964404i	0.876060	−	0.482202i	$-0.160163\pi$
$80$	1.58372			0.0197965
$81$	−18.6015			−0.229648
$82$	−11.9657			−0.145924
$83$		−	115.062i		−	1.38629i	−0.720797	−	0.693147i	$-0.756224\pi$
$83$		−	115.062i		−	1.38629i	0.720797	−	0.693147i	$-0.243776\pi$
$84$		−	46.4688i		−	0.553200i
$85$			5.68701i			0.0669060i
$86$	−44.4897			−0.517323
$87$		−	223.989i		−	2.57458i
$88$	−40.2452	−	60.1724i	−0.457332	−	0.683777i
$89$	−46.9157			−0.527143			−0.263572	−	0.964640i	$-0.584901\pi$
$89$	−46.9157			−0.527143			−0.263572	+	0.964640i	$0.584901\pi$
$90$			3.01809i			0.0335344i
$91$	−15.3557			−0.168744
$92$	−15.1247			−0.164399
$93$	121.927			1.31105
$94$			27.7475i			0.295186i
$95$		−	7.91681i		−	0.0833348i
$96$			153.804i			1.60213i
$97$	−14.0830			−0.145185			−0.0725927	−	0.997362i	$-0.523127\pi$
$97$	−14.0830			−0.145185			−0.0725927	+	0.997362i	$0.523127\pi$
$98$			36.2359i			0.369755i
$99$	−124.269	+	83.1152i	−1.25524	+	0.839547i
$100$	−78.6592			−0.786592
$101$			182.129i			1.80325i	0.432514	+	0.901627i	$0.357627\pi$
$101$			182.129i			1.80325i	−0.432514	+	0.901627i	$0.642373\pi$
$102$	−103.012			−1.00993
$103$	79.4738			0.771590			0.385795	−	0.922584i	$-0.373927\pi$
$103$	79.4738			0.771590			0.385795	+	0.922584i	$0.373927\pi$
$104$	32.5979			0.313441
$105$		−	3.55679i		−	0.0338742i
$106$			5.09377i			0.0480545i
$107$		−	69.2284i		−	0.646994i	−0.946229	−	0.323497i	$-0.895141\pi$
$107$		−	69.2284i		−	0.646994i	0.946229	−	0.323497i	$-0.104859\pi$
$108$	68.8194			0.637216
$109$		−	136.265i		−	1.25014i	−0.780571	−	0.625068i	$-0.785071\pi$
$109$		−	136.265i		−	1.25014i	0.780571	−	0.625068i	$-0.214929\pi$
$110$	−1.35801	−	2.03042i	−0.0123455	−	0.0184583i
$111$	−239.349			−2.15629
$112$		−	20.3389i		−	0.181597i
$113$	46.4667			0.411210			0.205605	−	0.978635i	$-0.434084\pi$
$113$	46.4667			0.411210			0.205605	+	0.978635i	$0.434084\pi$
$114$	143.402			1.25791
$115$	−1.15767			−0.0100667
$116$		−	148.621i		−	1.28122i
$117$		−	67.3218i		−	0.575400i
$118$		−	29.9774i		−	0.254046i
$119$	73.0353			0.613742
$120$			7.55055i			0.0629212i
$121$	46.2037	−	111.831i	0.381849	−	0.924225i
$122$	−76.5578			−0.627523
$123$			61.8232i			0.502628i
$124$	80.9012			0.652429
$125$	−12.0555			−0.0964437
$126$	38.7598			0.307618
$127$			151.594i			1.19366i	0.802369	+	0.596828i	$0.203572\pi$
$127$			151.594i			1.19366i	−0.802369	+	0.596828i	$0.796428\pi$
$128$			126.194i			0.985894i
$129$			229.864i			1.78189i
$130$	1.09996			0.00846125
$131$		−	55.2684i		−	0.421896i	−0.977497	−	0.210948i	$-0.932345\pi$
$131$		−	55.2684i		−	0.421896i	0.977497	−	0.210948i	$-0.0676551\pi$
$132$	−137.057	+	91.6678i	−1.03831	+	0.694453i
$133$	−101.671			−0.764447
$134$		−	117.114i		−	0.873987i
$135$	5.26754			0.0390188
$136$	−155.043			−1.14002
$137$	205.118			1.49721			0.748605	−	0.663016i	$-0.230724\pi$
$137$	205.118			1.49721			0.748605	+	0.663016i	$0.230724\pi$
$138$		−	20.9696i		−	0.151954i
$139$			32.4284i			0.233298i	0.993173	+	0.116649i	$0.0372152\pi$
$139$			32.4284i			0.233298i	−0.993173	+	0.116649i	$0.962785\pi$
$140$		−	2.36000i		−	0.0168572i
$141$	143.362			1.01675
$142$			37.1528i			0.261639i
$143$	30.2918	+	45.2906i	0.211831	+	0.316718i
$144$	89.1689			0.619229
$145$		−	11.3757i		−	0.0784530i
$146$	52.8515			0.361996
$147$	187.220			1.27360
$148$	−158.813			−1.07306
$149$			220.472i			1.47968i	0.672783	+	0.739840i	$0.265099\pi$
$149$			220.472i			1.47968i	−0.672783	+	0.739840i	$0.734901\pi$
$150$		−	109.057i		−	0.727045i
$151$			1.92316i			0.0127361i	0.999980	+	0.00636807i	$0.00202703\pi$
$151$			1.92316i			0.0127361i	−0.999980	+	0.00636807i	$0.997973\pi$
$152$	215.834			1.41996
$153$			320.198i			2.09280i
$154$	−26.0756	+	17.4402i	−0.169322	+	0.113248i
$155$	6.19230			0.0399503
$156$		−	74.2493i		−	0.475957i
$157$	−82.1805			−0.523443			−0.261721	−	0.965143i	$-0.584290\pi$
$157$	−82.1805			−0.523443			−0.261721	+	0.965143i	$0.584290\pi$
$158$	70.0879			0.443594
$159$	26.3179			0.165521
$160$			7.81125i			0.0488203i
$161$			14.8673i			0.0923437i
$162$		−	17.1122i		−	0.105631i
$163$	275.874			1.69248			0.846240	−	0.532801i	$-0.178861\pi$
$163$	275.874			1.69248			0.846240	+	0.532801i	$0.178861\pi$
$164$			41.0209i			0.250128i
$165$	−10.4905	+	7.01640i	−0.0635789	+	0.0425236i
$166$	105.850			0.637650
$167$			118.203i			0.707805i	0.935282	+	0.353902i	$0.115145\pi$
$167$			118.203i			0.707805i	−0.935282	+	0.353902i	$0.884855\pi$
$168$	96.9677			0.577189
$169$	144.464			0.854818
$170$	−5.23168			−0.0307746
$171$		−	445.744i		−	2.60669i
$172$			152.520i			0.886742i
$173$			25.7292i			0.148724i	0.997231	+	0.0743619i	$0.0236920\pi$
$173$			25.7292i			0.148724i	−0.997231	+	0.0743619i	$0.976308\pi$
$174$	206.055			1.18422
$175$			77.3207i			0.441833i
$176$	−59.9883	+	40.1221i	−0.340842	+	0.227966i
$177$	−154.884			−0.875049
$178$		−	43.1594i		−	0.242469i
$179$	−332.909			−1.85983			−0.929914	−	0.367776i	$-0.880119\pi$
$179$	−332.909			−1.85983			−0.929914	+	0.367776i	$0.880119\pi$
$180$	10.3466			0.0574812
$181$	−20.9848			−0.115938			−0.0579690	−	0.998318i	$-0.518462\pi$
$181$	−20.9848			−0.115938			−0.0579690	+	0.998318i	$0.518462\pi$
$182$		−	14.1262i		−	0.0776167i
$183$			395.550i			2.16148i
$184$		−	31.5612i		−	0.171528i
$185$	−12.1558			−0.0657069
$186$			112.165i			0.603039i
$187$	−144.075	−	215.413i	−0.770455	−	1.15194i
$188$	95.1238			0.505978
$189$		−	67.6483i		−	0.357927i
$190$	7.28295			0.0383313
$191$	77.8598			0.407643			0.203822	−	0.979008i	$-0.434664\pi$
$191$	77.8598			0.407643			0.203822	+	0.979008i	$0.434664\pi$
$192$	−16.7554			−0.0872680
$193$		−	118.594i		−	0.614479i	−0.951632	−	0.307239i	$-0.900595\pi$
$193$		−	118.594i		−	0.614479i	0.951632	−	0.307239i	$-0.0994052\pi$
$194$		−	12.9554i		−	0.0667806i
$195$		−	5.68316i		−	0.0291444i
$196$	124.224			0.633796
$197$		−	155.835i		−	0.791039i	−0.918458	−	0.395520i	$-0.870565\pi$
$197$		−	155.835i		−	0.791039i	0.918458	−	0.395520i	$-0.129435\pi$
$198$	−76.4606	−	114.320i	−0.386164	−	0.577371i
$199$	217.530			1.09311			0.546557	−	0.837422i	$-0.315938\pi$
$199$	217.530			1.09311			0.546557	+	0.837422i	$0.315938\pi$
$200$		−	164.140i		−	0.820702i
$201$	−605.092			−3.01041
$202$	−167.547			−0.829439
$203$	−146.092			−0.719665
$204$			353.147i			1.73111i
$205$			3.13981i			0.0153161i
$206$			73.1107i			0.354907i
$207$	−65.1807			−0.314883
$208$		−	32.4981i		−	0.156241i
$209$	200.565	+	299.873i	0.959640	+	1.43480i
$210$	3.27202			0.0155810
$211$		−	58.2739i		−	0.276180i	−0.990420	−	0.138090i	$-0.955904\pi$
$211$		−	58.2739i		−	0.276180i	0.990420	−	0.138090i	$-0.0440963\pi$
$212$	17.4625			0.0823701
$213$	191.956			0.901204
$214$	63.6856			0.297596
$215$			11.6741i			0.0542981i
$216$			143.607i			0.664849i
$217$		−	79.5245i		−	0.366472i
$218$	125.355			0.575022
$219$		−	273.067i		−	1.24688i
$220$	−6.96068	+	4.65552i	−0.0316394	+	0.0211615i
$221$	116.698			0.528046
$222$		−	220.185i		−	0.991825i
$223$	59.5175			0.266895			0.133447	−	0.991056i	$-0.457395\pi$
$223$	59.5175			0.266895			0.133447	+	0.991056i	$0.457395\pi$
$224$	100.316			0.447838
$225$	−338.986			−1.50660
$226$			42.7464i			0.189143i
$227$			159.923i			0.704507i	0.935905	+	0.352254i	$0.114585\pi$
$227$			159.923i			0.704507i	−0.935905	+	0.352254i	$0.885415\pi$
$228$		−	491.611i		−	2.15619i
$229$	192.230			0.839432			0.419716	−	0.907655i	$-0.362130\pi$
$229$	192.230			0.839432			0.419716	+	0.907655i	$0.362130\pi$
$230$		−	1.06498i		−	0.00463035i
$231$	90.1079	+	134.724i	0.390078	+	0.583222i
$232$	310.132			1.33678
$233$			65.3915i			0.280650i	0.990105	+	0.140325i	$0.0448148\pi$
$233$			65.3915i			0.280650i	−0.990105	+	0.140325i	$0.955185\pi$
$234$	61.9317			0.264665
$235$	7.28093			0.0309827
$236$	−102.768			−0.435460
$237$		−	362.122i		−	1.52794i
$238$			67.1878i			0.282301i
$239$			385.273i			1.61202i	0.591902	+	0.806010i	$0.298377\pi$
$239$			385.273i			1.61202i	−0.591902	+	0.806010i	$0.701623\pi$
$240$	7.52744			0.0313643
$241$		−	87.4687i		−	0.362941i	−0.983396	−	0.181470i	$-0.941914\pi$
$241$		−	87.4687i		−	0.362941i	0.983396	−	0.181470i	$-0.0580857\pi$
$242$	102.877	+	42.5044i	0.425113	+	0.175638i
$243$	−284.808			−1.17205
$244$			262.455i			1.07564i
$245$	9.50830			0.0388094
$246$	−56.8733			−0.231192
$247$	−162.454			−0.657708
$248$			168.819i			0.680721i
$249$		−	546.893i		−	2.19636i
$250$		−	11.0902i		−	0.0443610i
$251$	316.144			1.25954			0.629768	−	0.776783i	$-0.283150\pi$
$251$	316.144			1.25954			0.629768	+	0.776783i	$0.283150\pi$
$252$		−	132.876i		−	0.527287i
$253$	43.8502	−	29.3284i	0.173321	−	0.115923i
$254$	−139.457			−0.549043
$255$			27.0304i			0.106002i
$256$	−130.192			−0.508561
$257$	−81.3376			−0.316489			−0.158244	−	0.987400i	$-0.550583\pi$
$257$	−81.3376			−0.316489			−0.158244	+	0.987400i	$0.550583\pi$
$258$	−211.460			−0.819613
$259$			156.110i			0.602742i
$260$		−	3.77089i		−	0.0145034i
$261$		−	640.490i		−	2.45399i
$262$	50.8434			0.194059
$263$			195.913i			0.744915i	0.928049	+	0.372457i	$0.121485\pi$
$263$			195.913i			0.744915i	−0.928049	+	0.372457i	$0.878515\pi$
$264$	−191.286	−	286.000i	−0.724568	−	1.08333i
$265$	1.33660			0.00504379
$266$		−	93.5311i		−	0.351621i
$267$	−222.991			−0.835173
$268$	−401.491			−1.49810
$269$	60.1229			0.223505			0.111753	−	0.993736i	$-0.464354\pi$
$269$	60.1229			0.223505			0.111753	+	0.993736i	$0.464354\pi$
$270$			4.84580i			0.0179474i
$271$		−	470.764i		−	1.73714i	−0.495571	−	0.868568i	$-0.665041\pi$
$271$		−	470.764i		−	1.73714i	0.495571	−	0.868568i	$-0.334959\pi$
$272$			154.569i			0.568268i
$273$	−72.9858			−0.267347
$274$			188.695i			0.688668i
$275$	228.052	−	152.529i	0.829281	−	0.554650i
$276$	−71.8879			−0.260463
$277$			221.514i			0.799690i	0.916583	+	0.399845i	$0.130936\pi$
$277$			221.514i			0.799690i	−0.916583	+	0.399845i	$0.869064\pi$
$278$	−29.8320			−0.107309
$279$	348.648			1.24963
$280$	4.92469			0.0175882
$281$		−	211.716i		−	0.753438i	−0.926328	−	0.376719i	$-0.877052\pi$
$281$		−	211.716i		−	0.753438i	0.926328	−	0.376719i	$-0.122948\pi$
$282$			131.884i			0.467674i
$283$			479.560i			1.69456i	0.531148	+	0.847279i	$0.321761\pi$
$283$			479.560i			1.69456i	−0.531148	+	0.847279i	$0.678239\pi$
$284$	127.367			0.448475
$285$		−	37.6287i		−	0.132030i
$286$	−41.6644	+	27.8665i	−0.145680	+	0.0974353i
$287$	40.3229			0.140498
$288$			439.800i			1.52708i
$289$	−266.044			−0.920568
$290$	10.4649			0.0360858
$291$	−66.9366			−0.230023
$292$		−	181.185i		−	0.620498i
$293$		−	173.206i		−	0.591146i	−0.955320	−	0.295573i	$-0.904489\pi$
$293$		−	173.206i		−	0.591146i	0.955320	−	0.295573i	$-0.0955106\pi$
$294$			172.230i			0.585816i
$295$	−7.86606			−0.0266646
$296$		−	331.399i		−	1.11959i
$297$	−199.524	+	133.448i	−0.671799	+	0.449320i
$298$	−202.820			−0.680604
$299$			23.7555i			0.0794498i
$300$	−373.868			−1.24623
$301$	149.924			0.498087
$302$	−1.76918			−0.00585821
$303$			865.660i			2.85696i
$304$		−	215.173i		−	0.707806i
$305$			20.0887i			0.0658647i
$306$	−294.562			−0.962620
$307$			569.909i			1.85638i	0.372106	+	0.928190i	$0.378636\pi$
$307$			569.909i			1.85638i	−0.372106	+	0.928190i	$0.621364\pi$
$308$	59.7884	+	89.3923i	0.194118	+	0.290235i
$309$	377.740			1.22246
$310$			5.69652i			0.0183759i
$311$	235.096			0.755935			0.377968	−	0.925819i	$-0.376623\pi$
$311$	235.096			0.755935			0.377968	+	0.925819i	$0.376623\pi$
$312$	154.938			0.496597
$313$	−258.020			−0.824346			−0.412173	−	0.911106i	$-0.635230\pi$
$313$	−258.020			−0.824346			−0.412173	+	0.911106i	$0.635230\pi$
$314$		−	75.6007i		−	0.240767i
$315$		−	10.1706i		−	0.0322875i
$316$		−	240.275i		−	0.760365i
$317$	−168.593			−0.531839			−0.265919	−	0.963995i	$-0.585675\pi$
$317$	−168.593			−0.531839			−0.265919	+	0.963995i	$0.585675\pi$
$318$			24.2108i			0.0761345i
$319$	288.192	+	430.889i	0.903424	+	1.35075i
$320$	−0.850957			−0.00265924
$321$		−	329.043i		−	1.02506i
$322$	−13.6770			−0.0424751
$323$	772.669			2.39216
$324$	−58.6640			−0.181062
$325$			123.545i			0.380140i
$326$			253.787i			0.778486i
$327$		−	647.668i		−	1.98064i
$328$	−85.5996			−0.260974
$329$		−	93.5051i		−	0.284210i
$330$	−6.45463	−	9.65060i	−0.0195595	−	0.0292443i
$331$	94.0201			0.284049			0.142024	−	0.989863i	$-0.454639\pi$
$331$	94.0201			0.284049			0.142024	+	0.989863i	$0.454639\pi$
$332$		−	362.874i		−	1.09299i
$333$	−684.412			−2.05529
$334$	−108.739			−0.325567
$335$	−30.7307			−0.0917335
$336$		−	96.6710i		−	0.287711i
$337$			63.6075i			0.188746i	0.995537	+	0.0943731i	$0.0300847\pi$
$337$			63.6075i			0.188746i	−0.995537	+	0.0943731i	$0.969915\pi$
$338$			132.898i			0.393188i
$339$	220.857			0.651496
$340$			17.9352i			0.0527507i
$341$	−234.552	+	156.876i	−0.687837	+	0.460047i
$342$	410.055			1.19899
$343$		−	274.013i		−	0.798871i
$344$	−318.267			−0.925195
$345$	−5.50241			−0.0159490
$346$	−23.6692			−0.0684081
$347$			62.9423i			0.181390i	0.995879	+	0.0906949i	$0.0289088\pi$
$347$			62.9423i			0.181390i	−0.995879	+	0.0906949i	$0.971091\pi$
$348$		−	706.397i		−	2.02988i
$349$		−	61.3543i		−	0.175800i	−0.996129	−	0.0879001i	$-0.971984\pi$
$349$		−	61.3543i		−	0.175800i	0.996129	−	0.0879001i	$-0.0280156\pi$
$350$	−71.1300			−0.203229
$351$		−	108.091i		−	0.307950i
$352$	−197.891	−	295.875i	−0.562189	−	0.840553i
$353$	−574.052			−1.62621			−0.813105	−	0.582117i	$-0.802224\pi$
$353$	−574.052			−1.62621			−0.813105	+	0.582117i	$0.802224\pi$
$354$		−	142.483i		−	0.402494i
$355$	9.74887			0.0274616
$356$	−147.959			−0.415615
$357$	347.138			0.972375
$358$		−	306.255i		−	0.855461i
$359$		−	125.281i		−	0.348972i	−0.984660	−	0.174486i	$-0.944174\pi$
$359$		−	125.281i		−	0.348972i	0.984660	−	0.174486i	$-0.0558264\pi$
$360$			21.5906i			0.0599739i
$361$	−714.622			−1.97956
$362$		−	19.3046i		−	0.0533277i
$363$	219.607	−	531.535i	0.604977	−	1.46428i
$364$	−48.4276			−0.133043
$365$		−	13.8682i		−	0.0379951i
$366$	−363.880			−0.994209
$367$	522.627			1.42405			0.712026	−	0.702153i	$-0.247778\pi$
$367$	522.627			1.42405			0.712026	+	0.702153i	$0.247778\pi$
$368$	−31.4646			−0.0855016
$369$			176.782i			0.479084i
$370$		−	11.1825i		−	0.0302230i
$371$		−	17.1653i		−	0.0462677i
$372$	384.524			1.03367
$373$			156.552i			0.419711i	0.977732	+	0.209855i	$0.0672993\pi$
$373$			156.552i			0.419711i	−0.977732	+	0.209855i	$0.932701\pi$
$374$	198.166	−	132.540i	0.529855	−	0.354384i
$375$	−57.2998			−0.152799
$376$			198.498i			0.527919i
$377$	−233.430			−0.619179
$378$	62.2320			0.164635
$379$	−512.268			−1.35163			−0.675815	−	0.737071i	$-0.736208\pi$
$379$	−512.268			−1.35163			−0.675815	+	0.737071i	$0.736208\pi$
$380$		−	24.9674i		−	0.0657037i
$381$			720.529i			1.89115i
$382$			71.6260i			0.187503i
$383$	422.863			1.10408			0.552041	−	0.833817i	$-0.313849\pi$
$383$	422.863			1.10408			0.552041	+	0.833817i	$0.313849\pi$
$384$			599.804i			1.56199i
$385$	4.57630	+	6.84223i	0.0118865	+	0.0177720i
$386$	109.099			0.282640
$387$			657.291i			1.69843i
$388$	−44.4138			−0.114469
$389$	238.322			0.612652			0.306326	−	0.951927i	$-0.400900\pi$
$389$	238.322			0.612652			0.306326	+	0.951927i	$0.400900\pi$
$390$	5.22814			0.0134055
$391$		−	112.987i		−	0.288969i
$392$			259.222i			0.661280i
$393$		−	262.692i		−	0.668426i
$394$	143.358			0.363852
$395$		−	18.3910i		−	0.0465596i
$396$	−391.910	+	262.122i	−0.989672	+	0.661924i
$397$	−228.549			−0.575691			−0.287845	−	0.957677i	$-0.592939\pi$
$397$	−228.549			−0.575691			−0.287845	+	0.957677i	$0.592939\pi$
$398$			200.113i			0.502797i
$399$	−483.245			−1.21114
$400$	−163.638			−0.409096
$401$	181.116			0.451662			0.225831	−	0.974166i	$-0.427490\pi$
$401$	181.116			0.451662			0.225831	+	0.974166i	$0.427490\pi$
$402$		−	556.645i		−	1.38469i
$403$		−	127.067i		−	0.315302i
$404$			574.383i			1.42174i
$405$	−4.49023			−0.0110870
$406$		−	134.395i		−	0.331023i
$407$	460.437	−	307.955i	1.13129	−	0.756646i
$408$	−736.922			−1.80618
$409$		−	243.302i		−	0.594870i	−0.954742	−	0.297435i	$-0.903869\pi$
$409$		−	243.302i		−	0.594870i	0.954742	−	0.297435i	$-0.0961312\pi$
$410$	−2.88842			−0.00704492
$411$	974.928			2.37209
$412$	250.638			0.608345
$413$			101.020i			0.244600i
$414$		−	59.9620i		−	0.144836i
$415$		−	27.7750i		−	0.0669276i
$416$	160.288			0.385307
$417$			154.133i			0.369623i
$418$	−275.864	+	184.507i	−0.659962	+	0.441403i
$419$	209.825			0.500775			0.250387	−	0.968146i	$-0.419442\pi$
$419$	209.825			0.500775			0.250387	+	0.968146i	$0.419442\pi$
$420$		−	11.2171i		−	0.0267074i
$421$	22.7473			0.0540315			0.0270158	−	0.999635i	$-0.491400\pi$
$421$	22.7473			0.0540315			0.0270158	+	0.999635i	$0.491400\pi$
$422$	53.6082			0.127034
$423$	409.941			0.969128
$424$			36.4394i			0.0859420i
$425$		−	587.612i		−	1.38262i
$426$			176.587i			0.414525i
$427$	257.989			0.604190
$428$		−	218.327i		−	0.510110i
$429$	143.977	+	215.267i	0.335612	+	0.501788i
$430$	−10.7394			−0.0249754
$431$			413.191i			0.958680i	0.877629	+	0.479340i	$0.159124\pi$
$431$			413.191i			0.958680i	−0.877629	+	0.479340i	$0.840876\pi$
$432$	143.168			0.331407
$433$	317.438			0.733113			0.366556	−	0.930396i	$-0.380537\pi$
$433$	317.438			0.733113			0.366556	+	0.930396i	$0.380537\pi$
$434$	73.1574			0.168565
$435$		−	54.0688i		−	0.124296i
$436$		−	429.741i		−	0.985644i
$437$			157.287i			0.359925i
$438$	251.204			0.573524
$439$		−	517.798i		−	1.17950i	−0.807588	−	0.589748i	$-0.799227\pi$
$439$		−	517.798i		−	1.17950i	0.807588	−	0.589748i	$-0.200773\pi$
$440$	−9.71481	−	14.5250i	−0.0220791	−	0.0330115i
$441$	535.350			1.21395
$442$			107.355i			0.242884i
$443$	609.883			1.37671			0.688356	−	0.725373i	$-0.258333\pi$
$443$	609.883			1.37671			0.688356	+	0.725373i	$0.258333\pi$
$444$	−754.838			−1.70009
$445$	−11.3250			−0.0254495
$446$			54.7523i			0.122763i
$447$			1047.91i			2.34431i
$448$			10.9284i			0.0243937i
$449$	−452.839			−1.00855			−0.504275	−	0.863543i	$-0.668240\pi$
$449$	−452.839			−1.00855			−0.504275	+	0.863543i	$0.668240\pi$
$450$		−	311.845i		−	0.692989i
$451$	−79.5440	−	118.930i	−0.176373	−	0.263702i
$452$	146.543			0.324210
$453$			9.14079i			0.0201783i
$454$	−147.119			−0.324051
$455$	−3.70672			−0.00814664
$456$	1025.86			2.24969
$457$		−	61.6607i		−	0.134925i	−0.997722	−	0.0674625i	$-0.978510\pi$
$457$		−	61.6607i		−	0.134925i	0.997722	−	0.0674625i	$-0.0214903\pi$
$458$			176.839i			0.386112i
$459$			514.104i			1.12005i
$460$	−3.65096			−0.00793687
$461$			135.343i			0.293586i	0.989167	+	0.146793i	$0.0468952\pi$
$461$			135.343i			0.293586i	−0.989167	+	0.146793i	$0.953105\pi$
$462$	−123.938	+	82.8935i	−0.268263	+	0.179423i
$463$	243.122			0.525101			0.262551	−	0.964918i	$-0.415436\pi$
$463$	243.122			0.525101			0.262551	+	0.964918i	$0.415436\pi$
$464$		−	309.183i		−	0.666342i
$465$	29.4321			0.0632948
$466$	−60.1559			−0.129090
$467$	−301.964			−0.646603			−0.323302	−	0.946296i	$-0.604793\pi$
$467$	−301.964			−0.646603			−0.323302	+	0.946296i	$0.604793\pi$
$468$		−	212.314i		−	0.453662i
$469$			394.659i			0.841490i
$470$			6.69798i			0.0142510i
$471$	−390.605			−0.829310
$472$		−	214.450i		−	0.454343i
$473$	−295.752	−	442.192i	−0.625269	−	0.934866i
$474$	333.129			0.702803
$475$			818.006i			1.72212i
$476$	230.333			0.483893
$477$	75.2554			0.157768
$478$	−354.426			−0.741477
$479$		−	62.5951i		−	0.130679i	−0.997863	−	0.0653394i	$-0.979187\pi$
$479$		−	62.5951i		−	0.130679i	0.997863	−	0.0653394i	$-0.0208130\pi$
$480$			37.1269i			0.0773478i
$481$			249.438i			0.518582i
$482$	80.4656			0.166941
$483$			70.6646i			0.146304i
$484$	145.714	−	352.684i	0.301061	−	0.728686i
$485$	−3.39950			−0.00700928
$486$		−	262.005i		−	0.539105i
$487$	671.784			1.37943			0.689716	−	0.724080i	$-0.257735\pi$
$487$	671.784			1.37943			0.689716	+	0.724080i	$0.257735\pi$
$488$	−547.673			−1.12228
$489$	1311.23			2.68146
$490$			8.74702i			0.0178511i
$491$		−	908.554i		−	1.85042i	−0.379461	−	0.925208i	$-0.623891\pi$
$491$		−	908.554i		−	1.85042i	0.379461	−	0.925208i	$-0.376109\pi$
$492$			194.973i			0.396287i
$493$	1110.25			2.25203
$494$		−	149.447i		−	0.302524i
$495$	−29.9974	+	20.0632i	−0.0606008	+	0.0405318i
$496$	168.302			0.339319
$497$		−	125.200i		−	0.251911i
$498$	503.106			1.01025
$499$	266.725			0.534518			0.267259	−	0.963625i	$-0.413882\pi$
$499$	266.725			0.534518			0.267259	+	0.963625i	$0.413882\pi$
$500$	−38.0196			−0.0760391
$501$			561.822i			1.12140i
$502$			290.832i			0.579346i
$503$			388.128i			0.771626i	0.922577	+	0.385813i	$0.126079\pi$
$503$			388.128i			0.771626i	−0.922577	+	0.385813i	$0.873921\pi$
$504$	277.277			0.550152
$505$			43.9642i			0.0870577i
$506$	26.9803	+	40.3394i	0.0533207	+	0.0797221i
$507$	686.640			1.35432
$508$			478.086i			0.941114i
$509$	−600.864			−1.18048			−0.590240	−	0.807228i	$-0.700967\pi$
$509$	−600.864			−1.18048			−0.590240	+	0.807228i	$0.700967\pi$
$510$	−24.8662			−0.0487573
$511$	−178.102			−0.348536
$512$			385.010i			0.751973i
$513$		−	715.678i		−	1.39508i
$514$		−	74.8253i		−	0.145575i
$515$	19.1842			0.0372509
$516$			724.928i			1.40490i
$517$	−275.787	+	184.455i	−0.533438	+	0.356780i
$518$	−143.611			−0.277242
$519$			122.291i			0.235629i
$520$	7.86882			0.0151324
$521$	−587.011			−1.12670			−0.563351	−	0.826218i	$-0.690488\pi$
$521$	−587.011			−1.12670			−0.563351	+	0.826218i	$0.690488\pi$
$522$	589.209			1.12875
$523$		−	50.8944i		−	0.0973124i	−0.998816	−	0.0486562i	$-0.984506\pi$
$523$		−	50.8944i		−	0.0973124i	0.998816	−	0.0486562i	$-0.0154939\pi$
$524$		−	174.301i		−	0.332636i
$525$			367.506i			0.700012i
$526$	−180.227			−0.342637
$527$			604.360i			1.14679i
$528$	−285.125	+	190.701i	−0.540009	+	0.361175i
$529$	23.0000			0.0434783
$530$			1.22959i			0.00231998i
$531$	−442.886			−0.834060
$532$	−320.643			−0.602713
$533$	64.4292			0.120880
$534$		−	205.137i		−	0.384152i
$535$		−	16.7111i		−	0.0312357i
$536$		−	837.802i		−	1.56306i
$537$	−1582.32			−2.94660
$538$			55.3092i			0.102805i
$539$	−360.156	+	240.884i	−0.668192	+	0.446908i
$540$	16.6123			0.0307636
$541$		−	702.333i		−	1.29821i	−0.760698	−	0.649106i	$-0.775143\pi$
$541$		−	702.333i		−	1.29821i	0.760698	−	0.649106i	$-0.224857\pi$
$542$	433.072			0.799026
$543$	−99.7408			−0.183685
$544$	−762.366			−1.40141
$545$		−	32.8930i		−	0.0603542i
$546$		−	67.1422i		−	0.122971i
$547$			352.041i			0.643585i	0.946810	+	0.321792i	$0.104285\pi$
$547$			352.041i			0.643585i	−0.946810	+	0.321792i	$0.895715\pi$
$548$	646.884			1.18045
$549$			1131.07i			2.06023i
$550$	140.317	+	209.793i	0.255121	+	0.381443i
$551$	−1545.56			−2.80502
$552$		−	150.011i		−	0.271758i
$553$	−236.187			−0.427100
$554$	−203.779			−0.367831
$555$	−57.7765			−0.104102
$556$			102.270i			0.183939i
$557$			48.4433i			0.0869717i	0.999054	+	0.0434859i	$0.0138463\pi$
$557$			48.4433i			0.0869717i	−0.999054	+	0.0434859i	$0.986154\pi$
$558$			320.734i			0.574791i
$559$	239.554			0.428540
$560$		−	4.90962i		−	0.00876718i
$561$	−684.790	−	1023.86i	−1.22066	−	1.82506i
$562$	194.765			0.346557
$563$			0.131791i			0.000234088i	1.00000		0.000117044i	$3.72562e-5\pi$
$563$			0.131791i			0.000234088i	−1.00000		0.000117044i	$0.999963\pi$
$564$	452.125			0.801639
$565$	11.2166			0.0198525
$566$	−441.164			−0.779442
$567$			57.6657i			0.101703i
$568$			265.780i			0.467923i
$569$		−	685.858i		−	1.20537i	−0.797978	−	0.602687i	$-0.794097\pi$
$569$		−	685.858i		−	1.20537i	0.797978	−	0.602687i	$-0.205903\pi$
$570$	34.6159			0.0607297
$571$		−	708.095i		−	1.24010i	−0.784563	−	0.620049i	$-0.787113\pi$
$571$		−	708.095i		−	1.24010i	0.784563	−	0.620049i	$-0.212887\pi$
$572$	95.5319	+	142.834i	0.167014	+	0.249710i
$573$	370.069			0.645844
$574$			37.0944i			0.0646245i
$575$	119.616			0.208028
$576$	−47.9118			−0.0831802
$577$	−648.540			−1.12399			−0.561993	−	0.827142i	$-0.689965\pi$
$577$	−648.540			−1.12399			−0.561993	+	0.827142i	$0.689965\pi$
$578$		−	244.743i		−	0.423431i
$579$		−	563.681i		−	0.973542i
$580$		−	35.8757i		−	0.0618547i
$581$	−356.699			−0.613940
$582$		−	61.5774i		−	0.105803i
$583$	−50.6279	+	33.8616i	−0.0868404	+	0.0580816i
$584$	378.085			0.647405
$585$		−	16.2508i		−	0.0277792i
$586$	159.338			0.271908
$587$	−697.051			−1.18748			−0.593740	−	0.804657i	$-0.702349\pi$
$587$	−697.051			−1.18748			−0.593740	+	0.804657i	$0.702349\pi$
$588$	590.438			1.00415
$589$		−	841.321i		−	1.42839i
$590$		−	7.23626i		−	0.0122649i
$591$		−	740.684i		−	1.25327i
$592$	−330.385			−0.558083
$593$		−	1062.57i		−	1.79185i	−0.444201	−	0.895927i	$-0.646512\pi$
$593$		−	1062.57i		−	1.79185i	0.444201	−	0.895927i	$-0.353488\pi$
$594$	−122.764	−	183.549i	−0.206673	−	0.309006i
$595$	17.6300			0.0296303
$596$			695.307i			1.16662i
$597$	1033.92			1.73186
$598$	−21.8535			−0.0365444
$599$	−763.078			−1.27392			−0.636960	−	0.770897i	$-0.719808\pi$
$599$	−763.078			−1.27392			−0.636960	+	0.770897i	$0.719808\pi$
$600$		−	780.162i		−	1.30027i
$601$			590.953i			0.983283i	0.870798	+	0.491641i	$0.163603\pi$
$601$			590.953i			0.983283i	−0.870798	+	0.491641i	$0.836397\pi$
$602$			137.921i			0.229104i
$603$	−1730.25			−2.86940
$604$			6.06510i			0.0100416i
$605$	11.1531	−	26.9950i	0.0184349	−	0.0446198i
$606$	−796.351			−1.31411
$607$		−	555.046i		−	0.914408i	−0.889362	−	0.457204i	$-0.848851\pi$
$607$		−	555.046i		−	0.914408i	0.889362	−	0.457204i	$-0.151149\pi$
$608$	1061.28			1.74553
$609$	−694.377			−1.14019
$610$	−18.4803			−0.0302956
$611$		−	149.405i		−	0.244526i
$612$			1009.82i			1.65003i
$613$		−	986.980i		−	1.61008i	−0.593219	−	0.805041i	$-0.702143\pi$
$613$		−	986.980i		−	1.61008i	0.593219	−	0.805041i	$-0.297857\pi$
$614$	−524.279			−0.853875
$615$			14.9235i			0.0242659i
$616$	−186.538	+	124.762i	−0.302821	+	0.202536i
$617$	43.7170			0.0708542			0.0354271	−	0.999372i	$-0.488721\pi$
$617$	43.7170			0.0708542			0.0354271	+	0.999372i	$0.488721\pi$
$618$			347.496i			0.562292i
$619$	276.474			0.446646			0.223323	−	0.974745i	$-0.428310\pi$
$619$	276.474			0.446646			0.223323	+	0.974745i	$0.428310\pi$
$620$	19.5288			0.0314980
$621$	−104.653			−0.168523
$622$			216.273i			0.347706i
$623$			145.441i			0.233453i
$624$		−	154.464i		−	0.247539i
$625$	620.633			0.993013
$626$		−	237.362i		−	0.379173i
$627$	953.287	+	1425.30i	1.52039	+	2.27321i
$628$	−259.174			−0.412698
$629$		−	1186.39i		−	1.88615i
$630$	9.35625			0.0148512
$631$	−663.581			−1.05163			−0.525817	−	0.850598i	$-0.676240\pi$
$631$	−663.581			−1.05163			−0.525817	+	0.850598i	$0.676240\pi$
$632$	501.389			0.793338
$633$		−	276.977i		−	0.437562i
$634$		−	155.095i		−	0.244629i
$635$			36.5934i			0.0576275i
$636$	82.9993			0.130502
$637$		−	195.111i		−	0.306297i
$638$	−396.390	+	265.118i	−0.621301	+	0.415546i
$639$	548.895			0.858990
$640$			30.4622i			0.0475971i
$641$	−871.988			−1.36036			−0.680178	−	0.733047i	$-0.738097\pi$
$641$	−871.988			−1.36036			−0.680178	+	0.733047i	$0.738097\pi$
$642$	302.699			0.471493
$643$	27.1370			0.0422038			0.0211019	−	0.999777i	$-0.493283\pi$
$643$	27.1370			0.0422038			0.0211019	+	0.999777i	$0.493283\pi$
$644$			46.8874i			0.0728065i
$645$			55.4871i			0.0860265i
$646$			710.805i			1.10032i
$647$	−104.324			−0.161242			−0.0806212	−	0.996745i	$-0.525690\pi$
$647$	−104.324			−0.161242			−0.0806212	+	0.996745i	$0.525690\pi$
$648$		−	122.416i		−	0.188913i
$649$	297.951	−	199.279i	0.459092	−	0.307056i
$650$	−113.654			−0.174852
$651$		−	377.981i		−	0.580616i
$652$	870.030			1.33440
$653$	−1186.19			−1.81652			−0.908262	−	0.418402i	$-0.862590\pi$
$653$	−1186.19			−1.81652			−0.908262	+	0.418402i	$0.862590\pi$
$654$	595.813			0.911028
$655$		−	13.3413i		−	0.0203684i
$656$			85.3377i			0.130088i
$657$		−	780.828i		−	1.18847i
$658$	86.0186			0.130727
$659$			229.570i			0.348362i	0.984714	+	0.174181i	$0.0557278\pi$
$659$			229.570i			0.348362i	−0.984714	+	0.174181i	$0.944272\pi$
$660$	−33.0842	+	22.1278i	−0.0501275	+	0.0335269i
$661$	−822.477			−1.24429			−0.622146	−	0.782902i	$-0.713739\pi$
$661$	−822.477			−1.24429			−0.622146	+	0.782902i	$0.713739\pi$
$662$			86.4924i			0.130653i
$663$	554.668			0.836603
$664$	757.220			1.14039
$665$	−24.5425			−0.0369061
$666$		−	629.614i		−	0.945367i
$667$			226.007i			0.338840i
$668$			372.780i			0.558054i
$669$	282.887			0.422851
$670$		−	28.2703i		−	0.0421944i
$671$	−508.929	−	760.923i	−0.758464	−	1.13401i
$672$	476.802			0.709527
$673$			1016.85i			1.51092i	0.655192	+	0.755462i	$0.272588\pi$
$673$			1016.85i			1.51092i	−0.655192	+	0.755462i	$0.727412\pi$
$674$	−58.5148			−0.0868172
$675$	−544.270			−0.806326
$676$	455.599			0.673964
$677$			527.044i			0.778499i	0.921132	+	0.389250i	$0.127266\pi$
$677$			527.044i			0.778499i	−0.921132	+	0.389250i	$0.872734\pi$
$678$			203.174i			0.299667i
$679$			43.6580i			0.0642975i
$680$	−37.4260			−0.0550382
$681$			760.117i			1.11618i
$682$	−144.316	−	215.773i	−0.211607	−	0.316383i
$683$	−1263.63			−1.85012			−0.925059	−	0.379823i	$-0.875985\pi$
$683$	−1263.63			−1.85012			−0.925059	+	0.379823i	$0.875985\pi$
$684$		−	1405.75i		−	2.05519i
$685$	49.5135			0.0722825
$686$	252.074			0.367455
$687$	913.671			1.32994
$688$			317.293i			0.461182i
$689$		−	27.4273i		−	0.0398074i
$690$		−	5.06186i		−	0.00733603i
$691$	−51.0978			−0.0739476			−0.0369738	−	0.999316i	$-0.511772\pi$
$691$	−51.0978			−0.0739476			−0.0369738	+	0.999316i	$0.511772\pi$
$692$			81.1427i			0.117258i
$693$	257.661	+	385.241i	0.371806	+	0.555903i
$694$	−57.9028			−0.0834334
$695$			7.82791i			0.0112632i
$696$	1474.06			2.11790
$697$	−306.441			−0.439657
$698$	56.4420			0.0808624
$699$			310.806i			0.444644i
$700$			243.848i			0.348354i
$701$		−	260.871i		−	0.372141i	−0.982536	−	0.186071i	$-0.940425\pi$
$701$		−	260.871i		−	0.372141i	0.982536	−	0.186071i	$-0.0595754\pi$
$702$	99.4364			0.141647
$703$			1651.55i			2.34929i
$704$	32.2326	−	21.5582i	0.0457849	−	0.0306224i
$705$	34.6063			0.0490870
$706$		−	528.091i		−	0.748004i
$707$	564.609			0.798598
$708$	−488.460			−0.689915
$709$	200.950			0.283427			0.141713	−	0.989908i	$-0.454739\pi$
$709$	200.950			0.283427			0.141713	+	0.989908i	$0.454739\pi$
$710$			8.96833i			0.0126314i
$711$		−	1035.48i		−	1.45637i
$712$		−	308.751i		−	0.433638i
$713$	−123.026			−0.172547
$714$			319.344i			0.447261i
$715$	7.31216	+	10.9327i	0.0102268	+	0.0152905i
$716$	−1049.90			−1.46634
$717$			1831.21i			2.55398i
$718$	115.250			0.160516
$719$	1116.70			1.55312			0.776562	−	0.630041i	$-0.216962\pi$
$719$	1116.70			1.55312			0.776562	+	0.630041i	$0.216962\pi$
$720$	21.5245			0.0298952
$721$		−	246.373i		−	0.341710i
$722$		−	657.406i		−	0.910534i
$723$		−	415.740i		−	0.575021i
$724$	−66.1801			−0.0914089
$725$			1175.39i			1.62123i
$726$	488.978	+	202.024i	0.673523	+	0.278270i
$727$	967.146			1.33032			0.665162	−	0.746699i	$-0.268362\pi$
$727$	967.146			1.33032			0.665162	+	0.746699i	$0.268362\pi$
$728$		−	101.055i		−	0.138812i
$729$	−1186.28			−1.62727
$730$	12.7579			0.0174765
$731$	−1139.37			−1.55865
$732$			1247.45i			1.70417i
$733$		−	917.994i		−	1.25238i	−0.779671	−	0.626190i	$-0.784614\pi$
$733$		−	917.994i		−	1.25238i	0.779671	−	0.626190i	$-0.215386\pi$
$734$			480.783i			0.655017i
$735$	45.1930			0.0614871
$736$		−	155.190i		−	0.210856i
$737$	1164.02	−	778.534i	1.57940	−	1.05636i
$738$	−162.628			−0.220363
$739$		−	307.451i		−	0.416037i	−0.978125	−	0.208019i	$-0.933299\pi$
$739$		−	307.451i		−	0.416037i	0.978125	−	0.208019i	$-0.0667014\pi$
$740$	−38.3359			−0.0518052
$741$	−772.145			−1.04203
$742$	15.7910			0.0212816
$743$			93.6153i			0.125996i	0.998014	+	0.0629982i	$0.0200662\pi$
$743$			93.6153i			0.125996i	−0.998014	+	0.0629982i	$0.979934\pi$
$744$			802.398i			1.07849i
$745$			53.2199i			0.0714361i
$746$	−144.018			−0.193053
$747$		−	1563.83i		−	2.09348i
$748$	−454.372	−	679.352i	−0.607450	−	0.908224i
$749$	−214.612			−0.286531
$750$		−	52.7121i		−	0.0702828i
$751$	1095.93			1.45929			0.729646	−	0.683825i	$-0.239685\pi$
$751$	1095.93			1.45929			0.729646	+	0.683825i	$0.239685\pi$
$752$	197.890			0.263152
$753$	1502.63			1.99553
$754$		−	214.741i		−	0.284802i
$755$			0.464232i			0.000614877i
$756$		−	213.344i		−	0.282201i
$757$	768.810			1.01560			0.507800	−	0.861475i	$-0.330459\pi$
$757$	768.810			1.01560			0.507800	+	0.861475i	$0.330459\pi$
$758$		−	471.253i		−	0.621706i
$759$	208.421	−	139.398i	0.274599	−	0.183661i
$760$	52.1002			0.0685529
$761$		−	293.017i		−	0.385042i	−0.981293	−	0.192521i	$-0.938334\pi$
$761$		−	293.017i		−	0.385042i	0.981293	−	0.192521i	$-0.0616663\pi$
$762$	−662.840			−0.869869
$763$	−422.428			−0.553641
$764$	245.548			0.321398
$765$			77.2929i			0.101036i
$766$			389.007i			0.507842i
$767$			161.412i			0.210447i
$768$	−618.802			−0.805732
$769$		−	468.021i		−	0.608609i	−0.952575	−	0.304305i	$-0.901576\pi$
$769$		−	468.021i		−	0.608609i	0.952575	−	0.304305i	$-0.0984241\pi$
$770$	−6.29441	+	4.20990i	−0.00817455	+	0.00546740i
$771$	−386.599			−0.501425
$772$		−	374.013i		−	0.484473i
$773$	−350.939			−0.453996			−0.226998	−	0.973895i	$-0.572891\pi$
$773$	−350.939			−0.453996			−0.226998	+	0.973895i	$0.572891\pi$
$774$	−604.666			−0.781222
$775$	−639.821			−0.825575
$776$		−	92.6796i		−	0.119432i
$777$			741.993i			0.954946i
$778$			219.240i			0.281800i
$779$	426.592			0.547614
$780$		−	17.9231i		−	0.0229783i
$781$	−369.268	+	246.978i	−0.472814	+	0.316233i
$782$	103.941			0.132916
$783$		−	1028.36i		−	1.31336i
$784$	258.429			0.329628
$785$	−19.8376			−0.0252708
$786$	241.659			0.307454
$787$			528.020i			0.670927i	0.942053	+	0.335464i	$0.108893\pi$
$787$			528.020i			0.670927i	−0.942053	+	0.335464i	$0.891107\pi$
$788$		−	491.459i		−	0.623679i
$789$			931.175i			1.18020i
$790$	16.9186			0.0214159
$791$		−	144.049i		−	0.182110i
$792$	−546.977	−	817.810i	−0.690628	−	1.03259i
$793$	412.224			0.519828
$794$		−	210.250i		−	0.264799i
$795$	6.35289			0.00799106
$796$	686.027			0.861843
$797$	−517.639			−0.649484			−0.324742	−	0.945803i	$-0.605277\pi$
$797$	−517.639			−0.649484			−0.324742	+	0.945803i	$0.605277\pi$
$798$		−	444.555i		−	0.557086i
$799$			710.608i			0.889371i
$800$		−	807.099i		−	1.00887i
$801$	−637.638			−0.796052
$802$			166.615i			0.207750i
$803$	351.338	+	525.301i	0.437532	+	0.654173i
$804$	−1908.29			−2.37349
$805$			3.58883i			0.00445818i
$806$	116.893			0.145029
$807$	285.765			0.354108
$808$	−1198.58			−1.48339
$809$		−	915.954i		−	1.13221i	−0.824335	−	0.566103i	$-0.808451\pi$
$809$		−	915.954i		−	1.13221i	0.824335	−	0.566103i	$-0.191549\pi$
$810$		−	4.13072i		−	0.00509966i
$811$			474.314i			0.584851i	0.956288	+	0.292426i	$0.0944624\pi$
$811$			474.314i			0.584851i	−0.956288	+	0.292426i	$0.905538\pi$
$812$	−460.733			−0.567405
$813$		−	2237.54i		−	2.75221i
$814$	283.298	+	423.572i	0.348033	+	0.520359i
$815$	66.5935			0.0817098
$816$			734.668i			0.900328i
$817$	1586.11			1.94138
$818$	223.822			0.273621
$819$	−208.701			−0.254824
$820$			9.90207i			0.0120757i
$821$		−	185.729i		−	0.226223i	−0.993582	−	0.113111i	$-0.963918\pi$
$821$		−	185.729i		−	0.226223i	0.993582	−	0.113111i	$-0.0360817\pi$
$822$			896.870i			1.09108i
$823$	−342.547			−0.416217			−0.208109	−	0.978106i	$-0.566731\pi$
$823$	−342.547			−0.416217			−0.208109	+	0.978106i	$0.566731\pi$
$824$			523.014i			0.634725i
$825$	1083.94	−	724.971i	1.31386	−	0.878752i
$826$	−92.9315			−0.112508
$827$			226.568i			0.273964i	0.990574	+	0.136982i	$0.0437402\pi$
$827$			226.568i			0.273964i	−0.990574	+	0.136982i	$0.956260\pi$
$828$	−205.562			−0.248263
$829$	866.076			1.04472			0.522362	−	0.852724i	$-0.325051\pi$
$829$	866.076			1.04472			0.522362	+	0.852724i	$0.325051\pi$
$830$	25.5512			0.0307845
$831$			1052.86i			1.26698i
$832$			17.4617i			0.0209877i
$833$			927.996i			1.11404i
$834$	−141.792			−0.170014
$835$			28.5332i			0.0341715i
$836$	632.525	+	945.716i	0.756609	+	1.13124i
$837$	559.783			0.668797
$838$			193.025i			0.230340i
$839$	−840.329			−1.00158			−0.500792	−	0.865567i	$-0.666958\pi$
$839$	−840.329			−1.00158			−0.500792	+	0.865567i	$0.666958\pi$
$840$	23.4071			0.0278656
$841$	−1379.83			−1.64070
$842$			20.9260i			0.0248527i
$843$		−	1006.29i		−	1.19370i
$844$		−	183.780i		−	0.217748i
$845$	34.8723			0.0412690
$846$			377.119i			0.445767i
$847$	−346.683	−	143.234i	−0.409307	−	0.169107i
$848$	36.3279			0.0428395
$849$			2279.35i			2.68475i
$850$	540.565			0.635958
$851$	241.505			0.283790
$852$	605.377			0.710536
$853$			1146.48i			1.34405i	0.740528	+	0.672026i	$0.234576\pi$
$853$			1146.48i			1.34405i	−0.740528	+	0.672026i	$0.765424\pi$
$854$			237.333i			0.277908i
$855$		−	107.598i		−	0.125846i
$856$	455.589			0.532230
$857$		−	145.376i		−	0.169634i	−0.996397	−	0.0848170i	$-0.972969\pi$
$857$		−	145.376i		−	0.169634i	0.996397	−	0.0848170i	$-0.0270306\pi$
$858$	−198.032	+	132.450i	−0.230806	+	0.154370i
$859$	−589.556			−0.686328			−0.343164	−	0.939276i	$-0.611499\pi$
$859$	−589.556			−0.686328			−0.343164	+	0.939276i	$0.611499\pi$
$860$			36.8168i			0.0428102i
$861$	191.655			0.222596
$862$	−380.109			−0.440962
$863$	304.169			0.352456			0.176228	−	0.984349i	$-0.443610\pi$
$863$	304.169			0.352456			0.176228	+	0.984349i	$0.443610\pi$
$864$			706.135i			0.817286i
$865$			6.21079i			0.00718011i
$866$			292.022i			0.337208i
$867$	−1264.51			−1.45849
$868$		−	250.798i		−	0.288938i
$869$	465.920	+	696.617i	0.536156	+	0.801630i
$870$	49.7398			0.0571721
$871$			630.598i			0.723993i
$872$	896.753			1.02839
$873$	−191.404			−0.219248
$874$	−144.694			−0.165554
$875$			37.3726i			0.0427115i
$876$		−	861.176i		−	0.983078i
$877$		−	689.912i		−	0.786673i	−0.919395	−	0.393337i	$-0.871321\pi$
$877$		−	689.912i		−	0.786673i	0.919395	−	0.393337i	$-0.128679\pi$
$878$	476.341			0.542530
$879$		−	823.250i		−	0.936575i
$880$	−14.4806	+	9.68509i	−0.0164552	+	0.0110058i
$881$	−427.634			−0.485396			−0.242698	−	0.970102i	$-0.578032\pi$
$881$	−427.634			−0.485396			−0.242698	+	0.970102i	$0.578032\pi$
$882$			492.487i			0.558375i
$883$	567.615			0.642825			0.321413	−	0.946939i	$-0.395842\pi$
$883$	567.615			0.642825			0.321413	+	0.946939i	$0.395842\pi$
$884$	368.033			0.416327
$885$	−37.3875			−0.0422457
$886$			561.053i			0.633243i
$887$		−	1101.68i		−	1.24203i	−0.783800	−	0.621014i	$-0.786721\pi$
$887$		−	1101.68i		−	1.24203i	0.783800	−	0.621014i	$-0.213279\pi$
$888$		−	1575.14i		−	1.77381i
$889$	469.950			0.528628
$890$		−	10.4183i		−	0.0117059i
$891$	170.081	−	113.756i	0.190888	−	0.127672i
$892$	187.702			0.210428
$893$		−	989.227i		−	1.10776i
$894$	−964.006			−1.07831
$895$	−80.3612			−0.0897890
$896$	391.210			0.436618
$897$			112.910i			0.125875i
$898$		−	416.582i		−	0.463900i
$899$		−	1208.90i		−	1.34471i
$900$	−1069.07			−1.18785
$901$			130.451i			0.144784i
$902$	109.408	−	73.1753i	0.121295	−	0.0811257i
$903$	712.592			0.789138
$904$			305.796i			0.338270i
$905$	−5.06553			−0.00559727
$906$	−8.40893			−0.00928138
$907$	216.538			0.238740			0.119370	−	0.992850i	$-0.461912\pi$
$907$	216.538			0.238740			0.119370	+	0.992850i	$0.461912\pi$
$908$			504.353i			0.555455i
$909$			2475.33i			2.72314i
$910$		−	3.40994i		−	0.00374719i
$911$	−396.334			−0.435054			−0.217527	−	0.976054i	$-0.569799\pi$
$911$	−396.334			−0.435054			−0.217527	+	0.976054i	$0.569799\pi$
$912$		−	1022.72i		−	1.12140i
$913$	703.652	+	1052.06i	0.770704	+	1.15231i
$914$	56.7239			0.0620611
$915$			95.4820i			0.104352i
$916$	606.239			0.661833
$917$	−171.335			−0.186843
$918$	−472.943			−0.515188
$919$			1473.35i			1.60321i	0.597856	+	0.801604i	$0.296019\pi$
$919$			1473.35i			1.60321i	−0.597856	+	0.801604i	$0.703981\pi$
$920$		−	7.61857i		−	0.00828105i
$921$			2708.78i			2.94113i
$922$	−124.507			−0.135040
$923$		−	200.048i		−	0.216737i
$924$	284.175	+	424.883i	0.307549	+	0.459830i
$925$	1256.00			1.35783
$926$			223.656i			0.241530i
$927$	1080.14			1.16520
$928$	1524.96			1.64327
$929$	−32.1342			−0.0345901			−0.0172950	−	0.999850i	$-0.505505\pi$
$929$	−32.1342			−0.0345901			−0.0172950	+	0.999850i	$0.505505\pi$
$930$			27.0756i			0.0291136i
$931$		−	1291.85i		−	1.38759i
$932$			206.226i			0.221273i
$933$	1117.41			1.19766
$934$		−	277.787i		−	0.297417i
$935$	−34.7784	−	51.9987i	−0.0371961	−	0.0556135i
$936$	443.042			0.473335
$937$		−	422.290i		−	0.450683i	−0.974280	−	0.225341i	$-0.927650\pi$
$937$		−	422.290i		−	0.450683i	0.974280	−	0.225341i	$-0.0723498\pi$
$938$	−363.060			−0.387058
$939$	−1226.37			−1.30604
$940$	22.9620			0.0244277
$941$		−	1414.84i		−	1.50355i	−0.659422	−	0.751773i	$-0.729199\pi$
$941$		−	1414.84i		−	1.50355i	0.659422	−	0.751773i	$-0.270801\pi$
$942$		−	359.331i		−	0.381456i
$943$		−	62.3802i		−	0.0661507i
$944$	−213.794			−0.226476
$945$		−	16.3297i		−	0.0172801i
$946$	406.788	−	272.073i	0.430008	−	0.287603i
$947$	1748.72			1.84659			0.923295	−	0.384093i	$-0.125486\pi$
$947$	1748.72			1.84659			0.923295	+	0.384093i	$0.125486\pi$
$948$		−	1142.03i		−	1.20467i
$949$	−284.577			−0.299871
$950$	−752.512			−0.792118
$951$	−801.324			−0.842612
$952$			480.642i			0.504876i
$953$			1142.34i			1.19868i	0.800494	+	0.599341i	$0.204571\pi$
$953$			1142.34i			1.19868i	−0.800494	+	0.599341i	$0.795429\pi$
$954$			69.2301i			0.0725682i
$955$	18.7946			0.0196802
$956$			1215.04i			1.27096i
$957$	1369.78	+	2048.02i	1.43133	+	2.14004i
$958$	57.5834			0.0601080
$959$		−	635.876i		−	0.663062i
$960$	−4.04461			−0.00421313
$961$	−302.943			−0.315237
$962$	−229.467			−0.238531
$963$		−	940.891i		−	0.977042i
$964$		−	275.852i		−	0.286153i
$965$		−	28.6276i		−	0.0296659i
$966$	−65.0069			−0.0672949
$967$			263.434i			0.272424i	0.990680	+	0.136212i	$0.0434928\pi$
$967$			263.434i			0.272424i	−0.990680	+	0.136212i	$0.956507\pi$
$968$	735.956	+	304.065i	0.760286	+	0.314116i
$969$	3672.51			3.78999
$970$		−	3.12732i		−	0.00322404i
$971$	−1372.06			−1.41304			−0.706519	−	0.707694i	$-0.749736\pi$
$971$	−1372.06			−1.41304			−0.706519	+	0.707694i	$0.749736\pi$
$972$	−898.205			−0.924079
$973$	100.530			0.103319
$974$			617.997i			0.634494i
$975$			587.213i			0.602270i
$976$			545.998i			0.559424i
$977$	−96.5589			−0.0988320			−0.0494160	−	0.998778i	$-0.515736\pi$
$977$	−96.5589			−0.0988320			−0.0494160	+	0.998778i	$0.515736\pi$
$978$			1206.25i			1.23338i
$979$	428.970	−	286.909i	0.438171	−	0.293063i
$980$	29.9865			0.0305985
$981$		−	1851.99i		−	1.88786i
$982$	835.811			0.851131
$983$	−265.797			−0.270393			−0.135197	−	0.990819i	$-0.543167\pi$
$983$	−265.797			−0.270393			−0.135197	+	0.990819i	$0.543167\pi$
$984$	−406.856			−0.413471
$985$		−	37.6170i		−	0.0381899i
$986$			1021.36i			1.03586i
$987$		−	444.431i		−	0.450285i
$988$	−512.334			−0.518557
$989$		−	231.935i		−	0.234515i
$990$	−18.4569	−	27.5957i	−0.0186433	−	0.0278744i
$991$	1823.58			1.84014			0.920072	−	0.391750i	$-0.128130\pi$
$991$	1823.58			1.84014			0.920072	+	0.391750i	$0.128130\pi$
$992$			830.103i			0.836797i
$993$	446.879			0.450029
$994$	115.176			0.115871
$995$	52.5096			0.0527734
$996$		−	1724.75i		−	1.73167i
$997$		−	91.1503i		−	0.0914246i	−0.998955	−	0.0457123i	$-0.985444\pi$
$997$		−	91.1503i		−	0.0914246i	0.998955	−	0.0457123i	$-0.0145557\pi$
$998$			245.369i			0.245861i
$999$	−1098.88			−1.09998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.26	yes	44
11.10	odd	2	inner	253.3.c.a.208.19	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.19	✓	44	11.10	odd	2	inner
253.3.c.a.208.26	yes	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	253.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.919935i q^{2} +4.75301 q^{3} +3.15372 q^{4} +0.241391 q^{5} +4.37246i q^{6} -3.10005i q^{7} +6.58096i q^{8} +13.5911 q^{9} +0.222064i q^{10} +(-9.14341 + 6.11540i) q^{11} +14.9897 q^{12} -4.95337i q^{13} +2.85185 q^{14} +1.14733 q^{15} +6.56082 q^{16} +23.5594i q^{17} +12.5030i q^{18} -32.7967i q^{19} +0.761278 q^{20} -14.7346i q^{21} +(-5.62577 - 8.41134i) q^{22} -4.79583 q^{23} +31.2794i q^{24} -24.9417 q^{25} +4.55677 q^{26} +21.8217 q^{27} -9.77670i q^{28} -47.1256i q^{29} +1.05547i q^{30} +25.6526 q^{31} +32.3594i q^{32} +(-43.4587 + 29.0666i) q^{33} -21.6731 q^{34} -0.748324i q^{35} +42.8626 q^{36} -50.3573 q^{37} +30.1708 q^{38} -23.5434i q^{39} +1.58858i q^{40} +13.0072i q^{41} +13.5549 q^{42} +48.3618i q^{43} +(-28.8357 + 19.2863i) q^{44} +3.28077 q^{45} -4.41185i q^{46} +30.1624 q^{47} +31.1837 q^{48} +39.3897 q^{49} -22.9448i q^{50} +111.978i q^{51} -15.6215i q^{52} +5.53710 q^{53} +20.0745i q^{54} +(-2.20713 + 1.47620i) q^{55} +20.4013 q^{56} -155.883i q^{57} +43.3525 q^{58} -32.5864 q^{59} +3.61836 q^{60} +83.2209i q^{61} +23.5988i q^{62} -42.1332i q^{63} -3.52523 q^{64} -1.19570i q^{65} +(-26.7394 - 39.9792i) q^{66} -127.307 q^{67} +74.2997i q^{68} -22.7946 q^{69} +0.688409 q^{70} +40.3863 q^{71} +89.4426i q^{72} -57.4513i q^{73} -46.3254i q^{74} -118.548 q^{75} -103.431i q^{76} +(18.9581 + 28.3450i) q^{77} +21.6584 q^{78} -76.1879i q^{79} +1.58372 q^{80} -18.6015 q^{81} -11.9657 q^{82} -115.062i q^{83} -46.4688i q^{84} +5.68701i q^{85} -44.4897 q^{86} -223.989i q^{87} +(-40.2452 - 60.1724i) q^{88} -46.9157 q^{89} +3.01809i q^{90} -15.3557 q^{91} -15.1247 q^{92} +121.927 q^{93} +27.7475i q^{94} -7.91681i q^{95} +153.804i q^{96} -14.0830 q^{97} +36.2359i q^{98} +(-124.269 + 83.1152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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