LMFDB - Embedded newform 33.4.d.b.32.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(32,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("33.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 35x^{6} + 10x^{5} + 2614x^{4} + 16258x^{3} + 120841x^{2} + 205270x + 821047 $ x^8 - 2x^7 - 35x^6 + 10x^5 + 2614x^4 + 16258x^3 + 120841x^2 + 205270*x + 821047
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			32.2
Root			$-0.913072 - 4.51265i$ of defining polynomial
Character	$\chi$	$=$	33.32
Dual form			33.4.d.b.32.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.48911 q^{2} +(-2.57603 + 4.51265i) q^{3} +12.1521 q^{4} -12.2625i q^{5} +(11.5641 - 20.2578i) q^{6} -14.5320i q^{7} -18.6391 q^{8} +(-13.7281 - 23.2495i) q^{9} +O(q^{10})$	\(q-4.48911 q^{2} +(-2.57603 + 4.51265i) q^{3} +12.1521 q^{4} -12.2625i q^{5} +(11.5641 - 20.2578i) q^{6} -14.5320i q^{7} -18.6391 q^{8} +(-13.7281 - 23.2495i) q^{9} +55.0476i q^{10} +(27.6173 - 23.8387i) q^{11} +(-31.3041 + 54.8381i) q^{12} +14.5320i q^{13} +65.2358i q^{14} +(55.3364 + 31.5886i) q^{15} -13.5438 q^{16} -92.5127 q^{17} +(61.6269 + 104.369i) q^{18} -162.062i q^{19} -149.015i q^{20} +(65.5781 + 37.4350i) q^{21} +(-123.977 + 107.015i) q^{22} +23.8387i q^{23} +(48.0149 - 84.1117i) q^{24} -25.3686 q^{25} -65.2358i q^{26} +(140.281 - 2.05868i) q^{27} -176.594i q^{28} -52.5040 q^{29} +(-248.411 - 141.804i) q^{30} +82.5438 q^{31} +209.912 q^{32} +(36.4330 + 186.037i) q^{33} +415.299 q^{34} -178.199 q^{35} +(-166.825 - 282.529i) q^{36} -276.802 q^{37} +727.515i q^{38} +(-65.5781 - 37.4350i) q^{39} +228.561i q^{40} +175.468 q^{41} +(-294.387 - 168.050i) q^{42} +353.189i q^{43} +(335.607 - 289.690i) q^{44} +(-285.097 + 168.341i) q^{45} -107.015i q^{46} -387.790i q^{47} +(34.8893 - 61.1185i) q^{48} +131.820 q^{49} +113.882 q^{50} +(238.316 - 417.478i) q^{51} +176.594i q^{52} +79.9449i q^{53} +(-629.736 + 9.24164i) q^{54} +(-292.322 - 338.657i) q^{55} +270.864i q^{56} +(731.331 + 417.478i) q^{57} +235.696 q^{58} +291.749i q^{59} +(672.451 + 383.867i) q^{60} +147.530i q^{61} -370.548 q^{62} +(-337.863 + 199.497i) q^{63} -833.967 q^{64} +178.199 q^{65} +(-163.552 - 835.138i) q^{66} +201.106 q^{67} -1124.22 q^{68} +(-107.576 - 61.4094i) q^{69} +799.954 q^{70} -424.473i q^{71} +(255.879 + 433.349i) q^{72} -461.542i q^{73} +1242.59 q^{74} +(65.3504 - 114.480i) q^{75} -1969.39i q^{76} +(-346.426 - 401.335i) q^{77} +(294.387 + 168.050i) q^{78} +122.886i q^{79} +166.081i q^{80} +(-352.078 + 638.343i) q^{81} -787.696 q^{82} +151.843 q^{83} +(796.909 + 454.913i) q^{84} +1134.44i q^{85} -1585.50i q^{86} +(135.252 - 236.932i) q^{87} +(-514.760 + 444.332i) q^{88} +764.973i q^{89} +(1279.83 - 755.699i) q^{90} +211.180 q^{91} +289.690i q^{92} +(-212.636 + 372.492i) q^{93} +1740.83i q^{94} -1987.29 q^{95} +(-540.741 + 947.261i) q^{96} +218.967 q^{97} -591.753 q^{98} +(-933.372 - 314.827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 44 q^{4} - 30 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 44 * q^4 - 30 * q^9	$ 8 q + 6 q^{3} + 44 q^{4} - 30 q^{9} - 144 q^{12} + 150 q^{15} - 268 q^{16} - 300 q^{22} + 276 q^{25} + 324 q^{27} + 820 q^{31} + 834 q^{33} + 768 q^{34} - 696 q^{36} - 884 q^{37} - 120 q^{42} - 1722 q^{45} - 732 q^{48} - 2032 q^{49} - 476 q^{55} + 1992 q^{58} + 2772 q^{60} - 1084 q^{64} + 2076 q^{66} + 172 q^{67} - 834 q^{69} + 5016 q^{70} + 1800 q^{75} + 120 q^{78} - 4014 q^{81} - 6408 q^{82} - 3852 q^{88} + 4776 q^{91} + 1146 q^{93} - 3836 q^{97} + 1074 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 + 44 * q^4 - 30 * q^9 - 144 * q^12 + 150 * q^15 - 268 * q^16 - 300 * q^22 + 276 * q^25 + 324 * q^27 + 820 * q^31 + 834 * q^33 + 768 * q^34 - 696 * q^36 - 884 * q^37 - 120 * q^42 - 1722 * q^45 - 732 * q^48 - 2032 * q^49 - 476 * q^55 + 1992 * q^58 + 2772 * q^60 - 1084 * q^64 + 2076 * q^66 + 172 * q^67 - 834 * q^69 + 5016 * q^70 + 1800 * q^75 + 120 * q^78 - 4014 * q^81 - 6408 * q^82 - 3852 * q^88 + 4776 * q^91 + 1146 * q^93 - 3836 * q^97 + 1074 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−4.48911			−1.58714			−0.793569	−	0.608480i	$-0.791780\pi$
$2$	−4.48911			−1.58714			−0.793569	+	0.608480i	$0.791780\pi$
$3$	−2.57603	+	4.51265i	−0.495758	+	0.868461i
$3$	−2.57603	+	4.51265i	−0.495758	+	0.868461i
$4$	12.1521			1.51901
$5$		−	12.2625i		−	1.09679i	−0.836219	−	0.548395i	$-0.815239\pi$
$5$		−	12.2625i		−	1.09679i	0.836219	−	0.548395i	$-0.184761\pi$
$6$	11.5641	−	20.2578i	0.786836	−	1.37837i
$7$		−	14.5320i		−	0.784656i	−0.919825	−	0.392328i	$-0.871670\pi$
$7$		−	14.5320i		−	0.784656i	0.919825	−	0.392328i	$-0.128330\pi$
$8$	−18.6391			−0.823738
$9$	−13.7281	−	23.2495i	−0.508448	−	0.861093i
$10$			55.0476i			1.74076i
$11$	27.6173	−	23.8387i	0.756993	−	0.653423i
$11$	27.6173	−	23.8387i	0.756993	−	0.653423i
$12$	−31.3041	+	54.8381i	−0.753060	+	1.31920i
$13$			14.5320i			0.310036i	0.987912	+	0.155018i	$0.0495435\pi$
$13$			14.5320i			0.310036i	−0.987912	+	0.155018i	$0.950457\pi$
$14$			65.2358i			1.24536i
$15$	55.3364	+	31.5886i	0.952519	+	0.543742i
$16$	−13.5438			−0.211622
$17$	−92.5127			−1.31986			−0.659930	−	0.751327i	$-0.729414\pi$
$17$	−92.5127			−1.31986			−0.659930	+	0.751327i	$0.729414\pi$
$18$	61.6269	+	104.369i	0.806978	+	1.36667i
$19$		−	162.062i		−	1.95682i	−0.206667	−	0.978411i	$-0.566262\pi$
$19$		−	162.062i		−	1.95682i	0.206667	−	0.978411i	$-0.433738\pi$
$20$		−	149.015i		−	1.66603i
$21$	65.5781	+	37.4350i	0.681443	+	0.389000i
$22$	−123.977	+	107.015i	−1.20145	+	1.03707i
$23$			23.8387i			0.216118i	0.994144	+	0.108059i	$0.0344636\pi$
$23$			23.8387i			0.216118i	−0.994144	+	0.108059i	$0.965536\pi$
$24$	48.0149	−	84.1117i	0.408375	−	0.715384i
$25$	−25.3686			−0.202949
$26$		−	65.2358i		−	0.492069i
$27$	140.281	−	2.05868i	0.999892	−	0.0146738i
$28$		−	176.594i		−	1.19190i
$29$	−52.5040			−0.336198			−0.168099	−	0.985770i	$-0.553763\pi$
$29$	−52.5040			−0.336198			−0.168099	+	0.985770i	$0.553763\pi$
$30$	−248.411	−	141.804i	−1.51178	−	0.862995i
$31$	82.5438			0.478236			0.239118	−	0.970991i	$-0.423142\pi$
$31$	82.5438			0.478236			0.239118	+	0.970991i	$0.423142\pi$
$32$	209.912			1.15961
$33$	36.4330	+	186.037i	0.192187	+	0.981358i
$34$	415.299			2.09480
$35$	−178.199			−0.860603
$36$	−166.825	−	282.529i	−0.772337	−	1.30801i
$37$	−276.802			−1.22989			−0.614945	−	0.788570i	$-0.710822\pi$
$37$	−276.802			−1.22989			−0.614945	+	0.788570i	$0.710822\pi$
$38$			727.515i			3.10575i
$39$	−65.5781	−	37.4350i	−0.269254	−	0.153703i
$40$			228.561i			0.903468i
$41$	175.468			0.668379			0.334190	−	0.942506i	$-0.391537\pi$
$41$	175.468			0.668379			0.334190	+	0.942506i	$0.391537\pi$
$42$	−294.387	−	168.050i	−1.08154	−	0.617396i
$43$			353.189i			1.25258i	0.779592	+	0.626288i	$0.215427\pi$
$43$			353.189i			1.25258i	−0.779592	+	0.626288i	$0.784573\pi$
$44$	335.607	−	289.690i	1.14988	−	0.992555i
$45$	−285.097	+	168.341i	−0.944438	+	0.557661i
$46$		−	107.015i		−	0.343010i
$47$		−	387.790i		−	1.20351i	−0.798681	−	0.601755i	$-0.794468\pi$
$47$		−	387.790i		−	1.20351i	0.798681	−	0.601755i	$-0.205532\pi$
$48$	34.8893	−	61.1185i	0.104913	−	0.183785i
$49$	131.820			0.384315
$50$	113.882			0.322108
$51$	238.316	−	417.478i	0.654331	−	1.14625i
$52$			176.594i			0.470947i
$53$			79.9449i			0.207194i	0.994619	+	0.103597i	$0.0330352\pi$
$53$			79.9449i			0.207194i	−0.994619	+	0.103597i	$0.966965\pi$
$54$	−629.736	+	9.24164i	−1.58697	+	0.0232894i
$55$	−292.322	−	338.657i	−0.716668	−	0.830263i
$56$			270.864i			0.646351i
$57$	731.331	+	417.478i	1.69942	+	0.970110i
$58$	235.696			0.533593
$59$			291.749i			0.643770i	0.946779	+	0.321885i	$0.104317\pi$
$59$			291.749i			0.643770i	−0.946779	+	0.321885i	$0.895683\pi$
$60$	672.451	+	383.867i	1.44688	+	0.825949i
$61$			147.530i			0.309661i	0.987941	+	0.154830i	$0.0494831\pi$
$61$			147.530i			0.309661i	−0.987941	+	0.154830i	$0.950517\pi$
$62$	−370.548			−0.759026
$63$	−337.863	+	199.497i	−0.675662	+	0.398957i
$64$	−833.967			−1.62884
$65$	178.199			0.340044
$66$	−163.552	−	835.138i	−0.305027	−	1.55755i
$67$	201.106			0.366701			0.183351	−	0.983048i	$-0.441306\pi$
$67$	201.106			0.366701			0.183351	+	0.983048i	$0.441306\pi$
$68$	−1124.22			−2.00488
$69$	−107.576	−	61.4094i	−0.187690	−	0.107142i
$70$	799.954			1.36590
$71$		−	424.473i		−	0.709517i	−0.934958	−	0.354758i	$-0.884563\pi$
$71$		−	424.473i		−	0.709517i	0.934958	−	0.354758i	$-0.115437\pi$
$72$	255.879	+	433.349i	0.418828	+	0.709315i
$73$		−	461.542i		−	0.739992i	−0.929033	−	0.369996i	$-0.879359\pi$
$73$		−	461.542i		−	0.739992i	0.929033	−	0.369996i	$-0.120641\pi$
$74$	1242.59			1.95201
$75$	65.3504	−	114.480i	0.100613	−	0.176253i
$76$		−	1969.39i		−	2.97243i
$77$	−346.426	−	401.335i	−0.512712	−	0.593979i
$78$	294.387	+	168.050i	0.427343	+	0.243947i
$79$			122.886i			0.175009i	0.996164	+	0.0875047i	$0.0278893\pi$
$79$			122.886i			0.175009i	−0.996164	+	0.0875047i	$0.972111\pi$
$80$			166.081i			0.232105i
$81$	−352.078	+	638.343i	−0.482961	+	0.875642i
$82$	−787.696			−1.06081
$83$	151.843			0.200807			0.100403	−	0.994947i	$-0.467987\pi$
$83$	151.843			0.200807			0.100403	+	0.994947i	$0.467987\pi$
$84$	796.909	+	454.913i	1.03512	+	0.590894i
$85$			1134.44i			1.44761i
$86$		−	1585.50i		−	1.98801i
$87$	135.252	−	236.932i	0.166673	−	0.291975i
$88$	−514.760	+	444.332i	−0.623564	+	0.538249i
$89$			764.973i			0.911090i	0.890213	+	0.455545i	$0.150556\pi$
$89$			764.973i			0.911090i	−0.890213	+	0.455545i	$0.849444\pi$
$90$	1279.83	−	755.699i	1.49895	−	0.885085i
$91$	211.180			0.243271
$92$			289.690i			0.328286i
$93$	−212.636	+	372.492i	−0.237089	+	0.415329i
$94$			1740.83i			1.91014i
$95$	−1987.29			−2.14622
$96$	−540.741	+	947.261i	−0.574887	+	1.00708i
$97$	218.967			0.229203			0.114602	−	0.993412i	$-0.463441\pi$
$97$	218.967			0.229203			0.114602	+	0.993412i	$0.463441\pi$
$98$	−591.753			−0.609960
$99$	−933.372	−	314.827i	−0.947549	−	0.319609i
$100$	−308.281			−0.308281
$101$	−189.536			−0.186729			−0.0933643	−	0.995632i	$-0.529762\pi$
$101$	−189.536			−0.186729			−0.0933643	+	0.995632i	$0.529762\pi$
$102$	−1069.82	+	1874.10i	−1.03851	+	1.81925i
$103$	1518.95			1.45307			0.726536	−	0.687128i	$-0.241129\pi$
$103$	1518.95			1.45307			0.726536	+	0.687128i	$0.241129\pi$
$104$		−	270.864i		−	0.255388i
$105$	459.046	−	804.150i	0.426651	−	0.747400i
$106$		−	358.881i		−	0.328846i
$107$	1296.96			1.17179			0.585896	−	0.810386i	$-0.300743\pi$
$107$	1296.96			1.17179			0.585896	+	0.810386i	$0.300743\pi$
$108$	1704.70	−	25.0172i	1.51884	−	0.0222897i
$109$			1439.61i			1.26504i	0.774544	+	0.632521i	$0.217980\pi$
$109$			1439.61i			1.26504i	−0.774544	+	0.632521i	$0.782020\pi$
$110$	1312.27	+	1520.26i	1.13745	+	1.31774i
$111$	713.050	−	1249.11i	0.609728	−	1.06811i
$112$			196.819i			0.166050i
$113$		−	1054.98i		−	0.878264i	−0.898423	−	0.439132i	$-0.855286\pi$
$113$		−	1054.98i		−	0.878264i	0.898423	−	0.439132i	$-0.144714\pi$
$114$	−3283.02	−	1874.10i	−2.69722	−	1.53970i
$115$	292.322			0.237037
$116$	−638.032			−0.510688
$117$	337.863	−	199.497i	0.266969	−	0.157637i
$118$		−	1309.69i		−	1.02175i
$119$			1344.40i			1.03564i
$120$	−1031.42	−	588.782i	−0.784627	−	0.447901i
$121$	194.428	−	1316.72i	0.146077	−	0.989273i
$122$		−	662.279i		−	0.491475i
$123$	−452.012	+	791.828i	−0.331354	+	0.580461i
$124$	1003.08			0.726444
$125$		−	1221.73i		−	0.874198i
$126$	1516.70	−	895.564i	1.07237	−	0.633200i
$127$		−	2274.56i		−	1.58925i	−0.607100	−	0.794626i	$-0.707667\pi$
$127$		−	2274.56i		−	1.58925i	0.607100	−	0.794626i	$-0.292333\pi$
$128$	2064.47			1.42559
$129$	−1593.82	−	909.826i	−1.08781	−	0.620974i
$130$	−799.954			−0.539697
$131$	1221.78			0.814865			0.407433	−	0.913235i	$-0.366424\pi$
$131$	1221.78			0.814865			0.407433	+	0.913235i	$0.366424\pi$
$132$	442.736	+	2260.73i	0.291934	+	1.49069i
$133$	−2355.09			−1.53543
$134$	−902.785			−0.582006
$135$	−25.2446	−	1720.19i	−0.0160941	−	1.09667i
$136$	1724.35			1.08722
$137$			404.170i			0.252048i	0.992027	+	0.126024i	$0.0402216\pi$
$137$			404.170i			0.252048i	−0.992027	+	0.126024i	$0.959778\pi$
$138$	482.920	+	275.673i	0.297891	+	0.170050i
$139$		−	103.934i		−	0.0634214i	−0.999497	−	0.0317107i	$-0.989904\pi$
$139$		−	103.934i		−	0.0634214i	0.999497	−	0.0317107i	$-0.0100955\pi$
$140$	−2165.49			−1.30726
$141$	1749.96	+	998.960i	1.04520	+	0.596650i
$142$			1905.50i			1.12610i
$143$	346.426	+	401.335i	0.202584	+	0.234695i
$144$	185.931	+	314.887i	0.107599	+	0.182226i
$145$			643.829i			0.368739i
$146$			2071.91i			1.17447i
$147$	−339.573	+	594.858i	−0.190527	+	0.333762i
$148$	−3363.71			−1.86821
$149$	−335.088			−0.184238			−0.0921191	−	0.995748i	$-0.529364\pi$
$149$	−335.088			−0.184238			−0.0921191	+	0.995748i	$0.529364\pi$
$150$	−293.365	+	513.912i	−0.159688	+	0.279738i
$151$		−	1075.03i		−	0.579371i	−0.957122	−	0.289686i	$-0.906449\pi$
$151$		−	1075.03i		−	0.579371i	0.957122	−	0.289686i	$-0.0935508\pi$
$152$			3020.69i			1.61191i
$153$	1270.02	+	2150.87i	0.671081	+	1.13652i
$154$	1555.14	+	1801.64i	0.813746	+	0.942727i
$155$		−	1012.19i		−	0.524524i
$156$	−796.909	−	454.913i	−0.408999	−	0.233475i
$157$	−454.055			−0.230812			−0.115406	−	0.993318i	$-0.536817\pi$
$157$	−454.055			−0.230812			−0.115406	+	0.993318i	$0.536817\pi$
$158$		−	551.647i		−	0.277764i
$159$	−360.764	−	205.941i	−0.179940	−	0.102718i
$160$		−	2574.04i		−	1.27185i
$161$	346.426			0.169579
$162$	1580.52	−	2865.59i	0.766526	−	1.38976i
$163$	−1643.97			−0.789975			−0.394988	−	0.918686i	$-0.629251\pi$
$163$	−1643.97			−0.789975			−0.394988	+	0.918686i	$0.629251\pi$
$164$	2132.30			1.01527
$165$	2281.27	−	446.759i	1.07634	−	0.210789i
$166$	−681.640			−0.318708
$167$	2189.11			1.01436			0.507181	−	0.861840i	$-0.330688\pi$
$167$	2189.11			1.01436			0.507181	+	0.861840i	$0.330688\pi$
$168$	−1222.31	−	697.754i	−0.561331	−	0.320434i
$169$	1985.82			0.903878
$170$		−	5092.60i		−	2.29756i
$171$	−3767.87	+	2224.81i	−1.68501	+	0.994943i
$172$			4291.97i			1.90267i
$173$	500.257			0.219849			0.109924	−	0.993940i	$-0.464939\pi$
$173$	500.257			0.219849			0.109924	+	0.993940i	$0.464939\pi$
$174$	−607.160	+	1063.61i	−0.264533	+	0.463404i
$175$			368.658i			0.159245i
$176$	−374.043	+	322.867i	−0.160196	+	0.138279i
$177$	−1316.56	−	751.555i	−0.559089	−	0.319154i
$178$		−	3434.05i		−	1.44603i
$179$			1317.47i			0.550125i	0.961426	+	0.275063i	$0.0886986\pi$
$179$			1317.47i			0.550125i	−0.961426	+	0.275063i	$0.911301\pi$
$180$	−3464.51	+	2045.69i	−1.43461	+	0.847092i
$181$	−1747.44			−0.717602			−0.358801	−	0.933414i	$-0.616814\pi$
$181$	−1747.44			−0.717602			−0.358801	+	0.933414i	$0.616814\pi$
$182$	−948.010			−0.386105
$183$	−665.753	−	380.043i	−0.268928	−	0.153517i
$184$		−	444.332i		−	0.178025i
$185$			3394.28i			1.34893i
$186$	954.544	−	1672.15i	0.376293	−	0.659184i
$187$	−2554.95	+	2205.39i	−0.999125	+	0.862427i
$188$		−	4712.45i		−	1.82814i
$189$	−29.9168	−	2038.57i	−0.0115139	−	0.784572i
$190$	8921.14			3.40635
$191$			3876.65i			1.46861i	0.678820	+	0.734304i	$0.262492\pi$
$191$			3876.65i			1.46861i	−0.678820	+	0.734304i	$0.737508\pi$
$192$	2148.33	−	3763.41i	0.807511	−	1.41459i
$193$			1017.24i			0.379392i	0.981843	+	0.189696i	$0.0607503\pi$
$193$			1017.24i			0.379392i	−0.981843	+	0.189696i	$0.939250\pi$
$194$	−982.966			−0.363778
$195$	−459.046	+	804.150i	−0.168579	+	0.295315i
$196$	1601.88			0.583777
$197$	−3483.34			−1.25978			−0.629892	−	0.776682i	$-0.716901\pi$
$197$	−3483.34			−1.25978			−0.629892	+	0.776682i	$0.716901\pi$
$198$	4190.00	+	1413.29i	1.50389	+	0.507264i
$199$	4543.19			1.61838			0.809191	−	0.587546i	$-0.199906\pi$
$199$	4543.19			1.61838			0.809191	+	0.587546i	$0.199906\pi$
$200$	472.847			0.167177
$201$	−518.055	+	907.521i	−0.181795	+	0.318466i
$202$	850.849			0.296364
$203$			762.990i			0.263800i
$204$	2896.03	−	5073.22i	0.993935	−	1.74116i
$205$		−	2151.68i		−	0.733072i
$206$	−6818.72			−2.30623
$207$	554.239	−	327.261i	0.186098	−	0.109885i
$208$		−	196.819i		−	0.0656103i
$209$	−3863.36	−	4475.72i	−1.27863	−	1.48130i
$210$	−2060.71	+	3609.91i	−0.677154	+	1.18623i
$211$			2986.63i			0.974447i	0.873277	+	0.487224i	$0.161990\pi$
$211$			2986.63i			0.974447i	−0.873277	+	0.487224i	$0.838010\pi$
$212$			971.496i			0.314729i
$213$	1915.50	+	1093.46i	0.616187	+	0.351749i
$214$	−5822.18			−1.85980
$215$	4330.97			1.37381
$216$	−2614.71	+	38.3719i	−0.823650	+	0.0120874i
$217$		−	1199.53i		−	0.375251i
$218$		−	6462.55i		−	2.00780i
$219$	2082.78	+	1188.95i	0.642654	+	0.366857i
$220$	−3552.32	−	4115.38i	−1.08862	−	1.26118i
$221$		−	1344.40i		−	0.409204i
$222$	−3200.96	+	5607.39i	−0.967722	+	1.69524i
$223$	−5317.25			−1.59672			−0.798362	−	0.602178i	$-0.794300\pi$
$223$	−5317.25			−1.59672			−0.798362	+	0.602178i	$0.794300\pi$
$224$		−	3050.45i		−	0.909896i
$225$	348.263	+	589.807i	0.103189	+	0.174758i
$226$			4735.90i			1.39393i
$227$	5089.65			1.48816			0.744079	−	0.668091i	$-0.232888\pi$
$227$	5089.65			1.48816			0.744079	+	0.668091i	$0.232888\pi$
$228$	8887.18	+	5073.22i	2.58144	+	1.47361i
$229$	4438.60			1.28084			0.640418	−	0.768027i	$-0.278761\pi$
$229$	4438.60			1.28084			0.640418	+	0.768027i	$0.278761\pi$
$230$	−1312.27			−0.376210
$231$	2703.49	−	529.446i	0.770029	−	0.150801i
$232$	978.625			0.276939
$233$	1183.43			0.332743			0.166372	−	0.986063i	$-0.446795\pi$
$233$	1183.43			0.332743			0.166372	+	0.986063i	$0.446795\pi$
$234$	−1516.70	+	895.564i	−0.423717	+	0.250192i
$235$	−4755.27			−1.32000
$236$			3545.35i			0.977893i
$237$	−554.541	−	316.558i	−0.151989	−	0.0867623i
$238$		−	6035.14i		−	1.64370i
$239$	1686.66			0.456489			0.228244	−	0.973604i	$-0.426701\pi$
$239$	1686.66			0.456489			0.228244	+	0.973604i	$0.426701\pi$
$240$	−749.465	−	427.829i	−0.201574	−	0.115068i
$241$		−	5780.53i		−	1.54505i	−0.634985	−	0.772525i	$-0.718994\pi$
$241$		−	5780.53i		−	1.54505i	0.634985	−	0.772525i	$-0.281006\pi$
$242$	−872.809	+	5910.91i	−0.231844	+	1.57011i
$243$	−1973.66	−	3233.20i	−0.521029	−	0.853539i
$244$			1792.80i			0.470377i
$245$		−	1616.44i		−	0.421513i
$246$	2029.13	−	3554.60i	0.525905	−	0.921272i
$247$	2355.09			0.606685
$248$	−1538.54			−0.393941
$249$	−391.153	+	685.216i	−0.0995515	+	0.174393i
$250$			5484.47i			1.38747i
$251$			1829.21i			0.459996i	0.973191	+	0.229998i	$0.0738719\pi$
$251$			1829.21i			0.459996i	−0.973191	+	0.229998i	$0.926128\pi$
$252$	−4105.73	+	2424.30i	−1.02634	+	0.606019i
$253$	568.286	+	658.361i	0.141217	+	0.163600i
$254$			10210.8i			2.52236i
$255$	−5119.32	−	2922.34i	−1.25719	−	0.717664i
$256$	−2595.88			−0.633761
$257$		−	4066.01i		−	0.986891i	−0.869777	−	0.493446i	$-0.835737\pi$
$257$		−	4066.01i		−	0.986891i	0.869777	−	0.493446i	$-0.164263\pi$
$258$	7154.82	+	4084.30i	1.72651	+	0.985572i
$259$			4022.49i			0.965041i
$260$	2165.49			0.516530
$261$	720.780	+	1220.69i	0.170939	+	0.289498i
$262$	−5484.70			−1.29330
$263$	−6812.43			−1.59723			−0.798617	−	0.601840i	$-0.794435\pi$
$263$	−6812.43			−1.59723			−0.798617	+	0.601840i	$0.794435\pi$
$264$	−679.077	−	3467.55i	−0.158312	−	0.808382i
$265$	980.324			0.227248
$266$	10572.3			2.43694
$267$	−3452.06	−	1970.60i	−0.791246	−	0.451680i
$268$	2443.85			0.557022
$269$			1591.54i			0.360736i	0.983599	+	0.180368i	$0.0577289\pi$
$269$			1591.54i			0.360736i	−0.983599	+	0.180368i	$0.942271\pi$
$270$	113.326	+	7722.13i	0.0255436	+	1.74057i
$271$			1876.51i			0.420626i	0.977634	+	0.210313i	$0.0674483\pi$
$271$			1876.51i			0.420626i	−0.977634	+	0.210313i	$0.932552\pi$
$272$	1252.97			0.279311
$273$	−544.007	+	952.983i	−0.120604	+	0.211272i
$274$		−	1814.36i		−	0.400035i
$275$	−700.612	+	604.756i	−0.153631	+	0.132611i
$276$	−1307.27	−	746.251i	−0.285103	−	0.162750i
$277$		−	3827.28i		−	0.830177i	−0.909781	−	0.415089i	$-0.863751\pi$
$277$		−	3827.28i		−	0.830177i	0.909781	−	0.415089i	$-0.136249\pi$
$278$			466.571i			0.100659i
$279$	−1133.17	−	1919.10i	−0.243158	−	0.411805i
$280$	3321.46			0.708912
$281$	339.184			0.0720072			0.0360036	−	0.999352i	$-0.488537\pi$
$281$	339.184			0.0720072			0.0360036	+	0.999352i	$0.488537\pi$
$282$	−7855.76	−	4484.44i	−1.65888	−	0.946966i
$283$			4085.98i			0.858255i	0.903244	+	0.429127i	$0.141179\pi$
$283$			4085.98i			0.858255i	−0.903244	+	0.429127i	$0.858821\pi$
$284$		−	5158.23i		−	1.07776i
$285$	5119.32	−	8967.94i	1.06401	−	1.86391i
$286$	−1555.14	−	1801.64i	−0.321529	−	0.372493i
$287$		−	2549.91i		−	0.524448i
$288$	−2881.69	−	4880.35i	−0.589602	−	0.998533i
$289$	3645.60			0.742031
$290$		−	2890.22i		−	0.585239i
$291$	−564.067	+	988.123i	−0.113629	+	0.199054i
$292$		−	5608.69i		−	1.12405i
$293$	−5445.63			−1.08579			−0.542896	−	0.839800i	$-0.682672\pi$
$293$	−5445.63			−1.08579			−0.542896	+	0.839800i	$0.682672\pi$
$294$	1524.38	−	2670.38i	0.302393	−	0.529727i
$295$	3577.57			0.706081
$296$	5159.33			1.01311
$297$	3825.10	−	3400.98i	0.747323	−	0.664461i
$298$	1504.25			0.292411
$299$	−346.426			−0.0670044
$300$	794.142	−	1391.17i	0.152833	−	0.267730i
$301$	5132.55			0.982841
$302$			4825.94i			0.919543i
$303$	488.252	−	855.313i	0.0925722	−	0.162166i
$304$			2194.94i			0.414106i
$305$	1809.09			0.339633
$306$	−5701.27	−	9655.50i	−1.06510	−	1.80382i
$307$		−	3678.14i		−	0.683787i	−0.939739	−	0.341894i	$-0.888932\pi$
$307$		−	3678.14i		−	0.683787i	0.939739	−	0.341894i	$-0.111068\pi$
$308$	−4209.79	−	4877.05i	−0.778814	−	0.902260i
$309$	−3912.86	+	6854.49i	−0.720372	+	1.26194i
$310$			4543.84i			0.832492i
$311$		−	6388.00i		−	1.16473i	−0.812929	−	0.582363i	$-0.802128\pi$
$311$		−	6388.00i		−	1.16473i	0.812929	−	0.582363i	$-0.197872\pi$
$312$	1222.31	+	697.754i	0.221795	+	0.126611i
$313$	6242.25			1.12726			0.563631	−	0.826027i	$-0.309404\pi$
$313$	6242.25			1.12726			0.563631	+	0.826027i	$0.309404\pi$
$314$	2038.30			0.366331
$315$	2446.33	+	4143.04i	0.437572	+	0.741059i
$316$			1493.32i			0.265841i
$317$			268.015i			0.0474866i	0.999718	+	0.0237433i	$0.00755844\pi$
$317$			268.015i			0.0474866i	−0.999718	+	0.0237433i	$0.992442\pi$
$318$	1619.51	+	924.490i	0.285589	+	0.163028i
$319$	−1450.02	+	1251.63i	−0.254500	+	0.219680i
$320$			10226.5i			1.78650i
$321$	−3341.01	+	5852.72i	−0.580925	+	1.01765i
$322$	−1555.14			−0.269145
$323$			14992.8i			2.58273i
$324$	−4278.48	+	7757.19i	−0.733622	+	1.33011i
$325$		−	368.658i		−	0.0629214i
$326$	7379.97			1.25380
$327$	−6496.46	−	3708.48i	−1.09864	−	0.627154i
$328$	−3270.57			−0.550570
$329$	−5635.38			−0.944342
$330$	−10240.9	+	2005.55i	−1.70831	+	0.334551i
$331$	−451.238			−0.0749313			−0.0374656	−	0.999298i	$-0.511928\pi$
$331$	−451.238			−0.0749313			−0.0374656	+	0.999298i	$0.511928\pi$
$332$	1845.21			0.305027
$333$	3799.96	+	6435.50i	0.625335	+	1.05905i
$334$	−9827.15			−1.60993
$335$		−	2466.06i		−	0.402194i
$336$	−888.176	−	507.012i	−0.144208	−	0.0823208i
$337$			9096.65i			1.47040i	0.677848	+	0.735202i	$0.262913\pi$
$337$			9096.65i			1.47040i	−0.677848	+	0.735202i	$0.737087\pi$
$338$	−8914.55			−1.43458
$339$	4760.74	+	2717.66i	0.762738	+	0.435406i
$340$			13785.7i			2.19893i
$341$	2279.64	−	1967.74i	0.362021	−	0.312490i
$342$	16914.3	−	9987.39i	2.67434	−	1.57911i
$343$		−	6900.10i		−	1.08621i
$344$		−	6583.11i		−	1.03179i
$345$	−753.032	+	1319.15i	−0.117513	+	0.205857i
$346$	−2245.71			−0.348930
$347$	6325.38			0.978571			0.489286	−	0.872124i	$-0.337258\pi$
$347$	6325.38			0.978571			0.489286	+	0.872124i	$0.337258\pi$
$348$	1643.59	−	2879.22i	0.253177	−	0.443512i
$349$		−	5463.97i		−	0.838051i	−0.907974	−	0.419026i	$-0.862372\pi$
$349$		−	5463.97i		−	0.838051i	0.907974	−	0.419026i	$-0.137628\pi$
$350$		−	1654.94i		−	0.252744i
$351$	29.9168	+	2038.57i	0.00454941	+	0.310002i
$352$	5797.20	−	5004.04i	0.877818	−	0.757717i
$353$		−	3331.02i		−	0.502245i	−0.967955	−	0.251123i	$-0.919200\pi$
$353$		−	3331.02i		−	0.502245i	0.967955	−	0.251123i	$-0.0807997\pi$
$354$	5910.18	+	3373.81i	0.887352	+	0.506542i
$355$	−5205.10			−0.778191
$356$			9296.01i			1.38395i
$357$	−6066.80	−	3463.21i	−0.899410	−	0.513425i
$358$		−	5914.27i		−	0.873125i
$359$	−2130.28			−0.313181			−0.156591	−	0.987664i	$-0.550050\pi$
$359$	−2130.28			−0.313181			−0.156591	+	0.987664i	$0.550050\pi$
$360$	5313.94	−	3137.71i	0.777970	−	0.459367i
$361$	−19405.2			−2.82915
$362$	7844.43			1.13893
$363$	5441.06	+	4269.31i	0.786726	+	0.617302i
$364$	2566.27			0.369531
$365$	−5659.66			−0.811617
$366$	2988.63	+	1706.05i	0.426826	+	0.243652i
$367$	6515.65			0.926741			0.463370	−	0.886165i	$-0.346640\pi$
$367$	6515.65			0.926741			0.463370	+	0.886165i	$0.346640\pi$
$368$		−	322.867i		−	0.0457354i
$369$	−2408.85	−	4079.55i	−0.339836	−	0.575536i
$370$		−	15237.3i		−	2.14094i
$371$	1161.76			0.162576
$372$	−2583.96	+	4526.54i	−0.360140	+	0.630888i
$373$			11019.6i			1.52969i	0.644213	+	0.764846i	$0.277185\pi$
$373$			11019.6i			1.52969i	−0.644213	+	0.764846i	$0.722815\pi$
$374$	11469.4	−	9900.21i	1.58575	−	1.36879i
$375$	5513.24	+	3147.21i	0.759207	+	0.433391i
$376$			7228.04i			0.991377i
$377$		−	762.990i		−	0.104233i
$378$	134.300	+	9151.35i	0.0182742	+	1.24522i
$379$	57.5809			0.00780404			0.00390202	−	0.999992i	$-0.498758\pi$
$379$	57.5809			0.00780404			0.00390202	+	0.999992i	$0.498758\pi$
$380$	−24149.6			−3.26013
$381$	10264.3	+	5859.35i	1.38020	+	0.787884i
$382$		−	17402.7i		−	2.33089i
$383$		−	9660.60i		−	1.28886i	−0.764663	−	0.644430i	$-0.777095\pi$
$383$		−	9660.60i		−	1.28886i	0.764663	−	0.644430i	$-0.222905\pi$
$384$	−5318.14	+	9316.24i	−0.706746	+	1.23807i
$385$	−4921.37	+	4248.04i	−0.651471	+	0.562338i
$386$		−	4566.51i		−	0.602148i
$387$	8211.46	−	4848.61i	1.07858	−	0.636870i
$388$	2660.90			0.348162
$389$		−	11536.6i		−	1.50367i	−0.659351	−	0.751835i	$-0.729169\pi$
$389$		−	11536.6i		−	1.50367i	0.659351	−	0.751835i	$-0.270831\pi$
$390$	2060.71	−	3609.91i	0.267559	−	0.468706i
$391$		−	2205.39i		−	0.285246i
$392$	−2457.00			−0.316575
$393$	−3147.34	+	5513.47i	−0.403976	+	0.707678i
$394$	15637.1			1.99945
$395$	1506.89			0.191949
$396$	−11342.4	−	3825.80i	−1.43934	−	0.485489i
$397$	−6686.34			−0.845285			−0.422642	−	0.906297i	$-0.638897\pi$
$397$	−6686.34			−0.845285			−0.422642	+	0.906297i	$0.638897\pi$
$398$	−20394.8			−2.56860
$399$	6066.80	−	10627.7i	0.761203	−	1.33346i
$400$	343.587			0.0429484
$401$			5987.05i			0.745583i	0.927915	+	0.372792i	$0.121599\pi$
$401$			5987.05i			0.745583i	−0.927915	+	0.372792i	$0.878401\pi$
$402$	2325.61	−	4073.96i	0.288534	−	0.505449i
$403$			1199.53i			0.148270i
$404$	−2303.26			−0.283642
$405$	7827.67	+	4317.36i	0.960396	+	0.529707i
$406$		−	3425.14i		−	0.418687i
$407$	−7644.51	+	6598.61i	−0.931018	+	0.803638i
$408$	−4441.98	+	7781.40i	−0.538998	+	0.944207i
$409$		−	6409.23i		−	0.774856i	−0.921900	−	0.387428i	$-0.873364\pi$
$409$		−	6409.23i		−	0.774856i	0.921900	−	0.387428i	$-0.126636\pi$
$410$			9659.11i			1.16349i
$411$	−1823.88	−	1041.16i	−0.218894	−	0.124955i
$412$	18458.4			2.20723
$413$	4239.70			0.505138
$414$	−2488.04	+	1469.11i	−0.295363	+	0.174403i
$415$		−	1861.97i		−	0.220243i
$416$			3050.45i			0.359521i
$417$	469.019	+	267.738i	0.0550790	+	0.0314417i
$418$	17343.0	+	20092.0i	2.02937	+	2.35103i
$419$			6661.04i			0.776642i	0.921524	+	0.388321i	$0.126945\pi$
$419$			6661.04i			0.776642i	−0.921524	+	0.388321i	$0.873055\pi$
$420$	5578.36	−	9772.09i	0.648086	−	1.13531i
$421$	−3531.81			−0.408860			−0.204430	−	0.978881i	$-0.565534\pi$
$421$	−3531.81			−0.408860			−0.204430	+	0.978881i	$0.565534\pi$
$422$		−	13407.3i		−	1.54658i
$423$	−9015.92	+	5323.62i	−1.03633	+	0.611923i
$424$		−	1490.10i		−	0.170674i
$425$	2346.92			0.267864
$426$	−8598.88	−	4908.64i	−0.977975	−	0.558274i
$427$	2143.91			0.242977
$428$	15760.7			1.77996
$429$	−2703.49	+	529.446i	−0.304256	+	0.0595848i
$430$	−19442.2			−2.18043
$431$	4009.57			0.448107			0.224053	−	0.974577i	$-0.428071\pi$
$431$	4009.57			0.448107			0.224053	+	0.974577i	$0.428071\pi$
$432$	−1899.94	+	27.8824i	−0.211599	+	0.00310530i
$433$	−7430.09			−0.824636			−0.412318	−	0.911040i	$-0.635281\pi$
$433$	−7430.09			−0.824636			−0.412318	+	0.911040i	$0.635281\pi$
$434$			5384.81i			0.595575i
$435$	−2905.38	−	1658.53i	−0.320235	−	0.182805i
$436$			17494.2i			1.92161i
$437$	3863.36			0.422905
$438$	−9349.82	−	5337.32i	−1.01998	−	0.582253i
$439$		−	13645.8i		−	1.48356i	−0.670646	−	0.741778i	$-0.733983\pi$
$439$		−	13645.8i		−	1.48356i	0.670646	−	0.741778i	$-0.266017\pi$
$440$	5448.62	+	6312.24i	0.590347	+	0.683919i
$441$	−1809.64	−	3064.75i	−0.195404	−	0.330930i
$442$			6035.14i			0.649463i
$443$		−	3300.00i		−	0.353922i	−0.984218	−	0.176961i	$-0.943373\pi$
$443$		−	3300.00i		−	0.353922i	0.984218	−	0.176961i	$-0.0566267\pi$
$444$	8665.04	−	15179.3i	0.926181	−	1.62247i
$445$	9380.48			0.999275
$446$	23869.7			2.53422
$447$	863.198	−	1512.14i	0.0913375	−	0.160004i
$448$			12119.2i			1.27808i
$449$			9305.54i			0.978075i	0.872263	+	0.489037i	$0.162652\pi$
$449$			9305.54i			0.978075i	−0.872263	+	0.489037i	$0.837348\pi$
$450$	−1563.39	−	2647.71i	−0.163775	−	0.277365i
$451$	4845.96	−	4182.95i	0.505958	−	0.436734i
$452$		−	12820.1i		−	1.33409i
$453$	4851.26	+	2769.33i	0.503161	+	0.287228i
$454$	−22848.0			−2.36191
$455$		−	2589.59i		−	0.266818i
$456$	−13631.3	−	7781.40i	−1.39988	−	0.799117i
$457$			12342.0i			1.26332i	0.775246	+	0.631659i	$0.217626\pi$
$457$			12342.0i			1.26332i	−0.775246	+	0.631659i	$0.782374\pi$
$458$	−19925.4			−2.03286
$459$	−12977.8	+	190.454i	−1.31972	+	0.0193674i
$460$	3552.32			0.360060
$461$	−2304.33			−0.232806			−0.116403	−	0.993202i	$-0.537136\pi$
$461$	−2304.33			−0.232806			−0.116403	+	0.993202i	$0.537136\pi$
$462$	−12136.3	+	2376.74i	−1.22214	+	0.239342i
$463$	5178.38			0.519783			0.259892	−	0.965638i	$-0.416313\pi$
$463$	5178.38			0.519783			0.259892	+	0.965638i	$0.416313\pi$
$464$	711.103			0.0711468
$465$	4567.67	+	2607.44i	0.455529	+	0.260037i
$466$	−5312.55			−0.528110
$467$		−	10169.0i		−	1.00763i	−0.863811	−	0.503817i	$-0.831929\pi$
$467$		−	10169.0i		−	1.00763i	0.863811	−	0.503817i	$-0.168071\pi$
$468$	4105.73	−	2424.30i	0.405529	−	0.239452i
$469$		−	2922.48i		−	0.287734i
$470$	21346.9			2.09502
$471$	1169.66	−	2048.99i	0.114427	−	0.200451i
$472$		−	5437.92i		−	0.530298i
$473$	8419.57	+	9754.11i	0.818462	+	0.948191i
$474$	2489.39	+	1421.06i	0.241227	+	0.137704i
$475$			4111.29i			0.397135i
$476$			16337.2i			1.57314i
$477$	1858.68	−	1097.49i	0.178413	−	0.105347i
$478$	−7571.59			−0.724511
$479$	−17457.5			−1.66525			−0.832625	−	0.553837i	$-0.813163\pi$
$479$	−17457.5			−1.66525			−0.832625	+	0.553837i	$0.813163\pi$
$480$	11615.8	+	6630.82i	1.10455	+	0.630530i
$481$		−	4022.49i		−	0.381309i
$482$			25949.4i			2.45221i
$483$	−892.404	+	1563.30i	−0.0840699	+	0.147272i
$484$	2362.70	−	16000.9i	0.221892	−	1.50271i
$485$		−	2685.08i		−	0.251388i
$486$	8859.95	+	14514.2i	0.826945	+	1.35468i
$487$	11525.7			1.07245			0.536223	−	0.844076i	$-0.319851\pi$
$487$	11525.7			1.07245			0.536223	+	0.844076i	$0.319851\pi$
$488$		−	2749.83i		−	0.255079i
$489$	4234.93	−	7418.68i	0.391636	−	0.686062i
$490$			7256.37i			0.668999i
$491$	−7241.13			−0.665555			−0.332777	−	0.943005i	$-0.607986\pi$
$491$	−7241.13			−0.665555			−0.332777	+	0.943005i	$0.607986\pi$
$492$	−5492.88	+	9622.35i	−0.503330	+	0.881725i
$493$	4857.28			0.443734
$494$	−10572.3			−0.962892
$495$	−3860.56	+	11445.5i	−0.350544	+	1.03926i
$496$	−1117.96			−0.101205
$497$	−6168.46			−0.556727
$498$	1755.93	−	3076.00i	0.158002	−	0.276785i
$499$	−1625.41			−0.145818			−0.0729091	−	0.997339i	$-0.523228\pi$
$499$	−1625.41			−0.145818			−0.0729091	+	0.997339i	$0.523228\pi$
$500$		−	14846.5i		−	1.32791i
$501$	−5639.22	+	9878.70i	−0.502878	+	0.880934i
$502$		−	8211.53i		−	0.730077i
$503$	19854.0			1.75993			0.879966	−	0.475037i	$-0.157565\pi$
$503$	19854.0			1.75993			0.879966	+	0.475037i	$0.157565\pi$
$504$	6297.44	−	3718.44i	0.556568	−	0.328636i
$505$			2324.19i			0.204802i
$506$	−2551.10	−	2955.45i	−0.224130	−	0.259656i
$507$	−5115.54	+	8961.32i	−0.448105	+	0.784983i
$508$		−	27640.7i		−	2.41409i
$509$			16340.1i			1.42291i	0.702730	+	0.711456i	$0.251964\pi$
$509$			16340.1i			1.42291i	−0.702730	+	0.711456i	$0.748036\pi$
$510$	22981.2	+	13118.7i	1.99534	+	1.13903i
$511$	−6707.15			−0.580640
$512$	−4862.56			−0.419720
$513$	−333.635	−	22734.3i	−0.0287141	−	1.95661i
$514$			18252.8i			1.56633i
$515$		−	18626.1i		−	1.59372i
$516$	−19368.2	−	11056.3i	−1.65240	−	0.943265i
$517$	−9244.43	−	10709.7i	−0.786401	−	0.911049i
$518$		−	18057.4i		−	1.53165i
$519$	−1288.68	+	2257.49i	−0.108992	+	0.190930i
$520$	−3321.46			−0.280107
$521$			5338.31i			0.448898i	0.974486	+	0.224449i	$0.0720582\pi$
$521$			5338.31i			0.448898i	−0.974486	+	0.224449i	$0.927942\pi$
$522$	−3235.66	−	5479.81i	−0.271304	−	0.459473i
$523$		−	5078.98i		−	0.424643i	−0.977200	−	0.212322i	$-0.931898\pi$
$523$		−	5078.98i		−	0.424643i	0.977200	−	0.212322i	$-0.0681024\pi$
$524$	14847.1			1.23779
$525$	−1663.62	−	949.674i	−0.138298	−	0.0789470i
$526$	30581.7			2.53503
$527$	−7636.35			−0.631204
$528$	−493.441	−	2519.64i	−0.0406710	−	0.207677i
$529$	11598.7			0.953293
$530$	−4400.78			−0.360675
$531$	6783.01	−	4005.16i	0.554346	−	0.327324i
$532$	−28619.3			−2.33234
$533$			2549.91i			0.207221i
$534$	15496.7	+	8846.22i	1.25582	+	0.716879i
$535$		−	15903.9i		−	1.28521i
$536$	−3748.43			−0.302066
$537$	−5945.29	−	3393.85i	−0.477762	−	0.272729i
$538$		−	7144.60i		−	0.572538i
$539$	3640.51	−	3142.42i	0.290923	−	0.251120i
$540$	−306.774	−	20903.9i	−0.0244471	−	1.66585i
$541$			17212.7i			1.36789i	0.729531	+	0.683947i	$0.239738\pi$
$541$			17212.7i			1.36789i	−0.729531	+	0.683947i	$0.760262\pi$
$542$		−	8423.84i		−	0.667592i
$543$	4501.46	−	7885.58i	0.355757	−	0.623209i
$544$	−19419.5			−1.53052
$545$	17653.2			1.38748
$546$	2442.10	−	4278.04i	0.191415	−	0.335317i
$547$			12457.6i			0.973766i	0.873467	+	0.486883i	$0.161866\pi$
$547$			12457.6i			0.973766i	−0.873467	+	0.486883i	$0.838134\pi$
$548$			4911.50i			0.382863i
$549$	3430.00	−	2025.31i	0.266647	−	0.157446i
$550$	3145.12	−	2714.81i	0.243833	−	0.210473i
$551$			8508.91i			0.657880i
$552$	2005.12	+	1144.61i	0.154608	+	0.0882573i
$553$	1785.78			0.137322
$554$			17181.1i			1.31761i
$555$	−15317.2	−	8743.77i	−1.17149	−	0.668743i
$556$		−	1263.01i		−	0.0963377i
$557$	−9161.87			−0.696950			−0.348475	−	0.937318i	$-0.613300\pi$
$557$	−9161.87			−0.696950			−0.348475	+	0.937318i	$0.613300\pi$
$558$	5086.92	+	8615.05i	0.385925	+	0.653592i
$559$	−5132.55			−0.388343
$560$	2413.49			0.182122
$561$	−3370.51	−	17210.8i	−0.253660	−	1.29526i
$562$	−1522.63			−0.114285
$563$	−12769.3			−0.955881			−0.477940	−	0.878392i	$-0.658616\pi$
$563$	−12769.3			−0.955881			−0.477940	+	0.878392i	$0.658616\pi$
$564$	21265.7	+	12139.4i	1.58767	+	0.906316i
$565$	−12936.6			−0.963272
$566$		−	18342.4i		−	1.36217i
$567$	9276.42	+	5116.42i	0.687078	+	0.378958i
$568$			7911.78i			0.584456i
$569$	16454.4			1.21231			0.606154	−	0.795347i	$-0.292712\pi$
$569$	16454.4			1.21231			0.606154	+	0.795347i	$0.292712\pi$
$570$	−22981.2	+	40258.0i	−1.68873	+	2.95829i
$571$			8779.22i			0.643431i	0.946836	+	0.321715i	$0.104259\pi$
$571$			8779.22i			0.643431i	−0.946836	+	0.321715i	$0.895741\pi$
$572$	4209.79	+	4877.05i	0.307727	+	0.356503i
$573$	−17494.0	−	9986.37i	−1.27543	−	0.728074i
$574$			11446.8i			0.832372i
$575$		−	604.756i		−	0.0438610i
$576$	11448.8	+	19389.3i	0.828182	+	1.40258i
$577$	23766.8			1.71478			0.857389	−	0.514669i	$-0.172085\pi$
$577$	23766.8			1.71478			0.857389	+	0.514669i	$0.172085\pi$
$578$	−16365.5			−1.17771
$579$	−4590.46	−	2620.45i	−0.329487	−	0.188087i
$580$			7823.86i			0.560117i
$581$		−	2206.59i		−	0.157564i
$582$	2532.15	−	4435.79i	0.180346	−	0.315927i
$583$	1905.79	+	2207.86i	0.135385	+	0.156844i
$584$			8602.72i			0.609560i
$585$	−2446.33	−	4143.04i	−0.172895	−	0.292809i
$586$	24446.0			1.72330
$587$			10669.2i			0.750194i	0.926986	+	0.375097i	$0.122391\pi$
$587$			10669.2i			0.750194i	−0.926986	+	0.375097i	$0.877609\pi$
$588$	−4126.51	+	7228.75i	−0.289412	+	0.506988i
$589$		−	13377.2i		−	0.935822i
$590$	−16060.1			−1.12065
$591$	8973.20	−	15719.1i	0.624548	−	1.09407i
$592$	3748.95			0.260272
$593$	18602.1			1.28819			0.644095	−	0.764946i	$-0.277234\pi$
$593$	18602.1			1.28819			0.644095	+	0.764946i	$0.277234\pi$
$594$	−17171.3	+	15267.4i	−1.18611	+	1.05459i
$595$	16485.7			1.13588
$596$	−4072.01			−0.279859
$597$	−11703.4	+	20501.8i	−0.802326	+	1.40550i
$598$	1555.14			0.106345
$599$		−	7674.09i		−	0.523464i	−0.965141	−	0.261732i	$-0.915706\pi$
$599$		−	7674.09i		−	0.523464i	0.965141	−	0.261732i	$-0.0842936\pi$
$600$	−1218.07	+	2133.80i	−0.0828792	+	0.145186i
$601$			7503.89i			0.509301i	0.967033	+	0.254651i	$0.0819604\pi$
$601$			7503.89i			0.509301i	−0.967033	+	0.254651i	$0.918040\pi$
$602$	−23040.6			−1.55991
$603$	−2760.80	−	4675.61i	−0.186449	−	0.315764i
$604$		−	13063.9i		−	0.880070i
$605$	−16146.3	−	2384.17i	−1.08503	−	0.160216i
$606$	−2191.82	+	3839.59i	−0.146925	+	0.257381i
$607$			17630.0i			1.17888i	0.807812	+	0.589441i	$0.200652\pi$
$607$			17630.0i			1.17888i	−0.807812	+	0.589441i	$0.799348\pi$
$608$		−	34018.8i		−	2.26915i
$609$	−3443.11	−	1965.49i	−0.229100	−	0.130781i
$610$	−8121.18			−0.539044
$611$	5635.38			0.373131
$612$	15433.4	+	26137.6i	1.01938	+	1.72639i
$613$			11241.0i			0.740654i	0.928902	+	0.370327i	$0.120754\pi$
$613$			11241.0i			0.740654i	−0.928902	+	0.370327i	$0.879246\pi$
$614$			16511.6i			1.08527i
$615$	9709.78	+	5542.80i	0.636644	+	0.363426i
$616$	6457.05	+	7480.52i	0.422341	+	0.489283i
$617$		−	13977.6i		−	0.912023i	−0.889974	−	0.456011i	$-0.849278\pi$
$617$		−	13977.6i		−	0.912023i	0.889974	−	0.456011i	$-0.150722\pi$
$618$	17565.3	−	30770.5i	1.14333	−	2.00287i
$619$	−20314.8			−1.31910			−0.659548	−	0.751662i	$-0.729252\pi$
$619$	−20314.8			−1.31910			−0.659548	+	0.751662i	$0.729252\pi$
$620$		−	12300.2i		−	0.796757i
$621$	49.0764	+	3344.12i	0.00317129	+	0.216095i
$622$			28676.4i			1.84858i
$623$	11116.6			0.714893
$624$	888.176	+	507.012i	0.0569800	+	0.0325268i
$625$	−18152.5			−1.16176
$626$	−28022.1			−1.78912
$627$	30149.5	−	5904.41i	1.92034	−	0.376076i
$628$	−5517.70			−0.350606
$629$	25607.7			1.62328
$630$	−10981.8	−	18598.5i	−0.694488	−	1.17616i
$631$	3831.37			0.241718			0.120859	−	0.992670i	$-0.461435\pi$
$631$	3831.37			0.241718			0.120859	+	0.992670i	$0.461435\pi$
$632$		−	2290.48i		−	0.144162i
$633$	−13477.6	−	7693.67i	−0.846269	−	0.483090i
$634$		−	1203.15i		−	0.0753678i
$635$	−27891.8			−1.74308
$636$	−4384.03	−	2502.61i	−0.273330	−	0.156030i
$637$			1915.61i			0.119151i
$638$	6509.28	−	5618.69i	0.403926	−	0.348662i
$639$	−9868.79	+	5827.21i	−0.610960	+	0.360752i
$640$		−	25315.5i		−	1.56357i
$641$			18907.4i			1.16505i	0.812813	+	0.582525i	$0.197935\pi$
$641$			18907.4i			1.16505i	−0.812813	+	0.582525i	$0.802065\pi$
$642$	14998.1	−	26273.5i	0.922008	−	1.61516i
$643$	−2635.94			−0.161666			−0.0808331	−	0.996728i	$-0.525758\pi$
$643$	−2635.94			−0.161666			−0.0808331	+	0.996728i	$0.525758\pi$
$644$	4209.79			0.257591
$645$	−11156.7	+	19544.2i	−0.681079	+	1.19310i
$646$		−	67304.3i		−	4.09915i
$647$			10197.9i			0.619662i	0.950792	+	0.309831i	$0.100273\pi$
$647$			10197.9i			0.619662i	−0.950792	+	0.309831i	$0.899727\pi$
$648$	6562.41	−	11898.1i	0.397833	−	0.721300i
$649$	6954.93	+	8057.31i	0.420654	+	0.487330i
$650$			1654.94i			0.0998649i
$651$	5413.06	+	3090.03i	0.325890	+	0.186033i
$652$	−19977.7			−1.19998
$653$		−	32680.3i		−	1.95847i	−0.202731	−	0.979234i	$-0.564982\pi$
$653$		−	32680.3i		−	1.95847i	0.202731	−	0.979234i	$-0.435018\pi$
$654$	29163.3	+	16647.8i	1.74369	+	0.995381i
$655$		−	14982.1i		−	0.893736i
$656$	−2376.51			−0.141444
$657$	−10730.6	+	6336.10i	−0.637202	+	0.376248i
$658$	25297.8			1.49880
$659$	20357.6			1.20337			0.601685	−	0.798734i	$-0.294496\pi$
$659$	20357.6			1.20337			0.601685	+	0.798734i	$0.294496\pi$
$660$	27722.2	−	5429.05i	1.63498	−	0.320190i
$661$	8285.93			0.487572			0.243786	−	0.969829i	$-0.421610\pi$
$661$	8285.93			0.487572			0.243786	+	0.969829i	$0.421610\pi$
$662$	2025.65			0.118926
$663$	6066.80	+	3463.21i	0.355377	+	0.202866i
$664$	−2830.21			−0.165412
$665$			28879.3i			1.68405i
$666$	−17058.4	−	28889.6i	−0.992493	−	1.68086i
$667$		−	1251.63i		−	0.0726586i
$668$	26602.2			1.54082
$669$	13697.4	−	23994.9i	0.791588	−	1.38669i
$670$			11070.4i			0.638338i
$671$	3516.94	+	4074.38i	0.202339	+	0.234411i
$672$	13765.6	+	7858.06i	0.790209	+	0.451088i
$673$		−	14861.6i		−	0.851225i	−0.904906	−	0.425612i	$-0.860059\pi$
$673$		−	14861.6i		−	0.851225i	0.904906	−	0.425612i	$-0.139941\pi$
$674$		−	40835.8i		−	2.33373i
$675$	−3558.73	+	52.2259i	−0.202927	+	0.00297804i
$676$	24131.8			1.37300
$677$	−18246.3			−1.03584			−0.517920	−	0.855429i	$-0.673294\pi$
$677$	−18246.3			−1.03584			−0.517920	+	0.855429i	$0.673294\pi$
$678$	−21371.5	−	12199.8i	−1.21057	−	0.691050i
$679$		−	3182.04i		−	0.179846i
$680$		−	21144.8i		−	1.19245i
$681$	−13111.1	+	22967.8i	−0.737766	+	1.29241i
$682$	−10233.5	+	8833.40i	−0.574577	+	0.495965i
$683$			32684.8i			1.83111i	0.402193	+	0.915555i	$0.368248\pi$
$683$			32684.8i			1.83111i	−0.402193	+	0.915555i	$0.631752\pi$
$684$	−45787.4	+	27036.0i	−2.55954	+	1.51133i
$685$	4956.13			0.276444
$686$			30975.3i			1.72397i
$687$	−11434.0	+	20029.9i	−0.634984	+	1.11235i
$688$		−	4783.51i		−	0.265072i
$689$	−1161.76			−0.0642375
$690$	3380.44	−	5921.80i	0.186509	−	0.326723i
$691$	−15447.5			−0.850437			−0.425219	−	0.905091i	$-0.639803\pi$
$691$	−15447.5			−0.850437			−0.425219	+	0.905091i	$0.639803\pi$
$692$	6079.15			0.333952
$693$	−4575.08	+	13563.8i	−0.250783	+	0.743501i
$694$	−28395.3			−1.55313
$695$	−1274.49			−0.0695600
$696$	−2520.97	+	4416.20i	−0.137295	+	0.240511i
$697$	−16233.0			−0.882167
$698$			24528.4i			1.33010i
$699$	−3048.56	+	5340.42i	−0.164960	+	0.288974i
$700$			4479.95i			0.241895i
$701$	−31681.4			−1.70697			−0.853487	−	0.521114i	$-0.825516\pi$
$701$	−31681.4			−1.70697			−0.853487	+	0.521114i	$0.825516\pi$
$702$	−134.300	−	9151.35i	−0.00722054	−	0.492016i
$703$			44859.1i			2.40668i
$704$	−23031.9	+	19880.7i	−1.23302	+	1.06432i
$705$	12249.7	−	21458.9i	0.654400	−	1.14637i
$706$			14953.3i			0.797133i
$707$			2754.35i			0.146518i
$708$	−15998.9	−	9132.94i	−0.849261	−	0.484798i
$709$	11198.2			0.593167			0.296584	−	0.955007i	$-0.404153\pi$
$709$	11198.2			0.593167			0.296584	+	0.955007i	$0.404153\pi$
$710$	23366.2			1.23510
$711$	2857.03	−	1686.99i	0.150699	−	0.0889832i
$712$		−	14258.4i		−	0.750500i
$713$			1967.74i			0.103356i
$714$	27234.5	+	15546.7i	1.42749	+	0.814877i
$715$	4921.37	−	4248.04i	0.257411	−	0.222193i
$716$			16010.0i			0.835645i
$717$	−4344.89	+	7611.30i	−0.226308	+	0.396443i
$718$	9563.07			0.497062
$719$		−	15023.4i		−	0.779245i	−0.920975	−	0.389622i	$-0.872605\pi$
$719$		−	15023.4i		−	0.779245i	0.920975	−	0.389622i	$-0.127395\pi$
$720$	3861.29	−	2279.97i	0.199864	−	0.118013i
$721$		−	22073.4i		−	1.14016i
$722$	87111.9			4.49026
$723$	26085.5	+	14890.8i	1.34181	+	0.765970i
$724$	−21235.0			−1.09004
$725$	1331.95			0.0682310
$726$	−24425.5	−	19165.4i	−1.24864	−	0.979744i
$727$	−8061.98			−0.411283			−0.205641	−	0.978627i	$-0.565928\pi$
$727$	−8061.98			−0.411283			−0.205641	+	0.978627i	$0.565928\pi$
$728$	−3936.20			−0.200392
$729$	19674.5	−	577.588i	0.999569	−	0.0293445i
$730$	25406.8			1.28815
$731$		−	32674.4i		−	1.65322i
$732$	−8090.27	−	4618.31i	−0.408504	−	0.233193i
$733$		−	32633.9i		−	1.64442i	−0.569183	−	0.822211i	$-0.692740\pi$
$733$		−	32633.9i		−	1.64442i	0.569183	−	0.822211i	$-0.307260\pi$
$734$	−29249.4			−1.47087
$735$	7294.44	+	4164.00i	0.366067	+	0.208968i
$736$			5004.04i			0.250613i
$737$	5554.00	−	4794.11i	0.277590	−	0.239611i
$738$	10813.6	+	18313.5i	0.539367	+	0.913456i
$739$		−	5965.10i		−	0.296928i	−0.988918	−	0.148464i	$-0.952567\pi$
$739$		−	5965.10i		−	0.296928i	0.988918	−	0.148464i	$-0.0474329\pi$
$740$			41247.5i			2.04904i
$741$	−6066.80	+	10627.7i	−0.300769	+	0.526882i
$742$	−5215.28			−0.258031
$743$	840.592			0.0415051			0.0207526	−	0.999785i	$-0.493394\pi$
$743$	840.592			0.0415051			0.0207526	+	0.999785i	$0.493394\pi$
$744$	3963.33	−	6942.90i	0.195299	−	0.342122i
$745$			4109.01i			0.202071i
$746$		−	49468.3i		−	2.42783i
$747$	−2084.52	−	3530.28i	−0.102100	−	0.172913i
$748$	−31047.9	+	26800.0i	−1.51768	+	1.31003i
$749$		−	18847.4i		−	0.919453i
$750$	−24749.5	−	14128.2i	−1.20497	−	0.687851i
$751$	−22433.9			−1.09005			−0.545024	−	0.838421i	$-0.683479\pi$
$751$	−22433.9			−1.09005			−0.545024	+	0.838421i	$0.683479\pi$
$752$			5252.15i			0.254689i
$753$	−8254.61	−	4712.12i	−0.399488	−	0.228047i
$754$			3425.14i			0.165433i
$755$	−13182.6			−0.635449
$756$	−363.552	−	24772.8i	−0.0174897	−	1.19177i
$757$	2259.73			0.108496			0.0542478	−	0.998528i	$-0.482724\pi$
$757$	2259.73			0.108496			0.0542478	+	0.998528i	$0.482724\pi$
$758$	−258.487			−0.0123861
$759$	−4434.88	+	868.517i	−0.212090	+	0.0415351i
$760$	37041.2			1.76793
$761$	33640.2			1.60244			0.801220	−	0.598370i	$-0.204185\pi$
$761$	33640.2			1.60244			0.801220	+	0.598370i	$0.204185\pi$
$762$	−46077.6	−	26303.3i	−2.19057	−	1.25048i
$763$	20920.4			0.992622
$764$			47109.3i			2.23083i
$765$	26375.1	−	15573.6i	1.24653	−	0.736035i
$766$			43367.5i			2.04560i
$767$	−4239.70			−0.199592
$768$	6687.09	−	11714.3i	0.314192	−	0.550396i
$769$		−	18780.1i		−	0.880659i	−0.897836	−	0.440330i	$-0.854862\pi$
$769$		−	18780.1i		−	0.880659i	0.897836	−	0.440330i	$-0.145138\pi$
$770$	22092.5	−	19069.9i	1.03397	−	0.892508i
$771$	18348.5	+	10474.2i	0.857076	+	0.489259i
$772$			12361.6i			0.576300i
$773$			22814.4i			1.06155i	0.847513	+	0.530775i	$0.178099\pi$
$773$			22814.4i			1.06155i	−0.847513	+	0.530775i	$0.821901\pi$
$774$	−36862.1	+	21765.9i	−1.71186	+	1.01080i
$775$	−2094.02			−0.0970574
$776$	−4081.34			−0.188804
$777$	−18152.1	−	10362.1i	−0.838100	−	0.478426i
$778$			51788.9i			2.38653i
$779$		−	28436.8i		−	1.30790i
$780$	−5578.36	+	9772.09i	−0.256074	+	0.448586i
$781$	−10118.9	−	11722.8i	−0.463615	−	0.537099i
$782$			9900.21i			0.452725i
$783$	−7365.31	+	108.089i	−0.336162	+	0.00493331i
$784$	−1785.34			−0.0813294
$785$			5567.84i			0.253153i
$786$	14128.8	−	24750.5i	0.641166	−	1.12318i
$787$			9762.98i			0.442202i	0.975251	+	0.221101i	$0.0709650\pi$
$787$			9762.98i			0.442202i	−0.975251	+	0.221101i	$0.929035\pi$
$788$	−42329.8			−1.91362
$789$	17549.0	−	30742.1i	0.791841	−	1.38713i
$790$	−6764.57			−0.304649
$791$	−15331.0			−0.689135
$792$	17397.2	+	5868.09i	0.780533	+	0.263274i
$793$	−2143.91			−0.0960058
$794$	30015.7			1.34158
$795$	−2525.35	+	4423.86i	−0.112660	+	0.197356i
$796$	55209.1			2.45834
$797$			13025.4i			0.578902i	0.957193	+	0.289451i	$0.0934727\pi$
$797$			13025.4i			0.578902i	−0.957193	+	0.289451i	$0.906527\pi$
$798$	−27234.5	+	47709.0i	−1.20813	+	2.11639i
$799$			35875.5i			1.58847i
$800$	−5325.18			−0.235342
$801$	17785.3	−	10501.6i	0.784533	−	0.463242i
$802$		−	26876.5i		−	1.18334i
$803$	−11002.6	−	12746.5i	−0.483528	−	0.560169i
$804$	−6295.44	+	11028.3i	−0.276148	+	0.483752i
$805$		−	4248.04i		−	0.185992i
$806$		−	5384.81i		−	0.235325i
$807$	−7182.08	−	4099.87i	−0.313285	−	0.178838i
$808$	3532.78			0.153815
$809$	−22339.8			−0.970860			−0.485430	−	0.874276i	$-0.661337\pi$
$809$	−22339.8			−0.970860			−0.485430	+	0.874276i	$0.661337\pi$
$810$	−35139.2	−	19381.1i	−1.52428	−	0.840718i
$811$		−	35155.3i		−	1.52216i	−0.648659	−	0.761079i	$-0.724670\pi$
$811$		−	35155.3i		−	1.52216i	0.648659	−	0.761079i	$-0.275330\pi$
$812$			9271.90i			0.400714i
$813$	−8468.03	−	4833.94i	−0.365297	−	0.208529i
$814$	34317.0	−	29621.8i	1.47765	−	1.27549i
$815$			20159.2i			0.866437i
$816$	−3227.70	+	5654.24i	−0.138471	+	0.242571i
$817$	57238.5			2.45107
$818$			28771.7i			1.22980i
$819$	−2899.10	−	4909.83i	−0.123691	−	0.209479i
$820$		−	26147.3i		−	1.11354i
$821$	34380.7			1.46151			0.730753	−	0.682642i	$-0.239169\pi$
$821$	34380.7			1.46151			0.730753	+	0.682642i	$0.239169\pi$
$822$	8187.58	+	4673.85i	0.347415	+	0.198320i
$823$	−33496.1			−1.41871			−0.709357	−	0.704850i	$-0.751014\pi$
$823$	−33496.1			−1.41871			−0.709357	+	0.704850i	$0.751014\pi$
$824$	−28311.8			−1.19695
$825$	−924.254	−	4719.49i	−0.0390041	−	0.199166i
$826$	−19032.5			−0.801725
$827$	8303.08			0.349125			0.174562	−	0.984646i	$-0.444149\pi$
$827$	8303.08			0.349125			0.174562	+	0.984646i	$0.444149\pi$
$828$	6735.15	−	3976.89i	0.282684	−	0.166916i
$829$	21903.6			0.917665			0.458832	−	0.888523i	$-0.348268\pi$
$829$	21903.6			0.917665			0.458832	+	0.888523i	$0.348268\pi$
$830$			8358.60i			0.349556i
$831$	17271.2	+	9859.21i	0.720976	+	0.411567i
$832$		−	12119.2i		−	0.504999i
$833$	−12195.0			−0.507242
$834$	−2105.47	−	1201.90i	−0.0874180	−	0.0499023i
$835$		−	26843.9i		−	1.11254i
$836$	−46947.8	−	54389.2i	−1.94225	−	2.25011i
$837$	11579.3	−	169.931i	0.478184	−	0.00701755i
$838$		−	29902.1i		−	1.23264i
$839$		−	32602.6i		−	1.34156i	−0.741657	−	0.670779i	$-0.765960\pi$
$839$		−	32602.6i		−	1.34156i	0.741657	−	0.670779i	$-0.234040\pi$
$840$	−8556.20	+	14988.6i	−0.351449	+	0.615662i
$841$	−21632.3			−0.886971
$842$	15854.7			0.648917
$843$	−873.749	+	1530.62i	−0.0356981	+	0.0625354i
$844$			36293.8i			1.48019i
$845$		−	24351.1i		−	0.991365i
$846$	40473.4	−	23898.3i	1.64481	−	0.971206i
$847$	−19134.7	−	2825.44i	−0.776239	−	0.114620i
$848$		−	1082.76i		−	0.0438468i
$849$	−18438.6	−	10525.6i	−0.745361	−	0.425487i
$850$	−10535.6			−0.425137
$851$		−	6598.61i		−	0.265802i
$852$	23277.3	+	13287.8i	0.935994	+	0.534309i
$853$			32544.8i			1.30635i	0.757208	+	0.653174i	$0.226563\pi$
$853$			32544.8i			1.30635i	−0.757208	+	0.653174i	$0.773437\pi$
$854$	−9624.26			−0.385639
$855$	27281.7	+	46203.4i	1.09124	+	1.84810i
$856$	−24174.1			−0.965249
$857$	566.319			0.0225730			0.0112865	−	0.999936i	$-0.496407\pi$
$857$	566.319			0.0225730			0.0112865	+	0.999936i	$0.496407\pi$
$858$	12136.3	−	2376.74i	0.482896	−	0.0945693i
$859$	12811.9			0.508888			0.254444	−	0.967087i	$-0.418107\pi$
$859$	12811.9			0.508888			0.254444	+	0.967087i	$0.418107\pi$
$860$	52630.2			2.08683
$861$	11506.9	+	6568.66i	0.455462	+	0.259999i
$862$	−17999.4			−0.711208
$863$		−	10242.5i		−	0.404009i	−0.979385	−	0.202004i	$-0.935254\pi$
$863$		−	10242.5i		−	0.404009i	0.979385	−	0.202004i	$-0.0647456\pi$
$864$	29446.7	−	432.142i	1.15949	−	0.0170159i
$865$		−	6134.39i		−	0.241128i
$866$	33354.5			1.30881
$867$	−9391.18	+	16451.3i	−0.367868	+	0.644425i
$868$		−	14576.8i		−	0.570009i
$869$	2929.44	+	3393.77i	0.114355	+	0.132481i
$870$	13042.6	+	7445.30i	0.508257	+	0.290137i
$871$			2922.48i			0.113690i
$872$		−	26833.0i		−	1.04206i
$873$	−3006.00	−	5090.87i	−0.116538	−	0.197365i
$874$	−17343.0			−0.671209
$875$	−17754.2			−0.685945
$876$	25310.1	+	14448.2i	0.976197	+	0.557259i
$877$			14958.4i			0.575952i	0.957638	+	0.287976i	$0.0929823\pi$
$877$			14958.4i			0.575952i	−0.957638	+	0.287976i	$0.907018\pi$
$878$			61257.6i			2.35461i
$879$	14028.1	−	24574.3i	0.538290	−	0.942969i
$880$	3959.15	+	4586.70i	0.151663	+	0.175702i
$881$		−	26977.7i		−	1.03167i	−0.856687	−	0.515836i	$-0.827481\pi$
$881$		−	26977.7i		−	1.03167i	0.856687	−	0.515836i	$-0.172519\pi$
$882$	8123.65	+	13758.0i	0.310133	+	0.525232i
$883$	−38095.3			−1.45188			−0.725940	−	0.687758i	$-0.758595\pi$
$883$	−38095.3			−1.45188			−0.725940	+	0.687758i	$0.758595\pi$
$884$		−	16337.2i		−	0.621584i
$885$	−9215.93	+	16144.3i	−0.350045	+	0.613204i
$886$			14814.0i			0.561723i
$887$	−24913.9			−0.943097			−0.471548	−	0.881840i	$-0.656305\pi$
$887$	−24913.9			−0.943097			−0.471548	+	0.881840i	$0.656305\pi$
$888$	−13290.6	+	23282.3i	−0.502256	+	0.879844i
$889$	−33054.1			−1.24702
$890$	−42110.0			−1.58599
$891$	5493.85	+	26022.4i	0.206567	+	0.978433i
$892$	−64615.6			−2.42544
$893$	−62846.1			−2.35506
$894$	−3874.99	+	6788.14i	−0.144965	+	0.253948i
$895$	16155.5			0.603372
$896$		−	30000.9i		−	1.11860i
$897$	892.404	−	1563.30i	0.0332179	−	0.0581907i
$898$		−	41773.6i		−	1.55234i
$899$	−4333.88			−0.160782
$900$	4232.11	+	7167.38i	0.156745	+	0.265458i
$901$		−	7395.92i		−	0.273467i
$902$	−21754.0	+	18777.7i	−0.803026	+	0.693158i
$903$	−13221.6	+	23161.4i	−0.487251	+	0.853559i
$904$			19663.8i			0.723460i
$905$			21427.9i			0.787059i
$906$	−21777.8	−	12431.8i	−0.798587	−	0.455871i
$907$	44889.9			1.64338			0.821690	−	0.569934i	$-0.193031\pi$
$907$	44889.9			1.64338			0.821690	+	0.569934i	$0.193031\pi$
$908$	61849.8			2.26053
$909$	2601.98	+	4406.63i	0.0949418	+	0.160791i
$910$			11625.0i			0.423476i
$911$			44920.0i			1.63366i	0.576876	+	0.816832i	$0.304272\pi$
$911$			44920.0i			1.63366i	−0.576876	+	0.816832i	$0.695728\pi$
$912$	−9905.00	−	5654.24i	−0.359635	−	0.205297i
$913$	4193.49	−	3619.75i	0.152009	−	0.131212i
$914$		−	55404.8i		−	2.00506i
$915$	−4660.27	+	8163.79i	−0.168376	+	0.294958i
$916$	53938.2			1.94560
$917$		−	17754.9i		−	0.639389i
$918$	58258.6	−	854.969i	2.09458	−	0.0307388i
$919$			44178.6i			1.58577i	0.609374	+	0.792883i	$0.291421\pi$
$919$			44178.6i			1.58577i	−0.609374	+	0.792883i	$0.708579\pi$
$920$	−5448.62			−0.195256
$921$	16598.2	+	9475.02i	0.593842	+	0.338993i
$922$	10344.4			0.369495
$923$	6168.46			0.219975
$924$	32853.0	−	6433.86i	1.16968	−	0.229068i
$925$	7022.07			0.249605
$926$	−23246.3			−0.824968
$927$	−20852.3	−	35314.8i	−0.738812	−	1.25123i
$928$	−11021.2			−0.389859
$929$			36498.3i			1.28899i	0.764610	+	0.644494i	$0.222932\pi$
$929$			36498.3i			1.28899i	−0.764610	+	0.644494i	$0.777068\pi$
$930$	−20504.8	−	11705.1i	−0.722987	−	0.412715i
$931$		−	21363.0i		−	0.752036i
$932$	14381.1			0.505440
$933$	28826.8	+	16455.7i	1.01152	+	0.577422i
$934$			45649.7i			1.59925i
$935$	27043.5	+	31330.0i	0.945902	+	1.09583i
$936$	−6297.44	+	3718.44i	−0.219913	+	0.129852i
$937$			30491.6i			1.06309i	0.847030	+	0.531545i	$0.178388\pi$
$937$			30491.6i			1.06309i	−0.847030	+	0.531545i	$0.821612\pi$
$938$			13119.3i			0.456674i
$939$	−16080.3	+	28169.1i	−0.558849	+	0.978983i
$940$	−57786.4			−2.00509
$941$	9316.95			0.322767			0.161384	−	0.986892i	$-0.448404\pi$
$941$	9316.95			0.322767			0.161384	+	0.986892i	$0.448404\pi$
$942$	−5250.73	+	9198.14i	−0.181611	+	0.318144i
$943$			4182.95i			0.144449i
$944$		−	3951.39i		−	0.136236i
$945$	−24997.9	+	366.855i	−0.860511	+	0.0126284i
$946$	−37796.4	−	43787.2i	−1.29901	−	1.50491i
$947$			31678.7i			1.08703i	0.839399	+	0.543516i	$0.182907\pi$
$947$			31678.7i			1.08703i	−0.839399	+	0.543516i	$0.817093\pi$
$948$	−6738.82	−	3846.83i	−0.230872	−	0.131793i
$949$	6707.15			0.229424
$950$		−	18456.0i		−	0.630308i
$951$	−1209.46	−	690.417i	−0.0412402	−	0.0235419i
$952$		−	25058.3i		−	0.853093i
$953$	42487.3			1.44417			0.722087	−	0.691802i	$-0.243183\pi$
$953$	42487.3			1.44417			0.722087	+	0.691802i	$0.243183\pi$
$954$	−8343.81	+	4926.76i	−0.283166	+	0.167201i
$955$	47537.3			1.61076
$956$	20496.4			0.693410
$957$	−1912.88	−	9767.66i	−0.0646129	−	0.329931i
$958$	78368.7			2.64298
$959$	5873.41			0.197771
$960$	−46148.7	−	26343.8i	−1.55150	−	0.885670i
$961$	−22977.5			−0.771291
$962$			18057.4i			0.605191i
$963$	−17804.8	−	30153.6i	−0.595795	−	1.00902i
$964$		−	70245.4i		−	2.34694i
$965$	12473.9			0.416114
$966$	4006.10	−	7017.81i	0.133431	−	0.233742i
$967$		−	19898.2i		−	0.661721i	−0.943680	−	0.330860i	$-0.892661\pi$
$967$		−	19898.2i		−	0.661721i	0.943680	−	0.330860i	$-0.107339\pi$
$968$	−3623.96	+	24542.5i	−0.120329	+	0.814902i
$969$	−67657.4	−	38622.0i	−2.24300	−	1.28041i
$970$			12053.6i			0.398988i
$971$		−	24273.9i		−	0.802251i	−0.916023	−	0.401125i	$-0.868619\pi$
$971$		−	24273.9i		−	0.802251i	0.916023	−	0.401125i	$-0.131381\pi$
$972$	−23984.0	−	39290.1i	−0.791447	−	1.29653i
$973$	−1510.37			−0.0497640
$974$	−51740.3			−1.70212
$975$	1663.62	+	949.674i	0.0546447	+	0.0311938i
$976$		−	1998.12i		−	0.0655310i
$977$		−	8504.73i		−	0.278496i	−0.990258	−	0.139248i	$-0.955532\pi$
$977$		−	8504.73i		−	0.278496i	0.990258	−	0.139248i	$-0.0444685\pi$
$978$	−19011.1	+	33303.3i	−0.621581	+	1.08888i
$979$	18236.0	+	21126.5i	0.595327	+	0.689689i
$980$		−	19643.1i		−	0.640281i
$981$	33470.2	−	19763.1i	1.08932	−	0.643208i
$982$	32506.2			1.05633
$983$		−	21918.9i		−	0.711194i	−0.934639	−	0.355597i	$-0.884278\pi$
$983$		−	21918.9i		−	0.711194i	0.934639	−	0.355597i	$-0.115722\pi$
$984$	8425.09	−	14758.9i	0.272949	−	0.478148i
$985$			42714.4i			1.38172i
$986$	−21804.9			−0.704268
$987$	14516.9	−	25430.5i	0.468165	−	0.820124i
$988$	28619.3			0.921559
$989$	−8419.57			−0.270705
$990$	17330.5	−	51379.9i	0.556362	−	1.64945i
$991$	6904.12			0.221308			0.110654	−	0.993859i	$-0.464705\pi$
$991$	6904.12			0.221308			0.110654	+	0.993859i	$0.464705\pi$
$992$	17326.9			0.554567
$993$	1162.40	−	2036.28i	0.0371478	−	0.0650749i
$994$	27690.9			0.883602
$995$		−	55710.8i		−	1.77503i
$996$	−4753.32	+	8326.79i	−0.151220	+	0.264904i
$997$			22130.0i			0.702973i	0.936193	+	0.351486i	$0.114324\pi$
$997$			22130.0i			0.702973i	−0.936193	+	0.351486i	$0.885676\pi$
$998$	7296.63			0.231434
$999$	−38830.0	+	569.847i	−1.22976	+	0.0180472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.d.b.32.2	yes	8
3.2	odd	2	inner	33.4.d.b.32.7	yes	8
4.3	odd	2		528.4.b.e.65.6		8
11.10	odd	2	inner	33.4.d.b.32.8	yes	8
12.11	even	2		528.4.b.e.65.8		8
33.32	even	2	inner	33.4.d.b.32.1	✓	8
44.43	even	2		528.4.b.e.65.5		8
132.131	odd	2		528.4.b.e.65.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.d.b.32.1	✓	8	33.32	even	2	inner
33.4.d.b.32.2	yes	8	1.1	even	1	trivial
33.4.d.b.32.7	yes	8	3.2	odd	2	inner
33.4.d.b.32.8	yes	8	11.10	odd	2	inner
528.4.b.e.65.5		8	44.43	even	2
528.4.b.e.65.6		8	4.3	odd	2
528.4.b.e.65.7		8	132.131	odd	2
528.4.b.e.65.8		8	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.48911 q^{2} +(-2.57603 + 4.51265i) q^{3} +12.1521 q^{4} -12.2625i q^{5} +(11.5641 - 20.2578i) q^{6} -14.5320i q^{7} -18.6391 q^{8} +(-13.7281 - 23.2495i) q^{9} +O(q^{10})\)	\(q-4.48911 q^{2} +(-2.57603 + 4.51265i) q^{3} +12.1521 q^{4} -12.2625i q^{5} +(11.5641 - 20.2578i) q^{6} -14.5320i q^{7} -18.6391 q^{8} +(-13.7281 - 23.2495i) q^{9} +55.0476i q^{10} +(27.6173 - 23.8387i) q^{11} +(-31.3041 + 54.8381i) q^{12} +14.5320i q^{13} +65.2358i q^{14} +(55.3364 + 31.5886i) q^{15} -13.5438 q^{16} -92.5127 q^{17} +(61.6269 + 104.369i) q^{18} -162.062i q^{19} -149.015i q^{20} +(65.5781 + 37.4350i) q^{21} +(-123.977 + 107.015i) q^{22} +23.8387i q^{23} +(48.0149 - 84.1117i) q^{24} -25.3686 q^{25} -65.2358i q^{26} +(140.281 - 2.05868i) q^{27} -176.594i q^{28} -52.5040 q^{29} +(-248.411 - 141.804i) q^{30} +82.5438 q^{31} +209.912 q^{32} +(36.4330 + 186.037i) q^{33} +415.299 q^{34} -178.199 q^{35} +(-166.825 - 282.529i) q^{36} -276.802 q^{37} +727.515i q^{38} +(-65.5781 - 37.4350i) q^{39} +228.561i q^{40} +175.468 q^{41} +(-294.387 - 168.050i) q^{42} +353.189i q^{43} +(335.607 - 289.690i) q^{44} +(-285.097 + 168.341i) q^{45} -107.015i q^{46} -387.790i q^{47} +(34.8893 - 61.1185i) q^{48} +131.820 q^{49} +113.882 q^{50} +(238.316 - 417.478i) q^{51} +176.594i q^{52} +79.9449i q^{53} +(-629.736 + 9.24164i) q^{54} +(-292.322 - 338.657i) q^{55} +270.864i q^{56} +(731.331 + 417.478i) q^{57} +235.696 q^{58} +291.749i q^{59} +(672.451 + 383.867i) q^{60} +147.530i q^{61} -370.548 q^{62} +(-337.863 + 199.497i) q^{63} -833.967 q^{64} +178.199 q^{65} +(-163.552 - 835.138i) q^{66} +201.106 q^{67} -1124.22 q^{68} +(-107.576 - 61.4094i) q^{69} +799.954 q^{70} -424.473i q^{71} +(255.879 + 433.349i) q^{72} -461.542i q^{73} +1242.59 q^{74} +(65.3504 - 114.480i) q^{75} -1969.39i q^{76} +(-346.426 - 401.335i) q^{77} +(294.387 + 168.050i) q^{78} +122.886i q^{79} +166.081i q^{80} +(-352.078 + 638.343i) q^{81} -787.696 q^{82} +151.843 q^{83} +(796.909 + 454.913i) q^{84} +1134.44i q^{85} -1585.50i q^{86} +(135.252 - 236.932i) q^{87} +(-514.760 + 444.332i) q^{88} +764.973i q^{89} +(1279.83 - 755.699i) q^{90} +211.180 q^{91} +289.690i q^{92} +(-212.636 + 372.492i) q^{93} +1740.83i q^{94} -1987.29 q^{95} +(-540.741 + 947.261i) q^{96} +218.967 q^{97} -591.753 q^{98} +(-933.372 - 314.827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 44 q^{4} - 30 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 44 * q^4 - 30 * q^9	\( 8 q + 6 q^{3} + 44 q^{4} - 30 q^{9} - 144 q^{12} + 150 q^{15} - 268 q^{16} - 300 q^{22} + 276 q^{25} + 324 q^{27} + 820 q^{31} + 834 q^{33} + 768 q^{34} - 696 q^{36} - 884 q^{37} - 120 q^{42} - 1722 q^{45} - 732 q^{48} - 2032 q^{49} - 476 q^{55} + 1992 q^{58} + 2772 q^{60} - 1084 q^{64} + 2076 q^{66} + 172 q^{67} - 834 q^{69} + 5016 q^{70} + 1800 q^{75} + 120 q^{78} - 4014 q^{81} - 6408 q^{82} - 3852 q^{88} + 4776 q^{91} + 1146 q^{93} - 3836 q^{97} + 1074 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 44 * q^4 - 30 * q^9 - 144 * q^12 + 150 * q^15 - 268 * q^16 - 300 * q^22 + 276 * q^25 + 324 * q^27 + 820 * q^31 + 834 * q^33 + 768 * q^34 - 696 * q^36 - 884 * q^37 - 120 * q^42 - 1722 * q^45 - 732 * q^48 - 2032 * q^49 - 476 * q^55 + 1992 * q^58 + 2772 * q^60 - 1084 * q^64 + 2076 * q^66 + 172 * q^67 - 834 * q^69 + 5016 * q^70 + 1800 * q^75 + 120 * q^78 - 4014 * q^81 - 6408 * q^82 - 3852 * q^88 + 4776 * q^91 + 1146 * q^93 - 3836 * q^97 + 1074 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more