LMFDB - Embedded newform 744.2.o.e.557.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [744,2,Mod(557,744)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(744, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("744.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 744 = 2^{3} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	744.o (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:	$5.94086991038$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			557.6
Character	$\chi$	$=$	744.557
Dual form			744.2.o.e.557.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34962 - 0.422518i) q^{2} +(0.637359 - 1.61052i) q^{3} +(1.64296 + 1.14048i) q^{4} +2.38521 q^{5} +(-1.54067 + 1.90430i) q^{6} -4.12791 q^{7} +(-1.73550 - 2.23339i) q^{8} +(-2.18755 - 2.05296i) q^{9} +O(q^{10})$	\(q+(-1.34962 - 0.422518i) q^{2} +(0.637359 - 1.61052i) q^{3} +(1.64296 + 1.14048i) q^{4} +2.38521 q^{5} +(-1.54067 + 1.90430i) q^{6} -4.12791 q^{7} +(-1.73550 - 2.23339i) q^{8} +(-2.18755 - 2.05296i) q^{9} +(-3.21913 - 1.00780i) q^{10} +2.23254i q^{11} +(2.88392 - 1.91912i) q^{12} -5.19885 q^{13} +(5.57112 + 1.74412i) q^{14} +(1.52024 - 3.84143i) q^{15} +(1.39861 + 3.74752i) q^{16} -3.54273 q^{17} +(2.08495 + 3.69500i) q^{18} +8.66700i q^{19} +(3.91880 + 2.72029i) q^{20} +(-2.63096 + 6.64808i) q^{21} +(0.943290 - 3.01309i) q^{22} -6.02115 q^{23} +(-4.70306 + 1.37158i) q^{24} +0.689240 q^{25} +(7.01648 + 2.19661i) q^{26} +(-4.70058 + 2.21461i) q^{27} +(-6.78198 - 4.70780i) q^{28} -7.20826i q^{29} +(-3.67482 + 4.54215i) q^{30} +(-2.20750 - 5.11145i) q^{31} +(-0.304205 - 5.64867i) q^{32} +(3.59555 + 1.42293i) q^{33} +(4.78134 + 1.49687i) q^{34} -9.84594 q^{35} +(-1.25269 - 5.86777i) q^{36} +9.47722 q^{37} +(3.66196 - 11.6972i) q^{38} +(-3.31354 + 8.37285i) q^{39} +(-4.13953 - 5.32712i) q^{40} +0.0465909i q^{41} +(6.35974 - 7.86076i) q^{42} -0.296011 q^{43} +(-2.54617 + 3.66797i) q^{44} +(-5.21776 - 4.89675i) q^{45} +(8.12627 + 2.54404i) q^{46} -0.421034i q^{47} +(6.92687 + 0.136020i) q^{48} +10.0396 q^{49} +(-0.930213 - 0.291216i) q^{50} +(-2.25799 + 5.70564i) q^{51} +(-8.54149 - 5.92918i) q^{52} -10.6156i q^{53} +(7.27972 - 1.00281i) q^{54} +5.32509i q^{55} +(7.16397 + 9.21925i) q^{56} +(13.9584 + 5.52399i) q^{57} +(-3.04562 + 9.72842i) q^{58} -5.39444 q^{59} +(6.87876 - 4.57751i) q^{60} -5.51694 q^{61} +(0.819605 + 7.83124i) q^{62} +(9.02999 + 8.47443i) q^{63} +(-1.97610 + 7.75210i) q^{64} -12.4004 q^{65} +(-4.25142 - 3.43961i) q^{66} -2.49710i q^{67} +(-5.82055 - 4.04041i) q^{68} +(-3.83763 + 9.69717i) q^{69} +(13.2883 + 4.16009i) q^{70} +3.20397i q^{71} +(-0.788591 + 8.44856i) q^{72} +0.219270i q^{73} +(-12.7907 - 4.00430i) q^{74} +(0.439294 - 1.11003i) q^{75} +(-9.88453 + 14.2395i) q^{76} -9.21573i q^{77} +(8.00970 - 9.90015i) q^{78} -4.21234i q^{79} +(3.33599 + 8.93862i) q^{80} +(0.570713 + 8.98189i) q^{81} +(0.0196855 - 0.0628801i) q^{82} +6.88347i q^{83} +(-11.9046 + 7.92195i) q^{84} -8.45016 q^{85} +(0.399503 + 0.125070i) q^{86} +(-11.6090 - 4.59425i) q^{87} +(4.98615 - 3.87457i) q^{88} +1.83293 q^{89} +(4.97304 + 8.81335i) q^{90} +21.4604 q^{91} +(-9.89248 - 6.86699i) q^{92} +(-9.63906 + 0.297385i) q^{93} +(-0.177895 + 0.568237i) q^{94} +20.6726i q^{95} +(-9.29118 - 3.11030i) q^{96} +1.83069 q^{97} +(-13.5497 - 4.24193i) q^{98} +(4.58332 - 4.88379i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9}+O(q^{10}) $ 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9	$ 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9} - 52 q^{10} - 60 q^{16} - 4 q^{18} + 168 q^{25} - 20 q^{28} + 16 q^{31} + 8 q^{33} + 8 q^{39} - 64 q^{40} - 64 q^{49} + 56 q^{63} + 72 q^{64} + 4 q^{66} - 84 q^{70} - 44 q^{72} - 28 q^{76} + 56 q^{78} - 112 q^{81} - 108 q^{82} - 168 q^{87} + 104 q^{90} + 8 q^{94} + 72 q^{97}+O(q^{100}) $ 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9 - 52 * q^10 - 60 * q^16 - 4 * q^18 + 168 * q^25 - 20 * q^28 + 16 * q^31 + 8 * q^33 + 8 * q^39 - 64 * q^40 - 64 * q^49 + 56 * q^63 + 72 * q^64 + 4 * q^66 - 84 * q^70 - 44 * q^72 - 28 * q^76 + 56 * q^78 - 112 * q^81 - 108 * q^82 - 168 * q^87 + 104 * q^90 + 8 * q^94 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/744\mathbb{Z}\right)^\times$.

$n$	$313$	$373$	$497$	$559$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34962	−	0.422518i	−0.954327	−	0.298765i
$2$	−1.34962	−	0.422518i	−0.954327	−	0.298765i
$3$	0.637359	−	1.61052i	0.367980	−	0.929834i
$3$	0.637359	−	1.61052i	0.367980	−	0.929834i
$4$	1.64296	+	1.14048i	0.821478	+	0.570240i
$5$	2.38521			1.06670			0.533350	−	0.845895i	$-0.320933\pi$
$5$	2.38521			1.06670			0.533350	+	0.845895i	$0.320933\pi$
$6$	−1.54067	+	1.90430i	−0.628975	+	0.777426i
$7$	−4.12791			−1.56020			−0.780102	−	0.625653i	$-0.784833\pi$
$7$	−4.12791			−1.56020			−0.780102	+	0.625653i	$0.784833\pi$
$8$	−1.73550	−	2.23339i	−0.613591	−	0.789624i
$9$	−2.18755	−	2.05296i	−0.729182	−	0.684320i
$10$	−3.21913	−	1.00780i	−1.01798	−	0.318693i
$11$			2.23254i			0.673137i	0.941659	+	0.336568i	$0.109266\pi$
$11$			2.23254i			0.673137i	−0.941659	+	0.336568i	$0.890734\pi$
$12$	2.88392	−	1.91912i	0.832515	−	0.554002i
$13$	−5.19885			−1.44190			−0.720951	−	0.692986i	$-0.756295\pi$
$13$	−5.19885			−1.44190			−0.720951	+	0.692986i	$0.756295\pi$
$14$	5.57112	+	1.74412i	1.48894	+	0.466135i
$15$	1.52024	−	3.84143i	0.392524	−	0.991853i
$16$	1.39861	+	3.74752i	0.349653	+	0.936879i
$17$	−3.54273			−0.859238			−0.429619	−	0.903010i	$-0.641352\pi$
$17$	−3.54273			−0.859238			−0.429619	+	0.903010i	$0.641352\pi$
$18$	2.08495	+	3.69500i	0.491427	+	0.870919i
$19$			8.66700i			1.98835i	0.107799	+	0.994173i	$0.465620\pi$
$19$			8.66700i			1.98835i	−0.107799	+	0.994173i	$0.534380\pi$
$20$	3.91880	+	2.72029i	0.876271	+	0.608274i
$21$	−2.63096	+	6.64808i	−0.574123	+	1.45073i
$22$	0.943290	−	3.01309i	0.201110	−	0.642392i
$23$	−6.02115			−1.25550			−0.627748	−	0.778417i	$-0.716023\pi$
$23$	−6.02115			−1.25550			−0.627748	+	0.778417i	$0.716023\pi$
$24$	−4.70306	+	1.37158i	−0.960008	+	0.279972i
$25$	0.689240			0.137848
$26$	7.01648	+	2.19661i	1.37605	+	0.430791i
$27$	−4.70058	+	2.21461i	−0.904628	+	0.426202i
$28$	−6.78198	−	4.70780i	−1.28167	−	0.889690i
$29$		−	7.20826i		−	1.33854i	−0.743019	−	0.669270i	$-0.766607\pi$
$29$		−	7.20826i		−	1.33854i	0.743019	−	0.669270i	$-0.233393\pi$
$30$	−3.67482	+	4.54215i	−0.670927	+	0.829279i
$31$	−2.20750	−	5.11145i	−0.396478	−	0.918044i
$31$	−2.20750	−	5.11145i	−0.396478	−	0.918044i
$32$	−0.304205	−	5.64867i	−0.0537764	−	0.998553i
$33$	3.59555	+	1.42293i	0.625905	+	0.247701i
$34$	4.78134	+	1.49687i	0.819994	+	0.256711i
$35$	−9.84594			−1.66427
$36$	−1.25269	−	5.86777i	−0.208781	−	0.977962i
$37$	9.47722			1.55804			0.779022	−	0.626996i	$-0.215716\pi$
$37$	9.47722			1.55804			0.779022	+	0.626996i	$0.215716\pi$
$38$	3.66196	−	11.6972i	0.594049	−	1.89753i
$39$	−3.31354	+	8.37285i	−0.530591	+	1.34073i
$40$	−4.13953	−	5.32712i	−0.654517	−	0.842292i
$41$			0.0465909i			0.00727628i	0.999993	+	0.00363814i	$0.00115806\pi$
$41$			0.0465909i			0.00727628i	−0.999993	+	0.00363814i	$0.998842\pi$
$42$	6.35974	−	7.86076i	0.981329	−	1.21294i
$43$	−0.296011			−0.0451413			−0.0225707	−	0.999745i	$-0.507185\pi$
$43$	−0.296011			−0.0451413			−0.0225707	+	0.999745i	$0.507185\pi$
$44$	−2.54617	+	3.66797i	−0.383849	+	0.552967i
$45$	−5.21776	−	4.89675i	−0.777818	−	0.729964i
$46$	8.12627	+	2.54404i	1.19815	+	0.375099i
$47$		−	0.421034i		−	0.0614141i	−0.999528	−	0.0307071i	$-0.990224\pi$
$47$		−	0.421034i		−	0.0614141i	0.999528	−	0.0307071i	$-0.00977590\pi$
$48$	6.92687	+	0.136020i	0.999807	+	0.0196329i
$49$	10.0396			1.43423
$50$	−0.930213	−	0.291216i	−0.131552	−	0.0411842i
$51$	−2.25799	+	5.70564i	−0.316182	+	0.798949i
$52$	−8.54149	−	5.92918i	−1.18449	−	0.822230i
$53$		−	10.6156i		−	1.45817i	−0.684424	−	0.729084i	$-0.739946\pi$
$53$		−	10.6156i		−	1.45817i	0.684424	−	0.729084i	$-0.260054\pi$
$54$	7.27972	−	1.00281i	0.990645	−	0.136465i
$55$			5.32509i			0.718035i
$56$	7.16397	+	9.21925i	0.957326	+	1.23197i
$57$	13.9584	+	5.52399i	1.84883	+	0.731671i
$58$	−3.04562	+	9.72842i	−0.399910	+	1.27740i
$59$	−5.39444			−0.702296			−0.351148	−	0.936320i	$-0.614209\pi$
$59$	−5.39444			−0.702296			−0.351148	+	0.936320i	$0.614209\pi$
$60$	6.87876	−	4.57751i	0.888044	−	0.590953i
$61$	−5.51694			−0.706372			−0.353186	−	0.935553i	$-0.614902\pi$
$61$	−5.51694			−0.706372			−0.353186	+	0.935553i	$0.614902\pi$
$62$	0.819605	+	7.83124i	0.104090	+	0.994568i
$63$	9.02999	+	8.47443i	1.13767	+	1.06768i
$64$	−1.97610	+	7.75210i	−0.247013	+	0.969012i
$65$	−12.4004			−1.53808
$66$	−4.25142	−	3.43961i	−0.523314	−	0.423386i
$67$		−	2.49710i		−	0.305069i	−0.988298	−	0.152535i	$-0.951256\pi$
$67$		−	2.49710i		−	0.305069i	0.988298	−	0.152535i	$-0.0487435\pi$
$68$	−5.82055	−	4.04041i	−0.705846	−	0.489972i
$69$	−3.83763	+	9.69717i	−0.461997	+	1.16740i
$70$	13.2883	+	4.16009i	1.58826	+	0.497226i
$71$			3.20397i			0.380242i	0.981761	+	0.190121i	$0.0608880\pi$
$71$			3.20397i			0.380242i	−0.981761	+	0.190121i	$0.939112\pi$
$72$	−0.788591	+	8.44856i	−0.0929363	+	0.995672i
$73$			0.219270i			0.0256637i	0.999918	+	0.0128318i	$0.00408461\pi$
$73$			0.219270i			0.0256637i	−0.999918	+	0.0128318i	$0.995915\pi$
$74$	−12.7907	−	4.00430i	−1.48688	−	0.465490i
$75$	0.439294	−	1.11003i	0.0507252	−	0.128176i
$76$	−9.88453	+	14.2395i	−1.13383	+	1.63338i
$77$		−	9.21573i		−	1.05023i
$78$	8.00970	−	9.90015i	0.906920	−	1.12097i
$79$		−	4.21234i		−	0.473925i	−0.971519	−	0.236963i	$-0.923848\pi$
$79$		−	4.21234i		−	0.473925i	0.971519	−	0.236963i	$-0.0761519\pi$
$80$	3.33599	+	8.93862i	0.372975	+	0.999369i
$81$	0.570713	+	8.98189i	0.0634126	+	0.997987i
$82$	0.0196855	−	0.0628801i	0.00217390	−	0.00694394i
$83$			6.88347i			0.755559i	0.925896	+	0.377779i	$0.123312\pi$
$83$			6.88347i			0.755559i	−0.925896	+	0.377779i	$0.876688\pi$
$84$	−11.9046	+	7.92195i	−1.29889	+	0.864356i
$85$	−8.45016			−0.916549
$86$	0.399503	+	0.125070i	0.0430796	+	0.0134867i
$87$	−11.6090	−	4.59425i	−1.24462	−	0.492556i
$88$	4.98615	−	3.87457i	0.531525	−	0.413030i
$89$	1.83293			0.194291			0.0971453	−	0.995270i	$-0.469029\pi$
$89$	1.83293			0.194291			0.0971453	+	0.995270i	$0.469029\pi$
$90$	4.97304	+	8.81335i	0.524204	+	0.929009i
$91$	21.4604			2.24966
$92$	−9.89248	−	6.86699i	−1.03136	−	0.715933i
$93$	−9.63906	+	0.297385i	−0.999524	+	0.0308374i
$94$	−0.177895	+	0.568237i	−0.0183484	+	0.0586091i
$95$			20.6726i			2.12097i
$96$	−9.29118	−	3.11030i	−0.948277	−	0.317444i
$97$	1.83069			0.185879			0.0929394	−	0.995672i	$-0.470374\pi$
$97$	1.83069			0.185879			0.0929394	+	0.995672i	$0.470374\pi$
$98$	−13.5497	−	4.24193i	−1.36873	−	0.428500i
$99$	4.58332	−	4.88379i	0.460641	−	0.490839i
$100$	1.13239	+	0.786064i	0.113239	+	0.0786064i
$101$	7.37767			0.734105			0.367053	−	0.930200i	$-0.380367\pi$
$101$	7.37767			0.734105			0.367053	+	0.930200i	$0.380367\pi$
$102$	5.45817	−	6.74641i	0.540439	−	0.667994i
$103$	−6.33227			−0.623937			−0.311968	−	0.950092i	$-0.600988\pi$
$103$	−6.33227			−0.623937			−0.311968	+	0.950092i	$0.600988\pi$
$104$	9.02259	+	11.6111i	0.884738	+	1.13856i
$105$	−6.27541	+	15.8571i	−0.612417	+	1.54749i
$106$	−4.48530	+	14.3271i	−0.435650	+	1.39157i
$107$	13.2038			1.27646			0.638231	−	0.769845i	$-0.279666\pi$
$107$	13.2038			1.27646			0.638231	+	0.769845i	$0.279666\pi$
$108$	−10.2486	−	1.72241i	−0.986170	−	0.165739i
$109$			13.1333i			1.25794i	0.777429	+	0.628971i	$0.216524\pi$
$109$			13.1333i			1.25794i	−0.777429	+	0.628971i	$0.783476\pi$
$110$	2.24995	−	7.18685i	0.214524	−	0.685240i
$111$	6.04039	−	15.2632i	0.573329	−	1.44872i
$112$	−5.77335	−	15.4694i	−0.545531	−	1.46172i
$113$		−	9.51587i		−	0.895178i	−0.894239	−	0.447589i	$-0.852283\pi$
$113$		−	9.51587i		−	0.895178i	0.894239	−	0.447589i	$-0.147717\pi$
$114$	−16.5045	−	13.3530i	−1.54579	−	1.25062i
$115$	−14.3617			−1.33924
$116$	8.22087	−	11.8429i	0.763289	−	1.09958i
$117$	11.3727	+	10.6730i	1.05141	+	0.986722i
$118$	7.28045	+	2.27925i	0.670220	+	0.209822i
$119$	14.6241			1.34059
$120$	−11.2178	+	3.27150i	−1.02404	+	0.298646i
$121$	6.01576			0.546887
$122$	7.44578	+	2.33101i	0.674110	+	0.211040i
$123$	0.0750356	+	0.0296952i	0.00676573	+	0.00267752i
$124$	2.20268	−	10.9155i	0.197807	−	0.980241i
$125$	−10.2821			−0.919657
$126$	−8.60647	−	15.2526i	−0.766725	−	1.35881i
$127$			13.4622i			1.19457i	0.802028	+	0.597287i	$0.203755\pi$
$127$			13.4622i			1.19457i	−0.802028	+	0.597287i	$0.796245\pi$
$128$	5.94239	−	9.62746i	0.525238	−	0.850955i
$129$	−0.188666	+	0.476732i	−0.0166111	+	0.0419739i
$130$	16.7358	+	5.23938i	1.46783	+	0.459524i
$131$	8.23424			0.719429			0.359715	−	0.933062i	$-0.382874\pi$
$131$	8.23424			0.719429			0.359715	+	0.933062i	$0.382874\pi$
$132$	4.28451	+	6.43847i	0.372919	+	0.560397i
$133$		−	35.7766i		−	3.10222i
$134$	−1.05507	+	3.37014i	−0.0911441	+	0.291136i
$135$	−11.2119	+	5.28232i	−0.964966	+	0.454630i
$136$	6.14840	+	7.91231i	0.527221	+	0.678475i
$137$	−12.0896			−1.03289			−0.516443	−	0.856321i	$-0.672744\pi$
$137$	−12.0896			−1.03289			−0.516443	+	0.856321i	$0.672744\pi$
$138$	9.27659	−	11.4660i	0.789675	−	0.976054i
$139$	−21.6194			−1.83373			−0.916867	−	0.399193i	$-0.869290\pi$
$139$	−21.6194			−1.83373			−0.916867	+	0.399193i	$0.869290\pi$
$140$	−16.1765	−	11.2291i	−1.36716	−	0.949032i
$141$	−0.678083	−	0.268350i	−0.0571049	−	0.0225991i
$142$	1.35374	−	4.32415i	0.113603	−	0.362875i
$143$		−	11.6067i		−	0.970597i
$144$	4.63397	−	11.0692i	0.386164	−	0.922430i
$145$		−	17.1932i		−	1.42782i
$146$	0.0926457	−	0.295932i	0.00766741	−	0.0244915i
$147$	6.39886	−	16.1690i	0.527769	−	1.33360i
$148$	15.5707	+	10.8086i	1.27990	+	0.888459i
$149$	−7.33733			−0.601098			−0.300549	−	0.953766i	$-0.597170\pi$
$149$	−7.33733			−0.601098			−0.300549	+	0.953766i	$0.597170\pi$
$150$	−1.06189	+	1.31252i	−0.0867029	+	0.107167i
$151$		−	17.9568i		−	1.46130i	−0.682752	−	0.730650i	$-0.739217\pi$
$151$		−	17.9568i		−	1.46130i	0.682752	−	0.730650i	$-0.260783\pi$
$152$	19.3568	−	15.0415i	1.57005	−	1.22003i
$153$	7.74988	+	7.27308i	0.626541	+	0.587994i
$154$	−3.89382	+	12.4378i	−0.313773	+	1.00226i
$155$	−5.26535	−	12.1919i	−0.422923	−	0.979277i
$156$	−14.9931	+	9.97721i	−1.20041	+	0.798816i
$157$			9.96016i			0.794908i	0.917622	+	0.397454i	$0.130106\pi$
$157$			9.96016i			0.794908i	−0.917622	+	0.397454i	$0.869894\pi$
$158$	−1.77979	+	5.68506i	−0.141593	+	0.452279i
$159$	−17.0967	−	6.76597i	−1.35585	−	0.536576i
$160$	−0.725595	−	13.4733i	−0.0573633	−	1.06516i
$161$	24.8547			1.95883
$162$	3.02476	−	12.3633i	0.237648	−	0.971351i
$163$			8.54995i			0.669684i	0.942274	+	0.334842i	$0.108683\pi$
$163$			8.54995i			0.669684i	−0.942274	+	0.334842i	$0.891317\pi$
$164$	−0.0531360	+	0.0765468i	−0.00414922	+	0.00597730i
$165$	8.57616	+	3.39400i	0.667653	+	0.264222i
$166$	2.90839	−	9.29008i	0.225735	−	0.721050i
$167$	−15.4640			−1.19664			−0.598319	−	0.801258i	$-0.704164\pi$
$167$	−15.4640			−1.19664			−0.598319	+	0.801258i	$0.704164\pi$
$168$	19.4138	−	5.66174i	1.49781	−	0.436813i
$169$	14.0281			1.07908
$170$	11.4045	+	3.57035i	0.874687	+	0.273833i
$171$	17.7930	−	18.9595i	1.36066	−	1.44987i
$172$	−0.486334	−	0.337595i	−0.0370826	−	0.0257414i
$173$	−21.6469			−1.64579			−0.822893	−	0.568197i	$-0.807641\pi$
$173$	−21.6469			−1.64579			−0.822893	+	0.568197i	$0.807641\pi$
$174$	13.7267	+	11.1055i	1.04062	+	0.841908i
$175$	−2.84512			−0.215071
$176$	−8.36649	+	3.12246i	−0.630648	+	0.235365i
$177$	−3.43820	+	8.68785i	−0.258431	+	0.653018i
$178$	−2.47377	−	0.774448i	−0.185417	−	0.0580473i
$179$			0.593797i			0.0443825i	0.999754	+	0.0221912i	$0.00706427\pi$
$179$			0.593797i			0.0443825i	−0.999754	+	0.0221912i	$0.992936\pi$
$180$	−2.98792	−	13.9959i	−0.222706	−	1.04319i
$181$	8.60096			0.639304			0.319652	−	0.947535i	$-0.396434\pi$
$181$	8.60096			0.639304			0.319652	+	0.947535i	$0.396434\pi$
$182$	−28.9634	−	9.06741i	−2.14691	−	0.672121i
$183$	−3.51627	+	8.88514i	−0.259931	+	0.656809i
$184$	10.4497	+	13.4476i	0.770360	+	0.991370i
$185$	22.6052			1.66197
$186$	13.1347	+	3.67132i	0.963086	+	0.269194i
$187$		−	7.90929i		−	0.578385i
$188$	0.480181	−	0.691741i	0.0350208	−	0.0504504i
$189$	19.4036	−	9.14172i	1.41140	−	0.664962i
$190$	8.73456	−	27.9002i	0.633672	−	2.02410i
$191$		−	0.987731i		−	0.0714697i	−0.999361	−	0.0357349i	$-0.988623\pi$
$191$		−	0.987731i		−	0.0714697i	0.999361	−	0.0357349i	$-0.0113772\pi$
$192$	11.2254	+	8.12343i	0.810125	+	0.586258i
$193$	13.7170			0.987375			0.493687	−	0.869639i	$-0.335649\pi$
$193$	13.7170			0.987375			0.493687	+	0.869639i	$0.335649\pi$
$194$	−2.47074	−	0.773501i	−0.177389	−	0.0555341i
$195$	−7.90349	+	19.9710i	−0.565981	+	1.43016i
$196$	16.4947	+	11.4500i	1.17819	+	0.817858i
$197$			0.796643i			0.0567585i	0.999597	+	0.0283792i	$0.00903460\pi$
$197$			0.796643i			0.0567585i	−0.999597	+	0.0283792i	$0.990965\pi$
$198$	−8.24924	+	4.65473i	−0.586248	+	0.330797i
$199$		−	9.23148i		−	0.654402i	−0.944955	−	0.327201i	$-0.893895\pi$
$199$		−	9.23148i		−	0.654402i	0.944955	−	0.327201i	$-0.106105\pi$
$200$	−1.19617	−	1.53934i	−0.0845822	−	0.108848i
$201$	−4.02163	−	1.59155i	−0.283664	−	0.112259i
$202$	−9.95706	−	3.11720i	−0.700576	−	0.219325i
$203$			29.7550i			2.08839i
$204$	−10.2169	+	6.79892i	−0.715329	+	0.476019i
$205$			0.111129i			0.00776160i
$206$	8.54617	+	2.67550i	0.595440	+	0.186411i
$207$	13.1715	+	12.3612i	0.915485	+	0.859161i
$208$	−7.27119	−	19.4828i	−0.504166	−	1.35089i
$209$	−19.3494			−1.33843
$210$	15.1693	−	18.7496i	1.04678	−	1.29384i
$211$		−	18.9315i		−	1.30330i	−0.758520	−	0.651650i	$-0.774077\pi$
$211$		−	18.9315i		−	1.30330i	0.758520	−	0.651650i	$-0.225923\pi$
$212$	12.1069	−	17.4410i	0.831506	−	1.19785i
$213$	5.16006	+	2.04208i	0.353562	+	0.139921i
$214$	−17.8202	−	5.57886i	−1.21816	−	0.381363i
$215$	−0.706050			−0.0481522
$216$	13.1040	+	6.65481i	0.891611	+	0.452802i
$217$	9.11235	+	21.0996i	0.618587	+	1.43234i
$218$	5.54906	−	17.7250i	0.375830	−	1.20049i
$219$	0.353139	+	0.139754i	0.0238629	+	0.00944370i
$220$	−6.07315	+	8.74889i	−0.409452	+	0.589850i
$221$	18.4181			1.23894
$222$	−14.6012	+	18.0474i	−0.979971	+	1.21126i
$223$		−	4.04977i		−	0.271193i	−0.990764	−	0.135596i	$-0.956705\pi$
$223$		−	4.04977i		−	0.271193i	0.990764	−	0.135596i	$-0.0432951\pi$
$224$	1.25573	+	23.3172i	0.0839022	+	1.55795i
$225$	−1.50774	−	1.41498i	−0.100516	−	0.0943321i
$226$	−4.02063	+	12.8428i	−0.267448	+	0.854292i
$227$	−19.2276			−1.27618			−0.638089	−	0.769962i	$-0.720275\pi$
$227$	−19.2276			−1.27618			−0.638089	+	0.769962i	$0.720275\pi$
$228$	16.6330	+	24.9949i	1.10155	+	1.65533i
$229$	−3.00318			−0.198456			−0.0992279	−	0.995065i	$-0.531637\pi$
$229$	−3.00318			−0.198456			−0.0992279	+	0.995065i	$0.531637\pi$
$230$	19.3829	+	6.06808i	1.27807	+	0.400118i
$231$	−14.8421	−	5.87374i	−0.976540	−	0.386463i
$232$	−16.0989	+	12.5099i	−1.05694	+	0.821316i
$233$			4.30702i			0.282163i	0.989998	+	0.141081i	$0.0450579\pi$
$233$			4.30702i			0.282163i	−0.989998	+	0.141081i	$0.954942\pi$
$234$	−10.8393	−	19.2097i	−0.708589	−	1.25578i
$235$		−	1.00426i		−	0.0655104i
$236$	−8.86283	−	6.15224i	−0.576921	−	0.400477i
$237$	−6.78406	−	2.68477i	−0.440672	−	0.174395i
$238$	−19.7370	−	6.17894i	−1.27936	−	0.400521i
$239$	2.05791			0.133115			0.0665575	−	0.997783i	$-0.478798\pi$
$239$	2.05791			0.133115			0.0665575	+	0.997783i	$0.478798\pi$
$240$	16.5221	+	0.324438i	1.06649	+	0.0209424i
$241$		−	14.8810i		−	0.958571i	−0.877659	−	0.479285i	$-0.840896\pi$
$241$		−	14.8810i		−	0.958571i	0.877659	−	0.479285i	$-0.159104\pi$
$242$	−8.11899	−	2.54177i	−0.521909	−	0.163391i
$243$	14.8293	+	4.80555i	0.951297	+	0.308276i
$244$	−9.06410	−	6.29196i	−0.580269	−	0.402801i
$245$	23.9467			1.52990
$246$	−0.0887229	−	0.0717811i	−0.00565676	−	0.00457660i
$247$		−	45.0584i		−	2.86700i
$248$	−7.58479	+	13.8011i	−0.481634	+	0.876372i
$249$	11.0860	+	4.38724i	0.702544	+	0.278030i
$250$	13.8769	+	4.34437i	0.877653	+	0.274762i
$251$		−	5.55231i		−	0.350458i	−0.984528	−	0.175229i	$-0.943933\pi$
$251$		−	5.55231i		−	0.350458i	0.984528	−	0.175229i	$-0.0560666\pi$
$252$	5.17097	+	24.2216i	0.325741	+	1.52582i
$253$		−	13.4425i		−	0.845120i
$254$	5.68801	−	18.1688i	0.356897	−	1.14001i
$255$	−5.38579	+	13.6092i	−0.337271	+	0.852238i
$256$	−12.0878	+	10.4827i	−0.755485	+	0.655166i
$257$		−	25.8205i		−	1.61064i	−0.592843	−	0.805318i	$-0.701995\pi$
$257$		−	25.8205i		−	1.61064i	0.592843	−	0.805318i	$-0.298005\pi$
$258$	0.456055	−	0.563693i	0.0283928	−	0.0350940i
$259$	−39.1211			−2.43087
$260$	−20.3733	−	14.1424i	−1.26350	−	0.877072i
$261$	−14.7983	+	15.7684i	−0.915990	+	0.976039i
$262$	−11.1131	−	3.47912i	−0.686570	−	0.214941i
$263$	−9.36114			−0.577233			−0.288616	−	0.957445i	$-0.593195\pi$
$263$	−9.36114			−0.577233			−0.288616	+	0.957445i	$0.593195\pi$
$264$	−3.06210	−	10.4998i	−0.188459	−	0.646217i
$265$		−	25.3205i		−	1.55543i
$266$	−15.1163	+	48.2849i	−0.926837	+	2.96053i
$267$	1.16824	−	2.95198i	0.0714950	−	0.180658i
$268$	2.84789	−	4.10263i	0.173963	−	0.250608i
$269$			27.4685i			1.67478i	0.546605	+	0.837391i	$0.315920\pi$
$269$			27.4685i			1.67478i	−0.546605	+	0.837391i	$0.684080\pi$
$270$	17.3637	−	2.39190i	1.05672	−	0.145567i
$271$			20.1421i			1.22355i	0.791033	+	0.611773i	$0.209543\pi$
$271$			20.1421i			1.22355i	−0.791033	+	0.611773i	$0.790457\pi$
$272$	−4.95491	−	13.2764i	−0.300436	−	0.805002i
$273$	13.6780	−	34.5624i	0.827829	−	2.09181i
$274$	16.3164	+	5.10809i	0.985711	+	0.308591i
$275$			1.53876i			0.0927905i
$276$	−17.3645	+	11.5553i	−1.04522	+	0.695547i
$277$	−8.22392			−0.494127			−0.247064	−	0.968999i	$-0.579466\pi$
$277$	−8.22392			−0.494127			−0.247064	+	0.968999i	$0.579466\pi$
$278$	29.1780	+	9.13459i	1.74998	+	0.547856i
$279$	−5.66460	+	15.7134i	−0.339131	+	0.940739i
$280$	17.0876	+	21.9899i	1.02118	+	1.31415i
$281$		−	11.2034i		−	0.668339i	−0.942513	−	0.334170i	$-0.891544\pi$
$281$		−	11.2034i		−	0.668339i	0.942513	−	0.334170i	$-0.108456\pi$
$282$	0.801773	+	0.648674i	0.0477449	+	0.0386279i
$283$			4.28208i			0.254543i	0.991868	+	0.127272i	$0.0406220\pi$
$283$			4.28208i			0.254543i	−0.991868	+	0.127272i	$0.959378\pi$
$284$	−3.65407	+	5.26399i	−0.216829	+	0.312360i
$285$	33.2937	+	13.1759i	1.97215	+	0.780473i
$286$	−4.90402	+	15.6646i	−0.289981	+	0.926267i
$287$		−	0.192323i		−	0.0113525i
$288$	−10.9310	+	12.9812i	−0.644117	+	0.764927i
$289$	−4.44907			−0.261710
$290$	−7.26445	+	23.2044i	−0.426583	+	1.36261i
$291$	1.16681	−	2.94837i	0.0683996	−	0.172836i
$292$	−0.250073	+	0.360252i	−0.0146344	+	0.0210821i
$293$	6.94855			0.405939			0.202969	−	0.979185i	$-0.434941\pi$
$293$	6.94855			0.405939			0.202969	+	0.979185i	$0.434941\pi$
$294$	−15.4678	+	19.1185i	−0.902098	+	1.11501i
$295$	−12.8669			−0.749139
$296$	−16.4477	−	21.1664i	−0.956002	−	1.23027i
$297$	−4.94421	−	10.4943i	−0.286892	−	0.608938i
$298$	9.90262	+	3.10016i	0.573644	+	0.179587i
$299$	31.3030			1.81030
$300$	1.98771	−	1.32273i	0.114761	−	0.0763680i
$301$	1.22191			0.0704296
$302$	−7.58706	+	24.2348i	−0.436586	+	1.39456i
$303$	4.70223	−	11.8819i	0.270136	−	0.682596i
$304$	−32.4797	+	12.1218i	−1.86284	+	0.695232i
$305$	−13.1591			−0.753487
$306$	−7.38640	−	13.0904i	−0.422252	−	0.748327i
$307$		−	9.33068i		−	0.532530i	−0.963900	−	0.266265i	$-0.914210\pi$
$307$		−	9.33068i		−	0.532530i	0.963900	−	0.266265i	$-0.0857896\pi$
$308$	10.5104	−	15.1411i	0.598883	−	0.862742i
$309$	−4.03593	+	10.1982i	−0.229596	+	0.580158i
$310$	1.95493	+	18.6792i	0.111033	+	1.06091i
$311$		−	20.4781i		−	1.16121i	−0.814186	−	0.580604i	$-0.802816\pi$
$311$		−	20.4781i		−	1.16121i	0.814186	−	0.580604i	$-0.197184\pi$
$312$	24.4505	−	7.13062i	1.38424	−	0.403692i
$313$			17.9316i			1.01355i	0.862078	+	0.506776i	$0.169163\pi$
$313$			17.9316i			1.01355i	−0.862078	+	0.506776i	$0.830837\pi$
$314$	4.20835	−	13.4425i	0.237491	−	0.758602i
$315$	21.5385	+	20.2133i	1.21355	+	1.13889i
$316$	4.80409	−	6.92069i	0.270251	−	0.389319i
$317$	−0.936684			−0.0526094			−0.0263047	−	0.999654i	$-0.508374\pi$
$317$	−0.936684			−0.0526094			−0.0263047	+	0.999654i	$0.508374\pi$
$318$	20.2153	+	16.3552i	1.13362	+	0.917152i
$319$	16.0927			0.901021
$320$	−4.71343	+	18.4904i	−0.263489	+	1.03364i
$321$	8.41559	−	21.2650i	0.469712	−	1.18690i
$322$	−33.5445	−	10.5016i	−1.86936	−	0.585230i
$323$		−	30.7048i		−	1.70846i
$324$	−9.30600	+	15.4077i	−0.517000	+	0.855985i
$325$	−3.58326			−0.198763
$326$	3.61251	−	11.5392i	0.200078	−	0.639097i
$327$	21.1514	+	8.37063i	1.16968	+	0.462897i
$328$	0.104056	−	0.0808583i	0.00574552	−	0.00446466i
$329$			1.73799i			0.0958185i
$330$	−10.1405	−	8.20419i	−0.558218	−	0.451626i
$331$	20.1340			1.10667			0.553333	−	0.832960i	$-0.313356\pi$
$331$	20.1340			1.10667			0.553333	+	0.832960i	$0.313356\pi$
$332$	−7.85045	+	11.3092i	−0.430850	+	0.620675i
$333$	−20.7318	−	19.4563i	−1.13610	−	1.06620i
$334$	20.8705	+	6.53381i	1.14198	+	0.357514i
$335$		−	5.95611i		−	0.325417i
$336$	−28.5935	−	0.561480i	−1.55990	−	0.0306313i
$337$			17.0523i			0.928898i	0.885600	+	0.464449i	$0.153748\pi$
$337$			17.0523i			0.928898i	−0.885600	+	0.464449i	$0.846252\pi$
$338$	−18.9326	−	5.92711i	−1.02980	−	0.322392i
$339$	−15.3255	−	6.06503i	−0.832367	−	0.329407i
$340$	−13.8833	−	9.63724i	−0.752925	−	0.522653i
$341$	11.4115	−	4.92833i	0.617969	−	0.266884i
$342$	−32.0245	+	18.0702i	−1.73169	+	0.977126i
$343$	−12.5474			−0.677495
$344$	0.513727	+	0.661110i	0.0276983	+	0.0356447i
$345$	−9.15357	+	23.1298i	−0.492812	+	1.24527i
$346$	29.2152	+	9.14622i	1.57062	+	0.491704i
$347$			11.1775i			0.600041i	0.953933	+	0.300020i	$0.0969935\pi$
$347$			11.1775i			0.600041i	−0.953933	+	0.300020i	$0.903007\pi$
$348$	−13.8335	−	20.7880i	−0.741554	−	1.11436i
$349$		−	12.0945i		−	0.647401i	−0.946160	−	0.323701i	$-0.895073\pi$
$349$		−	12.0945i		−	0.647401i	0.946160	−	0.323701i	$-0.104927\pi$
$350$	3.83984	+	1.20212i	0.205248	+	0.0642558i
$351$	24.4376	−	11.5134i	1.30438	−	0.614542i
$352$	12.6109	−	0.679151i	0.672163	−	0.0361989i
$353$	21.7912			1.15983			0.579915	−	0.814677i	$-0.303086\pi$
$353$	21.7912			1.15983			0.579915	+	0.814677i	$0.303086\pi$
$354$	8.31104	−	10.2726i	0.441727	−	0.545983i
$355$			7.64216i			0.405604i
$356$	3.01143	+	2.09042i	0.159606	+	0.110792i
$357$	9.32079	−	23.5524i	0.493309	−	1.24652i
$358$	0.250890	−	0.801402i	0.0132600	−	0.0423554i
$359$			19.6962i			1.03952i	0.854311	+	0.519762i	$0.173979\pi$
$359$			19.6962i			1.03952i	−0.854311	+	0.519762i	$0.826021\pi$
$360$	−1.88096	+	20.1516i	−0.0991351	+	1.06208i
$361$	−56.1168			−2.95352
$362$	−11.6080	−	3.63406i	−0.610105	−	0.191002i
$363$	3.83420	−	9.68849i	0.201243	−	0.508514i
$364$	35.2585	+	24.4751i	1.84805	+	1.28285i
$365$			0.523006i			0.0273754i
$366$	8.49977	−	10.5059i	0.444290	−	0.549152i
$367$			15.7038i			0.819734i	0.912145	+	0.409867i	$0.134425\pi$
$367$			15.7038i			0.819734i	−0.912145	+	0.409867i	$0.865575\pi$
$368$	−8.42126	−	22.5643i	−0.438988	−	1.17625i
$369$	0.0956492	−	0.101920i	0.00497930	−	0.00530573i
$370$	−30.5084	−	9.55110i	−1.58606	−	0.496538i
$371$			43.8204i			2.27504i
$372$	−16.1757	−	10.5046i	−0.838672	−	0.544636i
$373$			3.30304i			0.171025i	0.996337	+	0.0855125i	$0.0272527\pi$
$373$			3.30304i			0.171025i	−0.996337	+	0.0855125i	$0.972747\pi$
$374$	−3.34182	+	10.6746i	−0.172801	+	0.551968i
$375$	−6.55338	+	16.5595i	−0.338415	+	0.855128i
$376$	−0.940335	+	0.730703i	−0.0484941	+	0.0376831i
$377$			37.4747i			1.93004i
$378$	−30.0500	+	4.13949i	−1.54561	+	0.212912i
$379$		−	18.0007i		−	0.924635i	−0.886715	−	0.462317i	$-0.847018\pi$
$379$		−	18.0007i		−	0.924635i	0.886715	−	0.462317i	$-0.152982\pi$
$380$	−23.5767	+	33.9642i	−1.20946	+	1.74233i
$381$	21.6811	+	8.58024i	1.11076	+	0.439579i
$382$	−0.417334	+	1.33306i	−0.0213527	+	0.0682055i
$383$	12.0584			0.616156			0.308078	−	0.951361i	$-0.400314\pi$
$383$	12.0584			0.616156			0.308078	+	0.951361i	$0.400314\pi$
$384$	−11.7178	−	15.7065i	−0.597970	−	0.801519i
$385$		−	21.9815i		−	1.12028i
$386$	−18.5128	−	5.79570i	−0.942278	−	0.294994i
$387$	0.647538	+	0.607699i	0.0329162	+	0.0308911i
$388$	3.00775	+	2.08787i	0.152695	+	0.105995i
$389$			7.63264i			0.386990i	0.981101	+	0.193495i	$0.0619824\pi$
$389$			7.63264i			0.386990i	−0.981101	+	0.193495i	$0.938018\pi$
$390$	19.1048	−	23.6140i	0.967412	−	1.19574i
$391$	21.3313			1.07877
$392$	−17.4238	−	22.4225i	−0.880033	−	1.13251i
$393$	5.24817	−	13.2614i	0.264735	−	0.668950i
$394$	0.336596	−	1.07517i	0.0169575	−	0.0541661i
$395$		−	10.0473i		−	0.505536i
$396$	13.1001	−	2.79667i	0.658302	−	0.140538i
$397$			12.4036i			0.622519i	0.950325	+	0.311260i	$0.100751\pi$
$397$			12.4036i			0.622519i	−0.950325	+	0.311260i	$0.899249\pi$
$398$	−3.90047	+	12.4590i	−0.195513	+	0.624513i
$399$	−57.6189	−	22.8025i	−2.88455	−	1.14156i
$400$	0.963980	+	2.58294i	0.0481990	+	0.129147i
$401$	−3.68839			−0.184189			−0.0920947	−	0.995750i	$-0.529356\pi$
$401$	−3.68839			−0.184189			−0.0920947	+	0.995750i	$0.529356\pi$
$402$	4.75521	+	3.84720i	0.237169	+	0.191881i
$403$	11.4765	+	26.5737i	0.571683	+	1.32373i
$404$	12.1212	+	8.41408i	0.603052	+	0.418616i
$405$	1.36127	+	21.4237i	0.0676422	+	1.06455i
$406$	12.5720	−	40.1581i	0.623940	−	1.99301i
$407$			21.1583i			1.04878i
$408$	16.6617	−	4.85912i	0.824876	−	0.240562i
$409$			16.4281i			0.812317i	0.913803	+	0.406158i	$0.133132\pi$
$409$			16.4281i			0.812317i	−0.913803	+	0.406158i	$0.866868\pi$
$410$	0.0469541	−	0.149982i	0.00231890	−	0.00740710i
$411$	−7.70544	+	19.4706i	−0.380081	+	0.960413i
$412$	−10.4036	−	7.22182i	−0.512551	−	0.355794i
$413$	22.2678			1.09572
$414$	−12.5538	−	22.2481i	−0.616984	−	1.09344i
$415$			16.4185i			0.805954i
$416$	1.58152	+	29.3666i	0.0775403	+	1.43982i
$417$	−13.7793	+	34.8185i	−0.674777	+	1.70507i
$418$	26.1144	+	8.17549i	1.27730	+	0.399876i
$419$	−19.4681			−0.951077			−0.475538	−	0.879695i	$-0.657747\pi$
$419$	−19.4681			−0.951077			−0.475538	+	0.879695i	$0.657747\pi$
$420$	−28.3949	+	18.8955i	−1.38553	+	0.922008i
$421$			25.4688i			1.24127i	0.784098	+	0.620636i	$0.213126\pi$
$421$			25.4688i			1.24127i	−0.784098	+	0.620636i	$0.786874\pi$
$422$	−7.99892	+	25.5504i	−0.389381	+	1.24377i
$423$	−0.864366	+	0.921031i	−0.0420269	+	0.0447821i
$424$	−23.7089	+	18.4234i	−1.15141	+	0.894719i
$425$	−2.44179			−0.118444
$426$	−6.10131	−	4.93626i	−0.295610	−	0.239163i
$427$	22.7734			1.10208
$428$	21.6933	+	15.0587i	1.04859	+	0.727890i
$429$	−18.6927	−	7.39761i	−0.902494	−	0.357160i
$430$	0.952900	+	0.298319i	0.0459529	+	0.0143862i
$431$		−	33.3359i		−	1.60574i	−0.596157	−	0.802868i	$-0.703307\pi$
$431$		−	33.3359i		−	1.60574i	0.596157	−	0.802868i	$-0.296693\pi$
$432$	−14.8736	−	14.5181i	−0.715606	−	0.698504i
$433$			29.9163i			1.43769i	0.695172	+	0.718843i	$0.255328\pi$
$433$			29.9163i			1.43769i	−0.695172	+	0.718843i	$0.744672\pi$
$434$	−3.38326	−	32.3266i	−0.162401	−	1.55173i
$435$	−27.6900	−	10.9583i	−1.32764	−	0.525409i
$436$	−14.9783	+	21.5774i	−0.717329	+	1.03337i
$437$		−	52.1852i		−	2.49636i
$438$	−0.417556	−	0.337823i	−0.0199516	−	0.0161418i
$439$	−6.14948			−0.293499			−0.146749	−	0.989174i	$-0.546881\pi$
$439$	−6.14948			−0.293499			−0.146749	+	0.989174i	$0.546881\pi$
$440$	11.8930	−	9.24167i	0.566978	−	0.440579i
$441$	−21.9622	−	20.6110i	−1.04582	−	0.981475i
$442$	−24.8575	−	7.78199i	−1.18235	−	0.370152i
$443$	−12.2848			−0.583667			−0.291834	−	0.956469i	$-0.594265\pi$
$443$	−12.2848			−0.583667			−0.291834	+	0.956469i	$0.594265\pi$
$444$	27.3315	−	18.1879i	1.29710	−	0.863160i
$445$	4.37194			0.207250
$446$	−1.71110	+	5.46566i	−0.0810231	+	0.258807i
$447$	−4.67652	+	11.8169i	−0.221192	+	0.558921i
$448$	8.15718	−	32.0000i	0.385390	−	1.51186i
$449$	−34.1805			−1.61308			−0.806538	−	0.591182i	$-0.798662\pi$
$449$	−34.1805			−1.61308			−0.806538	+	0.591182i	$0.798662\pi$
$450$	1.43703	+	2.54674i	0.0677421	+	0.120054i
$451$	−0.104016			−0.00489793
$452$	10.8527	−	15.6342i	0.510466	−	0.735369i
$453$	−28.9197	−	11.4449i	−1.35877	−	0.537729i
$454$	25.9499	+	8.12400i	1.21789	+	0.381278i
$455$	51.1876			2.39971
$456$	−11.8874	−	40.7614i	−0.556681	−	1.90883i
$457$		−	29.6801i		−	1.38838i	−0.719792	−	0.694189i	$-0.755763\pi$
$457$		−	29.6801i		−	1.38838i	0.719792	−	0.694189i	$-0.244237\pi$
$458$	4.05316	+	1.26890i	0.189392	+	0.0592917i
$459$	16.6529	−	7.84577i	0.777291	−	0.366209i
$460$	−23.5957	−	16.3792i	−1.10015	−	0.763686i
$461$			5.96757i			0.277937i	0.990297	+	0.138969i	$0.0443787\pi$
$461$			5.96757i			0.277937i	−0.990297	+	0.138969i	$0.955621\pi$
$462$	17.5495	+	14.1984i	0.816476	+	0.660569i
$463$		−	33.7220i		−	1.56719i	−0.621269	−	0.783597i	$-0.713383\pi$
$463$		−	33.7220i		−	1.56719i	0.621269	−	0.783597i	$-0.286617\pi$
$464$	27.0131	−	10.0816i	1.25405	−	0.468025i
$465$	−22.9912	+	0.709327i	−1.06619	+	0.0328943i
$466$	1.81980	−	5.81285i	0.0843004	−	0.269275i
$467$	16.4681			0.762053			0.381026	−	0.924564i	$-0.375571\pi$
$467$	16.4681			0.762053			0.381026	+	0.924564i	$0.375571\pi$
$468$	6.51252	+	30.5057i	0.301042	+	1.41013i
$469$			10.3078i			0.475970i
$470$	−0.424316	+	1.35537i	−0.0195723	+	0.0625183i
$471$	16.0410	+	6.34821i	0.739132	+	0.292510i
$472$	9.36203	+	12.0479i	0.430922	+	0.554550i
$473$		−	0.660858i		−	0.0303863i
$474$	8.02154	+	6.48982i	0.368442	+	0.298087i
$475$			5.97364i			0.274089i
$476$	24.0267	+	16.6785i	1.10126	+	0.764456i
$477$	−21.7935	+	23.2222i	−0.997854	+	1.06327i
$478$	−2.77740	−	0.869504i	−0.127035	−	0.0397702i
$479$			3.10253i			0.141758i	0.997485	+	0.0708791i	$0.0225804\pi$
$479$			3.10253i			0.141758i	−0.997485	+	0.0708791i	$0.977420\pi$
$480$	−22.1614	−	7.41874i	−1.01153	−	0.338617i
$481$	−49.2706			−2.24655
$482$	−6.28750	+	20.0837i	−0.286388	+	0.914790i
$483$	15.8414	−	40.0291i	0.720809	−	1.82139i
$484$	9.88363	+	6.86085i	0.449256	+	0.311857i
$485$	4.36659			0.198277
$486$	−17.9834	−	12.7513i	−0.815746	−	0.578411i
$487$			7.20412i			0.326450i	0.986589	+	0.163225i	$0.0521897\pi$
$487$			7.20412i			0.326450i	−0.986589	+	0.163225i	$0.947810\pi$
$488$	9.57463	+	12.3215i	0.433423	+	0.557768i
$489$	13.7699	+	5.44939i	0.622695	+	0.246430i
$490$	−32.3190	−	10.1179i	−1.46002	−	0.457081i
$491$			32.8033i			1.48039i	0.672391	+	0.740196i	$0.265267\pi$
$491$			32.8033i			1.48039i	−0.672391	+	0.740196i	$0.734733\pi$
$492$	0.0894135	+	0.134364i	0.00403107	+	0.00605761i
$493$			25.5369i			1.15012i
$494$	−19.0380	+	60.8118i	−0.856561	+	2.73605i
$495$	10.9322	−	11.6489i	0.491365	−	0.523578i
$496$	16.0678	−	15.4216i	0.721466	−	0.692450i
$497$		−	13.2257i		−	0.593255i
$498$	−13.1082	−	10.6051i	−0.587391	−	0.475228i
$499$	11.3699			0.508987			0.254493	−	0.967075i	$-0.418091\pi$
$499$	11.3699			0.508987			0.254493	+	0.967075i	$0.418091\pi$
$500$	−16.8930	−	11.7265i	−0.755479	−	0.524425i
$501$	−9.85611	+	24.9050i	−0.440338	+	1.11267i
$502$	−2.34595	+	7.49351i	−0.104705	+	0.334452i
$503$		−	23.6890i		−	1.05624i	−0.849169	−	0.528121i	$-0.822897\pi$
$503$		−	23.6890i		−	1.05624i	0.849169	−	0.528121i	$-0.177103\pi$
$504$	3.25523	−	34.8749i	0.145000	−	1.55345i
$505$	17.5973			0.783070
$506$	−5.67968	+	18.1422i	−0.252493	+	0.806521i
$507$	8.94092	−	22.5925i	0.397080	−	1.00337i
$508$	−15.3533	+	22.1178i	−0.681193	+	0.981317i
$509$		−	1.33161i		−	0.0590227i	−0.999564	−	0.0295114i	$-0.990605\pi$
$509$		−	1.33161i		−	0.0590227i	0.999564	−	0.0295114i	$-0.00939512\pi$
$510$	13.0189	−	16.0916i	0.576486	−	0.712549i
$511$		−	0.905128i		−	0.0400405i
$512$	20.7430	−	9.04032i	0.916720	−	0.399529i
$513$	−19.1940	−	40.7400i	−0.847437	−	1.79871i
$514$	−10.9096	+	34.8479i	−0.481203	+	1.53707i
$515$	−15.1038			−0.665553
$516$	−0.853673	+	0.568081i	−0.0375808	+	0.0250084i
$517$	0.939976			0.0413401
$518$	52.7987	+	16.5294i	2.31984	+	0.726259i
$519$	−13.7969	+	34.8628i	−0.605616	+	1.53031i
$520$	21.5208	+	27.6949i	0.943749	+	1.21450i
$521$			29.8338i			1.30704i	0.756907	+	0.653522i	$0.226709\pi$
$521$			29.8338i			1.30704i	−0.756907	+	0.653522i	$0.773291\pi$
$522$	26.6345	−	15.0288i	1.16576	−	0.657794i
$523$	−21.6365			−0.946099			−0.473050	−	0.881036i	$-0.656847\pi$
$523$	−21.6365			−0.946099			−0.473050	+	0.881036i	$0.656847\pi$
$524$	13.5285	+	9.39098i	0.590996	+	0.410247i
$525$	−1.81336	+	4.58212i	−0.0791417	+	0.199980i
$526$	12.6340	+	3.95525i	0.550868	+	0.172457i
$527$	7.82057	+	18.1085i	0.340669	+	0.788819i
$528$	−0.303671	+	15.4645i	−0.0132156	+	0.673007i
$529$	13.2542			0.576269
$530$	−10.6984	+	34.1731i	−0.464708	+	1.48439i
$531$	11.8006	+	11.0746i	0.512101	+	0.480595i
$532$	40.8025	−	58.7794i	1.76901	−	2.54841i
$533$		−	0.242219i		−	0.0104917i
$534$	−2.82394	+	3.49045i	−0.122204	+	0.151046i
$535$	31.4939			1.36160
$536$	−5.57701	+	4.33371i	−0.240890	+	0.187188i
$537$	0.956322	+	0.378462i	0.0412683	+	0.0163319i
$538$	11.6059	−	37.0720i	0.500367	−	1.59829i
$539$			22.4139i			0.965436i
$540$	−24.4450	−	4.10831i	−1.05195	−	0.176794i
$541$		−	13.4111i		−	0.576588i	−0.957542	−	0.288294i	$-0.906912\pi$
$541$		−	13.4111i		−	0.576588i	0.957542	−	0.288294i	$-0.0930881\pi$
$542$	8.51041	−	27.1842i	0.365553	−	1.16766i
$543$	5.48190	−	13.8520i	0.235251	−	0.594447i
$544$	1.07772	+	20.0117i	0.0462068	+	0.857995i
$545$			31.3257i			1.34185i
$546$	−33.0633	+	40.8669i	−1.41498	+	1.74894i
$547$			3.33464i			0.142579i	0.997456	+	0.0712895i	$0.0227114\pi$
$547$			3.33464i			0.142579i	−0.997456	+	0.0712895i	$0.977289\pi$
$548$	−19.8627	−	13.7880i	−0.848494	−	0.588993i
$549$	12.0686	+	11.3261i	0.515074	+	0.483384i
$550$	0.650153	−	2.07674i	0.0277226	−	0.0885525i
$551$	62.4740			2.66148
$552$	28.3178	−	8.25846i	1.20529	−	0.351503i
$553$			17.3882i			0.739420i
$554$	11.0992	+	3.47475i	0.471559	+	0.147628i
$555$	14.4076	−	36.4061i	0.611570	−	1.54535i
$556$	−35.5197	−	24.6565i	−1.50637	−	1.04567i
$557$		−	26.4602i		−	1.12116i	−0.828101	−	0.560578i	$-0.810579\pi$
$557$		−	26.4602i		−	1.12116i	0.828101	−	0.560578i	$-0.189421\pi$
$558$	14.2843	−	18.8138i	0.604702	−	0.796452i
$559$	1.53892			0.0650894
$560$	−13.7707	−	36.8978i	−0.581917	−	1.55922i
$561$	−12.7381	−	5.04106i	−0.537802	−	0.212834i
$562$	−4.73364	+	15.1204i	−0.199677	+	0.637814i
$563$	9.94195			0.419003			0.209502	−	0.977808i	$-0.432816\pi$
$563$	9.94195			0.419003			0.209502	+	0.977808i	$0.432816\pi$
$564$	−0.808014	−	1.21423i	−0.0340235	−	0.0511282i
$565$		−	22.6974i		−	0.954886i
$566$	1.80926	−	5.77919i	0.0760487	−	0.242917i
$567$	−2.35585	−	37.0764i	−0.0989366	−	1.55706i
$568$	7.15574	−	5.56049i	0.300248	−	0.233313i
$569$	24.7451			1.03737			0.518683	−	0.854966i	$-0.326422\pi$
$569$	24.7451			1.03737			0.518683	+	0.854966i	$0.326422\pi$
$570$	−39.3668	−	31.8497i	−1.64889	−	1.33404i
$571$	−33.2223			−1.39031			−0.695155	−	0.718860i	$-0.744664\pi$
$571$	−33.2223			−1.39031			−0.695155	+	0.718860i	$0.744664\pi$
$572$	13.2372	−	19.0692i	0.553473	−	0.797325i
$573$	−1.59076	−	0.629540i	−0.0664550	−	0.0262994i
$574$	−0.0812600	+	0.259563i	−0.00339173	+	0.0108340i
$575$	−4.15001			−0.173068
$576$	20.2376	−	12.9012i	0.843232	−	0.537550i
$577$	3.91897			0.163149			0.0815745	−	0.996667i	$-0.474005\pi$
$577$	3.91897			0.163149			0.0815745	+	0.996667i	$0.474005\pi$
$578$	6.00455	+	1.87981i	0.249757	+	0.0781898i
$579$	8.74269	−	22.0916i	0.363334	−	0.918094i
$580$	19.6085	−	28.2477i	0.814200	−	1.17292i
$581$		−	28.4143i		−	1.17883i
$582$	−2.82049	+	3.48618i	−0.116913	+	0.144507i
$583$	23.6998			0.981547
$584$	0.489717	−	0.380543i	0.0202646	−	0.0157470i
$585$	27.1264	+	25.4575i	1.12154	+	1.05254i
$586$	−9.37791	−	2.93589i	−0.387398	−	0.121280i
$587$			22.9915i			0.948962i	0.880266	+	0.474481i	$0.157364\pi$
$587$			22.9915i			0.948962i	−0.880266	+	0.474481i	$0.842636\pi$
$588$	28.9535	−	19.2673i	1.19402	−	0.794569i
$589$	44.3009	−	19.1324i	1.82539	−	0.788336i
$590$	17.3654	+	5.43649i	0.714923	+	0.223817i
$591$	1.28301	+	0.507748i	0.0527759	+	0.0208860i
$592$	13.2550	+	35.5160i	0.544776	+	1.45970i
$593$		−	17.1546i		−	0.704455i	−0.935914	−	0.352227i	$-0.885424\pi$
$593$		−	17.1546i		−	0.704455i	0.935914	−	0.352227i	$-0.114576\pi$
$594$	2.23881	+	16.2523i	0.0918593	+	0.666840i
$595$	34.8815			1.43000
$596$	−12.0549	−	8.36808i	−0.493789	−	0.342770i
$597$	−14.8675	−	5.88377i	−0.608485	−	0.240807i
$598$	−42.2473	−	13.2261i	−1.72762	−	0.540856i
$599$			27.1239i			1.10825i	0.832432	+	0.554127i	$0.186948\pi$
$599$			27.1239i			1.10825i	−0.832432	+	0.554127i	$0.813052\pi$
$600$	−3.24154	+	0.945345i	−0.132335	+	0.0385935i
$601$		−	23.5071i		−	0.958874i	−0.877576	−	0.479437i	$-0.840841\pi$
$601$		−	23.5071i		−	0.958874i	0.877576	−	0.479437i	$-0.159159\pi$
$602$	−1.64911	−	0.516279i	−0.0672129	−	0.0210419i
$603$	−5.12644	+	5.46252i	−0.208765	+	0.222451i
$604$	20.4793	−	29.5022i	0.833291	−	1.20043i
$605$	14.3489			0.583364
$606$	−11.3665	+	14.0493i	−0.461734	+	0.570712i
$607$	−10.7755			−0.437363			−0.218682	−	0.975796i	$-0.570176\pi$
$607$	−10.7755			−0.437363			−0.218682	+	0.975796i	$0.570176\pi$
$608$	48.9570	−	2.63655i	1.98547	−	0.106926i
$609$	47.9211	+	18.9647i	1.94186	+	0.768487i
$610$	17.7598	+	5.55995i	0.719072	+	0.225116i
$611$			2.18889i			0.0885532i
$612$	4.43792	+	20.7879i	0.179392	+	0.840303i
$613$	7.55968			0.305333			0.152666	−	0.988278i	$-0.451214\pi$
$613$	7.55968			0.305333			0.152666	+	0.988278i	$0.451214\pi$
$614$	−3.94238	+	12.5929i	−0.159102	+	0.508207i
$615$	0.178976	+	0.0708293i	0.00721700	+	0.00285611i
$616$	−20.5824	+	15.9939i	−0.829287	+	0.644412i
$617$		−	34.7335i		−	1.39832i	−0.714967	−	0.699159i	$-0.753558\pi$
$617$		−	34.7335i		−	1.39832i	0.714967	−	0.699159i	$-0.246442\pi$
$618$	9.75592	−	12.0585i	0.392441	−	0.485065i
$619$	2.44700			0.0983534			0.0491767	−	0.998790i	$-0.484340\pi$
$619$	2.44700			0.0983534			0.0491767	+	0.998790i	$0.484340\pi$
$620$	5.25387	−	26.0358i	0.211000	−	1.04562i
$621$	28.3029	−	13.3345i	1.13576	−	0.535095i
$622$	−8.65239	+	27.6377i	−0.346929	+	1.10817i
$623$	−7.56619			−0.303133
$624$	−36.0118	−	0.707150i	−1.44162	−	0.0283087i
$625$	−27.9711			−1.11885
$626$	7.57641	−	24.2008i	0.302814	−	0.967260i
$627$	−12.3325	+	31.1626i	−0.492514	+	1.24452i
$628$	−11.3594	+	16.3641i	−0.453288	+	0.652999i
$629$	−33.5752			−1.33873
$630$	−20.5283	−	36.3807i	−0.817866	−	1.44944i
$631$		−	4.07575i		−	0.162253i	−0.996704	−	0.0811265i	$-0.974148\pi$
$631$		−	4.07575i		−	0.162253i	0.996704	−	0.0811265i	$-0.0258518\pi$
$632$	−9.40782	+	7.31050i	−0.374223	+	0.290796i
$633$	−30.4896	−	12.0662i	−1.21185	−	0.479588i
$634$	1.26417	+	0.395766i	0.0502066	+	0.0157179i
$635$			32.1101i			1.27425i
$636$	−20.3726	−	30.6146i	−0.807828	−	1.21395i
$637$	−52.1946			−2.06803
$638$	−21.7191	−	6.79948i	−0.859868	−	0.269194i
$639$	6.57763	−	7.00884i	0.260207	−	0.277265i
$640$	14.1739	−	22.9635i	0.560272	−	0.907713i
$641$	0.00454800			0.000179635			8.98177e−5	−	1.00000i	$-0.499971\pi$
$641$	0.00454800			0.000179635			8.98177e−5		1.00000i	$0.499971\pi$
$642$	−20.3427	+	25.1440i	−0.802863	+	0.992355i
$643$	41.9899			1.65592			0.827959	−	0.560789i	$-0.189502\pi$
$643$	41.9899			1.65592			0.827959	+	0.560789i	$0.189502\pi$
$644$	40.8353	+	28.3463i	1.60914	+	1.11700i
$645$	−0.450008	+	1.13711i	−0.0177190	+	0.0447736i
$646$	−12.9733	+	41.4399i	−0.510430	+	1.63043i
$647$	−21.8598			−0.859396			−0.429698	−	0.902973i	$-0.641380\pi$
$647$	−21.8598			−0.859396			−0.429698	+	0.902973i	$0.641380\pi$
$648$	19.0696	−	16.8627i	0.749126	−	0.662428i
$649$		−	12.0433i		−	0.472741i
$650$	4.83604	+	1.51399i	0.189685	+	0.0593836i
$651$	39.7892	−	1.22758i	1.55946	−	0.0481126i
$652$	−9.75104	+	14.0472i	−0.381880	+	0.550131i
$653$	−28.1154			−1.10024			−0.550120	−	0.835086i	$-0.685418\pi$
$653$	−28.1154			−1.10024			−0.550120	+	0.835086i	$0.685418\pi$
$654$	−25.0097	−	20.2341i	−0.977956	−	0.791214i
$655$	19.6404			0.767415
$656$	−0.174600	+	0.0651627i	−0.00681699	+	0.00254417i
$657$	0.450153	−	0.479664i	0.0175621	−	0.0187135i
$658$	0.734333	−	2.34563i	0.0286273	−	0.0914422i
$659$	−37.3498			−1.45494			−0.727471	−	0.686138i	$-0.759304\pi$
$659$	−37.3498			−1.45494			−0.727471	+	0.686138i	$0.759304\pi$
$660$	10.2195	+	15.3571i	0.397793	+	0.597775i
$661$			6.82285i			0.265378i	0.991158	+	0.132689i	$0.0423612\pi$
$661$			6.82285i			0.265378i	−0.991158	+	0.132689i	$0.957639\pi$
$662$	−27.1733	−	8.50700i	−1.05612	−	0.330634i
$663$	11.7390	−	29.6628i	0.455904	−	1.15201i
$664$	15.3735	−	11.9462i	0.596607	−	0.463604i
$665$		−	85.3348i		−	3.30914i
$666$	19.7595	+	35.0183i	0.765665	+	1.35693i
$667$			43.4020i			1.68053i
$668$	−25.4066	−	17.6363i	−0.983012	−	0.682370i
$669$	−6.52224	−	2.58116i	−0.252164	−	0.0997935i
$670$	−2.51657	+	8.03850i	−0.0972234	+	0.310554i
$671$		−	12.3168i		−	0.475485i
$672$	38.3532	+	12.8391i	1.47951	+	0.495277i
$673$			18.9784i			0.731563i	0.930701	+	0.365782i	$0.119198\pi$
$673$			18.9784i			0.731563i	−0.930701	+	0.365782i	$0.880802\pi$
$674$	7.20491	−	23.0142i	0.277523	−	0.886472i
$675$	−3.23983	+	1.52640i	−0.124701	+	0.0587511i
$676$	23.0475	+	15.9987i	0.886442	+	0.615335i
$677$		−	38.0957i		−	1.46414i	−0.681232	−	0.732068i	$-0.738556\pi$
$677$		−	38.0957i		−	1.46414i	0.681232	−	0.732068i	$-0.261444\pi$
$678$	18.1210	+	14.6608i	0.695934	+	0.563045i
$679$	−7.55694			−0.290009
$680$	14.6652	+	18.8726i	0.562386	+	0.723729i
$681$	−12.2549	+	30.9664i	−0.469608	+	1.18663i
$682$	−17.4836	+	1.82980i	−0.669480	+	0.0700667i
$683$	−9.03704			−0.345793			−0.172896	−	0.984940i	$-0.555313\pi$
$683$	−9.03704			−0.345793			−0.172896	+	0.984940i	$0.555313\pi$
$684$	50.8560	−	10.8570i	1.94453	−	0.415128i
$685$	−28.8363			−1.10178
$686$	16.9342	+	5.30150i	0.646551	+	0.202412i
$687$	−1.91411	+	4.83668i	−0.0730277	+	0.184531i
$688$	−0.414006	−	1.10931i	−0.0157838	−	0.0422920i
$689$			55.1891i			2.10254i
$690$	22.1266	−	27.3489i	0.842346	−	1.04116i
$691$		−	42.4374i		−	1.61439i	−0.590282	−	0.807197i	$-0.700984\pi$
$691$		−	42.4374i		−	1.61439i	0.590282	−	0.807197i	$-0.299016\pi$
$692$	−35.5650	−	24.6879i	−1.35198	−	0.938492i
$693$	−18.9195	+	20.1598i	−0.718693	+	0.765809i
$694$	4.72271	−	15.0854i	0.179271	−	0.572635i
$695$	−51.5669			−1.95604
$696$	9.88667	+	33.9009i	0.374753	+	1.28501i
$697$		−	0.165059i		−	0.00625205i
$698$	−5.11013	+	16.3229i	−0.193421	+	0.617832i
$699$	6.93655	+	2.74512i	0.262364	+	0.103830i
$700$	−4.67441	−	3.24480i	−0.176676	−	0.122642i
$701$	27.4649			1.03733			0.518667	−	0.854976i	$-0.326428\pi$
$701$	27.4649			1.03733			0.518667	+	0.854976i	$0.326428\pi$
$702$	−37.8462	+	5.21344i	−1.42841	+	0.196768i
$703$			82.1390i			3.09793i
$704$	−17.3069	−	4.41173i	−0.652278	−	0.166273i
$705$	−1.61737	−	0.640072i	−0.0609138	−	0.0241065i
$706$	−29.4099	−	9.20719i	−1.10686	−	0.346517i
$707$	−30.4543			−1.14535
$708$	−15.5571	+	10.3526i	−0.584672	+	0.389073i
$709$	−19.4646			−0.731008			−0.365504	−	0.930810i	$-0.619103\pi$
$709$	−19.4646			−0.731008			−0.365504	+	0.930810i	$0.619103\pi$
$710$	3.22895	−	10.3140i	0.121180	−	0.387078i
$711$	−8.64776	+	9.21469i	−0.324316	+	0.345578i
$712$	−3.18105	−	4.09366i	−0.119215	−	0.153417i
$713$	13.2917	+	30.7768i	0.497777	+	1.15260i
$714$	−22.5308	+	27.8486i	−0.843195	+	1.04221i
$715$		−	27.6843i		−	1.03534i
$716$	−0.677214	+	0.975583i	−0.0253087	+	0.0364593i
$717$	1.31163	−	3.31430i	0.0489836	−	0.123775i
$718$	8.32199	−	26.5824i	0.310574	−	0.992045i
$719$	−43.3124			−1.61528			−0.807641	−	0.589675i	$-0.799256\pi$
$719$	−43.3124			−1.61528			−0.807641	+	0.589675i	$0.799256\pi$
$720$	11.0530	−	26.4023i	0.411921	−	0.983956i
$721$	26.1390			0.973469
$722$	75.7365	+	23.7104i	2.81862	+	0.882409i
$723$	−23.9662	−	9.48456i	−0.891312	−	0.352735i
$724$	14.1310	+	9.80922i	0.525175	+	0.364557i
$725$		−	4.96822i		−	0.184515i
$726$	−9.26828	+	11.4558i	−0.343978	+	0.425164i
$727$	40.0995			1.48721			0.743604	−	0.668621i	$-0.233115\pi$
$727$	40.0995			1.48721			0.743604	+	0.668621i	$0.233115\pi$
$728$	−37.2444	−	47.9295i	−1.38037	−	1.77639i
$729$	17.1910	−	20.8199i	0.636703	−	0.771109i
$730$	0.220980	−	0.705861i	0.00817883	−	0.0261251i
$731$	1.04869			0.0387871
$732$	−15.9104	+	10.5877i	−0.588066	+	0.391331i
$733$		−	5.01090i		−	0.185082i	−0.995709	−	0.0925410i	$-0.970501\pi$
$733$		−	5.01090i		−	0.185082i	0.995709	−	0.0925410i	$-0.0294989\pi$
$734$	6.63516	−	21.1943i	0.244908	−	0.782294i
$735$	15.2626	−	38.5666i	0.562971	−	1.42255i
$736$	1.83166	+	34.0115i	0.0675161	+	1.25368i
$737$	5.57488			0.205353
$738$	−0.172153	+	0.0971395i	−0.00633705	+	0.00357576i
$739$	14.4790			0.532620			0.266310	−	0.963887i	$-0.414195\pi$
$739$	14.4790			0.532620			0.266310	+	0.963887i	$0.414195\pi$
$740$	37.1393	+	25.7807i	1.36527	+	0.947719i
$741$	−72.5675	−	28.7184i	−2.66583	−	1.05500i
$742$	18.5149	−	59.1409i	0.679703	−	2.17113i
$743$	−9.42294			−0.345694			−0.172847	−	0.984949i	$-0.555297\pi$
$743$	−9.42294			−0.345694			−0.172847	+	0.984949i	$0.555297\pi$
$744$	17.3927	+	21.0117i	0.637649	+	0.770327i
$745$	−17.5011			−0.641191
$746$	1.39559	−	4.45785i	0.0510963	−	0.163214i
$747$	14.1315	−	15.0579i	0.517044	−	0.550940i
$748$	9.02039	−	12.9946i	0.329818	−	0.475131i
$749$	−54.5042			−1.99154
$750$	15.8413	−	19.5801i	0.578441	−	0.714965i
$751$	10.8165			0.394701			0.197350	−	0.980333i	$-0.436766\pi$
$751$	10.8165			0.394701			0.197350	+	0.980333i	$0.436766\pi$
$752$	1.57783	−	0.588864i	0.0575376	−	0.0214737i
$753$	−8.94210	−	3.53881i	−0.325868	−	0.128962i
$754$	15.8337	−	50.5766i	0.576630	−	1.84189i
$755$		−	42.8307i		−	1.55877i
$756$	42.3052	+	7.10995i	1.53863	+	0.258586i
$757$	−12.4797			−0.453583			−0.226792	−	0.973943i	$-0.572824\pi$
$757$	−12.4797			−0.453583			−0.226792	+	0.973943i	$0.572824\pi$
$758$	−7.60563	+	24.2942i	−0.276249	+	0.882403i
$759$	−21.6493	−	8.56768i	−0.785821	−	0.310987i
$760$	46.1701	−	35.8773i	1.67477	−	1.30141i
$761$	−13.2447			−0.480119			−0.240059	−	0.970758i	$-0.577167\pi$
$761$	−13.2447			−0.480119			−0.240059	+	0.970758i	$0.577167\pi$
$762$	−25.6359	−	20.7407i	−0.928692	−	0.751357i
$763$		−	54.2131i		−	1.96265i
$764$	1.12649	−	1.62280i	0.0407549	−	0.0587108i
$765$	18.4851	+	17.3478i	0.668331	+	0.627213i
$766$	−16.2743	−	5.09490i	−0.588014	−	0.184086i
$767$	28.0449			1.01264
$768$	9.17827	+	26.1488i	0.331192	+	0.943563i
$769$	18.1028			0.652804			0.326402	−	0.945231i	$-0.394164\pi$
$769$	18.1028			0.652804			0.326402	+	0.945231i	$0.394164\pi$
$770$	−9.28758	+	29.6667i	−0.334701	+	1.06911i
$771$	−41.5844	−	16.4569i	−1.49762	−	0.592681i
$772$	22.5365	+	15.6440i	0.811107	+	0.563040i
$773$			6.75287i			0.242884i	0.992599	+	0.121442i	$0.0387518\pi$
$773$			6.75287i			0.242884i	−0.992599	+	0.121442i	$0.961248\pi$
$774$	−0.617168	−	1.09376i	−0.0221836	−	0.0393144i
$775$	−1.52150	−	3.52302i	−0.0546537	−	0.126551i
$776$	−3.17716	−	4.08866i	−0.114053	−	0.146774i
$777$	−24.9342	+	63.0053i	−0.894510	+	2.26030i
$778$	3.22493	−	10.3012i	0.115619	−	0.369315i
$779$	−0.403803			−0.0144678
$780$	−35.7616	+	23.7978i	−1.28047	+	0.852097i
$781$	−7.15301			−0.255955
$782$	−28.7892	−	9.01286i	−1.02950	−	0.322299i
$783$	15.9635	+	33.8830i	0.570489	+	1.21088i
$784$	14.0416	+	37.6237i	0.501485	+	1.34370i
$785$			23.7571i			0.847928i
$786$	−12.6862	+	15.6804i	−0.452503	+	0.559303i
$787$	−25.5878			−0.912108			−0.456054	−	0.889952i	$-0.650738\pi$
$787$	−25.5878			−0.912108			−0.456054	+	0.889952i	$0.650738\pi$
$788$	−0.908555	+	1.30885i	−0.0323659	+	0.0466259i
$789$	−5.96641	+	15.0763i	−0.212410	+	0.536730i
$790$	−4.24518	+	13.5601i	−0.151037	+	0.482446i
$791$			39.2807i			1.39666i
$792$	−18.8618	−	1.76056i	−0.670223	−	0.0625589i
$793$	28.6818			1.01852
$794$	5.24075	−	16.7402i	0.185987	−	0.594087i
$795$	−40.7792	−	16.1383i	−1.44629	−	0.572366i
$796$	10.5283	−	15.1669i	0.373166	−	0.537577i
$797$			11.7767i			0.417152i	0.978006	+	0.208576i	$0.0668829\pi$
$797$			11.7767i			0.417152i	−0.978006	+	0.208576i	$0.933117\pi$
$798$	68.1292	+	55.1198i	2.41175	+	1.95122i
$799$			1.49161i			0.0527694i
$800$	−0.209670	−	3.89329i	−0.00741297	−	0.137648i
$801$	−4.00963	−	3.76294i	−0.141673	−	0.132957i
$802$	4.97793	+	1.55841i	0.175777	+	0.0550294i
$803$	−0.489530			−0.0172751
$804$	−4.79223	−	7.20143i	−0.169009	−	0.253975i
$805$	59.2839			2.08948
$806$	−4.26100	−	40.7134i	−0.150087	−	1.43407i
$807$	44.2385	+	17.5073i	1.55727	+	0.616286i
$808$	−12.8039	−	16.4772i	−0.450440	−	0.579667i
$809$	−27.3610			−0.961960			−0.480980	−	0.876732i	$-0.659719\pi$
$809$	−27.3610			−0.961960			−0.480980	+	0.876732i	$0.659719\pi$
$810$	7.21470	−	29.4891i	0.253499	−	1.03614i
$811$		−	11.9529i		−	0.419724i	−0.977731	−	0.209862i	$-0.932699\pi$
$811$		−	11.9529i		−	0.419724i	0.977731	−	0.209862i	$-0.0673014\pi$
$812$	−33.9350	+	48.8863i	−1.19089	+	1.71557i
$813$	32.4393	+	12.8378i	1.13769	+	0.450240i
$814$	8.93976	−	28.5557i	0.313338	−	1.00088i
$815$			20.3934i			0.714351i
$816$	−24.5400	−	0.481884i	−0.859073	−	0.0168693i
$817$		−	2.56553i		−	0.0897565i
$818$	6.94117	−	22.1717i	0.242692	−	0.775215i
$819$	−46.9456	−	44.0573i	−1.64041	−	1.53949i
$820$	−0.126741	+	0.182580i	−0.00442597	+	0.00637599i
$821$			31.6969i			1.10623i	0.833105	+	0.553115i	$0.186561\pi$
$821$			31.6969i			1.10623i	−0.833105	+	0.553115i	$0.813439\pi$
$822$	18.6261	−	23.0222i	0.649660	−	0.802992i
$823$			13.5988i			0.474025i	0.971507	+	0.237012i	$0.0761682\pi$
$823$			13.5988i			0.474025i	−0.971507	+	0.237012i	$0.923832\pi$
$824$	10.9896	+	14.1425i	0.382842	+	0.492676i
$825$	2.47820	+	0.980741i	0.0862798	+	0.0341450i
$826$	−30.0530	−	9.40853i	−1.04568	−	0.327365i
$827$		−	18.8408i		−	0.655159i	−0.944824	−	0.327580i	$-0.893767\pi$
$827$		−	18.8408i		−	0.655159i	0.944824	−	0.327580i	$-0.106233\pi$
$828$	7.54260	+	35.3307i	0.262123	+	1.22783i
$829$	35.7426			1.24139			0.620697	−	0.784051i	$-0.286850\pi$
$829$	35.7426			1.24139			0.620697	+	0.784051i	$0.286850\pi$
$830$	6.93713	−	22.1588i	0.240791	−	0.769143i
$831$	−5.24159	+	13.2448i	−0.181829	+	0.459456i
$832$	10.2735	−	40.3020i	0.356168	−	1.39722i
$833$	−35.5677			−1.23235
$834$	33.3083	−	41.1697i	1.15337	−	1.42559i
$835$	−36.8848			−1.27645
$836$	−31.7903	−	22.0676i	−1.09949	−	0.763225i
$837$	21.6964	+	19.1381i	0.749938	+	0.661508i
$838$	26.2745	+	8.22561i	0.907638	+	0.284149i
$839$		−	31.8678i		−	1.10020i	−0.835099	−	0.550100i	$-0.814590\pi$
$839$		−	31.8678i		−	1.10020i	0.835099	−	0.550100i	$-0.185410\pi$
$840$	46.3061	−	13.5045i	1.59771	−	0.465948i
$841$	−22.9590			−0.791690
$842$	10.7610	−	34.3732i	0.370849	−	1.18458i
$843$	−18.0433	−	7.14060i	−0.621445	−	0.245935i
$844$	21.5910	−	31.1037i	0.743193	−	1.07063i
$845$	33.4599			1.15106
$846$	1.55572	−	0.877833i	0.0534867	−	0.0301805i
$847$	−24.8325			−0.853255
$848$	39.7822	−	14.8472i	1.36613	−	0.509854i
$849$	6.89637	+	2.72922i	0.236683	+	0.0936667i
$850$	3.29549	+	1.03170i	0.113034	+	0.0353870i
$851$	−57.0637			−1.95612
$852$	6.14881	+	9.24000i	0.210655	+	0.316557i
$853$			40.9762i			1.40300i	0.712671	+	0.701499i	$0.247485\pi$
$853$			40.9762i			1.40300i	−0.712671	+	0.701499i	$0.752515\pi$
$854$	−30.7355	−	9.62219i	−1.05175	−	0.329265i
$855$	42.4401	−	45.2223i	1.45142	−	1.54657i
$856$	−22.9152	−	29.4894i	−0.783226	−	1.00793i
$857$			21.9627i			0.750230i	0.926978	+	0.375115i	$0.122397\pi$
$857$			21.9627i			0.750230i	−0.926978	+	0.375115i	$0.877603\pi$
$858$	22.1025	+	17.8820i	0.754567	+	0.610481i
$859$	−11.0404			−0.376692			−0.188346	−	0.982103i	$-0.560313\pi$
$859$	−11.0404			−0.376692			−0.188346	+	0.982103i	$0.560313\pi$
$860$	−1.16001	−	0.805236i	−0.0395560	−	0.0274583i
$861$	−0.309740	−	0.122579i	−0.0105559	−	0.00417748i
$862$	−14.0850	+	44.9909i	−0.479738	+	1.53240i
$863$	−6.07085			−0.206654			−0.103327	−	0.994647i	$-0.532949\pi$
$863$	−6.07085			−0.206654			−0.103327	+	0.994647i	$0.532949\pi$
$864$	13.9396	+	25.8783i	0.474233	+	0.880399i
$865$	−51.6325			−1.75556
$866$	12.6402	−	40.3757i	0.429531	−	1.37202i
$867$	−2.83565	+	7.16531i	−0.0963039	+	0.243347i
$868$	−9.09248	+	45.0582i	−0.308619	+	1.52938i
$869$	9.40423			0.319017
$870$	32.7410	+	26.4891i	1.11002	+	0.898063i
$871$			12.9820i			0.439880i
$872$	29.3318	−	22.7928i	0.993302	−	0.771862i
$873$	−4.00472	−	3.75834i	−0.135539	−	0.127201i
$874$	−22.0492	+	70.4303i	−0.745826	+	2.38234i
$875$	42.4435			1.43485
$876$	0.420806	+	0.632358i	0.0142177	+	0.0213654i
$877$			12.5585i			0.424071i	0.977262	+	0.212036i	$0.0680093\pi$
$877$			12.5585i			0.424071i	−0.977262	+	0.212036i	$0.931991\pi$
$878$	8.29947	+	2.59827i	0.280093	+	0.0876872i
$879$	4.42872	−	11.1908i	0.149377	−	0.377456i
$880$	−19.9559	+	7.44774i	−0.672712	+	0.251063i
$881$	−34.8916			−1.17553			−0.587763	−	0.809033i	$-0.699991\pi$
$881$	−34.8916			−1.17553			−0.587763	+	0.809033i	$0.699991\pi$
$882$	20.9321	+	37.0965i	0.704821	+	1.24910i
$883$	45.7890			1.54092			0.770462	−	0.637486i	$-0.220026\pi$
$883$	45.7890			1.54092			0.770462	+	0.637486i	$0.220026\pi$
$884$	30.2602	+	21.0055i	1.01776	+	0.706491i
$885$	−8.20083	+	20.7224i	−0.275668	+	0.696575i
$886$	16.5798	+	5.19054i	0.557009	+	0.174380i
$887$			13.9009i			0.466747i	0.972387	+	0.233374i	$0.0749765\pi$
$887$			13.9009i			0.466747i	−0.972387	+	0.233374i	$0.925023\pi$
$888$	−44.5719	+	12.9987i	−1.49574	+	0.436208i
$889$		−	55.5706i		−	1.86378i
$890$	−5.90046	−	1.84722i	−0.197784	−	0.0619191i
$891$	−20.0524	+	1.27414i	−0.671782	+	0.0426853i
$892$	4.61868	−	6.65360i	0.154645	−	0.222779i
$893$	3.64910			0.122112
$894$	11.3044	−	13.9725i	0.378075	−	0.467309i
$895$			1.41633i			0.0473428i
$896$	−24.5297	+	39.7413i	−0.819479	+	1.32766i
$897$	19.9513	−	50.4142i	0.666154	−	1.68328i
$898$	46.1307	+	14.4419i	1.53940	+	0.481932i
$899$	−36.8447	+	15.9122i	−1.22884	+	0.530702i
$900$	−0.863400	−	4.04430i	−0.0287800	−	0.134810i
$901$			37.6083i			1.25291i
$902$	0.140382	+	0.0439487i	0.00467422	+	0.00146333i
$903$	0.778795	−	1.96791i	0.0259167	−	0.0654879i
$904$	−21.2527	+	16.5148i	−0.706854	+	0.549273i
$905$	20.5151			0.681946
$906$	34.1950	+	27.6654i	1.13605	+	0.919121i
$907$			30.3309i			1.00712i	0.863960	+	0.503560i	$0.167977\pi$
$907$			30.3309i			1.00712i	−0.863960	+	0.503560i	$0.832023\pi$
$908$	−31.5901	−	21.9286i	−1.04835	−	0.727728i
$909$	−16.1390	−	15.1461i	−0.535296	−	0.502363i
$910$	−69.0839	−	21.6277i	−2.29011	−	0.716951i
$911$	−8.61768			−0.285516			−0.142758	−	0.989758i	$-0.545597\pi$
$911$	−8.61768			−0.285516			−0.142758	+	0.989758i	$0.545597\pi$
$912$	−1.17889	+	60.0351i	−0.0390369	+	1.98796i
$913$	−15.3676			−0.508594
$914$	−12.5404	+	40.0570i	−0.414800	+	1.32497i
$915$	−8.38706	+	21.1930i	−0.277268	+	0.700617i
$916$	−4.93410	−	3.42507i	−0.163027	−	0.113167i
$917$	−33.9902			−1.12246
$918$	−25.7901	+	3.55267i	−0.851200	+	0.117256i
$919$	−2.94809			−0.0972484			−0.0486242	−	0.998817i	$-0.515484\pi$
$919$	−2.94809			−0.0972484			−0.0486242	+	0.998817i	$0.515484\pi$
$920$	24.9247	+	32.0754i	0.821743	+	1.05749i
$921$	−15.0272	−	5.94699i	−0.495164	−	0.195960i
$922$	2.52141	−	8.05396i	0.0830381	−	0.265243i
$923$		−	16.6570i		−	0.548271i
$924$	−17.6861	−	26.5774i	−0.581829	−	0.874333i
$925$	6.53207			0.214773
$926$	−14.2482	+	45.5119i	−0.468223	+	1.49561i
$927$	13.8521	+	12.9999i	0.454964	+	0.426972i
$928$	−40.7171	+	2.19279i	−1.33660	+	0.0719819i
$929$	45.2470			1.48451			0.742253	−	0.670120i	$-0.233757\pi$
$929$	45.2470			1.48451			0.742253	+	0.670120i	$0.233757\pi$
$930$	31.3291	+	8.75689i	1.02732	+	0.287150i
$931$			87.0136i			2.85175i
$932$	−4.91207	+	7.07626i	−0.160900	+	0.231790i
$933$	−32.9804	−	13.0519i	−1.07973	−	0.427301i
$934$	−22.2257	−	6.95807i	−0.727247	−	0.227675i
$935$		−	18.8653i		−	0.616963i
$936$	4.09977	−	43.9228i	0.134005	−	1.43566i
$937$	−8.47108			−0.276738			−0.138369	−	0.990381i	$-0.544186\pi$
$937$	−8.47108			−0.276738			−0.138369	+	0.990381i	$0.544186\pi$
$938$	4.35523	−	13.9116i	0.142203	−	0.454231i
$939$	28.8791	+	11.4289i	0.942435	+	0.372966i
$940$	1.14533	−	1.64995i	0.0373566	−	0.0538154i
$941$			27.9616i			0.911522i	0.890102	+	0.455761i	$0.150633\pi$
$941$			27.9616i			0.911522i	−0.890102	+	0.455761i	$0.849367\pi$
$942$	−18.9671	−	15.3453i	−0.617982	−	0.499977i
$943$		−	0.280531i		−	0.00913533i
$944$	−7.54473	−	20.2157i	−0.245560	−	0.657966i
$945$	46.2817	−	21.8049i	1.50554	−	0.709315i
$946$	−0.279224	+	0.891908i	−0.00907837	+	0.0289984i
$947$			32.6693i			1.06161i	0.847494	+	0.530805i	$0.178110\pi$
$947$			32.6693i			1.06161i	−0.847494	+	0.530805i	$0.821890\pi$
$948$	−8.08398	−	12.1480i	−0.262555	−	0.394550i
$949$		−	1.13995i		−	0.0370045i
$950$	2.52397	−	8.06215i	0.0818884	−	0.261571i
$951$	−0.597005	+	1.50855i	−0.0193592	+	0.0489180i
$952$	−25.3800	−	32.6613i	−0.822571	−	1.05856i
$953$	−10.3080			−0.333908			−0.166954	−	0.985965i	$-0.553393\pi$
$953$	−10.3080			−0.333908			−0.166954	+	0.985965i	$0.553393\pi$
$954$	39.2247	−	22.1330i	1.26995	−	0.716583i
$955$		−	2.35595i		−	0.0762367i
$956$	3.38105	+	2.34700i	0.109351	+	0.0759075i
$957$	10.2569	−	25.9177i	0.331557	−	0.837799i
$958$	1.31087	−	4.18724i	0.0423524	−	0.135284i
$959$	49.9049			1.61151
$960$	26.7750	+	19.3761i	0.864160	+	0.625361i
$961$	−21.2539	+	22.5670i	−0.685610	+	0.727969i
$962$	66.4967	+	20.8177i	2.14394	+	0.671191i
$963$	−28.8840	−	27.1069i	−0.930774	−	0.873509i
$964$	16.9715	−	24.4489i	0.546615	−	0.787445i
$965$	32.7181			1.05323
$966$	−38.2929	+	47.3308i	−1.23205	+	1.52284i
$967$			44.5415i			1.43236i	0.697916	+	0.716179i	$0.254111\pi$
$967$			44.5415i			1.43236i	−0.697916	+	0.716179i	$0.745889\pi$
$968$	−10.4403	−	13.4356i	−0.335565	−	0.431835i
$969$	−49.4507	−	19.5700i	−1.58859	−	0.628679i
$970$	−5.89325	−	1.84496i	−0.189221	−	0.0592382i
$971$	29.6280			0.950808			0.475404	−	0.879768i	$-0.342302\pi$
$971$	29.6280			0.950808			0.475404	+	0.879768i	$0.342302\pi$
$972$	18.8832	+	24.8078i	0.605679	+	0.795709i
$973$	89.2430			2.86100
$974$	3.04387	−	9.72284i	0.0975320	−	0.311540i
$975$	−2.28382	+	5.77090i	−0.0731408	+	0.184817i
$976$	−7.71607	−	20.6748i	−0.246985	−	0.661785i
$977$			43.2433i			1.38348i	0.722148	+	0.691738i	$0.243155\pi$
$977$			43.2433i			1.38348i	−0.722148	+	0.691738i	$0.756845\pi$
$978$	−16.2816	−	13.1726i	−0.520629	−	0.421214i
$979$			4.09210i			0.130784i
$980$	39.3434	+	27.3107i	1.25678	+	0.872408i
$981$	26.9621	−	28.7297i	0.860835	−	0.917269i
$982$	13.8600	−	44.2721i	0.442290	−	1.41278i
$983$	−33.6856			−1.07440			−0.537202	−	0.843453i	$-0.680519\pi$
$983$	−33.6856			−1.07440			−0.537202	+	0.843453i	$0.680519\pi$
$984$	−0.0639029	−	0.219120i	−0.00203715	−	0.00698529i
$985$			1.90016i			0.0605442i
$986$	10.7898	−	34.4652i	0.343618	−	1.09759i
$987$	2.79907	+	1.10772i	0.0890953	+	0.0352593i
$988$	51.3882	−	74.0291i	1.63488	−	2.35518i
$989$	1.78233			0.0566747
$990$	−19.6762	+	11.1025i	−0.625350	+	0.352861i
$991$		−	4.52756i		−	0.143823i	−0.997411	−	0.0719114i	$-0.977090\pi$
$991$		−	4.52756i		−	0.143823i	0.997411	−	0.0719114i	$-0.0229099\pi$
$992$	−28.2014	+	14.0244i	−0.895394	+	0.445274i
$993$	12.8326	−	32.4263i	0.407231	−	1.02902i
$994$	−5.58811	+	17.8497i	−0.177244	+	0.566159i
$995$		−	22.0190i		−	0.698050i
$996$	13.2102	+	19.8514i	0.418581	+	0.629014i
$997$			54.0483i			1.71173i	0.517202	+	0.855864i	$0.326974\pi$
$997$			54.0483i			1.71173i	−0.517202	+	0.855864i	$0.673026\pi$
$998$	−15.3451	−	4.80399i	−0.485740	−	0.152068i
$999$	−44.5485	+	20.9884i	−1.40945	+	0.664042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	744.2.o.e.557.6	yes	96
3.2	odd	2	inner	744.2.o.e.557.92	yes	96
8.5	even	2	inner	744.2.o.e.557.89	yes	96
24.5	odd	2	inner	744.2.o.e.557.7	yes	96
31.30	odd	2	inner	744.2.o.e.557.5	✓	96
93.92	even	2	inner	744.2.o.e.557.91	yes	96
248.61	odd	2	inner	744.2.o.e.557.90	yes	96
744.557	even	2	inner	744.2.o.e.557.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
744.2.o.e.557.5	✓	96	31.30	odd	2	inner
744.2.o.e.557.6	yes	96	1.1	even	1	trivial
744.2.o.e.557.7	yes	96	24.5	odd	2	inner
744.2.o.e.557.8	yes	96	744.557	even	2	inner
744.2.o.e.557.89	yes	96	8.5	even	2	inner
744.2.o.e.557.90	yes	96	248.61	odd	2	inner
744.2.o.e.557.91	yes	96	93.92	even	2	inner
744.2.o.e.557.92	yes	96	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 744 = 2^{3} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	744.o (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34962 - 0.422518i) q^{2} +(0.637359 - 1.61052i) q^{3} +(1.64296 + 1.14048i) q^{4} +2.38521 q^{5} +(-1.54067 + 1.90430i) q^{6} -4.12791 q^{7} +(-1.73550 - 2.23339i) q^{8} +(-2.18755 - 2.05296i) q^{9} +O(q^{10})\)	\(q+(-1.34962 - 0.422518i) q^{2} +(0.637359 - 1.61052i) q^{3} +(1.64296 + 1.14048i) q^{4} +2.38521 q^{5} +(-1.54067 + 1.90430i) q^{6} -4.12791 q^{7} +(-1.73550 - 2.23339i) q^{8} +(-2.18755 - 2.05296i) q^{9} +(-3.21913 - 1.00780i) q^{10} +2.23254i q^{11} +(2.88392 - 1.91912i) q^{12} -5.19885 q^{13} +(5.57112 + 1.74412i) q^{14} +(1.52024 - 3.84143i) q^{15} +(1.39861 + 3.74752i) q^{16} -3.54273 q^{17} +(2.08495 + 3.69500i) q^{18} +8.66700i q^{19} +(3.91880 + 2.72029i) q^{20} +(-2.63096 + 6.64808i) q^{21} +(0.943290 - 3.01309i) q^{22} -6.02115 q^{23} +(-4.70306 + 1.37158i) q^{24} +0.689240 q^{25} +(7.01648 + 2.19661i) q^{26} +(-4.70058 + 2.21461i) q^{27} +(-6.78198 - 4.70780i) q^{28} -7.20826i q^{29} +(-3.67482 + 4.54215i) q^{30} +(-2.20750 - 5.11145i) q^{31} +(-0.304205 - 5.64867i) q^{32} +(3.59555 + 1.42293i) q^{33} +(4.78134 + 1.49687i) q^{34} -9.84594 q^{35} +(-1.25269 - 5.86777i) q^{36} +9.47722 q^{37} +(3.66196 - 11.6972i) q^{38} +(-3.31354 + 8.37285i) q^{39} +(-4.13953 - 5.32712i) q^{40} +0.0465909i q^{41} +(6.35974 - 7.86076i) q^{42} -0.296011 q^{43} +(-2.54617 + 3.66797i) q^{44} +(-5.21776 - 4.89675i) q^{45} +(8.12627 + 2.54404i) q^{46} -0.421034i q^{47} +(6.92687 + 0.136020i) q^{48} +10.0396 q^{49} +(-0.930213 - 0.291216i) q^{50} +(-2.25799 + 5.70564i) q^{51} +(-8.54149 - 5.92918i) q^{52} -10.6156i q^{53} +(7.27972 - 1.00281i) q^{54} +5.32509i q^{55} +(7.16397 + 9.21925i) q^{56} +(13.9584 + 5.52399i) q^{57} +(-3.04562 + 9.72842i) q^{58} -5.39444 q^{59} +(6.87876 - 4.57751i) q^{60} -5.51694 q^{61} +(0.819605 + 7.83124i) q^{62} +(9.02999 + 8.47443i) q^{63} +(-1.97610 + 7.75210i) q^{64} -12.4004 q^{65} +(-4.25142 - 3.43961i) q^{66} -2.49710i q^{67} +(-5.82055 - 4.04041i) q^{68} +(-3.83763 + 9.69717i) q^{69} +(13.2883 + 4.16009i) q^{70} +3.20397i q^{71} +(-0.788591 + 8.44856i) q^{72} +0.219270i q^{73} +(-12.7907 - 4.00430i) q^{74} +(0.439294 - 1.11003i) q^{75} +(-9.88453 + 14.2395i) q^{76} -9.21573i q^{77} +(8.00970 - 9.90015i) q^{78} -4.21234i q^{79} +(3.33599 + 8.93862i) q^{80} +(0.570713 + 8.98189i) q^{81} +(0.0196855 - 0.0628801i) q^{82} +6.88347i q^{83} +(-11.9046 + 7.92195i) q^{84} -8.45016 q^{85} +(0.399503 + 0.125070i) q^{86} +(-11.6090 - 4.59425i) q^{87} +(4.98615 - 3.87457i) q^{88} +1.83293 q^{89} +(4.97304 + 8.81335i) q^{90} +21.4604 q^{91} +(-9.89248 - 6.86699i) q^{92} +(-9.63906 + 0.297385i) q^{93} +(-0.177895 + 0.568237i) q^{94} +20.6726i q^{95} +(-9.29118 - 3.11030i) q^{96} +1.83069 q^{97} +(-13.5497 - 4.24193i) q^{98} +(4.58332 - 4.88379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9}+O(q^{10}) \) 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9	\( 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9} - 52 q^{10} - 60 q^{16} - 4 q^{18} + 168 q^{25} - 20 q^{28} + 16 q^{31} + 8 q^{33} + 8 q^{39} - 64 q^{40} - 64 q^{49} + 56 q^{63} + 72 q^{64} + 4 q^{66} - 84 q^{70} - 44 q^{72} - 28 q^{76} + 56 q^{78} - 112 q^{81} - 108 q^{82} - 168 q^{87} + 104 q^{90} + 8 q^{94} + 72 q^{97}+O(q^{100}) \) 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9 - 52 * q^10 - 60 * q^16 - 4 * q^18 + 168 * q^25 - 20 * q^28 + 16 * q^31 + 8 * q^33 + 8 * q^39 - 64 * q^40 - 64 * q^49 + 56 * q^63 + 72 * q^64 + 4 * q^66 - 84 * q^70 - 44 * q^72 - 28 * q^76 + 56 * q^78 - 112 * q^81 - 108 * q^82 - 168 * q^87 + 104 * q^90 + 8 * q^94 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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