LMFDB - Embedded newform 744.2.o.e.557.7

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			557.7
Character	$\chi$	$=$	744.557
Dual form			744.2.o.e.557.5

$q$-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} +(5.13897 + 5.96582i) 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} +(-6.82512 + 6.81305i) 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	$-0.243705\pi$
$13$	5.19885			1.44190			0.720951	+	0.692986i	$0.243705\pi$
$14$	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	$-0.358648\pi$
$17$	3.54273			0.859238			0.429619	+	0.903010i	$0.358648\pi$
$18$	2.08495	−	3.69500i	0.491427	−	0.870919i
$19$		−	8.66700i		−	1.98835i	−0.107799	−	0.994173i	$-0.534380\pi$
$19$		−	8.66700i		−	1.98835i	0.107799	−	0.994173i	$-0.465620\pi$
$20$	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	$-0.283977\pi$
$23$	6.02115			1.25550			0.627748	+	0.778417i	$0.283977\pi$
$24$	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	$-0.784284\pi$
$37$	−9.47722			−1.55804			−0.779022	+	0.626996i	$0.784284\pi$
$38$	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	$-0.998842\pi$
$41$		−	0.0465909i		−	0.00727628i	0.999993	−	0.00363814i	$-0.00115806\pi$
$42$	−6.35974	−	7.86076i	−0.981329	−	1.21294i
$43$	0.296011			0.0451413			0.0225707	−	0.999745i	$-0.492815\pi$
$43$	0.296011			0.0451413			0.0225707	+	0.999745i	$0.492815\pi$
$44$	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	$0.00977590\pi$
$47$			0.421034i			0.0614141i	−0.999528	+	0.0307071i	$0.990224\pi$
$48$	−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	$-0.385098\pi$
$61$	5.51694			0.706372			0.353186	+	0.935553i	$0.385098\pi$
$62$	5.13897	+	5.96582i	0.652650	+	0.757660i
$63$	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	$0.0487435\pi$
$67$			2.49710i			0.305069i	−0.988298	+	0.152535i	$0.951256\pi$
$68$	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	$-0.939112\pi$
$71$		−	3.20397i		−	0.380242i	0.981761	−	0.190121i	$-0.0608880\pi$
$72$	−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	$-0.530971\pi$
$89$	−1.83293			−0.194291			−0.0971453	+	0.995270i	$0.530971\pi$
$90$	4.97304	−	8.81335i	0.524204	−	0.929009i
$91$	−21.4604			−2.24966
$92$	9.89248	−	6.86699i	1.03136	−	0.715933i
$93$	−6.82512	+	6.81305i	−0.707732	+	0.706481i
$94$	−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	$-0.783476\pi$
$109$		−	13.1333i		−	1.25794i	0.777429	−	0.628971i	$-0.216524\pi$
$110$	−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	$0.147717\pi$
$113$			9.51587i			0.895178i	−0.894239	+	0.447589i	$0.852283\pi$
$114$	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
$124$	−9.45633	−	5.88029i	−0.849204	−	0.528066i
$125$	−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	$-0.327256\pi$
$137$	12.0896			1.03289			0.516443	+	0.856321i	$0.327256\pi$
$138$	9.27659	+	11.4660i	0.789675	+	0.976054i
$139$	21.6194			1.83373			0.916867	−	0.399193i	$-0.130710\pi$
$139$	21.6194			1.83373			0.916867	+	0.399193i	$0.130710\pi$
$140$	−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	$-0.869894\pi$
$157$		−	9.96016i		−	0.794908i	0.917622	−	0.397454i	$-0.130106\pi$
$158$	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	$-0.891317\pi$
$163$		−	8.54995i		−	0.669684i	0.942274	−	0.334842i	$-0.108683\pi$
$164$	−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	$-0.295836\pi$
$167$	15.4640			1.19664			0.598319	+	0.801258i	$0.295836\pi$
$168$	−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	$-0.603566\pi$
$181$	−8.60096			−0.639304			−0.319652	+	0.947535i	$0.603566\pi$
$182$	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
$186$	6.33270	−	12.0788i	0.464336	−	0.885659i
$187$			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	$0.0113772\pi$
$191$			0.987731i			0.0714697i	−0.999361	+	0.0357349i	$0.988623\pi$
$192$	−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	$0.225923\pi$
$211$			18.9315i			1.30330i	−0.758520	+	0.651650i	$0.774077\pi$
$212$	−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	$-0.468363\pi$
$229$	3.00318			0.198456			0.0992279	+	0.995065i	$0.468363\pi$
$230$	−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	$-0.954942\pi$
$233$		−	4.30702i		−	0.282163i	0.989998	−	0.141081i	$-0.0450579\pi$
$234$	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	$-0.521202\pi$
$239$	−2.05791			−0.133115			−0.0665575	+	0.997783i	$0.521202\pi$
$240$	−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
$248$	15.2470	+	3.94070i	0.968185	+	0.250234i
$249$	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	$0.298005\pi$
$257$			25.8205i			1.61064i	−0.592843	+	0.805318i	$0.701995\pi$
$258$	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	$-0.406805\pi$
$263$	9.36114			0.577233			0.288616	+	0.957445i	$0.406805\pi$
$264$	−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	$-0.420534\pi$
$277$	8.22392			0.494127			0.247064	+	0.968999i	$0.420534\pi$
$278$	−29.1780	+	9.13459i	−1.74998	+	0.547856i
$279$	15.3226	+	6.64963i	0.917341	+	0.398103i
$280$	17.0876	−	21.9899i	1.02118	−	1.31415i
$281$			11.2034i			0.668339i	0.942513	+	0.334170i	$0.108456\pi$
$281$			11.2034i			0.668339i	−0.942513	+	0.334170i	$0.891544\pi$
$282$	−0.801773	+	0.648674i	−0.0477449	+	0.0386279i
$283$		−	4.28208i		−	0.254543i	−0.991868	−	0.127272i	$-0.959378\pi$
$283$		−	4.28208i		−	0.254543i	0.991868	−	0.127272i	$-0.0406220\pi$
$284$	−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	$0.0857896\pi$
$307$			9.33068i			0.532530i	−0.963900	+	0.266265i	$0.914210\pi$
$308$	−10.5104	−	15.1411i	−0.598883	−	0.862742i
$309$	4.03593	+	10.1982i	0.229596	+	0.580158i
$310$	12.2575	+	14.2297i	0.696181	+	0.808195i
$311$			20.4781i			1.16121i	0.814186	+	0.580604i	$0.197184\pi$
$311$			20.4781i			1.16121i	−0.814186	+	0.580604i	$0.802816\pi$
$312$	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	$-0.686644\pi$
$331$	−20.1340			−1.10667			−0.553333	+	0.832960i	$0.686644\pi$
$332$	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	$0.104927\pi$
$349$			12.0945i			0.647401i	−0.946160	+	0.323701i	$0.895073\pi$
$350$	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	$-0.696914\pi$
$353$	−21.7912			−1.15983			−0.579915	+	0.814677i	$0.696914\pi$
$354$	−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	$-0.826021\pi$
$359$		−	19.6962i		−	1.03952i	0.854311	−	0.519762i	$-0.173979\pi$
$360$	−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
$372$	−3.44324	+	18.9775i	−0.178524	+	0.983936i
$373$		−	3.30304i		−	0.171025i	−0.996337	−	0.0855125i	$-0.972747\pi$
$373$		−	3.30304i		−	0.171025i	0.996337	−	0.0855125i	$-0.0272527\pi$
$374$	−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	$0.152982\pi$
$379$			18.0007i			0.924635i	−0.886715	+	0.462317i	$0.847018\pi$
$380$	−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	$-0.599686\pi$
$383$	−12.0584			−0.616156			−0.308078	+	0.951361i	$0.599686\pi$
$384$	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	$-0.899249\pi$
$397$		−	12.4036i		−	0.622519i	0.950325	−	0.311260i	$-0.100751\pi$
$398$	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	$-0.470644\pi$
$401$	3.68839			0.184189			0.0920947	+	0.995750i	$0.470644\pi$
$402$	−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	$-0.786874\pi$
$421$		−	25.4688i		−	1.24127i	0.784098	−	0.620636i	$-0.213126\pi$
$422$	−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	$0.296693\pi$
$431$			33.3359i			1.60574i	−0.596157	+	0.802868i	$0.703307\pi$
$432$	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	$0.744672\pi$
$434$	−21.2132	−	24.6264i	−1.01827	−	1.18210i
$435$	−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	$-0.201338\pi$
$449$	34.1805			1.61308			0.806538	+	0.591182i	$0.201338\pi$
$450$	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
$465$	−16.2794	+	16.2506i	−0.754938	+	0.753602i
$466$	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	$-0.977420\pi$
$479$		−	3.10253i		−	0.141758i	0.997485	−	0.0708791i	$-0.0225804\pi$
$480$	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
$496$	−22.2427	+	1.12369i	−0.998726	+	0.0504550i
$497$			13.2257i			0.593255i
$498$	−13.1082	+	10.6051i	−0.587391	+	0.475228i
$499$	−11.3699			−0.508987			−0.254493	−	0.967075i	$-0.581909\pi$
$499$	−11.3699			−0.508987			−0.254493	+	0.967075i	$0.581909\pi$
$500$	−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	$0.177103\pi$
$503$			23.6890i			1.05624i	−0.849169	+	0.528121i	$0.822897\pi$
$504$	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	$-0.773291\pi$
$521$		−	29.8338i		−	1.30704i	0.756907	−	0.653522i	$-0.226709\pi$
$522$	−26.6345	−	15.0288i	−1.16576	−	0.657794i
$523$	21.6365			0.946099			0.473050	−	0.881036i	$-0.343153\pi$
$523$	21.6365			0.946099			0.473050	+	0.881036i	$0.343153\pi$
$524$	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	$0.0930881\pi$
$541$			13.4111i			0.576588i	−0.957542	+	0.288294i	$0.906912\pi$
$542$	−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	$-0.977289\pi$
$547$		−	3.33464i		−	0.142579i	0.997456	−	0.0712895i	$-0.0227114\pi$
$548$	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	$-0.189421\pi$
$558$	−23.4893	−	2.50041i	−0.994382	−	0.105851i
$559$	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	$-0.673578\pi$
$569$	−24.7451			−1.03737			−0.518683	+	0.854966i	$0.673578\pi$
$570$	39.3668	−	31.8497i	1.64889	−	1.33404i
$571$	33.2223			1.39031			0.695155	−	0.718860i	$-0.255336\pi$
$571$	33.2223			1.39031			0.695155	+	0.718860i	$0.255336\pi$
$572$	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	$0.114576\pi$
$593$			17.1546i			0.704455i	−0.935914	+	0.352227i	$0.885424\pi$
$594$	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	$-0.813052\pi$
$599$		−	27.1239i		−	1.10825i	0.832432	−	0.554127i	$-0.186948\pi$
$600$	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	$-0.548786\pi$
$613$	−7.55968			−0.305333			−0.152666	+	0.988278i	$0.548786\pi$
$614$	−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	$0.246442\pi$
$617$			34.7335i			1.39832i	−0.714967	+	0.699159i	$0.753558\pi$
$618$	−9.75592	−	12.0585i	−0.392441	−	0.485065i
$619$	−2.44700			−0.0983534			−0.0491767	−	0.998790i	$-0.515660\pi$
$619$	−2.44700			−0.0983534			−0.0491767	+	0.998790i	$0.515660\pi$
$620$	−22.5554	−	14.0257i	−0.905845	−	0.563287i
$621$	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	$-0.500029\pi$
$641$	−0.00454800			−0.000179635			−8.98177e−5		1.00000i	$0.500029\pi$
$642$	20.3427	+	25.1440i	0.802863	+	0.992355i
$643$	−41.9899			−1.65592			−0.827959	−	0.560789i	$-0.810498\pi$
$643$	−41.9899			−1.65592			−0.827959	+	0.560789i	$0.810498\pi$
$644$	−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	$-0.358620\pi$
$647$	21.8598			0.859396			0.429698	+	0.902973i	$0.358620\pi$
$648$	19.0696	+	16.8627i	0.749126	+	0.662428i
$649$		−	12.0433i		−	0.472741i
$650$	−4.83604	+	1.51399i	−0.189685	+	0.0593836i
$651$	28.1735	−	28.1237i	1.10421	−	1.10225i
$652$	−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	$-0.957639\pi$
$661$		−	6.82285i		−	0.265378i	0.991158	−	0.132689i	$-0.0423612\pi$
$662$	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
$682$	−13.3189	+	11.4730i	−0.510009	+	0.439322i
$683$	−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	$0.299016\pi$
$691$			42.4374i			1.61439i	−0.590282	+	0.807197i	$0.700984\pi$
$692$	−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	$-0.380897\pi$
$709$	19.4646			0.731008			0.365504	+	0.930810i	$0.380897\pi$
$710$	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	$-0.200744\pi$
$719$	43.3124			1.61528			0.807641	+	0.589675i	$0.200744\pi$
$720$	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	$0.0294989\pi$
$733$			5.01090i			0.185082i	−0.995709	+	0.0925410i	$0.970501\pi$
$734$	−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	$-0.585805\pi$
$739$	−14.4790			−0.532620			−0.266310	+	0.963887i	$0.585805\pi$
$740$	−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	$-0.444703\pi$
$743$	9.42294			0.345694			0.172847	+	0.984949i	$0.444703\pi$
$744$	−3.37125	−	27.0672i	−0.123596	−	0.992333i
$745$	−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	$-0.427176\pi$
$757$	12.4797			0.453583			0.226792	+	0.973943i	$0.427176\pi$
$758$	−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	$-0.422833\pi$
$761$	13.2447			0.480119			0.240059	+	0.970758i	$0.422833\pi$
$762$	−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	$-0.349262\pi$
$787$	25.5878			0.912108			0.456054	+	0.889952i	$0.349262\pi$
$788$	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
$806$	26.7167	+	31.0154i	0.941057	+	1.09247i
$807$	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	$-0.340281\pi$
$809$	27.3610			0.961960			0.480980	+	0.876732i	$0.340281\pi$
$810$	7.21470	+	29.4891i	0.253499	+	1.03614i
$811$			11.9529i			0.419724i	0.977731	+	0.209862i	$0.0673014\pi$
$811$			11.9529i			0.419724i	−0.977731	+	0.209862i	$0.932699\pi$
$812$	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	$-0.713150\pi$
$829$	−35.7426			−1.24139			−0.620697	+	0.784051i	$0.713150\pi$
$830$	−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
$837$	0.943354	−	28.9156i	0.0326071	−	0.999468i
$838$	26.2745	−	8.22561i	0.907638	−	0.284149i
$839$			31.8678i			1.10020i	0.835099	+	0.550100i	$0.185410\pi$
$839$			31.8678i			1.10020i	−0.835099	+	0.550100i	$0.814590\pi$
$840$	−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	$-0.752515\pi$
$853$		−	40.9762i		−	1.40300i	0.712671	−	0.701499i	$-0.247485\pi$
$854$	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	$-0.877603\pi$
$857$		−	21.9627i		−	0.750230i	0.926978	−	0.375115i	$-0.122397\pi$
$858$	−22.1025	+	17.8820i	−0.754567	+	0.610481i
$859$	11.0404			0.376692			0.188346	−	0.982103i	$-0.439687\pi$
$859$	11.0404			0.376692			0.188346	+	0.982103i	$0.439687\pi$
$860$	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	$-0.467051\pi$
$863$	6.07085			0.206654			0.103327	+	0.994647i	$0.467051\pi$
$864$	−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
$868$	39.0349	+	24.2733i	1.32493	+	0.823890i
$869$	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	$-0.931991\pi$
$877$		−	12.5585i		−	0.424071i	0.977262	−	0.212036i	$-0.0680093\pi$
$878$	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	$-0.300009\pi$
$881$	34.8916			1.17553			0.587763	+	0.809033i	$0.300009\pi$
$882$	20.9321	−	37.0965i	0.704821	−	1.24910i
$883$	−45.7890			−1.54092			−0.770462	−	0.637486i	$-0.779974\pi$
$883$	−45.7890			−1.54092			−0.770462	+	0.637486i	$0.779974\pi$
$884$	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	$-0.925023\pi$
$887$		−	13.9009i		−	0.466747i	0.972387	−	0.233374i	$-0.0749765\pi$
$888$	−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	$-0.832023\pi$
$907$		−	30.3309i		−	1.00712i	0.863960	−	0.503560i	$-0.167977\pi$
$908$	−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	$-0.454403\pi$
$911$	8.61768			0.285516			0.142758	+	0.989758i	$0.454403\pi$
$912$	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	$-0.766243\pi$
$929$	−45.2470			−1.48451			−0.742253	+	0.670120i	$0.766243\pi$
$930$	15.1048	−	28.8105i	0.495307	−	0.944732i
$931$		−	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	$-0.446607\pi$
$953$	10.3080			0.333908			0.166954	+	0.985965i	$0.446607\pi$
$954$	−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	$-0.756845\pi$
$977$		−	43.2433i		−	1.38348i	0.722148	−	0.691738i	$-0.243155\pi$
$978$	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	$-0.319481\pi$
$983$	33.6856			1.07440			0.537202	+	0.843453i	$0.319481\pi$
$984$	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	$-0.0229099\pi$
$992$	29.5444	−	10.9145i	0.938037	−	0.346535i
$993$	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	$-0.673026\pi$
$997$		−	54.0483i		−	1.71173i	0.517202	−	0.855864i	$-0.326974\pi$
$998$	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.557.7	yes	96
3.2	odd	2	inner	744.2.o.e.557.89	yes	96
8.5	even	2	inner	744.2.o.e.557.92	yes	96
24.5	odd	2	inner	744.2.o.e.557.6	yes	96
31.30	odd	2	inner	744.2.o.e.557.8	yes	96
93.92	even	2	inner	744.2.o.e.557.90	yes	96
248.61	odd	2	inner	744.2.o.e.557.91	yes	96
744.557	even	2	inner	744.2.o.e.557.5	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
744.2.o.e.557.5	✓	96	744.557	even	2	inner
744.2.o.e.557.6	yes	96	24.5	odd	2	inner
744.2.o.e.557.7	yes	96	1.1	even	1	trivial
744.2.o.e.557.8	yes	96	31.30	odd	2	inner
744.2.o.e.557.89	yes	96	3.2	odd	2	inner
744.2.o.e.557.90	yes	96	93.92	even	2	inner
744.2.o.e.557.91	yes	96	248.61	odd	2	inner
744.2.o.e.557.92	yes	96	8.5	even	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} +(5.13897 + 5.96582i) 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} +(-6.82512 + 6.81305i) 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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