LMFDB - Embedded newform 603.2.u.a.91.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [603,2,Mod(64,603)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(603, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("603.64"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.u (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			91.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	603.91
Dual form			603.2.u.a.550.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.915415 + 2.00448i) q^{2} +(-1.87023 - 2.15836i) q^{4} +(0.0405070 - 0.281733i) q^{5} +(0.226900 - 0.496841i) q^{7} +(1.80972 - 0.531382i) q^{8} +(0.527646 + 0.339098i) q^{10} +(0.508975 - 3.54000i) q^{11} +(0.942270 + 0.276675i) q^{13} +(0.788201 + 0.909632i) q^{14} +(0.221378 - 1.53972i) q^{16} +(-0.862774 + 0.995695i) q^{17} +(-3.05062 - 6.67992i) q^{19} +(-0.683838 + 0.439476i) q^{20} +(6.62993 + 4.26080i) q^{22} +(6.22839 - 4.00274i) q^{23} +(4.71973 + 1.38584i) q^{25} +(-1.41716 + 1.63549i) q^{26} +(-1.49672 + 0.439476i) q^{28} +3.42094 q^{29} +(-5.85621 + 1.71954i) q^{31} +(6.05710 + 3.89266i) q^{32} +(-1.20605 - 2.64089i) q^{34} +(-0.130785 - 0.0840506i) q^{35} +5.01428 q^{37} +16.1823 q^{38} +(-0.0764012 - 0.531382i) q^{40} +(-0.877875 + 1.01312i) q^{41} +(5.80088 - 6.69457i) q^{43} +(-8.59250 + 5.52206i) q^{44} +(2.32186 + 16.1489i) q^{46} +(-4.50791 + 2.89705i) q^{47} +(4.38866 + 5.06478i) q^{49} +(-7.09840 + 8.19199i) q^{50} +(-1.16510 - 2.55121i) q^{52} +(-4.58316 - 5.28925i) q^{53} +(-0.976716 - 0.286790i) q^{55} +(0.146613 - 1.01971i) q^{56} +(-3.13158 + 6.85720i) q^{58} +(0.837324 - 0.245860i) q^{59} +(-1.86953 - 13.0029i) q^{61} +(1.91408 - 13.3127i) q^{62} +(-10.7303 + 6.89594i) q^{64} +(0.116117 - 0.254261i) q^{65} +(-1.18356 + 8.09933i) q^{67} +3.76266 q^{68} +(0.288201 - 0.185215i) q^{70} +(2.89602 + 3.34218i) q^{71} +(0.738601 + 5.13708i) q^{73} +(-4.59015 + 10.0510i) q^{74} +(-8.71232 + 19.0773i) q^{76} +(-1.64333 - 1.05610i) q^{77} +(7.48653 + 2.19824i) q^{79} +(-0.424822 - 0.124739i) q^{80} +(-1.22716 - 2.68711i) q^{82} +(0.929807 - 6.46695i) q^{83} +(0.245571 + 0.283404i) q^{85} +(8.10892 + 17.7561i) q^{86} +(-0.959989 - 6.67687i) q^{88} +(-12.8365 - 8.24949i) q^{89} +(0.351265 - 0.405381i) q^{91} +(-20.2879 - 5.95707i) q^{92} +(-1.68048 - 11.6880i) q^{94} +(-2.00552 + 0.588874i) q^{95} -5.39459 q^{97} +(-14.1697 + 4.16060i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28}+ \cdots - 47 q^{98}+O(q^{100}) $ 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.915415	+	2.00448i	−0.647296	+	1.41738i	0.246605	+	0.969116i	$0.420685\pi$
$2$	−0.915415	+	2.00448i	−0.647296	+	1.41738i	−0.893901	+	0.448265i	$0.852042\pi$
$3$		0			0
$3$		0			0
$4$	−1.87023	−	2.15836i	−0.935116	−	1.07918i
$5$	0.0405070	−	0.281733i	0.0181153	−	0.125995i	−0.978757	−	0.205024i	$-0.934273\pi$
$5$	0.0405070	−	0.281733i	0.0181153	−	0.125995i	0.996872	+	0.0790290i	$0.0251820\pi$
$6$		0			0
$7$	0.226900	−	0.496841i	0.0857601	−	0.187788i	−0.861893	−	0.507090i	$-0.830721\pi$
$7$	0.226900	−	0.496841i	0.0857601	−	0.187788i	0.947653	+	0.319302i	$0.103448\pi$
$8$	1.80972	−	0.531382i	0.639833	−	0.187872i
$9$		0			0
$10$	0.527646	+	0.339098i	0.166856	+	0.107232i
$11$	0.508975	−	3.54000i	0.153462	−	1.06735i	−0.756898	−	0.653533i	$-0.773286\pi$
$11$	0.508975	−	3.54000i	0.153462	−	1.06735i	0.910360	−	0.413817i	$-0.135805\pi$
$12$		0			0
$13$	0.942270	+	0.276675i	0.261339	+	0.0767360i	0.409777	−	0.912186i	$-0.365606\pi$
$13$	0.942270	+	0.276675i	0.261339	+	0.0767360i	−0.148438	+	0.988922i	$0.547425\pi$
$14$	0.788201	+	0.909632i	0.210655	+	0.243109i
$15$		0			0
$16$	0.221378	−	1.53972i	0.0553446	−	0.384930i
$17$	−0.862774	+	0.995695i	−0.209254	+	0.241491i	−0.850668	−	0.525703i	$-0.823802\pi$
$17$	−0.862774	+	0.995695i	−0.209254	+	0.241491i	0.641415	+	0.767194i	$0.278348\pi$
$18$		0			0
$19$	−3.05062	−	6.67992i	−0.699859	−	1.53248i	−0.840142	−	0.542367i	$-0.817528\pi$
$19$	−3.05062	−	6.67992i	−0.699859	−	1.53248i	0.140283	−	0.990111i	$-0.455199\pi$
$20$	−0.683838	+	0.439476i	−0.152911	+	0.0982699i
$21$		0			0
$22$	6.62993	+	4.26080i	1.41351	+	0.908405i
$23$	6.22839	−	4.00274i	1.29871	−	0.834630i	0.305639	−	0.952148i	$-0.401130\pi$
$23$	6.22839	−	4.00274i	1.29871	−	0.834630i	0.993071	+	0.117518i	$0.0374936\pi$
$24$		0			0
$25$	4.71973	+	1.38584i	0.943946	+	0.277168i
$26$	−1.41716	+	1.63549i	−0.277928	+	0.320746i
$27$		0			0
$28$	−1.49672	+	0.439476i	−0.282853	+	0.0830532i
$29$	3.42094			0.635252			0.317626	−	0.948216i	$-0.397114\pi$
$29$	3.42094			0.635252			0.317626	+	0.948216i	$0.397114\pi$
$30$		0			0
$31$	−5.85621	+	1.71954i	−1.05181	+	0.308838i	−0.761547	−	0.648110i	$-0.775560\pi$
$31$	−5.85621	+	1.71954i	−1.05181	+	0.308838i	−0.290260	+	0.956948i	$0.593742\pi$
$32$	6.05710	+	3.89266i	1.07075	+	0.688132i
$33$		0			0
$34$	−1.20605	−	2.64089i	−0.206836	−	0.452908i
$35$	−0.130785	−	0.0840506i	−0.0221068	−	0.0142071i
$36$		0			0
$37$	5.01428			0.824343			0.412172	−	0.911106i	$-0.364770\pi$
$37$	5.01428			0.824343			0.412172	+	0.911106i	$0.364770\pi$
$38$	16.1823			2.62512
$39$		0			0
$40$	−0.0764012	−	0.531382i	−0.0120801	−	0.0840189i
$41$	−0.877875	+	1.01312i	−0.137101	+	0.158223i	−0.820148	−	0.572151i	$-0.806109\pi$
$41$	−0.877875	+	1.01312i	−0.137101	+	0.158223i	0.683047	+	0.730374i	$0.260654\pi$
$42$		0			0
$43$	5.80088	−	6.69457i	0.884626	−	1.02091i	−0.114995	−	0.993366i	$-0.536685\pi$
$43$	5.80088	−	6.69457i	0.884626	−	1.02091i	0.999621	−	0.0275467i	$-0.00876948\pi$
$44$	−8.59250	+	5.52206i	−1.29537	+	0.832482i
$45$		0			0
$46$	2.32186	+	16.1489i	0.342339	+	2.38102i
$47$	−4.50791	+	2.89705i	−0.657546	+	0.422579i	−0.826416	−	0.563059i	$-0.809624\pi$
$47$	−4.50791	+	2.89705i	−0.657546	+	0.422579i	0.168871	+	0.985638i	$0.445988\pi$
$48$		0			0
$49$	4.38866	+	5.06478i	0.626951	+	0.723540i
$50$	−7.09840	+	8.19199i	−1.00387	+	1.15852i
$51$		0			0
$52$	−1.16510	−	2.55121i	−0.161570	−	0.353789i
$53$	−4.58316	−	5.28925i	−0.629546	−	0.726535i	0.347944	−	0.937515i	$-0.386880\pi$
$53$	−4.58316	−	5.28925i	−0.629546	−	0.726535i	−0.977490	+	0.210980i	$0.932334\pi$
$54$		0			0
$55$	−0.976716	−	0.286790i	−0.131700	−	0.0386707i
$56$	0.146613	−	1.01971i	0.0195920	−	0.136265i
$57$		0			0
$58$	−3.13158	+	6.85720i	−0.411196	+	0.900394i
$59$	0.837324	−	0.245860i	0.109010	−	0.0320083i	−0.226773	−	0.973948i	$-0.572817\pi$
$59$	0.837324	−	0.245860i	0.109010	−	0.0320083i	0.335783	+	0.941939i	$0.390999\pi$
$60$		0			0
$61$	−1.86953	−	13.0029i	−0.239369	−	1.66485i	−0.655239	−	0.755422i	$-0.727432\pi$
$61$	−1.86953	−	13.0029i	−0.239369	−	1.66485i	0.415870	−	0.909424i	$-0.363477\pi$
$62$	1.91408	−	13.3127i	0.243089	−	1.69072i
$63$		0			0
$64$	−10.7303	+	6.89594i	−1.34129	+	0.861992i
$65$	0.116117	−	0.254261i	0.0144025	−	0.0315372i
$66$		0			0
$67$	−1.18356	+	8.09933i	−0.144595	+	0.989491i
$67$	−1.18356	+	8.09933i	−0.144595	+	0.989491i
$68$	3.76266			0.456289
$69$		0			0
$70$	0.288201	−	0.185215i	0.0344466	−	0.0221375i
$71$	2.89602	+	3.34218i	0.343694	+	0.396644i	0.901111	−	0.433589i	$-0.142753\pi$
$71$	2.89602	+	3.34218i	0.343694	+	0.396644i	−0.557417	+	0.830233i	$0.688207\pi$
$72$		0			0
$73$	0.738601	+	5.13708i	0.0864467	+	0.601250i	0.986288	+	0.165033i	$0.0527730\pi$
$73$	0.738601	+	5.13708i	0.0864467	+	0.601250i	−0.899841	+	0.436217i	$0.856318\pi$
$74$	−4.59015	+	10.0510i	−0.533594	+	1.16841i
$75$		0			0
$76$	−8.71232	+	19.0773i	−0.999372	+	2.18832i
$77$	−1.64333	−	1.05610i	−0.187275	−	0.120354i
$78$		0			0
$79$	7.48653	+	2.19824i	0.842300	+	0.247322i	0.674293	−	0.738464i	$-0.264449\pi$
$79$	7.48653	+	2.19824i	0.842300	+	0.247322i	0.168007	+	0.985786i	$0.446267\pi$
$80$	−0.424822	−	0.124739i	−0.0474966	−	0.0139462i
$81$		0			0
$82$	−1.22716	−	2.68711i	−0.135517	−	0.296742i
$83$	0.929807	−	6.46695i	0.102060	−	0.709840i	−0.872972	−	0.487771i	$-0.837810\pi$
$83$	0.929807	−	6.46695i	0.102060	−	0.709840i	0.975031	−	0.222068i	$-0.0712809\pi$
$84$		0			0
$85$	0.245571	+	0.283404i	0.0266359	+	0.0307395i
$86$	8.10892	+	17.7561i	0.874407	+	1.91468i
$87$		0			0
$88$	−0.959989	−	6.67687i	−0.102335	−	0.711757i
$89$	−12.8365	−	8.24949i	−1.36066	−	0.874444i	−0.362323	−	0.932053i	$-0.618016\pi$
$89$	−12.8365	−	8.24949i	−1.36066	−	0.874444i	−0.998339	+	0.0576083i	$0.981653\pi$
$90$		0			0
$91$	0.351265	−	0.405381i	0.0368226	−	0.0424955i
$92$	−20.2879	−	5.95707i	−2.11516	−	0.621067i
$93$		0			0
$94$	−1.68048	−	11.6880i	−0.173329	−	1.20553i
$95$	−2.00552	+	0.588874i	−0.205762	+	0.0604172i
$96$		0			0
$97$	−5.39459			−0.547737			−0.273869	−	0.961767i	$-0.588303\pi$
$97$	−5.39459			−0.547737			−0.273869	+	0.961767i	$0.588303\pi$
$98$	−14.1697	+	4.16060i	−1.43135	+	0.420284i
$99$		0			0
$100$	−5.83585	−	12.7787i	−0.583585	−	1.27787i
$101$	7.05137	+	15.4403i	0.701638	+	1.53637i	0.837974	+	0.545709i	$0.183740\pi$
$101$	7.05137	+	15.4403i	0.701638	+	1.53637i	−0.136337	+	0.990663i	$0.543533\pi$
$102$		0			0
$103$	0.568757	−	0.167002i	0.0560413	−	0.0164552i	−0.253592	−	0.967311i	$-0.581612\pi$
$103$	0.568757	−	0.167002i	0.0560413	−	0.0164552i	0.309633	+	0.950856i	$0.399794\pi$
$104$	1.85227			0.181630
$105$		0			0
$106$	14.7977	−	4.34500i	1.43728	−	0.422023i
$107$	−0.266995	−	1.85699i	−0.0258113	−	0.179522i	0.972837	−	0.231489i	$-0.0743598\pi$
$107$	−0.266995	−	1.85699i	−0.0258113	−	0.179522i	−0.998649	+	0.0519676i	$0.983451\pi$
$108$		0			0
$109$	−11.2065	−	3.29052i	−1.07339	−	0.315175i	−0.303156	−	0.952941i	$-0.598040\pi$
$109$	−11.2065	−	3.29052i	−1.07339	−	0.315175i	−0.770230	+	0.637766i	$0.779859\pi$
$110$	1.46896	−	1.69528i	0.140060	−	0.161638i
$111$		0			0
$112$	−0.714766	−	0.459352i	−0.0675391	−	0.0434047i
$113$	−1.53683	−	10.6889i	−0.144573	−	1.00553i	−0.924915	−	0.380175i	$-0.875864\pi$
$113$	−1.53683	−	10.6889i	−0.144573	−	1.00553i	0.780341	−	0.625354i	$-0.215045\pi$
$114$		0			0
$115$	−0.875410	−	1.91688i	−0.0816324	−	0.178750i
$116$	−6.39794	−	7.38362i	−0.594034	−	0.685552i
$117$		0			0
$118$	−0.273677	+	1.90346i	−0.0251940	+	0.175228i
$119$	0.298939	+	0.654585i	0.0274037	+	0.0600057i
$120$		0			0
$121$	−1.71811	−	0.504483i	−0.156192	−	0.0458621i
$122$	27.7754	+	8.15558i	2.51466	+	0.738372i
$123$		0			0
$124$	14.6639	+	9.42389i	1.31685	+	0.846290i
$125$	1.17282	−	2.56811i	0.104900	−	0.229699i
$126$		0			0
$127$	4.37570	−	9.58144i	0.388281	−	0.850216i	−0.610045	−	0.792367i	$-0.708849\pi$
$127$	4.37570	−	9.58144i	0.388281	−	0.850216i	0.998325	−	0.0578488i	$-0.0184241\pi$
$128$	−1.95074	−	13.5677i	−0.172423	−	1.19923i
$129$		0			0
$130$	0.403365	+	0.465508i	0.0353775	+	0.0408278i
$131$	15.7460	−	10.1193i	1.37573	−	0.884129i	0.376625	−	0.926366i	$-0.377085\pi$
$131$	15.7460	−	10.1193i	1.37573	−	0.884129i	0.999108	+	0.0422366i	$0.0134483\pi$
$132$		0			0
$133$	−4.01104			−0.347802
$134$	−15.1515	−	9.78667i	−1.30889	−	0.845440i
$135$		0			0
$136$	−1.03229	+	2.26039i	−0.0885179	+	0.193827i
$137$	8.50699	−	5.46711i	0.726801	−	0.467087i	−0.124196	−	0.992258i	$-0.539635\pi$
$137$	8.50699	−	5.46711i	0.726801	−	0.467087i	0.850997	+	0.525171i	$0.175999\pi$
$138$		0			0
$139$	2.58225	−	17.9599i	0.219023	−	1.52334i	−0.522632	−	0.852558i	$-0.675050\pi$
$139$	2.58225	−	17.9599i	0.219023	−	1.52334i	0.741655	−	0.670781i	$-0.234041\pi$
$140$	0.0631871	+	0.439476i	0.00534029	+	0.0371425i
$141$		0			0
$142$	−9.35039	+	2.74552i	−0.784667	+	0.230399i
$143$	1.45902	−	3.19481i	0.122010	−	0.267164i
$144$		0			0
$145$	0.138572	−	0.963789i	0.0115078	−	0.0800383i
$146$	−10.9733	−	3.22205i	−0.908157	−	0.266659i
$147$		0			0
$148$	−9.37787	−	10.8226i	−0.770856	−	0.889615i
$149$	1.08126	+	2.36763i	0.0885802	+	0.193964i	0.948737	−	0.316065i	$-0.102362\pi$
$149$	1.08126	+	2.36763i	0.0885802	+	0.193964i	−0.860157	+	0.510029i	$0.829635\pi$
$150$		0			0
$151$	−6.04091	+	6.97159i	−0.491603	+	0.567340i	−0.946293	−	0.323310i	$-0.895204\pi$
$151$	−6.04091	+	6.97159i	−0.491603	+	0.567340i	0.454691	+	0.890649i	$0.349750\pi$
$152$	−9.07035	−	10.4677i	−0.735703	−	0.849046i
$153$		0			0
$154$	3.62127	−	2.32725i	0.291810	−	0.187535i
$155$	0.247232	+	1.71954i	0.0198582	+	0.138117i
$156$		0			0
$157$	7.73089	−	4.96834i	0.616993	−	0.396517i	−0.194481	−	0.980906i	$-0.562302\pi$
$157$	7.73089	−	4.96834i	0.616993	−	0.396517i	0.811473	+	0.584389i	$0.198666\pi$
$158$	−11.2596	+	12.9943i	−0.895766	+	1.03377i
$159$		0			0
$160$	1.34204	−	1.54880i	0.106098	−	0.122444i
$161$	−0.575508	−	4.00274i	−0.0453564	−	0.315460i
$162$		0			0
$163$	11.0877			0.868456			0.434228	−	0.900803i	$-0.357021\pi$
$163$	11.0877			0.868456			0.434228	+	0.900803i	$0.357021\pi$
$164$	3.82851			0.298957
$165$		0			0
$166$	12.1117	+	7.78372i	0.940050	+	0.604134i
$167$	−6.41212	−	14.0406i	−0.496185	−	1.08649i	−0.977691	−	0.210050i	$-0.932637\pi$
$167$	−6.41212	−	14.0406i	−0.496185	−	1.08649i	0.481506	−	0.876443i	$-0.340090\pi$
$168$		0			0
$169$	−10.1250	−	6.50692i	−0.778844	−	0.500533i
$170$	−0.792878	+	0.232810i	−0.0608109	+	0.0178557i
$171$		0			0
$172$	−25.2983			−1.92898
$173$	−11.7878	+	3.46122i	−0.896212	+	0.263152i	−0.697227	−	0.716851i	$-0.745583\pi$
$173$	−11.7878	+	3.46122i	−0.896212	+	0.263152i	−0.198985	+	0.980002i	$0.563765\pi$
$174$		0			0
$175$	1.75945	−	2.03051i	0.133002	−	0.153492i
$176$	−5.33793	−	1.56736i	−0.402362	−	0.118144i
$177$		0			0
$178$	28.2866	−	18.1787i	2.12017	−	1.36255i
$179$	−10.5816	−	6.80035i	−0.790903	−	0.508282i	0.0817330	−	0.996654i	$-0.473955\pi$
$179$	−10.5816	−	6.80035i	−0.790903	−	0.508282i	−0.872635	+	0.488372i	$0.837591\pi$
$180$		0			0
$181$	−18.9004	+	12.1466i	−1.40486	+	0.902847i	−0.999934	−	0.0115037i	$-0.996338\pi$
$181$	−18.9004	+	12.1466i	−1.40486	+	0.902847i	−0.404923	+	0.914351i	$0.632702\pi$
$182$	0.491025	+	1.07519i	0.0363972	+	0.0796987i
$183$		0			0
$184$	9.14467	−	10.5535i	0.674154	−	0.778015i
$185$	0.203114	−	1.41269i	0.0149332	−	0.103863i
$186$		0			0
$187$	3.08563	+	3.56100i	0.225643	+	0.260406i
$188$	14.6837	+	4.31153i	1.07092	+	0.314451i
$189$		0			0
$190$	0.655498	−	4.55909i	0.0475548	−	0.330751i
$191$	9.29425	+	5.97305i	0.672508	+	0.432195i	0.831829	−	0.555032i	$-0.187294\pi$
$191$	9.29425	+	5.97305i	0.672508	+	0.432195i	−0.159321	+	0.987227i	$0.550930\pi$
$192$		0			0
$193$	3.14016	−	0.922035i	0.226034	−	0.0663695i	−0.166754	−	0.985998i	$-0.553329\pi$
$193$	3.14016	−	0.922035i	0.226034	−	0.0663695i	0.392788	+	0.919629i	$0.371511\pi$
$194$	4.93828	−	10.8133i	0.354548	−	0.776352i
$195$		0			0
$196$	2.72383	−	18.9446i	0.194559	−	1.35319i
$197$	16.2726	+	18.7796i	1.15938	+	1.33799i	0.931258	+	0.364360i	$0.118712\pi$
$197$	16.2726	+	18.7796i	1.15938	+	1.33799i	0.228120	+	0.973633i	$0.426742\pi$
$198$		0			0
$199$	−5.27273	+	11.5457i	−0.373774	+	0.818451i	0.625495	+	0.780228i	$0.284897\pi$
$199$	−5.27273	+	11.5457i	−0.373774	+	0.818451i	−0.999269	+	0.0382230i	$0.987830\pi$
$200$	9.27781			0.656040
$201$		0			0
$202$	−37.4048			−2.63179
$203$	0.776210	−	1.69966i	0.0544793	−	0.119293i
$204$		0			0
$205$	0.249869	+	0.288364i	0.0174516	+	0.0201402i
$206$	−0.185897	+	1.29294i	−0.0129520	+	0.0900833i
$207$		0			0
$208$	0.634601	−	1.38958i	0.0440017	−	0.0963502i
$209$	−25.1996	+	7.39927i	−1.74309	+	0.511818i
$210$		0			0
$211$	7.79814	+	5.01156i	0.536846	+	0.345010i	0.780804	−	0.624776i	$-0.214810\pi$
$211$	7.79814	+	5.01156i	0.536846	+	0.345010i	−0.243958	+	0.969786i	$0.578446\pi$
$212$	−2.84455	+	19.7843i	−0.195364	+	1.35879i
$213$		0			0
$214$	3.96670	+	1.16473i	0.271158	+	0.0796193i
$215$	−1.65110	−	1.90547i	−0.112604	−	0.129952i
$216$		0			0
$217$	−0.474435	+	3.29977i	−0.0322068	+	0.224003i
$218$	16.8544	−	19.4510i	1.14152	−	1.31739i
$219$		0			0
$220$	1.20769	+	2.64447i	0.0814223	+	0.178290i
$221$	−1.08845	+	0.699505i	−0.0732171	+	0.0470538i
$222$		0			0
$223$	1.93895	+	1.24609i	0.129842	+	0.0834441i	0.603949	−	0.797023i	$-0.293593\pi$
$223$	1.93895	+	1.24609i	0.129842	+	0.0834441i	−0.474108	+	0.880467i	$0.657229\pi$
$224$	3.30839	−	2.12617i	0.221051	−	0.142061i
$225$		0			0
$226$	22.8325	+	6.70424i	1.51880	+	0.445959i
$227$	−8.35734	+	9.64488i	−0.554696	+	0.640153i	−0.961971	−	0.273152i	$-0.911934\pi$
$227$	−8.35734	+	9.64488i	−0.554696	+	0.640153i	0.407275	+	0.913306i	$0.366479\pi$
$228$		0			0
$229$	−7.29074	+	2.14075i	−0.481786	+	0.141465i	−0.513602	−	0.858029i	$-0.671689\pi$
$229$	−7.29074	+	2.14075i	−0.481786	+	0.141465i	0.0318160	+	0.999494i	$0.489871\pi$
$230$	4.64371			0.306197
$231$		0			0
$232$	6.19094	−	1.81782i	0.406455	−	0.119346i
$233$	−12.1270	−	7.79355i	−0.794466	−	0.510572i	0.0793395	−	0.996848i	$-0.474719\pi$
$233$	−12.1270	−	7.79355i	−0.794466	−	0.510572i	−0.873806	+	0.486275i	$0.838355\pi$
$234$		0			0
$235$	0.633593	+	1.38737i	0.0413310	+	0.0905024i
$236$	−2.09664	−	1.34743i	−0.136480	−	0.0877103i
$237$		0			0
$238$	−1.58576			−0.102789
$239$	−22.2474			−1.43906			−0.719532	−	0.694459i	$-0.755644\pi$
$239$	−22.2474			−1.43906			−0.719532	+	0.694459i	$0.755644\pi$
$240$		0			0
$241$	3.28427	+	22.8426i	0.211558	+	1.47142i	0.767955	+	0.640504i	$0.221275\pi$
$241$	3.28427	+	22.8426i	0.211558	+	1.47142i	−0.556396	+	0.830917i	$0.687816\pi$
$242$	2.58401	−	2.98211i	0.166107	−	0.191697i
$243$		0			0
$244$	−24.5684	+	28.3535i	−1.57283	+	1.81515i
$245$	1.60469	−	1.03127i	0.102520	−	0.0658853i
$246$		0			0
$247$	−1.02633	−	7.13832i	−0.0653041	−	0.454200i
$248$	−9.68438	+	6.22377i	−0.614959	+	0.395210i
$249$		0			0
$250$	4.07411	+	4.70177i	0.257669	+	0.297366i
$251$	−7.66631	+	8.84739i	−0.483893	+	0.558442i	−0.944223	−	0.329305i	$-0.893185\pi$
$251$	−7.66631	+	8.84739i	−0.483893	+	0.558442i	0.460330	+	0.887748i	$0.347731\pi$
$252$		0			0
$253$	−10.9996	−	24.0858i	−0.691540	−	1.51426i
$254$	15.2002	+	17.5420i	0.953747	+	1.10068i
$255$		0			0
$256$	4.50498	+	1.32278i	0.281561	+	0.0826739i
$257$	−2.78579	+	19.3756i	−0.173773	+	1.20862i	0.697051	+	0.717022i	$0.254495\pi$
$257$	−2.78579	+	19.3756i	−0.173773	+	1.20862i	−0.870824	+	0.491596i	$0.836414\pi$
$258$		0			0
$259$	1.13774	−	2.49130i	0.0706957	−	0.154802i
$260$	−0.765953	+	0.224904i	−0.0475024	+	0.0139480i
$261$		0			0
$262$	5.86987	+	40.8259i	0.362642	+	2.52223i
$263$	0.157085	−	1.09255i	0.00968627	−	0.0673695i	−0.984405	−	0.175917i	$-0.943711\pi$
$263$	0.157085	−	1.09255i	0.00968627	−	0.0673695i	0.994091	+	0.108548i	$0.0346200\pi$
$264$		0			0
$265$	−1.67581	+	1.07697i	−0.102944	+	0.0661580i
$266$	3.67177	−	8.04005i	0.225131	−	0.492967i
$267$		0			0
$268$	19.6948	−	12.5931i	1.20305	−	0.769244i
$269$	−11.1258			−0.678354			−0.339177	−	0.940723i	$-0.610149\pi$
$269$	−11.1258			−0.678354			−0.339177	+	0.940723i	$0.610149\pi$
$270$		0			0
$271$	−0.371014	+	0.238436i	−0.0225375	+	0.0144840i	−0.551861	−	0.833936i	$-0.686082\pi$
$271$	−0.371014	+	0.238436i	−0.0225375	+	0.0144840i	0.529324	+	0.848420i	$0.322446\pi$
$272$	1.34209	+	1.54886i	0.0813763	+	0.0939133i
$273$		0			0
$274$	3.17128	+	22.0568i	0.191584	+	1.33250i
$275$	7.30809	−	16.0025i	0.440695	−	0.964986i
$276$		0			0
$277$	−4.30520	+	9.42708i	−0.258674	+	0.566418i	−0.993758	−	0.111559i	$-0.964416\pi$
$277$	−4.30520	+	9.42708i	−0.258674	+	0.566418i	0.735083	+	0.677977i	$0.237143\pi$
$278$	33.6364	+	21.6168i	2.01738	+	1.29649i
$279$		0			0
$280$	−0.281348	−	0.0826112i	−0.0168138	−	0.00493697i
$281$	19.6848	+	5.77998i	1.17430	+	0.344805i	0.809973	−	0.586468i	$-0.199482\pi$
$281$	19.6848	+	5.77998i	1.17430	+	0.344805i	0.364324	+	0.931272i	$0.381300\pi$
$282$		0			0
$283$	3.82870	+	8.38369i	0.227593	+	0.498359i	0.988634	−	0.150345i	$-0.0480386\pi$
$283$	3.82870	+	8.38369i	0.227593	+	0.498359i	−0.761041	+	0.648704i	$0.775311\pi$
$284$	1.79742	−	12.5013i	0.106657	−	0.741816i
$285$		0			0
$286$	5.06833	+	5.84916i	0.299696	+	0.345868i
$287$	0.304171	+	0.666042i	0.0179546	+	0.0393152i
$288$		0			0
$289$	2.17232	+	15.1088i	0.127784	+	0.888756i
$290$	1.80504	+	1.16003i	0.105996	+	0.0681194i
$291$		0			0
$292$	9.70633	−	11.2017i	0.568020	−	0.655530i
$293$	31.4261	+	9.22753i	1.83593	+	0.539078i	0.999953	−	0.00968446i	$-0.00308271\pi$
$293$	31.4261	+	9.22753i	1.83593	+	0.539078i	0.835978	+	0.548763i	$0.184901\pi$
$294$		0			0
$295$	−0.0353494	−	0.245860i	−0.00205812	−	0.0143145i
$296$	9.07446	−	2.66450i	0.527442	−	0.154871i
$297$		0			0
$298$	−5.73566			−0.332258
$299$	6.97629	−	2.04842i	0.403449	−	0.118463i
$300$		0			0
$301$	−2.00992	−	4.40111i	−0.115850	−	0.253676i
$302$	−8.44446	−	18.4908i	−0.485924	−	1.06402i
$303$		0			0
$304$	−10.9605	+	3.21831i	−0.628631	+	0.184583i
$305$	−3.73906			−0.214098
$306$		0			0
$307$	−12.4577	+	3.65791i	−0.710999	+	0.208768i	−0.617181	−	0.786821i	$-0.711725\pi$
$307$	−12.4577	+	3.65791i	−0.710999	+	0.208768i	−0.0938179	+	0.995589i	$0.529907\pi$
$308$	0.793953	+	5.52206i	0.0452397	+	0.314649i
$309$		0			0
$310$	−3.67310	−	1.07852i	−0.208618	−	0.0612558i
$311$	−3.59740	+	4.15163i	−0.203990	+	0.235417i	−0.848522	−	0.529161i	$-0.822507\pi$
$311$	−3.59740	+	4.15163i	−0.203990	+	0.235417i	0.644532	+	0.764578i	$0.277052\pi$
$312$		0			0
$313$	−9.81322	−	6.30657i	−0.554676	−	0.356469i	0.233078	−	0.972458i	$-0.425120\pi$
$313$	−9.81322	−	6.30657i	−0.554676	−	0.356469i	−0.787755	+	0.615989i	$0.788756\pi$
$314$	2.88197	+	20.0445i	0.162639	+	1.13118i
$315$		0			0
$316$	−9.25693	−	20.2699i	−0.520743	−	1.14027i
$317$	1.37986	+	1.59245i	0.0775008	+	0.0894407i	0.793176	−	0.608993i	$-0.208426\pi$
$317$	1.37986	+	1.59245i	0.0775008	+	0.0894407i	−0.715675	+	0.698434i	$0.753881\pi$
$318$		0			0
$319$	1.74117	−	12.1101i	0.0974869	−	0.678036i
$320$	1.50816	+	3.30241i	0.0843086	+	0.184610i
$321$		0			0
$322$	8.55025	+	2.51058i	0.476487	+	0.139909i
$323$	9.28315	+	2.72578i	0.516528	+	0.151666i
$324$		0			0
$325$	4.06384	+	2.61167i	0.225421	+	0.144869i
$326$	−10.1499	+	22.2251i	−0.562148	+	1.23093i
$327$		0			0
$328$	−1.05035	+	2.29995i	−0.0579961	+	0.126994i
$329$	0.416534	+	2.89705i	0.0229642	+	0.159720i
$330$		0			0
$331$	0.400012	+	0.461638i	0.0219866	+	0.0253739i	0.766636	−	0.642081i	$-0.221929\pi$
$331$	0.400012	+	0.461638i	0.0219866	+	0.0253739i	−0.744650	+	0.667455i	$0.767383\pi$
$332$	−15.6970	+	10.0878i	−0.861483	+	0.553641i
$333$		0			0
$334$	34.0138			1.86115
$335$	2.23390	+	0.661527i	0.122051	+	0.0361431i
$336$		0			0
$337$	4.63800	−	10.1558i	0.252648	−	0.553222i	−0.740230	−	0.672353i	$-0.765284\pi$
$337$	4.63800	−	10.1558i	0.252648	−	0.553222i	0.992879	+	0.119131i	$0.0380109\pi$
$338$	22.3115	−	14.3388i	1.21359	−	0.779926i
$339$		0			0
$340$	0.152414	−	1.06006i	0.00826581	−	0.0574900i
$341$	3.10650	+	21.6062i	0.168226	+	1.17004i
$342$		0			0
$343$	7.18071	−	2.10845i	0.387722	−	0.113845i
$344$	6.94060	−	15.1978i	0.374212	−	0.819410i
$345$		0			0
$346$	3.85281	−	26.7969i	0.207129	−	1.44061i
$347$	−12.0537	−	3.53930i	−0.647079	−	0.190000i	−0.0583070	−	0.998299i	$-0.518570\pi$
$347$	−12.0537	−	3.53930i	−0.647079	−	0.190000i	−0.588772	+	0.808299i	$0.700388\pi$
$348$		0			0
$349$	14.4252	+	16.6476i	0.772164	+	0.891125i	0.996518	−	0.0833826i	$-0.0265724\pi$
$349$	14.4252	+	16.6476i	0.772164	+	0.891125i	−0.224353	+	0.974508i	$0.572027\pi$
$350$	2.45949	+	5.38554i	0.131465	+	0.287869i
$351$		0			0
$352$	16.8629	−	19.4609i	0.898797	−	1.03727i
$353$	6.10368	+	7.04403i	0.324866	+	0.374916i	0.894565	−	0.446938i	$-0.147486\pi$
$353$	6.10368	+	7.04403i	0.324866	+	0.374916i	−0.569699	+	0.821854i	$0.692940\pi$
$354$		0			0
$355$	1.05891	−	0.680520i	0.0562011	−	0.0361183i
$356$	6.20176	+	43.1342i	0.328693	+	2.28611i
$357$		0			0
$358$	23.3177	−	14.9854i	1.23238	−	0.792001i
$359$	16.0332	−	18.5033i	0.846201	−	0.976568i	−0.153733	−	0.988112i	$-0.549129\pi$
$359$	16.0332	−	18.5033i	0.846201	−	0.976568i	0.999933	+	0.0115449i	$0.00367494\pi$
$360$		0			0
$361$	−22.8727	+	26.3965i	−1.20383	+	1.38929i
$362$	−7.04580	−	49.0046i	−0.370319	−	2.57563i
$363$		0			0
$364$	−1.53191			−0.0802937
$365$	1.47720			0.0773203
$366$		0			0
$367$	18.8542	+	12.1168i	0.984179	+	0.632493i	0.930587	−	0.366070i	$-0.119297\pi$
$367$	18.8542	+	12.1168i	0.984179	+	0.632493i	0.0535914	+	0.998563i	$0.482933\pi$
$368$	−4.78428	−	10.4761i	−0.249398	−	0.546105i
$369$		0			0
$370$	2.64577	+	1.70033i	0.137547	+	0.0883961i
$371$	−3.66784	+	1.07697i	−0.190425	+	0.0559137i
$372$		0			0
$373$	20.0794			1.03967			0.519837	−	0.854266i	$-0.325993\pi$
$373$	20.0794			1.03967			0.519837	+	0.854266i	$0.325993\pi$
$374$	−9.96259	+	2.92528i	−0.515153	+	0.151263i
$375$		0			0
$376$	−6.61861	+	7.63828i	−0.341329	+	0.393914i
$377$	3.22345	+	0.946489i	0.166016	+	0.0487467i
$378$		0			0
$379$	−20.0919	+	12.9123i	−1.03205	+	0.663260i	−0.943009	−	0.332768i	$-0.892018\pi$
$379$	−20.0919	+	12.9123i	−1.03205	+	0.663260i	−0.0890439	+	0.996028i	$0.528381\pi$
$380$	5.02179	+	3.22731i	0.257612	+	0.165557i
$381$		0			0
$382$	−20.4809	+	13.1623i	−1.04790	+	0.673442i
$383$	4.04039	+	8.84722i	0.206454	+	0.452072i	0.984328	−	0.176349i	$-0.0564288\pi$
$383$	4.04039	+	8.84722i	0.206454	+	0.452072i	−0.777873	+	0.628421i	$0.783702\pi$
$384$		0			0
$385$	−0.364106	+	0.420200i	−0.0185565	+	0.0214154i
$386$	−1.02635	+	7.13844i	−0.0522400	+	0.363337i
$387$		0			0
$388$	10.0891	+	11.6435i	0.512198	+	0.591107i
$389$	11.0080	+	3.23225i	0.558130	+	0.163882i	0.548618	−	0.836073i	$-0.315154\pi$
$389$	11.0080	+	3.23225i	0.558130	+	0.163882i	0.00951188	+	0.999955i	$0.496972\pi$
$390$		0			0
$391$	−1.38819	+	9.65504i	−0.0702036	+	0.488277i
$392$	10.6336	+	6.83379i	0.537077	+	0.345158i
$393$		0			0
$394$	−52.5396	+	15.4270i	−2.64691	+	0.777202i
$395$	0.922573	−	2.02015i	0.0464197	−	0.101645i
$396$		0			0
$397$	4.38098	−	30.4704i	0.219875	−	1.52926i	−0.518619	−	0.855005i	$-0.673554\pi$
$397$	4.38098	−	30.4704i	0.219875	−	1.52926i	0.738494	−	0.674260i	$-0.235537\pi$
$398$	−18.3163	−	21.1382i	−0.918114	−	1.05956i
$399$		0			0
$400$	3.17865	−	6.96028i	0.158933	−	0.348014i
$401$	−14.3770			−0.717954			−0.358977	−	0.933346i	$-0.616874\pi$
$401$	−14.3770			−0.717954			−0.358977	+	0.933346i	$0.616874\pi$
$402$		0			0
$403$	−5.99389			−0.298577
$404$	20.1382	−	44.0964i	1.00191	−	2.19388i
$405$		0			0
$406$	2.69638	+	3.11179i	0.133819	+	0.154436i
$407$	2.55214	−	17.7506i	0.126505	−	0.879862i
$408$		0			0
$409$	−8.65239	+	18.9461i	−0.427833	+	0.936824i	0.565840	+	0.824515i	$0.308552\pi$
$409$	−8.65239	+	18.9461i	−0.427833	+	0.936824i	−0.993673	+	0.112309i	$0.964175\pi$
$410$	−0.806755	+	0.236885i	−0.0398428	+	0.0116989i
$411$		0			0
$412$	−1.42416	−	0.915251i	−0.0701633	−	0.0450912i
$413$	0.0678350	−	0.471803i	0.00333794	−	0.0232159i
$414$		0			0
$415$	−1.78429	−	0.523914i	−0.0875871	−	0.0257179i
$416$	4.63042	+	5.34379i	0.227025	+	0.262001i
$417$		0			0
$418$	8.23640	−	57.2854i	0.402856	−	2.80192i
$419$	17.2766	−	19.9383i	0.844018	−	0.974049i	−0.155888	−	0.987775i	$-0.549824\pi$
$419$	17.2766	−	19.9383i	0.844018	−	0.974049i	0.999906	+	0.0137262i	$0.00436932\pi$
$420$		0			0
$421$	−2.23208	−	4.88757i	−0.108785	−	0.238206i	0.847408	−	0.530941i	$-0.178162\pi$
$421$	−2.23208	−	4.88757i	−0.108785	−	0.238206i	−0.956193	+	0.292736i	$0.905434\pi$
$422$	−17.1841	+	11.0436i	−0.836509	+	0.537592i
$423$		0			0
$424$	−11.1049	−	7.13666i	−0.539300	−	0.346587i
$425$	−5.45194	+	3.50375i	−0.264458	+	0.169957i
$426$		0			0
$427$	−6.88456	−	2.02149i	−0.333167	−	0.0978267i
$428$	−3.50871	+	4.04927i	−0.169600	+	0.195729i
$429$		0			0
$430$	5.33093	−	1.56530i	0.257080	−	0.0754855i
$431$	32.5222			1.56654			0.783270	−	0.621682i	$-0.213550\pi$
$431$	32.5222			1.56654			0.783270	+	0.621682i	$0.213550\pi$
$432$		0			0
$433$	−34.9882	+	10.2735i	−1.68143	+	0.493711i	−0.976490	−	0.215561i	$-0.930842\pi$
$433$	−34.9882	+	10.2735i	−1.68143	+	0.493711i	−0.704935	+	0.709272i	$0.749024\pi$
$434$	−6.18002	−	3.97166i	−0.296650	−	0.190646i
$435$		0			0
$436$	13.8566	+	30.3417i	0.663610	+	1.45310i
$437$	−45.7384	−	29.3943i	−2.18797	−	1.40612i
$438$		0			0
$439$	19.9742			0.953319			0.476659	−	0.879088i	$-0.341848\pi$
$439$	19.9742			0.953319			0.476659	+	0.879088i	$0.341848\pi$
$440$	−1.91998			−0.0915314
$441$		0			0
$442$	−0.405759	−	2.82211i	−0.0193000	−	0.134234i
$443$	−18.6353	+	21.5062i	−0.885388	+	1.02179i	0.114211	+	0.993457i	$0.463566\pi$
$443$	−18.6353	+	21.5062i	−0.885388	+	1.02179i	−0.999598	+	0.0283355i	$0.990979\pi$
$444$		0			0
$445$	−2.84412	+	3.28229i	−0.134824	+	0.155595i
$446$	−4.27269	+	2.74589i	−0.202318	+	0.130022i
$447$		0			0
$448$	0.991486	+	6.89594i	0.0468433	+	0.325802i
$449$	−34.6098	+	22.2424i	−1.63334	+	1.04968i	−0.686922	+	0.726732i	$0.741038\pi$
$449$	−34.6098	+	22.2424i	−1.63334	+	1.04968i	−0.946416	+	0.322951i	$0.895325\pi$
$450$		0			0
$451$	3.13963	+	3.62333i	0.147840	+	0.170616i
$452$	−20.1963	+	23.3078i	−0.949954	+	1.09631i
$453$		0			0
$454$	−11.6825	−	25.5812i	−0.548288	−	1.20058i
$455$	−0.0999804	−	0.115383i	−0.00468715	−	0.00540926i
$456$		0			0
$457$	22.1392	+	6.50065i	1.03563	+	0.304088i	0.754997	−	0.655728i	$-0.227638\pi$
$457$	22.1392	+	6.50065i	1.03563	+	0.304088i	0.280630	+	0.959816i	$0.409457\pi$
$458$	2.38296	−	16.5738i	0.111348	−	0.774444i
$459$		0			0
$460$	−2.50010	+	5.47446i	−0.116568	+	0.255248i
$461$	2.61328	−	0.767328i	0.121713	−	0.0357380i	−0.220309	−	0.975430i	$-0.570707\pi$
$461$	2.61328	−	0.767328i	0.121713	−	0.0357380i	0.342022	+	0.939692i	$0.388888\pi$
$462$		0			0
$463$	−4.69086	−	32.6256i	−0.218003	−	1.51624i	−0.745397	−	0.666621i	$-0.767740\pi$
$463$	−4.69086	−	32.6256i	−0.218003	−	1.51624i	0.527394	−	0.849621i	$-0.323169\pi$
$464$	0.757322	−	5.26729i	0.0351578	−	0.244528i
$465$		0			0
$466$	26.7232	−	17.1740i	1.23793	−	0.795570i
$467$	−1.94526	+	4.25953i	−0.0900160	+	0.197108i	−0.949285	−	0.314416i	$-0.898191\pi$
$467$	−1.94526	+	4.25953i	−0.0900160	+	0.197108i	0.859269	+	0.511523i	$0.170919\pi$
$468$		0			0
$469$	3.75553	+	2.42578i	0.173414	+	0.112012i
$470$	−3.36096			−0.155030
$471$		0			0
$472$	1.38468	−	0.889878i	0.0637349	−	0.0409599i
$473$	−20.7463	−	23.9425i	−0.953915	−	1.10088i
$474$		0			0
$475$	−5.14080	−	35.7551i	−0.235876	−	1.64056i
$476$	0.853746	−	1.86944i	0.0391314	−	0.0856858i
$477$		0			0
$478$	20.3656	−	44.5944i	0.931501	−	2.03970i
$479$	27.8247	+	17.8819i	1.27134	+	0.817044i	0.989794	−	0.142503i	$-0.0455150\pi$
$479$	27.8247	+	17.8819i	1.27134	+	0.817044i	0.281550	+	0.959546i	$0.409151\pi$
$480$		0			0
$481$	4.72481	+	1.38733i	0.215433	+	0.0632568i
$482$	−48.7940	−	14.3272i	−2.22250	−	0.652586i
$483$		0			0
$484$	2.12441	+	4.65181i	0.0965641	+	0.211446i
$485$	−0.218519	+	1.51983i	−0.00992242	+	0.0690119i
$486$		0			0
$487$	−19.0731	−	22.0116i	−0.864286	−	0.997440i	−0.999978	−	0.00668857i	$-0.997871\pi$
$487$	−19.0731	−	22.0116i	−0.864286	−	0.997440i	0.135691	−	0.990751i	$-0.456675\pi$
$488$	−10.2928	−	22.5381i	−0.465934	−	1.02025i
$489$		0			0
$490$	0.598203	+	4.16060i	0.0270241	+	0.187957i
$491$	7.56919	+	4.86442i	0.341593	+	0.219528i	0.700177	−	0.713969i	$-0.253104\pi$
$491$	7.56919	+	4.86442i	0.341593	+	0.219528i	−0.358585	+	0.933497i	$0.616741\pi$
$492$		0			0
$493$	−2.95150	+	3.40621i	−0.132929	+	0.153408i
$494$	15.2481	+	4.47726i	0.686046	+	0.201441i
$495$		0			0
$496$	1.35117	+	9.39760i	0.0606694	+	0.421965i
$497$	2.31764	−	0.680520i	0.103960	−	0.0305255i
$498$		0			0
$499$	−7.67344			−0.343510			−0.171755	−	0.985140i	$-0.554944\pi$
$499$	−7.67344			−0.343510			−0.171755	+	0.985140i	$0.554944\pi$
$500$	−7.73634	+	2.27159i	−0.345980	+	0.101589i
$501$		0			0
$502$	−10.7166	−	23.4660i	−0.478303	−	1.04734i
$503$	6.96032	+	15.2410i	0.310345	+	0.679561i	0.998961	−	0.0455647i	$-0.0145087\pi$
$503$	6.96032	+	15.2410i	0.310345	+	0.679561i	−0.688616	+	0.725126i	$0.741781\pi$
$504$		0			0
$505$	4.63568	−	1.36116i	0.206285	−	0.0605707i
$506$	58.3487			2.59392
$507$		0			0
$508$	−28.8638	+	8.47517i	−1.28062	+	0.376025i
$509$	0.747769	+	5.20085i	0.0331443	+	0.230524i	0.999660	−	0.0260848i	$-0.00830400\pi$
$509$	0.747769	+	5.20085i	0.0331443	+	0.230524i	−0.966515	+	0.256608i	$0.917395\pi$
$510$		0			0
$511$	2.71990	+	0.798636i	0.120321	+	0.0353296i
$512$	11.1772	−	12.8992i	0.493967	−	0.570069i
$513$		0			0
$514$	−36.2879	−	23.3208i	−1.60059	−	1.02864i
$515$	−0.0240113	−	0.167002i	−0.00105806	−	0.00735900i
$516$		0			0
$517$	7.96116	+	17.4325i	0.350131	+	0.766681i
$518$	3.95226	+	4.56115i	0.173652	+	0.200406i
$519$		0			0
$520$	0.0750298	−	0.521844i	0.00329028	−	0.0228844i
$521$	1.41043	+	3.08842i	0.0617921	+	0.135306i	0.938009	−	0.346612i	$-0.112668\pi$
$521$	1.41043	+	3.08842i	0.0617921	+	0.135306i	−0.876217	+	0.481917i	$0.839941\pi$
$522$		0			0
$523$	4.78551	+	1.40515i	0.209256	+	0.0614430i	0.384680	−	0.923050i	$-0.374312\pi$
$523$	4.78551	+	1.40515i	0.209256	+	0.0614430i	−0.175425	+	0.984493i	$0.556130\pi$
$524$	−51.2898	−	15.0600i	−2.24060	−	0.657901i
$525$		0			0
$526$	2.04620	+	1.31501i	0.0892184	+	0.0573372i
$527$	3.34045	−	7.31457i	0.145512	−	0.318628i
$528$		0			0
$529$	13.2164	−	28.9398i	0.574624	−	1.25825i
$530$	−0.624716	−	4.34500i	−0.0271359	−	0.188735i
$531$		0			0
$532$	7.50158	+	8.65728i	0.325235	+	0.375341i
$533$	−1.10750	+	0.711748i	−0.0479712	+	0.0308292i
$534$		0			0
$535$	−0.533989			−0.0230864
$536$	2.16193	+	15.2865i	0.0933810	+	0.660274i
$537$		0			0
$538$	10.1848	−	22.3015i	0.439096	−	0.961486i
$539$	20.1630	−	12.9580i	0.868483	−	0.558140i
$540$		0			0
$541$	−0.597192	+	4.15356i	−0.0256753	+	0.178576i	−0.998624	−	0.0524469i	$-0.983298\pi$
$541$	−0.597192	+	4.15356i	−0.0256753	+	0.178576i	0.972948	+	0.231022i	$0.0742071\pi$
$542$	−0.138309	−	0.961959i	−0.00594087	−	0.0413197i
$543$		0			0
$544$	−9.10181	+	2.67253i	−0.390237	+	0.114584i
$545$	−1.38099	+	3.02394i	−0.0591550	+	0.129531i
$546$		0			0
$547$	−2.30946	+	16.0627i	−0.0987455	+	0.686790i	0.878973	+	0.476871i	$0.158229\pi$
$547$	−2.30946	+	16.0627i	−0.0987455	+	0.686790i	−0.977719	+	0.209919i	$0.932680\pi$
$548$	−27.7100	−	8.13640i	−1.18371	−	0.347570i
$549$		0			0
$550$	25.3867	+	29.2978i	1.08249	+	1.24926i
$551$	−10.4360	−	22.8516i	−0.444587	−	0.973510i
$552$		0			0
$553$	2.79087	−	3.22083i	0.118680	−	0.136964i
$554$	−14.9553	−	17.2594i	−0.635391	−	0.733281i
$555$		0			0
$556$	−43.5934	+	28.0158i	−1.84877	+	1.18813i
$557$	5.34345	+	37.1645i	0.226409	+	1.57471i	0.713054	+	0.701110i	$0.247312\pi$
$557$	5.34345	+	37.1645i	0.226409	+	1.57471i	−0.486645	+	0.873600i	$0.661779\pi$
$558$		0			0
$559$	7.31822	−	4.70313i	0.309528	−	0.198921i
$560$	−0.158368	+	0.182766i	−0.00669225	+	0.00772327i
$561$		0			0
$562$	−29.6056	+	34.1667i	−1.24884	+	1.44124i
$563$	−1.27221	−	8.84845i	−0.0536175	−	0.372918i	−0.998909	−	0.0466918i	$-0.985132\pi$
$563$	−1.27221	−	8.84845i	−0.0536175	−	0.372918i	0.945292	−	0.326226i	$-0.105777\pi$
$564$		0			0
$565$	−3.07367			−0.129310
$566$	−20.3098			−0.853684
$567$		0			0
$568$	7.01696	+	4.50953i	0.294425	+	0.189215i
$569$	−0.0245931	−	0.0538514i	−0.00103100	−	0.00225757i	0.909116	−	0.416543i	$-0.136759\pi$
$569$	−0.0245931	−	0.0538514i	−0.00103100	−	0.00225757i	−0.910147	+	0.414286i	$0.864031\pi$
$570$		0			0
$571$	11.5983	+	7.45376i	0.485373	+	0.311930i	0.760342	−	0.649523i	$-0.225031\pi$
$571$	11.5983	+	7.45376i	0.485373	+	0.311930i	−0.274969	+	0.961453i	$0.588668\pi$
$572$	−9.62427	+	2.82594i	−0.402411	+	0.118159i
$573$		0			0
$574$	−1.61351			−0.0673466
$575$	34.9435	−	10.2603i	1.45724	−	0.427886i
$576$		0			0
$577$	26.7559	−	30.8780i	1.11386	−	1.28547i	0.159375	−	0.987218i	$-0.449052\pi$
$577$	26.7559	−	30.8780i	1.11386	−	1.28547i	0.954488	−	0.298248i	$-0.0964024\pi$
$578$	−32.2739	−	9.47648i	−1.34242	−	0.394170i
$579$		0			0
$580$	−2.33937	+	1.50342i	−0.0971369	+	0.0624261i
$581$	−3.00207	−	1.92932i	−0.124547	−	0.0800415i
$582$		0			0
$583$	−21.0567	+	13.5323i	−0.872078	+	0.560450i
$584$	4.06642	+	8.90421i	0.168270	+	0.368459i
$585$		0			0
$586$	−47.2643	+	54.5459i	−1.95247	+	2.25327i
$587$	−5.29614	+	36.8354i	−0.218595	+	1.52036i	0.524636	+	0.851327i	$0.324201\pi$
$587$	−5.29614	+	36.8354i	−0.218595	+	1.52036i	−0.743231	+	0.669035i	$0.766708\pi$
$588$		0			0
$589$	29.3514	+	33.8734i	1.20940	+	1.39573i
$590$	0.525181	+	0.154207i	0.0216214	+	0.00634861i
$591$		0			0
$592$	1.11005	−	7.72060i	0.0456230	−	0.317315i
$593$	30.3866	+	19.5283i	1.24783	+	0.801931i	0.986570	−	0.163337i	$-0.0522259\pi$
$593$	30.3866	+	19.5283i	1.24783	+	0.801931i	0.261259	+	0.965269i	$0.415862\pi$
$594$		0			0
$595$	0.196527	−	0.0577055i	0.00805682	−	0.00236570i
$596$	3.08799	−	6.76176i	0.126489	−	0.276972i
$597$		0			0
$598$	−2.28018	+	15.8590i	−0.0932434	+	0.648522i
$599$	5.56121	+	6.41798i	0.227225	+	0.262231i	0.857901	−	0.513814i	$-0.171768\pi$
$599$	5.56121	+	6.41798i	0.227225	+	0.262231i	−0.630677	+	0.776046i	$0.717223\pi$
$600$		0			0
$601$	15.1590	−	33.1935i	0.618347	−	1.35399i	−0.298369	−	0.954451i	$-0.596442\pi$
$601$	15.1590	−	33.1935i	0.618347	−	1.35399i	0.916716	−	0.399540i	$-0.130830\pi$
$602$	10.6619			0.434545
$603$		0			0
$604$	26.3451			1.07197
$605$	−0.211725	+	0.463613i	−0.00860784	+	0.0188485i
$606$		0			0
$607$	6.95205	+	8.02309i	0.282175	+	0.325647i	0.879089	−	0.476658i	$-0.158152\pi$
$607$	6.95205	+	8.02309i	0.282175	+	0.325647i	−0.596914	+	0.802305i	$0.703607\pi$
$608$	7.52477	−	52.3359i	0.305170	−	2.12250i
$609$		0			0
$610$	3.42279	−	7.49487i	0.138585	−	0.303458i
$611$	−5.04921	+	1.48258i	−0.204269	+	0.0599788i
$612$		0			0
$613$	25.9153	+	16.6548i	1.04671	+	0.672680i	0.946638	−	0.322300i	$-0.104456\pi$
$613$	25.9153	+	16.6548i	1.04671	+	0.672680i	0.100073	+	0.994980i	$0.468092\pi$
$614$	4.07176	−	28.3197i	0.164323	−	1.14289i
$615$		0			0
$616$	−3.53517	−	1.03802i	−0.142436	−	0.0418230i
$617$	−3.99460	−	4.61001i	−0.160816	−	0.185592i	0.669623	−	0.742701i	$-0.266456\pi$
$617$	−3.99460	−	4.61001i	−0.160816	−	0.185592i	−0.830439	+	0.557109i	$0.811910\pi$
$618$		0			0
$619$	4.29086	−	29.8436i	0.172464	−	1.19952i	−0.701192	−	0.712972i	$-0.747349\pi$
$619$	4.29086	−	29.8436i	0.172464	−	1.19952i	0.873656	−	0.486543i	$-0.161742\pi$
$620$	3.24900	−	3.74955i	0.130483	−	0.150586i
$621$		0			0
$622$	−5.02873	−	11.0114i	−0.201634	−	0.441516i
$623$	−7.01128	+	4.50588i	−0.280901	+	0.180524i
$624$		0			0
$625$	20.0146	+	12.8626i	0.800582	+	0.514503i
$626$	21.6246	−	13.8973i	0.864292	−	0.555446i
$627$		0			0
$628$	−25.1820	−	7.39411i	−1.00487	−	0.295057i
$629$	−4.32620	+	4.99270i	−0.172497	+	0.199072i
$630$		0			0
$631$	−10.3693	+	3.04470i	−0.412795	+	0.121207i	−0.481534	−	0.876427i	$-0.659920\pi$
$631$	−10.3693	+	3.04470i	−0.412795	+	0.121207i	0.0687397	+	0.997635i	$0.478102\pi$
$632$	14.7166			0.585396
$633$		0			0
$634$	−4.45518	+	1.30816i	−0.176938	+	0.0519536i
$635$	−2.52216	−	1.62089i	−0.100089	−	0.0643232i
$636$		0			0
$637$	2.73400	+	5.98663i	0.108325	+	0.237199i
$638$	22.6806	+	14.5759i	0.897932	+	0.577066i
$639$		0			0
$640$	−3.90148			−0.154219
$641$	−29.3401			−1.15886			−0.579431	−	0.815021i	$-0.696725\pi$
$641$	−29.3401			−1.15886			−0.579431	+	0.815021i	$0.696725\pi$
$642$		0			0
$643$	3.70761	+	25.7870i	0.146214	+	1.01694i	0.922345	+	0.386368i	$0.126271\pi$
$643$	3.70761	+	25.7870i	0.146214	+	1.01694i	−0.776131	+	0.630572i	$0.782820\pi$
$644$	−7.56304	+	8.72821i	−0.298025	+	0.343940i
$645$		0			0
$646$	−13.9617	+	16.1127i	−0.549316	+	0.633944i
$647$	21.3283	−	13.7068i	0.838501	−	0.538872i	−0.0494680	−	0.998776i	$-0.515753\pi$
$647$	21.3283	−	13.7068i	0.838501	−	0.538872i	0.887969	+	0.459904i	$0.152116\pi$
$648$		0			0
$649$	−0.444169	−	3.08926i	−0.0174351	−	0.121264i
$650$	−8.95513	+	5.75511i	−0.351249	+	0.225734i
$651$		0			0
$652$	−20.7366	−	23.9313i	−0.812107	−	0.937221i
$653$	−6.21081	+	7.16766i	−0.243048	+	0.280492i	−0.864147	−	0.503240i	$-0.832141\pi$
$653$	−6.21081	+	7.16766i	−0.243048	+	0.280492i	0.621099	+	0.783732i	$0.286687\pi$
$654$		0			0
$655$	−2.21312	−	4.84606i	−0.0864738	−	0.189351i
$656$	1.36558	+	1.57597i	0.0533170	+	0.0615311i
$657$		0			0
$658$	−6.18839	−	1.81707i	−0.241248	−	0.0708369i
$659$	0.660761	−	4.59569i	0.0257396	−	0.179023i	−0.972896	−	0.231243i	$-0.925721\pi$
$659$	0.660761	−	4.59569i	0.0257396	−	0.179023i	0.998636	+	0.0522203i	$0.0166298\pi$
$660$		0			0
$661$	−4.73995	+	10.3790i	−0.184362	+	0.403698i	−0.979135	−	0.203210i	$-0.934863\pi$
$661$	−4.73995	+	10.3790i	−0.184362	+	0.403698i	0.794773	+	0.606907i	$0.207590\pi$
$662$	−1.29152	+	0.379225i	−0.0501964	+	0.0147390i
$663$		0			0
$664$	−1.75373	−	12.1975i	−0.0680579	−	0.473353i
$665$	−0.162475	+	1.13004i	−0.00630053	+	0.0438211i
$666$		0			0
$667$	21.3069	−	13.6931i	0.825008	−	0.530200i
$668$	−18.3125	+	40.0988i	−0.708532	+	1.55147i
$669$		0			0
$670$	−3.37097	+	3.87224i	−0.130232	+	0.149598i
$671$	−46.9817			−1.81371
$672$		0			0
$673$	−25.2653	+	16.2370i	−0.973905	+	0.625891i	−0.927813	−	0.373047i	$-0.878313\pi$
$673$	−25.2653	+	16.2370i	−0.973905	+	0.625891i	−0.0460922	+	0.998937i	$0.514677\pi$
$674$	16.1114	+	18.5936i	0.620588	+	0.716197i
$675$		0			0
$676$	4.89174	+	34.0228i	0.188144	+	1.30857i
$677$	15.3384	−	33.5863i	0.589501	−	1.29083i	−0.346242	−	0.938145i	$-0.612542\pi$
$677$	15.3384	−	33.5863i	0.589501	−	1.29083i	0.935743	−	0.352683i	$-0.114730\pi$
$678$		0			0
$679$	−1.22403	+	2.68025i	−0.0469740	+	0.102859i
$680$	0.595011	+	0.382391i	0.0228176	+	0.0146640i
$681$		0			0
$682$	−46.1529	−	13.5517i	−1.76729	−	0.518922i
$683$	−9.30659	−	2.73266i	−0.356107	−	0.104562i	0.0987858	−	0.995109i	$-0.468504\pi$
$683$	−9.30659	−	2.73266i	−0.356107	−	0.104562i	−0.454893	+	0.890546i	$0.650322\pi$
$684$		0			0
$685$	−1.19567	−	2.61815i	−0.0456842	−	0.100034i
$686$	−2.34699	+	16.3237i	−0.0896085	+	0.623241i
$687$		0			0
$688$	−9.02358	−	10.4138i	−0.344021	−	0.397021i
$689$	−2.85517	−	6.25195i	−0.108773	−	0.238181i
$690$		0			0
$691$	0.843754	+	5.86844i	0.0320979	+	0.223246i	0.999556	−	0.0297840i	$-0.00948195\pi$
$691$	0.843754	+	5.86844i	0.0320979	+	0.223246i	−0.967458	+	0.253030i	$0.918573\pi$
$692$	29.5165	+	18.9691i	1.12205	+	0.721098i
$693$		0			0
$694$	18.1286	−	20.9216i	0.688153	−	0.794171i
$695$	−4.95529	−	1.45501i	−0.187965	−	0.0551915i
$696$		0			0
$697$	−0.251352	−	1.74819i	−0.00952063	−	0.0662174i
$698$	−46.5748	+	13.6756i	−1.76288	+	0.517629i
$699$		0			0
$700$	−7.67315			−0.290018
$701$	4.58927	−	1.34753i	0.173334	−	0.0508955i	−0.193914	−	0.981019i	$-0.562118\pi$
$701$	4.58927	−	1.34753i	0.173334	−	0.0508955i	0.367248	+	0.930123i	$0.380300\pi$
$702$		0			0
$703$	−15.2967	−	33.4950i	−0.576924	−	1.26329i
$704$	18.9502	+	41.4951i	0.714211	+	1.56390i
$705$		0			0
$706$	−19.7070	+	5.78650i	−0.741683	+	0.217778i
$707$	9.27136			0.348685
$708$		0			0
$709$	−3.42695	+	1.00624i	−0.128702	+	0.0377903i	−0.345449	−	0.938437i	$-0.612273\pi$
$709$	−3.42695	+	1.00624i	−0.128702	+	0.0377903i	0.216747	+	0.976228i	$0.430455\pi$
$710$	0.394747	+	2.74552i	0.0148146	+	0.103038i
$711$		0			0
$712$	−27.6140	−	8.10822i	−1.03488	−	0.303868i
$713$	−29.5919	+	34.1509i	−1.10823	+	1.27896i
$714$		0			0
$715$	−0.840982	−	0.540467i	−0.0314510	−	0.0202123i
$716$	5.11233	+	35.5571i	0.191057	+	1.32883i
$717$		0			0
$718$	22.4125	+	49.0765i	0.836426	+	1.83152i
$719$	−12.9385	−	14.9318i	−0.482523	−	0.556862i	0.461329	−	0.887229i	$-0.347373\pi$
$719$	−12.9385	−	14.9318i	−0.482523	−	0.556862i	−0.943852	+	0.330367i	$0.892827\pi$
$720$		0			0
$721$	0.0460773	−	0.320475i	0.00171601	−	0.0119351i
$722$	−31.9732	−	70.0115i	−1.18992	−	2.60556i
$723$		0			0
$724$	61.5648	+	18.0771i	2.28804	+	0.671829i
$725$	16.1459	+	4.74087i	0.599644	+	0.176071i
$726$		0			0
$727$	38.7246	+	24.8868i	1.43622	+	0.923001i	0.999729	+	0.0232908i	$0.00741435\pi$
$727$	38.7246	+	24.8868i	1.43622	+	0.923001i	0.436488	+	0.899710i	$0.356222\pi$
$728$	0.420279	−	0.920283i	0.0155766	−	0.0341079i
$729$		0			0
$730$	−1.35225	+	2.96102i	−0.0500491	+	0.109592i
$731$	1.66090	+	11.5518i	0.0614306	+	0.427259i
$732$		0			0
$733$	3.39442	+	3.91737i	0.125376	+	0.144691i	0.814967	−	0.579508i	$-0.196755\pi$
$733$	3.39442	+	3.91737i	0.125376	+	0.144691i	−0.689591	+	0.724199i	$0.742210\pi$
$734$	−41.5473	+	26.7008i	−1.53354	+	0.985546i
$735$		0			0
$736$	53.3073			1.96493
$737$	28.0692	+	8.31216i	1.03394	+	0.306182i
$738$		0			0
$739$	−6.36588	+	13.9393i	−0.234173	+	0.512767i	−0.989839	−	0.142190i	$-0.954586\pi$
$739$	−6.36588	+	13.9393i	−0.234173	+	0.512767i	0.755667	+	0.654956i	$0.227313\pi$
$740$	−3.42896	+	2.20366i	−0.126051	+	0.0810081i
$741$		0			0
$742$	1.19882	−	8.33799i	0.0440101	−	0.306097i
$743$	0.254925	+	1.77304i	0.00935228	+	0.0650466i	0.993963	−	0.109715i	$-0.0349937\pi$
$743$	0.254925	+	1.77304i	0.00935228	+	0.0650466i	−0.984611	+	0.174761i	$0.944085\pi$
$744$		0			0
$745$	0.710836	−	0.208720i	0.0260430	−	0.00764692i
$746$	−18.3810	+	40.2488i	−0.672977	+	1.47361i
$747$		0			0
$748$	1.91510	−	13.3198i	0.0700229	−	0.487020i
$749$	−0.983209	−	0.288696i	−0.0359257	−	0.0105487i
$750$		0			0
$751$	−12.1719	−	14.0471i	−0.444159	−	0.512586i	0.488886	−	0.872348i	$-0.337403\pi$
$751$	−12.1719	−	14.0471i	−0.444159	−	0.512586i	−0.933044	+	0.359762i	$0.882858\pi$
$752$	3.46270	+	7.58226i	0.126272	+	0.276497i
$753$		0			0
$754$	−4.84801	+	5.59490i	−0.176554	+	0.203754i
$755$	1.71942	+	1.98432i	0.0625762	+	0.0722168i
$756$		0			0
$757$	6.71681	−	4.31663i	0.244127	−	0.156891i	−0.412856	−	0.910796i	$-0.635469\pi$
$757$	6.71681	−	4.31663i	0.244127	−	0.156891i	0.656983	+	0.753906i	$0.271832\pi$
$758$	−7.48998	−	52.0940i	−0.272048	−	1.89214i
$759$		0			0
$760$	−3.31652	+	2.13140i	−0.120303	+	0.0773139i
$761$	−6.63262	+	7.65445i	−0.240432	+	0.277474i	−0.863122	−	0.504995i	$-0.831494\pi$
$761$	−6.63262	+	7.65445i	−0.240432	+	0.277474i	0.622690	+	0.782469i	$0.286040\pi$
$762$		0			0
$763$	−4.17762	+	4.82123i	−0.151240	+	0.174540i
$764$	−4.49039	−	31.2313i	−0.162456	−	1.12991i
$765$		0			0
$766$	−21.4327			−0.774395
$767$	0.857009			0.0309448
$768$		0			0
$769$	1.75606	+	1.12855i	0.0633253	+	0.0406967i	0.571920	−	0.820309i	$-0.306199\pi$
$769$	1.75606	+	1.12855i	0.0633253	+	0.0406967i	−0.508595	+	0.861006i	$0.669835\pi$
$770$	−0.508975	−	1.11450i	−0.0183422	−	0.0401638i
$771$		0			0
$772$	−7.86292	−	5.05319i	−0.282993	−	0.181868i
$773$	6.90178	−	2.02654i	0.248240	−	0.0728898i	−0.155246	−	0.987876i	$-0.549617\pi$
$773$	6.90178	−	2.02654i	0.248240	−	0.0728898i	0.403485	+	0.914986i	$0.367799\pi$
$774$		0			0
$775$	−30.0228			−1.07845
$776$	−9.76270	+	2.86659i	−0.350460	+	0.102904i
$777$		0			0
$778$	−16.5559	+	19.1065i	−0.593558	+	0.685003i
$779$	9.44563	+	2.77349i	0.338425	+	0.0993705i
$780$		0			0
$781$	13.3053	−	8.55081i	0.476102	−	0.305972i
$782$	−18.0826	−	11.6210i	−0.646631	−	0.415565i
$783$		0			0
$784$	8.76990	−	5.63607i	0.313211	−	0.201288i
$785$	−1.08659	−	2.37930i	−0.0387820	−	0.0849208i
$786$		0			0
$787$	1.20779	−	1.39386i	0.0430531	−	0.0496859i	−0.733815	−	0.679350i	$-0.762262\pi$
$787$	1.20779	−	1.39386i	0.0430531	−	0.0496859i	0.776868	+	0.629664i	$0.216807\pi$
$788$	10.0996	−	70.2445i	0.359785	−	2.50236i
$789$		0			0
$790$	3.20482	+	3.69856i	0.114022	+	0.131589i
$791$	−5.65940	−	1.66175i	−0.201225	−	0.0590850i
$792$		0			0
$793$	1.83597	−	12.7695i	0.0651973	−	0.453457i
$794$	57.0668	+	36.6746i	2.02523	+	1.30153i
$795$		0			0
$796$	34.7810	−	10.2126i	1.23278	−	0.361976i
$797$	18.5672	−	40.6564i	0.657682	−	1.44012i	−0.226984	−	0.973898i	$-0.572886\pi$
$797$	18.5672	−	40.6564i	0.657682	−	1.44012i	0.884666	−	0.466225i	$-0.154386\pi$
$798$		0			0
$799$	1.00472	−	6.98800i	0.0355445	−	0.247218i
$800$	23.1933	+	26.7665i	0.820007	+	0.946338i
$801$		0			0
$802$	13.1609	−	28.8184i	0.464729	−	1.01761i
$803$	18.5612			0.655011
$804$		0			0
$805$	−1.15102			−0.0405680
$806$	5.48689	−	12.0146i	0.193268	−	0.423197i
$807$		0			0
$808$	20.9657	+	24.1958i	0.737572	+	0.851204i
$809$	−4.51678	+	31.4149i	−0.158802	+	1.10449i	0.742044	+	0.670351i	$0.233856\pi$
$809$	−4.51678	+	31.4149i	−0.158802	+	1.10449i	−0.900846	+	0.434139i	$0.857053\pi$
$810$		0			0
$811$	−9.02380	+	19.7594i	−0.316869	+	0.693845i	−0.999312	−	0.0370932i	$-0.988190\pi$
$811$	−9.02380	+	19.7594i	−0.316869	+	0.693845i	0.682443	+	0.730939i	$0.260917\pi$
$812$	−5.12018	+	1.50342i	−0.179683	+	0.0527597i
$813$		0			0
$814$	33.2444	+	21.3648i	1.16521	+	0.748838i
$815$	0.449130	−	3.12377i	0.0157323	−	0.109421i
$816$		0			0
$817$	−62.4154	−	18.3268i	−2.18364	−	0.641175i
$818$	−30.0565	−	34.6871i	−1.05090	−	1.21280i
$819$		0			0
$820$	0.155082	−	1.07862i	0.00541568	−	0.0376669i
$821$	−3.62234	+	4.18041i	−0.126421	+	0.145897i	−0.815431	−	0.578854i	$-0.803500\pi$
$821$	−3.62234	+	4.18041i	−0.126421	+	0.145897i	0.689010	+	0.724752i	$0.258045\pi$
$822$		0			0
$823$	4.80851	+	10.5292i	0.167614	+	0.367024i	0.974736	−	0.223362i	$-0.0717031\pi$
$823$	4.80851	+	10.5292i	0.167614	+	0.367024i	−0.807122	+	0.590385i	$0.798976\pi$
$824$	0.940551	−	0.604455i	0.0327656	−	0.0210572i
$825$		0			0
$826$	0.883621	+	0.567869i	0.0307451	+	0.0197587i
$827$	1.44149	−	0.926390i	0.0501255	−	0.0322137i	−0.515338	−	0.856987i	$-0.672334\pi$
$827$	1.44149	−	0.926390i	0.0501255	−	0.0322137i	0.565464	+	0.824773i	$0.308697\pi$
$828$		0			0
$829$	−25.5613	−	7.50548i	−0.887781	−	0.260676i	−0.194120	−	0.980978i	$-0.562185\pi$
$829$	−25.5613	−	7.50548i	−0.887781	−	0.260676i	−0.693661	+	0.720302i	$0.744003\pi$
$830$	2.68354	−	3.09697i	0.0931469	−	0.107497i
$831$		0			0
$832$	−12.0188	+	3.52903i	−0.416676	+	0.122347i
$833$	−8.82940			−0.305920
$834$		0			0
$835$	−4.21542	+	1.23776i	−0.145881	+	0.0428345i
$836$	63.0993	+	40.5515i	2.18234	+	1.40250i
$837$		0			0
$838$	24.1506	+	52.8824i	0.834268	+	1.82679i
$839$	37.5911	+	24.1583i	1.29779	+	0.834038i	0.992969	−	0.118373i	$-0.0377678\pi$
$839$	37.5911	+	24.1583i	1.29779	+	0.834038i	0.304819	+	0.952410i	$0.401404\pi$
$840$		0			0
$841$	−17.2972			−0.596455
$842$	11.8403			0.408044
$843$		0			0
$844$	−3.76756	−	26.2040i	−0.129685	−	0.901978i
$845$	−2.24335	+	2.58896i	−0.0771734	+	0.0890629i
$846$		0			0
$847$	−0.640487	+	0.739162i	−0.0220074	+	0.0253979i
$848$	−9.15859	+	5.88587i	−0.314507	+	0.202122i
$849$		0			0
$850$	−2.03240	−	14.1357i	−0.0697109	−	0.484850i
$851$	31.2309	−	20.0709i	1.07058	−	0.688022i
$852$		0			0
$853$	−24.0374	−	27.7406i	−0.823024	−	0.949820i	0.176381	−	0.984322i	$-0.443561\pi$
$853$	−24.0374	−	27.7406i	−0.823024	−	0.949820i	−0.999405	+	0.0345019i	$0.989016\pi$
$854$	10.3543	−	11.9494i	0.354315	−	0.408902i
$855$		0			0
$856$	−1.46996	−	3.21875i	−0.0502421	−	0.110015i
$857$	13.5874	+	15.6807i	0.464137	+	0.535643i	0.938772	−	0.344540i	$-0.111965\pi$
$857$	13.5874	+	15.6807i	0.464137	+	0.535643i	−0.474634	+	0.880183i	$0.657420\pi$
$858$		0			0
$859$	37.7484	+	11.0839i	1.28796	+	0.378179i	0.852830	−	0.522189i	$-0.174885\pi$
$859$	37.7484	+	11.0839i	1.28796	+	0.378179i	0.435129	+	0.900368i	$0.356703\pi$
$860$	−1.02476	+	7.12735i	−0.0349440	+	0.243041i
$861$		0			0
$862$	−29.7713	+	65.1901i	−1.01402	+	2.22038i
$863$	−22.8978	+	6.72340i	−0.779450	+	0.228867i	−0.647170	−	0.762345i	$-0.724048\pi$
$863$	−22.8978	+	6.72340i	−0.779450	+	0.228867i	−0.132279	+	0.991212i	$0.542230\pi$
$864$		0			0
$865$	0.497648	+	3.46122i	0.0169205	+	0.117685i
$866$	11.4358	−	79.5376i	0.388604	−	2.70280i
$867$		0			0
$868$	8.00940	−	5.14733i	0.271857	−	0.174712i
$869$	11.5922	−	25.3834i	0.393239	−	0.861074i
$870$		0			0
$871$	−3.35612	+	7.30430i	−0.113718	+	0.247497i
$872$	−22.0291			−0.746001
$873$		0			0
$874$	100.790	−	64.7738i	3.40927	−	2.19100i
$875$	−1.00983	−	1.16541i	−0.0341385	−	0.0393979i
$876$		0			0
$877$	2.65800	+	18.4868i	0.0897543	+	0.624255i	0.984198	+	0.177074i	$0.0566631\pi$
$877$	2.65800	+	18.4868i	0.0897543	+	0.624255i	−0.894443	+	0.447181i	$0.852428\pi$
$878$	−18.2847	+	40.0380i	−0.617080	+	1.35122i
$879$		0			0
$880$	−0.657800	+	1.44038i	−0.0221744	+	0.0485552i
$881$	−16.1239	−	10.3622i	−0.543227	−	0.349111i	0.240073	−	0.970755i	$-0.422829\pi$
$881$	−16.1239	−	10.3622i	−0.543227	−	0.349111i	−0.783300	+	0.621644i	$0.786465\pi$
$882$		0			0
$883$	38.8494	+	11.4072i	1.30739	+	0.383883i	0.859925	−	0.510421i	$-0.170510\pi$
$883$	38.8494	+	11.4072i	1.30739	+	0.383883i	0.447460	+	0.894304i	$0.352329\pi$
$884$	3.54544	+	1.04103i	0.119246	+	0.0350138i
$885$		0			0
$886$	−26.0498	−	57.0411i	−0.875160	−	1.91633i
$887$	6.99387	−	48.6435i	0.234831	−	1.63329i	−0.441905	−	0.897062i	$-0.645697\pi$
$887$	6.99387	−	48.6435i	0.234831	−	1.63329i	0.676736	−	0.736226i	$-0.263394\pi$
$888$		0			0
$889$	−3.76761	−	4.34806i	−0.126362	−	0.145829i
$890$	−3.97573	−	8.70563i	−0.133267	−	0.291813i
$891$		0			0
$892$	−0.936776	−	6.51542i	−0.0313656	−	0.218152i
$893$	33.1040	+	21.2746i	1.10778	+	0.711928i
$894$		0			0
$895$	−2.34451	+	2.70571i	−0.0783683	+	0.0904418i
$896$	−7.18361	−	2.10930i	−0.239988	−	0.0704667i
$897$		0			0
$898$	−12.9020	−	89.7356i	−0.430546	−	2.99452i
$899$	−20.0337	+	5.88243i	−0.668162	+	0.196190i
$900$		0			0
$901$	9.22072			0.307187
$902$	−10.1370	+	2.97648i	−0.337524	+	0.0991059i
$903$		0			0
$904$	−8.46114	−	18.5273i	−0.281413	−	0.616209i
$905$	2.65648	+	5.81688i	0.0883045	+	0.193360i
$906$		0			0
$907$	33.3691	−	9.79804i	1.10800	−	0.325339i	0.323975	−	0.946066i	$-0.394981\pi$
$907$	33.3691	−	9.79804i	1.10800	−	0.325339i	0.784027	+	0.620727i	$0.213162\pi$
$908$	36.4473			1.20955
$909$		0			0
$910$	0.322807	−	0.0947848i	0.0107010	−	0.00314209i
$911$	−2.14785	−	14.9386i	−0.0711613	−	0.494938i	−0.993968	−	0.109674i	$-0.965019\pi$
$911$	−2.14785	−	14.9386i	−0.0711613	−	0.494938i	0.922806	−	0.385264i	$-0.125890\pi$
$912$		0			0
$913$	−22.4197	−	6.58303i	−0.741985	−	0.217866i
$914$	−33.2970	+	38.4267i	−1.10137	+	1.27104i
$915$		0			0
$916$	18.2559	+	11.7324i	0.603192	+	0.387648i
$917$	−1.45494	−	10.1193i	−0.0480463	−	0.334169i
$918$		0			0
$919$	−21.8018	−	47.7392i	−0.719174	−	1.57477i	−0.815058	−	0.579379i	$-0.803295\pi$
$919$	−21.8018	−	47.7392i	−0.719174	−	1.57477i	0.0958838	−	0.995393i	$-0.469432\pi$
$920$	−2.60284	−	3.00384i	−0.0858132	−	0.0990337i
$921$		0			0
$922$	−0.854142	+	5.94069i	−0.0281297	+	0.195646i
$923$	1.80413	+	3.95049i	0.0593837	+	0.130032i
$924$		0			0
$925$	23.6661	+	6.94899i	0.778136	+	0.228481i
$926$	69.6915	+	20.4633i	2.29020	+	0.672465i
$927$		0			0
$928$	20.7210	+	13.3165i	0.680199	+	0.437137i
$929$	−6.43052	+	14.0809i	−0.210979	+	0.461979i	−0.985304	−	0.170809i	$-0.945362\pi$
$929$	−6.43052	+	14.0809i	−0.210979	+	0.461979i	0.774326	+	0.632787i	$0.218089\pi$
$930$		0			0
$931$	20.4442	−	44.7666i	0.670032	−	1.46716i
$932$	5.85899	+	40.7502i	0.191918	+	1.33482i
$933$		0			0
$934$	−6.75742	−	7.79848i	−0.221109	−	0.255174i
$935$	1.12824	−	0.725076i	0.0368974	−	0.0237125i
$936$		0			0
$937$	−39.5235			−1.29118			−0.645588	−	0.763686i	$-0.723388\pi$
$937$	−39.5235			−1.29118			−0.645588	+	0.763686i	$0.723388\pi$
$938$	−8.30029	+	5.30729i	−0.271014	+	0.173289i
$939$		0			0
$940$	1.80949	−	3.96223i	0.0590191	−	0.129234i
$941$	−7.18636	+	4.61840i	−0.234269	+	0.150555i	−0.652509	−	0.757781i	$-0.726283\pi$
$941$	−7.18636	+	4.61840i	−0.234269	+	0.150555i	0.418240	+	0.908337i	$0.362647\pi$
$942$		0			0
$943$	−1.41248	+	9.82403i	−0.0459967	+	0.319914i
$944$	−0.193191	−	1.34367i	−0.00628783	−	0.0437328i
$945$		0			0
$946$	66.9837	−	19.6682i	2.17783	−	0.639468i
$947$	3.45450	−	7.56431i	0.112256	−	0.245807i	−0.845163	−	0.534509i	$-0.820496\pi$
$947$	3.45450	−	7.56431i	0.112256	−	0.245807i	0.957419	+	0.288702i	$0.0932238\pi$
$948$		0			0
$949$	−0.725343	+	5.04487i	−0.0235456	+	0.163764i
$950$	76.3763	+	22.4261i	2.47797	+	0.727599i
$951$		0			0
$952$	0.888831	+	1.02577i	0.0288072	+	0.0332453i
$953$	−1.18325	−	2.59096i	−0.0383293	−	0.0839295i	0.889499	−	0.456937i	$-0.151054\pi$
$953$	−1.18325	−	2.59096i	−0.0383293	−	0.0839295i	−0.927828	+	0.373008i	$0.878326\pi$
$954$		0			0
$955$	2.05928	−	2.37654i	0.0666369	−	0.0769031i
$956$	41.6078	+	48.0179i	1.34569	+	1.55301i
$957$		0			0
$958$	−61.3150	+	39.4048i	−1.98100	+	1.27311i
$959$	−0.786051	−	5.46711i	−0.0253829	−	0.176542i
$960$		0			0
$961$	5.25954	−	3.38010i	0.169662	−	0.109035i
$962$	−7.10603	+	8.20080i	−0.229108	+	0.264404i
$963$		0			0
$964$	43.1602	−	49.8096i	1.39010	−	1.60426i
$965$	−0.132569	−	0.922035i	−0.00426754	−	0.0296814i
$966$		0			0
$967$	52.4305			1.68605			0.843025	−	0.537874i	$-0.180772\pi$
$967$	52.4305			1.68605			0.843025	+	0.537874i	$0.180772\pi$
$968$	−3.37738			−0.108553
$969$		0			0
$970$	−2.84643	−	1.82929i	−0.0913935	−	0.0587350i
$971$	−11.2254	−	24.5803i	−0.360241	−	0.788818i	−0.999798	−	0.0200748i	$-0.993610\pi$
$971$	−11.2254	−	24.5803i	−0.360241	−	0.788818i	0.639557	−	0.768744i	$-0.279118\pi$
$972$		0			0
$973$	−8.33731	−	5.35807i	−0.267282	−	0.171772i
$974$	61.5816	−	18.0820i	1.97320	−	0.579384i
$975$		0			0
$976$	−20.4347			−0.654097
$977$	−17.7363	+	5.20786i	−0.567436	+	0.166614i	−0.552852	−	0.833280i	$-0.686460\pi$
$977$	−17.7363	+	5.20786i	−0.567436	+	0.166614i	−0.0145837	+	0.999894i	$0.504642\pi$
$978$		0			0
$979$	−35.7366	+	41.2423i	−1.14215	+	1.31811i
$980$	−5.22698	−	1.53478i	−0.166970	−	0.0490268i
$981$		0			0
$982$	−16.6796	+	10.7193i	−0.532267	+	0.342067i
$983$	−29.6994	−	19.0866i	−0.947264	−	0.608769i	−0.0268181	−	0.999640i	$-0.508537\pi$
$983$	−29.6994	−	19.0866i	−0.947264	−	0.608769i	−0.920445	+	0.390871i	$0.872174\pi$
$984$		0			0
$985$	5.94999	−	3.82383i	0.189582	−	0.121837i
$986$	−4.12583	−	9.03431i	−0.131393	−	0.287711i
$987$		0			0
$988$	−13.4876	+	15.5655i	−0.429097	+	0.495205i
$989$	9.33349	−	64.9159i	0.296788	−	2.06420i
$990$		0			0
$991$	0.0496487	+	0.0572976i	0.00157714	+	0.00182012i	0.756538	−	0.653950i	$-0.226889\pi$
$991$	0.0496487	+	0.0572976i	0.00157714	+	0.00182012i	−0.754960	+	0.655770i	$0.772344\pi$
$992$	−42.1652	−	12.3808i	−1.33875	−	0.393092i
$993$		0			0
$994$	−0.757513	+	5.26862i	−0.0240269	+	0.167110i
$995$	3.03921	+	1.95318i	0.0963494	+	0.0619200i
$996$		0			0
$997$	41.9162	−	12.3077i	1.32750	−	0.389789i	0.460305	−	0.887761i	$-0.347740\pi$
$997$	41.9162	−	12.3077i	1.32750	−	0.389789i	0.867193	+	0.497972i	$0.165922\pi$
$998$	7.02438	−	15.3813i	0.222353	−	0.486885i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.u.a.91.1		10
3.2	odd	2		67.2.e.b.24.1	yes	10
67.14	even	11	inner	603.2.u.a.550.1		10
201.14	odd	22		67.2.e.b.14.1	✓	10
201.125	even	22		4489.2.a.h.1.1		5
201.143	odd	22		4489.2.a.i.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.b.14.1	✓	10	201.14	odd	22
67.2.e.b.24.1	yes	10	3.2	odd	2
603.2.u.a.91.1		10	1.1	even	1	trivial
603.2.u.a.550.1		10	67.14	even	11	inner
4489.2.a.h.1.1		5	201.125	even	22
4489.2.a.i.1.5		5	201.143	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.915415 + 2.00448i) q^{2} +(-1.87023 - 2.15836i) q^{4} +(0.0405070 - 0.281733i) q^{5} +(0.226900 - 0.496841i) q^{7} +(1.80972 - 0.531382i) q^{8} +(0.527646 + 0.339098i) q^{10} +(0.508975 - 3.54000i) q^{11} +(0.942270 + 0.276675i) q^{13} +(0.788201 + 0.909632i) q^{14} +(0.221378 - 1.53972i) q^{16} +(-0.862774 + 0.995695i) q^{17} +(-3.05062 - 6.67992i) q^{19} +(-0.683838 + 0.439476i) q^{20} +(6.62993 + 4.26080i) q^{22} +(6.22839 - 4.00274i) q^{23} +(4.71973 + 1.38584i) q^{25} +(-1.41716 + 1.63549i) q^{26} +(-1.49672 + 0.439476i) q^{28} +3.42094 q^{29} +(-5.85621 + 1.71954i) q^{31} +(6.05710 + 3.89266i) q^{32} +(-1.20605 - 2.64089i) q^{34} +(-0.130785 - 0.0840506i) q^{35} +5.01428 q^{37} +16.1823 q^{38} +(-0.0764012 - 0.531382i) q^{40} +(-0.877875 + 1.01312i) q^{41} +(5.80088 - 6.69457i) q^{43} +(-8.59250 + 5.52206i) q^{44} +(2.32186 + 16.1489i) q^{46} +(-4.50791 + 2.89705i) q^{47} +(4.38866 + 5.06478i) q^{49} +(-7.09840 + 8.19199i) q^{50} +(-1.16510 - 2.55121i) q^{52} +(-4.58316 - 5.28925i) q^{53} +(-0.976716 - 0.286790i) q^{55} +(0.146613 - 1.01971i) q^{56} +(-3.13158 + 6.85720i) q^{58} +(0.837324 - 0.245860i) q^{59} +(-1.86953 - 13.0029i) q^{61} +(1.91408 - 13.3127i) q^{62} +(-10.7303 + 6.89594i) q^{64} +(0.116117 - 0.254261i) q^{65} +(-1.18356 + 8.09933i) q^{67} +3.76266 q^{68} +(0.288201 - 0.185215i) q^{70} +(2.89602 + 3.34218i) q^{71} +(0.738601 + 5.13708i) q^{73} +(-4.59015 + 10.0510i) q^{74} +(-8.71232 + 19.0773i) q^{76} +(-1.64333 - 1.05610i) q^{77} +(7.48653 + 2.19824i) q^{79} +(-0.424822 - 0.124739i) q^{80} +(-1.22716 - 2.68711i) q^{82} +(0.929807 - 6.46695i) q^{83} +(0.245571 + 0.283404i) q^{85} +(8.10892 + 17.7561i) q^{86} +(-0.959989 - 6.67687i) q^{88} +(-12.8365 - 8.24949i) q^{89} +(0.351265 - 0.405381i) q^{91} +(-20.2879 - 5.95707i) q^{92} +(-1.68048 - 11.6880i) q^{94} +(-2.00552 + 0.588874i) q^{95} -5.39459 q^{97} +(-14.1697 + 4.16060i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28}+ \cdots - 47 q^{98}+O(q^{100}) \) 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more