LMFDB - Embedded newform 968.2.c.h.485.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [968,2,Mod(485,968)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("968.485"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$968 = 2^{3} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	968.c (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,2,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} - x^{18} - 2 x^{16} - 2 x^{15} - 4 x^{14} - 4 x^{13} + 12 x^{12} + 16 x^{11} + 32 x^{9} + \cdots + 1024$ x^20 - x^18 - 2x^16 - 2x^15 - 4x^14 - 4x^13 + 12x^12 + 16x^11 + 32x^9 + 48x^8 - 32x^7 - 64x^6 - 64x^5 - 128x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{4}$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			485.5
Root			$-1.07012 + 0.924577i$ of defining polynomial
Character	$\chi$	$=$	968.485
Dual form			968.2.c.h.485.6

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07012 - 0.924577i) q^{2} +0.321222i q^{3} +(0.290315 + 1.97882i) q^{4} -1.28733i q^{5} +(0.296994 - 0.343746i) q^{6} -3.30669 q^{7} +(1.51890 - 2.38599i) q^{8} +2.89682 q^{9} +(-1.19023 + 1.37759i) q^{10} +(-0.635639 + 0.0932556i) q^{12} +3.08618i q^{13} +(3.53855 + 3.05728i) q^{14} +0.413517 q^{15} +(-3.83143 + 1.14896i) q^{16} -3.19795 q^{17} +(-3.09994 - 2.67833i) q^{18} +4.71799i q^{19} +(2.54738 - 0.373730i) q^{20} -1.06218i q^{21} -3.47634 q^{23} +(0.766432 + 0.487902i) q^{24} +3.34279 q^{25} +(2.85341 - 3.30259i) q^{26} +1.89419i q^{27} +(-0.959982 - 6.54333i) q^{28} -6.19081i q^{29} +(-0.442513 - 0.382328i) q^{30} -2.67961 q^{31} +(5.16240 + 2.31293i) q^{32} +(3.42219 + 2.95675i) q^{34} +4.25678i q^{35} +(0.840991 + 5.73227i) q^{36} +7.84394i q^{37} +(4.36214 - 5.04882i) q^{38} -0.991349 q^{39} +(-3.07155 - 1.95531i) q^{40} +5.18518 q^{41} +(-0.982066 + 1.13666i) q^{42} +2.37086i q^{43} -3.72915i q^{45} +(3.72010 + 3.21414i) q^{46} +3.19353 q^{47} +(-0.369072 - 1.23074i) q^{48} +3.93417 q^{49} +(-3.57719 - 3.09067i) q^{50} -1.02725i q^{51} +(-6.10699 + 0.895967i) q^{52} +4.72284i q^{53} +(1.75132 - 2.02701i) q^{54} +(-5.02251 + 7.88972i) q^{56} -1.51552 q^{57} +(-5.72388 + 6.62491i) q^{58} +14.1440i q^{59} +(0.120050 + 0.818274i) q^{60} +15.5658i q^{61} +(2.86751 + 2.47751i) q^{62} -9.57886 q^{63} +(-3.38591 - 7.24815i) q^{64} +3.97292 q^{65} +4.70162i q^{67} +(-0.928413 - 6.32815i) q^{68} -1.11668i q^{69} +(3.93572 - 4.55527i) q^{70} -9.17365 q^{71} +(4.39996 - 6.91178i) q^{72} -0.939086 q^{73} +(7.25233 - 8.39396i) q^{74} +1.07378i q^{75} +(-9.33604 + 1.36970i) q^{76} +(1.06086 + 0.916578i) q^{78} +9.56575 q^{79} +(1.47909 + 4.93230i) q^{80} +8.08200 q^{81} +(-5.54877 - 4.79410i) q^{82} -1.27824i q^{83} +(2.10186 - 0.308367i) q^{84} +4.11680i q^{85} +(2.19204 - 2.53711i) q^{86} +1.98862 q^{87} +15.3866 q^{89} +(-3.44788 + 3.99063i) q^{90} -10.2050i q^{91} +(-1.00924 - 6.87904i) q^{92} -0.860749i q^{93} +(-3.41746 - 2.95266i) q^{94} +6.07359 q^{95} +(-0.742962 + 1.65827i) q^{96} -13.9642 q^{97} +(-4.21004 - 3.63744i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30}+ \cdots - 72 q^{98}+O(q^{100})$ 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9 - 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 + 2 * q^17 - 5 * q^18 - 16 * q^20 - 4 * q^23 + 15 * q^24 - 2 * q^25 + 30 * q^26 - 14 * q^28 + 16 * q^30 + 2 * q^31 + 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 + 28 * q^39 + 10 * q^40 - 2 * q^41 - 20 * q^42 + 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 - 22 * q^50 - 20 * q^52 + 54 * q^54 - 16 * q^56 + 22 * q^57 + 12 * q^58 - 48 * q^60 + 4 * q^62 - 30 * q^63 + 38 * q^64 - 18 * q^65 - 21 * q^68 - 44 * q^70 - 34 * q^71 + 57 * q^72 + 2 * q^73 - 28 * q^74 - 67 * q^76 - 6 * q^78 - 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 - 44 * q^84 + 25 * q^86 + 34 * q^87 - 8 * q^89 - 42 * q^90 + 68 * q^92 + 60 * q^94 - 92 * q^95 + 35 * q^96 + 10 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$ .

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$1$

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

)

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

$2$	−1.07012	−	0.924577i	−0.756689	−	0.653775i
$2$	−1.07012	−	0.924577i	−0.756689	−	0.653775i
$3$			0.321222i			0.185457i	0.995691	+	0.0927287i	$0.0295589\pi$
$3$			0.321222i			0.185457i	−0.995691	+	0.0927287i	$0.970441\pi$
$4$	0.290315	+	1.97882i	0.145158	+	0.989409i
$5$		−	1.28733i		−	0.575709i	−0.957674	−	0.287855i	$-0.907058\pi$
$5$		−	1.28733i		−	0.575709i	0.957674	−	0.287855i	$-0.0929420\pi$
$6$	0.296994	−	0.343746i	0.121247	−	0.140334i
$7$	−3.30669			−1.24981			−0.624905	−	0.780701i	$-0.714862\pi$
$7$	−3.30669			−1.24981			−0.624905	+	0.780701i	$0.714862\pi$
$8$	1.51890	−	2.38599i	0.537011	−	0.843575i
$9$	2.89682			0.965606
$10$	−1.19023	+	1.37759i	−0.376384	+	0.435633i
$11$		0			0
$11$		0			0
$12$	−0.635639	+	0.0932556i	−0.183493	+	0.0269206i
$13$			3.08618i			0.855953i	0.903790	+	0.427977i	$0.140773\pi$
$13$			3.08618i			0.855953i	−0.903790	+	0.427977i	$0.859227\pi$
$14$	3.53855	+	3.05728i	0.945718	+	0.817094i
$15$	0.413517			0.106770
$16$	−3.83143	+	1.14896i	−0.957858	+	0.287241i
$17$	−3.19795			−0.775616			−0.387808	−	0.921740i	$-0.626768\pi$
$17$	−3.19795			−0.775616			−0.387808	+	0.921740i	$0.626768\pi$
$18$	−3.09994	−	2.67833i	−0.730663	−	0.631288i
$19$			4.71799i			1.08238i	0.840900	+	0.541190i	$0.182026\pi$
$19$			4.71799i			1.08238i	−0.840900	+	0.541190i	$0.817974\pi$
$20$	2.54738	−	0.373730i	0.569612	−	0.0835687i
$21$		−	1.06218i		−	0.231786i
$22$		0			0
$23$	−3.47634			−0.724867			−0.362433	−	0.932010i	$-0.618054\pi$
$23$	−3.47634			−0.724867			−0.362433	+	0.932010i	$0.618054\pi$
$24$	0.766432	+	0.487902i	0.156447	+	0.0995926i
$25$	3.34279			0.668559
$26$	2.85341	−	3.30259i	0.559600	−	0.647691i
$27$			1.89419i			0.364536i
$28$	−0.959982	−	6.54333i	−0.181420	−	1.23657i
$29$		−	6.19081i		−	1.14960i	−0.818292	−	0.574802i	$-0.805079\pi$
$29$		−	6.19081i		−	1.14960i	0.818292	−	0.574802i	$-0.194921\pi$
$30$	−0.442513	−	0.382328i	−0.0807914	−	0.0698032i
$31$	−2.67961			−0.481272			−0.240636	−	0.970615i	$-0.577356\pi$
$31$	−2.67961			−0.481272			−0.240636	+	0.970615i	$0.577356\pi$
$32$	5.16240	+	2.31293i	0.912592	+	0.408872i
$33$		0			0
$34$	3.42219	+	2.95675i	0.586900	+	0.507078i
$35$			4.25678i			0.719527i
$36$	0.840991	+	5.73227i	0.140165	+	0.955378i
$37$			7.84394i			1.28954i	0.764378	+	0.644768i	$0.223046\pi$
$37$			7.84394i			1.28954i	−0.764378	+	0.644768i	$0.776954\pi$
$38$	4.36214	−	5.04882i	0.707633	−	0.819026i
$39$	−0.991349			−0.158743
$40$	−3.07155	−	1.95531i	−0.485654	−	0.309162i
$41$	5.18518			0.809789			0.404895	−	0.914363i	$-0.367308\pi$
$41$	5.18518			0.809789			0.404895	+	0.914363i	$0.367308\pi$
$42$	−0.982066	+	1.13666i	−0.151536	+	0.175390i
$43$			2.37086i			0.361553i	0.983524	+	0.180776i	$0.0578610\pi$
$43$			2.37086i			0.361553i	−0.983524	+	0.180776i	$0.942139\pi$
$44$		0			0
$45$		−	3.72915i		−	0.555908i
$46$	3.72010	+	3.21414i	0.548499	+	0.473900i
$47$	3.19353			0.465824			0.232912	−	0.972498i	$-0.425175\pi$
$47$	3.19353			0.465824			0.232912	+	0.972498i	$0.425175\pi$
$48$	−0.369072	−	1.23074i	−0.0532709	−	0.177642i
$49$	3.93417			0.562024
$50$	−3.57719	−	3.09067i	−0.505891	−	0.437087i
$51$		−	1.02725i		−	0.143844i
$52$	−6.10699	+	0.895967i	−0.846887	+	0.124248i
$53$			4.72284i			0.648732i	0.945932	+	0.324366i	$0.105151\pi$
$53$			4.72284i			0.648732i	−0.945932	+	0.324366i	$0.894849\pi$
$54$	1.75132	−	2.02701i	0.238324	−	0.275841i
$55$		0			0
$56$	−5.02251	+	7.88972i	−0.671161	+	1.05431i
$57$	−1.51552			−0.200736
$58$	−5.72388	+	6.62491i	−0.751582	+	0.869894i
$59$			14.1440i			1.84139i	0.390284	+	0.920695i	$0.372377\pi$
$59$			14.1440i			1.84139i	−0.390284	+	0.920695i	$0.627623\pi$
$60$	0.120050	+	0.818274i	0.0154984	+	0.105639i
$61$			15.5658i			1.99300i	0.0835917	+	0.996500i	$0.473361\pi$
$61$			15.5658i			1.99300i	−0.0835917	+	0.996500i	$0.526639\pi$
$62$	2.86751	+	2.47751i	0.364174	+	0.314644i
$63$	−9.57886			−1.20682
$64$	−3.38591	−	7.24815i	−0.423239	−	0.906018i
$65$	3.97292			0.492780
$66$		0			0
$67$			4.70162i			0.574395i	0.957871	+	0.287197i	$0.0927236\pi$
$67$			4.70162i			0.574395i	−0.957871	+	0.287197i	$0.907276\pi$
$68$	−0.928413	−	6.32815i	−0.112587	−	0.767401i
$69$		−	1.11668i		−	0.134432i
$70$	3.93572	−	4.55527i	0.470409	−	0.544459i
$71$	−9.17365			−1.08871			−0.544356	−	0.838854i	$-0.683226\pi$
$71$	−9.17365			−1.08871			−0.544356	+	0.838854i	$0.683226\pi$
$72$	4.39996	−	6.91178i	0.518541	−	0.814561i
$73$	−0.939086			−0.109912			−0.0549558	−	0.998489i	$-0.517502\pi$
$73$	−0.939086			−0.109912			−0.0549558	+	0.998489i	$0.517502\pi$
$74$	7.25233	−	8.39396i	0.843066	−	0.975778i
$75$			1.07378i			0.123989i
$76$	−9.33604	+	1.36970i	−1.07092	+	0.157116i
$77$		0			0
$78$	1.06086	+	0.916578i	0.120119	+	0.103782i
$79$	9.56575			1.07623			0.538116	−	0.842871i	$-0.319136\pi$
$79$	9.56575			1.07623			0.538116	+	0.842871i	$0.319136\pi$
$80$	1.47909	+	4.93230i	0.165367	+	0.551448i
$81$	8.08200			0.898000
$82$	−5.54877	−	4.79410i	−0.612759	−	0.529419i
$83$		−	1.27824i		−	0.140306i	−0.997536	−	0.0701528i	$-0.977651\pi$
$83$		−	1.27824i		−	0.140306i	0.997536	−	0.0701528i	$-0.0223487\pi$
$84$	2.10186	−	0.308367i	0.229332	−	0.0336456i
$85$			4.11680i			0.446529i
$86$	2.19204	−	2.53711i	0.236374	−	0.273583i
$87$	1.98862			0.213203
$88$		0			0
$89$	15.3866			1.63098			0.815489	−	0.578773i	$-0.196468\pi$
$89$	15.3866			1.63098			0.815489	+	0.578773i	$0.196468\pi$
$90$	−3.44788	+	3.99063i	−0.363439	+	0.420650i
$91$		−	10.2050i		−	1.06978i
$92$	−1.00924	−	6.87904i	−0.105220	−	0.717190i
$93$		−	0.860749i		−	0.0892555i
$94$	−3.41746	−	2.95266i	−0.352484	−	0.304544i
$95$	6.07359			0.623137
$96$	−0.742962	+	1.65827i	−0.0758283	+	0.169247i
$97$	−13.9642			−1.41785			−0.708924	−	0.705285i	$-0.750819\pi$
$97$	−13.9642			−1.41785			−0.708924	+	0.705285i	$0.750819\pi$
$98$	−4.21004	−	3.63744i	−0.425278	−	0.367437i
$99$		0			0
$100$	0.970465	+	6.61478i	0.0970465	+	0.661478i
$101$			11.0160i			1.09614i	0.836433	+	0.548069i	$0.184637\pi$
$101$			11.0160i			1.09614i	−0.836433	+	0.548069i	$0.815363\pi$
$102$	−0.949771	+	1.09928i	−0.0940413	+	0.108845i
$103$	−10.8978			−1.07379			−0.536897	−	0.843648i	$-0.680404\pi$
$103$	−10.8978			−1.07379			−0.536897	+	0.843648i	$0.680404\pi$
$104$	7.36361	+	4.68759i	0.722061	+	0.459656i
$105$	−1.36737			−0.133442
$106$	4.36663	−	5.05401i	0.424125	−	0.490889i
$107$			14.4930i			1.40109i	0.713609	+	0.700544i	$0.247059\pi$
$107$			14.4930i			1.40109i	−0.713609	+	0.700544i	$0.752941\pi$
$108$	−3.74825	+	0.549911i	−0.360675	+	0.0529152i
$109$			1.96781i			0.188482i	0.995549	+	0.0942411i	$0.0300424\pi$
$109$			1.96781i			0.188482i	−0.995549	+	0.0942411i	$0.969958\pi$
$110$		0			0
$111$	−2.51964			−0.239154
$112$	12.6693	−	3.79926i	1.19714	−	0.358996i
$113$	−6.34757			−0.597129			−0.298565	−	0.954389i	$-0.596508\pi$
$113$	−6.34757			−0.597129			−0.298565	+	0.954389i	$0.596508\pi$
$114$	1.62179	+	1.40121i	0.151894	+	0.131236i
$115$			4.47518i			0.417313i
$116$	12.2505	−	1.79729i	1.13743	−	0.166874i
$117$			8.94011i			0.826513i
$118$	13.0772	−	15.1358i	1.20385	−	1.39336i
$119$	10.5746			0.969372
$120$	0.628089	−	0.986647i	0.0573364	−	0.0900682i
$121$		0			0
$122$	14.3918	−	16.6573i	1.30297	−	1.50808i
$123$			1.66559i			0.150181i
$124$	−0.777933	−	5.30246i	−0.0698604	−	0.476175i
$125$		−	10.7399i		−	0.960605i
$126$	10.2505	+	8.85639i	0.913190	+	0.788990i
$127$	16.7029			1.48215			0.741073	−	0.671425i	$-0.234317\pi$
$127$	16.7029			1.48215			0.741073	+	0.671425i	$0.234317\pi$
$128$	−3.07813	+	10.8869i	−0.272071	+	0.962277i
$129$	−0.761572			−0.0670526
$130$	−4.25150	−	3.67327i	−0.372882	−	0.322167i
$131$		−	9.29813i		−	0.812381i	−0.913788	−	0.406191i	$-0.866857\pi$
$131$		−	9.29813i		−	0.812381i	0.913788	−	0.406191i	$-0.133143\pi$
$132$		0			0
$133$		−	15.6009i		−	1.35277i
$134$	4.34701	−	5.03130i	0.375525	−	0.434638i
$135$	2.43843			0.209867
$136$	−4.85735	+	7.63027i	−0.416514	+	0.654290i
$137$	9.06748			0.774687			0.387344	−	0.921935i	$-0.373393\pi$
$137$	9.06748			0.774687			0.387344	+	0.921935i	$0.373393\pi$
$138$	−1.03245	+	1.19498i	−0.0878882	+	0.101723i
$139$			0.233509i			0.0198059i	0.999951	+	0.00990297i	$0.00315226\pi$
$139$			0.233509i			0.0198059i	−0.999951	+	0.00990297i	$0.996848\pi$
$140$	−8.42339	+	1.23581i	−0.711906	+	0.104445i
$141$			1.02583i			0.0863905i
$142$	9.81691	+	8.48174i	0.823817	+	0.711772i
$143$		0			0
$144$	−11.0990	+	3.32833i	−0.924913	+	0.277361i
$145$	−7.96959			−0.661838
$146$	1.00493	+	0.868257i	0.0831690	+	0.0718575i
$147$			1.26374i			0.104232i
$148$	−15.5217	+	2.27722i	−1.27588	+	0.187186i
$149$			2.28997i			0.187601i	0.995591	+	0.0938006i	$0.0299016\pi$
$149$			2.28997i			0.187601i	−0.995591	+	0.0938006i	$0.970098\pi$
$150$	0.992790	−	1.14907i	0.0810610	−	0.0938213i
$151$	3.79592			0.308907			0.154454	−	0.988000i	$-0.450638\pi$
$151$	3.79592			0.308907			0.154454	+	0.988000i	$0.450638\pi$
$152$	11.2571	+	7.16613i	0.913070	+	0.581250i
$153$	−9.26386			−0.748939
$154$		0			0
$155$			3.44953i			0.277073i
$156$	−0.287804	−	1.96170i	−0.0230427	−	0.157062i
$157$		−	12.1538i		−	0.969981i	−0.874519	−	0.484991i	$-0.838823\pi$
$157$		−	12.1538i		−	0.969981i	0.874519	−	0.484991i	$-0.161177\pi$
$158$	−10.2365	−	8.84427i	−0.814373	−	0.703612i
$159$	−1.51708			−0.120312
$160$	2.97749	−	6.64569i	0.235391	−	0.525388i
$161$	11.4952			0.905946
$162$	−8.64871	−	7.47243i	−0.679507	−	0.587089i
$163$		−	8.28822i		−	0.649183i	−0.945854	−	0.324592i	$-0.894773\pi$
$163$		−	8.28822i		−	0.649183i	0.945854	−	0.324592i	$-0.105227\pi$
$164$	1.50534	+	10.2605i	0.117547	+	0.801212i
$165$		0			0
$166$	−1.18183	+	1.36788i	−0.0917282	+	0.106168i
$167$	−8.92881			−0.690932			−0.345466	−	0.938431i	$-0.612279\pi$
$167$	−8.92881			−0.690932			−0.345466	+	0.938431i	$0.612279\pi$
$168$	−2.53435	−	1.61334i	−0.195529	−	0.124472i
$169$	3.47548			0.267344
$170$	3.80629	−	4.40547i	0.291929	−	0.337884i
$171$			13.6671i			1.04515i
$172$	−4.69150	+	0.688297i	−0.357723	+	0.0524822i
$173$		−	8.50496i		−	0.646620i	−0.946293	−	0.323310i	$-0.895204\pi$
$173$		−	8.50496i		−	0.646620i	0.946293	−	0.323310i	$-0.104796\pi$
$174$	−2.12807	−	1.83863i	−0.161328	−	0.139386i
$175$	−11.0536			−0.835571
$176$		0			0
$177$	−4.54335			−0.341499
$178$	−16.4655	−	14.2261i	−1.23414	−	1.06629i
$179$		−	2.94347i		−	0.220005i	−0.993931	−	0.110003i	$-0.964914\pi$
$179$		−	2.94347i		−	0.220005i	0.993931	−	0.110003i	$-0.0350859\pi$
$180$	7.37930	−	1.08263i	0.550020	−	0.0806944i
$181$		−	21.2709i		−	1.58105i	−0.612429	−	0.790526i	$-0.709808\pi$
$181$		−	21.2709i		−	1.58105i	0.612429	−	0.790526i	$-0.290192\pi$
$182$	−9.43534	+	10.9206i	−0.699394	+	0.809490i
$183$	−5.00008			−0.369617
$184$	−5.28020	+	8.29452i	−0.389261	+	0.611480i
$185$	10.0977			0.742398
$186$	−0.795829	+	0.921105i	−0.0583530	+	0.0675387i
$187$		0			0
$188$	0.927131	+	6.31941i	0.0676179	+	0.460890i
$189$		−	6.26347i		−	0.455601i
$190$	−6.49947	−	5.61550i	−0.471521	−	0.407391i
$191$	−5.15586			−0.373065			−0.186533	−	0.982449i	$-0.559725\pi$
$191$	−5.15586			−0.373065			−0.186533	+	0.982449i	$0.559725\pi$
$192$	2.32826	−	1.08763i	0.168028	−	0.0784928i
$193$	−27.0169			−1.94472			−0.972361	−	0.233482i	$-0.924988\pi$
$193$	−27.0169			−1.94472			−0.972361	+	0.233482i	$0.924988\pi$
$194$	14.9434	+	12.9110i	1.07287	+	0.926952i
$195$			1.27619i			0.0913897i
$196$	1.14215	+	7.78500i	0.0815822	+	0.556072i
$197$		−	6.68220i		−	0.476087i	−0.971254	−	0.238044i	$-0.923494\pi$
$197$		−	6.68220i		−	0.476087i	0.971254	−	0.238044i	$-0.0765061\pi$
$198$		0			0
$199$	−14.2586			−1.01076			−0.505382	−	0.862896i	$-0.668648\pi$
$199$	−14.2586			−1.01076			−0.505382	+	0.862896i	$0.668648\pi$
$200$	5.07736	−	7.97588i	0.359023	−	0.563980i
$201$	−1.51026			−0.106526
$202$	10.1852	−	11.7885i	0.716627	−	0.829436i
$203$			20.4711i			1.43679i
$204$	2.03274	−	0.298226i	0.142320	−	0.0208800i
$205$		−	6.67501i		−	0.466203i
$206$	11.6620	+	10.0759i	0.812528	+	0.702019i
$207$	−10.0703			−0.699936
$208$	−3.54591	−	11.8245i	−0.245864	−	0.819882i
$209$		0			0
$210$	1.46325	+	1.26424i	0.100974	+	0.0872407i
$211$		−	19.3294i		−	1.33069i	−0.746535	−	0.665346i	$-0.768284\pi$
$211$		−	19.3294i		−	1.33069i	0.746535	−	0.665346i	$-0.231716\pi$
$212$	−9.34564	+	1.37111i	−0.641861	+	0.0941685i
$213$		−	2.94678i		−	0.201910i
$214$	13.3999	−	15.5092i	0.915996	−	1.06019i
$215$	3.05207			0.208149
$216$	4.51951	+	2.87707i	0.307514	+	0.195760i
$217$	8.86063			0.601499
$218$	1.81939	−	2.10579i	0.123225	−	0.142622i
$219$		−	0.301655i		−	0.0203839i
$220$		0			0
$221$		−	9.86944i		−	0.663891i
$222$	2.69632	+	2.32960i	0.180965	+	0.156353i
$223$	−13.6844			−0.916378			−0.458189	−	0.888855i	$-0.651502\pi$
$223$	−13.6844			−0.916378			−0.458189	+	0.888855i	$0.651502\pi$
$224$	−17.0704	−	7.64812i	−1.14057	−	0.511012i
$225$	9.68346			0.645564
$226$	6.79267	+	5.86882i	0.451842	+	0.390388i
$227$			11.8877i			0.789016i	0.918893	+	0.394508i	$0.129085\pi$
$227$			11.8877i			0.789016i	−0.918893	+	0.394508i	$0.870915\pi$
$228$	−0.439979	−	2.99894i	−0.0291383	−	0.198609i
$229$			0.217689i			0.0143853i	0.999974	+	0.00719264i	$0.00228951\pi$
$229$			0.217689i			0.0143853i	−0.999974	+	0.00719264i	$0.997710\pi$
$230$	4.13765	−	4.78898i	0.272828	−	0.315776i
$231$		0			0
$232$	−14.7712	−	9.40320i	−0.969778	−	0.617350i
$233$	−3.67905			−0.241023			−0.120511	−	0.992712i	$-0.538453\pi$
$233$	−3.67905			−0.241023			−0.120511	+	0.992712i	$0.538453\pi$
$234$	8.26581	−	9.56699i	0.540353	−	0.625414i
$235$		−	4.11111i		−	0.268179i
$236$	−27.9883	+	4.10622i	−1.82189	+	0.267292i
$237$			3.07273i			0.199595i
$238$	−11.3161	−	9.77703i	−0.733514	−	0.633751i
$239$	−20.0477			−1.29678			−0.648388	−	0.761310i	$-0.724556\pi$
$239$	−20.0477			−1.29678			−0.648388	+	0.761310i	$0.724556\pi$
$240$	−1.58436	+	0.475115i	−0.102270	+	0.0306686i
$241$	14.4772			0.932561			0.466280	−	0.884637i	$-0.345594\pi$
$241$	14.4772			0.932561			0.466280	+	0.884637i	$0.345594\pi$
$242$		0			0
$243$			8.27867i			0.531077i
$244$	−30.8019	+	4.51900i	−1.97189	+	0.289299i
$245$		−	5.06456i		−	0.323563i
$246$	1.53997	−	1.78238i	0.0981848	−	0.113641i
$247$	−14.5606			−0.926467
$248$	−4.07005	+	6.39353i	−0.258449	+	0.405990i
$249$	0.410600			0.0260207
$250$	−9.92985	+	11.4930i	−0.628019	+	0.726880i
$251$			21.6387i			1.36582i	0.730502	+	0.682910i	$0.239286\pi$
$251$			21.6387i			1.36582i	−0.730502	+	0.682910i	$0.760714\pi$
$252$	−2.78089	−	18.9548i	−0.175180	−	1.19404i
$253$		0			0
$254$	−17.8741	−	15.4431i	−1.12152	−	0.968989i
$255$	−1.32240			−0.0828122
$256$	13.3598	−	8.80435i	0.834986	−	0.550272i
$257$	−8.50900			−0.530777			−0.265388	−	0.964142i	$-0.585500\pi$
$257$	−8.50900			−0.530777			−0.265388	+	0.964142i	$0.585500\pi$
$258$	0.814973	+	0.704131i	0.0507380	+	0.0438373i
$259$		−	25.9375i		−	1.61167i
$260$	1.15340	+	7.86168i	0.0715309	+	0.487561i
$261$		−	17.9336i		−	1.11006i
$262$	−8.59683	+	9.95011i	−0.531114	+	0.614720i
$263$	9.34658			0.576335			0.288167	−	0.957580i	$-0.406954\pi$
$263$	9.34658			0.576335			0.288167	+	0.957580i	$0.406954\pi$
$264$		0			0
$265$	6.07983			0.373481
$266$	−14.4242	+	16.6948i	−0.884407	+	1.02363i
$267$			4.94251i			0.302477i
$268$	−9.30365	+	1.36495i	−0.568311	+	0.0833778i
$269$			12.2303i			0.745692i	0.927893	+	0.372846i	$0.121618\pi$
$269$			12.2303i			0.745692i	−0.927893	+	0.372846i	$0.878382\pi$
$270$	−2.60942	−	2.25452i	−0.158804	−	0.137206i
$271$	−24.6688			−1.49852			−0.749262	−	0.662274i	$-0.769592\pi$
$271$	−24.6688			−1.49852			−0.749262	+	0.662274i	$0.769592\pi$
$272$	12.2527	−	3.67432i	0.742930	−	0.222788i
$273$	3.27808			0.198398
$274$	−9.70329	−	8.38358i	−0.586197	−	0.506471i
$275$		0			0
$276$	2.20970	−	0.324188i	0.133008	−	0.0195138i
$277$		−	8.05153i		−	0.483769i	−0.970305	−	0.241885i	$-0.922234\pi$
$277$		−	8.05153i		−	0.483769i	0.970305	−	0.241885i	$-0.0777656\pi$
$278$	0.215897	−	0.249882i	0.0129486	−	0.0149869i
$279$	−7.76234			−0.464719
$280$	10.1566	+	6.46561i	0.606975	+	0.386394i
$281$	13.2894			0.792778			0.396389	−	0.918083i	$-0.370263\pi$
$281$	13.2894			0.792778			0.396389	+	0.918083i	$0.370263\pi$
$282$	0.948459	−	1.09776i	0.0564799	−	0.0653708i
$283$			0.345924i			0.0205630i	0.999947	+	0.0102815i	$0.00327277\pi$
$283$			0.345924i			0.0205630i	−0.999947	+	0.0102815i	$0.996727\pi$
$284$	−2.66325	−	18.1530i	−0.158035	−	1.07718i
$285$			1.95097i			0.115565i
$286$		0			0
$287$	−17.1458			−1.01208
$288$	14.9545	+	6.70013i	0.881204	+	0.394809i
$289$	−6.77314			−0.398420
$290$	8.52842	+	7.36850i	0.500806	+	0.432693i
$291$		−	4.48560i		−	0.262950i
$292$	−0.272631	−	1.85828i	−0.0159545	−	0.108748i
$293$		−	3.82936i		−	0.223713i	−0.993724	−	0.111857i	$-0.964320\pi$
$293$		−	3.82936i		−	0.223713i	0.993724	−	0.111857i	$-0.0356798\pi$
$294$	1.16843	−	1.35235i	0.0681439	−	0.0788709i
$295$	18.2079			1.06010
$296$	18.7156	+	11.9141i	1.08782	+	0.692495i
$297$		0			0
$298$	2.11725	−	2.45054i	0.122649	−	0.141956i
$299$		−	10.7286i		−	0.620452i
$300$	−2.12481	+	0.311734i	−0.122676	+	0.0179980i
$301$		−	7.83969i		−	0.451872i
$302$	−4.06209	−	3.50962i	−0.233747	−	0.201956i
$303$	−3.53859			−0.203287
$304$	−5.42079	−	18.0767i	−0.310904	−	1.03677i
$305$	20.0383			1.14739
$306$	9.91345	+	8.56515i	0.566714	+	0.489637i
$307$			23.7376i			1.35478i	0.735626	+	0.677388i	$0.236888\pi$
$307$			23.7376i			1.35478i	−0.735626	+	0.677388i	$0.763112\pi$
$308$		0			0
$309$		−	3.50061i		−	0.199143i
$310$	3.18936	−	3.69141i	0.181143	−	0.209658i
$311$	8.82141			0.500216			0.250108	−	0.968218i	$-0.419534\pi$
$311$	8.82141			0.500216			0.250108	+	0.968218i	$0.419534\pi$
$312$	−1.50576	+	2.36535i	−0.0852466	+	0.133912i
$313$	−3.21543			−0.181747			−0.0908733	−	0.995862i	$-0.528966\pi$
$313$	−3.21543			−0.181747			−0.0908733	+	0.995862i	$0.528966\pi$
$314$	−11.2371	+	13.0061i	−0.634149	+	0.733974i
$315$			12.3311i			0.694779i
$316$	2.77709	+	18.9289i	0.156223	+	1.06483i
$317$		−	9.23560i		−	0.518723i	−0.965780	−	0.259362i	$-0.916488\pi$
$317$		−	9.23560i		−	0.518723i	0.965780	−	0.259362i	$-0.0835121\pi$
$318$	1.62346	+	1.40266i	0.0910390	+	0.0786571i
$319$		0			0
$320$	−9.33072	+	4.35877i	−0.521603	+	0.243663i
$321$	−4.65546			−0.259842
$322$	−12.3012	−	10.6282i	−0.685520	−	0.592284i
$323$		−	15.0879i		−	0.839512i
$324$	2.34633	+	15.9928i	0.130352	+	0.888488i
$325$			10.3165i			0.572255i
$326$	−7.66309	+	8.86939i	−0.424419	+	0.491230i
$327$	−0.632103			−0.0349554
$328$	7.87575	−	12.3718i	0.434865	−	0.683118i
$329$	−10.5600			−0.582191
$330$		0			0
$331$			4.00167i			0.219952i	0.993934	+	0.109976i	$0.0350774\pi$
$331$			4.00167i			0.219952i	−0.993934	+	0.109976i	$0.964923\pi$
$332$	2.52941	−	0.371094i	0.138819	−	0.0203664i
$333$			22.7225i			1.24518i
$334$	9.55490	+	8.25537i	0.522821	+	0.451714i
$335$	6.05252			0.330684
$336$	1.22040	+	4.06967i	0.0665785	+	0.222019i
$337$	2.35879			0.128492			0.0642459	−	0.997934i	$-0.479536\pi$
$337$	2.35879			0.128492			0.0642459	+	0.997934i	$0.479536\pi$
$338$	−3.71918	−	3.21334i	−0.202297	−	0.174783i
$339$		−	2.03898i		−	0.110742i
$340$	−8.14639	+	1.19517i	−0.441800	+	0.0648172i
$341$		0			0
$342$	12.6363	−	14.6255i	0.683294	−	0.790856i
$343$	10.1377			0.547386
$344$	5.65685	+	3.60109i	0.304997	+	0.194158i
$345$	−1.43752			−0.0773937
$346$	−7.86349	+	9.10133i	−0.422744	+	0.489290i
$347$		−	23.9187i		−	1.28402i	−0.766695	−	0.642012i	$-0.778100\pi$
$347$		−	23.9187i		−	1.28402i	0.766695	−	0.642012i	$-0.221900\pi$
$348$	0.577328	+	3.93512i	0.0309480	+	0.210945i
$349$			2.12274i			0.113628i	0.998385	+	0.0568139i	$0.0180942\pi$
$349$			2.12274i			0.113628i	−0.998385	+	0.0568139i	$0.981906\pi$
$350$	11.8286	+	10.2199i	0.632268	+	0.546275i
$351$	−5.84580			−0.312026
$352$		0			0
$353$	5.11533			0.272262			0.136131	−	0.990691i	$-0.456533\pi$
$353$	5.11533			0.272262			0.136131	+	0.990691i	$0.456533\pi$
$354$	4.86193	+	4.20068i	0.258409	+	0.223263i
$355$			11.8095i			0.626782i
$356$	4.46697	+	30.4473i	0.236749	+	1.61370i
$357$			3.39679i			0.179777i
$358$	−2.72146	+	3.14986i	−0.143834	+	0.166476i
$359$	28.9715			1.52906			0.764528	−	0.644591i	$-0.222972\pi$
$359$	28.9715			1.52906			0.764528	+	0.644591i	$0.222972\pi$
$360$	−8.89771	−	5.66418i	−0.468950	−	0.298529i
$361$	−3.25941			−0.171548
$362$	−19.6665	+	22.7624i	−1.03365	+	1.19636i
$363$		0			0
$364$	20.1939	−	2.96268i	1.05845	−	0.155287i
$365$			1.20891i			0.0632772i
$366$	5.35069	+	4.62296i	0.279685	+	0.241646i
$367$	29.6944			1.55004			0.775019	−	0.631938i	$-0.217740\pi$
$367$	29.6944			1.55004			0.775019	+	0.631938i	$0.217740\pi$
$368$	13.3194	−	3.99418i	0.694320	−	0.208211i
$369$	15.0205			0.781937
$370$	−10.8058	−	9.33611i	−0.561765	−	0.485361i
$371$		−	15.6170i		−	0.810792i
$372$	1.70327	−	0.249889i	0.0883102	−	0.0129561i
$373$			4.07522i			0.211007i	0.994419	+	0.105504i	$0.0336454\pi$
$373$			4.07522i			0.211007i	−0.994419	+	0.105504i	$0.966355\pi$
$374$		0			0
$375$	3.44988			0.178151
$376$	4.85064	−	7.61973i	0.250153	−	0.392958i
$377$	19.1060			0.984008
$378$	−5.79106	+	6.70267i	−0.297860	+	0.344748i
$379$		−	29.1300i		−	1.49631i	−0.663526	−	0.748154i	$-0.730941\pi$
$379$		−	29.1300i		−	1.49631i	0.663526	−	0.748154i	$-0.269059\pi$
$380$	1.76326	+	12.0185i	0.0904531	+	0.616537i
$381$			5.36534i			0.274875i
$382$	5.51739	+	4.76699i	0.282294	+	0.243900i
$383$	−18.8174			−0.961524			−0.480762	−	0.876851i	$-0.659640\pi$
$383$	−18.8174			−0.961524			−0.480762	+	0.876851i	$0.659640\pi$
$384$	−3.49712	−	0.988764i	−0.178461	−	0.0504576i
$385$		0			0
$386$	28.9114	+	24.9792i	1.47155	+	1.27141i
$387$			6.86795i			0.349117i
$388$	−4.05402	−	27.6326i	−0.205811	−	1.40283i
$389$		−	27.0108i		−	1.36950i	−0.728778	−	0.684750i	$-0.759911\pi$
$389$		−	27.0108i		−	1.36950i	0.728778	−	0.684750i	$-0.240089\pi$
$390$	1.17993	−	1.36568i	0.0597483	−	0.0691536i
$391$	11.1171			0.562218
$392$	5.97559	−	9.38690i	0.301813	−	0.474110i
$393$	2.98676			0.150662
$394$	−6.17821	+	7.15076i	−0.311254	+	0.360250i
$395$		−	12.3142i		−	0.619596i
$396$		0			0
$397$			28.1281i			1.41171i	0.708358	+	0.705854i	$0.249436\pi$
$397$			28.1281i			1.41171i	−0.708358	+	0.705854i	$0.750564\pi$
$398$	15.2584	+	13.1831i	0.764834	+	0.660811i
$399$	5.01135			0.250881
$400$	−12.8077	+	3.84074i	−0.640385	+	0.192037i
$401$	−8.33290			−0.416125			−0.208063	−	0.978115i	$-0.566716\pi$
$401$	−8.33290			−0.416125			−0.208063	+	0.978115i	$0.566716\pi$
$402$	1.61616	+	1.39635i	0.0806069	+	0.0696438i
$403$		−	8.26977i		−	0.411947i
$404$	−21.7987	+	3.19813i	−1.08453	+	0.159113i
$405$		−	10.4042i		−	0.516987i
$406$	18.9271	−	21.9065i	0.939335	−	1.08720i
$407$		0			0
$408$	−2.45101	−	1.56028i	−0.121343	−	0.0772456i
$409$	4.14774			0.205093			0.102546	−	0.994728i	$-0.467301\pi$
$409$	4.14774			0.205093			0.102546	+	0.994728i	$0.467301\pi$
$410$	−6.17156	+	7.14307i	−0.304792	+	0.352771i
$411$			2.91267i			0.143671i
$412$	−3.16380	−	21.5648i	−0.155869	−	1.06242i
$413$		−	46.7697i		−	2.30139i
$414$	10.7765	+	9.31078i	0.529634	+	0.457600i
$415$	−1.64552			−0.0807752
$416$	−7.13812	+	15.9321i	−0.349975	+	0.781136i
$417$	−0.0750080			−0.00367316
$418$		0			0
$419$			7.25457i			0.354409i	0.984174	+	0.177204i	$0.0567054\pi$
$419$			7.25457i			0.354409i	−0.984174	+	0.177204i	$0.943295\pi$
$420$	−0.396969	−	2.70577i	−0.0193701	−	0.132028i
$421$			35.1980i			1.71545i	0.514111	+	0.857724i	$0.328122\pi$
$421$			35.1980i			1.71545i	−0.514111	+	0.857724i	$0.671878\pi$
$422$	−17.8715	+	20.6848i	−0.869973	+	1.00692i
$423$	9.25107			0.449802
$424$	11.2687	+	7.17351i	0.547255	+	0.348376i
$425$	−10.6901			−0.518545
$426$	−2.72452	+	3.15340i	−0.132003	+	0.152783i
$427$		−	51.4713i		−	2.49087i
$428$	−28.6789	+	4.20753i	−1.38625	+	0.203379i
$429$		0			0
$430$	−3.26608	−	2.82187i	−0.157504	−	0.136083i
$431$	13.5078			0.650648			0.325324	−	0.945603i	$-0.394527\pi$
$431$	13.5078			0.650648			0.325324	+	0.945603i	$0.394527\pi$
$432$	−2.17635	−	7.25745i	−0.104710	−	0.349174i
$433$	14.5538			0.699412			0.349706	−	0.936859i	$-0.386281\pi$
$433$	14.5538			0.699412			0.349706	+	0.936859i	$0.386281\pi$
$434$	−9.48195	−	8.19234i	−0.455148	−	0.393245i
$435$		−	2.56000i		−	0.122743i
$436$	−3.89394	+	0.571286i	−0.186486	+	0.0273596i
$437$		−	16.4013i		−	0.784582i
$438$	−0.278903	+	0.322807i	−0.0133265	+	0.0154243i
$439$	8.11893			0.387495			0.193748	−	0.981051i	$-0.437936\pi$
$439$	8.11893			0.387495			0.193748	+	0.981051i	$0.437936\pi$
$440$		0			0
$441$	11.3966			0.542694
$442$	−9.12506	+	10.5615i	−0.434035	+	0.502359i
$443$		−	4.06209i		−	0.192996i	−0.995333	−	0.0964979i	$-0.969236\pi$
$443$		−	4.06209i		−	0.192996i	0.995333	−	0.0964979i	$-0.0307641\pi$
$444$	−0.731492	−	4.98592i	−0.0347151	−	0.236621i
$445$		−	19.8076i		−	0.938969i
$446$	14.6440	+	12.6523i	0.693414	+	0.599105i
$447$	−0.735586			−0.0347920
$448$	11.1961	+	23.9673i	0.528968	+	1.13235i
$449$	−8.28691			−0.391083			−0.195542	−	0.980695i	$-0.562646\pi$
$449$	−8.28691			−0.391083			−0.195542	+	0.980695i	$0.562646\pi$
$450$	−10.3625	−	8.95310i	−0.488491	−	0.422053i
$451$		0			0
$452$	−1.84280	−	12.5607i	−0.0866780	−	0.590805i
$453$			1.21933i			0.0572892i
$454$	10.9911	−	12.7213i	0.515838	−	0.597040i
$455$	−13.1372			−0.615881
$456$	−2.30192	+	3.61602i	−0.107797	+	0.169336i
$457$	−9.82837			−0.459752			−0.229876	−	0.973220i	$-0.573832\pi$
$457$	−9.82837			−0.459752			−0.229876	+	0.973220i	$0.573832\pi$
$458$	0.201270	−	0.232953i	0.00940473	−	0.0108852i
$459$		−	6.05750i		−	0.282740i
$460$	−8.85556	+	1.29921i	−0.412893	+	0.0605762i
$461$		−	24.4759i		−	1.13996i	−0.821660	−	0.569978i	$-0.806952\pi$
$461$		−	24.4759i		−	1.13996i	0.821660	−	0.569978i	$-0.193048\pi$
$462$		0			0
$463$	20.2431			0.940778			0.470389	−	0.882459i	$-0.344114\pi$
$463$	20.2431			0.940778			0.470389	+	0.882459i	$0.344114\pi$
$464$	7.11301	+	23.7197i	0.330213	+	1.10116i
$465$	−1.10806			−0.0513853
$466$	3.93703	+	3.40157i	0.182379	+	0.157575i
$467$			24.3857i			1.12844i	0.825625	+	0.564219i	$0.190822\pi$
$467$			24.3857i			1.12844i	−0.825625	+	0.564219i	$0.809178\pi$
$468$	−17.6908	+	2.59545i	−0.817759	+	0.119975i
$469$		−	15.5468i		−	0.717884i
$470$	−3.80104	+	4.39938i	−0.175329	+	0.202928i
$471$	3.90407			0.179890
$472$	33.7474	+	21.4832i	1.55335	+	0.988846i
$473$		0			0
$474$	2.84097	−	3.28819i	0.130490	−	0.151031i
$475$			15.7713i			0.723635i
$476$	3.06997	+	20.9252i	0.140712	+	0.959105i
$477$			13.6812i			0.626419i
$478$	21.4534	+	18.5356i	0.981256	+	0.847799i
$479$	−1.72894			−0.0789975			−0.0394987	−	0.999220i	$-0.512576\pi$
$479$	−1.72894			−0.0789975			−0.0394987	+	0.999220i	$0.512576\pi$
$480$	2.13474	+	0.956434i	0.0974370	+	0.0436550i
$481$	−24.2078			−1.10378
$482$	−15.4924	−	13.3853i	−0.705659	−	0.609684i
$483$			3.69250i			0.168014i
$484$		0			0
$485$			17.9764i			0.816268i
$486$	7.65426	−	8.85917i	0.347204	−	0.401860i
$487$	−2.65499			−0.120309			−0.0601545	−	0.998189i	$-0.519159\pi$
$487$	−2.65499			−0.120309			−0.0601545	+	0.998189i	$0.519159\pi$
$488$	37.1399	+	23.6429i	1.68125	+	1.07026i
$489$	2.66235			0.120396
$490$	−4.68257	+	5.41969i	−0.211537	+	0.244836i
$491$		−	29.3090i		−	1.32270i	−0.750079	−	0.661348i	$-0.769985\pi$
$491$		−	29.3090i		−	1.32270i	0.750079	−	0.661348i	$-0.230015\pi$
$492$	−3.29590	+	0.483547i	−0.148591	+	0.0218000i
$493$			19.7979i			0.891652i
$494$	15.5816	+	13.4624i	0.701048	+	0.605701i
$495$		0			0
$496$	10.2668	−	3.07877i	0.460991	−	0.138241i
$497$	30.3344			1.36068
$498$	−0.439391	−	0.379631i	−0.0196896	−	0.0170117i
$499$			8.05488i			0.360586i	0.983613	+	0.180293i	$0.0577046\pi$
$499$			8.05488i			0.360586i	−0.983613	+	0.180293i	$0.942295\pi$
$500$	21.2523	−	3.11796i	0.950431	−	0.139439i
$501$		−	2.86813i		−	0.128138i
$502$	20.0066	−	23.1560i	0.892939	−	1.03350i
$503$	30.0379			1.33932			0.669661	−	0.742667i	$-0.266439\pi$
$503$	30.0379			1.33932			0.669661	+	0.742667i	$0.266439\pi$
$504$	−14.5493	+	22.8551i	−0.648077	+	1.01805i
$505$	14.1812			0.631057
$506$		0			0
$507$			1.11640i			0.0495810i
$508$	4.84912	+	33.0520i	0.215145	+	1.46645i
$509$		−	2.76641i		−	0.122619i	−0.998119	−	0.0613095i	$-0.980472\pi$
$509$		−	2.76641i		−	0.122619i	0.998119	−	0.0613095i	$-0.0195277\pi$
$510$	1.41513	+	1.22266i	0.0626631	+	0.0541405i
$511$	3.10526			0.137369
$512$	−22.4369	−	2.93042i	−0.991578	−	0.129508i
$513$	−8.93674			−0.394567
$514$	9.10565	+	7.86722i	0.401633	+	0.347008i
$515$			14.0290i			0.618193i
$516$	−0.221096	−	1.50701i	−0.00973321	−	0.0663425i
$517$		0			0
$518$	−23.9812	+	27.7562i	−1.05367	+	1.21954i
$519$	2.73198			0.119920
$520$	6.03445	−	9.47936i	0.264628	−	0.415697i
$521$	12.0184			0.526536			0.263268	−	0.964723i	$-0.415200\pi$
$521$	12.0184			0.526536			0.263268	+	0.964723i	$0.415200\pi$
$522$	−16.5810	+	19.1912i	−0.725732	+	0.839974i
$523$			5.32522i			0.232856i	0.993199	+	0.116428i	$0.0371444\pi$
$523$			5.32522i			0.232856i	−0.993199	+	0.116428i	$0.962856\pi$
$524$	18.3993	−	2.69939i	0.803777	−	0.117923i
$525$		−	3.55065i		−	0.154963i
$526$	−10.0020	−	8.64163i	−0.436106	−	0.376793i
$527$	8.56925			0.373283
$528$		0			0
$529$	−10.9151			−0.474568
$530$	−6.50615	−	5.62127i	−0.282609	−	0.244173i
$531$			40.9725i			1.77806i
$532$	30.8713	−	4.52918i	1.33844	−	0.196365i
$533$			16.0024i			0.693141i
$534$	4.56973	−	5.28908i	0.197752	−	0.228881i
$535$	18.6572			0.806620
$536$	11.2180	+	7.14128i	0.484545	+	0.308456i
$537$	0.945505			0.0408016
$538$	11.3078	−	13.0879i	0.487515	−	0.564257i
$539$		0			0
$540$	0.707915	+	4.82521i	0.0304638	+	0.207644i
$541$			9.71132i			0.417522i	0.977967	+	0.208761i	$0.0669431\pi$
$541$			9.71132i			0.417522i	−0.977967	+	0.208761i	$0.933057\pi$
$542$	26.3986	+	22.8082i	1.13392	+	0.979697i
$543$	6.83266			0.293218
$544$	−16.5091	−	7.39661i	−0.707821	−	0.317127i
$545$	2.53321			0.108511
$546$	−3.50794	−	3.03084i	−0.150126	−	0.129708i
$547$		−	20.6628i		−	0.883476i	−0.897144	−	0.441738i	$-0.854362\pi$
$547$		−	20.6628i		−	0.883476i	0.897144	−	0.441738i	$-0.145638\pi$
$548$	2.63243	+	17.9429i	0.112452	+	0.766482i
$549$			45.0914i			1.92445i
$550$		0			0
$551$	29.2082			1.24431
$552$	−2.66438	−	1.69611i	−0.113403	−	0.0721914i
$553$	−31.6309			−1.34508
$554$	−7.44426	+	8.61611i	−0.316276	+	0.366063i
$555$			3.24360i			0.137683i
$556$	−0.462071	+	0.0677911i	−0.0195962	+	0.00287499i
$557$			26.5466i			1.12482i	0.826860	+	0.562408i	$0.190125\pi$
$557$			26.5466i			1.12482i	−0.826860	+	0.562408i	$0.809875\pi$
$558$	8.30664	+	7.17688i	0.351648	+	0.303822i
$559$	−7.31691			−0.309472
$560$	−4.89088	−	16.3096i	−0.206677	−	0.689205i
$561$		0			0
$562$	−14.2212	−	12.2871i	−0.599887	−	0.518298i
$563$		−	13.5955i		−	0.572982i	−0.958083	−	0.286491i	$-0.907511\pi$
$563$		−	13.5955i		−	0.572982i	0.958083	−	0.286491i	$-0.0924888\pi$
$564$	−2.02993	+	0.297814i	−0.0854755	+	0.0125402i
$565$			8.17139i			0.343773i
$566$	0.319833	−	0.370180i	0.0134436	−	0.0155598i
$567$	−26.7246			−1.12233
$568$	−13.9338	+	21.8883i	−0.584650	+	0.918411i
$569$	−24.4670			−1.02571			−0.512854	−	0.858476i	$-0.671412\pi$
$569$	−24.4670			−1.02571			−0.512854	+	0.858476i	$0.671412\pi$
$570$	1.80382	−	2.08777i	0.0755537	−	0.0874471i
$571$			12.1063i			0.506634i	0.967383	+	0.253317i	$0.0815216\pi$
$571$			12.1063i			0.506634i	−0.967383	+	0.253317i	$0.918478\pi$
$572$		0			0
$573$		−	1.65617i		−	0.0691877i
$574$	18.3480	+	15.8526i	0.765832	+	0.661674i
$575$	−11.6207			−0.484616
$576$	−9.80836	−	20.9965i	−0.408682	−	0.874856i
$577$	−2.33364			−0.0971505			−0.0485753	−	0.998820i	$-0.515468\pi$
$577$	−2.33364			−0.0971505			−0.0485753	+	0.998820i	$0.515468\pi$
$578$	7.24808	+	6.26229i	0.301480	+	0.260477i
$579$		−	8.67843i		−	0.360663i
$580$	−2.31369	−	15.7704i	−0.0960709	−	0.654828i
$581$			4.22675i			0.175355i
$582$	−4.14728	+	4.80013i	−0.171910	+	0.198972i
$583$		0			0
$584$	−1.42637	+	2.24065i	−0.0590238	+	0.0927188i
$585$	11.5088			0.475831
$586$	−3.54053	+	4.09787i	−0.146258	+	0.169282i
$587$		−	24.2039i		−	0.999001i	−0.866314	−	0.499500i	$-0.833517\pi$
$587$		−	24.2039i		−	0.999001i	0.866314	−	0.499500i	$-0.166483\pi$
$588$	−2.50071	+	0.366883i	−0.103128	+	0.0151300i
$589$		−	12.6424i		−	0.520920i
$590$	−19.4846	−	16.8346i	−0.802170	−	0.693070i
$591$	2.14647			0.0882939
$592$	−9.01240	−	30.0535i	−0.370407	−	1.23519i
$593$	−27.1495			−1.11490			−0.557448	−	0.830212i	$-0.688220\pi$
$593$	−27.1495			−1.11490			−0.557448	+	0.830212i	$0.688220\pi$
$594$		0			0
$595$		−	13.6130i		−	0.558077i
$596$	−4.53142	+	0.664812i	−0.185614	+	0.0272318i
$597$		−	4.58016i		−	0.187454i
$598$	−9.91943	+	11.4809i	−0.405636	+	0.469490i
$599$	7.01855			0.286770			0.143385	−	0.989667i	$-0.454201\pi$
$599$	7.01855			0.286770			0.143385	+	0.989667i	$0.454201\pi$
$600$	2.56202	+	1.63096i	0.104594	+	0.0665835i
$601$	2.81601			0.114867			0.0574337	−	0.998349i	$-0.481708\pi$
$601$	2.81601			0.114867			0.0574337	+	0.998349i	$0.481708\pi$
$602$	−7.24839	+	8.38941i	−0.295423	+	0.341927i
$603$			13.6197i			0.554639i
$604$	1.10201	+	7.51143i	0.0448403	+	0.305636i
$605$		0			0
$606$	3.78672	+	3.27170i	0.153825	+	0.132904i
$607$	−36.1882			−1.46884			−0.734418	−	0.678698i	$-0.762545\pi$
$607$	−36.1882			−1.46884			−0.734418	+	0.678698i	$0.762545\pi$
$608$	−10.9124	+	24.3561i	−0.442555	+	0.987772i
$609$	−6.57575			−0.266463
$610$	−21.4434	−	18.5269i	−0.868217	−	0.750134i
$611$			9.85581i			0.398723i
$612$	−2.68944	−	18.3315i	−0.108714	−	0.741007i
$613$			31.2100i			1.26056i	0.776369	+	0.630279i	$0.217060\pi$
$613$			31.2100i			1.26056i	−0.776369	+	0.630279i	$0.782940\pi$
$614$	21.9472	−	25.4021i	0.885718	−	1.02514i
$615$	2.14416			0.0864608
$616$		0			0
$617$	−34.6326			−1.39426			−0.697129	−	0.716946i	$-0.745539\pi$
$617$	−34.6326			−1.39426			−0.697129	+	0.716946i	$0.745539\pi$
$618$	−3.23659	+	3.74608i	−0.130195	+	0.150689i
$619$			15.8975i			0.638974i	0.947591	+	0.319487i	$0.103511\pi$
$619$			15.8975i			0.638974i	−0.947591	+	0.319487i	$0.896489\pi$
$620$	−6.82599	+	1.00145i	−0.274138	+	0.0402193i
$621$		−	6.58483i		−	0.264240i
$622$	−9.43997	−	8.15607i	−0.378508	−	0.327029i
$623$	−50.8787			−2.03841
$624$	3.79829	−	1.13902i	0.152053	−	0.0455974i
$625$	2.88824			0.115530
$626$	3.44089	+	2.97291i	0.137526	+	0.118821i
$627$		0			0
$628$	24.0502	−	3.52844i	0.959708	−	0.140800i
$629$		−	25.0845i		−	1.00018i
$630$	11.4011	−	13.1958i	0.454229	−	0.525732i
$631$	−14.6113			−0.581667			−0.290834	−	0.956774i	$-0.593933\pi$
$631$	−14.6113			−0.581667			−0.290834	+	0.956774i	$0.593933\pi$
$632$	14.5294	−	22.8238i	0.577948	−	0.907882i
$633$	6.20903			0.246787
$634$	−8.53902	+	9.88321i	−0.339128	+	0.392512i
$635$		−	21.5021i		−	0.853285i
$636$	−0.440431	−	3.00202i	−0.0174642	−	0.119038i
$637$			12.1416i			0.481066i
$638$		0			0
$639$	−26.5744			−1.05127
$640$	14.0150	+	3.96256i	0.553992	+	0.156634i
$641$	29.6286			1.17026			0.585130	−	0.810940i	$-0.301043\pi$
$641$	29.6286			1.17026			0.585130	+	0.810940i	$0.301043\pi$
$642$	4.98190	+	4.30433i	0.196620	+	0.169878i
$643$		−	29.5335i		−	1.16469i	−0.812943	−	0.582344i	$-0.802136\pi$
$643$		−	29.5335i		−	1.16469i	0.812943	−	0.582344i	$-0.197864\pi$
$644$	3.33722	+	22.7468i	0.131505	+	0.896350i
$645$			0.980390i			0.0386028i
$646$	−13.9499	+	16.1458i	−0.548851	+	0.635250i
$647$	7.18758			0.282573			0.141286	−	0.989969i	$-0.454876\pi$
$647$	7.18758			0.282573			0.141286	+	0.989969i	$0.454876\pi$
$648$	12.2757	−	19.2836i	0.482235	−	0.757530i
$649$		0			0
$650$	9.53837	−	11.0399i	0.374126	−	0.433019i
$651$			2.84623i			0.111552i
$652$	16.4009	−	2.40620i	0.642307	−	0.0942340i
$653$			28.4975i			1.11520i	0.830111	+	0.557598i	$0.188277\pi$
$653$			28.4975i			1.11520i	−0.830111	+	0.557598i	$0.811723\pi$
$654$	0.676427	+	0.584428i	0.0264504	+	0.0228530i
$655$	−11.9697			−0.467695
$656$	−19.8667	+	5.95758i	−0.775663	+	0.232604i
$657$	−2.72036			−0.106131
$658$	11.3005	+	9.76353i	0.440538	+	0.380622i
$659$		−	26.9704i		−	1.05062i	−0.850912	−	0.525308i	$-0.823950\pi$
$659$		−	26.9704i		−	1.05062i	0.850912	−	0.525308i	$-0.176050\pi$
$660$		0			0
$661$			40.1424i			1.56136i	0.624931	+	0.780680i	$0.285127\pi$
$661$			40.1424i			1.56136i	−0.624931	+	0.780680i	$0.714873\pi$
$662$	3.69985	−	4.28227i	0.143799	−	0.166435i
$663$	3.17028			0.123123
$664$	−3.04988	−	1.94152i	−0.118358	−	0.0753456i
$665$	−20.0834			−0.778802
$666$	21.0087	−	24.3158i	0.814069	−	0.942217i
$667$			21.5214i			0.833310i
$668$	−2.59217	−	17.6685i	−0.100294	−	0.683614i
$669$		−	4.39574i		−	0.169949i
$670$	−6.47692	−	5.59602i	−0.250225	−	0.216193i
$671$		0			0
$672$	2.45674	−	5.48339i	0.0947709	−	0.211526i
$673$	−19.5859			−0.754982			−0.377491	−	0.926013i	$-0.623213\pi$
$673$	−19.5859			−0.754982			−0.377491	+	0.926013i	$0.623213\pi$
$674$	−2.52419	−	2.18089i	−0.0972283	−	0.0840046i
$675$			6.33187i			0.243714i
$676$	1.00898	+	6.87733i	0.0388071	+	0.264513i
$677$		−	14.2527i		−	0.547777i	−0.961761	−	0.273889i	$-0.911690\pi$
$677$		−	14.2527i		−	0.547777i	0.961761	−	0.273889i	$-0.0883099\pi$
$678$	−1.88519	+	2.18195i	−0.0724004	+	0.0837974i
$679$	46.1751			1.77204
$680$	9.82264	+	6.25298i	0.376681	+	0.239791i
$681$	−3.81859			−0.146329
$682$		0			0
$683$		−	11.2957i		−	0.432218i	−0.976369	−	0.216109i	$-0.930663\pi$
$683$		−	11.2957i		−	0.432218i	0.976369	−	0.216109i	$-0.0693367\pi$
$684$	−27.0448	+	3.96778i	−1.03408	+	0.151712i
$685$		−	11.6728i		−	0.445995i
$686$	−10.8486	−	9.37312i	−0.414201	−	0.357867i
$687$	−0.0699264			−0.00266786
$688$	−2.72403	−	9.08379i	−0.103853	−	0.346316i
$689$	−14.5756			−0.555284
$690$	1.53832	+	1.32910i	0.0585630	+	0.0505980i
$691$			8.58370i			0.326539i	0.986581	+	0.163270i	$0.0522041\pi$
$691$			8.58370i			0.326539i	−0.986581	+	0.163270i	$0.947796\pi$
$692$	16.8298	−	2.46912i	0.639771	−	0.0938619i
$693$		0			0
$694$	−22.1147	+	25.5959i	−0.839462	+	0.971607i
$695$	0.300602			0.0114025
$696$	3.02051	−	4.74484i	0.114492	−	0.179853i
$697$	−16.5819			−0.628085
$698$	1.96264	−	2.27159i	0.0742869	−	0.0859809i
$699$		−	1.18179i		−	0.0446995i
$700$	−3.20902	−	21.8730i	−0.121290	−	0.826721i
$701$			25.6358i			0.968252i	0.874998	+	0.484126i	$0.160862\pi$
$701$			25.6358i			0.968252i	−0.874998	+	0.484126i	$0.839138\pi$
$702$	6.25571	+	5.40489i	0.236107	+	0.203995i
$703$	−37.0076			−1.39577
$704$		0			0
$705$	1.32058			0.0497358
$706$	−5.47402	−	4.72952i	−0.206017	−	0.177998i
$707$		−	36.4266i		−	1.36996i
$708$	−1.31901	−	8.99046i	−0.0495712	−	0.337882i
$709$			29.7950i			1.11898i	0.828838	+	0.559488i	$0.189002\pi$
$709$			29.7950i			1.11898i	−0.828838	+	0.559488i	$0.810998\pi$
$710$	10.9188	−	12.6376i	0.409774	−	0.474279i
$711$	27.7102			1.03921
$712$	23.3707	−	36.7123i	0.875852	−	1.37585i
$713$	9.31524			0.348859
$714$	3.14059	−	3.63498i	0.117534	−	0.136036i
$715$		0			0
$716$	5.82458	−	0.854534i	0.217675	−	0.0319354i
$717$		−	6.43974i		−	0.240497i
$718$	−31.0030	−	26.7863i	−1.15702	−	0.999657i
$719$	43.5670			1.62477			0.812387	−	0.583118i	$-0.198168\pi$
$719$	43.5670			1.62477			0.812387	+	0.583118i	$0.198168\pi$
$720$	4.28465	+	14.2880i	0.159679	+	0.532481i
$721$	36.0356			1.34204
$722$	3.48797	+	3.01358i	0.129809	+	0.112154i
$723$			4.65040i			0.172950i
$724$	42.0912	−	6.17526i	1.56431	−	0.229502i
$725$		−	20.6946i		−	0.768578i
$726$		0			0
$727$	51.1659			1.89764			0.948819	−	0.315820i	$-0.102280\pi$
$727$	51.1659			1.89764			0.948819	+	0.315820i	$0.102280\pi$
$728$	−24.3491	−	15.5004i	−0.902439	−	0.574483i
$729$	21.5867			0.799508
$730$	1.11773	−	1.29368i	0.0413690	−	0.0478812i
$731$		−	7.58188i		−	0.280426i
$732$	−1.45160	−	9.89425i	−0.0536527	−	0.365702i
$733$		−	17.3837i		−	0.642082i	−0.947065	−	0.321041i	$-0.895967\pi$
$733$		−	17.3837i		−	0.642082i	0.947065	−	0.321041i	$-0.104033\pi$
$734$	−31.7766	−	27.4548i	−1.17290	−	1.01338i
$735$	1.62685			0.0600071
$736$	−17.9463	−	8.04052i	−0.661508	−	0.296377i
$737$		0			0
$738$	−16.0738	−	13.8876i	−0.591683	−	0.511210i
$739$			10.3923i			0.382286i	0.981562	+	0.191143i	$0.0612195\pi$
$739$			10.3923i			0.382286i	−0.981562	+	0.191143i	$0.938781\pi$
$740$	2.93152	+	19.9815i	0.107765	+	0.734535i
$741$		−	4.67717i		−	0.171820i
$742$	−14.4391	+	16.7120i	−0.530075	+	0.613518i
$743$	−12.5580			−0.460707			−0.230353	−	0.973107i	$-0.573988\pi$
$743$	−12.5580			−0.460707			−0.230353	+	0.973107i	$0.573988\pi$
$744$	−2.05374	−	1.30739i	−0.0752938	−	0.0479312i
$745$	2.94793			0.108004
$746$	3.76786	−	4.36098i	0.137951	−	0.159667i
$747$		−	3.70284i		−	0.135480i
$748$		0			0
$749$		−	47.9237i		−	1.75109i
$750$	−3.69179	−	3.18968i	−0.134805	−	0.116471i
$751$	40.6689			1.48403			0.742014	−	0.670384i	$-0.233871\pi$
$751$	40.6689			1.48403			0.742014	+	0.670384i	$0.233871\pi$
$752$	−12.2358	+	3.66924i	−0.446193	+	0.133804i
$753$	−6.95081			−0.253302
$754$	−20.4457	−	17.6649i	−0.744588	−	0.643319i
$755$		−	4.88658i		−	0.177841i
$756$	12.3943	−	1.81838i	0.450775	−	0.0661340i
$757$		−	35.9968i		−	1.30832i	−0.756354	−	0.654162i	$-0.773021\pi$
$757$		−	35.9968i		−	1.30832i	0.756354	−	0.654162i	$-0.226979\pi$
$758$	−26.9329	+	31.1726i	−0.978247	+	1.13224i
$759$		0			0
$760$	9.22514	−	14.4915i	0.334631	−	0.525663i
$761$	−23.3625			−0.846890			−0.423445	−	0.905922i	$-0.639179\pi$
$761$	−23.3625			−0.846890			−0.423445	+	0.905922i	$0.639179\pi$
$762$	4.96067	−	5.74156i	0.179706	−	0.207995i
$763$		−	6.50693i		−	0.235567i
$764$	−1.49683	−	10.2025i	−0.0541533	−	0.369114i
$765$			11.9256i			0.431171i
$766$	20.1369	+	17.3981i	0.727575	+	0.628620i
$767$	−43.6509			−1.57614
$768$	2.82815	+	4.29145i	0.102052	+	0.154854i
$769$	8.08790			0.291657			0.145829	−	0.989310i	$-0.453415\pi$
$769$	8.08790			0.291657			0.145829	+	0.989310i	$0.453415\pi$
$770$		0			0
$771$		−	2.73327i		−	0.0984365i
$772$	−7.84344	−	53.4616i	−0.282291	−	1.92412i
$773$		−	27.9261i		−	1.00443i	−0.864742	−	0.502216i	$-0.832518\pi$
$773$		−	27.9261i		−	1.00443i	0.864742	−	0.502216i	$-0.167482\pi$
$774$	6.34994	−	7.34953i	0.228244	−	0.264173i
$775$	−8.95739			−0.321759
$776$	−21.2101	+	33.3184i	−0.761399	+	1.19606i
$777$	8.33167			0.298897
$778$	−24.9735	+	28.9048i	−0.895345	+	1.03629i
$779$			24.4636i			0.876500i
$780$	−2.52534	+	0.370497i	−0.0904218	+	0.0132659i
$781$		0			0
$782$	−11.8967	−	10.2787i	−0.425425	−	0.367564i
$783$	11.7265			0.419072
$784$	−15.0735	+	4.52021i	−0.538340	+	0.161436i
$785$	−15.6459			−0.558427
$786$	−3.19619	−	2.76149i	−0.114004	−	0.0984990i
$787$			33.0205i			1.17705i	0.808478	+	0.588527i	$0.200292\pi$
$787$			33.0205i			1.17705i	−0.808478	+	0.588527i	$0.799708\pi$
$788$	13.2229	−	1.93995i	0.471045	−	0.0691077i
$789$			3.00232i			0.106886i
$790$	−11.3855	+	13.1777i	−0.405076	+	0.468842i
$791$	20.9894			0.746298
$792$		0			0
$793$	−48.0390			−1.70591
$794$	26.0066	−	30.1004i	0.922938	−	1.06822i
$795$			1.95297i			0.0692649i
$796$	−4.13948	−	28.2151i	−0.146720	−	1.00006i
$797$			25.9022i			0.917504i	0.888564	+	0.458752i	$0.151703\pi$
$797$			25.9022i			0.917504i	−0.888564	+	0.458752i	$0.848297\pi$
$798$	−5.36275	−	4.63338i	−0.189839	−	0.164020i
$799$	−10.2127			−0.361300
$800$	17.2568	+	7.73164i	0.610121	+	0.273355i
$801$	44.5722			1.57488
$802$	8.91721	+	7.70441i	0.314878	+	0.272052i
$803$		0			0
$804$	−0.438453	−	2.98853i	−0.0154630	−	0.105397i
$805$		−	14.7980i		−	0.521561i
$806$	−7.64604	+	8.84965i	−0.269320	+	0.311716i
$807$	−3.92863			−0.138294
$808$	26.2842	+	16.7322i	0.924675	+	0.588638i
$809$	−6.52260			−0.229322			−0.114661	−	0.993405i	$-0.536578\pi$
$809$	−6.52260			−0.229322			−0.114661	+	0.993405i	$0.536578\pi$
$810$	−9.61944	+	11.1337i	−0.337993	+	0.391198i
$811$			25.5743i			0.898035i	0.893523	+	0.449018i	$0.148226\pi$
$811$			25.5743i			0.898035i	−0.893523	+	0.449018i	$0.851774\pi$
$812$	−40.5085	+	5.94307i	−1.42157	+	0.208561i
$813$		−	7.92416i		−	0.277912i
$814$		0			0
$815$	−10.6696			−0.373741
$816$	1.18027	+	3.93584i	0.0413177	+	0.137782i
$817$	−11.1857			−0.391338
$818$	−4.43858	−	3.83490i	−0.155191	−	0.134084i
$819$		−	29.5621i		−	1.03298i
$820$	13.2086	−	1.93786i	0.461265	−	0.0676730i
$821$		−	14.1096i		−	0.492429i	−0.969215	−	0.246215i	$-0.920813\pi$
$821$		−	14.1096i		−	0.492429i	0.969215	−	0.246215i	$-0.0791868\pi$
$822$	2.69299	−	3.11691i	0.0939287	−	0.108715i
$823$	22.9254			0.799128			0.399564	−	0.916705i	$-0.369161\pi$
$823$	22.9254			0.799128			0.399564	+	0.916705i	$0.369161\pi$
$824$	−16.5526	+	26.0021i	−0.576639	+	0.905826i
$825$		0			0
$826$	−43.2422	+	50.0492i	−1.50459	+	1.74143i
$827$			40.9219i			1.42299i	0.702690	+	0.711496i	$0.251982\pi$
$827$			40.9219i			1.42299i	−0.702690	+	0.711496i	$0.748018\pi$
$828$	−2.92357	−	19.9273i	−0.101601	−	0.692522i
$829$			2.56458i			0.0890716i	0.999008	+	0.0445358i	$0.0141809\pi$
$829$			2.56458i			0.0890716i	−0.999008	+	0.0445358i	$0.985819\pi$
$830$	1.76090	+	1.52141i	0.0611217	+	0.0528088i
$831$	2.58633			0.0897186
$832$	22.3691	−	10.4495i	0.775509	−	0.362273i
$833$	−12.5813			−0.435915
$834$	0.0802676	+	0.0693507i	0.00277944	+	0.00240142i
$835$			11.4943i			0.397776i
$836$		0			0
$837$		−	5.07568i		−	0.175441i
$838$	6.70740	−	7.76326i	0.231703	−	0.268177i
$839$	−42.0345			−1.45119			−0.725595	−	0.688122i	$-0.758436\pi$
$839$	−42.0345			−1.45119			−0.725595	+	0.688122i	$0.758436\pi$
$840$	−2.07689	+	3.26253i	−0.0716596	+	0.112568i
$841$	−9.32614			−0.321591
$842$	32.5433	−	37.6661i	1.12152	−	1.29806i
$843$			4.26884i			0.147027i
$844$	38.2494	−	5.61163i	1.31660	−	0.193160i
$845$		−	4.47407i		−	0.153913i
$846$	−9.89975	−	8.55332i	−0.340361	−	0.294069i
$847$		0			0
$848$	−5.42637	−	18.0953i	−0.186342	−	0.621394i
$849$	−0.111118			−0.00381357
$850$	11.4397	+	9.88379i	0.392377	+	0.339011i
$851$		−	27.2682i		−	0.934742i
$852$	5.83113	−	0.855494i	0.199771	−	0.0293088i
$853$			20.4281i			0.699446i	0.936853	+	0.349723i	$0.113724\pi$
$853$			20.4281i			0.699446i	−0.936853	+	0.349723i	$0.886276\pi$
$854$	−47.5892	+	55.0805i	−1.62847	+	1.88482i
$855$	17.5941			0.601704
$856$	34.5801	+	22.0133i	1.18192	+	0.752400i
$857$	51.9575			1.77483			0.887417	−	0.460968i	$-0.152498\pi$
$857$	51.9575			1.77483			0.887417	+	0.460968i	$0.152498\pi$
$858$		0			0
$859$		−	44.6566i		−	1.52366i	−0.647775	−	0.761832i	$-0.724300\pi$
$859$		−	44.6566i		−	1.52366i	0.647775	−	0.761832i	$-0.275700\pi$
$860$	0.886062	+	6.03948i	0.0302145	+	0.205945i
$861$		−	5.50759i		−	0.187698i
$862$	−14.4550	−	12.4890i	−0.492338	−	0.425377i
$863$	50.4467			1.71723			0.858613	−	0.512624i	$-0.171327\pi$
$863$	50.4467			1.71723			0.858613	+	0.512624i	$0.171327\pi$
$864$	−4.38111	+	9.77854i	−0.149048	+	0.332673i
$865$	−10.9486			−0.372265
$866$	−15.5743	−	13.4561i	−0.529238	−	0.457258i
$867$		−	2.17568i		−	0.0738900i
$868$	2.57238	+	17.5336i	0.0873122	+	0.595128i
$869$		0			0
$870$	−2.36692	+	2.73951i	−0.0802461	+	0.0928782i
$871$	−14.5101			−0.491655
$872$	4.69518	+	2.98890i	0.158999	+	0.101217i
$873$	−40.4517			−1.36908
$874$	−15.1643	+	17.5514i	−0.512940	+	0.593685i
$875$			35.5134i			1.20057i
$876$	0.596919	−	0.0875750i	0.0201680	−	0.00295889i
$877$		−	18.0407i		−	0.609190i	−0.952482	−	0.304595i	$-0.901479\pi$
$877$		−	18.0407i		−	0.609190i	0.952482	−	0.304595i	$-0.0985211\pi$
$878$	−8.68824	−	7.50658i	−0.293214	−	0.253335i
$879$	1.23007			0.0414893
$880$		0			0
$881$	3.97122			0.133794			0.0668969	−	0.997760i	$-0.478690\pi$
$881$	3.97122			0.133794			0.0668969	+	0.997760i	$0.478690\pi$
$882$	−12.1957	−	10.5370i	−0.410651	−	0.354799i
$883$		−	49.5141i		−	1.66628i	−0.553059	−	0.833142i	$-0.686540\pi$
$883$		−	49.5141i		−	1.66628i	0.553059	−	0.833142i	$-0.313460\pi$
$884$	19.5298	−	2.86525i	0.656859	−	0.0963689i
$885$			5.84877i			0.196604i
$886$	−3.75572	+	4.34693i	−0.126176	+	0.146038i
$887$	33.4482			1.12308			0.561541	−	0.827449i	$-0.310209\pi$
$887$	33.4482			1.12308			0.561541	+	0.827449i	$0.310209\pi$
$888$	−3.82708	+	6.01185i	−0.128428	+	0.201744i
$889$	−55.2313			−1.85240
$890$	−18.3136	+	21.1965i	−0.613874	+	0.710508i
$891$		0			0
$892$	−3.97281	−	27.0790i	−0.133019	−	0.906673i
$893$			15.0670i			0.504199i
$894$	0.787166	+	0.680106i	0.0263268	+	0.0227461i
$895$	−3.78920			−0.126659
$896$	10.1784	−	35.9996i	0.340037	−	1.20266i
$897$	3.44626			0.115067
$898$	8.86799	+	7.66188i	0.295929	+	0.255680i
$899$			16.5890i			0.553273i
$900$	2.81126	+	19.1618i	0.0937086	+	0.638727i
$901$		−	15.1034i		−	0.503167i
$902$		0			0
$903$	2.51828			0.0838030
$904$	−9.64130	+	15.1453i	−0.320665	+	0.503724i
$905$	−27.3825			−0.910226
$906$	1.12737	−	1.30483i	0.0374542	−	0.0433501i
$907$		−	6.94962i		−	0.230759i	−0.993322	−	0.115379i	$-0.963192\pi$
$907$		−	6.94962i		−	0.230759i	0.993322	−	0.115379i	$-0.0368083\pi$
$908$	−23.5236	+	3.45119i	−0.780659	+	0.114532i
$909$			31.9115i			1.05844i
$910$	14.0584	+	12.1464i	0.466031	+	0.402648i
$911$	−42.4273			−1.40568			−0.702840	−	0.711348i	$-0.748085\pi$
$911$	−42.4273			−1.40568			−0.702840	+	0.711348i	$0.748085\pi$
$912$	5.80661	−	1.74128i	0.192276	−	0.0576594i
$913$		0			0
$914$	10.5175	+	9.08708i	0.347889	+	0.300574i
$915$			6.43673i			0.212792i
$916$	−0.430766	+	0.0631984i	−0.0142329	+	0.00208813i
$917$			30.7460i			1.01532i
$918$	−5.60063	+	6.48226i	−0.184848	+	0.213946i
$919$	3.22452			0.106367			0.0531836	−	0.998585i	$-0.483063\pi$
$919$	3.22452			0.106367			0.0531836	+	0.998585i	$0.483063\pi$
$920$	10.6777	+	6.79733i	0.352035	+	0.224101i
$921$	−7.62503			−0.251253
$922$	−22.6298	+	26.1921i	−0.745274	+	0.862592i
$923$		−	28.3116i		−	0.931886i
$924$		0			0
$925$			26.2207i			0.862131i
$926$	−21.6626	−	18.7163i	−0.711877	−	0.615057i
$927$	−31.5690			−1.03686
$928$	14.3189	−	31.9594i	0.470041	−	1.04912i
$929$	−23.9207			−0.784813			−0.392406	−	0.919792i	$-0.628357\pi$
$929$	−23.9207			−0.784813			−0.392406	+	0.919792i	$0.628357\pi$
$930$	1.18576	+	1.02449i	0.0388827	+	0.0335944i
$931$			18.5614i			0.608324i
$932$	−1.06809	−	7.28017i	−0.0349863	−	0.238470i
$933$			2.83363i			0.0927688i
$934$	22.5465	−	26.0957i	0.737743	−	0.853876i
$935$		0			0
$936$	21.3310	+	13.5791i	0.697226	+	0.443846i
$937$	24.2049			0.790739			0.395370	−	0.918522i	$-0.370617\pi$
$937$	24.2049			0.790739			0.395370	+	0.918522i	$0.370617\pi$
$938$	−14.3742	+	16.6369i	−0.469334	+	0.543215i
$939$		−	1.03286i		−	0.0337063i
$940$	8.13513	−	1.19352i	0.265339	−	0.0389283i
$941$			2.24680i			0.0732434i	0.999329	+	0.0366217i	$0.0116597\pi$
$941$			2.24680i			0.0732434i	−0.999329	+	0.0366217i	$0.988340\pi$
$942$	−4.17783	−	3.60961i	−0.136121	−	0.117608i
$943$	−18.0254			−0.586989
$944$	−16.2509	−	54.1917i	−0.528922	−	1.76379i
$945$	−8.06313			−0.262294
$946$		0			0
$947$		−	26.7519i		−	0.869321i	−0.900594	−	0.434660i	$-0.856868\pi$
$947$		−	26.7519i		−	0.869321i	0.900594	−	0.434660i	$-0.143132\pi$
$948$	−6.08036	+	0.892060i	−0.197481	+	0.0289728i
$949$		−	2.89819i		−	0.0940792i
$950$	14.5817	−	16.8771i	0.473094	−	0.547567i
$951$	2.96668			0.0962010
$952$	16.0617	−	25.2309i	0.520563	−	0.817738i
$953$	33.9853			1.10089			0.550445	−	0.834871i	$-0.314458\pi$
$953$	33.9853			1.10089			0.550445	+	0.834871i	$0.314458\pi$
$954$	12.6493	−	14.6405i	0.409537	−	0.474005i
$955$			6.63727i			0.214777i
$956$	−5.82015	−	39.6707i	−0.188237	−	1.28304i
$957$		0			0
$958$	1.85018	+	1.59854i	0.0597766	+	0.0516466i
$959$	−29.9833			−0.968211
$960$	−1.40013	−	2.99723i	−0.0451890	−	0.0967352i
$961$	−23.8197			−0.768377
$962$	25.9053	+	22.3820i	0.835221	+	0.721625i
$963$			41.9835i			1.35290i
$964$	4.20296	+	28.6478i	0.135368	+	0.922683i
$965$			34.7796i			1.11959i
$966$	3.41400	−	3.95141i	0.109843	−	0.127135i
$967$	3.94526			0.126871			0.0634356	−	0.997986i	$-0.479794\pi$
$967$	3.94526			0.126871			0.0634356	+	0.997986i	$0.479794\pi$
$968$		0			0
$969$	4.84655			0.155694
$970$	16.6206	−	19.2370i	0.533655	−	0.617661i
$971$		−	16.7355i		−	0.537067i	−0.963270	−	0.268534i	$-0.913461\pi$
$971$		−	16.7355i		−	0.537067i	0.963270	−	0.268534i	$-0.0865390\pi$
$972$	−16.3820	+	2.40343i	−0.525452	+	0.0770899i
$973$		−	0.772139i		−	0.0247537i
$974$	2.84116	+	2.45474i	0.0910366	+	0.0786550i
$975$	−3.31387			−0.106129
$976$	−17.8846	−	59.6394i	−0.572471	−	1.90901i
$977$	6.85898			0.219438			0.109719	−	0.993963i	$-0.465005\pi$
$977$	6.85898			0.219438			0.109719	+	0.993963i	$0.465005\pi$
$978$	−2.84904	−	2.46155i	−0.0911023	−	0.0787117i
$979$		0			0
$980$	10.0218	−	1.47032i	0.320136	−	0.0469676i
$981$			5.70039i			0.181999i
$982$	−27.0984	+	31.3641i	−0.864745	+	1.00087i
$983$	1.73756			0.0554196			0.0277098	−	0.999616i	$-0.491179\pi$
$983$	1.73756			0.0554196			0.0277098	+	0.999616i	$0.491179\pi$
$984$	3.97409	+	2.52986i	0.126689	+	0.0806490i
$985$	−8.60217			−0.274088
$986$	18.3047	−	21.1861i	0.582939	−	0.674703i
$987$		−	3.39210i		−	0.107972i
$988$	−4.22716	−	28.8127i	−0.134484	−	0.916655i
$989$		−	8.24192i		−	0.262078i
$990$		0			0
$991$	17.5645			0.557956			0.278978	−	0.960298i	$-0.410004\pi$
$991$	17.5645			0.557956			0.278978	+	0.960298i	$0.410004\pi$
$992$	−13.8332	−	6.19775i	−0.439205	−	0.196779i
$993$	−1.28542			−0.0407917
$994$	−32.4614	−	28.0465i	−1.02961	−	0.889580i
$995$			18.3554i			0.581906i
$996$	0.119203	+	0.812502i	0.00377711	+	0.0257451i
$997$			50.0422i			1.58485i	0.609967	+	0.792427i	$0.291183\pi$
$997$			50.0422i			1.58485i	−0.609967	+	0.792427i	$0.708817\pi$
$998$	7.44736	−	8.61969i	0.235742	−	0.272852i
$999$	−14.8579			−0.470083

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.c.h.485.5		20
4.3	odd	2		3872.2.c.h.1937.10		20
8.3	odd	2		3872.2.c.h.1937.11		20
8.5	even	2	inner	968.2.c.h.485.6		20
11.2	odd	10		968.2.o.d.565.6		40
11.3	even	5		88.2.o.a.53.2	yes	40
11.4	even	5		88.2.o.a.5.7	yes	40
11.5	even	5		968.2.o.j.245.10		40
11.6	odd	10		968.2.o.d.245.1		40
11.7	odd	10		968.2.o.i.269.4		40
11.8	odd	10		968.2.o.i.493.9		40
11.9	even	5		968.2.o.j.565.5		40
11.10	odd	2		968.2.c.i.485.16		20
33.14	odd	10		792.2.br.b.757.9		40
33.26	odd	10		792.2.br.b.181.4		40
44.3	odd	10		352.2.w.a.273.6		40
44.15	odd	10		352.2.w.a.49.5		40
44.43	even	2		3872.2.c.i.1937.10		20
88.3	odd	10		352.2.w.a.273.5		40
88.5	even	10		968.2.o.j.245.5		40
88.13	odd	10		968.2.o.d.565.1		40
88.21	odd	2		968.2.c.i.485.15		20
88.29	odd	10		968.2.o.i.269.9		40
88.37	even	10		88.2.o.a.5.2	✓	40
88.43	even	2		3872.2.c.i.1937.11		20
88.53	even	10		968.2.o.j.565.10		40
88.59	odd	10		352.2.w.a.49.6		40
88.61	odd	10		968.2.o.d.245.6		40
88.69	even	10		88.2.o.a.53.7	yes	40
88.85	odd	10		968.2.o.i.493.4		40
264.125	odd	10		792.2.br.b.181.9		40
264.245	odd	10		792.2.br.b.757.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.5.2	✓	40	88.37	even	10
88.2.o.a.5.7	yes	40	11.4	even	5
88.2.o.a.53.2	yes	40	11.3	even	5
88.2.o.a.53.7	yes	40	88.69	even	10
352.2.w.a.49.5		40	44.15	odd	10
352.2.w.a.49.6		40	88.59	odd	10
352.2.w.a.273.5		40	88.3	odd	10
352.2.w.a.273.6		40	44.3	odd	10
792.2.br.b.181.4		40	33.26	odd	10
792.2.br.b.181.9		40	264.125	odd	10
792.2.br.b.757.4		40	264.245	odd	10
792.2.br.b.757.9		40	33.14	odd	10
968.2.c.h.485.5		20	1.1	even	1	trivial
968.2.c.h.485.6		20	8.5	even	2	inner
968.2.c.i.485.15		20	88.21	odd	2
968.2.c.i.485.16		20	11.10	odd	2
968.2.o.d.245.1		40	11.6	odd	10
968.2.o.d.245.6		40	88.61	odd	10
968.2.o.d.565.1		40	88.13	odd	10
968.2.o.d.565.6		40	11.2	odd	10
968.2.o.i.269.4		40	11.7	odd	10
968.2.o.i.269.9		40	88.29	odd	10
968.2.o.i.493.4		40	88.85	odd	10
968.2.o.i.493.9		40	11.8	odd	10
968.2.o.j.245.5		40	88.5	even	10
968.2.o.j.245.10		40	11.5	even	5
968.2.o.j.565.5		40	11.9	even	5
968.2.o.j.565.10		40	88.53	even	10
3872.2.c.h.1937.10		20	4.3	odd	2
3872.2.c.h.1937.11		20	8.3	odd	2
3872.2.c.i.1937.10		20	44.43	even	2
3872.2.c.i.1937.11		20	88.43	even	2

Overview	Random
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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

Introduction

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Modular forms

Varieties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	968.2.c.h.485.5

Level	$968$
Weight	$2$
Character	968.485
Analytic conductor	$7.730$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$