LMFDB - Embedded newform 464.3.h.c.463.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [464,3,Mod(463,464)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("464.463"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(464, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$N$	$=$	$464 = 2^{4} \cdot 29$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	464.h (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$12.6430842663$
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:	$x^{20} + 58 x^{18} + 2256 x^{16} + 48540 x^{14} + 757617 x^{12} + 7081908 x^{10} + 46200312 x^{8} + \cdots + 529984$ x^20 + 58x^18 + 2256x^16 + 48540x^14 + 757617x^12 + 7081908x^10 + 46200312x^8 + 108855714x^6 + 191707065x^4 + 10229128*x^2 + 529984
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$2^{39}\cdot 3^{2}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			463.5
Root			$-1.77151 - 3.06835i$ of defining polynomial
Character	$\chi$	$=$	464.463
Dual form			464.3.h.c.463.6

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-3.54302 q^{3} -5.75893 q^{5} -7.46178i q^{7} +3.55302 q^{9} +9.81450 q^{11} -24.4611 q^{13} +20.4040 q^{15} -31.6529i q^{17} -10.6965 q^{19} +26.4372i q^{21} +31.8662i q^{23} +8.16525 q^{25} +19.2988 q^{27} +(16.2958 + 23.9885i) q^{29} +43.2458 q^{31} -34.7730 q^{33} +42.9718i q^{35} +31.4675i q^{37} +86.6662 q^{39} +58.5936i q^{41} +0.780751 q^{43} -20.4616 q^{45} -58.1838 q^{47} -6.67809 q^{49} +112.147i q^{51} -6.29082 q^{53} -56.5210 q^{55} +37.8981 q^{57} -79.3877i q^{59} +97.5739i q^{61} -26.5118i q^{63} +140.870 q^{65} +61.4643i q^{67} -112.903i q^{69} -72.5104i q^{71} -65.6030i q^{73} -28.9297 q^{75} -73.2336i q^{77} +152.080 q^{79} -100.353 q^{81} +13.4889i q^{83} +182.287i q^{85} +(-57.7365 - 84.9917i) q^{87} -44.0106i q^{89} +182.523i q^{91} -153.221 q^{93} +61.6006 q^{95} +26.8651i q^{97} +34.8711 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q - 8 q^{5} + 52 q^{9} - 16 q^{13} + 12 q^{25} + 4 q^{29} - 96 q^{33} - 112 q^{45} - 76 q^{49} - 112 q^{53} + 120 q^{57} + 136 q^{65} - 52 q^{81}+O(q^{100})$ 20 * q - 8 * q^5 + 52 * q^9 - 16 * q^13 + 12 * q^25 + 4 * q^29 - 96 * q^33 - 112 * q^45 - 76 * q^49 - 112 * q^53 + 120 * q^57 + 136 * q^65 - 52 * q^81

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$ .

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$-1$	$-1$

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

)

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

$2$		0			0
$2$		0			0
$3$	−3.54302			−1.18101			−0.590504	−	0.807035i	$-0.701071\pi$
$3$	−3.54302			−1.18101			−0.590504	+	0.807035i	$0.701071\pi$
$4$		0			0
$5$	−5.75893			−1.15179			−0.575893	−	0.817525i	$-0.695345\pi$
$5$	−5.75893			−1.15179			−0.575893	+	0.817525i	$0.695345\pi$
$6$		0			0
$7$		−	7.46178i		−	1.06597i	−0.846125	−	0.532984i	$-0.821071\pi$
$7$		−	7.46178i		−	1.06597i	0.846125	−	0.532984i	$-0.178929\pi$
$8$		0			0
$9$	3.55302			0.394780
$10$		0			0
$11$	9.81450			0.892228			0.446114	−	0.894976i	$-0.352808\pi$
$11$	9.81450			0.892228			0.446114	+	0.894976i	$0.352808\pi$
$12$		0			0
$13$	−24.4611			−1.88162			−0.940810	−	0.338933i	$-0.889934\pi$
$13$	−24.4611			−1.88162			−0.940810	+	0.338933i	$0.889934\pi$
$14$		0			0
$15$	20.4040			1.36027
$16$		0			0
$17$		−	31.6529i		−	1.86193i	−0.365103	−	0.930967i	$-0.618966\pi$
$17$		−	31.6529i		−	1.86193i	0.365103	−	0.930967i	$-0.381034\pi$
$18$		0			0
$19$	−10.6965			−0.562976			−0.281488	−	0.959565i	$-0.590828\pi$
$19$	−10.6965			−0.562976			−0.281488	+	0.959565i	$0.590828\pi$
$20$		0			0
$21$			26.4372i			1.25892i
$22$		0			0
$23$			31.8662i			1.38549i	0.721184	+	0.692744i	$0.243598\pi$
$23$			31.8662i			1.38549i	−0.721184	+	0.692744i	$0.756402\pi$
$24$		0			0
$25$	8.16525			0.326610
$26$		0			0
$27$	19.2988			0.714770
$28$		0			0
$29$	16.2958	+	23.9885i	0.561925	+	0.827188i
$29$	16.2958	+	23.9885i	0.561925	+	0.827188i
$30$		0			0
$31$	43.2458			1.39503			0.697513	−	0.716572i	$-0.254290\pi$
$31$	43.2458			1.39503			0.697513	+	0.716572i	$0.254290\pi$
$32$		0			0
$33$	−34.7730			−1.05373
$34$		0			0
$35$			42.9718i			1.22777i
$36$		0			0
$37$			31.4675i			0.850473i	0.905082	+	0.425237i	$0.139809\pi$
$37$			31.4675i			0.850473i	−0.905082	+	0.425237i	$0.860191\pi$
$38$		0			0
$39$	86.6662			2.22221
$40$		0			0
$41$			58.5936i			1.42911i	0.699579	+	0.714556i	$0.253371\pi$
$41$			58.5936i			1.42911i	−0.699579	+	0.714556i	$0.746629\pi$
$42$		0			0
$43$	0.780751			0.0181570			0.00907850	−	0.999959i	$-0.497110\pi$
$43$	0.780751			0.0181570			0.00907850	+	0.999959i	$0.497110\pi$
$44$		0			0
$45$	−20.4616			−0.454701
$46$		0			0
$47$	−58.1838			−1.23795			−0.618977	−	0.785409i	$-0.712452\pi$
$47$	−58.1838			−1.23795			−0.618977	+	0.785409i	$0.712452\pi$
$48$		0			0
$49$	−6.67809			−0.136288
$50$		0			0
$51$			112.147i			2.19896i
$52$		0			0
$53$	−6.29082			−0.118695			−0.0593473	−	0.998237i	$-0.518902\pi$
$53$	−6.29082			−0.118695			−0.0593473	+	0.998237i	$0.518902\pi$
$54$		0			0
$55$	−56.5210			−1.02765
$56$		0			0
$57$	37.8981			0.664879
$58$		0			0
$59$		−	79.3877i		−	1.34555i	−0.739845	−	0.672777i	$-0.765101\pi$
$59$		−	79.3877i		−	1.34555i	0.739845	−	0.672777i	$-0.234899\pi$
$60$		0			0
$61$			97.5739i			1.59957i	0.600285	+	0.799786i	$0.295054\pi$
$61$			97.5739i			1.59957i	−0.600285	+	0.799786i	$0.704946\pi$
$62$		0			0
$63$		−	26.5118i		−	0.420822i
$64$		0			0
$65$	140.870			2.16722
$66$		0			0
$67$			61.4643i			0.917378i	0.888597	+	0.458689i	$0.151681\pi$
$67$			61.4643i			0.917378i	−0.888597	+	0.458689i	$0.848319\pi$
$68$		0			0
$69$		−	112.903i		−	1.63627i
$70$		0			0
$71$		−	72.5104i		−	1.02127i	−0.859797	−	0.510637i	$-0.829410\pi$
$71$		−	72.5104i		−	1.02127i	0.859797	−	0.510637i	$-0.170590\pi$
$72$		0			0
$73$		−	65.6030i		−	0.898671i	−0.893363	−	0.449335i	$-0.851661\pi$
$73$		−	65.6030i		−	0.898671i	0.893363	−	0.449335i	$-0.148339\pi$
$74$		0			0
$75$	−28.9297			−0.385729
$76$		0			0
$77$		−	73.2336i		−	0.951086i
$78$		0			0
$79$	152.080			1.92506			0.962532	−	0.271168i	$-0.0874098\pi$
$79$	152.080			1.92506			0.962532	+	0.271168i	$0.0874098\pi$
$80$		0			0
$81$	−100.353			−1.23893
$82$		0			0
$83$			13.4889i			0.162517i	0.996693	+	0.0812585i	$0.0258939\pi$
$83$			13.4889i			0.162517i	−0.996693	+	0.0812585i	$0.974106\pi$
$84$		0			0
$85$			182.287i			2.14455i
$86$		0			0
$87$	−57.7365	−	84.9917i	−0.663638	−	0.976916i
$88$		0			0
$89$		−	44.0106i		−	0.494501i	−0.968952	−	0.247251i	$-0.920473\pi$
$89$		−	44.0106i		−	0.494501i	0.968952	−	0.247251i	$-0.0795271\pi$
$90$		0			0
$91$			182.523i			2.00575i
$92$		0			0
$93$	−153.221			−1.64754
$94$		0			0
$95$	61.6006			0.648427
$96$		0			0
$97$			26.8651i			0.276960i	0.990365	+	0.138480i	$0.0442216\pi$
$97$			26.8651i			0.276960i	−0.990365	+	0.138480i	$0.955778\pi$
$98$		0			0
$99$	34.8711			0.352233
$100$		0			0
$101$		−	34.1355i		−	0.337975i	−0.985618	−	0.168987i	$-0.945950\pi$
$101$		−	34.1355i		−	0.337975i	0.985618	−	0.168987i	$-0.0540497\pi$
$102$		0			0
$103$			126.735i			1.23044i	0.788357	+	0.615219i	$0.210932\pi$
$103$			126.735i			1.23044i	−0.788357	+	0.615219i	$0.789068\pi$
$104$		0			0
$105$		−	152.250i		−	1.45000i
$106$		0			0
$107$		−	103.444i		−	0.966765i	−0.875409	−	0.483383i	$-0.839408\pi$
$107$		−	103.444i		−	0.966765i	0.875409	−	0.483383i	$-0.160592\pi$
$108$		0			0
$109$	10.2809			0.0943203			0.0471601	−	0.998887i	$-0.484983\pi$
$109$	10.2809			0.0943203			0.0471601	+	0.998887i	$0.484983\pi$
$110$		0			0
$111$		−	111.490i		−	1.00442i
$112$		0			0
$113$			16.0748i			0.142255i	0.997467	+	0.0711273i	$0.0226597\pi$
$113$			16.0748i			0.142255i	−0.997467	+	0.0711273i	$0.977340\pi$
$114$		0			0
$115$		−	183.515i		−	1.59578i
$116$		0			0
$117$	−86.9106			−0.742826
$118$		0			0
$119$	−236.187			−1.98476
$120$		0			0
$121$	−24.6755			−0.203930
$122$		0			0
$123$		−	207.598i		−	1.68779i
$124$		0			0
$125$	96.9501			0.775601
$126$		0			0
$127$	61.9767			0.488006			0.244003	−	0.969775i	$-0.421539\pi$
$127$	61.9767			0.488006			0.244003	+	0.969775i	$0.421539\pi$
$128$		0			0
$129$	−2.76622			−0.0214436
$130$		0			0
$131$	41.2258			0.314701			0.157350	−	0.987543i	$-0.449705\pi$
$131$	41.2258			0.314701			0.157350	+	0.987543i	$0.449705\pi$
$132$		0			0
$133$			79.8152i			0.600114i
$134$		0			0
$135$	−111.140			−0.823262
$136$		0			0
$137$		−	83.2253i		−	0.607484i	−0.952754	−	0.303742i	$-0.901764\pi$
$137$		−	83.2253i		−	0.607484i	0.952754	−	0.303742i	$-0.0982361\pi$
$138$		0			0
$139$			9.09746i			0.0654494i	0.999464	+	0.0327247i	$0.0104184\pi$
$139$			9.09746i			0.0654494i	−0.999464	+	0.0327247i	$0.989582\pi$
$140$		0			0
$141$	206.147			1.46203
$142$		0			0
$143$	−240.073			−1.67883
$144$		0			0
$145$	−93.8465	−	138.148i	−0.647217	−	0.952743i
$146$		0			0
$147$	23.6606			0.160957
$148$		0			0
$149$	−216.223			−1.45116			−0.725581	−	0.688137i	$-0.758429\pi$
$149$	−216.223			−1.45116			−0.725581	+	0.688137i	$0.758429\pi$
$150$		0			0
$151$			174.319i			1.15443i	0.816593	+	0.577214i	$0.195860\pi$
$151$			174.319i			1.15443i	−0.816593	+	0.577214i	$0.804140\pi$
$152$		0			0
$153$		−	112.463i		−	0.735054i
$154$		0			0
$155$	−249.050			−1.60677
$156$		0			0
$157$		−	60.1381i		−	0.383045i	−0.981488	−	0.191523i	$-0.938657\pi$
$157$		−	60.1381i		−	0.383045i	0.981488	−	0.191523i	$-0.0613425\pi$
$158$		0			0
$159$	22.2885			0.140179
$160$		0			0
$161$	237.779			1.47689
$162$		0			0
$163$	20.7060			0.127030			0.0635152	−	0.997981i	$-0.479769\pi$
$163$	20.7060			0.127030			0.0635152	+	0.997981i	$0.479769\pi$
$164$		0			0
$165$	200.255			1.21367
$166$		0			0
$167$			96.1260i			0.575605i	0.957690	+	0.287802i	$0.0929246\pi$
$167$			96.1260i			0.575605i	−0.957690	+	0.287802i	$0.907075\pi$
$168$		0			0
$169$	429.344			2.54050
$170$		0			0
$171$	−38.0050			−0.222251
$172$		0			0
$173$	84.2883			0.487216			0.243608	−	0.969874i	$-0.421669\pi$
$173$	84.2883			0.487216			0.243608	+	0.969874i	$0.421669\pi$
$174$		0			0
$175$		−	60.9272i		−	0.348156i
$176$		0			0
$177$			281.272i			1.58911i
$178$		0			0
$179$			53.6504i			0.299723i	0.988707	+	0.149862i	$0.0478828\pi$
$179$			53.6504i			0.299723i	−0.988707	+	0.149862i	$0.952117\pi$
$180$		0			0
$181$	−43.4191			−0.239885			−0.119942	−	0.992781i	$-0.538271\pi$
$181$	−43.4191			−0.239885			−0.119942	+	0.992781i	$0.538271\pi$
$182$		0			0
$183$		−	345.707i		−	1.88911i
$184$		0			0
$185$		−	181.219i		−	0.979563i
$186$		0			0
$187$		−	310.657i		−	1.66127i
$188$		0			0
$189$		−	144.003i		−	0.761922i
$190$		0			0
$191$	51.7388			0.270884			0.135442	−	0.990785i	$-0.456755\pi$
$191$	51.7388			0.270884			0.135442	+	0.990785i	$0.456755\pi$
$192$		0			0
$193$			288.657i			1.49563i	0.663906	+	0.747816i	$0.268897\pi$
$193$			288.657i			1.49563i	−0.663906	+	0.747816i	$0.731103\pi$
$194$		0			0
$195$	−499.104			−2.55951
$196$		0			0
$197$	−175.159			−0.889130			−0.444565	−	0.895747i	$-0.646642\pi$
$197$	−175.159			−0.889130			−0.444565	+	0.895747i	$0.646642\pi$
$198$		0			0
$199$			287.144i			1.44294i	0.692448	+	0.721468i	$0.256532\pi$
$199$			287.144i			1.44294i	−0.692448	+	0.721468i	$0.743468\pi$
$200$		0			0
$201$		−	217.769i		−	1.08343i
$202$		0			0
$203$	178.996	−	121.596i	0.881756	−	0.598994i
$204$		0			0
$205$		−	337.436i		−	1.64603i
$206$		0			0
$207$			113.221i			0.546962i
$208$		0			0
$209$	−104.981			−0.502302
$210$		0			0
$211$	−141.303			−0.669680			−0.334840	−	0.942275i	$-0.608682\pi$
$211$	−141.303			−0.669680			−0.334840	+	0.942275i	$0.608682\pi$
$212$		0			0
$213$			256.906i			1.20613i
$214$		0			0
$215$	−4.49629			−0.0209130
$216$		0			0
$217$		−	322.691i		−	1.48705i
$218$		0			0
$219$			232.433i			1.06134i
$220$		0			0
$221$			774.264i			3.50345i
$222$		0			0
$223$		−	55.8378i		−	0.250394i	−0.992132	−	0.125197i	$-0.960044\pi$
$223$		−	55.8378i		−	0.250394i	0.992132	−	0.125197i	$-0.0399562\pi$
$224$		0			0
$225$	29.0113			0.128939
$226$		0			0
$227$		−	15.8781i		−	0.0699477i	−0.999388	−	0.0349738i	$-0.988865\pi$
$227$		−	15.8781i		−	0.0699477i	0.999388	−	0.0349738i	$-0.0111348\pi$
$228$		0			0
$229$			123.314i			0.538491i	0.963072	+	0.269245i	$0.0867742\pi$
$229$			123.314i			0.538491i	−0.963072	+	0.269245i	$0.913226\pi$
$230$		0			0
$231$			259.468i			1.12324i
$232$		0			0
$233$	129.495			0.555771			0.277885	−	0.960614i	$-0.410366\pi$
$233$	129.495			0.555771			0.277885	+	0.960614i	$0.410366\pi$
$234$		0			0
$235$	335.076			1.42586
$236$		0			0
$237$	−538.823			−2.27352
$238$		0			0
$239$			318.026i			1.33065i	0.746553	+	0.665326i	$0.231707\pi$
$239$			318.026i			1.33065i	−0.746553	+	0.665326i	$0.768293\pi$
$240$		0			0
$241$	133.676			0.554672			0.277336	−	0.960773i	$-0.410548\pi$
$241$	133.676			0.554672			0.277336	+	0.960773i	$0.410548\pi$
$242$		0			0
$243$	181.865			0.748415
$244$		0			0
$245$	38.4587			0.156974
$246$		0			0
$247$	261.649			1.05931
$248$		0			0
$249$		−	47.7915i		−	0.191934i
$250$		0			0
$251$	332.888			1.32625			0.663124	−	0.748510i	$-0.269230\pi$
$251$	332.888			1.32625			0.663124	+	0.748510i	$0.269230\pi$
$252$		0			0
$253$			312.751i			1.23617i
$254$		0			0
$255$		−	645.846i		−	2.53273i
$256$		0			0
$257$	−236.189			−0.919024			−0.459512	−	0.888172i	$-0.651976\pi$
$257$	−236.189			−0.919024			−0.459512	+	0.888172i	$0.651976\pi$
$258$		0			0
$259$	234.804			0.906577
$260$		0			0
$261$	57.8993	+	85.2314i	0.221837	+	0.326557i
$262$		0			0
$263$	−107.908			−0.410298			−0.205149	−	0.978731i	$-0.565768\pi$
$263$	−107.908			−0.410298			−0.205149	+	0.978731i	$0.565768\pi$
$264$		0			0
$265$	36.2284			0.136711
$266$		0			0
$267$			155.931i			0.584010i
$268$		0			0
$269$			29.2789i			0.108843i	0.998518	+	0.0544217i	$0.0173315\pi$
$269$			29.2789i			0.108843i	−0.998518	+	0.0544217i	$0.982668\pi$
$270$		0			0
$271$	−414.903			−1.53101			−0.765503	−	0.643432i	$-0.777510\pi$
$271$	−414.903			−1.53101			−0.765503	+	0.643432i	$0.777510\pi$
$272$		0			0
$273$		−	646.683i		−	2.36880i
$274$		0			0
$275$	80.1378			0.291410
$276$		0			0
$277$	−194.376			−0.701720			−0.350860	−	0.936428i	$-0.614111\pi$
$277$	−194.376			−0.701720			−0.350860	+	0.936428i	$0.614111\pi$
$278$		0			0
$279$	153.653			0.550728
$280$		0			0
$281$	101.444			0.361011			0.180505	−	0.983574i	$-0.442227\pi$
$281$	101.444			0.361011			0.180505	+	0.983574i	$0.442227\pi$
$282$		0			0
$283$			199.393i			0.704570i	0.935893	+	0.352285i	$0.114595\pi$
$283$			199.393i			0.704570i	−0.935893	+	0.352285i	$0.885405\pi$
$284$		0			0
$285$	−218.252			−0.765798
$286$		0			0
$287$	437.212			1.52339
$288$		0			0
$289$	−712.905			−2.46680
$290$		0			0
$291$		−	95.1837i		−	0.327092i
$292$		0			0
$293$		−	216.369i		−	0.738462i	−0.929338	−	0.369231i	$-0.879621\pi$
$293$		−	216.369i		−	0.738462i	0.929338	−	0.369231i	$-0.120379\pi$
$294$		0			0
$295$			457.188i			1.54979i
$296$		0			0
$297$	189.408			0.637738
$298$		0			0
$299$		−	779.482i		−	2.60696i
$300$		0			0
$301$		−	5.82579i		−	0.0193548i
$302$		0			0
$303$			120.943i			0.399151i
$304$		0			0
$305$		−	561.921i		−	1.84236i
$306$		0			0
$307$	132.587			0.431878			0.215939	−	0.976407i	$-0.430719\pi$
$307$	132.587			0.431878			0.215939	+	0.976407i	$0.430719\pi$
$308$		0			0
$309$		−	449.025i		−	1.45316i
$310$		0			0
$311$	−193.555			−0.622363			−0.311181	−	0.950351i	$-0.600725\pi$
$311$	−193.555			−0.622363			−0.311181	+	0.950351i	$0.600725\pi$
$312$		0			0
$313$	344.412			1.10036			0.550180	−	0.835046i	$-0.314559\pi$
$313$	344.412			1.10036			0.550180	+	0.835046i	$0.314559\pi$
$314$		0			0
$315$			152.680i			0.484697i
$316$		0			0
$317$			243.318i			0.767564i	0.923424	+	0.383782i	$0.125379\pi$
$317$			243.318i			0.767564i	−0.923424	+	0.383782i	$0.874621\pi$
$318$		0			0
$319$	159.935	+	235.435i	0.501365	+	0.738040i
$320$		0			0
$321$			366.504i			1.14176i
$322$		0			0
$323$			338.576i			1.04822i
$324$		0			0
$325$	−199.731			−0.614556
$326$		0			0
$327$	−36.4255			−0.111393
$328$		0			0
$329$			434.154i			1.31962i
$330$		0			0
$331$	214.669			0.648546			0.324273	−	0.945964i	$-0.394880\pi$
$331$	214.669			0.648546			0.324273	+	0.945964i	$0.394880\pi$
$332$		0			0
$333$			111.805i			0.335750i
$334$		0			0
$335$		−	353.968i		−	1.05662i
$336$		0			0
$337$			500.765i			1.48595i	0.669319	+	0.742975i	$0.266586\pi$
$337$			500.765i			1.48595i	−0.669319	+	0.742975i	$0.733414\pi$
$338$		0			0
$339$		−	56.9533i		−	0.168004i
$340$		0			0
$341$	424.436			1.24468
$342$		0			0
$343$		−	315.797i		−	0.920690i
$344$		0			0
$345$			650.199i			1.88463i
$346$		0			0
$347$			591.142i			1.70358i	0.523884	+	0.851790i	$0.324483\pi$
$347$			591.142i			1.70358i	−0.523884	+	0.851790i	$0.675517\pi$
$348$		0			0
$349$	−503.562			−1.44287			−0.721435	−	0.692482i	$-0.756517\pi$
$349$	−503.562			−1.44287			−0.721435	+	0.692482i	$0.756517\pi$
$350$		0			0
$351$	−472.069			−1.34493
$352$		0			0
$353$	201.979			0.572178			0.286089	−	0.958203i	$-0.407645\pi$
$353$	201.979			0.572178			0.286089	+	0.958203i	$0.407645\pi$
$354$		0			0
$355$			417.582i			1.17629i
$356$		0			0
$357$	836.815			2.34402
$358$		0			0
$359$	197.013			0.548782			0.274391	−	0.961618i	$-0.411524\pi$
$359$	197.013			0.548782			0.274391	+	0.961618i	$0.411524\pi$
$360$		0			0
$361$	−246.584			−0.683058
$362$		0			0
$363$	87.4260			0.240843
$364$		0			0
$365$			377.803i			1.03508i
$366$		0			0
$367$	572.067			1.55877			0.779383	−	0.626547i	$-0.215532\pi$
$367$	572.067			1.55877			0.779383	+	0.626547i	$0.215532\pi$
$368$		0			0
$369$			208.184i			0.564184i
$370$		0			0
$371$			46.9407i			0.126525i
$372$		0			0
$373$	15.6158			0.0418654			0.0209327	−	0.999781i	$-0.493336\pi$
$373$	15.6158			0.0418654			0.0209327	+	0.999781i	$0.493336\pi$
$374$		0			0
$375$	−343.497			−0.915991
$376$		0			0
$377$	−398.613	−	586.783i	−1.05733	−	1.55645i
$378$		0			0
$379$	401.028			1.05812			0.529061	−	0.848584i	$-0.322544\pi$
$379$	401.028			1.05812			0.529061	+	0.848584i	$0.322544\pi$
$380$		0			0
$381$	−219.585			−0.576338
$382$		0			0
$383$			249.642i			0.651806i	0.945403	+	0.325903i	$0.105668\pi$
$383$			249.642i			0.651806i	−0.945403	+	0.325903i	$0.894332\pi$
$384$		0			0
$385$			421.747i			1.09545i
$386$		0			0
$387$	2.77402			0.00716801
$388$		0			0
$389$		−	653.665i		−	1.68037i	−0.542298	−	0.840186i	$-0.682446\pi$
$389$		−	653.665i		−	1.68037i	0.542298	−	0.840186i	$-0.317554\pi$
$390$		0			0
$391$	1008.66			2.57969
$392$		0			0
$393$	−146.064			−0.371664
$394$		0			0
$395$	−875.818			−2.21726
$396$		0			0
$397$	−87.5596			−0.220553			−0.110277	−	0.993901i	$-0.535174\pi$
$397$	−87.5596			−0.220553			−0.110277	+	0.993901i	$0.535174\pi$
$398$		0			0
$399$		−	282.787i		−	0.708739i
$400$		0			0
$401$	259.162			0.646289			0.323145	−	0.946350i	$-0.395260\pi$
$401$	259.162			0.646289			0.323145	+	0.946350i	$0.395260\pi$
$402$		0			0
$403$	−1057.84			−2.62491
$404$		0			0
$405$	577.927			1.42698
$406$		0			0
$407$			308.838i			0.758816i
$408$		0			0
$409$			557.887i			1.36403i	0.731339	+	0.682014i	$0.238896\pi$
$409$			557.887i			1.36403i	−0.731339	+	0.682014i	$0.761104\pi$
$410$		0			0
$411$			294.869i			0.717444i
$412$		0			0
$413$	−592.373			−1.43432
$414$		0			0
$415$		−	77.6817i		−	0.187185i
$416$		0			0
$417$		−	32.2325i		−	0.0772962i
$418$		0			0
$419$		−	35.2967i		−	0.0842404i	−0.999113	−	0.0421202i	$-0.986589\pi$
$419$		−	35.2967i		−	0.0842404i	0.999113	−	0.0421202i	$-0.0134112\pi$
$420$		0			0
$421$			141.845i			0.336925i	0.985708	+	0.168462i	$0.0538802\pi$
$421$			141.845i			0.336925i	−0.985708	+	0.168462i	$0.946120\pi$
$422$		0			0
$423$	−206.728			−0.488719
$424$		0			0
$425$		−	258.454i		−	0.608126i
$426$		0			0
$427$	728.075			1.70509
$428$		0			0
$429$	850.585			1.98272
$430$		0			0
$431$		−	72.3234i		−	0.167804i	−0.996474	−	0.0839019i	$-0.973262\pi$
$431$		−	72.3234i		−	0.167804i	0.996474	−	0.0839019i	$-0.0267382\pi$
$432$		0			0
$433$			449.396i			1.03787i	0.854815	+	0.518933i	$0.173671\pi$
$433$			449.396i			1.03787i	−0.854815	+	0.518933i	$0.826329\pi$
$434$		0			0
$435$	332.500	+	489.461i	0.764368	+	1.12520i
$436$		0			0
$437$		−	340.858i		−	0.779996i
$438$		0			0
$439$		−	42.7259i		−	0.0973255i	−0.998815	−	0.0486628i	$-0.984504\pi$
$439$		−	42.7259i		−	0.0973255i	0.998815	−	0.0486628i	$-0.0154960\pi$
$440$		0			0
$441$	−23.7274			−0.0538036
$442$		0			0
$443$	−74.3554			−0.167845			−0.0839226	−	0.996472i	$-0.526745\pi$
$443$	−74.3554			−0.167845			−0.0839226	+	0.996472i	$0.526745\pi$
$444$		0			0
$445$			253.454i			0.569560i
$446$		0			0
$447$	766.083			1.71383
$448$		0			0
$449$			6.57664i			0.0146473i	0.999973	+	0.00732365i	$0.00233121\pi$
$449$			6.57664i			0.0146473i	−0.999973	+	0.00732365i	$0.997669\pi$
$450$		0			0
$451$			575.067i			1.27509i
$452$		0			0
$453$		−	617.615i		−	1.36339i
$454$		0			0
$455$		−	1051.14i		−	2.31019i
$456$		0			0
$457$	−794.811			−1.73919			−0.869597	−	0.493763i	$-0.835621\pi$
$457$	−794.811			−1.73919			−0.869597	+	0.493763i	$0.835621\pi$
$458$		0			0
$459$		−	610.862i		−	1.33085i
$460$		0			0
$461$			133.708i			0.290040i	0.989429	+	0.145020i	$0.0463246\pi$
$461$			133.708i			0.290040i	−0.989429	+	0.145020i	$0.953675\pi$
$462$		0			0
$463$			364.812i			0.787930i	0.919125	+	0.393965i	$0.128897\pi$
$463$			364.812i			0.787930i	−0.919125	+	0.393965i	$0.871103\pi$
$464$		0			0
$465$	882.389			1.89761
$466$		0			0
$467$	−214.489			−0.459292			−0.229646	−	0.973274i	$-0.573757\pi$
$467$	−214.489			−0.459292			−0.229646	+	0.973274i	$0.573757\pi$
$468$		0			0
$469$	458.633			0.977895
$470$		0			0
$471$			213.071i			0.452379i
$472$		0			0
$473$	7.66268			0.0162002
$474$		0			0
$475$	−87.3399			−0.183873
$476$		0			0
$477$	−22.3514			−0.0468582
$478$		0			0
$479$	−691.711			−1.44407			−0.722036	−	0.691855i	$-0.756794\pi$
$479$	−691.711			−1.44407			−0.722036	+	0.691855i	$0.756794\pi$
$480$		0			0
$481$		−	769.729i		−	1.60027i
$482$		0			0
$483$	−842.455			−1.74421
$484$		0			0
$485$		−	154.714i		−	0.318998i
$486$		0			0
$487$		−	651.298i		−	1.33737i	−0.743547	−	0.668683i	$-0.766858\pi$
$487$		−	651.298i		−	1.33737i	0.743547	−	0.668683i	$-0.233142\pi$
$488$		0			0
$489$	−73.3617			−0.150024
$490$		0			0
$491$	388.866			0.791988			0.395994	−	0.918253i	$-0.370400\pi$
$491$	388.866			0.791988			0.395994	+	0.918253i	$0.370400\pi$
$492$		0			0
$493$	759.304	−	515.810i	1.54017	−	1.04627i
$494$		0			0
$495$	−200.820			−0.405697
$496$		0			0
$497$	−541.056			−1.08864
$498$		0			0
$499$			73.2897i			0.146873i	0.997300	+	0.0734365i	$0.0233966\pi$
$499$			73.2897i			0.146873i	−0.997300	+	0.0734365i	$0.976603\pi$
$500$		0			0
$501$		−	340.577i		−	0.679794i
$502$		0			0
$503$	232.895			0.463013			0.231506	−	0.972833i	$-0.425635\pi$
$503$	232.895			0.463013			0.231506	+	0.972833i	$0.425635\pi$
$504$		0			0
$505$			196.584i			0.389275i
$506$		0			0
$507$	−1521.18			−3.00035
$508$		0			0
$509$	−420.913			−0.826941			−0.413471	−	0.910517i	$-0.635684\pi$
$509$	−420.913			−0.826941			−0.413471	+	0.910517i	$0.635684\pi$
$510$		0			0
$511$	−489.515			−0.957954
$512$		0			0
$513$	−206.430			−0.402398
$514$		0			0
$515$		−	729.858i		−	1.41720i
$516$		0			0
$517$	−571.045			−1.10454
$518$		0			0
$519$	−298.636			−0.575406
$520$		0			0
$521$	−153.918			−0.295428			−0.147714	−	0.989030i	$-0.547191\pi$
$521$	−153.918			−0.295428			−0.147714	+	0.989030i	$0.547191\pi$
$522$		0			0
$523$		−	1006.66i		−	1.92479i	−0.271659	−	0.962394i	$-0.587572\pi$
$523$		−	1006.66i		−	1.92479i	0.271659	−	0.962394i	$-0.412428\pi$
$524$		0			0
$525$			215.867i			0.411175i
$526$		0			0
$527$		−	1368.86i		−	2.59745i
$528$		0			0
$529$	−486.456			−0.919577
$530$		0			0
$531$		−	282.066i		−	0.531197i
$532$		0			0
$533$		−	1433.26i		−	2.68905i
$534$		0			0
$535$			595.726i			1.11351i
$536$		0			0
$537$		−	190.085i		−	0.353975i
$538$		0			0
$539$	−65.5422			−0.121600
$540$		0			0
$541$		−	133.788i		−	0.247297i	−0.992326	−	0.123648i	$-0.960541\pi$
$541$		−	133.788i		−	0.247297i	0.992326	−	0.123648i	$-0.0394595\pi$
$542$		0			0
$543$	153.835			0.283306
$544$		0			0
$545$	−59.2070			−0.108637
$546$		0			0
$547$		−	936.556i		−	1.71217i	−0.516836	−	0.856084i	$-0.672890\pi$
$547$		−	936.556i		−	1.71217i	0.516836	−	0.856084i	$-0.327110\pi$
$548$		0			0
$549$			346.682i			0.631479i
$550$		0			0
$551$	−174.309	−	256.593i	−0.316350	−	0.465687i
$552$		0			0
$553$		−	1134.79i		−	2.05206i
$554$		0			0
$555$			642.064i			1.15687i
$556$		0			0
$557$	279.029			0.500950			0.250475	−	0.968123i	$-0.419413\pi$
$557$	279.029			0.500950			0.250475	+	0.968123i	$0.419413\pi$
$558$		0			0
$559$	−19.0980			−0.0341646
$560$		0			0
$561$			1100.67i			1.96197i
$562$		0			0
$563$	−488.328			−0.867367			−0.433683	−	0.901065i	$-0.642786\pi$
$563$	−488.328			−0.867367			−0.433683	+	0.901065i	$0.642786\pi$
$564$		0			0
$565$		−	92.5734i		−	0.163847i
$566$		0			0
$567$			748.813i			1.32066i
$568$		0			0
$569$			144.177i			0.253387i	0.991942	+	0.126694i	$0.0404365\pi$
$569$			144.177i			0.253387i	−0.991942	+	0.126694i	$0.959563\pi$
$570$		0			0
$571$			229.348i			0.401660i	0.979626	+	0.200830i	$0.0643639\pi$
$571$			229.348i			0.401660i	−0.979626	+	0.200830i	$0.935636\pi$
$572$		0			0
$573$	−183.312			−0.319916
$574$		0			0
$575$			260.196i			0.452514i
$576$		0			0
$577$			376.336i			0.652230i	0.945330	+	0.326115i	$0.105740\pi$
$577$			376.336i			0.652230i	−0.945330	+	0.326115i	$0.894260\pi$
$578$		0			0
$579$		−	1022.72i		−	1.76635i
$580$		0			0
$581$	100.651			0.173238
$582$		0			0
$583$	−61.7412			−0.105903
$584$		0			0
$585$	500.512			0.855576
$586$		0			0
$587$			188.714i			0.321489i	0.986996	+	0.160745i	$0.0513896\pi$
$587$			188.714i			0.321489i	−0.986996	+	0.160745i	$0.948610\pi$
$588$		0			0
$589$	−462.581			−0.785366
$590$		0			0
$591$	620.591			1.05007
$592$		0			0
$593$	924.578			1.55915			0.779577	−	0.626307i	$-0.215434\pi$
$593$	924.578			1.55915			0.779577	+	0.626307i	$0.215434\pi$
$594$		0			0
$595$	1360.18			2.28602
$596$		0			0
$597$		−	1017.36i		−	1.70412i
$598$		0			0
$599$	−1072.25			−1.79007			−0.895036	−	0.445995i	$-0.852850\pi$
$599$	−1072.25			−1.79007			−0.895036	+	0.445995i	$0.852850\pi$
$600$		0			0
$601$			532.609i			0.886204i	0.896471	+	0.443102i	$0.146122\pi$
$601$			532.609i			0.886204i	−0.896471	+	0.443102i	$0.853878\pi$
$602$		0			0
$603$			218.384i			0.362162i
$604$		0			0
$605$	142.105			0.234884
$606$		0			0
$607$	−518.495			−0.854193			−0.427096	−	0.904206i	$-0.640464\pi$
$607$	−518.495			−0.854193			−0.427096	+	0.904206i	$0.640464\pi$
$608$		0			0
$609$	−634.189	+	430.817i	−1.04136	+	0.707417i
$610$		0			0
$611$	1423.24			2.32936
$612$		0			0
$613$	616.223			1.00526			0.502629	−	0.864502i	$-0.332366\pi$
$613$	616.223			1.00526			0.502629	+	0.864502i	$0.332366\pi$
$614$		0			0
$615$			1195.54i			1.94397i
$616$		0			0
$617$			483.931i			0.784330i	0.919895	+	0.392165i	$0.128274\pi$
$617$			483.931i			0.784330i	−0.919895	+	0.392165i	$0.871726\pi$
$618$		0			0
$619$	−57.1495			−0.0923255			−0.0461628	−	0.998934i	$-0.514699\pi$
$619$	−57.1495			−0.0923255			−0.0461628	+	0.998934i	$0.514699\pi$
$620$		0			0
$621$			614.980i			0.990305i
$622$		0			0
$623$	−328.397			−0.527123
$624$		0			0
$625$	−762.460			−1.21994
$626$		0			0
$627$	371.951			0.593223
$628$		0			0
$629$	996.038			1.58353
$630$		0			0
$631$			935.223i			1.48213i	0.671434	+	0.741064i	$0.265679\pi$
$631$			935.223i			1.48213i	−0.671434	+	0.741064i	$0.734321\pi$
$632$		0			0
$633$	500.638			0.790898
$634$		0			0
$635$	−356.919			−0.562078
$636$		0			0
$637$	163.353			0.256442
$638$		0			0
$639$		−	257.631i		−	0.403178i
$640$		0			0
$641$			210.650i			0.328628i	0.986408	+	0.164314i	$0.0525410\pi$
$641$			210.650i			0.328628i	−0.986408	+	0.164314i	$0.947459\pi$
$642$		0			0
$643$		−	14.7441i		−	0.0229301i	−0.999934	−	0.0114651i	$-0.996350\pi$
$643$		−	14.7441i		−	0.0229301i	0.999934	−	0.0114651i	$-0.00364952\pi$
$644$		0			0
$645$	15.9305			0.0246984
$646$		0			0
$647$		−	100.936i		−	0.156007i	−0.996953	−	0.0780033i	$-0.975146\pi$
$647$		−	100.936i		−	0.156007i	0.996953	−	0.0780033i	$-0.0248545\pi$
$648$		0			0
$649$		−	779.151i		−	1.20054i
$650$		0			0
$651$			1143.30i			1.75622i
$652$		0			0
$653$		−	432.885i		−	0.662918i	−0.943470	−	0.331459i	$-0.892459\pi$
$653$		−	432.885i		−	0.662918i	0.943470	−	0.331459i	$-0.107541\pi$
$654$		0			0
$655$	−237.416			−0.362468
$656$		0			0
$657$		−	233.088i		−	0.354777i
$658$		0			0
$659$	−529.589			−0.803626			−0.401813	−	0.915722i	$-0.631620\pi$
$659$	−529.589			−0.803626			−0.401813	+	0.915722i	$0.631620\pi$
$660$		0			0
$661$	228.628			0.345882			0.172941	−	0.984932i	$-0.444673\pi$
$661$	228.628			0.345882			0.172941	+	0.984932i	$0.444673\pi$
$662$		0			0
$663$		−	2743.23i		−	4.13761i
$664$		0			0
$665$		−	459.650i		−	0.691203i
$666$		0			0
$667$	−764.422	+	519.286i	−1.14606	+	0.778540i
$668$		0			0
$669$			197.835i			0.295717i
$670$		0			0
$671$			957.640i			1.42718i
$672$		0			0
$673$	−767.269			−1.14007			−0.570036	−	0.821620i	$-0.693071\pi$
$673$	−767.269			−1.14007			−0.570036	+	0.821620i	$0.693071\pi$
$674$		0			0
$675$	157.579			0.233451
$676$		0			0
$677$			247.667i			0.365830i	0.983129	+	0.182915i	$0.0585533\pi$
$677$			247.667i			0.365830i	−0.983129	+	0.182915i	$0.941447\pi$
$678$		0			0
$679$	200.461			0.295230
$680$		0			0
$681$			56.2566i			0.0826088i
$682$		0			0
$683$		−	628.821i		−	0.920674i	−0.887744	−	0.460337i	$-0.847729\pi$
$683$		−	628.821i		−	0.920674i	0.887744	−	0.460337i	$-0.152271\pi$
$684$		0			0
$685$			479.289i			0.699692i
$686$		0			0
$687$		−	436.906i		−	0.635962i
$688$		0			0
$689$	153.880			0.223338
$690$		0			0
$691$			843.107i			1.22013i	0.792353	+	0.610063i	$0.208856\pi$
$691$			843.107i			1.22013i	−0.792353	+	0.610063i	$0.791144\pi$
$692$		0			0
$693$		−	260.200i		−	0.375469i
$694$		0			0
$695$		−	52.3916i		−	0.0753836i
$696$		0			0
$697$	1854.66			2.66091
$698$		0			0
$699$	−458.803			−0.656370
$700$		0			0
$701$	871.033			1.24256			0.621279	−	0.783589i	$-0.286613\pi$
$701$	871.033			1.24256			0.621279	+	0.783589i	$0.286613\pi$
$702$		0			0
$703$		−	336.593i		−	0.478796i
$704$		0			0
$705$	−1187.18			−1.68395
$706$		0			0
$707$	−254.711			−0.360270
$708$		0			0
$709$	−741.810			−1.04628			−0.523138	−	0.852248i	$-0.675239\pi$
$709$	−741.810			−1.04628			−0.523138	+	0.852248i	$0.675239\pi$
$710$		0			0
$711$	540.343			0.759976
$712$		0			0
$713$			1378.08i			1.93279i
$714$		0			0
$715$	1382.56			1.93366
$716$		0			0
$717$		−	1126.77i		−	1.57151i
$718$		0			0
$719$			1371.48i			1.90749i	0.300620	+	0.953744i	$0.402806\pi$
$719$			1371.48i			1.90749i	−0.300620	+	0.953744i	$0.597194\pi$
$720$		0			0
$721$	945.668			1.31161
$722$		0			0
$723$	−473.617			−0.655072
$724$		0			0
$725$	133.059	+	195.872i	0.183530	+	0.270168i
$726$		0			0
$727$	−933.942			−1.28465			−0.642326	−	0.766432i	$-0.722030\pi$
$727$	−933.942			−1.28465			−0.642326	+	0.766432i	$0.722030\pi$
$728$		0			0
$729$	258.828			0.355045
$730$		0			0
$731$		−	24.7130i		−	0.0338071i
$732$		0			0
$733$			995.137i			1.35762i	0.734313	+	0.678811i	$0.237504\pi$
$733$			995.137i			1.35762i	−0.734313	+	0.678811i	$0.762496\pi$
$734$		0			0
$735$	−136.260			−0.185388
$736$		0			0
$737$			603.242i			0.818510i
$738$		0			0
$739$	972.701			1.31624			0.658120	−	0.752913i	$-0.271352\pi$
$739$	972.701			1.31624			0.658120	+	0.752913i	$0.271352\pi$
$740$		0			0
$741$	−927.028			−1.25105
$742$		0			0
$743$	−13.0054			−0.0175040			−0.00875198	−	0.999962i	$-0.502786\pi$
$743$	−13.0054			−0.0175040			−0.00875198	+	0.999962i	$0.502786\pi$
$744$		0			0
$745$	1245.21			1.67143
$746$		0			0
$747$			47.9263i			0.0641584i
$748$		0			0
$749$	−771.875			−1.03054
$750$		0			0
$751$	−26.0513			−0.0346889			−0.0173444	−	0.999850i	$-0.505521\pi$
$751$	−26.0513			−0.0346889			−0.0173444	+	0.999850i	$0.505521\pi$
$752$		0			0
$753$	−1179.43			−1.56631
$754$		0			0
$755$		−	1003.89i		−	1.32965i
$756$		0			0
$757$			1235.28i			1.63181i	0.578187	+	0.815904i	$0.303760\pi$
$757$			1235.28i			1.63181i	−0.578187	+	0.815904i	$0.696240\pi$
$758$		0			0
$759$		−	1108.08i		−	1.45993i
$760$		0			0
$761$	−1186.76			−1.55948			−0.779740	−	0.626104i	$-0.784649\pi$
$761$	−1186.76			−1.55948			−0.779740	+	0.626104i	$0.784649\pi$
$762$		0			0
$763$		−	76.7138i		−	0.100542i
$764$		0			0
$765$			647.668i			0.846624i
$766$		0			0
$767$			1941.91i			2.53182i
$768$		0			0
$769$			246.172i			0.320120i	0.987107	+	0.160060i	$0.0511688\pi$
$769$			246.172i			0.320120i	−0.987107	+	0.160060i	$0.948831\pi$
$770$		0			0
$771$	836.824			1.08537
$772$		0			0
$773$			834.241i			1.07923i	0.841913	+	0.539613i	$0.181429\pi$
$773$			834.241i			1.07923i	−0.841913	+	0.539613i	$0.818571\pi$
$774$		0			0
$775$	353.113			0.455630
$776$		0			0
$777$	−831.914			−1.07067
$778$		0			0
$779$		−	626.748i		−	0.804555i
$780$		0			0
$781$		−	711.653i		−	0.911208i
$782$		0			0
$783$	314.490	+	462.948i	0.401647	+	0.591249i
$784$		0			0
$785$			346.331i			0.441186i
$786$		0			0
$787$			451.426i			0.573603i	0.957990	+	0.286801i	$0.0925920\pi$
$787$			451.426i			0.573603i	−0.957990	+	0.286801i	$0.907408\pi$
$788$		0			0
$789$	382.322			0.484565
$790$		0			0
$791$	119.946			0.151639
$792$		0			0
$793$		−	2386.76i		−	3.00979i
$794$		0			0
$795$	−128.358			−0.161456
$796$		0			0
$797$		−	1027.33i		−	1.28899i	−0.764607	−	0.644497i	$-0.777067\pi$
$797$		−	1027.33i		−	1.28899i	0.764607	−	0.644497i	$-0.222933\pi$
$798$		0			0
$799$			1841.69i			2.30499i
$800$		0			0
$801$		−	156.370i		−	0.195219i
$802$		0			0
$803$		−	643.861i		−	0.801819i
$804$		0			0
$805$	−1369.35			−1.70106
$806$		0			0
$807$		−	103.736i		−	0.128545i
$808$		0			0
$809$		−	363.423i		−	0.449225i	−0.974448	−	0.224612i	$-0.927888\pi$
$809$		−	363.423i		−	0.449225i	0.974448	−	0.224612i	$-0.0721116\pi$
$810$		0			0
$811$		−	240.783i		−	0.296897i	−0.988920	−	0.148448i	$-0.952572\pi$
$811$		−	240.783i		−	0.296897i	0.988920	−	0.148448i	$-0.0474279\pi$
$812$		0			0
$813$	1470.01			1.80813
$814$		0			0
$815$	−119.244			−0.146312
$816$		0			0
$817$	−8.35133			−0.0102219
$818$		0			0
$819$			648.507i			0.791828i
$820$		0			0
$821$	799.656			0.974003			0.487001	−	0.873401i	$-0.338091\pi$
$821$	799.656			0.974003			0.487001	+	0.873401i	$0.338091\pi$
$822$		0			0
$823$	512.391			0.622589			0.311295	−	0.950313i	$-0.399237\pi$
$823$	512.391			0.622589			0.311295	+	0.950313i	$0.399237\pi$
$824$		0			0
$825$	−283.930			−0.344158
$826$		0			0
$827$	131.517			0.159028			0.0795142	−	0.996834i	$-0.474663\pi$
$827$	131.517			0.159028			0.0795142	+	0.996834i	$0.474663\pi$
$828$		0			0
$829$			717.705i			0.865748i	0.901454	+	0.432874i	$0.142501\pi$
$829$			717.705i			0.865748i	−0.901454	+	0.432874i	$0.857499\pi$
$830$		0			0
$831$	688.680			0.828736
$832$		0			0
$833$			211.381i			0.253759i
$834$		0			0
$835$		−	553.583i		−	0.662973i
$836$		0			0
$837$	834.592			0.997123
$838$		0			0
$839$	577.760			0.688629			0.344314	−	0.938854i	$-0.388111\pi$
$839$	577.760			0.688629			0.344314	+	0.938854i	$0.388111\pi$
$840$		0			0
$841$	−309.892	+	781.823i	−0.368481	+	0.929635i
$842$		0			0
$843$	−359.418			−0.426356
$844$		0			0
$845$	−2472.56			−2.92611
$846$		0			0
$847$			184.123i			0.217383i
$848$		0			0
$849$		−	706.456i		−	0.832103i
$850$		0			0
$851$	−1002.75			−1.17832
$852$		0			0
$853$		−	1051.19i		−	1.23234i	−0.787613	−	0.616171i	$-0.788683\pi$
$853$		−	1051.19i		−	1.23234i	0.787613	−	0.616171i	$-0.211317\pi$
$854$		0			0
$855$	218.868			0.255986
$856$		0			0
$857$	−328.819			−0.383686			−0.191843	−	0.981426i	$-0.561447\pi$
$857$	−328.819			−0.383686			−0.191843	+	0.981426i	$0.561447\pi$
$858$		0			0
$859$	1499.83			1.74602			0.873010	−	0.487702i	$-0.162165\pi$
$859$	1499.83			1.74602			0.873010	+	0.487702i	$0.162165\pi$
$860$		0			0
$861$	−1549.05			−1.79913
$862$		0			0
$863$		−	317.712i		−	0.368149i	−0.982912	−	0.184074i	$-0.941071\pi$
$863$		−	317.712i		−	0.368149i	0.982912	−	0.184074i	$-0.0589287\pi$
$864$		0			0
$865$	−485.410			−0.561168
$866$		0			0
$867$	2525.84			2.91331
$868$		0			0
$869$	1492.59			1.71760
$870$		0			0
$871$		−	1503.48i		−	1.72616i
$872$		0			0
$873$			95.4521i			0.109338i
$874$		0			0
$875$		−	723.420i		−	0.826766i
$876$		0			0
$877$	−333.544			−0.380324			−0.190162	−	0.981753i	$-0.560901\pi$
$877$	−333.544			−0.380324			−0.190162	+	0.981753i	$0.560901\pi$
$878$		0			0
$879$			766.602i			0.872129i
$880$		0			0
$881$			1251.86i			1.42095i	0.703723	+	0.710475i	$0.251520\pi$
$881$			1251.86i			1.42095i	−0.703723	+	0.710475i	$0.748480\pi$
$882$		0			0
$883$		−	698.623i		−	0.791193i	−0.918424	−	0.395596i	$-0.870538\pi$
$883$		−	698.623i		−	0.791193i	0.918424	−	0.395596i	$-0.129462\pi$
$884$		0			0
$885$		−	1619.83i		−	1.83031i
$886$		0			0
$887$	1287.75			1.45181			0.725903	−	0.687797i	$-0.241422\pi$
$887$	1287.75			1.45181			0.725903	+	0.687797i	$0.241422\pi$
$888$		0			0
$889$		−	462.456i		−	0.520198i
$890$		0			0
$891$	−984.917			−1.10541
$892$		0			0
$893$	622.365			0.696938
$894$		0			0
$895$		−	308.969i		−	0.345217i
$896$		0			0
$897$			2761.72i			3.07884i
$898$		0			0
$899$	704.727	+	1037.40i	0.783900	+	1.15395i
$900$		0			0
$901$			199.122i			0.221002i
$902$		0			0
$903$			20.6409i			0.0228581i
$904$		0			0
$905$	250.047			0.276296
$906$		0			0
$907$	334.053			0.368305			0.184153	−	0.982898i	$-0.441046\pi$
$907$	334.053			0.368305			0.184153	+	0.982898i	$0.441046\pi$
$908$		0			0
$909$		−	121.284i		−	0.133426i
$910$		0			0
$911$	1256.51			1.37927			0.689634	−	0.724159i	$-0.257772\pi$
$911$	1256.51			1.37927			0.689634	+	0.724159i	$0.257772\pi$
$912$		0			0
$913$			132.387i			0.145002i
$914$		0			0
$915$			1990.90i			2.17585i
$916$		0			0
$917$		−	307.617i		−	0.335461i
$918$		0			0
$919$			331.555i			0.360778i	0.983595	+	0.180389i	$0.0577357\pi$
$919$			331.555i			0.360778i	−0.983595	+	0.180389i	$0.942264\pi$
$920$		0			0
$921$	−469.757			−0.510052
$922$		0			0
$923$			1773.68i			1.92165i
$924$		0			0
$925$			256.940i			0.277773i
$926$		0			0
$927$			450.292i			0.485751i
$928$		0			0
$929$	−1486.64			−1.60026			−0.800128	−	0.599829i	$-0.795235\pi$
$929$	−1486.64			−1.60026			−0.800128	+	0.599829i	$0.795235\pi$
$930$		0			0
$931$	71.4325			0.0767266
$932$		0			0
$933$	685.769			0.735015
$934$		0			0
$935$			1789.05i			1.91343i
$936$		0			0
$937$	43.0561			0.0459510			0.0229755	−	0.999736i	$-0.492686\pi$
$937$	43.0561			0.0459510			0.0229755	+	0.999736i	$0.492686\pi$
$938$		0			0
$939$	−1220.26			−1.29953
$940$		0			0
$941$	−1364.69			−1.45026			−0.725128	−	0.688614i	$-0.758219\pi$
$941$	−1364.69			−1.45026			−0.725128	+	0.688614i	$0.758219\pi$
$942$		0			0
$943$	−1867.16			−1.98002
$944$		0			0
$945$			829.304i			0.877571i
$946$		0			0
$947$	589.717			0.622721			0.311361	−	0.950292i	$-0.399215\pi$
$947$	589.717			0.622721			0.311361	+	0.950292i	$0.399215\pi$
$948$		0			0
$949$			1604.72i			1.69096i
$950$		0			0
$951$		−	862.081i		−	0.906499i
$952$		0			0
$953$	161.902			0.169887			0.0849433	−	0.996386i	$-0.472929\pi$
$953$	161.902			0.169887			0.0849433	+	0.996386i	$0.472929\pi$
$954$		0			0
$955$	−297.960			−0.312000
$956$		0			0
$957$	−566.655	−	834.151i	−0.592116	−	0.871631i
$958$		0			0
$959$	−621.009			−0.647559
$960$		0			0
$961$	909.202			0.946100
$962$		0			0
$963$		−	367.538i		−	0.381659i
$964$		0			0
$965$		−	1662.35i		−	1.72265i
$966$		0			0
$967$	598.309			0.618727			0.309363	−	0.950944i	$-0.399884\pi$
$967$	598.309			0.618727			0.309363	+	0.950944i	$0.399884\pi$
$968$		0			0
$969$		−	1199.58i		−	1.23796i
$970$		0			0
$971$	1089.66			1.12221			0.561104	−	0.827745i	$-0.310377\pi$
$971$	1089.66			1.12221			0.561104	+	0.827745i	$0.310377\pi$
$972$		0			0
$973$	67.8832			0.0697669
$974$		0			0
$975$	707.651			0.725795
$976$		0			0
$977$	−106.382			−0.108887			−0.0544433	−	0.998517i	$-0.517338\pi$
$977$	−106.382			−0.108887			−0.0544433	+	0.998517i	$0.517338\pi$
$978$		0			0
$979$		−	431.942i		−	0.441208i
$980$		0			0
$981$	36.5282			0.0372357
$982$		0			0
$983$	435.444			0.442975			0.221488	−	0.975163i	$-0.428909\pi$
$983$	435.444			0.442975			0.221488	+	0.975163i	$0.428909\pi$
$984$		0			0
$985$	1008.73			1.02409
$986$		0			0
$987$		−	1538.22i		−	1.55848i
$988$		0			0
$989$			24.8796i			0.0251563i
$990$		0			0
$991$		−	1344.06i		−	1.35627i	−0.734938	−	0.678134i	$-0.762789\pi$
$991$		−	1344.06i		−	1.35627i	0.734938	−	0.678134i	$-0.237211\pi$
$992$		0			0
$993$	−760.576			−0.765937
$994$		0			0
$995$		−	1653.64i		−	1.66195i
$996$		0			0
$997$			1266.34i			1.27015i	0.772450	+	0.635075i	$0.219031\pi$
$997$			1266.34i			1.27015i	−0.772450	+	0.635075i	$0.780969\pi$
$998$		0			0
$999$			607.285i			0.607893i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.3.h.c.463.5	✓	20
4.3	odd	2	inner	464.3.h.c.463.16	yes	20
29.28	even	2	inner	464.3.h.c.463.15	yes	20
116.115	odd	2	inner	464.3.h.c.463.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
464.3.h.c.463.5	✓	20	1.1	even	1	trivial
464.3.h.c.463.6	yes	20	116.115	odd	2	inner
464.3.h.c.463.15	yes	20	29.28	even	2	inner
464.3.h.c.463.16	yes	20	4.3	odd	2	inner

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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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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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	464.3.h.c.463.5

Level	$464$
Weight	$3$
Character	464.463
Analytic conductor	$12.643$
Analytic rank	$0$
Dimension	$20$
Inner twists	$4$