LMFDB - Embedded newform 768.4.f.e.383.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,4,Mod(383,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("768.383");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	768.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$45.3134668844$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 39x^{10} + 549x^{8} + 3500x^{6} + 10236x^{4} + 11952x^{2} + 4624 $ x^12 + 39x^10 + 549x^8 + 3500x^6 + 10236x^4 + 11952*x^2 + 4624
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 384)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			383.8
Root			$-2.29679i$ of defining polynomial
Character	$\chi$	$=$	768.383
Dual form			768.4.f.e.383.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40813 + 5.00172i) q^{3} -5.86626 q^{5} +5.92149i q^{7} +(-23.0343 + 14.0861i) q^{9} +O(q^{10})$	\(q+(1.40813 + 5.00172i) q^{3} -5.86626 q^{5} +5.92149i q^{7} +(-23.0343 + 14.0861i) q^{9} -27.9652i q^{11} +0.0653967i q^{13} +(-8.26046 - 29.3414i) q^{15} -36.9675i q^{17} -30.7691 q^{19} +(-29.6176 + 8.33823i) q^{21} +61.2864 q^{23} -90.5870 q^{25} +(-102.890 - 95.3761i) q^{27} +143.566 q^{29} -299.568i q^{31} +(139.874 - 39.3787i) q^{33} -34.7370i q^{35} +340.559i q^{37} +(-0.327096 + 0.0920870i) q^{39} -379.315i q^{41} -470.926 q^{43} +(135.125 - 82.6330i) q^{45} +428.593 q^{47} +307.936 q^{49} +(184.901 - 52.0551i) q^{51} +505.868 q^{53} +164.051i q^{55} +(-43.3269 - 153.898i) q^{57} +207.827i q^{59} -578.221i q^{61} +(-83.4109 - 136.398i) q^{63} -0.383634i q^{65} +415.350 q^{67} +(86.2992 + 306.537i) q^{69} -547.669 q^{71} -194.572 q^{73} +(-127.558 - 453.090i) q^{75} +165.596 q^{77} -308.374i q^{79} +(332.162 - 648.930i) q^{81} +62.3019i q^{83} +216.861i q^{85} +(202.159 + 718.076i) q^{87} -1065.01i q^{89} -0.387246 q^{91} +(1498.36 - 421.831i) q^{93} +180.500 q^{95} +703.293 q^{97} +(393.922 + 644.161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 12 q^{5}+O(q^{10}) $ 12 * q - 2 * q^3 - 12 * q^5	$ 12 q - 2 q^{3} - 12 q^{5} - 84 q^{15} - 180 q^{19} - 156 q^{21} - 120 q^{23} + 300 q^{25} + 130 q^{27} - 588 q^{29} - 116 q^{33} + 620 q^{39} + 372 q^{43} + 740 q^{45} + 1248 q^{47} - 948 q^{49} + 360 q^{51} + 948 q^{53} + 172 q^{57} - 2744 q^{63} - 2292 q^{67} - 3280 q^{69} - 2040 q^{71} + 216 q^{73} + 2522 q^{75} - 4824 q^{77} - 1076 q^{81} + 4156 q^{87} - 3480 q^{91} + 4180 q^{93} + 5448 q^{95} - 48 q^{97} + 3048 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 12 * q^5 - 84 * q^15 - 180 * q^19 - 156 * q^21 - 120 * q^23 + 300 * q^25 + 130 * q^27 - 588 * q^29 - 116 * q^33 + 620 * q^39 + 372 * q^43 + 740 * q^45 + 1248 * q^47 - 948 * q^49 + 360 * q^51 + 948 * q^53 + 172 * q^57 - 2744 * q^63 - 2292 * q^67 - 3280 * q^69 - 2040 * q^71 + 216 * q^73 + 2522 * q^75 - 4824 * q^77 - 1076 * q^81 + 4156 * q^87 - 3480 * q^91 + 4180 * q^93 + 5448 * q^95 - 48 * q^97 + 3048 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$-1$

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
$3$	1.40813	+	5.00172i	0.270995	+	0.962581i
$3$	1.40813	+	5.00172i	0.270995	+	0.962581i
$4$		0			0
$5$	−5.86626			−0.524694			−0.262347	−	0.964974i	$-0.584497\pi$
$5$	−5.86626			−0.524694			−0.262347	+	0.964974i	$0.584497\pi$
$6$		0			0
$7$			5.92149i			0.319730i	0.987139	+	0.159865i	$0.0511060\pi$
$7$			5.92149i			0.319730i	−0.987139	+	0.159865i	$0.948894\pi$
$8$		0			0
$9$	−23.0343	+	14.0861i	−0.853124	+	0.521709i
$10$		0			0
$11$		−	27.9652i		−	0.766531i	−0.923638	−	0.383265i	$-0.874799\pi$
$11$		−	27.9652i		−	0.766531i	0.923638	−	0.383265i	$-0.125201\pi$
$12$		0			0
$13$			0.0653967i			0.00139521i	1.00000		0.000697607i	$0.000222055\pi$
$13$			0.0653967i			0.00139521i	−1.00000		0.000697607i	$0.999778\pi$
$14$		0			0
$15$	−8.26046	−	29.3414i	−0.142189	−	0.505061i
$16$		0			0
$17$		−	36.9675i		−	0.527408i	−0.964604	−	0.263704i	$-0.915056\pi$
$17$		−	36.9675i		−	0.527408i	0.964604	−	0.263704i	$-0.0849443\pi$
$18$		0			0
$19$	−30.7691			−0.371522			−0.185761	−	0.982595i	$-0.559475\pi$
$19$	−30.7691			−0.371522			−0.185761	+	0.982595i	$0.559475\pi$
$20$		0			0
$21$	−29.6176	+	8.33823i	−0.307766	+	0.0866452i
$22$		0			0
$23$	61.2864			0.555613			0.277806	−	0.960637i	$-0.410393\pi$
$23$	61.2864			0.555613			0.277806	+	0.960637i	$0.410393\pi$
$24$		0			0
$25$	−90.5870			−0.724696
$26$		0			0
$27$	−102.890	−	95.3761i	−0.733379	−	0.679820i
$28$		0			0
$29$	143.566			0.919294			0.459647	−	0.888102i	$-0.347976\pi$
$29$	143.566			0.919294			0.459647	+	0.888102i	$0.347976\pi$
$30$		0			0
$31$		−	299.568i		−	1.73562i	−0.496900	−	0.867808i	$-0.665529\pi$
$31$		−	299.568i		−	1.73562i	0.496900	−	0.867808i	$-0.334471\pi$
$32$		0			0
$33$	139.874	−	39.3787i	0.737848	−	0.207726i
$34$		0			0
$35$		−	34.7370i		−	0.167761i
$36$		0			0
$37$			340.559i			1.51318i	0.653891	+	0.756589i	$0.273135\pi$
$37$			340.559i			1.51318i	−0.653891	+	0.756589i	$0.726865\pi$
$38$		0			0
$39$	−0.327096	+	0.0920870i	−0.00134301	+	0.000378095i
$40$		0			0
$41$		−	379.315i		−	1.44486i	−0.691447	−	0.722428i	$-0.743026\pi$
$41$		−	379.315i		−	1.44486i	0.691447	−	0.722428i	$-0.256974\pi$
$42$		0			0
$43$	−470.926			−1.67013			−0.835065	−	0.550152i	$-0.814570\pi$
$43$	−470.926			−1.67013			−0.835065	+	0.550152i	$0.814570\pi$
$44$		0			0
$45$	135.125	−	82.6330i	0.447629	−	0.273738i
$46$		0			0
$47$	428.593			1.33014			0.665072	−	0.746779i	$-0.268401\pi$
$47$	428.593			1.33014			0.665072	+	0.746779i	$0.268401\pi$
$48$		0			0
$49$	307.936			0.897772
$50$		0			0
$51$	184.901	−	52.0551i	0.507673	−	0.142925i
$52$		0			0
$53$	505.868			1.31106			0.655531	−	0.755168i	$-0.272445\pi$
$53$	505.868			1.31106			0.655531	+	0.755168i	$0.272445\pi$
$54$		0			0
$55$			164.051i			0.402194i
$56$		0			0
$57$	−43.3269	−	153.898i	−0.100681	−	0.357620i
$58$		0			0
$59$			207.827i			0.458589i	0.973357	+	0.229295i	$0.0736419\pi$
$59$			207.827i			0.458589i	−0.973357	+	0.229295i	$0.926358\pi$
$60$		0			0
$61$		−	578.221i		−	1.21367i	−0.794830	−	0.606833i	$-0.792440\pi$
$61$		−	578.221i		−	1.21367i	0.794830	−	0.606833i	$-0.207560\pi$
$62$		0			0
$63$	−83.4109	−	136.398i	−0.166806	−	0.272770i
$64$		0			0
$65$		−	0.383634i		−	0.000732061i
$66$		0			0
$67$	415.350			0.757359			0.378679	−	0.925528i	$-0.376378\pi$
$67$	415.350			0.757359			0.378679	+	0.925528i	$0.376378\pi$
$68$		0			0
$69$	86.2992	+	306.537i	0.150568	+	0.534822i
$70$		0			0
$71$	−547.669			−0.915441			−0.457721	−	0.889096i	$-0.651334\pi$
$71$	−547.669			−0.915441			−0.457721	+	0.889096i	$0.651334\pi$
$72$		0			0
$73$	−194.572			−0.311957			−0.155979	−	0.987760i	$-0.549853\pi$
$73$	−194.572			−0.311957			−0.155979	+	0.987760i	$0.549853\pi$
$74$		0			0
$75$	−127.558	−	453.090i	−0.196389	−	0.697578i
$76$		0			0
$77$	165.596			0.245083
$78$		0			0
$79$		−	308.374i		−	0.439175i	−0.975593	−	0.219587i	$-0.929529\pi$
$79$		−	308.374i		−	0.439175i	0.975593	−	0.219587i	$-0.0704711\pi$
$80$		0			0
$81$	332.162	−	648.930i	0.455640	−	0.890164i
$82$		0			0
$83$			62.3019i			0.0823918i	0.999151	+	0.0411959i	$0.0131168\pi$
$83$			62.3019i			0.0823918i	−0.999151	+	0.0411959i	$0.986883\pi$
$84$		0			0
$85$			216.861i			0.276728i
$86$		0			0
$87$	202.159	+	718.076i	0.249124	+	0.884895i
$88$		0			0
$89$		−	1065.01i		−	1.26844i	−0.773153	−	0.634220i	$-0.781321\pi$
$89$		−	1065.01i		−	1.26844i	0.773153	−	0.634220i	$-0.218679\pi$
$90$		0			0
$91$	−0.387246			−0.000446092
$92$		0			0
$93$	1498.36	−	421.831i	1.67067	−	0.470343i
$94$		0			0
$95$	180.500			0.194936
$96$		0			0
$97$	703.293			0.736171			0.368085	−	0.929792i	$-0.380013\pi$
$97$	703.293			0.736171			0.368085	+	0.929792i	$0.380013\pi$
$98$		0			0
$99$	393.922	+	644.161i	0.399906	+	0.653946i
$100$		0			0
$101$	942.553			0.928589			0.464295	−	0.885681i	$-0.346308\pi$
$101$	942.553			0.928589			0.464295	+	0.885681i	$0.346308\pi$
$102$		0			0
$103$			86.0316i			0.0823005i	0.999153	+	0.0411502i	$0.0131022\pi$
$103$			86.0316i			0.0823005i	−0.999153	+	0.0411502i	$0.986898\pi$
$104$		0			0
$105$	173.745	−	48.9142i	0.161483	−	0.0454623i
$106$		0			0
$107$			688.082i			0.621676i	0.950463	+	0.310838i	$0.100610\pi$
$107$			688.082i			0.621676i	−0.950463	+	0.310838i	$0.899390\pi$
$108$		0			0
$109$			1849.94i			1.62561i	0.582534	+	0.812807i	$0.302061\pi$
$109$			1849.94i			1.62561i	−0.582534	+	0.812807i	$0.697939\pi$
$110$		0			0
$111$	−1703.38	+	479.551i	−1.45656	+	0.410063i
$112$		0			0
$113$		−	1054.54i		−	0.877902i	−0.898511	−	0.438951i	$-0.855350\pi$
$113$		−	1054.54i		−	0.877902i	0.898511	−	0.438951i	$-0.144650\pi$
$114$		0			0
$115$	−359.522			−0.291527
$116$		0			0
$117$	−0.921186	−	1.50637i	−0.000727895	−	0.00119029i
$118$		0			0
$119$	218.903			0.168628
$120$		0			0
$121$	548.945			0.412431
$122$		0			0
$123$	1897.23	−	534.125i	1.39079	−	0.391548i
$124$		0			0
$125$	1264.69			0.904938
$126$		0			0
$127$			957.493i			0.669006i	0.942395	+	0.334503i	$0.108568\pi$
$127$			957.493i			0.669006i	−0.942395	+	0.334503i	$0.891432\pi$
$128$		0			0
$129$	−663.125	−	2355.44i	−0.452596	−	1.60763i
$130$		0			0
$131$		−	550.306i		−	0.367026i	−0.983017	−	0.183513i	$-0.941253\pi$
$131$		−	550.306i		−	0.367026i	0.983017	−	0.183513i	$-0.0587470\pi$
$132$		0			0
$133$		−	182.199i		−	0.118787i
$134$		0			0
$135$	603.581	+	559.501i	0.384800	+	0.356698i
$136$		0			0
$137$		−	1991.37i		−	1.24185i	−0.783869	−	0.620926i	$-0.786757\pi$
$137$		−	1991.37i		−	1.24185i	0.783869	−	0.620926i	$-0.213243\pi$
$138$		0			0
$139$	746.850			0.455733			0.227867	−	0.973692i	$-0.426825\pi$
$139$	746.850			0.455733			0.227867	+	0.973692i	$0.426825\pi$
$140$		0			0
$141$	603.515	+	2143.70i	0.360462	+	1.28037i
$142$		0			0
$143$	1.82883			0.00106947
$144$		0			0
$145$	−842.195			−0.482348
$146$		0			0
$147$	433.614	+	1540.21i	0.243292	+	0.864179i
$148$		0			0
$149$	3198.80			1.75877			0.879383	−	0.476114i	$-0.157955\pi$
$149$	3198.80			1.75877			0.879383	+	0.476114i	$0.157955\pi$
$150$		0			0
$151$		−	1475.50i		−	0.795195i	−0.917560	−	0.397598i	$-0.869844\pi$
$151$		−	1475.50i		−	0.795195i	0.917560	−	0.397598i	$-0.130156\pi$
$152$		0			0
$153$	520.730	+	851.523i	0.275154	+	0.449945i
$154$		0			0
$155$			1757.35i			0.910668i
$156$		0			0
$157$		−	713.140i		−	0.362514i	−0.983436	−	0.181257i	$-0.941983\pi$
$157$		−	713.140i		−	0.362514i	0.983436	−	0.181257i	$-0.0580166\pi$
$158$		0			0
$159$	712.328	+	2530.21i	0.355291	+	1.26200i
$160$		0			0
$161$			362.907i			0.177646i
$162$		0			0
$163$	−1986.44			−0.954538			−0.477269	−	0.878757i	$-0.658373\pi$
$163$	−1986.44			−0.954538			−0.477269	+	0.878757i	$0.658373\pi$
$164$		0			0
$165$	−820.539	+	231.006i	−0.387145	+	0.108993i
$166$		0			0
$167$	−3376.74			−1.56467			−0.782336	−	0.622857i	$-0.785972\pi$
$167$	−3376.74			−1.56467			−0.782336	+	0.622857i	$0.785972\pi$
$168$		0			0
$169$	2197.00			0.999998
$170$		0			0
$171$	708.747	−	433.418i	0.316954	−	0.193826i
$172$		0			0
$173$	−2696.12			−1.18487			−0.592435	−	0.805619i	$-0.701833\pi$
$173$	−2696.12			−1.18487			−0.592435	+	0.805619i	$0.701833\pi$
$174$		0			0
$175$		−	536.410i		−	0.231707i
$176$		0			0
$177$	−1039.49	+	292.647i	−0.441429	+	0.124275i
$178$		0			0
$179$		−	3347.25i		−	1.39768i	−0.715276	−	0.698842i	$-0.753699\pi$
$179$		−	3347.25i		−	1.39768i	0.715276	−	0.698842i	$-0.246301\pi$
$180$		0			0
$181$		−	1843.89i		−	0.757210i	−0.925558	−	0.378605i	$-0.876404\pi$
$181$		−	1843.89i		−	0.757210i	0.925558	−	0.378605i	$-0.123596\pi$
$182$		0			0
$183$	2892.10	−	814.210i	1.16825	−	0.328897i
$184$		0			0
$185$		−	1997.81i		−	0.793956i
$186$		0			0
$187$	−1033.81			−0.404275
$188$		0			0
$189$	564.769	−	609.263i	0.217359	−	0.234483i
$190$		0			0
$191$	2382.31			0.902501			0.451251	−	0.892397i	$-0.350978\pi$
$191$	2382.31			0.902501			0.451251	+	0.892397i	$0.350978\pi$
$192$		0			0
$193$	−2546.25			−0.949654			−0.474827	−	0.880079i	$-0.657489\pi$
$193$	−2546.25			−0.949654			−0.474827	+	0.880079i	$0.657489\pi$
$194$		0			0
$195$	1.91883	−	0.540207i	0.000704668	−	0.000198385i
$196$		0			0
$197$	2189.58			0.791885			0.395943	−	0.918275i	$-0.370418\pi$
$197$	2189.58			0.791885			0.395943	+	0.918275i	$0.370418\pi$
$198$		0			0
$199$		−	5379.16i		−	1.91617i	−0.286476	−	0.958087i	$-0.592484\pi$
$199$		−	5379.16i		−	1.91617i	0.286476	−	0.958087i	$-0.407516\pi$
$200$		0			0
$201$	584.866	+	2077.46i	0.205240	+	0.729019i
$202$		0			0
$203$			850.124i			0.293926i
$204$		0			0
$205$			2225.16i			0.758107i
$206$		0			0
$207$	−1411.69	+	863.288i	−0.474006	+	0.289868i
$208$		0			0
$209$			860.466i			0.284783i
$210$		0			0
$211$	−5320.28			−1.73584			−0.867922	−	0.496701i	$-0.834544\pi$
$211$	−5320.28			−1.73584			−0.867922	+	0.496701i	$0.834544\pi$
$212$		0			0
$213$	−771.189	−	2739.28i	−0.248080	−	0.881186i
$214$		0			0
$215$	2762.58			0.876307
$216$		0			0
$217$	1773.89			0.554929
$218$		0			0
$219$	−273.982	−	973.192i	−0.0845388	−	0.300284i
$220$		0			0
$221$	2.41755			0.000735847
$222$		0			0
$223$		−	2708.41i		−	0.813310i	−0.913582	−	0.406655i	$-0.866695\pi$
$223$		−	2708.41i		−	0.813310i	0.913582	−	0.406655i	$-0.133305\pi$
$224$		0			0
$225$	2086.61	−	1276.02i	0.618255	−	0.378080i
$226$		0			0
$227$		−	2335.26i		−	0.682806i	−0.939917	−	0.341403i	$-0.889098\pi$
$227$		−	2335.26i		−	0.682806i	0.939917	−	0.341403i	$-0.110902\pi$
$228$		0			0
$229$			139.302i			0.0401980i	0.999798	+	0.0200990i	$0.00639814\pi$
$229$			139.302i			0.0401980i	−0.999798	+	0.0200990i	$0.993602\pi$
$230$		0			0
$231$	233.181	+	828.264i	0.0664162	+	0.235912i
$232$		0			0
$233$		−	7.07987i		−	0.00199064i	−1.00000		0.000995318i	$-0.999683\pi$
$233$		−	7.07987i		−	0.00199064i	1.00000		0.000995318i	$-0.000316819\pi$
$234$		0			0
$235$	−2514.24			−0.697919
$236$		0			0
$237$	1542.40	−	434.231i	0.422741	−	0.119014i
$238$		0			0
$239$	−890.272			−0.240949			−0.120475	−	0.992716i	$-0.538442\pi$
$239$	−890.272			−0.240949			−0.120475	+	0.992716i	$0.538442\pi$
$240$		0			0
$241$	1273.98			0.340515			0.170258	−	0.985400i	$-0.445540\pi$
$241$	1273.98			0.340515			0.170258	+	0.985400i	$0.445540\pi$
$242$		0			0
$243$	3713.49	+	747.601i	0.980331	+	0.197361i
$244$		0			0
$245$	−1806.43			−0.471056
$246$		0			0
$247$		−	2.01220i		−	0.000518353i
$248$		0			0
$249$	−311.616	+	87.7291i	−0.0793088	+	0.0223277i
$250$		0			0
$251$		−	3032.85i		−	0.762678i	−0.924435	−	0.381339i	$-0.875463\pi$
$251$		−	3032.85i		−	0.762678i	0.924435	−	0.381339i	$-0.124537\pi$
$252$		0			0
$253$		−	1713.89i		−	0.425894i
$254$		0			0
$255$	−1084.68	+	305.369i	−0.266373	+	0.0749919i
$256$		0			0
$257$			2585.22i			0.627478i	0.949509	+	0.313739i	$0.101582\pi$
$257$			2585.22i			0.627478i	−0.949509	+	0.313739i	$0.898418\pi$
$258$		0			0
$259$	−2016.62			−0.483809
$260$		0			0
$261$	−3306.95	+	2022.29i	−0.784271	+	0.479604i
$262$		0			0
$263$	−5444.20			−1.27644			−0.638220	−	0.769854i	$-0.720329\pi$
$263$	−5444.20			−1.27644			−0.638220	+	0.769854i	$0.720329\pi$
$264$		0			0
$265$	−2967.55			−0.687907
$266$		0			0
$267$	5326.89	−	1499.68i	1.22098	−	0.343740i
$268$		0			0
$269$	−2061.38			−0.467229			−0.233614	−	0.972329i	$-0.575055\pi$
$269$	−2061.38			−0.467229			−0.233614	+	0.972329i	$0.575055\pi$
$270$		0			0
$271$		−	5846.72i		−	1.31056i	−0.755384	−	0.655282i	$-0.772550\pi$
$271$		−	5846.72i		−	1.31056i	0.755384	−	0.655282i	$-0.227450\pi$
$272$		0			0
$273$	−0.545292	−	1.93689i	−0.000120889	−	0.000429400i
$274$		0			0
$275$			2533.29i			0.555502i
$276$		0			0
$277$			1488.28i			0.322823i	0.986887	+	0.161412i	$0.0516046\pi$
$277$			1488.28i			0.322823i	−0.986887	+	0.161412i	$0.948395\pi$
$278$		0			0
$279$	4219.76	+	6900.36i	0.905485	+	1.48069i
$280$		0			0
$281$			6456.97i			1.37079i	0.728174	+	0.685393i	$0.240369\pi$
$281$			6456.97i			1.37079i	−0.728174	+	0.685393i	$0.759631\pi$
$282$		0			0
$283$	−5390.67			−1.13231			−0.566153	−	0.824301i	$-0.691569\pi$
$283$	−5390.67			−1.13231			−0.566153	+	0.824301i	$0.691569\pi$
$284$		0			0
$285$	254.167	+	902.809i	0.0528265	+	0.187641i
$286$		0			0
$287$	2246.11			0.461964
$288$		0			0
$289$	3546.40			0.721840
$290$		0			0
$291$	990.328	+	3517.67i	0.199498	+	0.708624i
$292$		0			0
$293$	−5400.85			−1.07686			−0.538432	−	0.842669i	$-0.680983\pi$
$293$	−5400.85			−1.07686			−0.538432	+	0.842669i	$0.680983\pi$
$294$		0			0
$295$		−	1219.17i		−	0.240619i
$296$		0			0
$297$	−2667.22	+	2877.35i	−0.521103	+	0.562157i
$298$		0			0
$299$			4.00793i			0.000775198i
$300$		0			0
$301$		−	2788.58i		−	0.533991i
$302$		0			0
$303$	1327.24	+	4714.38i	0.251643	+	0.893842i
$304$		0			0
$305$			3391.99i			0.636803i
$306$		0			0
$307$	3598.12			0.668910			0.334455	−	0.942412i	$-0.391448\pi$
$307$	3598.12			0.668910			0.334455	+	0.942412i	$0.391448\pi$
$308$		0			0
$309$	−430.306	+	121.144i	−0.0792209	+	0.0223030i
$310$		0			0
$311$	7894.55			1.43942			0.719709	−	0.694276i	$-0.244275\pi$
$311$	7894.55			1.43942			0.719709	+	0.694276i	$0.244275\pi$
$312$		0			0
$313$	−8500.57			−1.53508			−0.767541	−	0.641000i	$-0.778520\pi$
$313$	−8500.57			−1.53508			−0.767541	+	0.641000i	$0.778520\pi$
$314$		0			0
$315$	489.310	+	800.144i	0.0875222	+	0.143121i
$316$		0			0
$317$	−7352.01			−1.30262			−0.651309	−	0.758813i	$-0.725780\pi$
$317$	−7352.01			−1.30262			−0.651309	+	0.758813i	$0.725780\pi$
$318$		0			0
$319$		−	4014.86i		−	0.704667i
$320$		0			0
$321$	−3441.59	+	968.908i	−0.598414	+	0.168471i
$322$		0			0
$323$			1137.46i			0.195944i
$324$		0			0
$325$		−	5.92409i		−	0.00101111i
$326$		0			0
$327$	−9252.86	+	2604.95i	−1.56478	+	0.440533i
$328$		0			0
$329$			2537.91i			0.425287i
$330$		0			0
$331$	−4348.48			−0.722097			−0.361048	−	0.932547i	$-0.617581\pi$
$331$	−4348.48			−0.722097			−0.361048	+	0.932547i	$0.617581\pi$
$332$		0			0
$333$	−4797.16	−	7844.55i	−0.789438	−	1.29093i
$334$		0			0
$335$	−2436.55			−0.397382
$336$		0			0
$337$	−2451.75			−0.396307			−0.198153	−	0.980171i	$-0.563494\pi$
$337$	−2451.75			−0.396307			−0.198153	+	0.980171i	$0.563494\pi$
$338$		0			0
$339$	5274.52	−	1484.93i	0.845051	−	0.237907i
$340$		0			0
$341$	−8377.50			−1.33040
$342$		0			0
$343$			3854.51i			0.606776i
$344$		0			0
$345$	−506.254	−	1798.23i	−0.0790023	−	0.280618i
$346$		0			0
$347$			3671.15i			0.567947i	0.958832	+	0.283974i	$0.0916528\pi$
$347$			3671.15i			0.567947i	−0.958832	+	0.283974i	$0.908347\pi$
$348$		0			0
$349$		−	2543.31i		−	0.390086i	−0.980795	−	0.195043i	$-0.937515\pi$
$349$		−	2543.31i		−	0.390086i	0.980795	−	0.195043i	$-0.0624847\pi$
$350$		0			0
$351$	6.23728	−	6.72868i	0.000948494	−	0.00102322i
$352$		0			0
$353$			12015.9i			1.81173i	0.423562	+	0.905867i	$0.360779\pi$
$353$			12015.9i			1.81173i	−0.423562	+	0.905867i	$0.639221\pi$
$354$		0			0
$355$	3212.77			0.480327
$356$		0			0
$357$	308.244	+	1094.89i	0.0456974	+	0.162319i
$358$		0			0
$359$	−11569.3			−1.70085			−0.850424	−	0.526097i	$-0.823655\pi$
$359$	−11569.3			−1.70085			−0.850424	+	0.526097i	$0.823655\pi$
$360$		0			0
$361$	−5912.26			−0.861971
$362$		0			0
$363$	772.986	+	2745.67i	0.111767	+	0.396998i
$364$		0			0
$365$	1141.41			0.163682
$366$		0			0
$367$			675.208i			0.0960370i	0.998846	+	0.0480185i	$0.0152906\pi$
$367$			675.208i			0.0960370i	−0.998846	+	0.0480185i	$0.984709\pi$
$368$		0			0
$369$	5343.08	+	8737.27i	0.753793	+	1.23264i
$370$		0			0
$371$			2995.49i			0.419186i
$372$		0			0
$373$			9000.61i			1.24942i	0.780857	+	0.624710i	$0.214783\pi$
$373$			9000.61i			1.24942i	−0.780857	+	0.624710i	$0.785217\pi$
$374$		0			0
$375$	1780.85	+	6325.62i	0.245234	+	0.871076i
$376$		0			0
$377$			9.38873i			0.00128261i
$378$		0			0
$379$	−6453.84			−0.874700			−0.437350	−	0.899291i	$-0.644083\pi$
$379$	−6453.84			−0.874700			−0.437350	+	0.899291i	$0.644083\pi$
$380$		0			0
$381$	−4789.11	+	1348.28i	−0.643973	+	0.181297i
$382$		0			0
$383$	5211.10			0.695234			0.347617	−	0.937637i	$-0.386991\pi$
$383$	5211.10			0.695234			0.347617	+	0.937637i	$0.386991\pi$
$384$		0			0
$385$	−971.429			−0.128594
$386$		0			0
$387$	10847.5	−	6633.53i	1.42483	−	0.871321i
$388$		0			0
$389$	−1399.05			−0.182351			−0.0911756	−	0.995835i	$-0.529062\pi$
$389$	−1399.05			−0.182351			−0.0911756	+	0.995835i	$0.529062\pi$
$390$		0			0
$391$		−	2265.61i		−	0.293035i
$392$		0			0
$393$	2752.47	−	774.902i	0.353292	−	0.0994622i
$394$		0			0
$395$			1809.00i			0.230433i
$396$		0			0
$397$		−	6624.77i		−	0.837500i	−0.908101	−	0.418750i	$-0.862468\pi$
$397$		−	6624.77i		−	0.837500i	0.908101	−	0.418750i	$-0.137532\pi$
$398$		0			0
$399$	911.308	−	256.560i	0.114342	−	0.0321906i
$400$		0			0
$401$		−	5283.09i		−	0.657918i	−0.944344	−	0.328959i	$-0.893302\pi$
$401$		−	5283.09i		−	0.657918i	0.944344	−	0.328959i	$-0.106698\pi$
$402$		0			0
$403$	19.5908			0.00242155
$404$		0			0
$405$	−1948.55	+	3806.79i	−0.239072	+	0.467064i
$406$		0			0
$407$	9523.81			1.15990
$408$		0			0
$409$	7555.96			0.913492			0.456746	−	0.889597i	$-0.349015\pi$
$409$	7555.96			0.913492			0.456746	+	0.889597i	$0.349015\pi$
$410$		0			0
$411$	9960.25	−	2804.10i	1.19538	−	0.336536i
$412$		0			0
$413$	−1230.65			−0.146625
$414$		0			0
$415$		−	365.479i		−	0.0432305i
$416$		0			0
$417$	1051.66	+	3735.53i	0.123501	+	0.438680i
$418$		0			0
$419$			6784.17i			0.790999i	0.918466	+	0.395500i	$0.129429\pi$
$419$			6784.17i			0.790999i	−0.918466	+	0.395500i	$0.870571\pi$
$420$		0			0
$421$		−	12740.9i		−	1.47495i	−0.675374	−	0.737476i	$-0.736018\pi$
$421$		−	12740.9i		−	1.47495i	0.675374	−	0.737476i	$-0.263982\pi$
$422$		0			0
$423$	−9872.36	+	6037.22i	−1.13478	+	0.693947i
$424$		0			0
$425$			3348.78i			0.382211i
$426$		0			0
$427$	3423.93			0.388046
$428$		0			0
$429$	2.57524	+	9.14731i	0.000289822	+	0.00102946i
$430$		0			0
$431$	−16239.7			−1.81493			−0.907467	−	0.420123i	$-0.861987\pi$
$431$	−16239.7			−1.81493			−0.907467	+	0.420123i	$0.861987\pi$
$432$		0			0
$433$	4832.73			0.536365			0.268183	−	0.963368i	$-0.413577\pi$
$433$	4832.73			0.536365			0.268183	+	0.963368i	$0.413577\pi$
$434$		0			0
$435$	−1185.92	−	4212.42i	−0.130714	−	0.464299i
$436$		0			0
$437$	−1885.73			−0.206422
$438$		0			0
$439$		−	4286.58i		−	0.466031i	−0.972473	−	0.233015i	$-0.925141\pi$
$439$		−	4286.58i		−	0.466031i	0.972473	−	0.233015i	$-0.0748592\pi$
$440$		0			0
$441$	−7093.10	+	4337.63i	−0.765911	+	0.468376i
$442$		0			0
$443$		−	2140.54i		−	0.229572i	−0.993390	−	0.114786i	$-0.963382\pi$
$443$		−	2140.54i		−	0.229572i	0.993390	−	0.114786i	$-0.0366182\pi$
$444$		0			0
$445$			6247.64i			0.665543i
$446$		0			0
$447$	4504.33	+	15999.5i	0.476617	+	1.69296i
$448$		0			0
$449$		−	9598.09i		−	1.00882i	−0.863463	−	0.504412i	$-0.831709\pi$
$449$		−	9598.09i		−	1.00882i	0.863463	−	0.504412i	$-0.168291\pi$
$450$		0			0
$451$	−10607.6			−1.10753
$452$		0			0
$453$	7380.03	−	2077.70i	0.765440	−	0.215494i
$454$		0			0
$455$	2.27168			0.000234062
$456$		0			0
$457$	9542.53			0.976763			0.488382	−	0.872630i	$-0.337587\pi$
$457$	9542.53			0.976763			0.488382	+	0.872630i	$0.337587\pi$
$458$		0			0
$459$	−3525.82	+	3803.60i	−0.358543	+	0.386790i
$460$		0			0
$461$	8017.02			0.809956			0.404978	−	0.914326i	$-0.367279\pi$
$461$	8017.02			0.809956			0.404978	+	0.914326i	$0.367279\pi$
$462$		0			0
$463$		−	10933.1i		−	1.09742i	−0.836014	−	0.548709i	$-0.815120\pi$
$463$		−	10933.1i		−	1.09742i	0.836014	−	0.548709i	$-0.184880\pi$
$464$		0			0
$465$	−8789.75	+	2474.57i	−0.876591	+	0.246786i
$466$		0			0
$467$			3991.55i			0.395518i	0.980251	+	0.197759i	$0.0633664\pi$
$467$			3991.55i			0.395518i	−0.980251	+	0.197759i	$0.936634\pi$
$468$		0			0
$469$			2459.49i			0.242151i
$470$		0			0
$471$	3566.92	−	1004.19i	0.348949	−	0.0982394i
$472$		0			0
$473$			13169.6i			1.28021i
$474$		0			0
$475$	2787.28			0.269241
$476$		0			0
$477$	−11652.3	+	7125.72i	−1.11850	+	0.683993i
$478$		0			0
$479$	10524.5			1.00392			0.501958	−	0.864892i	$-0.332613\pi$
$479$	10524.5			1.00392			0.501958	+	0.864892i	$0.332613\pi$
$480$		0			0
$481$	−22.2714			−0.00211120
$482$		0			0
$483$	−1815.16	+	511.020i	−0.170999	+	0.0481412i
$484$		0			0
$485$	−4125.70			−0.386265
$486$		0			0
$487$		−	10750.1i		−	1.00028i	−0.865946	−	0.500138i	$-0.833283\pi$
$487$		−	10750.1i		−	1.00028i	0.865946	−	0.500138i	$-0.166717\pi$
$488$		0			0
$489$	−2797.16	−	9935.60i	−0.258675	−	0.918820i
$490$		0			0
$491$		−	18059.8i		−	1.65994i	−0.557811	−	0.829968i	$-0.688359\pi$
$491$		−	18059.8i		−	1.65994i	0.557811	−	0.829968i	$-0.311641\pi$
$492$		0			0
$493$		−	5307.28i		−	0.484843i
$494$		0			0
$495$	−2310.85	−	3778.82i	−0.209828	−	0.343122i
$496$		0			0
$497$		−	3243.02i		−	0.292694i
$498$		0			0
$499$	−15164.6			−1.36044			−0.680221	−	0.733007i	$-0.738116\pi$
$499$	−15164.6			−1.36044			−0.680221	+	0.733007i	$0.738116\pi$
$500$		0			0
$501$	−4754.89	−	16889.5i	−0.424018	−	1.50612i
$502$		0			0
$503$	21362.1			1.89362			0.946808	−	0.321799i	$-0.104288\pi$
$503$	21362.1			1.89362			0.946808	+	0.321799i	$0.104288\pi$
$504$		0			0
$505$	−5529.26			−0.487226
$506$		0			0
$507$	3093.66	+	10988.8i	0.270994	+	0.962579i
$508$		0			0
$509$	4921.82			0.428597			0.214299	−	0.976768i	$-0.431253\pi$
$509$	4921.82			0.428597			0.214299	+	0.976768i	$0.431253\pi$
$510$		0			0
$511$		−	1152.15i		−	0.0997422i
$512$		0			0
$513$	3165.84	+	2934.64i	0.272467	+	0.252568i
$514$		0			0
$515$		−	504.684i		−	0.0431826i
$516$		0			0
$517$		−	11985.7i		−	1.01960i
$518$		0			0
$519$	−3796.49	−	13485.2i	−0.321093	−	1.14053i
$520$		0			0
$521$			9816.25i			0.825446i	0.910857	+	0.412723i	$0.135422\pi$
$521$			9816.25i			0.825446i	−0.910857	+	0.412723i	$0.864578\pi$
$522$		0			0
$523$	−11120.7			−0.929783			−0.464891	−	0.885368i	$-0.653907\pi$
$523$	−11120.7			−0.929783			−0.464891	+	0.885368i	$0.653907\pi$
$524$		0			0
$525$	2682.97	−	755.335i	0.223037	−	0.0627914i
$526$		0			0
$527$	−11074.3			−0.915378
$528$		0			0
$529$	−8410.98			−0.691295
$530$		0			0
$531$	−2927.48	−	4787.16i	−0.239250	−	0.391233i
$532$		0			0
$533$	24.8059			0.00201588
$534$		0			0
$535$		−	4036.47i		−	0.326190i
$536$		0			0
$537$	16742.0	−	4713.37i	1.34538	−	0.378765i
$538$		0			0
$539$		−	8611.50i		−	0.688170i
$540$		0			0
$541$			15949.1i			1.26748i	0.773546	+	0.633740i	$0.218481\pi$
$541$			15949.1i			1.26748i	−0.773546	+	0.633740i	$0.781519\pi$
$542$		0			0
$543$	9222.60	−	2596.43i	0.728876	−	0.205200i
$544$		0			0
$545$		−	10852.2i		−	0.852950i
$546$		0			0
$547$	−12775.8			−0.998637			−0.499318	−	0.866419i	$-0.666416\pi$
$547$	−12775.8			−0.998637			−0.499318	+	0.866419i	$0.666416\pi$
$548$		0			0
$549$	8144.89	+	13318.9i	0.633180	+	1.03541i
$550$		0			0
$551$	−4417.40			−0.341538
$552$		0			0
$553$	1826.04			0.140418
$554$		0			0
$555$	9992.47	−	2813.17i	0.764246	−	0.215158i
$556$		0			0
$557$	9120.09			0.693772			0.346886	−	0.937907i	$-0.387239\pi$
$557$	9120.09			0.693772			0.346886	+	0.937907i	$0.387239\pi$
$558$		0			0
$559$		−	30.7970i		−	0.00233019i
$560$		0			0
$561$	−1455.73	−	5170.80i	−0.109556	−	0.389147i
$562$		0			0
$563$		−	4530.65i		−	0.339155i	−0.985517	−	0.169577i	$-0.945760\pi$
$563$		−	4530.65i		−	0.339155i	0.985517	−	0.169577i	$-0.0542403\pi$
$564$		0			0
$565$			6186.21i			0.460630i
$566$		0			0
$567$	3842.63	+	1966.89i	0.284612	+	0.145682i
$568$		0			0
$569$		−	17896.0i		−	1.31853i	−0.751913	−	0.659263i	$-0.770868\pi$
$569$		−	17896.0i		−	1.31853i	0.751913	−	0.659263i	$-0.229132\pi$
$570$		0			0
$571$	11840.1			0.867760			0.433880	−	0.900971i	$-0.357144\pi$
$571$	11840.1			0.867760			0.433880	+	0.900971i	$0.357144\pi$
$572$		0			0
$573$	3354.60	+	11915.6i	0.244573	+	0.868731i
$574$		0			0
$575$	−5551.75			−0.402650
$576$		0			0
$577$	−18102.9			−1.30612			−0.653060	−	0.757306i	$-0.726515\pi$
$577$	−18102.9			−1.30612			−0.653060	+	0.757306i	$0.726515\pi$
$578$		0			0
$579$	−3585.45	−	12735.6i	−0.257351	−	0.914119i
$580$		0			0
$581$	−368.920			−0.0263432
$582$		0			0
$583$		−	14146.7i		−	1.00497i
$584$		0			0
$585$	5.40392	+	8.83676i	0.000381922	+	0.000624538i
$586$		0			0
$587$			21946.7i			1.54317i	0.636129	+	0.771583i	$0.280535\pi$
$587$			21946.7i			1.54317i	−0.636129	+	0.771583i	$0.719465\pi$
$588$		0			0
$589$			9217.46i			0.644820i
$590$		0			0
$591$	3083.22	+	10951.7i	0.214597	+	0.762253i
$592$		0			0
$593$		−	8554.64i		−	0.592406i	−0.955125	−	0.296203i	$-0.904279\pi$
$593$		−	8554.64i		−	0.592406i	0.955125	−	0.296203i	$-0.0957206\pi$
$594$		0			0
$595$	−1284.14			−0.0884784
$596$		0			0
$597$	26905.0	−	7574.56i	1.84447	−	0.519273i
$598$		0			0
$599$	19321.4			1.31795			0.658973	−	0.752167i	$-0.270991\pi$
$599$	19321.4			1.31795			0.658973	+	0.752167i	$0.270991\pi$
$600$		0			0
$601$	18248.6			1.23856			0.619281	−	0.785170i	$-0.287424\pi$
$601$	18248.6			1.23856			0.619281	+	0.785170i	$0.287424\pi$
$602$		0			0
$603$	−9567.30	+	5850.67i	−0.646121	+	0.395121i
$604$		0			0
$605$	−3220.26			−0.216400
$606$		0			0
$607$			18473.4i			1.23528i	0.786462	+	0.617639i	$0.211911\pi$
$607$			18473.4i			1.23528i	−0.786462	+	0.617639i	$0.788089\pi$
$608$		0			0
$609$	−4252.08	+	1197.08i	−0.282928	+	0.0796524i
$610$		0			0
$611$			28.0286i			0.00185583i
$612$		0			0
$613$		−	1007.68i		−	0.0663946i	−0.999449	−	0.0331973i	$-0.989431\pi$
$613$		−	1007.68i		−	0.0663946i	0.999449	−	0.0331973i	$-0.0105690\pi$
$614$		0			0
$615$	−11129.6	+	3133.32i	−0.729740	+	0.205443i
$616$		0			0
$617$		−	8342.82i		−	0.544359i	−0.962247	−	0.272179i	$-0.912256\pi$
$617$		−	8342.82i		−	0.544359i	0.962247	−	0.272179i	$-0.0877444\pi$
$618$		0			0
$619$	−5153.14			−0.334608			−0.167304	−	0.985905i	$-0.553506\pi$
$619$	−5153.14			−0.334608			−0.167304	+	0.985905i	$0.553506\pi$
$620$		0			0
$621$	−6305.77	−	5845.26i	−0.407475	−	0.377717i
$622$		0			0
$623$	6306.46			0.405559
$624$		0			0
$625$	3904.37			0.249880
$626$		0			0
$627$	−4303.81	+	1211.65i	−0.274127	+	0.0771748i
$628$		0			0
$629$	12589.6			0.798062
$630$		0			0
$631$		−	3224.67i		−	0.203442i	−0.994813	−	0.101721i	$-0.967565\pi$
$631$		−	3224.67i		−	0.203442i	0.994813	−	0.101721i	$-0.0324350\pi$
$632$		0			0
$633$	−7491.64	−	26610.5i	−0.470404	−	1.67089i
$634$		0			0
$635$		−	5616.91i		−	0.351024i
$636$		0			0
$637$			20.1380i			0.00125258i
$638$		0			0
$639$	12615.2	−	7714.54i	0.780985	−	0.477594i
$640$		0			0
$641$		−	13243.1i		−	0.816025i	−0.912976	−	0.408013i	$-0.866222\pi$
$641$		−	13243.1i		−	0.816025i	0.912976	−	0.408013i	$-0.133778\pi$
$642$		0			0
$643$	17030.3			1.04449			0.522246	−	0.852795i	$-0.325094\pi$
$643$	17030.3			1.04449			0.522246	+	0.852795i	$0.325094\pi$
$644$		0			0
$645$	3890.07	+	13817.6i	0.237475	+	0.843517i
$646$		0			0
$647$	−29077.9			−1.76688			−0.883438	−	0.468548i	$-0.844777\pi$
$647$	−29077.9			−1.76688			−0.883438	+	0.468548i	$0.844777\pi$
$648$		0			0
$649$	5811.93			0.351523
$650$		0			0
$651$	2497.87	+	8872.50i	0.150383	+	0.534164i
$652$		0			0
$653$	14617.7			0.876008			0.438004	−	0.898973i	$-0.355685\pi$
$653$	14617.7			0.876008			0.438004	+	0.898973i	$0.355685\pi$
$654$		0			0
$655$			3228.24i			0.192577i
$656$		0			0
$657$	4481.83	−	2740.76i	0.266138	−	0.162751i
$658$		0			0
$659$		−	3426.04i		−	0.202518i	−0.994860	−	0.101259i	$-0.967713\pi$
$659$		−	3426.04i		−	0.202518i	0.994860	−	0.101259i	$-0.0322871\pi$
$660$		0			0
$661$			9256.76i			0.544699i	0.962198	+	0.272350i	$0.0878008\pi$
$661$			9256.76i			0.544699i	−0.962198	+	0.272350i	$0.912199\pi$
$662$		0			0
$663$	3.40423	+	12.0919i	0.000199411	+	0.000708312i
$664$		0			0
$665$			1068.83i			0.0623269i
$666$		0			0
$667$	8798.63			0.510771
$668$		0			0
$669$	13546.7	−	3813.79i	0.782877	−	0.220403i
$670$		0			0
$671$	−16170.1			−0.930312
$672$		0			0
$673$	26622.1			1.52482			0.762412	−	0.647092i	$-0.224015\pi$
$673$	26622.1			1.52482			0.762412	+	0.647092i	$0.224015\pi$
$674$		0			0
$675$	9320.51	+	8639.84i	0.531476	+	0.492663i
$676$		0			0
$677$	23048.4			1.30845			0.654225	−	0.756300i	$-0.272995\pi$
$677$	23048.4			1.30845			0.654225	+	0.756300i	$0.272995\pi$
$678$		0			0
$679$			4164.54i			0.235376i
$680$		0			0
$681$	11680.3	−	3288.36i	0.657256	−	0.185037i
$682$		0			0
$683$		−	27884.8i		−	1.56220i	−0.624406	−	0.781100i	$-0.714659\pi$
$683$		−	27884.8i		−	1.56220i	0.624406	−	0.781100i	$-0.285341\pi$
$684$		0			0
$685$			11681.9i			0.651593i
$686$		0			0
$687$	−696.749	+	196.155i	−0.0386938	+	0.0108934i
$688$		0			0
$689$			33.0821i			0.00182921i
$690$		0			0
$691$	8029.81			0.442067			0.221034	−	0.975266i	$-0.429057\pi$
$691$	8029.81			0.442067			0.221034	+	0.975266i	$0.429057\pi$
$692$		0			0
$693$	−3814.39	+	2332.61i	−0.209086	+	0.127862i
$694$		0			0
$695$	−4381.22			−0.239121
$696$		0			0
$697$	−14022.3			−0.762029
$698$		0			0
$699$	35.4115	−	9.96938i	0.00191615	−	0.000539452i
$700$		0			0
$701$	19827.7			1.06830			0.534152	−	0.845388i	$-0.320631\pi$
$701$	19827.7			1.06830			0.534152	+	0.845388i	$0.320631\pi$
$702$		0			0
$703$		−	10478.7i		−	0.562179i
$704$		0			0
$705$	−3540.38	−	12575.5i	−0.189132	−	0.671803i
$706$		0			0
$707$			5581.32i			0.296898i
$708$		0			0
$709$		−	5444.68i		−	0.288405i	−0.989548	−	0.144202i	$-0.953938\pi$
$709$		−	5444.68i		−	0.288405i	0.989548	−	0.144202i	$-0.0460617\pi$
$710$		0			0
$711$	4343.80	+	7103.20i	0.229121	+	0.374671i
$712$		0			0
$713$		−	18359.5i		−	0.964330i
$714$		0			0
$715$	−10.7284			−0.000561147
$716$		0			0
$717$	−1253.62	−	4452.89i	−0.0652960	−	0.231933i
$718$		0			0
$719$	−4118.06			−0.213599			−0.106799	−	0.994281i	$-0.534060\pi$
$719$	−4118.06			−0.213599			−0.106799	+	0.994281i	$0.534060\pi$
$720$		0			0
$721$	−509.435			−0.0263140
$722$		0			0
$723$	1793.93	+	6372.08i	0.0922779	+	0.327774i
$724$		0			0
$725$	−13005.2			−0.666208
$726$		0			0
$727$			26169.4i			1.33504i	0.744594	+	0.667518i	$0.232643\pi$
$727$			26169.4i			1.33504i	−0.744594	+	0.667518i	$0.767357\pi$
$728$		0			0
$729$	1489.78	+	19626.5i	0.0756889	+	0.997131i
$730$		0			0
$731$			17409.0i			0.880840i
$732$		0			0
$733$		−	28634.0i		−	1.44286i	−0.692485	−	0.721432i	$-0.743484\pi$
$733$		−	28634.0i		−	1.44286i	0.692485	−	0.721432i	$-0.256516\pi$
$734$		0			0
$735$	−2543.69	−	9035.27i	−0.127654	−	0.453430i
$736$		0			0
$737$		−	11615.4i		−	0.580539i
$738$		0			0
$739$	1607.43			0.0800139			0.0400070	−	0.999199i	$-0.487262\pi$
$739$	1607.43			0.0800139			0.0400070	+	0.999199i	$0.487262\pi$
$740$		0			0
$741$	10.0644	−	2.83344i	0.000498957	−	0.000140471i
$742$		0			0
$743$	600.872			0.0296687			0.0148344	−	0.999890i	$-0.495278\pi$
$743$	600.872			0.0296687			0.0148344	+	0.999890i	$0.495278\pi$
$744$		0			0
$745$	−18765.0			−0.922815
$746$		0			0
$747$	−877.593	−	1435.08i	−0.0429845	−	0.0702904i
$748$		0			0
$749$	−4074.47			−0.198769
$750$		0			0
$751$			16005.7i			0.777707i	0.921300	+	0.388854i	$0.127129\pi$
$751$			16005.7i			0.777707i	−0.921300	+	0.388854i	$0.872871\pi$
$752$		0			0
$753$	15169.5	−	4270.65i	0.734139	−	0.206682i
$754$		0			0
$755$			8655.67i			0.417235i
$756$		0			0
$757$			16731.0i			0.803300i	0.915793	+	0.401650i	$0.131563\pi$
$757$			16731.0i			0.803300i	−0.915793	+	0.401650i	$0.868437\pi$
$758$		0			0
$759$	8572.38	−	2413.38i	0.409958	−	0.115415i
$760$		0			0
$761$			2885.92i			0.137470i	0.997635	+	0.0687349i	$0.0218963\pi$
$761$			2885.92i			0.137470i	−0.997635	+	0.0687349i	$0.978104\pi$
$762$		0			0
$763$	−10954.4			−0.519758
$764$		0			0
$765$	−3054.74	−	4995.26i	−0.144372	−	0.236083i
$766$		0			0
$767$	−13.5912			−0.000639830
$768$		0			0
$769$	5456.60			0.255878			0.127939	−	0.991782i	$-0.459164\pi$
$769$	5456.60			0.255878			0.127939	+	0.991782i	$0.459164\pi$
$770$		0			0
$771$	−12930.6	+	3640.33i	−0.603998	+	0.170043i
$772$		0			0
$773$	−1995.30			−0.0928407			−0.0464204	−	0.998922i	$-0.514781\pi$
$773$	−1995.30			−0.0928407			−0.0464204	+	0.998922i	$0.514781\pi$
$774$		0			0
$775$			27137.0i			1.25779i
$776$		0			0
$777$	−2839.66	−	10086.5i	−0.131110	−	0.465705i
$778$		0			0
$779$			11671.2i			0.536796i
$780$		0			0
$781$			15315.7i			0.701714i
$782$		0			0
$783$	−14771.5	−	13692.8i	−0.674191	−	0.624954i
$784$		0			0
$785$			4183.46i			0.190209i
$786$		0			0
$787$	38385.1			1.73860			0.869302	−	0.494282i	$-0.164569\pi$
$787$	38385.1			1.73860			0.869302	+	0.494282i	$0.164569\pi$
$788$		0			0
$789$	−7666.14	−	27230.4i	−0.345909	−	1.22868i
$790$		0			0
$791$	6244.45			0.280692
$792$		0			0
$793$	37.8137			0.00169332
$794$		0			0
$795$	−4178.70	−	14842.9i	−0.186419	−	0.662166i
$796$		0			0
$797$	27449.4			1.21996			0.609980	−	0.792417i	$-0.291178\pi$
$797$	27449.4			1.21996			0.609980	+	0.792417i	$0.291178\pi$
$798$		0			0
$799$		−	15844.0i		−	0.701529i
$800$		0			0
$801$	15001.9	+	24531.9i	0.661756	+	1.08214i
$802$		0			0
$803$			5441.24i			0.239125i
$804$		0			0
$805$		−	2128.91i		−	0.0932100i
$806$		0			0
$807$	−2902.69	−	10310.4i	−0.126617	−	0.449745i
$808$		0			0
$809$		−	430.948i		−	0.0187285i	−0.999956	−	0.00936424i	$-0.997019\pi$
$809$		−	430.948i		−	0.0187285i	0.999956	−	0.00936424i	$-0.00298077\pi$
$810$		0			0
$811$	30047.5			1.30100			0.650500	−	0.759506i	$-0.274559\pi$
$811$	30047.5			1.30100			0.650500	+	0.759506i	$0.274559\pi$
$812$		0			0
$813$	29243.6	−	8232.94i	1.26152	−	0.355156i
$814$		0			0
$815$	11653.0			0.500841
$816$		0			0
$817$	14490.0			0.620490
$818$		0			0
$819$	8.91995	−	5.45480i	0.000380572	−	0.000232730i
$820$		0			0
$821$	27225.8			1.15736			0.578678	−	0.815556i	$-0.303569\pi$
$821$	27225.8			1.15736			0.578678	+	0.815556i	$0.303569\pi$
$822$		0			0
$823$			41196.3i			1.74485i	0.488748	+	0.872425i	$0.337454\pi$
$823$			41196.3i			1.74485i	−0.488748	+	0.872425i	$0.662546\pi$
$824$		0			0
$825$	−12670.8	+	3567.20i	−0.534715	+	0.150538i
$826$		0			0
$827$		−	9322.06i		−	0.391971i	−0.980607	−	0.195985i	$-0.937209\pi$
$827$		−	9322.06i		−	0.391971i	0.980607	−	0.195985i	$-0.0627905\pi$
$828$		0			0
$829$		−	39860.8i		−	1.66999i	−0.550256	−	0.834996i	$-0.685470\pi$
$829$		−	39860.8i		−	1.66999i	0.550256	−	0.834996i	$-0.314530\pi$
$830$		0			0
$831$	−7443.95	+	2095.69i	−0.310743	+	0.0874833i
$832$		0			0
$833$		−	11383.6i		−	0.473493i
$834$		0			0
$835$	19808.9			0.820975
$836$		0			0
$837$	−28571.7	+	30822.6i	−1.17991	+	1.27286i
$838$		0			0
$839$	−8509.74			−0.350165			−0.175083	−	0.984554i	$-0.556019\pi$
$839$	−8509.74			−0.350165			−0.175083	+	0.984554i	$0.556019\pi$
$840$		0			0
$841$	−3777.83			−0.154899
$842$		0			0
$843$	−32295.9	+	9092.26i	−1.31949	+	0.371476i
$844$		0			0
$845$	−12888.2			−0.524693
$846$		0			0
$847$			3250.57i			0.131867i
$848$		0			0
$849$	−7590.77	−	26962.6i	−0.306849	−	1.08994i
$850$		0			0
$851$			20871.6i			0.840740i
$852$		0			0
$853$			37505.9i			1.50548i	0.658317	+	0.752741i	$0.271269\pi$
$853$			37505.9i			1.50548i	−0.658317	+	0.752741i	$0.728731\pi$
$854$		0			0
$855$	−4157.69	+	2542.54i	−0.166304	+	0.101700i
$856$		0			0
$857$		−	40647.9i		−	1.62019i	−0.586296	−	0.810097i	$-0.699415\pi$
$857$		−	40647.9i		−	1.62019i	0.586296	−	0.810097i	$-0.300585\pi$
$858$		0			0
$859$	−14040.1			−0.557673			−0.278836	−	0.960339i	$-0.589949\pi$
$859$	−14040.1			−0.557673			−0.278836	+	0.960339i	$0.589949\pi$
$860$		0			0
$861$	3162.81	+	11234.4i	0.125190	+	0.444678i
$862$		0			0
$863$	12519.6			0.493826			0.246913	−	0.969038i	$-0.420584\pi$
$863$	12519.6			0.493826			0.246913	+	0.969038i	$0.420584\pi$
$864$		0			0
$865$	15816.2			0.621694
$866$		0			0
$867$	4993.79	+	17738.1i	0.195615	+	0.694830i
$868$		0			0
$869$	−8623.76			−0.336641
$870$		0			0
$871$			27.1625i			0.00105668i
$872$		0			0
$873$	−16199.9	+	9906.68i	−0.628045	+	0.384067i
$874$		0			0
$875$			7488.85i			0.289336i
$876$		0			0
$877$			27995.4i			1.07792i	0.842330	+	0.538962i	$0.181183\pi$
$877$			27995.4i			1.07792i	−0.842330	+	0.538962i	$0.818817\pi$
$878$		0			0
$879$	−7605.11	−	27013.5i	−0.291825	−	1.03657i
$880$		0			0
$881$			16934.0i			0.647583i	0.946128	+	0.323792i	$0.104958\pi$
$881$			16934.0i			0.647583i	−0.946128	+	0.323792i	$0.895042\pi$
$882$		0			0
$883$	5835.41			0.222398			0.111199	−	0.993798i	$-0.464531\pi$
$883$	5835.41			0.222398			0.111199	+	0.993798i	$0.464531\pi$
$884$		0			0
$885$	6097.93	−	1716.75i	0.231615	−	0.0652066i
$886$		0			0
$887$	−12966.0			−0.490818			−0.245409	−	0.969420i	$-0.578922\pi$
$887$	−12966.0			−0.490818			−0.245409	+	0.969420i	$0.578922\pi$
$888$		0			0
$889$	−5669.79			−0.213902
$890$		0			0
$891$	−18147.5	−	9288.98i	−0.682338	−	0.349262i
$892$		0			0
$893$	−13187.4			−0.494178
$894$		0			0
$895$			19635.9i			0.733357i
$896$		0			0
$897$	−20.0465	+	5.64368i	−0.000746191	+	0.000210075i
$898$		0			0
$899$		−	43007.8i		−	1.59554i
$900$		0			0
$901$		−	18700.7i		−	0.691465i
$902$		0			0
$903$	13947.7	−	3926.69i	0.514009	−	0.144709i
$904$		0			0
$905$			10816.7i			0.397304i
$906$		0			0
$907$	14718.0			0.538812			0.269406	−	0.963027i	$-0.413173\pi$
$907$	14718.0			0.538812			0.269406	+	0.963027i	$0.413173\pi$
$908$		0			0
$909$	−21711.1	+	13276.9i	−0.792202	+	0.484453i
$910$		0			0
$911$	38859.8			1.41326			0.706632	−	0.707581i	$-0.250214\pi$
$911$	38859.8			1.41326			0.706632	+	0.707581i	$0.250214\pi$
$912$		0			0
$913$	1742.29			0.0631559
$914$		0			0
$915$	−16965.8	+	4776.37i	−0.612975	+	0.172570i
$916$		0			0
$917$	3258.63			0.117349
$918$		0			0
$919$		−	38295.3i		−	1.37459i	−0.726380	−	0.687294i	$-0.758799\pi$
$919$		−	38295.3i		−	1.37459i	0.726380	−	0.687294i	$-0.241201\pi$
$920$		0			0
$921$	5066.61	+	17996.8i	0.181271	+	0.643880i
$922$		0			0
$923$		−	35.8157i		−	0.00127724i
$924$		0			0
$925$		−	30850.2i		−	1.09659i
$926$		0			0
$927$	−1211.85	−	1981.68i	−0.0429369	−	0.0702125i
$928$		0			0
$929$			43777.6i			1.54607i	0.634364	+	0.773034i	$0.281262\pi$
$929$			43777.6i			1.54607i	−0.634364	+	0.773034i	$0.718738\pi$
$930$		0			0
$931$	−9474.92			−0.333542
$932$		0			0
$933$	11116.6	+	39486.3i	0.390075	+	1.38556i
$934$		0			0
$935$	6064.58			0.212121
$936$		0			0
$937$	28384.6			0.989631			0.494816	−	0.868998i	$-0.335236\pi$
$937$	28384.6			0.989631			0.494816	+	0.868998i	$0.335236\pi$
$938$		0			0
$939$	−11969.9	−	42517.4i	−0.415999	−	1.47764i
$940$		0			0
$941$	−54057.6			−1.87272			−0.936359	−	0.351044i	$-0.885827\pi$
$941$	−54057.6			−1.87272			−0.936359	+	0.351044i	$0.885827\pi$
$942$		0			0
$943$		−	23246.8i		−	0.802780i
$944$		0			0
$945$	−3313.08	+	3574.10i	−0.114047	+	0.123032i
$946$		0			0
$947$		−	54179.3i		−	1.85912i	−0.368665	−	0.929562i	$-0.620185\pi$
$947$		−	54179.3i		−	1.85912i	0.368665	−	0.929562i	$-0.379815\pi$
$948$		0			0
$949$		−	12.7243i		−	0.000435247i
$950$		0			0
$951$	−10352.6	−	36772.7i	−0.353003	−	1.25388i
$952$		0			0
$953$			2964.61i			0.100769i	0.998730	+	0.0503846i	$0.0160447\pi$
$953$			2964.61i			0.100769i	−0.998730	+	0.0503846i	$0.983955\pi$
$954$		0			0
$955$	−13975.2			−0.473537
$956$		0			0
$957$	20081.2	−	5653.44i	0.678299	−	0.190961i
$958$		0			0
$959$	11791.8			0.397058
$960$		0			0
$961$	−59950.2			−2.01236
$962$		0			0
$963$	−9692.41	−	15849.5i	−0.324334	−	0.530367i
$964$		0			0
$965$	14937.0			0.498278
$966$		0			0
$967$			12087.0i			0.401956i	0.979596	+	0.200978i	$0.0644119\pi$
$967$			12087.0i			0.401956i	−0.979596	+	0.200978i	$0.935588\pi$
$968$		0			0
$969$	−5689.25	+	1601.69i	−0.188612	+	0.0530998i
$970$		0			0
$971$			34336.2i			1.13481i	0.823439	+	0.567405i	$0.192053\pi$
$971$			34336.2i			1.13481i	−0.823439	+	0.567405i	$0.807947\pi$
$972$		0			0
$973$			4422.46i			0.145712i
$974$		0			0
$975$	29.6306	−	8.34188i	0.000973271	−	0.000274004i
$976$		0			0
$977$			12445.9i			0.407555i	0.979017	+	0.203777i	$0.0653218\pi$
$977$			12445.9i			0.407555i	−0.979017	+	0.203777i	$0.934678\pi$
$978$		0			0
$979$	−29783.3			−0.972298
$980$		0			0
$981$	−26058.5	−	42612.1i	−0.848097	−	1.38685i
$982$		0			0
$983$	−50850.7			−1.64994			−0.824968	−	0.565180i	$-0.808807\pi$
$983$	−50850.7			−1.64994			−0.824968	+	0.565180i	$0.808807\pi$
$984$		0			0
$985$	−12844.7			−0.415498
$986$		0			0
$987$	−12693.9	+	3573.71i	−0.409373	+	0.115251i
$988$		0			0
$989$	−28861.3			−0.927945
$990$		0			0
$991$			16973.3i			0.544071i	0.962287	+	0.272035i	$0.0876968\pi$
$991$			16973.3i			0.544071i	−0.962287	+	0.272035i	$0.912303\pi$
$992$		0			0
$993$	−6123.23	−	21749.9i	−0.195684	−	0.695077i
$994$		0			0
$995$			31555.6i			1.00541i
$996$		0			0
$997$		−	20434.2i		−	0.649104i	−0.945868	−	0.324552i	$-0.894787\pi$
$997$		−	20434.2i		−	0.649104i	0.945868	−	0.324552i	$-0.105213\pi$
$998$		0			0
$999$	32481.2	−	35040.2i	1.02869	−	1.10973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.4.f.e.383.8		12
3.2	odd	2		768.4.f.f.383.7		12
4.3	odd	2		768.4.f.g.383.5		12
8.3	odd	2		768.4.f.f.383.8		12
8.5	even	2		768.4.f.h.383.5		12
12.11	even	2		768.4.f.h.383.6		12
16.3	odd	4		384.4.c.b.383.11	yes	12
16.5	even	4		384.4.c.a.383.11	✓	12
16.11	odd	4		384.4.c.d.383.2	yes	12
16.13	even	4		384.4.c.c.383.2	yes	12
24.5	odd	2		768.4.f.g.383.6		12
24.11	even	2	inner	768.4.f.e.383.7		12
48.5	odd	4		384.4.c.d.383.1	yes	12
48.11	even	4		384.4.c.a.383.12	yes	12
48.29	odd	4		384.4.c.b.383.12	yes	12
48.35	even	4		384.4.c.c.383.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.4.c.a.383.11	✓	12	16.5	even	4
384.4.c.a.383.12	yes	12	48.11	even	4
384.4.c.b.383.11	yes	12	16.3	odd	4
384.4.c.b.383.12	yes	12	48.29	odd	4
384.4.c.c.383.1	yes	12	48.35	even	4
384.4.c.c.383.2	yes	12	16.13	even	4
384.4.c.d.383.1	yes	12	48.5	odd	4
384.4.c.d.383.2	yes	12	16.11	odd	4
768.4.f.e.383.7		12	24.11	even	2	inner
768.4.f.e.383.8		12	1.1	even	1	trivial
768.4.f.f.383.7		12	3.2	odd	2
768.4.f.f.383.8		12	8.3	odd	2
768.4.f.g.383.5		12	4.3	odd	2
768.4.f.g.383.6		12	24.5	odd	2
768.4.f.h.383.5		12	8.5	even	2
768.4.f.h.383.6		12	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	768.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40813 + 5.00172i) q^{3} -5.86626 q^{5} +5.92149i q^{7} +(-23.0343 + 14.0861i) q^{9} +O(q^{10})\)	\(q+(1.40813 + 5.00172i) q^{3} -5.86626 q^{5} +5.92149i q^{7} +(-23.0343 + 14.0861i) q^{9} -27.9652i q^{11} +0.0653967i q^{13} +(-8.26046 - 29.3414i) q^{15} -36.9675i q^{17} -30.7691 q^{19} +(-29.6176 + 8.33823i) q^{21} +61.2864 q^{23} -90.5870 q^{25} +(-102.890 - 95.3761i) q^{27} +143.566 q^{29} -299.568i q^{31} +(139.874 - 39.3787i) q^{33} -34.7370i q^{35} +340.559i q^{37} +(-0.327096 + 0.0920870i) q^{39} -379.315i q^{41} -470.926 q^{43} +(135.125 - 82.6330i) q^{45} +428.593 q^{47} +307.936 q^{49} +(184.901 - 52.0551i) q^{51} +505.868 q^{53} +164.051i q^{55} +(-43.3269 - 153.898i) q^{57} +207.827i q^{59} -578.221i q^{61} +(-83.4109 - 136.398i) q^{63} -0.383634i q^{65} +415.350 q^{67} +(86.2992 + 306.537i) q^{69} -547.669 q^{71} -194.572 q^{73} +(-127.558 - 453.090i) q^{75} +165.596 q^{77} -308.374i q^{79} +(332.162 - 648.930i) q^{81} +62.3019i q^{83} +216.861i q^{85} +(202.159 + 718.076i) q^{87} -1065.01i q^{89} -0.387246 q^{91} +(1498.36 - 421.831i) q^{93} +180.500 q^{95} +703.293 q^{97} +(393.922 + 644.161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 12 q^{5}+O(q^{10}) \) 12 * q - 2 * q^3 - 12 * q^5	\( 12 q - 2 q^{3} - 12 q^{5} - 84 q^{15} - 180 q^{19} - 156 q^{21} - 120 q^{23} + 300 q^{25} + 130 q^{27} - 588 q^{29} - 116 q^{33} + 620 q^{39} + 372 q^{43} + 740 q^{45} + 1248 q^{47} - 948 q^{49} + 360 q^{51} + 948 q^{53} + 172 q^{57} - 2744 q^{63} - 2292 q^{67} - 3280 q^{69} - 2040 q^{71} + 216 q^{73} + 2522 q^{75} - 4824 q^{77} - 1076 q^{81} + 4156 q^{87} - 3480 q^{91} + 4180 q^{93} + 5448 q^{95} - 48 q^{97} + 3048 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 12 * q^5 - 84 * q^15 - 180 * q^19 - 156 * q^21 - 120 * q^23 + 300 * q^25 + 130 * q^27 - 588 * q^29 - 116 * q^33 + 620 * q^39 + 372 * q^43 + 740 * q^45 + 1248 * q^47 - 948 * q^49 + 360 * q^51 + 948 * q^53 + 172 * q^57 - 2744 * q^63 - 2292 * q^67 - 3280 * q^69 - 2040 * q^71 + 216 * q^73 + 2522 * q^75 - 4824 * q^77 - 1076 * q^81 + 4156 * q^87 - 3480 * q^91 + 4180 * q^93 + 5448 * q^95 - 48 * q^97 + 3048 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more