LMFDB - Embedded newform 128.3.f.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(31,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("128.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.f (of order $4$, degree $2$, 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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Root			$0.264658 - 1.38923i$ of defining polynomial
Character	$\chi$	$=$	128.31
Dual form			128.3.f.a.95.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.24914 - 3.24914i) q^{3} +(0.0586332 + 0.0586332i) q^{5} -4.61555 q^{7} +12.1138i q^{9} +O(q^{10})$	\(q+(-3.24914 - 3.24914i) q^{3} +(0.0586332 + 0.0586332i) q^{5} -4.61555 q^{7} +12.1138i q^{9} +(-5.36641 + 5.36641i) q^{11} +(-11.0552 + 11.0552i) q^{13} -0.381015i q^{15} -12.8793 q^{17} +(2.63359 + 2.63359i) q^{19} +(14.9966 + 14.9966i) q^{21} -16.3810 q^{23} -24.9931i q^{25} +(10.1173 - 10.1173i) q^{27} +(26.0518 - 26.0518i) q^{29} -20.2345i q^{31} +34.8724 q^{33} +(-0.270624 - 0.270624i) q^{35} +(-41.2829 - 41.2829i) q^{37} +71.8398 q^{39} +3.29640i q^{41} +(-0.786951 + 0.786951i) q^{43} +(-0.710272 + 0.710272i) q^{45} +79.7517i q^{47} -27.6967 q^{49} +(41.8466 + 41.8466i) q^{51} +(-1.06207 - 1.06207i) q^{53} -0.629299 q^{55} -17.1138i q^{57} +(32.5163 - 32.5163i) q^{59} +(-15.2897 + 15.2897i) q^{61} -55.9119i q^{63} -1.29640 q^{65} +(-60.0631 - 60.0631i) q^{67} +(53.2242 + 53.2242i) q^{69} -56.3535 q^{71} -9.70663i q^{73} +(-81.2062 + 81.2062i) q^{75} +(24.7689 - 24.7689i) q^{77} -84.4278i q^{79} +43.2796 q^{81} +(26.7577 + 26.7577i) q^{83} +(-0.755154 - 0.755154i) q^{85} -169.292 q^{87} +115.555i q^{89} +(51.0258 - 51.0258i) q^{91} +(-65.7448 + 65.7448i) q^{93} +0.308832i q^{95} -146.245 q^{97} +(-65.0077 - 65.0077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 6 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	$ 6 q - 2 q^{3} + 2 q^{5} + 4 q^{7} - 18 q^{11} + 2 q^{13} - 4 q^{17} + 30 q^{19} + 20 q^{21} - 60 q^{23} + 64 q^{27} + 18 q^{29} - 4 q^{33} - 100 q^{35} - 46 q^{37} + 196 q^{39} - 114 q^{43} - 66 q^{45} - 46 q^{49} + 156 q^{51} - 78 q^{53} - 252 q^{55} + 206 q^{59} - 30 q^{61} + 12 q^{65} - 226 q^{67} + 116 q^{69} + 260 q^{71} - 238 q^{75} + 212 q^{77} + 86 q^{81} + 318 q^{83} + 212 q^{85} - 444 q^{87} + 188 q^{91} + 32 q^{93} - 4 q^{97} - 226 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 - 18 * q^11 + 2 * q^13 - 4 * q^17 + 30 * q^19 + 20 * q^21 - 60 * q^23 + 64 * q^27 + 18 * q^29 - 4 * q^33 - 100 * q^35 - 46 * q^37 + 196 * q^39 - 114 * q^43 - 66 * q^45 - 46 * q^49 + 156 * q^51 - 78 * q^53 - 252 * q^55 + 206 * q^59 - 30 * q^61 + 12 * q^65 - 226 * q^67 + 116 * q^69 + 260 * q^71 - 238 * q^75 + 212 * q^77 + 86 * q^81 + 318 * q^83 + 212 * q^85 - 444 * q^87 + 188 * q^91 + 32 * q^93 - 4 * q^97 - 226 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.24914	−	3.24914i	−1.08305	−	1.08305i	−0.996224	−	0.0868231i	$-0.972329\pi$
$3$	−3.24914	−	3.24914i	−1.08305	−	1.08305i	−0.0868231	−	0.996224i	$-0.527671\pi$
$4$		0			0
$5$	0.0586332	+	0.0586332i	0.0117266	+	0.0117266i	0.712946	−	0.701219i	$-0.247361\pi$
$5$	0.0586332	+	0.0586332i	0.0117266	+	0.0117266i	−0.701219	+	0.712946i	$0.747361\pi$
$6$		0			0
$7$	−4.61555			−0.659364			−0.329682	−	0.944092i	$-0.606942\pi$
$7$	−4.61555			−0.659364			−0.329682	+	0.944092i	$0.606942\pi$
$8$		0			0
$9$			12.1138i			1.34598i
$10$		0			0
$11$	−5.36641	+	5.36641i	−0.487855	+	0.487855i	−0.907629	−	0.419774i	$-0.862109\pi$
$11$	−5.36641	+	5.36641i	−0.487855	+	0.487855i	0.419774	+	0.907629i	$0.362109\pi$
$12$		0			0
$13$	−11.0552	+	11.0552i	−0.850400	+	0.850400i	−0.990182	−	0.139783i	$-0.955360\pi$
$13$	−11.0552	+	11.0552i	−0.850400	+	0.850400i	0.139783	+	0.990182i	$0.455360\pi$
$14$		0			0
$15$		−	0.381015i		−	0.0254010i
$16$		0			0
$17$	−12.8793			−0.757606			−0.378803	−	0.925477i	$-0.623664\pi$
$17$	−12.8793			−0.757606			−0.378803	+	0.925477i	$0.623664\pi$
$18$		0			0
$19$	2.63359	+	2.63359i	0.138610	+	0.138610i	0.773007	−	0.634397i	$-0.218752\pi$
$19$	2.63359	+	2.63359i	0.138610	+	0.138610i	−0.634397	+	0.773007i	$0.718752\pi$
$20$		0			0
$21$	14.9966	+	14.9966i	0.714122	+	0.714122i
$22$		0			0
$23$	−16.3810			−0.712218			−0.356109	−	0.934444i	$-0.615897\pi$
$23$	−16.3810			−0.712218			−0.356109	+	0.934444i	$0.615897\pi$
$24$		0			0
$25$		−	24.9931i		−	0.999725i
$26$		0			0
$27$	10.1173	−	10.1173i	0.374714	−	0.374714i
$28$		0			0
$29$	26.0518	−	26.0518i	0.898336	−	0.898336i	−0.0969525	−	0.995289i	$-0.530910\pi$
$29$	26.0518	−	26.0518i	0.898336	−	0.898336i	0.995289	+	0.0969525i	$0.0309095\pi$
$30$		0			0
$31$		−	20.2345i		−	0.652727i	−0.945244	−	0.326363i	$-0.894177\pi$
$31$		−	20.2345i		−	0.652727i	0.945244	−	0.326363i	$-0.105823\pi$
$32$		0			0
$33$	34.8724			1.05674
$34$		0			0
$35$	−0.270624	−	0.270624i	−0.00773212	−	0.00773212i
$36$		0			0
$37$	−41.2829	−	41.2829i	−1.11575	−	1.11575i	−0.992358	−	0.123395i	$-0.960622\pi$
$37$	−41.2829	−	41.2829i	−1.11575	−	1.11575i	−0.123395	−	0.992358i	$-0.539378\pi$
$38$		0			0
$39$	71.8398			1.84205
$40$		0			0
$41$			3.29640i			0.0804001i	0.999192	+	0.0402000i	$0.0127995\pi$
$41$			3.29640i			0.0804001i	−0.999192	+	0.0402000i	$0.987200\pi$
$42$		0			0
$43$	−0.786951	+	0.786951i	−0.0183012	+	0.0183012i	−0.716198	−	0.697897i	$-0.754119\pi$
$43$	−0.786951	+	0.786951i	−0.0183012	+	0.0183012i	0.697897	+	0.716198i	$0.254119\pi$
$44$		0			0
$45$	−0.710272	+	0.710272i	−0.0157838	+	0.0157838i
$46$		0			0
$47$			79.7517i			1.69685i	0.529320	+	0.848423i	$0.322447\pi$
$47$			79.7517i			1.69685i	−0.529320	+	0.848423i	$0.677553\pi$
$48$		0			0
$49$	−27.6967			−0.565239
$50$		0			0
$51$	41.8466	+	41.8466i	0.820522	+	0.820522i
$52$		0			0
$53$	−1.06207	−	1.06207i	−0.0200391	−	0.0200391i	0.697016	−	0.717055i	$-0.254511\pi$
$53$	−1.06207	−	1.06207i	−0.0200391	−	0.0200391i	−0.717055	+	0.697016i	$0.754511\pi$
$54$		0			0
$55$	−0.629299			−0.0114418
$56$		0			0
$57$		−	17.1138i		−	0.300243i
$58$		0			0
$59$	32.5163	−	32.5163i	0.551124	−	0.551124i	−0.375641	−	0.926765i	$-0.622577\pi$
$59$	32.5163	−	32.5163i	0.551124	−	0.551124i	0.926765	+	0.375641i	$0.122577\pi$
$60$		0			0
$61$	−15.2897	+	15.2897i	−0.250651	+	0.250651i	−0.821238	−	0.570586i	$-0.806716\pi$
$61$	−15.2897	+	15.2897i	−0.250651	+	0.250651i	0.570586	+	0.821238i	$0.306716\pi$
$62$		0			0
$63$		−	55.9119i		−	0.887491i
$64$		0			0
$65$	−1.29640			−0.0199446
$66$		0			0
$67$	−60.0631	−	60.0631i	−0.896465	−	0.896465i	0.0986569	−	0.995122i	$-0.468545\pi$
$67$	−60.0631	−	60.0631i	−0.896465	−	0.896465i	−0.995122	+	0.0986569i	$0.968545\pi$
$68$		0			0
$69$	53.2242	+	53.2242i	0.771365	+	0.771365i
$70$		0			0
$71$	−56.3535			−0.793711			−0.396856	−	0.917881i	$-0.629899\pi$
$71$	−56.3535			−0.793711			−0.396856	+	0.917881i	$0.629899\pi$
$72$		0			0
$73$		−	9.70663i		−	0.132968i	−0.997788	−	0.0664838i	$-0.978822\pi$
$73$		−	9.70663i		−	0.132968i	0.997788	−	0.0664838i	$-0.0211781\pi$
$74$		0			0
$75$	−81.2062	+	81.2062i	−1.08275	+	1.08275i
$76$		0			0
$77$	24.7689	−	24.7689i	0.321674	−	0.321674i
$78$		0			0
$79$		−	84.4278i		−	1.06871i	−0.845261	−	0.534353i	$-0.820555\pi$
$79$		−	84.4278i		−	1.06871i	0.845261	−	0.534353i	$-0.179445\pi$
$80$		0			0
$81$	43.2796			0.534316
$82$		0			0
$83$	26.7577	+	26.7577i	0.322382	+	0.322382i	0.849680	−	0.527298i	$-0.176795\pi$
$83$	26.7577	+	26.7577i	0.322382	+	0.322382i	−0.527298	+	0.849680i	$0.676795\pi$
$84$		0			0
$85$	−0.755154	−	0.755154i	−0.00888416	−	0.00888416i
$86$		0			0
$87$	−169.292			−1.94588
$88$		0			0
$89$			115.555i			1.29838i	0.760628	+	0.649188i	$0.224891\pi$
$89$			115.555i			1.29838i	−0.760628	+	0.649188i	$0.775109\pi$
$90$		0			0
$91$	51.0258	−	51.0258i	0.560723	−	0.560723i
$92$		0			0
$93$	−65.7448	+	65.7448i	−0.706934	+	0.706934i
$94$		0			0
$95$			0.308832i			0.00325086i
$96$		0			0
$97$	−146.245			−1.50768			−0.753841	−	0.657056i	$-0.771801\pi$
$97$	−146.245			−1.50768			−0.753841	+	0.657056i	$0.771801\pi$
$98$		0			0
$99$	−65.0077	−	65.0077i	−0.656644	−	0.656644i
$100$		0			0
$101$	53.8554	+	53.8554i	0.533222	+	0.533222i	0.921530	−	0.388308i	$-0.126940\pi$
$101$	53.8554	+	53.8554i	0.533222	+	0.533222i	−0.388308	+	0.921530i	$0.626940\pi$
$102$		0			0
$103$	158.184			1.53577			0.767885	−	0.640588i	$-0.221309\pi$
$103$	158.184			1.53577			0.767885	+	0.640588i	$0.221309\pi$
$104$		0			0
$105$			1.75859i			0.0167485i
$106$		0			0
$107$	−57.6009	+	57.6009i	−0.538327	+	0.538327i	−0.923037	−	0.384711i	$-0.874301\pi$
$107$	−57.6009	+	57.6009i	−0.538327	+	0.538327i	0.384711	+	0.923037i	$0.374301\pi$
$108$		0			0
$109$	−56.8795	+	56.8795i	−0.521830	+	0.521830i	−0.918124	−	0.396294i	$-0.870296\pi$
$109$	−56.8795	+	56.8795i	−0.521830	+	0.521830i	0.396294	+	0.918124i	$0.370296\pi$
$110$		0			0
$111$			268.268i			2.41683i
$112$		0			0
$113$	135.731			1.20116			0.600580	−	0.799565i	$-0.294936\pi$
$113$	135.731			1.20116			0.600580	+	0.799565i	$0.294936\pi$
$114$		0			0
$115$	−0.960471	−	0.960471i	−0.00835192	−	0.00835192i
$116$		0			0
$117$	−133.921	−	133.921i	−1.14462	−	1.14462i
$118$		0			0
$119$	59.4450			0.499538
$120$		0			0
$121$			63.4034i			0.523995i
$122$		0			0
$123$	10.7105	−	10.7105i	0.0870770	−	0.0870770i
$124$		0			0
$125$	2.93125	−	2.93125i	0.0234500	−	0.0234500i
$126$		0			0
$127$		−	166.552i		−	1.31144i	−0.755006	−	0.655718i	$-0.772366\pi$
$127$		−	166.552i		−	1.31144i	0.755006	−	0.655718i	$-0.227634\pi$
$128$		0			0
$129$	5.11383			0.0396421
$130$		0			0
$131$	22.2547	+	22.2547i	0.169883	+	0.169883i	0.786928	−	0.617045i	$-0.211670\pi$
$131$	22.2547	+	22.2547i	0.169883	+	0.169883i	−0.617045	+	0.786928i	$0.711670\pi$
$132$		0			0
$133$	−12.1555	−	12.1555i	−0.0913945	−	0.0913945i
$134$		0			0
$135$	1.18641			0.00878826
$136$		0			0
$137$		−	174.890i		−	1.27657i	−0.769800	−	0.638285i	$-0.779644\pi$
$137$		−	174.890i		−	1.27657i	0.769800	−	0.638285i	$-0.220356\pi$
$138$		0			0
$139$	99.8891	−	99.8891i	0.718627	−	0.718627i	−0.249697	−	0.968324i	$-0.580331\pi$
$139$	99.8891	−	99.8891i	0.718627	−	0.718627i	0.968324	+	0.249697i	$0.0803310\pi$
$140$		0			0
$141$	259.125	−	259.125i	1.83776	−	1.83776i
$142$		0			0
$143$		−	118.653i		−	0.829744i
$144$		0			0
$145$	3.05499			0.0210689
$146$		0			0
$147$	89.9905	+	89.9905i	0.612181	+	0.612181i
$148$		0			0
$149$	74.8860	+	74.8860i	0.502590	+	0.502590i	0.912242	−	0.409652i	$-0.134350\pi$
$149$	74.8860	+	74.8860i	0.502590	+	0.502590i	−0.409652	+	0.912242i	$0.634350\pi$
$150$		0			0
$151$	−70.0357			−0.463813			−0.231906	−	0.972738i	$-0.574496\pi$
$151$	−70.0357			−0.463813			−0.231906	+	0.972738i	$0.574496\pi$
$152$		0			0
$153$		−	156.018i		−	1.01972i
$154$		0			0
$155$	1.18641	−	1.18641i	0.00765429	−	0.00765429i
$156$		0			0
$157$	29.5307	−	29.5307i	0.188094	−	0.188094i	−0.606778	−	0.794872i	$-0.707538\pi$
$157$	29.5307	−	29.5307i	0.188094	−	0.188094i	0.794872	+	0.606778i	$0.207538\pi$
$158$		0			0
$159$			6.90164i			0.0434065i
$160$		0			0
$161$	75.6074			0.469611
$162$		0			0
$163$	47.7990	+	47.7990i	0.293245	+	0.293245i	0.838361	−	0.545116i	$-0.183514\pi$
$163$	47.7990	+	47.7990i	0.293245	+	0.293245i	−0.545116	+	0.838361i	$0.683514\pi$
$164$		0			0
$165$	2.04468	+	2.04468i	0.0123920	+	0.0123920i
$166$		0			0
$167$	156.268			0.935734			0.467867	−	0.883799i	$-0.345023\pi$
$167$	156.268			0.935734			0.467867	+	0.883799i	$0.345023\pi$
$168$		0			0
$169$		−	75.4347i		−	0.446359i
$170$		0			0
$171$	−31.9029	+	31.9029i	−0.186567	+	0.186567i
$172$		0			0
$173$	−190.103	+	190.103i	−1.09886	+	1.09886i	−0.104319	+	0.994544i	$0.533266\pi$
$173$	−190.103	+	190.103i	−1.09886	+	1.09886i	−0.994544	+	0.104319i	$0.966734\pi$
$174$		0			0
$175$			115.357i			0.659183i
$176$		0			0
$177$	−211.300			−1.19379
$178$		0			0
$179$	54.2749	+	54.2749i	0.303212	+	0.303212i	0.842269	−	0.539057i	$-0.181219\pi$
$179$	54.2749	+	54.2749i	0.303212	+	0.303212i	−0.539057	+	0.842269i	$0.681219\pi$
$180$		0			0
$181$	−19.7343	−	19.7343i	−0.109029	−	0.109029i	0.650487	−	0.759517i	$-0.274565\pi$
$181$	−19.7343	−	19.7343i	−0.109029	−	0.109029i	−0.759517	+	0.650487i	$0.774565\pi$
$182$		0			0
$183$	99.3569			0.542934
$184$		0			0
$185$		−	4.84109i		−	0.0261680i
$186$		0			0
$187$	69.1155	−	69.1155i	0.369602	−	0.369602i
$188$		0			0
$189$	−46.6967	+	46.6967i	−0.247073	+	0.247073i
$190$		0			0
$191$			166.552i			0.872002i	0.899946	+	0.436001i	$0.143606\pi$
$191$			166.552i			0.872002i	−0.899946	+	0.436001i	$0.856394\pi$
$192$		0			0
$193$	2.18257			0.0113087			0.00565434	−	0.999984i	$-0.498200\pi$
$193$	2.18257			0.0113087			0.00565434	+	0.999984i	$0.498200\pi$
$194$		0			0
$195$	4.21219	+	4.21219i	0.0216010	+	0.0216010i
$196$		0			0
$197$	−67.4310	−	67.4310i	−0.342290	−	0.342290i	0.514938	−	0.857227i	$-0.327815\pi$
$197$	−67.4310	−	67.4310i	−0.342290	−	0.342290i	−0.857227	+	0.514938i	$0.827815\pi$
$198$		0			0
$199$	−222.906			−1.12013			−0.560065	−	0.828449i	$-0.689224\pi$
$199$	−222.906			−1.12013			−0.560065	+	0.828449i	$0.689224\pi$
$200$		0			0
$201$			390.307i			1.94183i
$202$		0			0
$203$	−120.243	+	120.243i	−0.592331	+	0.592331i
$204$		0			0
$205$	−0.193278	+	0.193278i	−0.000942822	+	0.000942822i
$206$		0			0
$207$		−	198.437i		−	0.958632i
$208$		0			0
$209$	−28.2659			−0.135243
$210$		0			0
$211$	−147.118	−	147.118i	−0.697240	−	0.697240i	0.266574	−	0.963814i	$-0.414108\pi$
$211$	−147.118	−	147.118i	−0.697240	−	0.697240i	−0.963814	+	0.266574i	$0.914108\pi$
$212$		0			0
$213$	183.100	+	183.100i	0.859627	+	0.859627i
$214$		0			0
$215$	−0.0922828			−0.000429223
$216$		0			0
$217$			93.3934i			0.430385i
$218$		0			0
$219$	−31.5382	+	31.5382i	−0.144010	+	0.144010i
$220$		0			0
$221$	142.383	−	142.383i	0.644268	−	0.644268i
$222$		0			0
$223$			60.7036i			0.272213i	0.990694	+	0.136107i	$0.0434590\pi$
$223$			60.7036i			0.272213i	−0.990694	+	0.136107i	$0.956541\pi$
$224$		0			0
$225$	302.762			1.34561
$226$		0			0
$227$	−225.526	−	225.526i	−0.993505	−	0.993505i	0.00647371	−	0.999979i	$-0.497939\pi$
$227$	−225.526	−	225.526i	−0.993505	−	0.993505i	−0.999979	+	0.00647371i	$0.997939\pi$
$228$		0			0
$229$	−227.796	−	227.796i	−0.994743	−	0.994743i	0.00524305	−	0.999986i	$-0.498331\pi$
$229$	−227.796	−	227.796i	−0.994743	−	0.994743i	−0.999986	+	0.00524305i	$0.998331\pi$
$230$		0			0
$231$	−160.955			−0.696776
$232$		0			0
$233$			121.053i			0.519540i	0.965671	+	0.259770i	$0.0836467\pi$
$233$			121.053i			0.519540i	−0.965671	+	0.259770i	$0.916353\pi$
$234$		0			0
$235$	−4.67610	+	4.67610i	−0.0198983	+	0.0198983i
$236$		0			0
$237$	−274.318	+	274.318i	−1.15746	+	1.15746i
$238$		0			0
$239$		−	221.393i		−	0.926332i	−0.886271	−	0.463166i	$-0.846713\pi$
$239$		−	221.393i		−	0.926332i	0.886271	−	0.463166i	$-0.153287\pi$
$240$		0			0
$241$	84.2667			0.349654			0.174827	−	0.984599i	$-0.444063\pi$
$241$	84.2667			0.349654			0.174827	+	0.984599i	$0.444063\pi$
$242$		0			0
$243$	−231.677	−	231.677i	−0.953403	−	0.953403i
$244$		0			0
$245$	−1.62395	−	1.62395i	−0.00662835	−	0.00662835i
$246$		0			0
$247$	−58.2298			−0.235748
$248$		0			0
$249$		−	173.879i		−	0.698310i
$250$		0			0
$251$	−176.615	+	176.615i	−0.703646	+	0.703646i	−0.965191	−	0.261545i	$-0.915768\pi$
$251$	−176.615	+	176.615i	−0.703646	+	0.703646i	0.261545	+	0.965191i	$0.415768\pi$
$252$		0			0
$253$	87.9072	−	87.9072i	0.347459	−	0.347459i
$254$		0			0
$255$			4.90720i			0.0192439i
$256$		0			0
$257$	−163.001			−0.634244			−0.317122	−	0.948385i	$-0.602717\pi$
$257$	−163.001			−0.634244			−0.317122	+	0.948385i	$0.602717\pi$
$258$		0			0
$259$	190.543	+	190.543i	0.735687	+	0.735687i
$260$		0			0
$261$	315.587	+	315.587i	1.20914	+	1.20914i
$262$		0			0
$263$	−175.001			−0.665404			−0.332702	−	0.943032i	$-0.607960\pi$
$263$	−175.001			−0.665404			−0.332702	+	0.943032i	$0.607960\pi$
$264$		0			0
$265$		−	0.124545i		−	0.000469982i
$266$		0			0
$267$	375.456	−	375.456i	1.40620	−	1.40620i
$268$		0			0
$269$	−29.7489	+	29.7489i	−0.110591	+	0.110591i	−0.760237	−	0.649646i	$-0.774917\pi$
$269$	−29.7489	+	29.7489i	−0.110591	+	0.110591i	0.649646	+	0.760237i	$0.274917\pi$
$270$		0			0
$271$			275.891i			1.01805i	0.860753	+	0.509024i	$0.169993\pi$
$271$			275.891i			1.01805i	−0.860753	+	0.509024i	$0.830007\pi$
$272$		0			0
$273$	−331.580			−1.21458
$274$		0			0
$275$	134.123	+	134.123i	0.487721	+	0.487721i
$276$		0			0
$277$	278.337	+	278.337i	1.00483	+	1.00483i	0.999988	+	0.00484003i	$0.00154063\pi$
$277$	278.337	+	278.337i	1.00483	+	1.00483i	0.00484003	+	0.999988i	$0.498459\pi$
$278$		0			0
$279$	245.118			0.878558
$280$		0			0
$281$		−	202.356i		−	0.720128i	−0.932928	−	0.360064i	$-0.882755\pi$
$281$		−	202.356i		−	0.720128i	0.932928	−	0.360064i	$-0.117245\pi$
$282$		0			0
$283$	−292.256	+	292.256i	−1.03271	+	1.03271i	−0.0332615	+	0.999447i	$0.510589\pi$
$283$	−292.256	+	292.256i	−1.03271	+	1.03271i	−0.999447	+	0.0332615i	$0.989411\pi$
$284$		0			0
$285$	1.00344	−	1.00344i	0.00352083	−	0.00352083i
$286$		0			0
$287$		−	15.2147i		−	0.0530129i
$288$		0			0
$289$	−123.124			−0.426034
$290$		0			0
$291$	475.171	+	475.171i	1.63289	+	1.63289i
$292$		0			0
$293$	−331.170	−	331.170i	−1.13027	−	1.13027i	−0.990132	−	0.140141i	$-0.955244\pi$
$293$	−331.170	−	331.170i	−1.13027	−	1.13027i	−0.140141	−	0.990132i	$-0.544756\pi$
$294$		0			0
$295$	3.81307			0.0129257
$296$		0			0
$297$			108.587i			0.365612i
$298$		0			0
$299$	181.095	−	181.095i	0.605670	−	0.605670i
$300$		0			0
$301$	3.63221	−	3.63221i	0.0120671	−	0.0120671i
$302$		0			0
$303$		−	349.968i		−	1.15501i
$304$		0			0
$305$	−1.79297			−0.00587859
$306$		0			0
$307$	23.7513	+	23.7513i	0.0773656	+	0.0773656i	0.744731	−	0.667365i	$-0.232578\pi$
$307$	23.7513	+	23.7513i	0.0773656	+	0.0773656i	−0.667365	+	0.744731i	$0.732578\pi$
$308$		0			0
$309$	−513.963	−	513.963i	−1.66331	−	1.66331i
$310$		0			0
$311$	157.757			0.507258			0.253629	−	0.967302i	$-0.418376\pi$
$311$	157.757			0.507258			0.253629	+	0.967302i	$0.418376\pi$
$312$		0			0
$313$		−	58.5936i		−	0.187200i	−0.995610	−	0.0936000i	$-0.970163\pi$
$313$		−	58.5936i		−	0.187200i	0.995610	−	0.0936000i	$-0.0298375\pi$
$314$		0			0
$315$	3.27829	−	3.27829i	0.0104073	−	0.0104073i
$316$		0			0
$317$	−27.0040	+	27.0040i	−0.0851863	+	0.0851863i	−0.748416	−	0.663230i	$-0.769185\pi$
$317$	−27.0040	+	27.0040i	−0.0851863	+	0.0851863i	0.663230	+	0.748416i	$0.269185\pi$
$318$		0			0
$319$			279.609i			0.876516i
$320$		0			0
$321$	374.307			1.16607
$322$		0			0
$323$	−33.9188	−	33.9188i	−0.105012	−	0.105012i
$324$		0			0
$325$	276.304	+	276.304i	0.850166	+	0.850166i
$326$		0			0
$327$	369.619			1.13033
$328$		0			0
$329$		−	368.098i		−	1.11884i
$330$		0			0
$331$	−182.195	+	182.195i	−0.550437	+	0.550437i	−0.926567	−	0.376130i	$-0.877255\pi$
$331$	−182.195	+	182.195i	−0.550437	+	0.550437i	0.376130	+	0.926567i	$0.377255\pi$
$332$		0			0
$333$	500.093	−	500.093i	1.50178	−	1.50178i
$334$		0			0
$335$		−	7.04338i		−	0.0210250i
$336$		0			0
$337$	510.137			1.51376			0.756881	−	0.653553i	$-0.226722\pi$
$337$	510.137			1.51376			0.756881	+	0.653553i	$0.226722\pi$
$338$		0			0
$339$	−441.009	−	441.009i	−1.30091	−	1.30091i
$340$		0			0
$341$	108.587	+	108.587i	0.318436	+	0.318436i
$342$		0			0
$343$	353.997			1.03206
$344$		0			0
$345$			6.24141i			0.0180910i
$346$		0			0
$347$	432.614	−	432.614i	1.24673	−	1.24673i	0.289570	−	0.957157i	$-0.406488\pi$
$347$	432.614	−	432.614i	1.24673	−	1.24673i	0.957157	−	0.289570i	$-0.0935122\pi$
$348$		0			0
$349$	148.839	−	148.839i	0.426472	−	0.426472i	−0.460953	−	0.887425i	$-0.652492\pi$
$349$	148.839	−	148.839i	0.426472	−	0.426472i	0.887425	+	0.460953i	$0.152492\pi$
$350$		0			0
$351$			223.697i			0.637313i
$352$		0			0
$353$	−268.587			−0.760869			−0.380434	−	0.924808i	$-0.624226\pi$
$353$	−268.587			−0.760869			−0.380434	+	0.924808i	$0.624226\pi$
$354$		0			0
$355$	−3.30418	−	3.30418i	−0.00930756	−	0.00930756i
$356$		0			0
$357$	−193.145	−	193.145i	−0.541023	−	0.541023i
$358$		0			0
$359$	−628.520			−1.75075			−0.875376	−	0.483442i	$-0.839386\pi$
$359$	−628.520			−1.75075			−0.875376	+	0.483442i	$0.839386\pi$
$360$		0			0
$361$		−	347.128i		−	0.961574i
$362$		0			0
$363$	206.006	−	206.006i	0.567511	−	0.567511i
$364$		0			0
$365$	0.569131	−	0.569131i	0.00155926	−	0.00155926i
$366$		0			0
$367$		−	396.386i		−	1.08007i	−0.841643	−	0.540035i	$-0.818411\pi$
$367$		−	396.386i		−	1.08007i	0.841643	−	0.540035i	$-0.181589\pi$
$368$		0			0
$369$	−39.9320			−0.108217
$370$		0			0
$371$	4.90204	+	4.90204i	0.0132130	+	0.0132130i
$372$		0			0
$373$	−134.275	−	134.275i	−0.359987	−	0.359987i	0.503821	−	0.863808i	$-0.331927\pi$
$373$	−134.275	−	134.275i	−0.359987	−	0.359987i	−0.863808	+	0.503821i	$0.831927\pi$
$374$		0			0
$375$	−19.0481			−0.0507950
$376$		0			0
$377$			576.015i			1.52789i
$378$		0			0
$379$	−350.491	+	350.491i	−0.924777	+	0.924777i	−0.997362	−	0.0725851i	$-0.976875\pi$
$379$	−350.491	+	350.491i	−0.924777	+	0.924777i	0.0725851	+	0.997362i	$0.476875\pi$
$380$		0			0
$381$	−541.152	+	541.152i	−1.42035	+	1.42035i
$382$		0			0
$383$			403.778i			1.05425i	0.849787	+	0.527126i	$0.176730\pi$
$383$			403.778i			1.05425i	−0.849787	+	0.527126i	$0.823270\pi$
$384$		0			0
$385$	2.90456			0.00754431
$386$		0			0
$387$	−9.53299	−	9.53299i	−0.0246330	−	0.0246330i
$388$		0			0
$389$	125.310	+	125.310i	0.322134	+	0.322134i	0.849585	−	0.527452i	$-0.176852\pi$
$389$	125.310	+	125.310i	0.322134	+	0.322134i	−0.527452	+	0.849585i	$0.676852\pi$
$390$		0			0
$391$	210.976			0.539580
$392$		0			0
$393$		−	144.617i		−	0.367983i
$394$		0			0
$395$	4.95027	−	4.95027i	0.0125323	−	0.0125323i
$396$		0			0
$397$	69.8722	−	69.8722i	0.176001	−	0.176001i	−0.613609	−	0.789610i	$-0.710283\pi$
$397$	69.8722	−	69.8722i	0.176001	−	0.176001i	0.789610	+	0.613609i	$0.210283\pi$
$398$		0			0
$399$			78.9897i			0.197969i
$400$		0			0
$401$	11.3010			0.0281821			0.0140911	−	0.999901i	$-0.495515\pi$
$401$	11.3010			0.0281821			0.0140911	+	0.999901i	$0.495515\pi$
$402$		0			0
$403$	223.697	+	223.697i	0.555079	+	0.555079i
$404$		0			0
$405$	2.53762	+	2.53762i	0.00626573	+	0.00626573i
$406$		0			0
$407$	443.081			1.08865
$408$		0			0
$409$			614.595i			1.50268i	0.659917	+	0.751339i	$0.270592\pi$
$409$			614.595i			1.50268i	−0.659917	+	0.751339i	$0.729408\pi$
$410$		0			0
$411$	−568.242	+	568.242i	−1.38258	+	1.38258i
$412$		0			0
$413$	−150.081	+	150.081i	−0.363391	+	0.363391i
$414$		0			0
$415$			3.13778i			0.00756092i
$416$		0			0
$417$	−649.108			−1.55661
$418$		0			0
$419$	78.7092	+	78.7092i	0.187850	+	0.187850i	0.794766	−	0.606916i	$-0.207594\pi$
$419$	78.7092	+	78.7092i	0.187850	+	0.187850i	−0.606916	+	0.794766i	$0.707594\pi$
$420$		0			0
$421$	374.618	+	374.618i	0.889829	+	0.889829i	0.994506	−	0.104678i	$-0.0333811\pi$
$421$	374.618	+	374.618i	0.889829	+	0.889829i	−0.104678	+	0.994506i	$0.533381\pi$
$422$		0			0
$423$	−966.099			−2.28392
$424$		0			0
$425$			321.894i			0.757397i
$426$		0			0
$427$	70.5705	−	70.5705i	0.165270	−	0.165270i
$428$		0			0
$429$	−385.521	+	385.521i	−0.898651	+	0.898651i
$430$		0			0
$431$		−	616.593i		−	1.43061i	−0.698813	−	0.715305i	$-0.746288\pi$
$431$		−	616.593i		−	1.43061i	0.698813	−	0.715305i	$-0.253712\pi$
$432$		0			0
$433$	219.246			0.506342			0.253171	−	0.967422i	$-0.418526\pi$
$433$	219.246			0.506342			0.253171	+	0.967422i	$0.418526\pi$
$434$		0			0
$435$	−9.92610	−	9.92610i	−0.0228186	−	0.0228186i
$436$		0			0
$437$	−43.1409	−	43.1409i	−0.0987207	−	0.0987207i
$438$		0			0
$439$	−575.292			−1.31046			−0.655231	−	0.755429i	$-0.727429\pi$
$439$	−575.292			−1.31046			−0.655231	+	0.755429i	$0.727429\pi$
$440$		0			0
$441$		−	335.513i		−	0.760801i
$442$		0			0
$443$	371.895	−	371.895i	0.839492	−	0.839492i	−0.149300	−	0.988792i	$-0.547702\pi$
$443$	371.895	−	371.895i	0.839492	−	0.839492i	0.988792	+	0.149300i	$0.0477021\pi$
$444$		0			0
$445$	−6.77538	+	6.77538i	−0.0152256	+	0.0152256i
$446$		0			0
$447$		−	486.630i		−	1.08866i
$448$		0			0
$449$	−498.135			−1.10943			−0.554716	−	0.832040i	$-0.687173\pi$
$449$	−498.135			−1.10943			−0.554716	+	0.832040i	$0.687173\pi$
$450$		0			0
$451$	−17.6898	−	17.6898i	−0.0392236	−	0.0392236i
$452$		0			0
$453$	227.556	+	227.556i	0.502331	+	0.502331i
$454$		0			0
$455$	5.98361			0.0131508
$456$		0			0
$457$		−	61.1711i		−	0.133854i	−0.997758	−	0.0669268i	$-0.978681\pi$
$457$		−	61.1711i		−	0.133854i	0.997758	−	0.0669268i	$-0.0213194\pi$
$458$		0			0
$459$	−130.303	+	130.303i	−0.283885	+	0.283885i
$460$		0			0
$461$	443.183	−	443.183i	0.961352	−	0.961352i	−0.0379287	−	0.999280i	$-0.512076\pi$
$461$	443.183	−	443.183i	0.961352	−	0.961352i	0.999280	+	0.0379287i	$0.0120760\pi$
$462$		0			0
$463$			706.883i			1.52675i	0.645958	+	0.763373i	$0.276458\pi$
$463$			706.883i			1.52675i	−0.645958	+	0.763373i	$0.723542\pi$
$464$		0			0
$465$	−7.70966			−0.0165799
$466$		0			0
$467$	−406.857	−	406.857i	−0.871214	−	0.871214i	0.121391	−	0.992605i	$-0.461265\pi$
$467$	−406.857	−	406.857i	−0.871214	−	0.871214i	−0.992605	+	0.121391i	$0.961265\pi$
$468$		0			0
$469$	277.224	+	277.224i	0.591096	+	0.591096i
$470$		0			0
$471$	−191.899			−0.407429
$472$		0			0
$473$		−	8.44620i		−	0.0178567i
$474$		0			0
$475$	65.8217	−	65.8217i	0.138572	−	0.138572i
$476$		0			0
$477$	12.8657	−	12.8657i	0.0269722	−	0.0269722i
$478$		0			0
$479$		−	133.063i		−	0.277793i	−0.990307	−	0.138896i	$-0.955645\pi$
$479$		−	133.063i		−	0.277793i	0.990307	−	0.138896i	$-0.0443555\pi$
$480$		0			0
$481$	912.780			1.89767
$482$		0			0
$483$	−245.659	−	245.659i	−0.508611	−	0.508611i
$484$		0			0
$485$	−8.57482	−	8.57482i	−0.0176800	−	0.0176800i
$486$		0			0
$487$	208.075			0.427259			0.213629	−	0.976915i	$-0.431471\pi$
$487$	208.075			0.427259			0.213629	+	0.976915i	$0.431471\pi$
$488$		0			0
$489$		−	310.611i		−	0.635197i
$490$		0			0
$491$	−98.9374	+	98.9374i	−0.201502	+	0.201502i	−0.800643	−	0.599141i	$-0.795509\pi$
$491$	−98.9374	+	98.9374i	−0.201502	+	0.201502i	0.599141	+	0.800643i	$0.295509\pi$
$492$		0			0
$493$	−335.528	+	335.528i	−0.680585	+	0.680585i
$494$		0			0
$495$		−	7.62322i		−	0.0154004i
$496$		0			0
$497$	260.102			0.523345
$498$		0			0
$499$	−287.076	−	287.076i	−0.575304	−	0.575304i	0.358302	−	0.933606i	$-0.383356\pi$
$499$	−287.076	−	287.076i	−0.575304	−	0.575304i	−0.933606	+	0.358302i	$0.883356\pi$
$500$		0			0
$501$	−507.735	−	507.735i	−1.01344	−	1.01344i
$502$		0			0
$503$	78.7359			0.156533			0.0782663	−	0.996932i	$-0.475062\pi$
$503$	78.7359			0.156533			0.0782663	+	0.996932i	$0.475062\pi$
$504$		0			0
$505$			6.31543i			0.0125058i
$506$		0			0
$507$	−245.098	+	245.098i	−0.483428	+	0.483428i
$508$		0			0
$509$	242.477	−	242.477i	0.476378	−	0.476378i	−0.427593	−	0.903971i	$-0.640638\pi$
$509$	242.477	−	242.477i	0.476378	−	0.476378i	0.903971	+	0.427593i	$0.140638\pi$
$510$		0			0
$511$			44.8014i			0.0876740i
$512$		0			0
$513$	53.2895			0.103878
$514$		0			0
$515$	9.27484	+	9.27484i	0.0180094	+	0.0180094i
$516$		0			0
$517$	−427.980	−	427.980i	−0.827815	−	0.827815i
$518$		0			0
$519$	1235.34			2.38024
$520$		0			0
$521$			561.306i			1.07736i	0.842510	+	0.538681i	$0.181077\pi$
$521$			561.306i			1.07736i	−0.842510	+	0.538681i	$0.818923\pi$
$522$		0			0
$523$	396.152	−	396.152i	0.757460	−	0.757460i	−0.218399	−	0.975859i	$-0.570084\pi$
$523$	396.152	−	396.152i	0.757460	−	0.757460i	0.975859	+	0.218399i	$0.0700836\pi$
$524$		0			0
$525$	374.811	−	374.811i	0.713926	−	0.713926i
$526$		0			0
$527$			260.607i			0.494510i
$528$		0			0
$529$	−260.662			−0.492745
$530$		0			0
$531$	393.897	+	393.897i	0.741803	+	0.741803i
$532$		0			0
$533$	−36.4424	−	36.4424i	−0.0683722	−	0.0683722i
$534$		0			0
$535$	−6.75465			−0.0126255
$536$		0			0
$537$		−	352.694i		−	0.656785i
$538$		0			0
$539$	148.632	−	148.632i	0.275755	−	0.275755i
$540$		0			0
$541$	22.5728	−	22.5728i	0.0417242	−	0.0417242i	−0.685937	−	0.727661i	$-0.740607\pi$
$541$	22.5728	−	22.5728i	0.0417242	−	0.0417242i	0.727661	+	0.685937i	$0.240607\pi$
$542$		0			0
$543$			128.239i			0.236168i
$544$		0			0
$545$	−6.67005			−0.0122386
$546$		0			0
$547$	601.634	+	601.634i	1.09988	+	1.09988i	0.994424	+	0.105456i	$0.0336302\pi$
$547$	601.634	+	601.634i	1.09988	+	1.09988i	0.105456	+	0.994424i	$0.466370\pi$
$548$		0			0
$549$	−185.217	−	185.217i	−0.337372	−	0.337372i
$550$		0			0
$551$	137.219			0.249037
$552$		0			0
$553$			389.681i			0.704666i
$554$		0			0
$555$	−15.7294	+	15.7294i	−0.0283412	+	0.0283412i
$556$		0			0
$557$	−502.883	+	502.883i	−0.902841	+	0.902841i	−0.995681	−	0.0928399i	$-0.970406\pi$
$557$	−502.883	+	502.883i	−0.902841	+	0.902841i	0.0928399	+	0.995681i	$0.470406\pi$
$558$		0			0
$559$		−	17.3998i		−	0.0311266i
$560$		0			0
$561$	−449.132			−0.800592
$562$		0			0
$563$	655.972	+	655.972i	1.16514	+	1.16514i	0.983335	+	0.181802i	$0.0581929\pi$
$563$	655.972	+	655.972i	1.16514	+	1.16514i	0.181802	+	0.983335i	$0.441807\pi$
$564$		0			0
$565$	7.95834	+	7.95834i	0.0140856	+	0.0140856i
$566$		0			0
$567$	−199.759			−0.352309
$568$		0			0
$569$		−	649.911i		−	1.14220i	−0.820881	−	0.571099i	$-0.806517\pi$
$569$		−	649.911i		−	1.14220i	0.820881	−	0.571099i	$-0.193483\pi$
$570$		0			0
$571$	269.718	−	269.718i	0.472360	−	0.472360i	−0.430317	−	0.902678i	$-0.641598\pi$
$571$	269.718	−	269.718i	0.472360	−	0.472360i	0.902678	+	0.430317i	$0.141598\pi$
$572$		0			0
$573$	541.152	−	541.152i	0.944419	−	0.944419i
$574$		0			0
$575$			409.413i			0.712022i
$576$		0			0
$577$	−142.675			−0.247271			−0.123635	−	0.992328i	$-0.539455\pi$
$577$	−142.675			−0.247271			−0.123635	+	0.992328i	$0.539455\pi$
$578$		0			0
$579$	−7.09149	−	7.09149i	−0.0122478	−	0.0122478i
$580$		0			0
$581$	−123.502	−	123.502i	−0.212567	−	0.212567i
$582$		0			0
$583$	11.3990			0.0195523
$584$		0			0
$585$		−	15.7044i		−	0.0268451i
$586$		0			0
$587$	−687.876	+	687.876i	−1.17185	+	1.17185i	−0.190082	+	0.981768i	$0.560875\pi$
$587$	−687.876	+	687.876i	−1.17185	+	1.17185i	−0.981768	+	0.190082i	$0.939125\pi$
$588$		0			0
$589$	53.2895	−	53.2895i	0.0904746	−	0.0904746i
$590$		0			0
$591$			438.186i			0.741431i
$592$		0			0
$593$	−58.8678			−0.0992711			−0.0496355	−	0.998767i	$-0.515806\pi$
$593$	−58.8678			−0.0992711			−0.0496355	+	0.998767i	$0.515806\pi$
$594$		0			0
$595$	3.48545	+	3.48545i	0.00585790	+	0.00585790i
$596$		0			0
$597$	724.252	+	724.252i	1.21315	+	1.21315i
$598$		0			0
$599$	670.449			1.11928			0.559641	−	0.828735i	$-0.310939\pi$
$599$	670.449			1.11928			0.559641	+	0.828735i	$0.310939\pi$
$600$		0			0
$601$		−	910.721i		−	1.51534i	−0.652636	−	0.757671i	$-0.726337\pi$
$601$		−	910.721i		−	1.51534i	0.652636	−	0.757671i	$-0.273663\pi$
$602$		0			0
$603$	727.594	−	727.594i	1.20662	−	1.20662i
$604$		0			0
$605$	−3.71754	+	3.71754i	−0.00614469	+	0.00614469i
$606$		0			0
$607$		−	761.794i		−	1.25501i	−0.778611	−	0.627507i	$-0.784075\pi$
$607$		−	761.794i		−	1.25501i	0.778611	−	0.627507i	$-0.215925\pi$
$608$		0			0
$609$	781.374			1.28304
$610$		0			0
$611$	−881.671	−	881.671i	−1.44300	−	1.44300i
$612$		0			0
$613$	−273.397	−	273.397i	−0.445999	−	0.445999i	0.448023	−	0.894022i	$-0.352128\pi$
$613$	−273.397	−	273.397i	−0.445999	−	0.445999i	−0.894022	+	0.448023i	$0.852128\pi$
$614$		0			0
$615$	1.25598			0.00204224
$616$		0			0
$617$		−	1088.68i		−	1.76448i	−0.470804	−	0.882238i	$-0.656036\pi$
$617$		−	1088.68i		−	1.76448i	0.470804	−	0.882238i	$-0.343964\pi$
$618$		0			0
$619$	−129.299	+	129.299i	−0.208884	+	0.208884i	−0.803793	−	0.594909i	$-0.797188\pi$
$619$	−129.299	+	129.299i	−0.208884	+	0.208884i	0.594909	+	0.803793i	$0.297188\pi$
$620$		0			0
$621$	−165.731	+	165.731i	−0.266878	+	0.266878i
$622$		0			0
$623$		−	533.351i		−	0.856102i
$624$		0			0
$625$	−624.484			−0.999175
$626$		0			0
$627$	91.8398	+	91.8398i	0.146475	+	0.146475i
$628$		0			0
$629$	531.694	+	531.694i	0.845301	+	0.845301i
$630$		0			0
$631$	−455.029			−0.721123			−0.360562	−	0.932735i	$-0.617415\pi$
$631$	−455.029			−0.721123			−0.360562	+	0.932735i	$0.617415\pi$
$632$		0			0
$633$			956.012i			1.51029i
$634$		0			0
$635$	9.76549	−	9.76549i	0.0153787	−	0.0153787i
$636$		0			0
$637$	306.193	−	306.193i	0.480679	−	0.480679i
$638$		0			0
$639$		−	682.657i		−	1.06832i
$640$		0			0
$641$	798.626			1.24591			0.622953	−	0.782259i	$-0.285933\pi$
$641$	798.626			1.24591			0.622953	+	0.782259i	$0.285933\pi$
$642$		0			0
$643$	−305.718	−	305.718i	−0.475455	−	0.475455i	0.428219	−	0.903675i	$-0.359141\pi$
$643$	−305.718	−	305.718i	−0.475455	−	0.475455i	−0.903675	+	0.428219i	$0.859141\pi$
$644$		0			0
$645$	0.299840	+	0.299840i	0.000464868	+	0.000464868i
$646$		0			0
$647$	−1161.90			−1.79583			−0.897916	−	0.440167i	$-0.854919\pi$
$647$	−1161.90			−1.79583			−0.897916	+	0.440167i	$0.854919\pi$
$648$		0			0
$649$			348.992i			0.537738i
$650$		0			0
$651$	303.448	−	303.448i	0.466127	−	0.466127i
$652$		0			0
$653$	−77.5410	+	77.5410i	−0.118746	+	0.118746i	−0.763983	−	0.645237i	$-0.776759\pi$
$653$	−77.5410	+	77.5410i	−0.118746	+	0.118746i	0.645237	+	0.763983i	$0.276759\pi$
$654$		0			0
$655$			2.60973i			0.00398431i
$656$		0			0
$657$	117.584			0.178972
$658$		0			0
$659$	836.993	+	836.993i	1.27010	+	1.27010i	0.946037	+	0.324059i	$0.105048\pi$
$659$	836.993	+	836.993i	1.27010	+	1.27010i	0.324059	+	0.946037i	$0.394952\pi$
$660$		0			0
$661$	−121.071	−	121.071i	−0.183164	−	0.183164i	0.609569	−	0.792733i	$-0.291342\pi$
$661$	−121.071	−	121.071i	−0.183164	−	0.183164i	−0.792733	+	0.609569i	$0.791342\pi$
$662$		0			0
$663$	−925.246			−1.39554
$664$		0			0
$665$		−	1.42543i		−	0.00214350i
$666$		0			0
$667$	−426.754	+	426.754i	−0.639811	+	0.639811i
$668$		0			0
$669$	197.235	−	197.235i	0.294820	−	0.294820i
$670$		0			0
$671$		−	164.102i		−	0.244563i
$672$		0			0
$673$	−954.371			−1.41808			−0.709042	−	0.705166i	$-0.750872\pi$
$673$	−954.371			−1.41808			−0.709042	+	0.705166i	$0.750872\pi$
$674$		0			0
$675$	−252.862	−	252.862i	−0.374611	−	0.374611i
$676$		0			0
$677$	−245.475	−	245.475i	−0.362593	−	0.362593i	0.502174	−	0.864767i	$-0.332534\pi$
$677$	−245.475	−	245.475i	−0.362593	−	0.362593i	−0.864767	+	0.502174i	$0.832534\pi$
$678$		0			0
$679$	675.002			0.994112
$680$		0			0
$681$			1465.53i			2.15203i
$682$		0			0
$683$	−911.271	+	911.271i	−1.33422	+	1.33422i	−0.432663	+	0.901556i	$0.642426\pi$
$683$	−911.271	+	911.271i	−1.33422	+	1.33422i	−0.901556	+	0.432663i	$0.857574\pi$
$684$		0			0
$685$	10.2544	−	10.2544i	0.0149699	−	0.0149699i
$686$		0			0
$687$			1480.28i			2.15471i
$688$		0			0
$689$	23.4828			0.0340824
$690$		0			0
$691$	−476.155	−	476.155i	−0.689081	−	0.689081i	0.272947	−	0.962029i	$-0.412001\pi$
$691$	−476.155	−	476.155i	−0.689081	−	0.689081i	−0.962029	+	0.272947i	$0.912001\pi$
$692$		0			0
$693$	300.046	+	300.046i	0.432967	+	0.432967i
$694$		0			0
$695$	11.7136			0.0168541
$696$		0			0
$697$		−	42.4553i		−	0.0609115i
$698$		0			0
$699$	393.317	−	393.317i	0.562686	−	0.562686i
$700$		0			0
$701$	−934.966	+	934.966i	−1.33376	+	1.33376i	−0.431782	+	0.901978i	$0.642115\pi$
$701$	−934.966	+	934.966i	−1.33376	+	1.33376i	−0.901978	+	0.431782i	$0.857885\pi$
$702$		0			0
$703$		−	217.444i		−	0.309309i
$704$		0			0
$705$	30.3866			0.0431015
$706$		0			0
$707$	−248.572	−	248.572i	−0.351587	−	0.351587i
$708$		0			0
$709$	−5.89548	−	5.89548i	−0.00831520	−	0.00831520i	0.702937	−	0.711252i	$-0.251872\pi$
$709$	−5.89548	−	5.89548i	−0.00831520	−	0.00831520i	−0.711252	+	0.702937i	$0.751872\pi$
$710$		0			0
$711$	1022.74			1.43846
$712$		0			0
$713$			331.462i			0.464884i
$714$		0			0
$715$	6.95702	−	6.95702i	0.00973010	−	0.00973010i
$716$		0			0
$717$	−719.338	+	719.338i	−1.00326	+	1.00326i
$718$		0			0
$719$		−	19.5965i		−	0.0272552i	−0.999907	−	0.0136276i	$-0.995662\pi$
$719$		−	19.5965i		−	0.0272552i	0.999907	−	0.0136276i	$-0.00433793\pi$
$720$		0			0
$721$	−730.107			−1.01263
$722$		0			0
$723$	−273.794	−	273.794i	−0.378692	−	0.378692i
$724$		0			0
$725$	−651.115	−	651.115i	−0.898089	−	0.898089i
$726$		0			0
$727$	−741.995			−1.02063			−0.510313	−	0.859989i	$-0.670470\pi$
$727$	−741.995			−1.02063			−0.510313	+	0.859989i	$0.670470\pi$
$728$		0			0
$729$			1115.99i			1.53084i
$730$		0			0
$731$	10.1354	−	10.1354i	0.0138651	−	0.0138651i
$732$		0			0
$733$	−349.267	+	349.267i	−0.476490	+	0.476490i	−0.904007	−	0.427517i	$-0.859388\pi$
$733$	−349.267	+	349.267i	−0.476490	+	0.476490i	0.427517	+	0.904007i	$0.359388\pi$
$734$		0			0
$735$			10.5529i			0.0143576i
$736$		0			0
$737$	644.646			0.874690
$738$		0			0
$739$	−358.932	−	358.932i	−0.485700	−	0.485700i	0.421246	−	0.906946i	$-0.361593\pi$
$739$	−358.932	−	358.932i	−0.485700	−	0.485700i	−0.906946	+	0.421246i	$0.861593\pi$
$740$		0			0
$741$	189.197	+	189.197i	0.255326	+	0.255326i
$742$		0			0
$743$	856.214			1.15237			0.576187	−	0.817318i	$-0.304540\pi$
$743$	856.214			1.15237			0.576187	+	0.817318i	$0.304540\pi$
$744$		0			0
$745$			8.78160i			0.0117874i
$746$		0			0
$747$	−324.139	+	324.139i	−0.433921	+	0.433921i
$748$		0			0
$749$	265.860	−	265.860i	0.354953	−	0.354953i
$750$		0			0
$751$			442.218i			0.588839i	0.955676	+	0.294420i	$0.0951264\pi$
$751$			442.218i			0.588839i	−0.955676	+	0.294420i	$0.904874\pi$
$752$		0			0
$753$	1147.69			1.52416
$754$		0			0
$755$	−4.10641	−	4.10641i	−0.00543896	−	0.00543896i
$756$		0			0
$757$	−489.198	−	489.198i	−0.646233	−	0.646233i	0.305848	−	0.952080i	$-0.401060\pi$
$757$	−489.198	−	489.198i	−0.646233	−	0.646233i	−0.952080	+	0.305848i	$0.901060\pi$
$758$		0			0
$759$	−571.246			−0.752629
$760$		0			0
$761$		−	404.015i		−	0.530899i	−0.964125	−	0.265450i	$-0.914480\pi$
$761$		−	404.015i		−	0.530899i	0.964125	−	0.265450i	$-0.0855204\pi$
$762$		0			0
$763$	262.530	−	262.530i	0.344076	−	0.344076i
$764$		0			0
$765$	9.14780	−	9.14780i	0.0119579	−	0.0119579i
$766$		0			0
$767$			718.949i			0.937352i
$768$		0			0
$769$	−387.336			−0.503688			−0.251844	−	0.967768i	$-0.581037\pi$
$769$	−387.336			−0.503688			−0.251844	+	0.967768i	$0.581037\pi$
$770$		0			0
$771$	529.612	+	529.612i	0.686916	+	0.686916i
$772$		0			0
$773$	960.396	+	960.396i	1.24243	+	1.24243i	0.958991	+	0.283436i	$0.0914745\pi$
$773$	960.396	+	960.396i	1.24243	+	1.24243i	0.283436	+	0.958991i	$0.408526\pi$
$774$		0			0
$775$	−505.724			−0.652547
$776$		0			0
$777$		−	1238.20i		−	1.59357i
$778$		0			0
$779$	−8.68138	+	8.68138i	−0.0111443	+	0.0111443i
$780$		0			0
$781$	302.416	−	302.416i	0.387216	−	0.387216i
$782$		0			0
$783$		−	527.145i		−	0.673238i
$784$		0			0
$785$	3.46296			0.00441141
$786$		0			0
$787$	−298.374	−	298.374i	−0.379129	−	0.379129i	0.491659	−	0.870788i	$-0.336391\pi$
$787$	−298.374	−	298.374i	−0.379129	−	0.379129i	−0.870788	+	0.491659i	$0.836391\pi$
$788$		0			0
$789$	568.604	+	568.604i	0.720664	+	0.720664i
$790$		0			0
$791$	−626.473			−0.792002
$792$		0			0
$793$		−	338.062i		−	0.426308i
$794$		0			0
$795$	−0.404665	+	0.404665i	−0.000509012	+	0.000509012i
$796$		0			0
$797$	870.093	−	870.093i	1.09171	−	1.09171i	0.0963642	−	0.995346i	$-0.469279\pi$
$797$	870.093	−	870.093i	1.09171	−	1.09171i	0.995346	−	0.0963642i	$-0.0307214\pi$
$798$		0			0
$799$		−	1027.15i		−	1.28554i
$800$		0			0
$801$	−1399.82			−1.74759
$802$		0			0
$803$	52.0897	+	52.0897i	0.0648689	+	0.0648689i
$804$		0			0
$805$	4.43310	+	4.43310i	0.00550695	+	0.00550695i
$806$		0			0
$807$	193.317			0.239550
$808$		0			0
$809$			107.642i			0.133055i	0.997785	+	0.0665277i	$0.0211921\pi$
$809$			107.642i			0.133055i	−0.997785	+	0.0665277i	$0.978808\pi$
$810$		0			0
$811$	829.739	−	829.739i	1.02311	−	1.02311i	0.0233795	−	0.999727i	$-0.492557\pi$
$811$	829.739	−	829.739i	1.02311	−	1.02311i	0.999727	−	0.0233795i	$-0.00744260\pi$
$812$		0			0
$813$	896.408	−	896.408i	1.10259	−	1.10259i
$814$		0			0
$815$			5.60521i			0.00687756i
$816$		0			0
$817$	−4.14502			−0.00507346
$818$		0			0
$819$	618.118	+	618.118i	0.754722	+	0.754722i
$820$		0			0
$821$	−506.899	−	506.899i	−0.617416	−	0.617416i	0.327452	−	0.944868i	$-0.393810\pi$
$821$	−506.899	−	506.899i	−0.617416	−	0.617416i	−0.944868	+	0.327452i	$0.893810\pi$
$822$		0			0
$823$	927.304			1.12674			0.563368	−	0.826206i	$-0.309505\pi$
$823$	927.304			1.12674			0.563368	+	0.826206i	$0.309505\pi$
$824$		0			0
$825$		−	871.571i		−	1.05645i
$826$		0			0
$827$	−19.4711	+	19.4711i	−0.0235443	+	0.0235443i	−0.718781	−	0.695237i	$-0.755300\pi$
$827$	−19.4711	+	19.4711i	−0.0235443	+	0.0235443i	0.695237	+	0.718781i	$0.255300\pi$
$828$		0			0
$829$	−409.028	+	409.028i	−0.493400	+	0.493400i	−0.909376	−	0.415976i	$-0.863440\pi$
$829$	−409.028	+	409.028i	−0.493400	+	0.493400i	0.415976	+	0.909376i	$0.363440\pi$
$830$		0			0
$831$		−	1808.71i		−	2.17655i
$832$		0			0
$833$	356.714			0.428228
$834$		0			0
$835$	9.16246	+	9.16246i	0.0109730	+	0.0109730i
$836$		0			0
$837$	−204.718	−	204.718i	−0.244586	−	0.244586i
$838$		0			0
$839$	−634.212			−0.755914			−0.377957	−	0.925823i	$-0.623373\pi$
$839$	−634.212			−0.755914			−0.377957	+	0.925823i	$0.623373\pi$
$840$		0			0
$841$		−	516.388i		−	0.614017i
$842$		0			0
$843$	−657.483	+	657.483i	−0.779933	+	0.779933i
$844$		0			0
$845$	4.42297	−	4.42297i	0.00523429	−	0.00523429i
$846$		0			0
$847$		−	292.641i		−	0.345503i
$848$		0			0
$849$	1899.16			2.23694
$850$		0			0
$851$	676.255	+	676.255i	0.794659	+	0.794659i
$852$		0			0
$853$	−687.203	−	687.203i	−0.805630	−	0.805630i	0.178339	−	0.983969i	$-0.442928\pi$
$853$	−687.203	−	687.203i	−0.805630	−	0.805630i	−0.983969	+	0.178339i	$0.942928\pi$
$854$		0			0
$855$	−3.74114			−0.00437560
$856$		0			0
$857$			995.675i			1.16181i	0.813970	+	0.580907i	$0.197302\pi$
$857$			995.675i			1.16181i	−0.813970	+	0.580907i	$0.802698\pi$
$858$		0			0
$859$	430.241	−	430.241i	0.500863	−	0.500863i	−0.410843	−	0.911706i	$-0.634766\pi$
$859$	430.241	−	430.241i	0.500863	−	0.500863i	0.911706	+	0.410843i	$0.134766\pi$
$860$		0			0
$861$	−49.4347	+	49.4347i	−0.0574154	+	0.0574154i
$862$		0			0
$863$			1014.03i			1.17501i	0.809222	+	0.587503i	$0.199889\pi$
$863$			1014.03i			1.17501i	−0.809222	+	0.587503i	$0.800111\pi$
$864$		0			0
$865$	−22.2927			−0.0257719
$866$		0			0
$867$	400.046	+	400.046i	0.461414	+	0.461414i
$868$		0			0
$869$	453.074	+	453.074i	0.521374	+	0.521374i
$870$		0			0
$871$	1328.02			1.52471
$872$		0			0
$873$		−	1771.59i		−	2.02931i
$874$		0			0
$875$	−13.5293	+	13.5293i	−0.0154621	+	0.0154621i
$876$		0			0
$877$	544.315	−	544.315i	0.620656	−	0.620656i	−0.325043	−	0.945699i	$-0.605379\pi$
$877$	544.315	−	544.315i	0.620656	−	0.620656i	0.945699	+	0.325043i	$0.105379\pi$
$878$		0			0
$879$			2152.03i			2.44828i
$880$		0			0
$881$	−645.905			−0.733150			−0.366575	−	0.930388i	$-0.619470\pi$
$881$	−645.905			−0.733150			−0.366575	+	0.930388i	$0.619470\pi$
$882$		0			0
$883$	586.952	+	586.952i	0.664725	+	0.664725i	0.956490	−	0.291765i	$-0.0942425\pi$
$883$	586.952	+	586.952i	0.664725	+	0.664725i	−0.291765	+	0.956490i	$0.594243\pi$
$884$		0			0
$885$	−12.3892	−	12.3892i	−0.0139991	−	0.0139991i
$886$		0			0
$887$	1221.93			1.37759			0.688797	−	0.724955i	$-0.258139\pi$
$887$	1221.93			1.37759			0.688797	+	0.724955i	$0.258139\pi$
$888$		0			0
$889$			768.730i			0.864713i
$890$		0			0
$891$	−232.256	+	232.256i	−0.260669	+	0.260669i
$892$		0			0
$893$	−210.034	+	210.034i	−0.235200	+	0.235200i
$894$		0			0
$895$			6.36462i			0.00711131i
$896$		0			0
$897$	−1176.81			−1.31194
$898$		0			0
$899$	−527.145	−	527.145i	−0.586368	−	0.586368i
$900$		0			0
$901$	13.6787	+	13.6787i	0.0151817	+	0.0151817i
$902$		0			0
$903$	−23.6031			−0.0261386
$904$		0			0
$905$		−	2.31417i		−	0.00255710i
$906$		0			0
$907$	310.014	−	310.014i	0.341801	−	0.341801i	−0.515243	−	0.857044i	$-0.672298\pi$
$907$	310.014	−	310.014i	0.341801	−	0.341801i	0.857044	+	0.515243i	$0.172298\pi$
$908$		0			0
$909$	−652.395	+	652.395i	−0.717707	+	0.717707i
$910$		0			0
$911$		−	1044.12i		−	1.14612i	−0.819513	−	0.573060i	$-0.805756\pi$
$911$		−	1044.12i		−	1.14612i	0.819513	−	0.573060i	$-0.194244\pi$
$912$		0			0
$913$	−287.186			−0.314552
$914$		0			0
$915$	5.82561	+	5.82561i	0.00636679	+	0.00636679i
$916$		0			0
$917$	−102.718	−	102.718i	−0.112015	−	0.112015i
$918$		0			0
$919$	−188.522			−0.205138			−0.102569	−	0.994726i	$-0.532706\pi$
$919$	−188.522			−0.205138			−0.102569	+	0.994726i	$0.532706\pi$
$920$		0			0
$921$		−	154.342i		−	0.167581i
$922$		0			0
$923$	622.999	−	622.999i	0.674972	−	0.674972i
$924$		0			0
$925$	−1031.79	+	1031.79i	−1.11545	+	1.11545i
$926$		0			0
$927$			1916.22i			2.06712i
$928$		0			0
$929$	−220.366			−0.237208			−0.118604	−	0.992942i	$-0.537842\pi$
$929$	−220.366			−0.237208			−0.118604	+	0.992942i	$0.537842\pi$
$930$		0			0
$931$	−72.9419	−	72.9419i	−0.0783479	−	0.0783479i
$932$		0			0
$933$	−512.576	−	512.576i	−0.549384	−	0.549384i
$934$		0			0
$935$	8.10493			0.00866837
$936$		0			0
$937$			558.321i			0.595860i	0.954588	+	0.297930i	$0.0962962\pi$
$937$			558.321i			0.595860i	−0.954588	+	0.297930i	$0.903704\pi$
$938$		0			0
$939$	−190.379	+	190.379i	−0.202746	+	0.202746i
$940$		0			0
$941$	794.760	−	794.760i	0.844591	−	0.844591i	−0.144861	−	0.989452i	$-0.546274\pi$
$941$	794.760	−	794.760i	0.844591	−	0.844591i	0.989452	+	0.144861i	$0.0462736\pi$
$942$		0			0
$943$		−	53.9984i		−	0.0572624i
$944$		0			0
$945$	−5.47595			−0.00579466
$946$		0			0
$947$	−44.9362	−	44.9362i	−0.0474511	−	0.0474511i	0.682983	−	0.730434i	$-0.260682\pi$
$947$	−44.9362	−	44.9362i	−0.0474511	−	0.0474511i	−0.730434	+	0.682983i	$0.760682\pi$
$948$		0			0
$949$	107.309	+	107.309i	0.113076	+	0.113076i
$950$		0			0
$951$	175.480			0.184521
$952$		0			0
$953$			304.232i			0.319236i	0.987179	+	0.159618i	$0.0510262\pi$
$953$			304.232i			0.319236i	−0.987179	+	0.159618i	$0.948974\pi$
$954$		0			0
$955$	−9.76549	+	9.76549i	−0.0102256	+	0.0102256i
$956$		0			0
$957$	908.488	−	908.488i	0.949308	−	0.949308i
$958$		0			0
$959$			807.213i			0.841724i
$960$		0			0
$961$	551.564			0.573948
$962$		0			0
$963$	−697.768	−	697.768i	−0.724577	−	0.724577i
$964$		0			0
$965$	0.127971	+	0.127971i	0.000132613	+	0.000132613i
$966$		0			0
$967$	−834.409			−0.862884			−0.431442	−	0.902141i	$-0.641995\pi$
$967$	−834.409			−0.862884			−0.431442	+	0.902141i	$0.641995\pi$
$968$		0			0
$969$			220.414i			0.227465i
$970$		0			0
$971$	211.499	−	211.499i	0.217816	−	0.217816i	−0.589761	−	0.807577i	$-0.700778\pi$
$971$	211.499	−	211.499i	0.217816	−	0.217816i	0.807577	+	0.589761i	$0.200778\pi$
$972$		0			0
$973$	−461.043	+	461.043i	−0.473837	+	0.473837i
$974$		0			0
$975$		−	1795.50i		−	1.84154i
$976$		0			0
$977$	891.561			0.912549			0.456275	−	0.889839i	$-0.349183\pi$
$977$	891.561			0.912549			0.456275	+	0.889839i	$0.349183\pi$
$978$		0			0
$979$	−620.117	−	620.117i	−0.633419	−	0.633419i
$980$		0			0
$981$	−689.028	−	689.028i	−0.702374	−	0.702374i
$982$		0			0
$983$	181.589			0.184730			0.0923648	−	0.995725i	$-0.470557\pi$
$983$	181.589			0.184730			0.0923648	+	0.995725i	$0.470557\pi$
$984$		0			0
$985$		−	7.90739i		−	0.00802781i
$986$		0			0
$987$	−1196.00	+	1196.00i	−1.21175	+	1.21175i
$988$		0			0
$989$	12.8911	−	12.8911i	0.0130344	−	0.0130344i
$990$		0			0
$991$		−	1140.89i		−	1.15125i	−0.817715	−	0.575624i	$-0.804759\pi$
$991$		−	1140.89i		−	1.15125i	0.817715	−	0.575624i	$-0.195241\pi$
$992$		0			0
$993$	1183.95			1.19230
$994$		0			0
$995$	−13.0697	−	13.0697i	−0.0131354	−	0.0131354i
$996$		0			0
$997$	742.946	+	742.946i	0.745182	+	0.745182i	0.973570	−	0.228388i	$-0.0733455\pi$
$997$	742.946	+	742.946i	0.745182	+	0.745182i	−0.228388	+	0.973570i	$0.573346\pi$
$998$		0			0
$999$	−835.339			−0.836175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.f.a.31.1		6
3.2	odd	2		1152.3.m.b.415.2		6
4.3	odd	2		128.3.f.b.31.3		6
8.3	odd	2		16.3.f.a.11.3	yes	6
8.5	even	2		64.3.f.a.15.3		6
12.11	even	2		1152.3.m.a.415.2		6
16.3	odd	4	inner	128.3.f.a.95.1		6
16.5	even	4		16.3.f.a.3.3	✓	6
16.11	odd	4		64.3.f.a.47.3		6
16.13	even	4		128.3.f.b.95.3		6
24.5	odd	2		576.3.m.a.271.2		6
24.11	even	2		144.3.m.a.91.1		6
32.3	odd	8		1024.3.c.j.1023.11		12
32.5	even	8		1024.3.d.k.511.12		12
32.11	odd	8		1024.3.d.k.511.11		12
32.13	even	8		1024.3.c.j.1023.12		12
32.19	odd	8		1024.3.c.j.1023.2		12
32.21	even	8		1024.3.d.k.511.1		12
32.27	odd	8		1024.3.d.k.511.2		12
32.29	even	8		1024.3.c.j.1023.1		12
40.3	even	4		400.3.k.d.299.3		6
40.19	odd	2		400.3.r.c.251.1		6
40.27	even	4		400.3.k.c.299.1		6
48.5	odd	4		144.3.m.a.19.1		6
48.11	even	4		576.3.m.a.559.2		6
48.29	odd	4		1152.3.m.a.991.2		6
48.35	even	4		1152.3.m.b.991.2		6
80.37	odd	4		400.3.k.d.99.3		6
80.53	odd	4		400.3.k.c.99.1		6
80.69	even	4		400.3.r.c.51.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.3	✓	6	16.5	even	4
16.3.f.a.11.3	yes	6	8.3	odd	2
64.3.f.a.15.3		6	8.5	even	2
64.3.f.a.47.3		6	16.11	odd	4
128.3.f.a.31.1		6	1.1	even	1	trivial
128.3.f.a.95.1		6	16.3	odd	4	inner
128.3.f.b.31.3		6	4.3	odd	2
128.3.f.b.95.3		6	16.13	even	4
144.3.m.a.19.1		6	48.5	odd	4
144.3.m.a.91.1		6	24.11	even	2
400.3.k.c.99.1		6	80.53	odd	4
400.3.k.c.299.1		6	40.27	even	4
400.3.k.d.99.3		6	80.37	odd	4
400.3.k.d.299.3		6	40.3	even	4
400.3.r.c.51.1		6	80.69	even	4
400.3.r.c.251.1		6	40.19	odd	2
576.3.m.a.271.2		6	24.5	odd	2
576.3.m.a.559.2		6	48.11	even	4
1024.3.c.j.1023.1		12	32.29	even	8
1024.3.c.j.1023.2		12	32.19	odd	8
1024.3.c.j.1023.11		12	32.3	odd	8
1024.3.c.j.1023.12		12	32.13	even	8
1024.3.d.k.511.1		12	32.21	even	8
1024.3.d.k.511.2		12	32.27	odd	8
1024.3.d.k.511.11		12	32.11	odd	8
1024.3.d.k.511.12		12	32.5	even	8
1152.3.m.a.415.2		6	12.11	even	2
1152.3.m.a.991.2		6	48.29	odd	4
1152.3.m.b.415.2		6	3.2	odd	2
1152.3.m.b.991.2		6	48.35	even	4

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.24914 - 3.24914i) q^{3} +(0.0586332 + 0.0586332i) q^{5} -4.61555 q^{7} +12.1138i q^{9} +O(q^{10})\)	\(q+(-3.24914 - 3.24914i) q^{3} +(0.0586332 + 0.0586332i) q^{5} -4.61555 q^{7} +12.1138i q^{9} +(-5.36641 + 5.36641i) q^{11} +(-11.0552 + 11.0552i) q^{13} -0.381015i q^{15} -12.8793 q^{17} +(2.63359 + 2.63359i) q^{19} +(14.9966 + 14.9966i) q^{21} -16.3810 q^{23} -24.9931i q^{25} +(10.1173 - 10.1173i) q^{27} +(26.0518 - 26.0518i) q^{29} -20.2345i q^{31} +34.8724 q^{33} +(-0.270624 - 0.270624i) q^{35} +(-41.2829 - 41.2829i) q^{37} +71.8398 q^{39} +3.29640i q^{41} +(-0.786951 + 0.786951i) q^{43} +(-0.710272 + 0.710272i) q^{45} +79.7517i q^{47} -27.6967 q^{49} +(41.8466 + 41.8466i) q^{51} +(-1.06207 - 1.06207i) q^{53} -0.629299 q^{55} -17.1138i q^{57} +(32.5163 - 32.5163i) q^{59} +(-15.2897 + 15.2897i) q^{61} -55.9119i q^{63} -1.29640 q^{65} +(-60.0631 - 60.0631i) q^{67} +(53.2242 + 53.2242i) q^{69} -56.3535 q^{71} -9.70663i q^{73} +(-81.2062 + 81.2062i) q^{75} +(24.7689 - 24.7689i) q^{77} -84.4278i q^{79} +43.2796 q^{81} +(26.7577 + 26.7577i) q^{83} +(-0.755154 - 0.755154i) q^{85} -169.292 q^{87} +115.555i q^{89} +(51.0258 - 51.0258i) q^{91} +(-65.7448 + 65.7448i) q^{93} +0.308832i q^{95} -146.245 q^{97} +(-65.0077 - 65.0077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 6 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	\( 6 q - 2 q^{3} + 2 q^{5} + 4 q^{7} - 18 q^{11} + 2 q^{13} - 4 q^{17} + 30 q^{19} + 20 q^{21} - 60 q^{23} + 64 q^{27} + 18 q^{29} - 4 q^{33} - 100 q^{35} - 46 q^{37} + 196 q^{39} - 114 q^{43} - 66 q^{45} - 46 q^{49} + 156 q^{51} - 78 q^{53} - 252 q^{55} + 206 q^{59} - 30 q^{61} + 12 q^{65} - 226 q^{67} + 116 q^{69} + 260 q^{71} - 238 q^{75} + 212 q^{77} + 86 q^{81} + 318 q^{83} + 212 q^{85} - 444 q^{87} + 188 q^{91} + 32 q^{93} - 4 q^{97} - 226 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 - 18 * q^11 + 2 * q^13 - 4 * q^17 + 30 * q^19 + 20 * q^21 - 60 * q^23 + 64 * q^27 + 18 * q^29 - 4 * q^33 - 100 * q^35 - 46 * q^37 + 196 * q^39 - 114 * q^43 - 66 * q^45 - 46 * q^49 + 156 * q^51 - 78 * q^53 - 252 * q^55 + 206 * q^59 - 30 * q^61 + 12 * q^65 - 226 * q^67 + 116 * q^69 + 260 * q^71 - 238 * q^75 + 212 * q^77 + 86 * q^81 + 318 * q^83 + 212 * q^85 - 444 * q^87 + 188 * q^91 + 32 * q^93 - 4 * q^97 - 226 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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