LMFDB - Embedded newform 80.5.p.b.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,5,Mod(17,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("80.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	80.p (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:	$8.26959704671$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	80.33
Dual form			80.5.p.b.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.00000 - 9.00000i) q^{3} +(-15.0000 - 20.0000i) q^{5} +(-29.0000 + 29.0000i) q^{7} +81.0000i q^{9} +118.000 q^{11} +(69.0000 + 69.0000i) q^{13} +(-45.0000 + 315.000i) q^{15} +(-271.000 + 271.000i) q^{17} +280.000i q^{19} +522.000 q^{21} +(-269.000 - 269.000i) q^{23} +(-175.000 + 600.000i) q^{25} -680.000i q^{29} -202.000 q^{31} +(-1062.00 - 1062.00i) q^{33} +(1015.00 + 145.000i) q^{35} +(-651.000 + 651.000i) q^{37} -1242.00i q^{39} +1682.00 q^{41} +(-1089.00 - 1089.00i) q^{43} +(1620.00 - 1215.00i) q^{45} +(-1269.00 + 1269.00i) q^{47} +719.000i q^{49} +4878.00 q^{51} +(-611.000 - 611.000i) q^{53} +(-1770.00 - 2360.00i) q^{55} +(2520.00 - 2520.00i) q^{57} +1160.00i q^{59} -5598.00 q^{61} +(-2349.00 - 2349.00i) q^{63} +(345.000 - 2415.00i) q^{65} +(751.000 - 751.000i) q^{67} +4842.00i q^{69} -6442.00 q^{71} +(-2951.00 - 2951.00i) q^{73} +(6975.00 - 3825.00i) q^{75} +(-3422.00 + 3422.00i) q^{77} +10560.0i q^{79} +6561.00 q^{81} +(6231.00 + 6231.00i) q^{83} +(9485.00 + 1355.00i) q^{85} +(-6120.00 + 6120.00i) q^{87} +14480.0i q^{89} -4002.00 q^{91} +(1818.00 + 1818.00i) q^{93} +(5600.00 - 4200.00i) q^{95} +(-7311.00 + 7311.00i) q^{97} +9558.00i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 18 q^{3} - 30 q^{5} - 58 q^{7} + 236 q^{11} + 138 q^{13} - 90 q^{15} - 542 q^{17} + 1044 q^{21} - 538 q^{23} - 350 q^{25} - 404 q^{31} - 2124 q^{33} + 2030 q^{35} - 1302 q^{37} + 3364 q^{41} - 2178 q^{43}+ \cdots - 14622 q^{97}+O(q^{100}) $ 2 * q - 18 * q^3 - 30 * q^5 - 58 * q^7 + 236 * q^11 + 138 * q^13 - 90 * q^15 - 542 * q^17 + 1044 * q^21 - 538 * q^23 - 350 * q^25 - 404 * q^31 - 2124 * q^33 + 2030 * q^35 - 1302 * q^37 + 3364 * q^41 - 2178 * q^43 + 3240 * q^45 - 2538 * q^47 + 9756 * q^51 - 1222 * q^53 - 3540 * q^55 + 5040 * q^57 - 11196 * q^61 - 4698 * q^63 + 690 * q^65 + 1502 * q^67 - 12884 * q^71 - 5902 * q^73 + 13950 * q^75 - 6844 * q^77 + 13122 * q^81 + 12462 * q^83 + 18970 * q^85 - 12240 * q^87 - 8004 * q^91 + 3636 * q^93 + 11200 * q^95 - 14622 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	−9.00000	−	9.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$3$	−9.00000	−	9.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$4$		0			0
$5$	−15.0000	−	20.0000i	−0.600000	−	0.800000i
$5$	−15.0000	−	20.0000i	−0.600000	−	0.800000i
$6$		0			0
$7$	−29.0000	+	29.0000i	−0.591837	+	0.591837i	−0.938127	−	0.346291i	$-0.887441\pi$
$7$	−29.0000	+	29.0000i	−0.591837	+	0.591837i	0.346291	+	0.938127i	$0.387441\pi$
$8$		0			0
$9$			81.0000i			1.00000i
$10$		0			0
$11$	118.000			0.975207			0.487603	−	0.873065i	$-0.337871\pi$
$11$	118.000			0.975207			0.487603	+	0.873065i	$0.337871\pi$
$12$		0			0
$13$	69.0000	+	69.0000i	0.408284	+	0.408284i	0.881140	−	0.472856i	$-0.156777\pi$
$13$	69.0000	+	69.0000i	0.408284	+	0.408284i	−0.472856	+	0.881140i	$0.656777\pi$
$14$		0			0
$15$	−45.0000	+	315.000i	−0.200000	+	1.40000i
$16$		0			0
$17$	−271.000	+	271.000i	−0.937716	+	0.937716i	−0.998171	−	0.0604547i	$-0.980745\pi$
$17$	−271.000	+	271.000i	−0.937716	+	0.937716i	0.0604547	+	0.998171i	$0.480745\pi$
$18$		0			0
$19$			280.000i			0.775623i	0.921739	+	0.387812i	$0.126769\pi$
$19$			280.000i			0.775623i	−0.921739	+	0.387812i	$0.873231\pi$
$20$		0			0
$21$	522.000			1.18367
$22$		0			0
$23$	−269.000	−	269.000i	−0.508507	−	0.508507i	0.405561	−	0.914068i	$-0.367076\pi$
$23$	−269.000	−	269.000i	−0.508507	−	0.508507i	−0.914068	+	0.405561i	$0.867076\pi$
$24$		0			0
$25$	−175.000	+	600.000i	−0.280000	+	0.960000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	680.000i		−	0.808561i	−0.914635	−	0.404281i	$-0.867522\pi$
$29$		−	680.000i		−	0.808561i	0.914635	−	0.404281i	$-0.132478\pi$
$30$		0			0
$31$	−202.000			−0.210198			−0.105099	−	0.994462i	$-0.533516\pi$
$31$	−202.000			−0.210198			−0.105099	+	0.994462i	$0.533516\pi$
$32$		0			0
$33$	−1062.00	−	1062.00i	−0.975207	−	0.975207i
$34$		0			0
$35$	1015.00	+	145.000i	0.828571	+	0.118367i
$36$		0			0
$37$	−651.000	+	651.000i	−0.475530	+	0.475530i	−0.903699	−	0.428169i	$-0.859159\pi$
$37$	−651.000	+	651.000i	−0.475530	+	0.475530i	0.428169	+	0.903699i	$0.359159\pi$
$38$		0			0
$39$		−	1242.00i		−	0.816568i
$40$		0			0
$41$	1682.00			1.00059			0.500297	−	0.865854i	$-0.333224\pi$
$41$	1682.00			1.00059			0.500297	+	0.865854i	$0.333224\pi$
$42$		0			0
$43$	−1089.00	−	1089.00i	−0.588967	−	0.588967i	0.348385	−	0.937352i	$-0.386730\pi$
$43$	−1089.00	−	1089.00i	−0.588967	−	0.588967i	−0.937352	+	0.348385i	$0.886730\pi$
$44$		0			0
$45$	1620.00	−	1215.00i	0.800000	−	0.600000i
$46$		0			0
$47$	−1269.00	+	1269.00i	−0.574468	+	0.574468i	−0.933374	−	0.358906i	$-0.883150\pi$
$47$	−1269.00	+	1269.00i	−0.574468	+	0.574468i	0.358906	+	0.933374i	$0.383150\pi$
$48$		0			0
$49$			719.000i			0.299459i
$50$		0			0
$51$	4878.00			1.87543
$52$		0			0
$53$	−611.000	−	611.000i	−0.217515	−	0.217515i	0.589935	−	0.807450i	$-0.299153\pi$
$53$	−611.000	−	611.000i	−0.217515	−	0.217515i	−0.807450	+	0.589935i	$0.799153\pi$
$54$		0			0
$55$	−1770.00	−	2360.00i	−0.585124	−	0.780165i
$56$		0			0
$57$	2520.00	−	2520.00i	0.775623	−	0.775623i
$58$		0			0
$59$			1160.00i			0.333238i	0.986021	+	0.166619i	$0.0532849\pi$
$59$			1160.00i			0.333238i	−0.986021	+	0.166619i	$0.946715\pi$
$60$		0			0
$61$	−5598.00			−1.50443			−0.752217	−	0.658915i	$-0.771016\pi$
$61$	−5598.00			−1.50443			−0.752217	+	0.658915i	$0.771016\pi$
$62$		0			0
$63$	−2349.00	−	2349.00i	−0.591837	−	0.591837i
$64$		0			0
$65$	345.000	−	2415.00i	0.0816568	−	0.571598i
$66$		0			0
$67$	751.000	−	751.000i	0.167298	−	0.167298i	−0.618493	−	0.785791i	$-0.712256\pi$
$67$	751.000	−	751.000i	0.167298	−	0.167298i	0.785791	+	0.618493i	$0.212256\pi$
$68$		0			0
$69$			4842.00i			1.01701i
$70$		0			0
$71$	−6442.00			−1.27792			−0.638961	−	0.769240i	$-0.720635\pi$
$71$	−6442.00			−1.27792			−0.638961	+	0.769240i	$0.720635\pi$
$72$		0			0
$73$	−2951.00	−	2951.00i	−0.553762	−	0.553762i	0.373762	−	0.927525i	$-0.378068\pi$
$73$	−2951.00	−	2951.00i	−0.553762	−	0.553762i	−0.927525	+	0.373762i	$0.878068\pi$
$74$		0			0
$75$	6975.00	−	3825.00i	1.24000	−	0.680000i
$76$		0			0
$77$	−3422.00	+	3422.00i	−0.577163	+	0.577163i
$78$		0			0
$79$			10560.0i			1.69204i	0.533154	+	0.846018i	$0.321007\pi$
$79$			10560.0i			1.69204i	−0.533154	+	0.846018i	$0.678993\pi$
$80$		0			0
$81$	6561.00			1.00000
$82$		0			0
$83$	6231.00	+	6231.00i	0.904485	+	0.904485i	0.995820	−	0.0913348i	$-0.0291134\pi$
$83$	6231.00	+	6231.00i	0.904485	+	0.904485i	−0.0913348	+	0.995820i	$0.529113\pi$
$84$		0			0
$85$	9485.00	+	1355.00i	1.31280	+	0.187543i
$86$		0			0
$87$	−6120.00	+	6120.00i	−0.808561	+	0.808561i
$88$		0			0
$89$			14480.0i			1.82805i	0.405656	+	0.914026i	$0.367043\pi$
$89$			14480.0i			1.82805i	−0.405656	+	0.914026i	$0.632957\pi$
$90$		0			0
$91$	−4002.00			−0.483275
$92$		0			0
$93$	1818.00	+	1818.00i	0.210198	+	0.210198i
$94$		0			0
$95$	5600.00	−	4200.00i	0.620499	−	0.465374i
$96$		0			0
$97$	−7311.00	+	7311.00i	−0.777022	+	0.777022i	−0.979323	−	0.202301i	$-0.935158\pi$
$97$	−7311.00	+	7311.00i	−0.777022	+	0.777022i	0.202301	+	0.979323i	$0.435158\pi$
$98$		0			0
$99$			9558.00i			0.975207i
$100$		0			0
$101$	−878.000			−0.0860700			−0.0430350	−	0.999074i	$-0.513703\pi$
$101$	−878.000			−0.0860700			−0.0430350	+	0.999074i	$0.513703\pi$
$102$		0			0
$103$	−10429.0	−	10429.0i	−0.983033	−	0.983033i	0.0168252	−	0.999858i	$-0.494644\pi$
$103$	−10429.0	−	10429.0i	−0.983033	−	0.983033i	−0.999858	+	0.0168252i	$0.994644\pi$
$104$		0			0
$105$	−7830.00	−	10440.0i	−0.710204	−	0.946939i
$106$		0			0
$107$	4711.00	−	4711.00i	0.411477	−	0.411477i	−0.470776	−	0.882253i	$-0.656026\pi$
$107$	4711.00	−	4711.00i	0.411477	−	0.411477i	0.882253	+	0.470776i	$0.156026\pi$
$108$		0			0
$109$		−	22040.0i		−	1.85506i	−0.373745	−	0.927531i	$-0.621927\pi$
$109$		−	22040.0i		−	1.85506i	0.373745	−	0.927531i	$-0.378073\pi$
$110$		0			0
$111$	11718.0			0.951059
$112$		0			0
$113$	−2111.00	−	2111.00i	−0.165322	−	0.165322i	0.619597	−	0.784920i	$-0.287296\pi$
$113$	−2111.00	−	2111.00i	−0.165322	−	0.165322i	−0.784920	+	0.619597i	$0.787296\pi$
$114$		0			0
$115$	−1345.00	+	9415.00i	−0.101701	+	0.711909i
$116$		0			0
$117$	−5589.00	+	5589.00i	−0.408284	+	0.408284i
$118$		0			0
$119$		−	15718.0i		−	1.10995i
$120$		0			0
$121$	−717.000			−0.0489721
$122$		0			0
$123$	−15138.0	−	15138.0i	−1.00059	−	1.00059i
$124$		0			0
$125$	14625.0	−	5500.00i	0.936000	−	0.352000i
$126$		0			0
$127$	−5909.00	+	5909.00i	−0.366359	+	0.366359i	−0.866147	−	0.499789i	$-0.833411\pi$
$127$	−5909.00	+	5909.00i	−0.366359	+	0.366359i	0.499789	+	0.866147i	$0.333411\pi$
$128$		0			0
$129$			19602.0i			1.17793i
$130$		0			0
$131$	6358.00			0.370491			0.185246	−	0.982692i	$-0.440692\pi$
$131$	6358.00			0.370491			0.185246	+	0.982692i	$0.440692\pi$
$132$		0			0
$133$	−8120.00	−	8120.00i	−0.459042	−	0.459042i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	20409.0	−	20409.0i	1.08738	−	1.08738i	0.0915804	−	0.995798i	$-0.470808\pi$
$137$	20409.0	−	20409.0i	1.08738	−	1.08738i	0.995798	−	0.0915804i	$-0.0291919\pi$
$138$		0			0
$139$		−	9400.00i		−	0.486517i	−0.969961	−	0.243259i	$-0.921784\pi$
$139$		−	9400.00i		−	0.486517i	0.969961	−	0.243259i	$-0.0782164\pi$
$140$		0			0
$141$	22842.0			1.14894
$142$		0			0
$143$	8142.00	+	8142.00i	0.398161	+	0.398161i
$144$		0			0
$145$	−13600.0	+	10200.0i	−0.646849	+	0.485137i
$146$		0			0
$147$	6471.00	−	6471.00i	0.299459	−	0.299459i
$148$		0			0
$149$		−	13800.0i		−	0.621594i	−0.950476	−	0.310797i	$-0.899404\pi$
$149$		−	13800.0i		−	0.621594i	0.950476	−	0.310797i	$-0.100596\pi$
$150$		0			0
$151$	18998.0			0.833209			0.416605	−	0.909088i	$-0.363220\pi$
$151$	18998.0			0.833209			0.416605	+	0.909088i	$0.363220\pi$
$152$		0			0
$153$	−21951.0	−	21951.0i	−0.937716	−	0.937716i
$154$		0			0
$155$	3030.00	+	4040.00i	0.126119	+	0.168158i
$156$		0			0
$157$	−16371.0	+	16371.0i	−0.664165	+	0.664165i	−0.956359	−	0.292194i	$-0.905615\pi$
$157$	−16371.0	+	16371.0i	−0.664165	+	0.664165i	0.292194	+	0.956359i	$0.405615\pi$
$158$		0			0
$159$			10998.0i			0.435030i
$160$		0			0
$161$	15602.0			0.601906
$162$		0			0
$163$	−20009.0	−	20009.0i	−0.753096	−	0.753096i	0.221960	−	0.975056i	$-0.428755\pi$
$163$	−20009.0	−	20009.0i	−0.753096	−	0.753096i	−0.975056	+	0.221960i	$0.928755\pi$
$164$		0			0
$165$	−5310.00	+	37170.0i	−0.195041	+	1.36529i
$166$		0			0
$167$	−1549.00	+	1549.00i	−0.0555416	+	0.0555416i	−0.734332	−	0.678790i	$-0.762504\pi$
$167$	−1549.00	+	1549.00i	−0.0555416	+	0.0555416i	0.678790	+	0.734332i	$0.262504\pi$
$168$		0			0
$169$		−	19039.0i		−	0.666608i
$170$		0			0
$171$	−22680.0			−0.775623
$172$		0			0
$173$	2789.00	+	2789.00i	0.0931872	+	0.0931872i	0.752164	−	0.658976i	$-0.229010\pi$
$173$	2789.00	+	2789.00i	0.0931872	+	0.0931872i	−0.658976	+	0.752164i	$0.729010\pi$
$174$		0			0
$175$	−12325.0	−	22475.0i	−0.402449	−	0.733878i
$176$		0			0
$177$	10440.0	−	10440.0i	0.333238	−	0.333238i
$178$		0			0
$179$		−	2600.00i		−	0.0811460i	−0.999177	−	0.0405730i	$-0.987082\pi$
$179$		−	2600.00i		−	0.0811460i	0.999177	−	0.0405730i	$-0.0129183\pi$
$180$		0			0
$181$	−44398.0			−1.35521			−0.677604	−	0.735427i	$-0.736982\pi$
$181$	−44398.0			−1.35521			−0.677604	+	0.735427i	$0.736982\pi$
$182$		0			0
$183$	50382.0	+	50382.0i	1.50443	+	1.50443i
$184$		0			0
$185$	22785.0	+	3255.00i	0.665741	+	0.0951059i
$186$		0			0
$187$	−31978.0	+	31978.0i	−0.914467	+	0.914467i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	14678.0			0.402346			0.201173	−	0.979556i	$-0.435525\pi$
$191$	14678.0			0.402346			0.201173	+	0.979556i	$0.435525\pi$
$192$		0			0
$193$	42849.0	+	42849.0i	1.15034	+	1.15034i	0.986484	+	0.163855i	$0.0523930\pi$
$193$	42849.0	+	42849.0i	1.15034	+	1.15034i	0.163855	+	0.986484i	$0.447607\pi$
$194$		0			0
$195$	−24840.0	+	18630.0i	−0.653254	+	0.489941i
$196$		0			0
$197$	−10971.0	+	10971.0i	−0.282692	+	0.282692i	−0.834182	−	0.551490i	$-0.814060\pi$
$197$	−10971.0	+	10971.0i	−0.282692	+	0.282692i	0.551490	+	0.834182i	$0.314060\pi$
$198$		0			0
$199$		−	38160.0i		−	0.963612i	−0.876278	−	0.481806i	$-0.839981\pi$
$199$		−	38160.0i		−	0.963612i	0.876278	−	0.481806i	$-0.160019\pi$
$200$		0			0
$201$	−13518.0			−0.334596
$202$		0			0
$203$	19720.0	+	19720.0i	0.478536	+	0.478536i
$204$		0			0
$205$	−25230.0	−	33640.0i	−0.600357	−	0.800476i
$206$		0			0
$207$	21789.0	−	21789.0i	0.508507	−	0.508507i
$208$		0			0
$209$			33040.0i			0.756393i
$210$		0			0
$211$	−72842.0			−1.63613			−0.818063	−	0.575128i	$-0.804952\pi$
$211$	−72842.0			−1.63613			−0.818063	+	0.575128i	$0.804952\pi$
$212$		0			0
$213$	57978.0	+	57978.0i	1.27792	+	1.27792i
$214$		0			0
$215$	−5445.00	+	38115.0i	−0.117793	+	0.824554i
$216$		0			0
$217$	5858.00	−	5858.00i	0.124403	−	0.124403i
$218$		0			0
$219$			53118.0i			1.10752i
$220$		0			0
$221$	−37398.0			−0.765709
$222$		0			0
$223$	30891.0	+	30891.0i	0.621187	+	0.621187i	0.945835	−	0.324648i	$-0.105246\pi$
$223$	30891.0	+	30891.0i	0.621187	+	0.621187i	−0.324648	+	0.945835i	$0.605246\pi$
$224$		0			0
$225$	−48600.0	−	14175.0i	−0.960000	−	0.280000i
$226$		0			0
$227$	54911.0	−	54911.0i	1.06563	−	1.06563i	0.0679438	−	0.997689i	$-0.478356\pi$
$227$	54911.0	−	54911.0i	1.06563	−	1.06563i	0.997689	−	0.0679438i	$-0.0216439\pi$
$228$		0			0
$229$			50280.0i			0.958792i	0.877599	+	0.479396i	$0.159144\pi$
$229$			50280.0i			0.958792i	−0.877599	+	0.479396i	$0.840856\pi$
$230$		0			0
$231$	61596.0			1.15433
$232$		0			0
$233$	−2391.00	−	2391.00i	−0.0440421	−	0.0440421i	0.684743	−	0.728785i	$-0.259915\pi$
$233$	−2391.00	−	2391.00i	−0.0440421	−	0.0440421i	−0.728785	+	0.684743i	$0.759915\pi$
$234$		0			0
$235$	44415.0	+	6345.00i	0.804255	+	0.114894i
$236$		0			0
$237$	95040.0	−	95040.0i	1.69204	−	1.69204i
$238$		0			0
$239$		−	17760.0i		−	0.310919i	−0.987842	−	0.155459i	$-0.950314\pi$
$239$		−	17760.0i		−	0.310919i	0.987842	−	0.155459i	$-0.0496858\pi$
$240$		0			0
$241$	−28238.0			−0.486183			−0.243092	−	0.970003i	$-0.578162\pi$
$241$	−28238.0			−0.486183			−0.243092	+	0.970003i	$0.578162\pi$
$242$		0			0
$243$	−59049.0	−	59049.0i	−1.00000	−	1.00000i
$244$		0			0
$245$	14380.0	−	10785.0i	0.239567	−	0.179675i
$246$		0			0
$247$	−19320.0	+	19320.0i	−0.316675	+	0.316675i
$248$		0			0
$249$		−	112158.i		−	1.80897i
$250$		0			0
$251$	−121002.			−1.92064			−0.960318	−	0.278907i	$-0.910028\pi$
$251$	−121002.			−1.92064			−0.960318	+	0.278907i	$0.910028\pi$
$252$		0			0
$253$	−31742.0	−	31742.0i	−0.495899	−	0.495899i
$254$		0			0
$255$	−73170.0	−	97560.0i	−1.12526	−	1.50035i
$256$		0			0
$257$	−72431.0	+	72431.0i	−1.09663	+	1.09663i	−0.101823	+	0.994803i	$0.532467\pi$
$257$	−72431.0	+	72431.0i	−1.09663	+	1.09663i	−0.994803	+	0.101823i	$0.967533\pi$
$258$		0			0
$259$		−	37758.0i		−	0.562872i
$260$		0			0
$261$	55080.0			0.808561
$262$		0			0
$263$	14771.0	+	14771.0i	0.213549	+	0.213549i	0.805773	−	0.592224i	$-0.201750\pi$
$263$	14771.0	+	14771.0i	0.213549	+	0.213549i	−0.592224	+	0.805773i	$0.701750\pi$
$264$		0			0
$265$	−3055.00	+	21385.0i	−0.0435030	+	0.304521i
$266$		0			0
$267$	130320.	−	130320.i	1.82805	−	1.82805i
$268$		0			0
$269$		−	89720.0i		−	1.23989i	−0.784644	−	0.619947i	$-0.787154\pi$
$269$		−	89720.0i		−	1.23989i	0.784644	−	0.619947i	$-0.212846\pi$
$270$		0			0
$271$	−68202.0			−0.928664			−0.464332	−	0.885661i	$-0.653706\pi$
$271$	−68202.0			−0.928664			−0.464332	+	0.885661i	$0.653706\pi$
$272$		0			0
$273$	36018.0	+	36018.0i	0.483275	+	0.483275i
$274$		0			0
$275$	−20650.0	+	70800.0i	−0.273058	+	0.936198i
$276$		0			0
$277$	18549.0	−	18549.0i	0.241747	−	0.241747i	−0.575826	−	0.817573i	$-0.695319\pi$
$277$	18549.0	−	18549.0i	0.241747	−	0.241747i	0.817573	+	0.575826i	$0.195319\pi$
$278$		0			0
$279$		−	16362.0i		−	0.210198i
$280$		0			0
$281$	2322.00			0.0294069			0.0147035	−	0.999892i	$-0.495320\pi$
$281$	2322.00			0.0294069			0.0147035	+	0.999892i	$0.495320\pi$
$282$		0			0
$283$	91711.0	+	91711.0i	1.14511	+	1.14511i	0.987501	+	0.157613i	$0.0503797\pi$
$283$	91711.0	+	91711.0i	1.14511	+	1.14511i	0.157613	+	0.987501i	$0.449620\pi$
$284$		0			0
$285$	−88200.0	−	12600.0i	−1.08587	−	0.155125i
$286$		0			0
$287$	−48778.0	+	48778.0i	−0.592189	+	0.592189i
$288$		0			0
$289$		−	63361.0i		−	0.758624i
$290$		0			0
$291$	131598.			1.55404
$292$		0			0
$293$	−4851.00	−	4851.00i	−0.0565062	−	0.0565062i	0.678289	−	0.734795i	$-0.262722\pi$
$293$	−4851.00	−	4851.00i	−0.0565062	−	0.0565062i	−0.734795	+	0.678289i	$0.762722\pi$
$294$		0			0
$295$	23200.0	−	17400.0i	0.266590	−	0.199943i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		−	37122.0i		−	0.415230i
$300$		0			0
$301$	63162.0			0.697145
$302$		0			0
$303$	7902.00	+	7902.00i	0.0860700	+	0.0860700i
$304$		0			0
$305$	83970.0	+	111960.i	0.902661	+	1.20355i
$306$		0			0
$307$	−42849.0	+	42849.0i	−0.454636	+	0.454636i	−0.896890	−	0.442254i	$-0.854179\pi$
$307$	−42849.0	+	42849.0i	−0.454636	+	0.454636i	0.442254	+	0.896890i	$0.354179\pi$
$308$		0			0
$309$			187722.i			1.96607i
$310$		0			0
$311$	72278.0			0.747283			0.373642	−	0.927573i	$-0.378109\pi$
$311$	72278.0			0.747283			0.373642	+	0.927573i	$0.378109\pi$
$312$		0			0
$313$	18249.0	+	18249.0i	0.186273	+	0.186273i	0.794083	−	0.607810i	$-0.207952\pi$
$313$	18249.0	+	18249.0i	0.186273	+	0.186273i	−0.607810	+	0.794083i	$0.707952\pi$
$314$		0			0
$315$	−11745.0	+	82215.0i	−0.118367	+	0.828571i
$316$		0			0
$317$	25149.0	−	25149.0i	0.250266	−	0.250266i	−0.570814	−	0.821080i	$-0.693372\pi$
$317$	25149.0	−	25149.0i	0.250266	−	0.250266i	0.821080	+	0.570814i	$0.193372\pi$
$318$		0			0
$319$		−	80240.0i		−	0.788514i
$320$		0			0
$321$	−84798.0			−0.822954
$322$		0			0
$323$	−75880.0	−	75880.0i	−0.727315	−	0.727315i
$324$		0			0
$325$	−53475.0	+	29325.0i	−0.506272	+	0.277633i
$326$		0			0
$327$	−198360.	+	198360.i	−1.85506	+	1.85506i
$328$		0			0
$329$		−	73602.0i		−	0.679983i
$330$		0			0
$331$	54038.0			0.493223			0.246611	−	0.969114i	$-0.420683\pi$
$331$	54038.0			0.493223			0.246611	+	0.969114i	$0.420683\pi$
$332$		0			0
$333$	−52731.0	−	52731.0i	−0.475530	−	0.475530i
$334$		0			0
$335$	−26285.0	−	3755.00i	−0.234217	−	0.0334596i
$336$		0			0
$337$	8529.00	−	8529.00i	0.0750997	−	0.0750997i	−0.668559	−	0.743659i	$-0.733089\pi$
$337$	8529.00	−	8529.00i	0.0750997	−	0.0750997i	0.743659	+	0.668559i	$0.233089\pi$
$338$		0			0
$339$			37998.0i			0.330645i
$340$		0			0
$341$	−23836.0			−0.204986
$342$		0			0
$343$	−90480.0	−	90480.0i	−0.769067	−	0.769067i
$344$		0			0
$345$	96840.0	−	72630.0i	0.813611	−	0.610208i
$346$		0			0
$347$	56551.0	−	56551.0i	0.469658	−	0.469658i	−0.432146	−	0.901804i	$-0.642244\pi$
$347$	56551.0	−	56551.0i	0.469658	−	0.469658i	0.901804	+	0.432146i	$0.142244\pi$
$348$		0			0
$349$			22520.0i			0.184892i	0.995718	+	0.0924459i	$0.0294685\pi$
$349$			22520.0i			0.184892i	−0.995718	+	0.0924459i	$0.970531\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−44511.0	−	44511.0i	−0.357205	−	0.357205i	0.505576	−	0.862782i	$-0.331280\pi$
$353$	−44511.0	−	44511.0i	−0.357205	−	0.357205i	−0.862782	+	0.505576i	$0.831280\pi$
$354$		0			0
$355$	96630.0	+	128840.i	0.766753	+	1.02234i
$356$		0			0
$357$	−141462.	+	141462.i	−1.10995	+	1.10995i
$358$		0			0
$359$		−	9680.00i		−	0.0751080i	−0.999295	−	0.0375540i	$-0.988043\pi$
$359$		−	9680.00i		−	0.0751080i	0.999295	−	0.0375540i	$-0.0119566\pi$
$360$		0			0
$361$	51921.0			0.398409
$362$		0			0
$363$	6453.00	+	6453.00i	0.0489721	+	0.0489721i
$364$		0			0
$365$	−14755.0	+	103285.i	−0.110752	+	0.775267i
$366$		0			0
$367$	14971.0	−	14971.0i	0.111152	−	0.111152i	−0.649343	−	0.760496i	$-0.724956\pi$
$367$	14971.0	−	14971.0i	0.111152	−	0.111152i	0.760496	+	0.649343i	$0.224956\pi$
$368$		0			0
$369$			136242.i			1.00059i
$370$		0			0
$371$	35438.0			0.257467
$372$		0			0
$373$	−13811.0	−	13811.0i	−0.0992676	−	0.0992676i	0.655729	−	0.754996i	$-0.272361\pi$
$373$	−13811.0	−	13811.0i	−0.0992676	−	0.0992676i	−0.754996	+	0.655729i	$0.772361\pi$
$374$		0			0
$375$	−181125.	−	82125.0i	−1.28800	−	0.584000i
$376$		0			0
$377$	46920.0	−	46920.0i	0.330123	−	0.330123i
$378$		0			0
$379$			251080.i			1.74797i	0.485954	+	0.873984i	$0.338472\pi$
$379$			251080.i			1.74797i	−0.485954	+	0.873984i	$0.661528\pi$
$380$		0			0
$381$	106362.			0.732717
$382$		0			0
$383$	86091.0	+	86091.0i	0.586895	+	0.586895i	0.936789	−	0.349894i	$-0.113783\pi$
$383$	86091.0	+	86091.0i	0.586895	+	0.586895i	−0.349894	+	0.936789i	$0.613783\pi$
$384$		0			0
$385$	119770.	+	17110.0i	0.808028	+	0.115433i
$386$		0			0
$387$	88209.0	−	88209.0i	0.588967	−	0.588967i
$388$		0			0
$389$			75000.0i			0.495635i	0.968807	+	0.247818i	$0.0797134\pi$
$389$			75000.0i			0.495635i	−0.968807	+	0.247818i	$0.920287\pi$
$390$		0			0
$391$	145798.			0.953670
$392$		0			0
$393$	−57222.0	−	57222.0i	−0.370491	−	0.370491i
$394$		0			0
$395$	211200.	−	158400.i	1.35363	−	1.01522i
$396$		0			0
$397$	29149.0	−	29149.0i	0.184945	−	0.184945i	−0.608562	−	0.793507i	$-0.708253\pi$
$397$	29149.0	−	29149.0i	0.184945	−	0.184945i	0.793507	+	0.608562i	$0.208253\pi$
$398$		0			0
$399$			146160.i			0.918085i
$400$		0			0
$401$	−45918.0			−0.285558			−0.142779	−	0.989755i	$-0.545604\pi$
$401$	−45918.0			−0.285558			−0.142779	+	0.989755i	$0.545604\pi$
$402$		0			0
$403$	−13938.0	−	13938.0i	−0.0858204	−	0.0858204i
$404$		0			0
$405$	−98415.0	−	131220.i	−0.600000	−	0.800000i
$406$		0			0
$407$	−76818.0	+	76818.0i	−0.463740	+	0.463740i
$408$		0			0
$409$		−	78720.0i		−	0.470585i	−0.971925	−	0.235293i	$-0.924395\pi$
$409$		−	78720.0i		−	0.470585i	0.971925	−	0.235293i	$-0.0756049\pi$
$410$		0			0
$411$	−367362.			−2.17476
$412$		0			0
$413$	−33640.0	−	33640.0i	−0.197222	−	0.197222i
$414$		0			0
$415$	31155.0	−	218085.i	0.180897	−	1.26628i
$416$		0			0
$417$	−84600.0	+	84600.0i	−0.486517	+	0.486517i
$418$		0			0
$419$		−	14760.0i		−	0.0840733i	−0.999116	−	0.0420367i	$-0.986615\pi$
$419$		−	14760.0i		−	0.0840733i	0.999116	−	0.0420367i	$-0.0133846\pi$
$420$		0			0
$421$	221282.			1.24848			0.624240	−	0.781232i	$-0.285409\pi$
$421$	221282.			1.24848			0.624240	+	0.781232i	$0.285409\pi$
$422$		0			0
$423$	−102789.	−	102789.i	−0.574468	−	0.574468i
$424$		0			0
$425$	−115175.	−	210025.i	−0.637647	−	1.16277i
$426$		0			0
$427$	162342.	−	162342.i	0.890379	−	0.890379i
$428$		0			0
$429$		−	146556.i		−	0.796323i
$430$		0			0
$431$	−212522.			−1.14406			−0.572031	−	0.820232i	$-0.693844\pi$
$431$	−212522.			−1.14406			−0.572031	+	0.820232i	$0.693844\pi$
$432$		0			0
$433$	145409.	+	145409.i	0.775560	+	0.775560i	0.979072	−	0.203512i	$-0.0652357\pi$
$433$	145409.	+	145409.i	0.775560	+	0.775560i	−0.203512	+	0.979072i	$0.565236\pi$
$434$		0			0
$435$	214200.	+	30600.0i	1.13199	+	0.161712i
$436$		0			0
$437$	75320.0	−	75320.0i	0.394410	−	0.394410i
$438$		0			0
$439$		−	299440.i		−	1.55375i	−0.629656	−	0.776874i	$-0.716804\pi$
$439$		−	299440.i		−	1.55375i	0.629656	−	0.776874i	$-0.283196\pi$
$440$		0			0
$441$	−58239.0			−0.299459
$442$		0			0
$443$	−240609.	−	240609.i	−1.22604	−	1.22604i	−0.965450	−	0.260590i	$-0.916083\pi$
$443$	−240609.	−	240609.i	−1.22604	−	1.22604i	−0.260590	−	0.965450i	$-0.583917\pi$
$444$		0			0
$445$	289600.	−	217200.i	1.46244	−	1.09683i
$446$		0			0
$447$	−124200.	+	124200.i	−0.621594	+	0.621594i
$448$		0			0
$449$			82480.0i			0.409125i	0.978854	+	0.204562i	$0.0655772\pi$
$449$			82480.0i			0.409125i	−0.978854	+	0.204562i	$0.934423\pi$
$450$		0			0
$451$	198476.			0.975787
$452$		0			0
$453$	−170982.	−	170982.i	−0.833209	−	0.833209i
$454$		0			0
$455$	60030.0	+	80040.0i	0.289965	+	0.386620i
$456$		0			0
$457$	−188151.	+	188151.i	−0.900895	+	0.900895i	−0.995514	−	0.0946187i	$-0.969837\pi$
$457$	−188151.	+	188151.i	−0.900895	+	0.900895i	0.0946187	+	0.995514i	$0.469837\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−326158.			−1.53471			−0.767355	−	0.641223i	$-0.778427\pi$
$461$	−326158.			−1.53471			−0.767355	+	0.641223i	$0.778427\pi$
$462$		0			0
$463$	218731.	+	218731.i	1.02035	+	1.02035i	0.999789	+	0.0205595i	$0.00654474\pi$
$463$	218731.	+	218731.i	1.02035	+	1.02035i	0.0205595	+	0.999789i	$0.493455\pi$
$464$		0			0
$465$	9090.00	−	63630.0i	0.0420395	−	0.294277i
$466$		0			0
$467$	−59249.0	+	59249.0i	−0.271673	+	0.271673i	−0.829774	−	0.558100i	$-0.811530\pi$
$467$	−59249.0	+	59249.0i	−0.271673	+	0.271673i	0.558100	+	0.829774i	$0.311530\pi$
$468$		0			0
$469$			43558.0i			0.198026i
$470$		0			0
$471$	294678.			1.32833
$472$		0			0
$473$	−128502.	−	128502.i	−0.574365	−	0.574365i
$474$		0			0
$475$	−168000.	−	49000.0i	−0.744598	−	0.217175i
$476$		0			0
$477$	49491.0	−	49491.0i	0.217515	−	0.217515i
$478$		0			0
$479$			273440.i			1.19177i	0.803071	+	0.595883i	$0.203198\pi$
$479$			273440.i			1.19177i	−0.803071	+	0.595883i	$0.796802\pi$
$480$		0			0
$481$	−89838.0			−0.388302
$482$		0			0
$483$	−140418.	−	140418.i	−0.601906	−	0.601906i
$484$		0			0
$485$	255885.	+	36555.0i	1.08783	+	0.155404i
$486$		0			0
$487$	123651.	−	123651.i	0.521362	−	0.521362i	−0.396620	−	0.917983i	$-0.629817\pi$
$487$	123651.	−	123651.i	0.521362	−	0.521362i	0.917983	+	0.396620i	$0.129817\pi$
$488$		0			0
$489$			360162.i			1.50619i
$490$		0			0
$491$	−198442.			−0.823134			−0.411567	−	0.911379i	$-0.635018\pi$
$491$	−198442.			−0.823134			−0.411567	+	0.911379i	$0.635018\pi$
$492$		0			0
$493$	184280.	+	184280.i	0.758201	+	0.758201i
$494$		0			0
$495$	191160.	−	143370.i	0.780165	−	0.585124i
$496$		0			0
$497$	186818.	−	186818.i	0.756321	−	0.756321i
$498$		0			0
$499$			269240.i			1.08128i	0.841254	+	0.540640i	$0.181818\pi$
$499$			269240.i			1.08128i	−0.841254	+	0.540640i	$0.818182\pi$
$500$		0			0
$501$	27882.0			0.111083
$502$		0			0
$503$	−109869.	−	109869.i	−0.434249	−	0.434249i	0.455822	−	0.890071i	$-0.349345\pi$
$503$	−109869.	−	109869.i	−0.434249	−	0.434249i	−0.890071	+	0.455822i	$0.849345\pi$
$504$		0			0
$505$	13170.0	+	17560.0i	0.0516420	+	0.0688560i
$506$		0			0
$507$	−171351.	+	171351.i	−0.666608	+	0.666608i
$508$		0			0
$509$			211000.i			0.814417i	0.913335	+	0.407209i	$0.133498\pi$
$509$			211000.i			0.814417i	−0.913335	+	0.407209i	$0.866502\pi$
$510$		0			0
$511$	171158.			0.655474
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−52145.0	+	365015.i	−0.196607	+	1.37625i
$516$		0			0
$517$	−149742.	+	149742.i	−0.560225	+	0.560225i
$518$		0			0
$519$		−	50202.0i		−	0.186374i
$520$		0			0
$521$	297282.			1.09520			0.547600	−	0.836740i	$-0.315542\pi$
$521$	297282.			1.09520			0.547600	+	0.836740i	$0.315542\pi$
$522$		0			0
$523$	25071.0	+	25071.0i	0.0916576	+	0.0916576i	0.751449	−	0.659791i	$-0.229355\pi$
$523$	25071.0	+	25071.0i	0.0916576	+	0.0916576i	−0.659791	+	0.751449i	$0.729355\pi$
$524$		0			0
$525$	−91350.0	+	313200.i	−0.331429	+	1.13633i
$526$		0			0
$527$	54742.0	−	54742.0i	0.197106	−	0.197106i
$528$		0			0
$529$		−	135119.i		−	0.482842i
$530$		0			0
$531$	−93960.0			−0.333238
$532$		0			0
$533$	116058.	+	116058.i	0.408527	+	0.408527i
$534$		0			0
$535$	−164885.	−	23555.0i	−0.576068	−	0.0822954i
$536$		0			0
$537$	−23400.0	+	23400.0i	−0.0811460	+	0.0811460i
$538$		0			0
$539$			84842.0i			0.292034i
$540$		0			0
$541$	−142478.			−0.486803			−0.243402	−	0.969926i	$-0.578263\pi$
$541$	−142478.			−0.486803			−0.243402	+	0.969926i	$0.578263\pi$
$542$		0			0
$543$	399582.	+	399582.i	1.35521	+	1.35521i
$544$		0			0
$545$	−440800.	+	330600.i	−1.48405	+	1.11304i
$546$		0			0
$547$	−291009.	+	291009.i	−0.972594	+	0.972594i	−0.999634	−	0.0270399i	$-0.991392\pi$
$547$	−291009.	+	291009.i	−0.972594	+	0.972594i	0.0270399	+	0.999634i	$0.491392\pi$
$548$		0			0
$549$		−	453438.i		−	1.50443i
$550$		0			0
$551$	190400.			0.627139
$552$		0			0
$553$	−306240.	−	306240.i	−1.00141	−	1.00141i
$554$		0			0
$555$	−175770.	−	234360.i	−0.570636	−	0.760847i
$556$		0			0
$557$	−83091.0	+	83091.0i	−0.267820	+	0.267820i	−0.828221	−	0.560401i	$-0.810647\pi$
$557$	−83091.0	+	83091.0i	−0.267820	+	0.267820i	0.560401	+	0.828221i	$0.310647\pi$
$558$		0			0
$559$		−	150282.i		−	0.480932i
$560$		0			0
$561$	575604.			1.82893
$562$		0			0
$563$	−43449.0	−	43449.0i	−0.137076	−	0.137076i	0.635239	−	0.772316i	$-0.280902\pi$
$563$	−43449.0	−	43449.0i	−0.137076	−	0.137076i	−0.772316	+	0.635239i	$0.780902\pi$
$564$		0			0
$565$	−10555.0	+	73885.0i	−0.0330645	+	0.231451i
$566$		0			0
$567$	−190269.	+	190269.i	−0.591837	+	0.591837i
$568$		0			0
$569$			270560.i			0.835678i	0.908521	+	0.417839i	$0.137212\pi$
$569$			270560.i			0.835678i	−0.908521	+	0.417839i	$0.862788\pi$
$570$		0			0
$571$	−57482.0			−0.176303			−0.0881515	−	0.996107i	$-0.528096\pi$
$571$	−57482.0			−0.176303			−0.0881515	+	0.996107i	$0.528096\pi$
$572$		0			0
$573$	−132102.	−	132102.i	−0.402346	−	0.402346i
$574$		0			0
$575$	208475.	−	114325.i	0.630548	−	0.345784i
$576$		0			0
$577$	195889.	−	195889.i	0.588381	−	0.588381i	−0.348812	−	0.937193i	$-0.613415\pi$
$577$	195889.	−	195889.i	0.588381	−	0.588381i	0.937193	+	0.348812i	$0.113415\pi$
$578$		0			0
$579$		−	771282.i		−	2.30068i
$580$		0			0
$581$	−361398.			−1.07062
$582$		0			0
$583$	−72098.0	−	72098.0i	−0.212122	−	0.212122i
$584$		0			0
$585$	195615.	+	27945.0i	0.571598	+	0.0816568i
$586$		0			0
$587$	404631.	−	404631.i	1.17431	−	1.17431i	0.193139	−	0.981171i	$-0.438133\pi$
$587$	404631.	−	404631.i	1.17431	−	1.17431i	0.981171	−	0.193139i	$-0.0618669\pi$
$588$		0			0
$589$		−	56560.0i		−	0.163034i
$590$		0			0
$591$	197478.			0.565384
$592$		0			0
$593$	−210991.	−	210991.i	−0.600005	−	0.600005i	0.340309	−	0.940314i	$-0.389468\pi$
$593$	−210991.	−	210991.i	−0.600005	−	0.600005i	−0.940314	+	0.340309i	$0.889468\pi$
$594$		0			0
$595$	−314360.	+	235770.i	−0.887960	+	0.665970i
$596$		0			0
$597$	−343440.	+	343440.i	−0.963612	+	0.963612i
$598$		0			0
$599$			300560.i			0.837679i	0.908060	+	0.418839i	$0.137563\pi$
$599$			300560.i			0.837679i	−0.908060	+	0.418839i	$0.862437\pi$
$600$		0			0
$601$	367442.			1.01728			0.508639	−	0.860980i	$-0.330149\pi$
$601$	367442.			1.01728			0.508639	+	0.860980i	$0.330149\pi$
$602$		0			0
$603$	60831.0	+	60831.0i	0.167298	+	0.167298i
$604$		0			0
$605$	10755.0	+	14340.0i	0.0293832	+	0.0391777i
$606$		0			0
$607$	−146469.	+	146469.i	−0.397529	+	0.397529i	−0.877360	−	0.479832i	$-0.840698\pi$
$607$	−146469.	+	146469.i	−0.397529	+	0.397529i	0.479832	+	0.877360i	$0.340698\pi$
$608$		0			0
$609$		−	354960.i		−	0.957072i
$610$		0			0
$611$	−175122.			−0.469092
$612$		0			0
$613$	160989.	+	160989.i	0.428425	+	0.428425i	0.888092	−	0.459666i	$-0.152031\pi$
$613$	160989.	+	160989.i	0.428425	+	0.428425i	−0.459666	+	0.888092i	$0.652031\pi$
$614$		0			0
$615$	−75690.0	+	529830.i	−0.200119	+	1.40083i
$616$		0			0
$617$	320409.	−	320409.i	0.841656	−	0.841656i	−0.147419	−	0.989074i	$-0.547096\pi$
$617$	320409.	−	320409.i	0.841656	−	0.841656i	0.989074	+	0.147419i	$0.0470965\pi$
$618$		0			0
$619$			341160.i			0.890383i	0.895435	+	0.445191i	$0.146864\pi$
$619$			341160.i			0.890383i	−0.895435	+	0.445191i	$0.853136\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−419920.	−	419920.i	−1.08191	−	1.08191i
$624$		0			0
$625$	−329375.	−	210000.i	−0.843200	−	0.537600i
$626$		0			0
$627$	297360.	−	297360.i	0.756393	−	0.756393i
$628$		0			0
$629$		−	352842.i		−	0.891824i
$630$		0			0
$631$	390998.			0.982010			0.491005	−	0.871157i	$-0.336630\pi$
$631$	390998.			0.982010			0.491005	+	0.871157i	$0.336630\pi$
$632$		0			0
$633$	655578.	+	655578.i	1.63613	+	1.63613i
$634$		0			0
$635$	206815.	+	29545.0i	0.512902	+	0.0732717i
$636$		0			0
$637$	−49611.0	+	49611.0i	−0.122264	+	0.122264i
$638$		0			0
$639$		−	521802.i		−	1.27792i
$640$		0			0
$641$	−585038.			−1.42386			−0.711931	−	0.702249i	$-0.752179\pi$
$641$	−585038.			−1.42386			−0.711931	+	0.702249i	$0.752179\pi$
$642$		0			0
$643$	31911.0	+	31911.0i	0.0771824	+	0.0771824i	0.744644	−	0.667462i	$-0.232619\pi$
$643$	31911.0	+	31911.0i	0.0771824	+	0.0771824i	−0.667462	+	0.744644i	$0.732619\pi$
$644$		0			0
$645$	392040.	−	294030.i	0.942347	−	0.706760i
$646$		0			0
$647$	280931.	−	280931.i	0.671106	−	0.671106i	−0.286865	−	0.957971i	$-0.592613\pi$
$647$	280931.	−	280931.i	0.671106	−	0.671106i	0.957971	+	0.286865i	$0.0926131\pi$
$648$		0			0
$649$			136880.i			0.324975i
$650$		0			0
$651$	−105444.			−0.248805
$652$		0			0
$653$	523989.	+	523989.i	1.22884	+	1.22884i	0.964402	+	0.264439i	$0.0851867\pi$
$653$	523989.	+	523989.i	1.22884	+	1.22884i	0.264439	+	0.964402i	$0.414813\pi$
$654$		0			0
$655$	−95370.0	−	127160.i	−0.222295	−	0.296393i
$656$		0			0
$657$	239031.	−	239031.i	0.553762	−	0.553762i
$658$		0			0
$659$		−	404360.i		−	0.931102i	−0.885021	−	0.465551i	$-0.845856\pi$
$659$		−	404360.i		−	0.931102i	0.885021	−	0.465551i	$-0.154144\pi$
$660$		0			0
$661$	−5278.00			−0.0120800			−0.00603999	−	0.999982i	$-0.501923\pi$
$661$	−5278.00			−0.0120800			−0.00603999	+	0.999982i	$0.501923\pi$
$662$		0			0
$663$	336582.	+	336582.i	0.765709	+	0.765709i
$664$		0			0
$665$	−40600.0	+	284200.i	−0.0918085	+	0.642659i
$666$		0			0
$667$	−182920.	+	182920.i	−0.411159	+	0.411159i
$668$		0			0
$669$		−	556038.i		−	1.24237i
$670$		0			0
$671$	−660564.			−1.46713
$672$		0			0
$673$	−332111.	−	332111.i	−0.733252	−	0.733252i	0.238011	−	0.971263i	$-0.423505\pi$
$673$	−332111.	−	332111.i	−0.733252	−	0.733252i	−0.971263	+	0.238011i	$0.923505\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	578309.	−	578309.i	1.26178	−	1.26178i	0.311546	−	0.950231i	$-0.399153\pi$
$677$	578309.	−	578309.i	1.26178	−	1.26178i	0.950231	−	0.311546i	$-0.100847\pi$
$678$		0			0
$679$		−	424038.i		−	0.919740i
$680$		0			0
$681$	−988398.			−2.13127
$682$		0			0
$683$	349311.	+	349311.i	0.748809	+	0.748809i	0.974255	−	0.225447i	$-0.0723842\pi$
$683$	349311.	+	349311.i	0.748809	+	0.748809i	−0.225447	+	0.974255i	$0.572384\pi$
$684$		0			0
$685$	−714315.	−	102045.i	−1.52233	−	0.217476i
$686$		0			0
$687$	452520.	−	452520.i	0.958792	−	0.958792i
$688$		0			0
$689$		−	84318.0i		−	0.177616i
$690$		0			0
$691$	−282762.			−0.592195			−0.296098	−	0.955158i	$-0.595685\pi$
$691$	−282762.			−0.592195			−0.296098	+	0.955158i	$0.595685\pi$
$692$		0			0
$693$	−277182.	−	277182.i	−0.577163	−	0.577163i
$694$		0			0
$695$	−188000.	+	141000.i	−0.389214	+	0.291910i
$696$		0			0
$697$	−455822.	+	455822.i	−0.938274	+	0.938274i
$698$		0			0
$699$			43038.0i			0.0880841i
$700$		0			0
$701$	270242.			0.549942			0.274971	−	0.961453i	$-0.411332\pi$
$701$	270242.			0.549942			0.274971	+	0.961453i	$0.411332\pi$
$702$		0			0
$703$	−182280.	−	182280.i	−0.368832	−	0.368832i
$704$		0			0
$705$	−342630.	−	456840.i	−0.689362	−	0.919149i
$706$		0			0
$707$	25462.0	−	25462.0i	0.0509394	−	0.0509394i
$708$		0			0
$709$			297800.i			0.592423i	0.955122	+	0.296212i	$0.0957234\pi$
$709$			297800.i			0.592423i	−0.955122	+	0.296212i	$0.904277\pi$
$710$		0			0
$711$	−855360.			−1.69204
$712$		0			0
$713$	54338.0	+	54338.0i	0.106887	+	0.106887i
$714$		0			0
$715$	40710.0	−	284970.i	0.0796323	−	0.557426i
$716$		0			0
$717$	−159840.	+	159840.i	−0.310919	+	0.310919i
$718$		0			0
$719$			913760.i			1.76756i	0.467902	+	0.883780i	$0.345010\pi$
$719$			913760.i			1.76756i	−0.467902	+	0.883780i	$0.654990\pi$
$720$		0			0
$721$	604882.			1.16359
$722$		0			0
$723$	254142.	+	254142.i	0.486183	+	0.486183i
$724$		0			0
$725$	408000.	+	119000.i	0.776219	+	0.226397i
$726$		0			0
$727$	417651.	−	417651.i	0.790214	−	0.790214i	−0.191315	−	0.981529i	$-0.561275\pi$
$727$	417651.	−	417651.i	0.790214	−	0.790214i	0.981529	+	0.191315i	$0.0612751\pi$
$728$		0			0
$729$			531441.i			1.00000i
$730$		0			0
$731$	590238.			1.10457
$732$		0			0
$733$	394549.	+	394549.i	0.734333	+	0.734333i	0.971475	−	0.237142i	$-0.0762107\pi$
$733$	394549.	+	394549.i	0.734333	+	0.734333i	−0.237142	+	0.971475i	$0.576211\pi$
$734$		0			0
$735$	−226485.	−	32355.0i	−0.419242	−	0.0598917i
$736$		0			0
$737$	88618.0	−	88618.0i	0.163150	−	0.163150i
$738$		0			0
$739$			109880.i			0.201201i	0.994927	+	0.100600i	$0.0320764\pi$
$739$			109880.i			0.201201i	−0.994927	+	0.100600i	$0.967924\pi$
$740$		0			0
$741$	347760.			0.633349
$742$		0			0
$743$	466451.	+	466451.i	0.844945	+	0.844945i	0.989497	−	0.144552i	$-0.0461742\pi$
$743$	466451.	+	466451.i	0.844945	+	0.844945i	−0.144552	+	0.989497i	$0.546174\pi$
$744$		0			0
$745$	−276000.	+	207000.i	−0.497275	+	0.372956i
$746$		0			0
$747$	−504711.	+	504711.i	−0.904485	+	0.904485i
$748$		0			0
$749$			273238.i			0.487054i
$750$		0			0
$751$	−1.01092e6			−1.79241			−0.896206	−	0.443638i	$-0.853687\pi$
$751$	−1.01092e6			−1.79241			−0.896206	+	0.443638i	$0.853687\pi$
$752$		0			0
$753$	1.08902e6	+	1.08902e6i	1.92064	+	1.92064i
$754$		0			0
$755$	−284970.	−	379960.i	−0.499925	−	0.666567i
$756$		0			0
$757$	313269.	−	313269.i	0.546671	−	0.546671i	−0.378806	−	0.925476i	$-0.623665\pi$
$757$	313269.	−	313269.i	0.546671	−	0.546671i	0.925476	+	0.378806i	$0.123665\pi$
$758$		0			0
$759$			571356.i			0.991798i
$760$		0			0
$761$	142082.			0.245341			0.122670	−	0.992447i	$-0.460854\pi$
$761$	142082.			0.245341			0.122670	+	0.992447i	$0.460854\pi$
$762$		0			0
$763$	639160.	+	639160.i	1.09789	+	1.09789i
$764$		0			0
$765$	−109755.	+	768285.i	−0.187543	+	1.31280i
$766$		0			0
$767$	−80040.0	+	80040.0i	−0.136056	+	0.136056i
$768$		0			0
$769$		−	13280.0i		−	0.0224567i	−0.999937	−	0.0112283i	$-0.996426\pi$
$769$		−	13280.0i		−	0.0224567i	0.999937	−	0.0112283i	$-0.00357417\pi$
$770$		0			0
$771$	1.30376e6			2.19325
$772$		0			0
$773$	−782211.	−	782211.i	−1.30908	−	1.30908i	−0.922082	−	0.386994i	$-0.873513\pi$
$773$	−782211.	−	782211.i	−1.30908	−	1.30908i	−0.386994	−	0.922082i	$-0.626487\pi$
$774$		0			0
$775$	35350.0	−	121200.i	0.0588554	−	0.201790i
$776$		0			0
$777$	−339822.	+	339822.i	−0.562872	+	0.562872i
$778$		0			0
$779$			470960.i			0.776085i
$780$		0			0
$781$	−760156.			−1.24624
$782$		0			0
$783$		0			0
$784$		0			0
$785$	572985.	+	81855.0i	0.929831	+	0.132833i
$786$		0			0
$787$	−201409.	+	201409.i	−0.325184	+	0.325184i	−0.850752	−	0.525568i	$-0.823853\pi$
$787$	−201409.	+	201409.i	−0.325184	+	0.325184i	0.525568	+	0.850752i	$0.323853\pi$
$788$		0			0
$789$		−	265878.i		−	0.427099i
$790$		0			0
$791$	122438.			0.195688
$792$		0			0
$793$	−386262.	−	386262.i	−0.614236	−	0.614236i
$794$		0			0
$795$	219960.	−	164970.i	0.348024	−	0.261018i
$796$		0			0
$797$	−36291.0	+	36291.0i	−0.0571324	+	0.0571324i	−0.735096	−	0.677963i	$-0.762863\pi$
$797$	−36291.0	+	36291.0i	−0.0571324	+	0.0571324i	0.677963	+	0.735096i	$0.262863\pi$
$798$		0			0
$799$		−	687798.i		−	1.07738i
$800$		0			0
$801$	−1.17288e6			−1.82805
$802$		0			0
$803$	−348218.	−	348218.i	−0.540033	−	0.540033i
$804$		0			0
$805$	−234030.	−	312040.i	−0.361143	−	0.481525i
$806$		0			0
$807$	−807480.	+	807480.i	−1.23989	+	1.23989i
$808$		0			0
$809$			71600.0i			0.109400i	0.998503	+	0.0546998i	$0.0174202\pi$
$809$			71600.0i			0.109400i	−0.998503	+	0.0546998i	$0.982580\pi$
$810$		0			0
$811$	103318.			0.157085			0.0785424	−	0.996911i	$-0.474973\pi$
$811$	103318.			0.157085			0.0785424	+	0.996911i	$0.474973\pi$
$812$		0			0
$813$	613818.	+	613818.i	0.928664	+	0.928664i
$814$		0			0
$815$	−100045.	+	700315.i	−0.150619	+	1.05433i
$816$		0			0
$817$	304920.	−	304920.i	0.456817	−	0.456817i
$818$		0			0
$819$		−	324162.i		−	0.483275i
$820$		0			0
$821$	−157438.			−0.233573			−0.116787	−	0.993157i	$-0.537259\pi$
$821$	−157438.			−0.233573			−0.116787	+	0.993157i	$0.537259\pi$
$822$		0			0
$823$	−791309.	−	791309.i	−1.16828	−	1.16828i	−0.982613	−	0.185666i	$-0.940556\pi$
$823$	−791309.	−	791309.i	−1.16828	−	1.16828i	−0.185666	−	0.982613i	$-0.559444\pi$
$824$		0			0
$825$	823050.	−	451350.i	1.20926	−	0.663140i
$826$		0			0
$827$	889671.	−	889671.i	1.30082	−	1.30082i	0.372987	−	0.927837i	$-0.378334\pi$
$827$	889671.	−	889671.i	1.30082	−	1.30082i	0.927837	−	0.372987i	$-0.121666\pi$
$828$		0			0
$829$			618280.i			0.899655i	0.893115	+	0.449828i	$0.148515\pi$
$829$			618280.i			0.899655i	−0.893115	+	0.449828i	$0.851485\pi$
$830$		0			0
$831$	−333882.			−0.483494
$832$		0			0
$833$	−194849.	−	194849.i	−0.280807	−	0.280807i
$834$		0			0
$835$	54215.0	+	7745.00i	0.0777583	+	0.0111083i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	821360.i		−	1.16684i	−0.812172	−	0.583418i	$-0.801715\pi$
$839$		−	821360.i		−	1.16684i	0.812172	−	0.583418i	$-0.198285\pi$
$840$		0			0
$841$	244881.			0.346229
$842$		0			0
$843$	−20898.0	−	20898.0i	−0.0294069	−	0.0294069i
$844$		0			0
$845$	−380780.	+	285585.i	−0.533287	+	0.399965i
$846$		0			0
$847$	20793.0	−	20793.0i	0.0289835	−	0.0289835i
$848$		0			0
$849$		−	1.65080e6i		−	2.29023i
$850$		0			0
$851$	350238.			0.483620
$852$		0			0
$853$	−698291.	−	698291.i	−0.959706	−	0.959706i	0.0395127	−	0.999219i	$-0.487419\pi$
$853$	−698291.	−	698291.i	−0.959706	−	0.959706i	−0.999219	+	0.0395127i	$0.987419\pi$
$854$		0			0
$855$	340200.	+	453600.i	0.465374	+	0.620499i
$856$		0			0
$857$	144489.	−	144489.i	0.196731	−	0.196731i	−0.601866	−	0.798597i	$-0.705576\pi$
$857$	144489.	−	144489.i	0.196731	−	0.196731i	0.798597	+	0.601866i	$0.205576\pi$
$858$		0			0
$859$		−	943480.i		−	1.27863i	−0.768943	−	0.639317i	$-0.779217\pi$
$859$		−	943480.i		−	1.27863i	0.768943	−	0.639317i	$-0.220783\pi$
$860$		0			0
$861$	878004.			1.18438
$862$		0			0
$863$	−438149.	−	438149.i	−0.588302	−	0.588302i	0.348869	−	0.937171i	$-0.386566\pi$
$863$	−438149.	−	438149.i	−0.588302	−	0.588302i	−0.937171	+	0.348869i	$0.886566\pi$
$864$		0			0
$865$	13945.0	−	97615.0i	0.0186374	−	0.130462i
$866$		0			0
$867$	−570249.	+	570249.i	−0.758624	+	0.758624i
$868$		0			0
$869$			1.24608e6i			1.65009i
$870$		0			0
$871$	103638.			0.136610
$872$		0			0
$873$	−592191.	−	592191.i	−0.777022	−	0.777022i
$874$		0			0
$875$	−264625.	+	583625.i	−0.345633	+	0.762286i
$876$		0			0
$877$	281469.	−	281469.i	0.365958	−	0.365958i	−0.500043	−	0.866001i	$-0.666682\pi$
$877$	281469.	−	281469.i	0.365958	−	0.365958i	0.866001	+	0.500043i	$0.166682\pi$
$878$		0			0
$879$			87318.0i			0.113012i
$880$		0			0
$881$	876722.			1.12956			0.564781	−	0.825241i	$-0.308961\pi$
$881$	876722.			1.12956			0.564781	+	0.825241i	$0.308961\pi$
$882$		0			0
$883$	327431.	+	327431.i	0.419951	+	0.419951i	0.885187	−	0.465236i	$-0.154031\pi$
$883$	327431.	+	327431.i	0.419951	+	0.419951i	−0.465236	+	0.885187i	$0.654031\pi$
$884$		0			0
$885$	−365400.	−	52200.0i	−0.466533	−	0.0666475i
$886$		0			0
$887$	477171.	−	477171.i	0.606494	−	0.606494i	−0.335534	−	0.942028i	$-0.608917\pi$
$887$	477171.	−	477171.i	0.606494	−	0.606494i	0.942028	+	0.335534i	$0.108917\pi$
$888$		0			0
$889$		−	342722.i		−	0.433649i
$890$		0			0
$891$	774198.			0.975207
$892$		0			0
$893$	−355320.	−	355320.i	−0.445571	−	0.445571i
$894$		0			0
$895$	−52000.0	+	39000.0i	−0.0649168	+	0.0486876i
$896$		0			0
$897$	−334098.	+	334098.i	−0.415230	+	0.415230i
$898$		0			0
$899$			137360.i			0.169958i
$900$		0			0
$901$	331162.			0.407935
$902$		0			0
$903$	−568458.	−	568458.i	−0.697145	−	0.697145i
$904$		0			0
$905$	665970.	+	887960.i	0.813125	+	1.08417i
$906$		0			0
$907$	−1.11209e6	+	1.11209e6i	−1.35184	+	1.35184i	−0.468235	+	0.883604i	$0.655110\pi$
$907$	−1.11209e6	+	1.11209e6i	−1.35184	+	1.35184i	−0.883604	+	0.468235i	$0.844890\pi$
$908$		0			0
$909$		−	71118.0i		−	0.0860700i
$910$		0			0
$911$	883958.			1.06511			0.532556	−	0.846395i	$-0.321232\pi$
$911$	883958.			1.06511			0.532556	+	0.846395i	$0.321232\pi$
$912$		0			0
$913$	735258.	+	735258.i	0.882060	+	0.882060i
$914$		0			0
$915$	251910.	−	1.76337e6i	0.300887	−	2.10621i
$916$		0			0
$917$	−184382.	+	184382.i	−0.219270	+	0.219270i
$918$		0			0
$919$			1.24040e6i			1.46869i	0.678775	+	0.734346i	$0.262511\pi$
$919$			1.24040e6i			1.46869i	−0.678775	+	0.734346i	$0.737489\pi$
$920$		0			0
$921$	771282.			0.909272
$922$		0			0
$923$	−444498.	−	444498.i	−0.521755	−	0.521755i
$924$		0			0
$925$	−276675.	−	504525.i	−0.323360	−	0.589657i
$926$		0			0
$927$	844749.	−	844749.i	0.983033	−	0.983033i
$928$		0			0
$929$		−	1.22744e6i		−	1.42223i	−0.703077	−	0.711113i	$-0.748191\pi$
$929$		−	1.22744e6i		−	1.42223i	0.703077	−	0.711113i	$-0.251809\pi$
$930$		0			0
$931$	−201320.			−0.232267
$932$		0			0
$933$	−650502.	−	650502.i	−0.747283	−	0.747283i
$934$		0			0
$935$	1.11923e6	+	159890.i	1.28025	+	0.182893i
$936$		0			0
$937$	−1.07047e6	+	1.07047e6i	−1.21926	+	1.21926i	−0.251366	+	0.967892i	$0.580880\pi$
$937$	−1.07047e6	+	1.07047e6i	−1.21926	+	1.21926i	−0.967892	+	0.251366i	$0.919120\pi$
$938$		0			0
$939$		−	328482.i		−	0.372546i
$940$		0			0
$941$	558642.			0.630891			0.315446	−	0.948944i	$-0.397846\pi$
$941$	558642.			0.630891			0.315446	+	0.948944i	$0.397846\pi$
$942$		0			0
$943$	−452458.	−	452458.i	−0.508809	−	0.508809i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	191711.	−	191711.i	0.213770	−	0.213770i	−0.592097	−	0.805867i	$-0.701700\pi$
$947$	191711.	−	191711.i	0.213770	−	0.213770i	0.805867	+	0.592097i	$0.201700\pi$
$948$		0			0
$949$		−	407238.i		−	0.452185i
$950$		0			0
$951$	−452682.			−0.500532
$952$		0			0
$953$	−630231.	−	630231.i	−0.693927	−	0.693927i	0.269166	−	0.963094i	$-0.413252\pi$
$953$	−630231.	−	630231.i	−0.693927	−	0.693927i	−0.963094	+	0.269166i	$0.913252\pi$
$954$		0			0
$955$	−220170.	−	293560.i	−0.241408	−	0.321877i
$956$		0			0
$957$	−722160.	+	722160.i	−0.788514	+	0.788514i
$958$		0			0
$959$			1.18372e6i			1.28710i
$960$		0			0
$961$	−882717.			−0.955817
$962$		0			0
$963$	381591.	+	381591.i	0.411477	+	0.411477i
$964$		0			0
$965$	214245.	−	1.49972e6i	0.230068	−	1.61048i
$966$		0			0
$967$	345491.	−	345491.i	0.369474	−	0.369474i	−0.497811	−	0.867285i	$-0.665863\pi$
$967$	345491.	−	345491.i	0.369474	−	0.369474i	0.867285	+	0.497811i	$0.165863\pi$
$968$		0			0
$969$			1.36584e6i			1.45463i
$970$		0			0
$971$	−1.08308e6			−1.14874			−0.574372	−	0.818595i	$-0.694753\pi$
$971$	−1.08308e6			−1.14874			−0.574372	+	0.818595i	$0.694753\pi$
$972$		0			0
$973$	272600.	+	272600.i	0.287939	+	0.287939i
$974$		0			0
$975$	745200.	+	217350.i	0.783905	+	0.228639i
$976$		0			0
$977$	−146751.	+	146751.i	−0.153742	+	0.153742i	−0.779787	−	0.626045i	$-0.784673\pi$
$977$	−146751.	+	146751.i	−0.153742	+	0.153742i	0.626045	+	0.779787i	$0.284673\pi$
$978$		0			0
$979$			1.70864e6i			1.78273i
$980$		0			0
$981$	1.78524e6			1.85506
$982$		0			0
$983$	−466909.	−	466909.i	−0.483198	−	0.483198i	0.422953	−	0.906151i	$-0.360993\pi$
$983$	−466909.	−	466909.i	−0.483198	−	0.483198i	−0.906151	+	0.422953i	$0.860993\pi$
$984$		0			0
$985$	383985.	+	54855.0i	0.395769	+	0.0565384i
$986$		0			0
$987$	−662418.	+	662418.i	−0.679983	+	0.679983i
$988$		0			0
$989$			585882.i			0.598987i
$990$		0			0
$991$	901238.			0.917682			0.458841	−	0.888518i	$-0.348265\pi$
$991$	901238.			0.917682			0.458841	+	0.888518i	$0.348265\pi$
$992$		0			0
$993$	−486342.	−	486342.i	−0.493223	−	0.493223i
$994$		0			0
$995$	−763200.	+	572400.i	−0.770890	+	0.578167i
$996$		0			0
$997$	152149.	−	152149.i	0.153066	−	0.153066i	−0.626420	−	0.779486i	$-0.715480\pi$
$997$	152149.	−	152149.i	0.153066	−	0.153066i	0.779486	+	0.626420i	$0.215480\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.5.p.b.33.1		2
4.3	odd	2		10.5.c.a.3.1	✓	2
5.2	odd	4	inner	80.5.p.b.17.1		2
5.3	odd	4		400.5.p.c.257.1		2
5.4	even	2		400.5.p.c.193.1		2
8.3	odd	2		320.5.p.b.193.1		2
8.5	even	2		320.5.p.i.193.1		2
12.11	even	2		90.5.g.b.73.1		2
20.3	even	4		50.5.c.b.7.1		2
20.7	even	4		10.5.c.a.7.1	yes	2
20.19	odd	2		50.5.c.b.43.1		2
40.27	even	4		320.5.p.b.257.1		2
40.37	odd	4		320.5.p.i.257.1		2
60.23	odd	4		450.5.g.a.307.1		2
60.47	odd	4		90.5.g.b.37.1		2
60.59	even	2		450.5.g.a.343.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.5.c.a.3.1	✓	2	4.3	odd	2
10.5.c.a.7.1	yes	2	20.7	even	4
50.5.c.b.7.1		2	20.3	even	4
50.5.c.b.43.1		2	20.19	odd	2
80.5.p.b.17.1		2	5.2	odd	4	inner
80.5.p.b.33.1		2	1.1	even	1	trivial
90.5.g.b.37.1		2	60.47	odd	4
90.5.g.b.73.1		2	12.11	even	2
320.5.p.b.193.1		2	8.3	odd	2
320.5.p.b.257.1		2	40.27	even	4
320.5.p.i.193.1		2	8.5	even	2
320.5.p.i.257.1		2	40.37	odd	4
400.5.p.c.193.1		2	5.4	even	2
400.5.p.c.257.1		2	5.3	odd	4
450.5.g.a.307.1		2	60.23	odd	4
450.5.g.a.343.1		2	60.59	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-9.00000 - 9.00000i) q^{3} +(-15.0000 - 20.0000i) q^{5} +(-29.0000 + 29.0000i) q^{7} +81.0000i q^{9} +118.000 q^{11} +(69.0000 + 69.0000i) q^{13} +(-45.0000 + 315.000i) q^{15} +(-271.000 + 271.000i) q^{17} +280.000i q^{19} +522.000 q^{21} +(-269.000 - 269.000i) q^{23} +(-175.000 + 600.000i) q^{25} -680.000i q^{29} -202.000 q^{31} +(-1062.00 - 1062.00i) q^{33} +(1015.00 + 145.000i) q^{35} +(-651.000 + 651.000i) q^{37} -1242.00i q^{39} +1682.00 q^{41} +(-1089.00 - 1089.00i) q^{43} +(1620.00 - 1215.00i) q^{45} +(-1269.00 + 1269.00i) q^{47} +719.000i q^{49} +4878.00 q^{51} +(-611.000 - 611.000i) q^{53} +(-1770.00 - 2360.00i) q^{55} +(2520.00 - 2520.00i) q^{57} +1160.00i q^{59} -5598.00 q^{61} +(-2349.00 - 2349.00i) q^{63} +(345.000 - 2415.00i) q^{65} +(751.000 - 751.000i) q^{67} +4842.00i q^{69} -6442.00 q^{71} +(-2951.00 - 2951.00i) q^{73} +(6975.00 - 3825.00i) q^{75} +(-3422.00 + 3422.00i) q^{77} +10560.0i q^{79} +6561.00 q^{81} +(6231.00 + 6231.00i) q^{83} +(9485.00 + 1355.00i) q^{85} +(-6120.00 + 6120.00i) q^{87} +14480.0i q^{89} -4002.00 q^{91} +(1818.00 + 1818.00i) q^{93} +(5600.00 - 4200.00i) q^{95} +(-7311.00 + 7311.00i) q^{97} +9558.00i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 18 q^{3} - 30 q^{5} - 58 q^{7} + 236 q^{11} + 138 q^{13} - 90 q^{15} - 542 q^{17} + 1044 q^{21} - 538 q^{23} - 350 q^{25} - 404 q^{31} - 2124 q^{33} + 2030 q^{35} - 1302 q^{37} + 3364 q^{41} - 2178 q^{43}+ \cdots - 14622 q^{97}+O(q^{100}) \) 2 * q - 18 * q^3 - 30 * q^5 - 58 * q^7 + 236 * q^11 + 138 * q^13 - 90 * q^15 - 542 * q^17 + 1044 * q^21 - 538 * q^23 - 350 * q^25 - 404 * q^31 - 2124 * q^33 + 2030 * q^35 - 1302 * q^37 + 3364 * q^41 - 2178 * q^43 + 3240 * q^45 - 2538 * q^47 + 9756 * q^51 - 1222 * q^53 - 3540 * q^55 + 5040 * q^57 - 11196 * q^61 - 4698 * q^63 + 690 * q^65 + 1502 * q^67 - 12884 * q^71 - 5902 * q^73 + 13950 * q^75 - 6844 * q^77 + 13122 * q^81 + 12462 * q^83 + 18970 * q^85 - 12240 * q^87 - 8004 * q^91 + 3636 * q^93 + 11200 * q^95 - 14622 * q^97

Introduction

L-functions

Modular forms

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Database

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