LMFDB - Embedded newform 320.3.r.a.271.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(111,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("320.111");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.r (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:	$8.71936845953$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			271.16
Character	$\chi$	$=$	320.271
Dual form			320.3.r.a.111.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.96156 + 3.96156i) q^{3} +(-1.58114 - 1.58114i) q^{5} -0.171519 q^{7} +22.3880i q^{9} +O(q^{10})$	\(q+(3.96156 + 3.96156i) q^{3} +(-1.58114 - 1.58114i) q^{5} -0.171519 q^{7} +22.3880i q^{9} +(-3.37561 + 3.37561i) q^{11} +(-13.2513 + 13.2513i) q^{13} -12.5276i q^{15} +1.67091 q^{17} +(20.7019 + 20.7019i) q^{19} +(-0.679485 - 0.679485i) q^{21} +29.6804 q^{23} +5.00000i q^{25} +(-53.0373 + 53.0373i) q^{27} +(7.65510 - 7.65510i) q^{29} -34.7971i q^{31} -26.7454 q^{33} +(0.271196 + 0.271196i) q^{35} +(-10.8454 - 10.8454i) q^{37} -104.991 q^{39} -46.3942i q^{41} +(27.1102 - 27.1102i) q^{43} +(35.3985 - 35.3985i) q^{45} +38.7366i q^{47} -48.9706 q^{49} +(6.61940 + 6.61940i) q^{51} +(24.0547 + 24.0547i) q^{53} +10.6746 q^{55} +164.024i q^{57} +(37.2621 - 37.2621i) q^{59} +(35.4044 - 35.4044i) q^{61} -3.83997i q^{63} +41.9042 q^{65} +(11.1498 + 11.1498i) q^{67} +(117.581 + 117.581i) q^{69} -3.07991 q^{71} -92.3346i q^{73} +(-19.8078 + 19.8078i) q^{75} +(0.578983 - 0.578983i) q^{77} +25.0660i q^{79} -218.729 q^{81} +(87.5940 + 87.5940i) q^{83} +(-2.64193 - 2.64193i) q^{85} +60.6523 q^{87} -135.913i q^{89} +(2.27285 - 2.27285i) q^{91} +(137.851 - 137.851i) q^{93} -65.4652i q^{95} +25.0559 q^{97} +(-75.5731 - 75.5731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) $ 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	3.96156	+	3.96156i	1.32052	+	1.32052i	0.913353	+	0.407168i	$0.133483\pi$
$3$	3.96156	+	3.96156i	1.32052	+	1.32052i	0.407168	+	0.913353i	$0.366517\pi$
$4$		0			0
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$6$		0			0
$7$	−0.171519			−0.0245028			−0.0122514	−	0.999925i	$-0.503900\pi$
$7$	−0.171519			−0.0245028			−0.0122514	+	0.999925i	$0.503900\pi$
$8$		0			0
$9$			22.3880i			2.48755i
$10$		0			0
$11$	−3.37561	+	3.37561i	−0.306874	+	0.306874i	−0.843696	−	0.536822i	$-0.819625\pi$
$11$	−3.37561	+	3.37561i	−0.306874	+	0.306874i	0.536822	+	0.843696i	$0.319625\pi$
$12$		0			0
$13$	−13.2513	+	13.2513i	−1.01933	+	1.01933i	−0.0195186	+	0.999809i	$0.506213\pi$
$13$	−13.2513	+	13.2513i	−1.01933	+	1.01933i	−0.999809	+	0.0195186i	$0.993787\pi$
$14$		0			0
$15$		−	12.5276i		−	0.835171i
$16$		0			0
$17$	1.67091			0.0982886			0.0491443	−	0.998792i	$-0.484351\pi$
$17$	1.67091			0.0982886			0.0491443	+	0.998792i	$0.484351\pi$
$18$		0			0
$19$	20.7019	+	20.7019i	1.08957	+	1.08957i	0.995572	+	0.0940016i	$0.0299659\pi$
$19$	20.7019	+	20.7019i	1.08957	+	1.08957i	0.0940016	+	0.995572i	$0.470034\pi$
$20$		0			0
$21$	−0.679485	−	0.679485i	−0.0323564	−	0.0323564i
$22$		0			0
$23$	29.6804			1.29045			0.645227	−	0.763991i	$-0.276763\pi$
$23$	29.6804			1.29045			0.645227	+	0.763991i	$0.276763\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	−53.0373	+	53.0373i	−1.96434	+	1.96434i
$28$		0			0
$29$	7.65510	−	7.65510i	0.263969	−	0.263969i	−0.562695	−	0.826664i	$-0.690236\pi$
$29$	7.65510	−	7.65510i	0.263969	−	0.263969i	0.826664	+	0.562695i	$0.190236\pi$
$30$		0			0
$31$		−	34.7971i		−	1.12249i	−0.827651	−	0.561244i	$-0.810323\pi$
$31$		−	34.7971i		−	1.12249i	0.827651	−	0.561244i	$-0.189677\pi$
$32$		0			0
$33$	−26.7454			−0.810467
$34$		0			0
$35$	0.271196	+	0.271196i	0.00774845	+	0.00774845i
$36$		0			0
$37$	−10.8454	−	10.8454i	−0.293119	−	0.293119i	0.545192	−	0.838311i	$-0.316457\pi$
$37$	−10.8454	−	10.8454i	−0.293119	−	0.293119i	−0.838311	+	0.545192i	$0.816457\pi$
$38$		0			0
$39$	−104.991			−2.69209
$40$		0			0
$41$		−	46.3942i		−	1.13157i	−0.824554	−	0.565783i	$-0.808574\pi$
$41$		−	46.3942i		−	1.13157i	0.824554	−	0.565783i	$-0.191426\pi$
$42$		0			0
$43$	27.1102	−	27.1102i	0.630470	−	0.630470i	−0.317716	−	0.948186i	$-0.602916\pi$
$43$	27.1102	−	27.1102i	0.630470	−	0.630470i	0.948186	+	0.317716i	$0.102916\pi$
$44$		0			0
$45$	35.3985	−	35.3985i	0.786633	−	0.786633i
$46$		0			0
$47$			38.7366i			0.824182i	0.911143	+	0.412091i	$0.135202\pi$
$47$			38.7366i			0.824182i	−0.911143	+	0.412091i	$0.864798\pi$
$48$		0			0
$49$	−48.9706			−0.999400
$50$		0			0
$51$	6.61940	+	6.61940i	0.129792	+	0.129792i
$52$		0			0
$53$	24.0547	+	24.0547i	0.453863	+	0.453863i	0.896634	−	0.442772i	$-0.146005\pi$
$53$	24.0547	+	24.0547i	0.453863	+	0.453863i	−0.442772	+	0.896634i	$0.646005\pi$
$54$		0			0
$55$	10.6746			0.194084
$56$		0			0
$57$			164.024i			2.87761i
$58$		0			0
$59$	37.2621	−	37.2621i	0.631562	−	0.631562i	−0.316898	−	0.948460i	$-0.602641\pi$
$59$	37.2621	−	37.2621i	0.631562	−	0.631562i	0.948460	+	0.316898i	$0.102641\pi$
$60$		0			0
$61$	35.4044	−	35.4044i	0.580401	−	0.580401i	−0.354613	−	0.935013i	$-0.615387\pi$
$61$	35.4044	−	35.4044i	0.580401	−	0.580401i	0.935013	+	0.354613i	$0.115387\pi$
$62$		0			0
$63$		−	3.83997i		−	0.0609519i
$64$		0			0
$65$	41.9042			0.644680
$66$		0			0
$67$	11.1498	+	11.1498i	0.166415	+	0.166415i	0.785402	−	0.618986i	$-0.212456\pi$
$67$	11.1498	+	11.1498i	0.166415	+	0.166415i	−0.618986	+	0.785402i	$0.712456\pi$
$68$		0			0
$69$	117.581	+	117.581i	1.70407	+	1.70407i
$70$		0			0
$71$	−3.07991			−0.0433790			−0.0216895	−	0.999765i	$-0.506905\pi$
$71$	−3.07991			−0.0433790			−0.0216895	+	0.999765i	$0.506905\pi$
$72$		0			0
$73$		−	92.3346i		−	1.26486i	−0.774619	−	0.632429i	$-0.782058\pi$
$73$		−	92.3346i		−	1.26486i	0.774619	−	0.632429i	$-0.217942\pi$
$74$		0			0
$75$	−19.8078	+	19.8078i	−0.264104	+	0.264104i
$76$		0			0
$77$	0.578983	−	0.578983i	0.00751925	−	0.00751925i
$78$		0			0
$79$			25.0660i			0.317291i	0.987336	+	0.158645i	$0.0507127\pi$
$79$			25.0660i			0.317291i	−0.987336	+	0.158645i	$0.949287\pi$
$80$		0			0
$81$	−218.729			−2.70036
$82$		0			0
$83$	87.5940	+	87.5940i	1.05535	+	1.05535i	0.998376	+	0.0569734i	$0.0181450\pi$
$83$	87.5940	+	87.5940i	1.05535	+	1.05535i	0.0569734	+	0.998376i	$0.481855\pi$
$84$		0			0
$85$	−2.64193	−	2.64193i	−0.0310816	−	0.0310816i
$86$		0			0
$87$	60.6523			0.697153
$88$		0			0
$89$		−	135.913i		−	1.52712i	−0.645738	−	0.763559i	$-0.723450\pi$
$89$		−	135.913i		−	1.52712i	0.645738	−	0.763559i	$-0.276550\pi$
$90$		0			0
$91$	2.27285	−	2.27285i	0.0249764	−	0.0249764i
$92$		0			0
$93$	137.851	−	137.851i	1.48227	−	1.48227i
$94$		0			0
$95$		−	65.4652i		−	0.689107i
$96$		0			0
$97$	25.0559			0.258308			0.129154	−	0.991625i	$-0.458774\pi$
$97$	25.0559			0.258308			0.129154	+	0.991625i	$0.458774\pi$
$98$		0			0
$99$	−75.5731	−	75.5731i	−0.763364	−	0.763364i
$100$		0			0
$101$	21.6565	+	21.6565i	0.214421	+	0.214421i	0.806143	−	0.591721i	$-0.201551\pi$
$101$	21.6565	+	21.6565i	0.214421	+	0.214421i	−0.591721	+	0.806143i	$0.701551\pi$
$102$		0			0
$103$	−59.5422			−0.578079			−0.289040	−	0.957317i	$-0.593336\pi$
$103$	−59.5422			−0.578079			−0.289040	+	0.957317i	$0.593336\pi$
$104$		0			0
$105$			2.14872i			0.0204640i
$106$		0			0
$107$	12.0199	−	12.0199i	0.112336	−	0.112336i	−0.648705	−	0.761040i	$-0.724689\pi$
$107$	12.0199	−	12.0199i	0.112336	−	0.112336i	0.761040	+	0.648705i	$0.224689\pi$
$108$		0			0
$109$	−67.5716	+	67.5716i	−0.619923	+	0.619923i	−0.945511	−	0.325589i	$-0.894437\pi$
$109$	−67.5716	+	67.5716i	−0.619923	+	0.619923i	0.325589	+	0.945511i	$0.394437\pi$
$110$		0			0
$111$		−	85.9294i		−	0.774139i
$112$		0			0
$113$	58.3821			0.516656			0.258328	−	0.966057i	$-0.416829\pi$
$113$	58.3821			0.516656			0.258328	+	0.966057i	$0.416829\pi$
$114$		0			0
$115$	−46.9289	−	46.9289i	−0.408077	−	0.408077i
$116$		0			0
$117$	−296.669	−	296.669i	−2.53563	−	2.53563i
$118$		0			0
$119$	−0.286593			−0.00240834
$120$		0			0
$121$			98.2105i			0.811657i
$122$		0			0
$123$	183.794	−	183.794i	1.49426	−	1.49426i
$124$		0			0
$125$	7.90569	−	7.90569i	0.0632456	−	0.0632456i
$126$		0			0
$127$		−	209.273i		−	1.64782i	−0.566721	−	0.823910i	$-0.691788\pi$
$127$		−	209.273i		−	1.64782i	0.566721	−	0.823910i	$-0.308212\pi$
$128$		0			0
$129$	214.798			1.66510
$130$		0			0
$131$	89.9316	+	89.9316i	0.686501	+	0.686501i	0.961457	−	0.274956i	$-0.0886633\pi$
$131$	89.9316	+	89.9316i	0.686501	+	0.686501i	−0.274956	+	0.961457i	$0.588663\pi$
$132$		0			0
$133$	−3.55078	−	3.55078i	−0.0266976	−	0.0266976i
$134$		0			0
$135$	167.719			1.24236
$136$		0			0
$137$		−	10.0315i		−	0.0732228i	−0.999330	−	0.0366114i	$-0.988344\pi$
$137$		−	10.0315i		−	0.0732228i	0.999330	−	0.0366114i	$-0.0116564\pi$
$138$		0			0
$139$	−3.11728	+	3.11728i	−0.0224265	+	0.0224265i	−0.718231	−	0.695805i	$-0.755048\pi$
$139$	−3.11728	+	3.11728i	−0.0224265	+	0.0224265i	0.695805	+	0.718231i	$0.255048\pi$
$140$		0			0
$141$	−153.457	+	153.457i	−1.08835	+	1.08835i
$142$		0			0
$143$		−	89.4623i		−	0.625610i
$144$		0			0
$145$	−24.2075			−0.166949
$146$		0			0
$147$	−194.000	−	194.000i	−1.31973	−	1.31973i
$148$		0			0
$149$	−65.2299	−	65.2299i	−0.437785	−	0.437785i	0.453481	−	0.891266i	$-0.350182\pi$
$149$	−65.2299	−	65.2299i	−0.437785	−	0.437785i	−0.891266	+	0.453481i	$0.850182\pi$
$150$		0			0
$151$	−152.779			−1.01178			−0.505891	−	0.862597i	$-0.668836\pi$
$151$	−152.779			−1.01178			−0.505891	+	0.862597i	$0.668836\pi$
$152$		0			0
$153$			37.4082i			0.244498i
$154$		0			0
$155$	−55.0190	+	55.0190i	−0.354962	+	0.354962i
$156$		0			0
$157$	−32.0163	+	32.0163i	−0.203926	+	0.203926i	−0.801680	−	0.597754i	$-0.796060\pi$
$157$	−32.0163	+	32.0163i	−0.203926	+	0.203926i	0.597754	+	0.801680i	$0.296060\pi$
$158$		0			0
$159$			190.589i			1.19867i
$160$		0			0
$161$	−5.09077			−0.0316197
$162$		0			0
$163$	13.6884	+	13.6884i	0.0839782	+	0.0839782i	0.747848	−	0.663870i	$-0.231087\pi$
$163$	13.6884	+	13.6884i	0.0839782	+	0.0839782i	−0.663870	+	0.747848i	$0.731087\pi$
$164$		0			0
$165$	42.2882	+	42.2882i	0.256292	+	0.256292i
$166$		0			0
$167$	165.352			0.990135			0.495067	−	0.868855i	$-0.335143\pi$
$167$	165.352			0.990135			0.495067	+	0.868855i	$0.335143\pi$
$168$		0			0
$169$		−	182.192i		−	1.07806i
$170$		0			0
$171$	−463.473	+	463.473i	−2.71037	+	2.71037i
$172$		0			0
$173$	−69.7841	+	69.7841i	−0.403376	+	0.403376i	−0.879421	−	0.476045i	$-0.842070\pi$
$173$	−69.7841	+	69.7841i	−0.403376	+	0.403376i	0.476045	+	0.879421i	$0.342070\pi$
$174$		0			0
$175$		−	0.857597i		−	0.00490055i
$176$		0			0
$177$	295.233			1.66798
$178$		0			0
$179$	28.0124	+	28.0124i	0.156494	+	0.156494i	0.781011	−	0.624517i	$-0.214704\pi$
$179$	28.0124	+	28.0124i	0.156494	+	0.156494i	−0.624517	+	0.781011i	$0.714704\pi$
$180$		0			0
$181$	171.169	+	171.169i	0.945686	+	0.945686i	0.998599	−	0.0529135i	$-0.0168508\pi$
$181$	171.169	+	171.169i	0.945686	+	0.945686i	−0.0529135	+	0.998599i	$0.516851\pi$
$182$		0			0
$183$	280.514			1.53286
$184$		0			0
$185$			34.2962i			0.185385i
$186$		0			0
$187$	−5.64033	+	5.64033i	−0.0301622	+	0.0301622i
$188$		0			0
$189$	9.09692	−	9.09692i	0.0481318	−	0.0481318i
$190$		0			0
$191$			255.795i			1.33924i	0.742704	+	0.669620i	$0.233543\pi$
$191$			255.795i			1.33924i	−0.742704	+	0.669620i	$0.766457\pi$
$192$		0			0
$193$	324.401			1.68083			0.840417	−	0.541941i	$-0.182310\pi$
$193$	324.401			1.68083			0.840417	+	0.541941i	$0.182310\pi$
$194$		0			0
$195$	166.006	+	166.006i	0.851313	+	0.851313i
$196$		0			0
$197$	138.367	+	138.367i	0.702370	+	0.702370i	0.964919	−	0.262549i	$-0.0845631\pi$
$197$	138.367	+	138.367i	0.702370	+	0.702370i	−0.262549	+	0.964919i	$0.584563\pi$
$198$		0			0
$199$	−244.276			−1.22752			−0.613759	−	0.789494i	$-0.710343\pi$
$199$	−244.276			−1.22752			−0.613759	+	0.789494i	$0.710343\pi$
$200$		0			0
$201$			88.3414i			0.439509i
$202$		0			0
$203$	−1.31300	+	1.31300i	−0.00646797	+	0.00646797i
$204$		0			0
$205$	−73.3557	+	73.3557i	−0.357833	+	0.357833i
$206$		0			0
$207$			664.485i			3.21007i
$208$		0			0
$209$	−139.763			−0.668723
$210$		0			0
$211$	−128.059	−	128.059i	−0.606913	−	0.606913i	0.335225	−	0.942138i	$-0.391188\pi$
$211$	−128.059	−	128.059i	−0.606913	−	0.606913i	−0.942138	+	0.335225i	$0.891188\pi$
$212$		0			0
$213$	−12.2013	−	12.2013i	−0.0572829	−	0.0572829i
$214$		0			0
$215$	−85.7300			−0.398744
$216$		0			0
$217$			5.96838i			0.0275040i
$218$		0			0
$219$	365.789	−	365.789i	1.67027	−	1.67027i
$220$		0			0
$221$	−22.1416	+	22.1416i	−0.100188	+	0.100188i
$222$		0			0
$223$			158.100i			0.708966i	0.935062	+	0.354483i	$0.115343\pi$
$223$			158.100i			0.708966i	−0.935062	+	0.354483i	$0.884657\pi$
$224$		0			0
$225$	−111.940			−0.497510
$226$		0			0
$227$	18.0851	+	18.0851i	0.0796702	+	0.0796702i	0.745819	−	0.666149i	$-0.232058\pi$
$227$	18.0851	+	18.0851i	0.0796702	+	0.0796702i	−0.666149	+	0.745819i	$0.732058\pi$
$228$		0			0
$229$	−280.982	−	280.982i	−1.22700	−	1.22700i	−0.965095	−	0.261900i	$-0.915651\pi$
$229$	−280.982	−	280.982i	−1.22700	−	1.22700i	−0.261900	−	0.965095i	$-0.584349\pi$
$230$		0			0
$231$	4.58735			0.0198587
$232$		0			0
$233$		−	210.065i		−	0.901565i	−0.892634	−	0.450782i	$-0.851145\pi$
$233$		−	210.065i		−	0.901565i	0.892634	−	0.450782i	$-0.148855\pi$
$234$		0			0
$235$	61.2479	−	61.2479i	0.260629	−	0.260629i
$236$		0			0
$237$	−99.3005	+	99.3005i	−0.418989	+	0.418989i
$238$		0			0
$239$		−	43.3929i		−	0.181560i	−0.995871	−	0.0907802i	$-0.971064\pi$
$239$		−	43.3929i		−	0.181560i	0.995871	−	0.0907802i	$-0.0289361\pi$
$240$		0			0
$241$	−395.278			−1.64016			−0.820079	−	0.572250i	$-0.806071\pi$
$241$	−395.278			−1.64016			−0.820079	+	0.572250i	$0.806071\pi$
$242$		0			0
$243$	−389.174	−	389.174i	−1.60154	−	1.60154i
$244$		0			0
$245$	77.4293	+	77.4293i	0.316038	+	0.316038i
$246$		0			0
$247$	−548.653			−2.22127
$248$		0			0
$249$			694.018i			2.78722i
$250$		0			0
$251$	−38.4294	+	38.4294i	−0.153105	+	0.153105i	−0.779503	−	0.626398i	$-0.784528\pi$
$251$	−38.4294	+	38.4294i	−0.153105	+	0.153105i	0.626398	+	0.779503i	$0.284528\pi$
$252$		0			0
$253$	−100.190	+	100.190i	−0.396006	+	0.396006i
$254$		0			0
$255$		−	20.9324i		−	0.0820877i
$256$		0			0
$257$	53.0395			0.206379			0.103190	−	0.994662i	$-0.467095\pi$
$257$	53.0395			0.206379			0.103190	+	0.994662i	$0.467095\pi$
$258$		0			0
$259$	1.86019	+	1.86019i	0.00718222	+	0.00718222i
$260$		0			0
$261$	171.382	+	171.382i	0.656636	+	0.656636i
$262$		0			0
$263$	−50.5789			−0.192315			−0.0961576	−	0.995366i	$-0.530655\pi$
$263$	−50.5789			−0.192315			−0.0961576	+	0.995366i	$0.530655\pi$
$264$		0			0
$265$		−	76.0677i		−	0.287048i
$266$		0			0
$267$	538.430	−	538.430i	2.01659	−	2.01659i
$268$		0			0
$269$	−50.4367	+	50.4367i	−0.187497	+	0.187497i	−0.794613	−	0.607116i	$-0.792326\pi$
$269$	−50.4367	+	50.4367i	−0.187497	+	0.187497i	0.607116	+	0.794613i	$0.292326\pi$
$270$		0			0
$271$		−	201.624i		−	0.744000i	−0.928233	−	0.372000i	$-0.878672\pi$
$271$		−	201.624i		−	0.744000i	0.928233	−	0.372000i	$-0.121328\pi$
$272$		0			0
$273$	18.0081			0.0659636
$274$		0			0
$275$	−16.8781	−	16.8781i	−0.0613748	−	0.0613748i
$276$		0			0
$277$	−65.2902	−	65.2902i	−0.235705	−	0.235705i	0.579364	−	0.815069i	$-0.303301\pi$
$277$	−65.2902	−	65.2902i	−0.235705	−	0.235705i	−0.815069	+	0.579364i	$0.803301\pi$
$278$		0			0
$279$	779.036			2.79224
$280$		0			0
$281$		−	543.533i		−	1.93428i	−0.254241	−	0.967141i	$-0.581826\pi$
$281$		−	543.533i		−	1.93428i	0.254241	−	0.967141i	$-0.418174\pi$
$282$		0			0
$283$	−104.692	+	104.692i	−0.369935	+	0.369935i	−0.867454	−	0.497518i	$-0.834245\pi$
$283$	−104.692	+	104.692i	−0.369935	+	0.369935i	0.497518	+	0.867454i	$0.334245\pi$
$284$		0			0
$285$	259.344	−	259.344i	0.909980	−	0.909980i
$286$		0			0
$287$			7.95751i			0.0277265i
$288$		0			0
$289$	−286.208			−0.990339
$290$		0			0
$291$	99.2604	+	99.2604i	0.341101	+	0.341101i
$292$		0			0
$293$	278.881	+	278.881i	0.951813	+	0.951813i	0.998891	−	0.0470785i	$-0.0149911\pi$
$293$	278.881	+	278.881i	0.951813	+	0.951813i	−0.0470785	+	0.998891i	$0.514991\pi$
$294$		0			0
$295$	−117.833			−0.399435
$296$		0			0
$297$		−	358.066i		−	1.20561i
$298$		0			0
$299$	−393.303	+	393.303i	−1.31540	+	1.31540i
$300$		0			0
$301$	−4.64992	+	4.64992i	−0.0154483	+	0.0154483i
$302$		0			0
$303$			171.588i			0.566296i
$304$		0			0
$305$	−111.959			−0.367078
$306$		0			0
$307$	−165.375	−	165.375i	−0.538682	−	0.538682i	0.384460	−	0.923142i	$-0.374388\pi$
$307$	−165.375	−	165.375i	−0.538682	−	0.538682i	−0.923142	+	0.384460i	$0.874388\pi$
$308$		0			0
$309$	−235.880	−	235.880i	−0.763366	−	0.763366i
$310$		0			0
$311$	569.732			1.83194			0.915968	−	0.401252i	$-0.131425\pi$
$311$	569.732			1.83194			0.915968	+	0.401252i	$0.131425\pi$
$312$		0			0
$313$			167.015i			0.533593i	0.963753	+	0.266797i	$0.0859652\pi$
$313$			167.015i			0.533593i	−0.963753	+	0.266797i	$0.914035\pi$
$314$		0			0
$315$	−6.07152	+	6.07152i	−0.0192747	+	0.0192747i
$316$		0			0
$317$	−326.774	+	326.774i	−1.03083	+	1.03083i	−0.0313243	+	0.999509i	$0.509972\pi$
$317$	−326.774	+	326.774i	−1.03083	+	1.03083i	−0.999509	+	0.0313243i	$0.990028\pi$
$318$		0			0
$319$			51.6813i			0.162010i
$320$		0			0
$321$	95.2353			0.296683
$322$		0			0
$323$	34.5909	+	34.5909i	0.107093	+	0.107093i
$324$		0			0
$325$	−66.2563	−	66.2563i	−0.203866	−	0.203866i
$326$		0			0
$327$	−535.378			−1.63724
$328$		0			0
$329$		−	6.64407i		−	0.0201947i
$330$		0			0
$331$	200.293	−	200.293i	0.605115	−	0.605115i	−0.336550	−	0.941665i	$-0.609260\pi$
$331$	200.293	−	200.293i	0.605115	−	0.605115i	0.941665	+	0.336550i	$0.109260\pi$
$332$		0			0
$333$	242.806	−	242.806i	0.729148	−	0.729148i
$334$		0			0
$335$		−	35.2588i		−	0.105250i
$336$		0			0
$337$	10.9488			0.0324891			0.0162445	−	0.999868i	$-0.494829\pi$
$337$	10.9488			0.0324891			0.0162445	+	0.999868i	$0.494829\pi$
$338$		0			0
$339$	231.284	+	231.284i	0.682255	+	0.682255i
$340$		0			0
$341$	117.461	+	117.461i	0.344462	+	0.344462i
$342$		0			0
$343$	16.8038			0.0489908
$344$		0			0
$345$		−	371.824i		−	1.07775i
$346$		0			0
$347$	34.7700	−	34.7700i	0.100202	−	0.100202i	−0.655229	−	0.755430i	$-0.727428\pi$
$347$	34.7700	−	34.7700i	0.100202	−	0.100202i	0.755430	+	0.655229i	$0.227428\pi$
$348$		0			0
$349$	−169.969	+	169.969i	−0.487016	+	0.487016i	−0.907363	−	0.420347i	$-0.861908\pi$
$349$	−169.969	+	169.969i	−0.487016	+	0.487016i	0.420347	+	0.907363i	$0.361908\pi$
$350$		0			0
$351$		−	1405.62i		−	4.00462i
$352$		0			0
$353$	196.803			0.557516			0.278758	−	0.960361i	$-0.410077\pi$
$353$	196.803			0.557516			0.278758	+	0.960361i	$0.410077\pi$
$354$		0			0
$355$	4.86976	+	4.86976i	0.0137176	+	0.0137176i
$356$		0			0
$357$	−1.13535	−	1.13535i	−0.00318026	−	0.00318026i
$358$		0			0
$359$	80.5658			0.224417			0.112209	−	0.993685i	$-0.464208\pi$
$359$	80.5658			0.224417			0.112209	+	0.993685i	$0.464208\pi$
$360$		0			0
$361$			496.137i			1.37434i
$362$		0			0
$363$	−389.067	+	389.067i	−1.07181	+	1.07181i
$364$		0			0
$365$	−145.994	+	145.994i	−0.399983	+	0.399983i
$366$		0			0
$367$			691.037i			1.88294i	0.337104	+	0.941468i	$0.390553\pi$
$367$			691.037i			1.88294i	−0.337104	+	0.941468i	$0.609447\pi$
$368$		0			0
$369$	1038.67			2.81483
$370$		0			0
$371$	−4.12585	−	4.12585i	−0.0111209	−	0.0111209i
$372$		0			0
$373$	−484.976	−	484.976i	−1.30020	−	1.30020i	−0.928252	−	0.371952i	$-0.878689\pi$
$373$	−484.976	−	484.976i	−1.30020	−	1.30020i	−0.371952	−	0.928252i	$-0.621311\pi$
$374$		0			0
$375$	62.6378			0.167034
$376$		0			0
$377$			202.879i			0.538142i
$378$		0			0
$379$	−205.910	+	205.910i	−0.543298	+	0.543298i	−0.924494	−	0.381196i	$-0.875512\pi$
$379$	−205.910	+	205.910i	−0.543298	+	0.543298i	0.381196	+	0.924494i	$0.375512\pi$
$380$		0			0
$381$	829.048	−	829.048i	2.17598	−	2.17598i
$382$		0			0
$383$		−	616.816i		−	1.61049i	−0.592945	−	0.805243i	$-0.702035\pi$
$383$		−	616.816i		−	1.61049i	0.592945	−	0.805243i	$-0.297965\pi$
$384$		0			0
$385$	−1.83090			−0.00475559
$386$		0			0
$387$	606.942	+	606.942i	1.56833	+	1.56833i
$388$		0			0
$389$	−122.768	−	122.768i	−0.315599	−	0.315599i	0.531475	−	0.847074i	$-0.321638\pi$
$389$	−122.768	−	122.768i	−0.315599	−	0.315599i	−0.847074	+	0.531475i	$0.821638\pi$
$390$		0			0
$391$	49.5932			0.126837
$392$		0			0
$393$			712.540i			1.81308i
$394$		0			0
$395$	39.6328	−	39.6328i	0.100336	−	0.100336i
$396$		0			0
$397$	314.618	−	314.618i	0.792489	−	0.792489i	−0.189410	−	0.981898i	$-0.560657\pi$
$397$	314.618	−	314.618i	0.792489	−	0.792489i	0.981898	+	0.189410i	$0.0606574\pi$
$398$		0			0
$399$		−	28.1332i		−	0.0705094i
$400$		0			0
$401$	−268.277			−0.669020			−0.334510	−	0.942392i	$-0.608571\pi$
$401$	−268.277			−0.669020			−0.334510	+	0.942392i	$0.608571\pi$
$402$		0			0
$403$	461.106	+	461.106i	1.14418	+	1.14418i
$404$		0			0
$405$	345.841	+	345.841i	0.853929	+	0.853929i
$406$		0			0
$407$	73.2197			0.179901
$408$		0			0
$409$		−	39.2885i		−	0.0960598i	−0.998846	−	0.0480299i	$-0.984706\pi$
$409$		−	39.2885i		−	0.0960598i	0.998846	−	0.0480299i	$-0.0152943\pi$
$410$		0			0
$411$	39.7405	−	39.7405i	0.0966922	−	0.0966922i
$412$		0			0
$413$	−6.39118	+	6.39118i	−0.0154750	+	0.0154750i
$414$		0			0
$415$		−	276.996i		−	0.667461i
$416$		0			0
$417$	−24.6986			−0.0592292
$418$		0			0
$419$	−496.748	−	496.748i	−1.18556	−	1.18556i	−0.978283	−	0.207272i	$-0.933541\pi$
$419$	−496.748	−	496.748i	−1.18556	−	1.18556i	−0.207272	−	0.978283i	$-0.566459\pi$
$420$		0			0
$421$	−364.178	−	364.178i	−0.865031	−	0.865031i	0.126886	−	0.991917i	$-0.459502\pi$
$421$	−364.178	−	364.178i	−0.865031	−	0.865031i	−0.991917	+	0.126886i	$0.959502\pi$
$422$		0			0
$423$	−867.233			−2.05020
$424$		0			0
$425$			8.35453i			0.0196577i
$426$		0			0
$427$	−6.07255	+	6.07255i	−0.0142214	+	0.0142214i
$428$		0			0
$429$	354.410	−	354.410i	0.826131	−	0.826131i
$430$		0			0
$431$			20.0721i			0.0465710i	0.999729	+	0.0232855i	$0.00741267\pi$
$431$			20.0721i			0.0465710i	−0.999729	+	0.0232855i	$0.992587\pi$
$432$		0			0
$433$	−232.812			−0.537672			−0.268836	−	0.963186i	$-0.586639\pi$
$433$	−232.812			−0.537672			−0.268836	+	0.963186i	$0.586639\pi$
$434$		0			0
$435$	−95.8997	−	95.8997i	−0.220459	−	0.220459i
$436$		0			0
$437$	614.441	+	614.441i	1.40604	+	1.40604i
$438$		0			0
$439$	−22.2811			−0.0507541			−0.0253771	−	0.999678i	$-0.508079\pi$
$439$	−22.2811			−0.0507541			−0.0253771	+	0.999678i	$0.508079\pi$
$440$		0			0
$441$		−	1096.35i		−	2.48606i
$442$		0			0
$443$	35.0164	−	35.0164i	0.0790437	−	0.0790437i	−0.666480	−	0.745523i	$-0.732200\pi$
$443$	35.0164	−	35.0164i	0.0790437	−	0.0790437i	0.745523	+	0.666480i	$0.232200\pi$
$444$		0			0
$445$	−214.898	+	214.898i	−0.482917	+	0.482917i
$446$		0			0
$447$		−	516.825i		−	1.15621i
$448$		0			0
$449$	−412.188			−0.918014			−0.459007	−	0.888433i	$-0.651795\pi$
$449$	−412.188			−0.918014			−0.459007	+	0.888433i	$0.651795\pi$
$450$		0			0
$451$	156.609	+	156.609i	0.347248	+	0.347248i
$452$		0			0
$453$	−605.244	−	605.244i	−1.33608	−	1.33608i
$454$		0			0
$455$	−7.18738			−0.0157964
$456$		0			0
$457$		−	174.028i		−	0.380805i	−0.981706	−	0.190402i	$-0.939021\pi$
$457$		−	174.028i		−	0.380805i	0.981706	−	0.190402i	$-0.0609793\pi$
$458$		0			0
$459$	−88.6203	+	88.6203i	−0.193072	+	0.193072i
$460$		0			0
$461$	464.386	−	464.386i	1.00734	−	1.00734i	0.00737146	−	0.999973i	$-0.497654\pi$
$461$	464.386	−	464.386i	1.00734	−	1.00734i	0.999973	−	0.00737146i	$-0.00234643\pi$
$462$		0			0
$463$		−	158.361i		−	0.342033i	−0.985268	−	0.171016i	$-0.945295\pi$
$463$		−	158.361i		−	0.342033i	0.985268	−	0.171016i	$-0.0547051\pi$
$464$		0			0
$465$	−435.923			−0.937469
$466$		0			0
$467$	13.3660	+	13.3660i	0.0286210	+	0.0286210i	0.721272	−	0.692651i	$-0.243558\pi$
$467$	13.3660	+	13.3660i	0.0286210	+	0.0286210i	−0.692651	+	0.721272i	$0.743558\pi$
$468$		0			0
$469$	−1.91241	−	1.91241i	−0.00407763	−	0.00407763i
$470$		0			0
$471$	−253.669			−0.538576
$472$		0			0
$473$			183.027i			0.386949i
$474$		0			0
$475$	−103.509	+	103.509i	−0.217915	+	0.217915i
$476$		0			0
$477$	−538.536	+	538.536i	−1.12901	+	1.12901i
$478$		0			0
$479$		−	457.254i		−	0.954602i	−0.878740	−	0.477301i	$-0.841615\pi$
$479$		−	457.254i		−	0.954602i	0.878740	−	0.477301i	$-0.158385\pi$
$480$		0			0
$481$	287.430			0.597569
$482$		0			0
$483$	−20.1674	−	20.1674i	−0.0417545	−	0.0417545i
$484$		0			0
$485$	−39.6168	−	39.6168i	−0.0816842	−	0.0816842i
$486$		0			0
$487$	235.510			0.483592			0.241796	−	0.970327i	$-0.422263\pi$
$487$	235.510			0.483592			0.241796	+	0.970327i	$0.422263\pi$
$488$		0			0
$489$			108.455i			0.221790i
$490$		0			0
$491$	−408.205	+	408.205i	−0.831375	+	0.831375i	−0.987705	−	0.156330i	$-0.950034\pi$
$491$	−408.205	+	408.205i	−0.831375	+	0.831375i	0.156330	+	0.987705i	$0.450034\pi$
$492$		0			0
$493$	12.7909	−	12.7909i	0.0259451	−	0.0259451i
$494$		0			0
$495$			238.983i			0.482794i
$496$		0			0
$497$	0.528264			0.00106290
$498$		0			0
$499$	−600.932	−	600.932i	−1.20427	−	1.20427i	−0.972854	−	0.231418i	$-0.925663\pi$
$499$	−600.932	−	600.932i	−1.20427	−	1.20427i	−0.231418	−	0.972854i	$-0.574337\pi$
$500$		0			0
$501$	655.054	+	655.054i	1.30749	+	1.30749i
$502$		0			0
$503$	559.682			1.11269			0.556344	−	0.830952i	$-0.312204\pi$
$503$	559.682			1.11269			0.556344	+	0.830952i	$0.312204\pi$
$504$		0			0
$505$		−	68.4840i		−	0.135612i
$506$		0			0
$507$	721.765	−	721.765i	1.42360	−	1.42360i
$508$		0			0
$509$	−56.7719	+	56.7719i	−0.111536	+	0.111536i	−0.760672	−	0.649136i	$-0.775131\pi$
$509$	−56.7719	+	56.7719i	−0.111536	+	0.111536i	0.649136	+	0.760672i	$0.275131\pi$
$510$		0			0
$511$			15.8372i			0.0309925i
$512$		0			0
$513$	−2195.94			−4.28059
$514$		0			0
$515$	94.1444	+	94.1444i	0.182805	+	0.182805i
$516$		0			0
$517$	−130.760	−	130.760i	−0.252920	−	0.252920i
$518$		0			0
$519$	−552.908			−1.06533
$520$		0			0
$521$			482.298i			0.925716i	0.886433	+	0.462858i	$0.153176\pi$
$521$			482.298i			0.925716i	−0.886433	+	0.462858i	$0.846824\pi$
$522$		0			0
$523$	221.568	−	221.568i	0.423649	−	0.423649i	−0.462809	−	0.886458i	$-0.653158\pi$
$523$	221.568	−	221.568i	0.423649	−	0.423649i	0.886458	+	0.462809i	$0.153158\pi$
$524$		0			0
$525$	3.39742	−	3.39742i	0.00647128	−	0.00647128i
$526$		0			0
$527$		−	58.1427i		−	0.110328i
$528$		0			0
$529$	351.928			0.665271
$530$		0			0
$531$	834.224	+	834.224i	1.57104	+	1.57104i
$532$		0			0
$533$	614.782	+	614.782i	1.15344	+	1.15344i
$534$		0			0
$535$	−38.0103			−0.0710473
$536$		0			0
$537$			221.946i			0.413306i
$538$		0			0
$539$	165.306	−	165.306i	0.306690	−	0.306690i
$540$		0			0
$541$	−111.572	+	111.572i	−0.206232	+	0.206232i	−0.802664	−	0.596432i	$-0.796585\pi$
$541$	−111.572	+	111.572i	−0.206232	+	0.206232i	0.596432	+	0.802664i	$0.296585\pi$
$542$		0			0
$543$			1356.19i			2.49760i
$544$		0			0
$545$	213.680			0.392073
$546$		0			0
$547$	−258.971	−	258.971i	−0.473438	−	0.473438i	0.429587	−	0.903025i	$-0.358659\pi$
$547$	−258.971	−	258.971i	−0.473438	−	0.473438i	−0.903025	+	0.429587i	$0.858659\pi$
$548$		0			0
$549$	792.633	+	792.633i	1.44378	+	1.44378i
$550$		0			0
$551$	316.950			0.575227
$552$		0			0
$553$		−	4.29930i		−	0.00777450i
$554$		0			0
$555$	−135.866	+	135.866i	−0.244804	+	0.244804i
$556$		0			0
$557$	637.308	−	637.308i	1.14418	−	1.14418i	0.156502	−	0.987678i	$-0.449978\pi$
$557$	637.308	−	637.308i	1.14418	−	1.14418i	0.987678	−	0.156502i	$-0.0500218\pi$
$558$		0			0
$559$			718.489i			1.28531i
$560$		0			0
$561$	−44.6890			−0.0796596
$562$		0			0
$563$	−456.197	−	456.197i	−0.810297	−	0.810297i	0.174381	−	0.984678i	$-0.444208\pi$
$563$	−456.197	−	456.197i	−0.810297	−	0.810297i	−0.984678	+	0.174381i	$0.944208\pi$
$564$		0			0
$565$	−92.3102	−	92.3102i	−0.163381	−	0.163381i
$566$		0			0
$567$	37.5163			0.0661663
$568$		0			0
$569$		−	43.4831i		−	0.0764202i	−0.999270	−	0.0382101i	$-0.987834\pi$
$569$		−	43.4831i		−	0.0764202i	0.999270	−	0.0382101i	$-0.0121656\pi$
$570$		0			0
$571$	448.304	−	448.304i	0.785120	−	0.785120i	−0.195570	−	0.980690i	$-0.562656\pi$
$571$	448.304	−	448.304i	0.785120	−	0.785120i	0.980690	+	0.195570i	$0.0626556\pi$
$572$		0			0
$573$	−1013.35	+	1013.35i	−1.76849	+	1.76849i
$574$		0			0
$575$			148.402i			0.258091i
$576$		0			0
$577$	−766.758			−1.32887			−0.664435	−	0.747346i	$-0.731328\pi$
$577$	−766.758			−1.32887			−0.664435	+	0.747346i	$0.731328\pi$
$578$		0			0
$579$	1285.13	+	1285.13i	2.21958	+	2.21958i
$580$		0			0
$581$	−15.0241	−	15.0241i	−0.0258590	−	0.0258590i
$582$		0			0
$583$	−162.399			−0.278557
$584$		0			0
$585$			938.149i			1.60367i
$586$		0			0
$587$	−422.279	+	422.279i	−0.719384	+	0.719384i	−0.968479	−	0.249095i	$-0.919867\pi$
$587$	−422.279	+	422.279i	−0.719384	+	0.719384i	0.249095	+	0.968479i	$0.419867\pi$
$588$		0			0
$589$	720.366	−	720.366i	1.22303	−	1.22303i
$590$		0			0
$591$			1096.30i			1.85499i
$592$		0			0
$593$	868.212			1.46410			0.732051	−	0.681250i	$-0.238563\pi$
$593$	868.212			1.46410			0.732051	+	0.681250i	$0.238563\pi$
$594$		0			0
$595$	0.453143	+	0.453143i	0.000761584	+	0.000761584i
$596$		0			0
$597$	−967.715	−	967.715i	−1.62096	−	1.62096i
$598$		0			0
$599$	−669.140			−1.11710			−0.558548	−	0.829473i	$-0.688641\pi$
$599$	−669.140			−1.11710			−0.558548	+	0.829473i	$0.688641\pi$
$600$		0			0
$601$			528.062i			0.878639i	0.898331	+	0.439319i	$0.144780\pi$
$601$			528.062i			0.878639i	−0.898331	+	0.439319i	$0.855220\pi$
$602$		0			0
$603$	−249.622	+	249.622i	−0.413966	+	0.413966i
$604$		0			0
$605$	155.284	−	155.284i	0.256668	−	0.256668i
$606$		0			0
$607$			323.639i			0.533178i	0.963810	+	0.266589i	$0.0858966\pi$
$607$			323.639i			0.533178i	−0.963810	+	0.266589i	$0.914103\pi$
$608$		0			0
$609$	−10.4030			−0.0170822
$610$		0			0
$611$	−513.309	−	513.309i	−0.840112	−	0.840112i
$612$		0			0
$613$	275.335	+	275.335i	0.449161	+	0.449161i	0.895075	−	0.445915i	$-0.147122\pi$
$613$	275.335	+	275.335i	0.449161	+	0.449161i	−0.445915	+	0.895075i	$0.647122\pi$
$614$		0			0
$615$	−581.207			−0.945052
$616$		0			0
$617$			0.213607i			0.000346203i	1.00000		0.000173102i	$5.51000e-5\pi$
$617$			0.213607i			0.000346203i	−1.00000		0.000173102i	$0.999945\pi$
$618$		0			0
$619$	25.0310	−	25.0310i	0.0404378	−	0.0404378i	−0.686599	−	0.727037i	$-0.740897\pi$
$619$	25.0310	−	25.0310i	0.0404378	−	0.0404378i	0.727037	+	0.686599i	$0.240897\pi$
$620$		0			0
$621$	−1574.17	+	1574.17i	−2.53489	+	2.53489i
$622$		0			0
$623$			23.3118i			0.0374186i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	−553.680	−	553.680i	−0.883063	−	0.883063i
$628$		0			0
$629$	−18.1216	−	18.1216i	−0.0288102	−	0.0288102i
$630$		0			0
$631$	856.751			1.35777			0.678884	−	0.734246i	$-0.262464\pi$
$631$	856.751			1.35777			0.678884	+	0.734246i	$0.262464\pi$
$632$		0			0
$633$		−	1014.62i		−	1.60288i
$634$		0			0
$635$	−330.890	+	330.890i	−0.521086	+	0.521086i
$636$		0			0
$637$	648.922	−	648.922i	1.01872	−	1.01872i
$638$		0			0
$639$		−	68.9529i		−	0.107907i
$640$		0			0
$641$	−286.443			−0.446869			−0.223434	−	0.974719i	$-0.571727\pi$
$641$	−286.443			−0.446869			−0.223434	+	0.974719i	$0.571727\pi$
$642$		0			0
$643$	870.643	+	870.643i	1.35403	+	1.35403i	0.881098	+	0.472934i	$0.156805\pi$
$643$	870.643	+	870.643i	1.35403	+	1.35403i	0.472934	+	0.881098i	$0.343195\pi$
$644$		0			0
$645$	−339.625	−	339.625i	−0.526550	−	0.526550i
$646$		0			0
$647$	982.880			1.51913			0.759567	−	0.650428i	$-0.225411\pi$
$647$	982.880			1.51913			0.759567	+	0.650428i	$0.225411\pi$
$648$		0			0
$649$			251.565i			0.387619i
$650$		0			0
$651$	−23.6441	+	23.6441i	−0.0363197	+	0.0363197i
$652$		0			0
$653$	−576.699	+	576.699i	−0.883153	+	0.883153i	−0.993854	−	0.110701i	$-0.964690\pi$
$653$	−576.699	+	576.699i	−0.883153	+	0.883153i	0.110701	+	0.993854i	$0.464690\pi$
$654$		0			0
$655$		−	284.389i		−	0.434181i
$656$		0			0
$657$	2067.18			3.14640
$658$		0			0
$659$	−339.061	−	339.061i	−0.514508	−	0.514508i	0.401397	−	0.915904i	$-0.368525\pi$
$659$	−339.061	−	339.061i	−0.514508	−	0.514508i	−0.915904	+	0.401397i	$0.868525\pi$
$660$		0			0
$661$	715.682	+	715.682i	1.08273	+	1.08273i	0.996254	+	0.0864713i	$0.0275591\pi$
$661$	715.682	+	715.682i	1.08273	+	1.08273i	0.0864713	+	0.996254i	$0.472441\pi$
$662$		0			0
$663$	−175.431			−0.264601
$664$		0			0
$665$			11.2285i			0.0168850i
$666$		0			0
$667$	227.207	−	227.207i	0.340640	−	0.340640i
$668$		0			0
$669$	−626.321	+	626.321i	−0.936205	+	0.936205i
$670$		0			0
$671$			239.023i			0.356220i
$672$		0			0
$673$	965.990			1.43535			0.717675	−	0.696378i	$-0.245206\pi$
$673$	965.990			1.43535			0.717675	+	0.696378i	$0.245206\pi$
$674$		0			0
$675$	−265.186	−	265.186i	−0.392869	−	0.392869i
$676$		0			0
$677$	−109.057	−	109.057i	−0.161089	−	0.161089i	0.621960	−	0.783049i	$-0.286337\pi$
$677$	−109.057	−	109.057i	−0.161089	−	0.161089i	−0.783049	+	0.621960i	$0.786337\pi$
$678$		0			0
$679$	−4.29757			−0.00632926
$680$		0			0
$681$			143.291i			0.210412i
$682$		0			0
$683$	−666.862	+	666.862i	−0.976372	+	0.976372i	−0.999727	−	0.0233557i	$-0.992565\pi$
$683$	−666.862	+	666.862i	−0.976372	+	0.976372i	0.0233557	+	0.999727i	$0.492565\pi$
$684$		0			0
$685$	−15.8612	+	15.8612i	−0.0231551	+	0.0231551i
$686$		0			0
$687$		−	2226.26i		−	3.24055i
$688$		0			0
$689$	−637.511			−0.925270
$690$		0			0
$691$	−452.813	−	452.813i	−0.655301	−	0.655301i	0.298964	−	0.954264i	$-0.403359\pi$
$691$	−452.813	−	452.813i	−0.655301	−	0.655301i	−0.954264	+	0.298964i	$0.903359\pi$
$692$		0			0
$693$	12.9622	+	12.9622i	0.0187045	+	0.0187045i
$694$		0			0
$695$	9.85770			0.0141837
$696$		0			0
$697$		−	77.5204i		−	0.111220i
$698$		0			0
$699$	832.184	−	832.184i	1.19054	−	1.19054i
$700$		0			0
$701$	357.476	−	357.476i	0.509951	−	0.509951i	−0.404560	−	0.914511i	$-0.632575\pi$
$701$	357.476	−	357.476i	0.509951	−	0.509951i	0.914511	+	0.404560i	$0.132575\pi$
$702$		0			0
$703$		−	449.041i		−	0.638749i
$704$		0			0
$705$	485.275			0.688333
$706$		0			0
$707$	−3.71452	−	3.71452i	−0.00525391	−	0.00525391i
$708$		0			0
$709$	237.180	+	237.180i	0.334527	+	0.334527i	0.854303	−	0.519776i	$-0.173984\pi$
$709$	237.180	+	237.180i	0.334527	+	0.334527i	−0.519776	+	0.854303i	$0.673984\pi$
$710$		0			0
$711$	−561.176			−0.789277
$712$		0			0
$713$		−	1032.79i		−	1.44852i
$714$		0			0
$715$	−141.452	+	141.452i	−0.197835	+	0.197835i
$716$		0			0
$717$	171.904	−	171.904i	0.239754	−	0.239754i
$718$		0			0
$719$		−	1109.99i		−	1.54379i	−0.635748	−	0.771896i	$-0.719308\pi$
$719$		−	1109.99i		−	1.54379i	0.635748	−	0.771896i	$-0.280692\pi$
$720$		0			0
$721$	10.2126			0.0141645
$722$		0			0
$723$	−1565.92	−	1565.92i	−2.16586	−	2.16586i
$724$		0			0
$725$	38.2755	+	38.2755i	0.0527938	+	0.0527938i
$726$		0			0
$727$	1085.51			1.49313			0.746565	−	0.665312i	$-0.231702\pi$
$727$	1085.51			1.49313			0.746565	+	0.665312i	$0.231702\pi$
$728$		0			0
$729$		−	1114.91i		−	1.52938i
$730$		0			0
$731$	45.2986	−	45.2986i	0.0619680	−	0.0619680i
$732$		0			0
$733$	631.788	−	631.788i	0.861921	−	0.861921i	−0.129640	−	0.991561i	$-0.541382\pi$
$733$	631.788	−	631.788i	0.861921	−	0.861921i	0.991561	+	0.129640i	$0.0413821\pi$
$734$		0			0
$735$			613.482i			0.834669i
$736$		0			0
$737$	−75.2749			−0.102137
$738$		0			0
$739$	−107.907	−	107.907i	−0.146017	−	0.146017i	0.630319	−	0.776336i	$-0.282924\pi$
$739$	−107.907	−	107.907i	−0.146017	−	0.146017i	−0.776336	+	0.630319i	$0.782924\pi$
$740$		0			0
$741$	−2173.52	−	2173.52i	−2.93323	−	2.93323i
$742$		0			0
$743$	148.683			0.200112			0.100056	−	0.994982i	$-0.468098\pi$
$743$	148.683			0.200112			0.100056	+	0.994982i	$0.468098\pi$
$744$		0			0
$745$			206.275i			0.276879i
$746$		0			0
$747$	−1961.05	+	1961.05i	−2.62524	+	2.62524i
$748$		0			0
$749$	−2.06165	+	2.06165i	−0.00275253	+	0.00275253i
$750$		0			0
$751$			374.911i			0.499216i	0.968347	+	0.249608i	$0.0803018\pi$
$751$			374.911i			0.499216i	−0.968347	+	0.249608i	$0.919698\pi$
$752$		0			0
$753$	−304.481			−0.404358
$754$		0			0
$755$	241.565	+	241.565i	0.319953	+	0.319953i
$756$		0			0
$757$	−1001.97	−	1001.97i	−1.32360	−	1.32360i	−0.910836	−	0.412768i	$-0.864562\pi$
$757$	−1001.97	−	1001.97i	−1.32360	−	1.32360i	−0.412768	−	0.910836i	$-0.635438\pi$
$758$		0			0
$759$	−793.815			−1.04587
$760$		0			0
$761$		−	592.474i		−	0.778547i	−0.921122	−	0.389274i	$-0.872726\pi$
$761$		−	592.474i		−	0.778547i	0.921122	−	0.389274i	$-0.127274\pi$
$762$		0			0
$763$	11.5898	−	11.5898i	0.0151898	−	0.0151898i
$764$		0			0
$765$	59.1475	−	59.1475i	0.0773170	−	0.0773170i
$766$		0			0
$767$			987.541i			1.28754i
$768$		0			0
$769$	327.948			0.426461			0.213230	−	0.977002i	$-0.431601\pi$
$769$	327.948			0.426461			0.213230	+	0.977002i	$0.431601\pi$
$770$		0			0
$771$	210.119	+	210.119i	0.272528	+	0.272528i
$772$		0			0
$773$	−969.561	−	969.561i	−1.25428	−	1.25428i	−0.953781	−	0.300503i	$-0.902846\pi$
$773$	−969.561	−	969.561i	−1.25428	−	1.25428i	−0.300503	−	0.953781i	$-0.597154\pi$
$774$		0			0
$775$	173.986			0.224497
$776$		0			0
$777$			14.7386i			0.0189685i
$778$		0			0
$779$	960.449	−	960.449i	1.23293	−	1.23293i
$780$		0			0
$781$	10.3966	−	10.3966i	0.0133119	−	0.0133119i
$782$		0			0
$783$			812.011i			1.03705i
$784$		0			0
$785$	101.245			0.128974
$786$		0			0
$787$	688.958	+	688.958i	0.875423	+	0.875423i	0.993057	−	0.117634i	$-0.0375310\pi$
$787$	688.958	+	688.958i	0.875423	+	0.875423i	−0.117634	+	0.993057i	$0.537531\pi$
$788$		0			0
$789$	−200.372	−	200.372i	−0.253956	−	0.253956i
$790$		0			0
$791$	−10.0137			−0.0126595
$792$		0			0
$793$			938.307i			1.18324i
$794$		0			0
$795$	301.347	−	301.347i	0.379053	−	0.379053i
$796$		0			0
$797$	−773.816	+	773.816i	−0.970911	+	0.970911i	−0.999589	−	0.0286777i	$-0.990870\pi$
$797$	−773.816	+	773.816i	−0.970911	+	0.970911i	0.0286777	+	0.999589i	$0.490870\pi$
$798$		0			0
$799$			64.7252i			0.0810077i
$800$		0			0
$801$	3042.83			3.79878
$802$		0			0
$803$	311.686	+	311.686i	0.388152	+	0.388152i
$804$		0			0
$805$	8.04921	+	8.04921i	0.00999902	+	0.00999902i
$806$		0			0
$807$	−399.616			−0.495187
$808$		0			0
$809$		−	1530.90i		−	1.89233i	−0.323683	−	0.946166i	$-0.604921\pi$
$809$		−	1530.90i		−	1.89233i	0.323683	−	0.946166i	$-0.395079\pi$
$810$		0			0
$811$	780.206	−	780.206i	0.962029	−	0.962029i	−0.0372757	−	0.999305i	$-0.511868\pi$
$811$	780.206	−	780.206i	0.962029	−	0.962029i	0.999305	+	0.0372757i	$0.0118680\pi$
$812$		0			0
$813$	798.746	−	798.746i	0.982468	−	0.982468i
$814$		0			0
$815$		−	43.2867i		−	0.0531125i
$816$		0			0
$817$	1122.47			1.37389
$818$		0			0
$819$	50.8844	+	50.8844i	0.0621300	+	0.0621300i
$820$		0			0
$821$	800.338	+	800.338i	0.974833	+	0.974833i	0.999691	−	0.0248582i	$-0.00791342\pi$
$821$	800.338	+	800.338i	0.974833	+	0.974833i	−0.0248582	+	0.999691i	$0.507913\pi$
$822$		0			0
$823$	−469.516			−0.570493			−0.285247	−	0.958454i	$-0.592076\pi$
$823$	−469.516			−0.570493			−0.285247	+	0.958454i	$0.592076\pi$
$824$		0			0
$825$		−	133.727i		−	0.162093i
$826$		0			0
$827$	−135.500	+	135.500i	−0.163845	+	0.163845i	−0.784268	−	0.620423i	$-0.786961\pi$
$827$	−135.500	+	135.500i	−0.163845	+	0.163845i	0.620423	+	0.784268i	$0.286961\pi$
$828$		0			0
$829$	−846.287	+	846.287i	−1.02085	+	1.02085i	−0.0210744	+	0.999778i	$0.506709\pi$
$829$	−846.287	+	846.287i	−1.02085	+	1.02085i	−0.999778	+	0.0210744i	$0.993291\pi$
$830$		0			0
$831$		−	517.303i		−	0.622506i
$832$		0			0
$833$	−81.8252			−0.0982295
$834$		0			0
$835$	−261.445	−	261.445i	−0.313108	−	0.313108i
$836$		0			0
$837$	1845.54	+	1845.54i	2.20495	+	2.20495i
$838$		0			0
$839$	915.064			1.09066			0.545330	−	0.838222i	$-0.316404\pi$
$839$	915.064			1.09066			0.545330	+	0.838222i	$0.316404\pi$
$840$		0			0
$841$			723.799i			0.860641i
$842$		0			0
$843$	2153.24	−	2153.24i	2.55426	−	2.55426i
$844$		0			0
$845$	−288.071	+	288.071i	−0.340912	+	0.340912i
$846$		0			0
$847$		−	16.8450i		−	0.0198878i
$848$		0			0
$849$	−829.486			−0.977015
$850$		0			0
$851$	−321.896	−	321.896i	−0.378256	−	0.378256i
$852$		0			0
$853$	431.036	+	431.036i	0.505318	+	0.505318i	0.913086	−	0.407768i	$-0.133693\pi$
$853$	431.036	+	431.036i	0.505318	+	0.505318i	−0.407768	+	0.913086i	$0.633693\pi$
$854$		0			0
$855$	1465.63			1.71419
$856$		0			0
$857$			1485.67i			1.73357i	0.498686	+	0.866783i	$0.333816\pi$
$857$			1485.67i			1.73357i	−0.498686	+	0.866783i	$0.666184\pi$
$858$		0			0
$859$	−562.643	+	562.643i	−0.654998	+	0.654998i	−0.954192	−	0.299194i	$-0.903282\pi$
$859$	−562.643	+	562.643i	−0.654998	+	0.654998i	0.299194	+	0.954192i	$0.403282\pi$
$860$		0			0
$861$	−31.5242	+	31.5242i	−0.0366134	+	0.0366134i
$862$		0			0
$863$		−	812.826i		−	0.941861i	−0.882170	−	0.470930i	$-0.843918\pi$
$863$		−	812.826i		−	0.941861i	0.882170	−	0.470930i	$-0.156082\pi$
$864$		0			0
$865$	220.677			0.255118
$866$		0			0
$867$	−1133.83	−	1133.83i	−1.30776	−	1.30776i
$868$		0			0
$869$	−84.6130	−	84.6130i	−0.0973683	−	0.0973683i
$870$		0			0
$871$	−295.498			−0.339263
$872$		0			0
$873$			560.950i			0.642555i
$874$		0			0
$875$	−1.35598	+	1.35598i	−0.00154969	+	0.00154969i
$876$		0			0
$877$	502.264	−	502.264i	0.572707	−	0.572707i	−0.360177	−	0.932884i	$-0.617284\pi$
$877$	502.264	−	502.264i	0.572707	−	0.572707i	0.932884	+	0.360177i	$0.117284\pi$
$878$		0			0
$879$			2209.61i			2.51378i
$880$		0			0
$881$	−979.412			−1.11171			−0.555853	−	0.831281i	$-0.687608\pi$
$881$	−979.412			−1.11171			−0.555853	+	0.831281i	$0.687608\pi$
$882$		0			0
$883$	891.876	+	891.876i	1.01005	+	1.01005i	0.999949	+	0.0101028i	$0.00321589\pi$
$883$	891.876	+	891.876i	1.01005	+	1.01005i	0.0101028	+	0.999949i	$0.496784\pi$
$884$		0			0
$885$	−466.804	−	466.804i	−0.527462	−	0.527462i
$886$		0			0
$887$	1509.83			1.70218			0.851090	−	0.525019i	$-0.175942\pi$
$887$	1509.83			1.70218			0.851090	+	0.525019i	$0.175942\pi$
$888$		0			0
$889$			35.8944i			0.0403761i
$890$		0			0
$891$	738.345	−	738.345i	0.828670	−	0.828670i
$892$		0			0
$893$	−801.921	+	801.921i	−0.898007	+	0.898007i
$894$		0			0
$895$		−	88.5829i		−	0.0989753i
$896$		0			0
$897$	−3116.19			−3.47402
$898$		0			0
$899$	−266.375	−	266.375i	−0.296302	−	0.296302i
$900$		0			0
$901$	40.1932	+	40.1932i	0.0446095	+	0.0446095i
$902$		0			0
$903$	−36.8419			−0.0407995
$904$		0			0
$905$		−	541.284i		−	0.598104i
$906$		0			0
$907$	−490.723	+	490.723i	−0.541040	+	0.541040i	−0.923834	−	0.382794i	$-0.874962\pi$
$907$	−490.723	+	490.723i	−0.541040	+	0.541040i	0.382794	+	0.923834i	$0.374962\pi$
$908$		0			0
$909$	−484.846	+	484.846i	−0.533384	+	0.533384i
$910$		0			0
$911$			1408.50i			1.54610i	0.634345	+	0.773050i	$0.281270\pi$
$911$			1408.50i			1.54610i	−0.634345	+	0.773050i	$0.718730\pi$
$912$		0			0
$913$	−591.366			−0.647718
$914$		0			0
$915$	−443.531	−	443.531i	−0.484734	−	0.484734i
$916$		0			0
$917$	−15.4250	−	15.4250i	−0.0168212	−	0.0168212i
$918$		0			0
$919$	1138.06			1.23837			0.619185	−	0.785245i	$-0.287463\pi$
$919$	1138.06			1.23837			0.619185	+	0.785245i	$0.287463\pi$
$920$		0			0
$921$		−	1310.29i		−	1.42268i
$922$		0			0
$923$	40.8127	−	40.8127i	0.0442174	−	0.0442174i
$924$		0			0
$925$	54.2270	−	54.2270i	0.0586238	−	0.0586238i
$926$		0			0
$927$		−	1333.03i		−	1.43800i
$928$		0			0
$929$	−713.947			−0.768511			−0.384256	−	0.923227i	$-0.625542\pi$
$929$	−713.947			−0.768511			−0.384256	+	0.923227i	$0.625542\pi$
$930$		0			0
$931$	−1013.78	−	1013.78i	−1.08892	−	1.08892i
$932$		0			0
$933$	2257.03	+	2257.03i	2.41911	+	2.41911i
$934$		0			0
$935$	17.8363			0.0190762
$936$		0			0
$937$		−	1123.98i		−	1.19955i	−0.800170	−	0.599774i	$-0.795257\pi$
$937$		−	1123.98i		−	1.19955i	0.800170	−	0.599774i	$-0.204743\pi$
$938$		0			0
$939$	−661.639	+	661.639i	−0.704621	+	0.704621i
$940$		0			0
$941$	576.544	−	576.544i	0.612693	−	0.612693i	−0.330954	−	0.943647i	$-0.607370\pi$
$941$	576.544	−	576.544i	0.612693	−	0.612693i	0.943647	+	0.330954i	$0.107370\pi$
$942$		0			0
$943$		−	1377.00i		−	1.46023i
$944$		0			0
$945$	−28.7670			−0.0304412
$946$		0			0
$947$	609.274	+	609.274i	0.643372	+	0.643372i	0.951383	−	0.308010i	$-0.0996632\pi$
$947$	609.274	+	609.274i	0.643372	+	0.643372i	−0.308010	+	0.951383i	$0.599663\pi$
$948$		0			0
$949$	1223.55	+	1223.55i	1.28930	+	1.28930i
$950$		0			0
$951$	−2589.07			−2.72247
$952$		0			0
$953$		−	324.830i		−	0.340850i	−0.985371	−	0.170425i	$-0.945486\pi$
$953$		−	324.830i		−	0.340850i	0.985371	−	0.170425i	$-0.0545141\pi$
$954$		0			0
$955$	404.447	−	404.447i	0.423505	−	0.423505i
$956$		0			0
$957$	−204.739	+	204.739i	−0.213938	+	0.213938i
$958$		0			0
$959$			1.72060i			0.00179416i
$960$		0			0
$961$	−249.838			−0.259977
$962$		0			0
$963$	269.102	+	269.102i	0.279441	+	0.279441i
$964$		0			0
$965$	−512.923	−	512.923i	−0.531526	−	0.531526i
$966$		0			0
$967$	−1268.54			−1.31183			−0.655913	−	0.754837i	$-0.727716\pi$
$967$	−1268.54			−1.31183			−0.655913	+	0.754837i	$0.727716\pi$
$968$		0			0
$969$			274.068i			0.282836i
$970$		0			0
$971$	78.3203	−	78.3203i	0.0806594	−	0.0806594i	−0.665626	−	0.746285i	$-0.731835\pi$
$971$	78.3203	−	78.3203i	0.0806594	−	0.0806594i	0.746285	+	0.665626i	$0.231835\pi$
$972$		0			0
$973$	0.534674	−	0.534674i	0.000549510	−	0.000549510i
$974$		0			0
$975$		−	524.957i		−	0.538418i
$976$		0			0
$977$	−1521.08			−1.55689			−0.778445	−	0.627713i	$-0.783991\pi$
$977$	−1521.08			−1.55689			−0.778445	+	0.627713i	$0.783991\pi$
$978$		0			0
$979$	458.791	+	458.791i	0.468632	+	0.468632i
$980$		0			0
$981$	−1512.79	−	1512.79i	−1.54209	−	1.54209i
$982$		0			0
$983$	−407.983			−0.415039			−0.207519	−	0.978231i	$-0.566539\pi$
$983$	−407.983			−0.415039			−0.207519	+	0.978231i	$0.566539\pi$
$984$		0			0
$985$		−	437.554i		−	0.444218i
$986$		0			0
$987$	26.3209	−	26.3209i	0.0266676	−	0.0266676i
$988$		0			0
$989$	804.643	−	804.643i	0.813592	−	0.813592i
$990$		0			0
$991$			482.285i			0.486665i	0.969943	+	0.243332i	$0.0782406\pi$
$991$			482.285i			0.486665i	−0.969943	+	0.243332i	$0.921759\pi$
$992$		0			0
$993$	1586.95			1.59813
$994$		0			0
$995$	386.234	+	386.234i	0.388175	+	0.388175i
$996$		0			0
$997$	−1.88526	−	1.88526i	−0.00189093	−	0.00189093i	0.706161	−	0.708052i	$-0.250426\pi$
$997$	−1.88526	−	1.88526i	−0.00189093	−	0.00189093i	−0.708052	+	0.706161i	$0.750426\pi$
$998$		0			0
$999$	1150.42			1.15157

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.r.a.271.16		32
4.3	odd	2		80.3.r.a.11.5	✓	32
8.3	odd	2		640.3.r.a.31.16		32
8.5	even	2		640.3.r.b.31.1		32
16.3	odd	4	inner	320.3.r.a.111.16		32
16.5	even	4		640.3.r.a.351.16		32
16.11	odd	4		640.3.r.b.351.1		32
16.13	even	4		80.3.r.a.51.5	yes	32
20.3	even	4		400.3.k.g.299.4		32
20.7	even	4		400.3.k.h.299.13		32
20.19	odd	2		400.3.r.f.251.12		32
80.13	odd	4		400.3.k.h.99.13		32
80.29	even	4		400.3.r.f.51.12		32
80.77	odd	4		400.3.k.g.99.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.5	✓	32	4.3	odd	2
80.3.r.a.51.5	yes	32	16.13	even	4
320.3.r.a.111.16		32	16.3	odd	4	inner
320.3.r.a.271.16		32	1.1	even	1	trivial
400.3.k.g.99.4		32	80.77	odd	4
400.3.k.g.299.4		32	20.3	even	4
400.3.k.h.99.13		32	80.13	odd	4
400.3.k.h.299.13		32	20.7	even	4
400.3.r.f.51.12		32	80.29	even	4
400.3.r.f.251.12		32	20.19	odd	2
640.3.r.a.31.16		32	8.3	odd	2
640.3.r.a.351.16		32	16.5	even	4
640.3.r.b.31.1		32	8.5	even	2
640.3.r.b.351.1		32	16.11	odd	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.r (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.96156 + 3.96156i) q^{3} +(-1.58114 - 1.58114i) q^{5} -0.171519 q^{7} +22.3880i q^{9} +O(q^{10})\)	\(q+(3.96156 + 3.96156i) q^{3} +(-1.58114 - 1.58114i) q^{5} -0.171519 q^{7} +22.3880i q^{9} +(-3.37561 + 3.37561i) q^{11} +(-13.2513 + 13.2513i) q^{13} -12.5276i q^{15} +1.67091 q^{17} +(20.7019 + 20.7019i) q^{19} +(-0.679485 - 0.679485i) q^{21} +29.6804 q^{23} +5.00000i q^{25} +(-53.0373 + 53.0373i) q^{27} +(7.65510 - 7.65510i) q^{29} -34.7971i q^{31} -26.7454 q^{33} +(0.271196 + 0.271196i) q^{35} +(-10.8454 - 10.8454i) q^{37} -104.991 q^{39} -46.3942i q^{41} +(27.1102 - 27.1102i) q^{43} +(35.3985 - 35.3985i) q^{45} +38.7366i q^{47} -48.9706 q^{49} +(6.61940 + 6.61940i) q^{51} +(24.0547 + 24.0547i) q^{53} +10.6746 q^{55} +164.024i q^{57} +(37.2621 - 37.2621i) q^{59} +(35.4044 - 35.4044i) q^{61} -3.83997i q^{63} +41.9042 q^{65} +(11.1498 + 11.1498i) q^{67} +(117.581 + 117.581i) q^{69} -3.07991 q^{71} -92.3346i q^{73} +(-19.8078 + 19.8078i) q^{75} +(0.578983 - 0.578983i) q^{77} +25.0660i q^{79} -218.729 q^{81} +(87.5940 + 87.5940i) q^{83} +(-2.64193 - 2.64193i) q^{85} +60.6523 q^{87} -135.913i q^{89} +(2.27285 - 2.27285i) q^{91} +(137.851 - 137.851i) q^{93} -65.4652i q^{95} +25.0559 q^{97} +(-75.5731 - 75.5731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) \) 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

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