LMFDB - Embedded newform 320.3.r.a.111.3

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			111.3
Character	$\chi$	$=$	320.111
Dual form			320.3.r.a.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.09850 + 3.09850i) q^{3} +(-1.58114 + 1.58114i) q^{5} +13.0357 q^{7} -10.2014i q^{9} +O(q^{10})$	\(q+(-3.09850 + 3.09850i) q^{3} +(-1.58114 + 1.58114i) q^{5} +13.0357 q^{7} -10.2014i q^{9} +(4.91205 + 4.91205i) q^{11} +(9.80153 + 9.80153i) q^{13} -9.79833i q^{15} -0.0570293 q^{17} +(-6.54734 + 6.54734i) q^{19} +(-40.3912 + 40.3912i) q^{21} -12.8882 q^{23} -5.00000i q^{25} +(3.72268 + 3.72268i) q^{27} +(-20.3776 - 20.3776i) q^{29} +60.4022i q^{31} -30.4400 q^{33} +(-20.6113 + 20.6113i) q^{35} +(-19.7620 + 19.7620i) q^{37} -60.7401 q^{39} +33.6023i q^{41} +(16.9664 + 16.9664i) q^{43} +(16.1299 + 16.1299i) q^{45} -67.8616i q^{47} +120.930 q^{49} +(0.176706 - 0.176706i) q^{51} +(8.59600 - 8.59600i) q^{53} -15.5333 q^{55} -40.5739i q^{57} +(30.7174 + 30.7174i) q^{59} +(11.8198 + 11.8198i) q^{61} -132.983i q^{63} -30.9952 q^{65} +(-18.9954 + 18.9954i) q^{67} +(39.9342 - 39.9342i) q^{69} -110.354 q^{71} -50.4761i q^{73} +(15.4925 + 15.4925i) q^{75} +(64.0320 + 64.0320i) q^{77} +77.2923i q^{79} +68.7435 q^{81} +(109.998 - 109.998i) q^{83} +(0.0901713 - 0.0901713i) q^{85} +126.280 q^{87} +93.1793i q^{89} +(127.770 + 127.770i) q^{91} +(-187.157 - 187.157i) q^{93} -20.7045i q^{95} -25.2768 q^{97} +(50.1100 - 50.1100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−3.09850	+	3.09850i	−1.03283	+	1.03283i	−0.0333921	+	0.999442i	$0.510631\pi$
$3$	−3.09850	+	3.09850i	−1.03283	+	1.03283i	−0.999442	+	0.0333921i	$0.989369\pi$
$4$		0			0
$5$	−1.58114	+	1.58114i	−0.316228	+	0.316228i
$5$	−1.58114	+	1.58114i	−0.316228	+	0.316228i
$6$		0			0
$7$	13.0357			1.86224			0.931122	−	0.364709i	$-0.118832\pi$
$7$	13.0357			1.86224			0.931122	+	0.364709i	$0.118832\pi$
$8$		0			0
$9$		−	10.2014i		−	1.13349i
$10$		0			0
$11$	4.91205	+	4.91205i	0.446550	+	0.446550i	0.894206	−	0.447656i	$-0.147741\pi$
$11$	4.91205	+	4.91205i	0.446550	+	0.446550i	−0.447656	+	0.894206i	$0.647741\pi$
$12$		0			0
$13$	9.80153	+	9.80153i	0.753964	+	0.753964i	0.975217	−	0.221253i	$-0.0710146\pi$
$13$	9.80153	+	9.80153i	0.753964	+	0.753964i	−0.221253	+	0.975217i	$0.571015\pi$
$14$		0			0
$15$		−	9.79833i		−	0.653222i
$16$		0			0
$17$	−0.0570293			−0.00335467			−0.00167733	−	0.999999i	$-0.500534\pi$
$17$	−0.0570293			−0.00335467			−0.00167733	+	0.999999i	$0.500534\pi$
$18$		0			0
$19$	−6.54734	+	6.54734i	−0.344597	+	0.344597i	−0.858092	−	0.513495i	$-0.828350\pi$
$19$	−6.54734	+	6.54734i	−0.344597	+	0.344597i	0.513495	+	0.858092i	$0.328350\pi$
$20$		0			0
$21$	−40.3912	+	40.3912i	−1.92339	+	1.92339i
$22$		0			0
$23$	−12.8882			−0.560358			−0.280179	−	0.959948i	$-0.590394\pi$
$23$	−12.8882			−0.560358			−0.280179	+	0.959948i	$0.590394\pi$
$24$		0			0
$25$		−	5.00000i		−	0.200000i
$26$		0			0
$27$	3.72268	+	3.72268i	0.137877	+	0.137877i
$28$		0			0
$29$	−20.3776	−	20.3776i	−0.702677	−	0.702677i	0.262307	−	0.964984i	$-0.415517\pi$
$29$	−20.3776	−	20.3776i	−0.702677	−	0.702677i	−0.964984	+	0.262307i	$0.915517\pi$
$30$		0			0
$31$			60.4022i			1.94846i	0.225559	+	0.974230i	$0.427579\pi$
$31$			60.4022i			1.94846i	−0.225559	+	0.974230i	$0.572421\pi$
$32$		0			0
$33$	−30.4400			−0.922424
$34$		0			0
$35$	−20.6113	+	20.6113i	−0.588893	+	0.588893i
$36$		0			0
$37$	−19.7620	+	19.7620i	−0.534108	+	0.534108i	−0.921792	−	0.387684i	$-0.873275\pi$
$37$	−19.7620	+	19.7620i	−0.534108	+	0.534108i	0.387684	+	0.921792i	$0.373275\pi$
$38$		0			0
$39$	−60.7401			−1.55744
$40$		0			0
$41$			33.6023i			0.819569i	0.912182	+	0.409785i	$0.134396\pi$
$41$			33.6023i			0.819569i	−0.912182	+	0.409785i	$0.865604\pi$
$42$		0			0
$43$	16.9664	+	16.9664i	0.394567	+	0.394567i	0.876311	−	0.481745i	$-0.159997\pi$
$43$	16.9664	+	16.9664i	0.394567	+	0.394567i	−0.481745	+	0.876311i	$0.659997\pi$
$44$		0			0
$45$	16.1299	+	16.1299i	0.358442	+	0.358442i
$46$		0			0
$47$		−	67.8616i		−	1.44386i	−0.691964	−	0.721932i	$-0.743254\pi$
$47$		−	67.8616i		−	1.44386i	0.691964	−	0.721932i	$-0.256746\pi$
$48$		0			0
$49$	120.930			2.46795
$50$		0			0
$51$	0.176706	−	0.176706i	0.00346481	−	0.00346481i
$52$		0			0
$53$	8.59600	−	8.59600i	0.162189	−	0.162189i	−0.621347	−	0.783536i	$-0.713414\pi$
$53$	8.59600	−	8.59600i	0.162189	−	0.162189i	0.783536	+	0.621347i	$0.213414\pi$
$54$		0			0
$55$	−15.5333			−0.282423
$56$		0			0
$57$		−	40.5739i		−	0.711823i
$58$		0			0
$59$	30.7174	+	30.7174i	0.520634	+	0.520634i	0.917763	−	0.397129i	$-0.129994\pi$
$59$	30.7174	+	30.7174i	0.520634	+	0.520634i	−0.397129	+	0.917763i	$0.629994\pi$
$60$		0			0
$61$	11.8198	+	11.8198i	0.193767	+	0.193767i	0.797322	−	0.603555i	$-0.206250\pi$
$61$	11.8198	+	11.8198i	0.193767	+	0.193767i	−0.603555	+	0.797322i	$0.706250\pi$
$62$		0			0
$63$		−	132.983i		−	2.11084i
$64$		0			0
$65$	−30.9952			−0.476849
$66$		0			0
$67$	−18.9954	+	18.9954i	−0.283513	+	0.283513i	−0.834508	−	0.550996i	$-0.814248\pi$
$67$	−18.9954	+	18.9954i	−0.283513	+	0.283513i	0.550996	+	0.834508i	$0.314248\pi$
$68$		0			0
$69$	39.9342	−	39.9342i	0.578757	−	0.578757i
$70$		0			0
$71$	−110.354			−1.55428			−0.777141	−	0.629326i	$-0.783331\pi$
$71$	−110.354			−1.55428			−0.777141	+	0.629326i	$0.783331\pi$
$72$		0			0
$73$		−	50.4761i		−	0.691453i	−0.938335	−	0.345727i	$-0.887632\pi$
$73$		−	50.4761i		−	0.691453i	0.938335	−	0.345727i	$-0.112368\pi$
$74$		0			0
$75$	15.4925	+	15.4925i	0.206567	+	0.206567i
$76$		0			0
$77$	64.0320	+	64.0320i	0.831584	+	0.831584i
$78$		0			0
$79$			77.2923i			0.978384i	0.872176	+	0.489192i	$0.162708\pi$
$79$			77.2923i			0.978384i	−0.872176	+	0.489192i	$0.837292\pi$
$80$		0			0
$81$	68.7435			0.848685
$82$		0			0
$83$	109.998	−	109.998i	1.32527	−	1.32527i	0.415829	−	0.909443i	$-0.363492\pi$
$83$	109.998	−	109.998i	1.32527	−	1.32527i	0.909443	−	0.415829i	$-0.136508\pi$
$84$		0			0
$85$	0.0901713	−	0.0901713i	0.00106084	−	0.00106084i
$86$		0			0
$87$	126.280			1.45150
$88$		0			0
$89$			93.1793i			1.04696i	0.852038	+	0.523479i	$0.175366\pi$
$89$			93.1793i			1.04696i	−0.852038	+	0.523479i	$0.824634\pi$
$90$		0			0
$91$	127.770	+	127.770i	1.40406	+	1.40406i
$92$		0			0
$93$	−187.157	−	187.157i	−2.01244	−	2.01244i
$94$		0			0
$95$		−	20.7045i		−	0.217942i
$96$		0			0
$97$	−25.2768			−0.260585			−0.130293	−	0.991476i	$-0.541592\pi$
$97$	−25.2768			−0.260585			−0.130293	+	0.991476i	$0.541592\pi$
$98$		0			0
$99$	50.1100	−	50.1100i	0.506161	−	0.506161i
$100$		0			0
$101$	−74.9842	+	74.9842i	−0.742418	+	0.742418i	−0.973043	−	0.230625i	$-0.925923\pi$
$101$	−74.9842	+	74.9842i	−0.742418	+	0.742418i	0.230625	+	0.973043i	$0.425923\pi$
$102$		0			0
$103$	25.6539			0.249067			0.124534	−	0.992215i	$-0.460257\pi$
$103$	25.6539			0.249067			0.124534	+	0.992215i	$0.460257\pi$
$104$		0			0
$105$		−	127.728i		−	1.21646i
$106$		0			0
$107$	−22.8432	−	22.8432i	−0.213488	−	0.213488i	0.592259	−	0.805747i	$-0.298236\pi$
$107$	−22.8432	−	22.8432i	−0.213488	−	0.213488i	−0.805747	+	0.592259i	$0.798236\pi$
$108$		0			0
$109$	−61.7645	−	61.7645i	−0.566647	−	0.566647i	0.364541	−	0.931187i	$-0.381226\pi$
$109$	−61.7645	−	61.7645i	−0.566647	−	0.566647i	−0.931187	+	0.364541i	$0.881226\pi$
$110$		0			0
$111$		−	122.465i		−	1.10329i
$112$		0			0
$113$	46.3648			0.410308			0.205154	−	0.978730i	$-0.434231\pi$
$113$	46.3648			0.410308			0.205154	+	0.978730i	$0.434231\pi$
$114$		0			0
$115$	20.3781	−	20.3781i	0.177201	−	0.177201i
$116$		0			0
$117$	99.9898	−	99.9898i	0.854613	−	0.854613i
$118$		0			0
$119$	−0.743417			−0.00624720
$120$		0			0
$121$		−	72.7436i		−	0.601187i
$122$		0			0
$123$	−104.117	−	104.117i	−0.846479	−	0.846479i
$124$		0			0
$125$	7.90569	+	7.90569i	0.0632456	+	0.0632456i
$126$		0			0
$127$			55.7091i			0.438655i	0.975651	+	0.219327i	$0.0703862\pi$
$127$			55.7091i			0.438655i	−0.975651	+	0.219327i	$0.929614\pi$
$128$		0			0
$129$	−105.141			−0.815044
$130$		0			0
$131$	56.1622	−	56.1622i	0.428719	−	0.428719i	−0.459473	−	0.888192i	$-0.651962\pi$
$131$	56.1622	−	56.1622i	0.428719	−	0.428719i	0.888192	+	0.459473i	$0.151962\pi$
$132$		0			0
$133$	−85.3492	+	85.3492i	−0.641723	+	0.641723i
$134$		0			0
$135$	−11.7722			−0.0872011
$136$		0			0
$137$			10.6030i			0.0773944i	0.999251	+	0.0386972i	$0.0123208\pi$
$137$			10.6030i			0.0773944i	−0.999251	+	0.0386972i	$0.987679\pi$
$138$		0			0
$139$	−149.445	−	149.445i	−1.07515	−	1.07515i	−0.996937	−	0.0782094i	$-0.975080\pi$
$139$	−149.445	−	149.445i	−1.07515	−	1.07515i	−0.0782094	−	0.996937i	$-0.524920\pi$
$140$		0			0
$141$	210.269	+	210.269i	1.49127	+	1.49127i
$142$		0			0
$143$			96.2911i			0.673364i
$144$		0			0
$145$	64.4397			0.444412
$146$		0			0
$147$	−374.701	+	374.701i	−2.54898	+	2.54898i
$148$		0			0
$149$	13.9342	−	13.9342i	0.0935181	−	0.0935181i	−0.658800	−	0.752318i	$-0.728936\pi$
$149$	13.9342	−	13.9342i	0.0935181	−	0.0935181i	0.752318	+	0.658800i	$0.228936\pi$
$150$		0			0
$151$	151.649			1.00430			0.502149	−	0.864781i	$-0.332543\pi$
$151$	151.649			1.00430			0.502149	+	0.864781i	$0.332543\pi$
$152$		0			0
$153$			0.581781i			0.00380249i
$154$		0			0
$155$	−95.5043	−	95.5043i	−0.616157	−	0.616157i
$156$		0			0
$157$	54.8400	+	54.8400i	0.349299	+	0.349299i	0.859849	−	0.510549i	$-0.170558\pi$
$157$	54.8400	+	54.8400i	0.349299	+	0.349299i	−0.510549	+	0.859849i	$0.670558\pi$
$158$		0			0
$159$			53.2695i			0.335028i
$160$		0			0
$161$	−168.007			−1.04352
$162$		0			0
$163$	49.7676	−	49.7676i	0.305323	−	0.305323i	−0.537769	−	0.843092i	$-0.680733\pi$
$163$	49.7676	−	49.7676i	0.305323	−	0.305323i	0.843092	+	0.537769i	$0.180733\pi$
$164$		0			0
$165$	48.1298	−	48.1298i	0.291696	−	0.291696i
$166$		0			0
$167$	214.237			1.28286			0.641428	−	0.767183i	$-0.278342\pi$
$167$	214.237			1.28286			0.641428	+	0.767183i	$0.278342\pi$
$168$		0			0
$169$			23.1400i			0.136923i
$170$		0			0
$171$	66.7924	+	66.7924i	0.390599	+	0.390599i
$172$		0			0
$173$	61.2673	+	61.2673i	0.354146	+	0.354146i	0.861650	−	0.507503i	$-0.169432\pi$
$173$	61.2673	+	61.2673i	0.354146	+	0.354146i	−0.507503	+	0.861650i	$0.669432\pi$
$174$		0			0
$175$		−	65.1785i		−	0.372449i
$176$		0			0
$177$	−190.356			−1.07546
$178$		0			0
$179$	15.2346	−	15.2346i	0.0851094	−	0.0851094i	−0.663270	−	0.748380i	$-0.730832\pi$
$179$	15.2346	−	15.2346i	0.0851094	−	0.0851094i	0.748380	+	0.663270i	$0.230832\pi$
$180$		0			0
$181$	97.2929	−	97.2929i	0.537530	−	0.537530i	−0.385273	−	0.922803i	$-0.625893\pi$
$181$	97.2929	−	97.2929i	0.537530	−	0.537530i	0.922803	+	0.385273i	$0.125893\pi$
$182$		0			0
$183$	−73.2472			−0.400258
$184$		0			0
$185$		−	62.4930i		−	0.337800i
$186$		0			0
$187$	−0.280131	−	0.280131i	−0.00149802	−	0.00149802i
$188$		0			0
$189$	48.5278	+	48.5278i	0.256761	+	0.256761i
$190$		0			0
$191$			226.751i			1.18718i	0.804769	+	0.593588i	$0.202289\pi$
$191$			226.751i			1.18718i	−0.804769	+	0.593588i	$0.797711\pi$
$192$		0			0
$193$	205.788			1.06626			0.533129	−	0.846034i	$-0.321016\pi$
$193$	205.788			1.06626			0.533129	+	0.846034i	$0.321016\pi$
$194$		0			0
$195$	96.0386	−	96.0386i	0.492506	−	0.492506i
$196$		0			0
$197$	−82.6531	+	82.6531i	−0.419559	+	0.419559i	−0.885052	−	0.465493i	$-0.845877\pi$
$197$	−82.6531	+	82.6531i	−0.419559	+	0.419559i	0.465493	+	0.885052i	$0.345877\pi$
$198$		0			0
$199$	102.229			0.513712			0.256856	−	0.966450i	$-0.417313\pi$
$199$	102.229			0.513712			0.256856	+	0.966450i	$0.417313\pi$
$200$		0			0
$201$		−	117.714i		−	0.585643i
$202$		0			0
$203$	−265.637	−	265.637i	−1.30856	−	1.30856i
$204$		0			0
$205$	−53.1300	−	53.1300i	−0.259171	−	0.259171i
$206$		0			0
$207$			131.479i			0.635162i
$208$		0			0
$209$	−64.3217			−0.307759
$210$		0			0
$211$	68.0879	−	68.0879i	0.322691	−	0.322691i	−0.527107	−	0.849799i	$-0.676723\pi$
$211$	68.0879	−	68.0879i	0.322691	−	0.322691i	0.849799	+	0.527107i	$0.176723\pi$
$212$		0			0
$213$	341.932	−	341.932i	1.60532	−	1.60532i
$214$		0			0
$215$	−53.6523			−0.249546
$216$		0			0
$217$			787.385i			3.62850i
$218$		0			0
$219$	156.400	+	156.400i	0.714157	+	0.714157i
$220$		0			0
$221$	−0.558975	−	0.558975i	−0.00252930	−	0.00252930i
$222$		0			0
$223$			133.074i			0.596743i	0.954450	+	0.298371i	$0.0964434\pi$
$223$			133.074i			0.596743i	−0.954450	+	0.298371i	$0.903557\pi$
$224$		0			0
$225$	−51.0072			−0.226699
$226$		0			0
$227$	167.095	−	167.095i	0.736102	−	0.736102i	−0.235719	−	0.971821i	$-0.575745\pi$
$227$	167.095	−	167.095i	0.736102	−	0.736102i	0.971821	+	0.235719i	$0.0757446\pi$
$228$		0			0
$229$	−30.3870	+	30.3870i	−0.132694	+	0.132694i	−0.770334	−	0.637640i	$-0.779911\pi$
$229$	−30.3870	+	30.3870i	−0.132694	+	0.132694i	0.637640	+	0.770334i	$0.279911\pi$
$230$		0			0
$231$	−396.806			−1.71778
$232$		0			0
$233$			2.96377i			0.0127200i	0.999980	+	0.00636002i	$0.00202447\pi$
$233$			2.96377i			0.0127200i	−0.999980	+	0.00636002i	$0.997976\pi$
$234$		0			0
$235$	107.299	+	107.299i	0.456590	+	0.456590i
$236$		0			0
$237$	−239.490	−	239.490i	−1.01051	−	1.01051i
$238$		0			0
$239$		−	27.2152i		−	0.113871i	−0.998378	−	0.0569355i	$-0.981867\pi$
$239$		−	27.2152i		−	0.113871i	0.998378	−	0.0569355i	$-0.0181329\pi$
$240$		0			0
$241$	218.212			0.905445			0.452722	−	0.891652i	$-0.350453\pi$
$241$	218.212			0.905445			0.452722	+	0.891652i	$0.350453\pi$
$242$		0			0
$243$	−246.506	+	246.506i	−1.01443	+	1.01443i
$244$		0			0
$245$	−191.206	+	191.206i	−0.780434	+	0.780434i
$246$		0			0
$247$	−128.348			−0.519627
$248$		0			0
$249$			681.656i			2.73757i
$250$		0			0
$251$	92.7841	+	92.7841i	0.369658	+	0.369658i	0.867352	−	0.497695i	$-0.165820\pi$
$251$	92.7841	+	92.7841i	0.369658	+	0.369658i	−0.497695	+	0.867352i	$0.665820\pi$
$252$		0			0
$253$	−63.3076	−	63.3076i	−0.250228	−	0.250228i
$254$		0			0
$255$			0.558792i			0.00219134i
$256$		0			0
$257$	−21.8974			−0.0852037			−0.0426019	−	0.999092i	$-0.513565\pi$
$257$	−21.8974			−0.0852037			−0.0426019	+	0.999092i	$0.513565\pi$
$258$		0			0
$259$	−257.612	+	257.612i	−0.994640	+	0.994640i
$260$		0			0
$261$	−207.881	+	207.881i	−0.796480	+	0.796480i
$262$		0			0
$263$	−240.673			−0.915108			−0.457554	−	0.889182i	$-0.651274\pi$
$263$	−240.673			−0.915108			−0.457554	+	0.889182i	$0.651274\pi$
$264$		0			0
$265$			27.1829i			0.102577i
$266$		0			0
$267$	−288.716	−	288.716i	−1.08133	−	1.08133i
$268$		0			0
$269$	−176.876	−	176.876i	−0.657532	−	0.657532i	0.297264	−	0.954795i	$-0.403926\pi$
$269$	−176.876	−	176.876i	−0.657532	−	0.657532i	−0.954795	+	0.297264i	$0.903926\pi$
$270$		0			0
$271$			121.276i			0.447514i	0.974645	+	0.223757i	$0.0718322\pi$
$271$			121.276i			0.447514i	−0.974645	+	0.223757i	$0.928168\pi$
$272$		0			0
$273$	−791.790			−2.90033
$274$		0			0
$275$	24.5602	−	24.5602i	0.0893099	−	0.0893099i
$276$		0			0
$277$	338.640	−	338.640i	1.22253	−	1.22253i	0.255799	−	0.966730i	$-0.417662\pi$
$277$	338.640	−	338.640i	1.22253	−	1.22253i	0.966730	−	0.255799i	$-0.0823384\pi$
$278$		0			0
$279$	616.190			2.20857
$280$		0			0
$281$		−	385.874i		−	1.37322i	−0.727027	−	0.686609i	$-0.759098\pi$
$281$		−	385.874i		−	1.37322i	0.727027	−	0.686609i	$-0.240902\pi$
$282$		0			0
$283$	192.343	+	192.343i	0.679657	+	0.679657i	0.959923	−	0.280265i	$-0.0904225\pi$
$283$	192.343	+	192.343i	0.679657	+	0.679657i	−0.280265	+	0.959923i	$0.590422\pi$
$284$		0			0
$285$	64.1530	+	64.1530i	0.225098	+	0.225098i
$286$		0			0
$287$			438.030i			1.52624i
$288$		0			0
$289$	−288.997			−0.999989
$290$		0			0
$291$	78.3201	−	78.3201i	0.269141	−	0.269141i
$292$		0			0
$293$	139.241	−	139.241i	0.475224	−	0.475224i	−0.428377	−	0.903600i	$-0.640914\pi$
$293$	139.241	−	139.241i	0.475224	−	0.475224i	0.903600	+	0.428377i	$0.140914\pi$
$294$		0			0
$295$	−97.1369			−0.329278
$296$		0			0
$297$			36.5720i			0.123138i
$298$		0			0
$299$	−126.324	−	126.324i	−0.422490	−	0.422490i
$300$		0			0
$301$	221.168	+	221.168i	0.734779	+	0.734779i
$302$		0			0
$303$		−	464.678i		−	1.53359i
$304$		0			0
$305$	−37.3774			−0.122549
$306$		0			0
$307$	349.705	−	349.705i	1.13910	−	1.13910i	0.150493	−	0.988611i	$-0.451914\pi$
$307$	349.705	−	349.705i	1.13910	−	1.13910i	0.988611	−	0.150493i	$-0.0480861\pi$
$308$		0			0
$309$	−79.4887	+	79.4887i	−0.257245	+	0.257245i
$310$		0			0
$311$	−494.988			−1.59160			−0.795800	−	0.605559i	$-0.792949\pi$
$311$	−494.988			−1.59160			−0.795800	+	0.605559i	$0.792949\pi$
$312$		0			0
$313$		−	401.720i		−	1.28345i	−0.766934	−	0.641726i	$-0.778219\pi$
$313$		−	401.720i		−	1.28345i	0.766934	−	0.641726i	$-0.221781\pi$
$314$		0			0
$315$	210.265	+	210.265i	0.667507	+	0.667507i
$316$		0			0
$317$	−219.838	−	219.838i	−0.693494	−	0.693494i	0.269505	−	0.962999i	$-0.413140\pi$
$317$	−219.838	−	219.838i	−0.693494	−	0.693494i	−0.962999	+	0.269505i	$0.913140\pi$
$318$		0			0
$319$		−	200.192i		−	0.627560i
$320$		0			0
$321$	141.560			0.440996
$322$		0			0
$323$	0.373390	−	0.373390i	0.00115601	−	0.00115601i
$324$		0			0
$325$	49.0076	−	49.0076i	0.150793	−	0.150793i
$326$		0			0
$327$	382.755			1.17050
$328$		0			0
$329$		−	884.623i		−	2.68882i
$330$		0			0
$331$	22.4039	+	22.4039i	0.0676854	+	0.0676854i	0.740139	−	0.672454i	$-0.234760\pi$
$331$	22.4039	+	22.4039i	0.0676854	+	0.0676854i	−0.672454	+	0.740139i	$0.734760\pi$
$332$		0			0
$333$	201.601	+	201.601i	0.605409	+	0.605409i
$334$		0			0
$335$		−	60.0686i		−	0.179309i
$336$		0			0
$337$	580.583			1.72280			0.861400	−	0.507928i	$-0.169588\pi$
$337$	580.583			1.72280			0.861400	+	0.507928i	$0.169588\pi$
$338$		0			0
$339$	−143.661	+	143.661i	−0.423780	+	0.423780i
$340$		0			0
$341$	−296.699	+	296.699i	−0.870084	+	0.870084i
$342$		0			0
$343$	937.652			2.73368
$344$		0			0
$345$			126.283i			0.366038i
$346$		0			0
$347$	−133.445	−	133.445i	−0.384569	−	0.384569i	0.488176	−	0.872745i	$-0.337662\pi$
$347$	−133.445	−	133.445i	−0.384569	−	0.384569i	−0.872745	+	0.488176i	$0.837662\pi$
$348$		0			0
$349$	431.761	+	431.761i	1.23714	+	1.23714i	0.961166	+	0.275971i	$0.0889995\pi$
$349$	431.761	+	431.761i	1.23714	+	1.23714i	0.275971	+	0.961166i	$0.411001\pi$
$350$		0			0
$351$			72.9760i			0.207909i
$352$		0			0
$353$	414.747			1.17492			0.587460	−	0.809253i	$-0.300128\pi$
$353$	414.747			1.17492			0.587460	+	0.809253i	$0.300128\pi$
$354$		0			0
$355$	174.485	−	174.485i	0.491507	−	0.491507i
$356$		0			0
$357$	2.30348	−	2.30348i	0.00645233	−	0.00645233i
$358$		0			0
$359$	−96.8897			−0.269888			−0.134944	−	0.990853i	$-0.543085\pi$
$359$	−96.8897			−0.269888			−0.134944	+	0.990853i	$0.543085\pi$
$360$		0			0
$361$			275.265i			0.762506i
$362$		0			0
$363$	225.396	+	225.396i	0.620927	+	0.620927i
$364$		0			0
$365$	79.8097	+	79.8097i	0.218657	+	0.218657i
$366$		0			0
$367$		−	617.339i		−	1.68212i	−0.540940	−	0.841061i	$-0.681932\pi$
$367$		−	617.339i		−	1.68212i	0.540940	−	0.841061i	$-0.318068\pi$
$368$		0			0
$369$	342.792			0.928977
$370$		0			0
$371$	112.055	−	112.055i	0.302035	−	0.302035i
$372$		0			0
$373$	−199.928	+	199.928i	−0.536000	+	0.536000i	−0.922352	−	0.386352i	$-0.873735\pi$
$373$	−199.928	+	199.928i	−0.536000	+	0.536000i	0.386352	+	0.922352i	$0.373735\pi$
$374$		0			0
$375$	−48.9916			−0.130644
$376$		0			0
$377$		−	399.464i		−	1.05959i
$378$		0			0
$379$	−259.882	−	259.882i	−0.685705	−	0.685705i	0.275575	−	0.961280i	$-0.411132\pi$
$379$	−259.882	−	259.882i	−0.685705	−	0.685705i	−0.961280	+	0.275575i	$0.911132\pi$
$380$		0			0
$381$	−172.615	−	172.615i	−0.453058	−	0.453058i
$382$		0			0
$383$			97.5182i			0.254617i	0.991863	+	0.127308i	$0.0406338\pi$
$383$			97.5182i			0.254617i	−0.991863	+	0.127308i	$0.959366\pi$
$384$		0			0
$385$	−202.487			−0.525940
$386$		0			0
$387$	173.081	−	173.081i	0.447239	−	0.447239i
$388$		0			0
$389$	379.310	−	379.310i	0.975089	−	0.975089i	−0.0246081	−	0.999697i	$-0.507834\pi$
$389$	379.310	−	379.310i	0.975089	−	0.975089i	0.999697	+	0.0246081i	$0.00783379\pi$
$390$		0			0
$391$	0.735007			0.00187981
$392$		0			0
$393$			348.038i			0.885592i
$394$		0			0
$395$	−122.210	−	122.210i	−0.309392	−	0.309392i
$396$		0			0
$397$	−517.509	−	517.509i	−1.30355	−	1.30355i	−0.925983	−	0.377566i	$-0.876761\pi$
$397$	−517.509	−	517.509i	−1.30355	−	1.30355i	−0.377566	−	0.925983i	$-0.623239\pi$
$398$		0			0
$399$		−	528.910i		−	1.32559i
$400$		0			0
$401$	−64.9181			−0.161890			−0.0809452	−	0.996719i	$-0.525794\pi$
$401$	−64.9181			−0.161890			−0.0809452	+	0.996719i	$0.525794\pi$
$402$		0			0
$403$	−592.034	+	592.034i	−1.46907	+	1.46907i
$404$		0			0
$405$	−108.693	+	108.693i	−0.268378	+	0.268378i
$406$		0			0
$407$	−194.144			−0.477012
$408$		0			0
$409$		−	430.056i		−	1.05148i	−0.850645	−	0.525740i	$-0.823788\pi$
$409$		−	430.056i		−	1.05148i	0.850645	−	0.525740i	$-0.176212\pi$
$410$		0			0
$411$	−32.8535	−	32.8535i	−0.0799356	−	0.0799356i
$412$		0			0
$413$	400.423	+	400.423i	0.969546	+	0.969546i
$414$		0			0
$415$			347.843i			0.838175i
$416$		0			0
$417$	926.114			2.22090
$418$		0			0
$419$	412.043	−	412.043i	0.983396	−	0.983396i	−0.0164682	−	0.999864i	$-0.505242\pi$
$419$	412.043	−	412.043i	0.983396	−	0.983396i	0.999864	+	0.0164682i	$0.00524222\pi$
$420$		0			0
$421$	−49.5575	+	49.5575i	−0.117714	+	0.117714i	−0.763510	−	0.645796i	$-0.776526\pi$
$421$	−49.5575	+	49.5575i	−0.117714	+	0.117714i	0.645796	+	0.763510i	$0.276526\pi$
$422$		0			0
$423$	−692.286			−1.63661
$424$		0			0
$425$			0.285147i			0.000670933i
$426$		0			0
$427$	154.079	+	154.079i	0.360841	+	0.360841i
$428$		0			0
$429$	−298.358	−	298.358i	−0.695474	−	0.695474i
$430$		0			0
$431$		−	534.386i		−	1.23988i	−0.784651	−	0.619938i	$-0.787158\pi$
$431$		−	534.386i		−	1.23988i	0.784651	−	0.619938i	$-0.212842\pi$
$432$		0			0
$433$	577.043			1.33266			0.666331	−	0.745656i	$-0.267864\pi$
$433$	577.043			1.33266			0.666331	+	0.745656i	$0.267864\pi$
$434$		0			0
$435$	−199.667	+	199.667i	−0.459004	+	0.459004i
$436$		0			0
$437$	84.3837	−	84.3837i	0.193098	−	0.193098i
$438$		0			0
$439$	260.941			0.594399			0.297200	−	0.954815i	$-0.403947\pi$
$439$	260.941			0.594399			0.297200	+	0.954815i	$0.403947\pi$
$440$		0			0
$441$		−	1233.66i		−	2.79741i
$442$		0			0
$443$	309.288	+	309.288i	0.698166	+	0.698166i	0.964015	−	0.265848i	$-0.0856521\pi$
$443$	309.288	+	309.288i	0.698166	+	0.698166i	−0.265848	+	0.964015i	$0.585652\pi$
$444$		0			0
$445$	−147.329	−	147.329i	−0.331077	−	0.331077i
$446$		0			0
$447$			86.3503i			0.193177i
$448$		0			0
$449$	−369.947			−0.823936			−0.411968	−	0.911198i	$-0.635158\pi$
$449$	−369.947			−0.823936			−0.411968	+	0.911198i	$0.635158\pi$
$450$		0			0
$451$	−165.056	+	165.056i	−0.365978	+	0.365978i
$452$		0			0
$453$	−469.885	+	469.885i	−1.03727	+	1.03727i
$454$		0			0
$455$	−404.044			−0.888008
$456$		0			0
$457$			439.029i			0.960676i	0.877084	+	0.480338i	$0.159486\pi$
$457$			439.029i			0.960676i	−0.877084	+	0.480338i	$0.840514\pi$
$458$		0			0
$459$	−0.212302	−	0.212302i	−0.000462532	−	0.000462532i
$460$		0			0
$461$	343.333	+	343.333i	0.744758	+	0.744758i	0.973490	−	0.228732i	$-0.0734578\pi$
$461$	343.333	+	343.333i	0.744758	+	0.744758i	−0.228732	+	0.973490i	$0.573458\pi$
$462$		0			0
$463$			24.6983i			0.0533441i	0.999644	+	0.0266720i	$0.00849098\pi$
$463$			24.6983i			0.0533441i	−0.999644	+	0.0266720i	$0.991509\pi$
$464$		0			0
$465$	591.841			1.27278
$466$		0			0
$467$	−449.801	+	449.801i	−0.963172	+	0.963172i	−0.999346	−	0.0361737i	$-0.988483\pi$
$467$	−449.801	+	449.801i	−0.963172	+	0.963172i	0.0361737	+	0.999346i	$0.488483\pi$
$468$		0			0
$469$	−247.618	+	247.618i	−0.527970	+	0.527970i
$470$		0			0
$471$	−339.844			−0.721537
$472$		0			0
$473$			166.679i			0.352387i
$474$		0			0
$475$	32.7367	+	32.7367i	0.0689194	+	0.0689194i
$476$		0			0
$477$	−87.6916	−	87.6916i	−0.183840	−	0.183840i
$478$		0			0
$479$			88.6758i			0.185127i	0.995707	+	0.0925635i	$0.0295061\pi$
$479$			88.6758i			0.185127i	−0.995707	+	0.0925635i	$0.970494\pi$
$480$		0			0
$481$	−387.396			−0.805397
$482$		0			0
$483$	520.571	−	520.571i	1.07779	−	1.07779i
$484$		0			0
$485$	39.9661	−	39.9661i	0.0824042	−	0.0824042i
$486$		0			0
$487$	−485.952			−0.997849			−0.498924	−	0.866646i	$-0.666271\pi$
$487$	−485.952			−0.997849			−0.498924	+	0.866646i	$0.666271\pi$
$488$		0			0
$489$			308.410i			0.630696i
$490$		0			0
$491$	423.526	+	423.526i	0.862578	+	0.862578i	0.991637	−	0.129058i	$-0.0411955\pi$
$491$	423.526	+	423.526i	0.862578	+	0.862578i	−0.129058	+	0.991637i	$0.541196\pi$
$492$		0			0
$493$	1.16212	+	1.16212i	0.00235725	+	0.00235725i
$494$		0			0
$495$			158.462i			0.320124i
$496$		0			0
$497$	−1438.54			−2.89445
$498$		0			0
$499$	−214.781	+	214.781i	−0.430422	+	0.430422i	−0.888772	−	0.458350i	$-0.848441\pi$
$499$	−214.781	+	214.781i	−0.430422	+	0.430422i	0.458350	+	0.888772i	$0.348441\pi$
$500$		0			0
$501$	−663.814	+	663.814i	−1.32498	+	1.32498i
$502$		0			0
$503$	271.633			0.540026			0.270013	−	0.962857i	$-0.412972\pi$
$503$	271.633			0.540026			0.270013	+	0.962857i	$0.412972\pi$
$504$		0			0
$505$		−	237.121i		−	0.469546i
$506$		0			0
$507$	−71.6993	−	71.6993i	−0.141419	−	0.141419i
$508$		0			0
$509$	429.444	+	429.444i	0.843701	+	0.843701i	0.989338	−	0.145637i	$-0.0465231\pi$
$509$	429.444	+	429.444i	0.843701	+	0.843701i	−0.145637	+	0.989338i	$0.546523\pi$
$510$		0			0
$511$		−	657.991i		−	1.28765i
$512$		0			0
$513$	−48.7473			−0.0950241
$514$		0			0
$515$	−40.5624	+	40.5624i	−0.0787619	+	0.0787619i
$516$		0			0
$517$	333.339	−	333.339i	0.644757	−	0.644757i
$518$		0			0
$519$	−379.674			−0.731549
$520$		0			0
$521$			229.061i			0.439657i	0.975539	+	0.219828i	$0.0705498\pi$
$521$			229.061i			0.439657i	−0.975539	+	0.219828i	$0.929450\pi$
$522$		0			0
$523$	−271.157	−	271.157i	−0.518464	−	0.518464i	0.398642	−	0.917106i	$-0.369481\pi$
$523$	−271.157	−	271.157i	−0.518464	−	0.518464i	−0.917106	+	0.398642i	$0.869481\pi$
$524$		0			0
$525$	201.956	+	201.956i	0.384678	+	0.384678i
$526$		0			0
$527$		−	3.44470i		−	0.00653643i
$528$		0			0
$529$	−362.894			−0.685999
$530$		0			0
$531$	313.362	−	313.362i	0.590135	−	0.590135i
$532$		0			0
$533$	−329.354	+	329.354i	−0.617926	+	0.617926i
$534$		0			0
$535$	72.2366			0.135022
$536$		0			0
$537$			94.4088i			0.175808i
$538$		0			0
$539$	594.011	+	594.011i	1.10206	+	1.10206i
$540$		0			0
$541$	−715.363	−	715.363i	−1.32230	−	1.32230i	−0.911913	−	0.410384i	$-0.865395\pi$
$541$	−715.363	−	715.363i	−1.32230	−	1.32230i	−0.410384	−	0.911913i	$-0.634605\pi$
$542$		0			0
$543$			602.925i			1.11036i
$544$		0			0
$545$	195.316			0.358379
$546$		0			0
$547$	−125.606	+	125.606i	−0.229627	+	0.229627i	−0.812537	−	0.582910i	$-0.801914\pi$
$547$	−125.606	+	125.606i	−0.229627	+	0.229627i	0.582910	+	0.812537i	$0.301914\pi$
$548$		0			0
$549$	120.579	−	120.579i	0.219633	−	0.219633i
$550$		0			0
$551$	266.839			0.484281
$552$		0			0
$553$			1007.56i			1.82199i
$554$		0			0
$555$	193.635	+	193.635i	0.348891	+	0.348891i
$556$		0			0
$557$	77.2625	+	77.2625i	0.138712	+	0.138712i	0.773053	−	0.634341i	$-0.218729\pi$
$557$	77.2625	+	77.2625i	0.138712	+	0.138712i	−0.634341	+	0.773053i	$0.718729\pi$
$558$		0			0
$559$			332.593i			0.594978i
$560$		0			0
$561$	1.73597			0.00309442
$562$		0			0
$563$	449.898	−	449.898i	0.799109	−	0.799109i	−0.183846	−	0.982955i	$-0.558855\pi$
$563$	449.898	−	449.898i	0.799109	−	0.799109i	0.982955	+	0.183846i	$0.0588548\pi$
$564$		0			0
$565$	−73.3091	+	73.3091i	−0.129751	+	0.129751i
$566$		0			0
$567$	896.120			1.58046
$568$		0			0
$569$			750.474i			1.31893i	0.751733	+	0.659467i	$0.229218\pi$
$569$			750.474i			1.31893i	−0.751733	+	0.659467i	$0.770782\pi$
$570$		0			0
$571$	655.499	+	655.499i	1.14798	+	1.14798i	0.986949	+	0.161035i	$0.0514832\pi$
$571$	655.499	+	655.499i	1.14798	+	1.14798i	0.161035	+	0.986949i	$0.448517\pi$
$572$		0			0
$573$	−702.588	−	702.588i	−1.22616	−	1.22616i
$574$		0			0
$575$			64.4411i			0.112072i
$576$		0			0
$577$	−60.2980			−0.104503			−0.0522513	−	0.998634i	$-0.516640\pi$
$577$	−60.2980			−0.104503			−0.0522513	+	0.998634i	$0.516640\pi$
$578$		0			0
$579$	−637.634	+	637.634i	−1.10127	+	1.10127i
$580$		0			0
$581$	1433.90	−	1433.90i	2.46798	−	2.46798i
$582$		0			0
$583$	84.4479			0.144851
$584$		0			0
$585$			316.195i			0.540505i
$586$		0			0
$587$	175.896	+	175.896i	0.299652	+	0.299652i	0.840878	−	0.541225i	$-0.182039\pi$
$587$	175.896	+	175.896i	0.299652	+	0.299652i	−0.541225	+	0.840878i	$0.682039\pi$
$588$		0			0
$589$	−395.474	−	395.474i	−0.671433	−	0.671433i
$590$		0			0
$591$		−	512.202i		−	0.866670i
$592$		0			0
$593$	−243.549			−0.410707			−0.205353	−	0.978688i	$-0.565834\pi$
$593$	−243.549			−0.410707			−0.205353	+	0.978688i	$0.565834\pi$
$594$		0			0
$595$	1.17545	−	1.17545i	0.00197554	−	0.00197554i
$596$		0			0
$597$	−316.756	+	316.756i	−0.530579	+	0.530579i
$598$		0			0
$599$	−914.700			−1.52704			−0.763522	−	0.645782i	$-0.776532\pi$
$599$	−914.700			−1.52704			−0.763522	+	0.645782i	$0.776532\pi$
$600$		0			0
$601$		−	709.196i		−	1.18003i	−0.807393	−	0.590013i	$-0.799122\pi$
$601$		−	709.196i		−	1.18003i	0.807393	−	0.590013i	$-0.200878\pi$
$602$		0			0
$603$	193.780	+	193.780i	0.321360	+	0.321360i
$604$		0			0
$605$	115.018	+	115.018i	0.190112	+	0.190112i
$606$		0			0
$607$		−	303.628i		−	0.500211i	−0.968219	−	0.250105i	$-0.919535\pi$
$607$		−	303.628i		−	0.500211i	0.968219	−	0.250105i	$-0.0804653\pi$
$608$		0			0
$609$	1646.15			2.70304
$610$		0			0
$611$	665.147	−	665.147i	1.08862	−	1.08862i
$612$		0			0
$613$	−410.563	+	410.563i	−0.669761	+	0.669761i	−0.957661	−	0.287900i	$-0.907043\pi$
$613$	−410.563	+	410.563i	−0.669761	+	0.669761i	0.287900	+	0.957661i	$0.407043\pi$
$614$		0			0
$615$	329.247			0.535360
$616$		0			0
$617$		−	566.954i		−	0.918888i	−0.888207	−	0.459444i	$-0.848049\pi$
$617$		−	566.954i		−	0.918888i	0.888207	−	0.459444i	$-0.151951\pi$
$618$		0			0
$619$	−323.738	−	323.738i	−0.523001	−	0.523001i	0.395475	−	0.918477i	$-0.370580\pi$
$619$	−323.738	−	323.738i	−0.523001	−	0.523001i	−0.918477	+	0.395475i	$0.870580\pi$
$620$		0			0
$621$	−47.9788	−	47.9788i	−0.0772605	−	0.0772605i
$622$		0			0
$623$			1214.66i			1.94969i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	199.301	−	199.301i	0.317864	−	0.317864i
$628$		0			0
$629$	1.12701	−	1.12701i	0.00179176	−	0.00179176i
$630$		0			0
$631$	19.8772			0.0315012			0.0157506	−	0.999876i	$-0.494986\pi$
$631$	19.8772			0.0315012			0.0157506	+	0.999876i	$0.494986\pi$
$632$		0			0
$633$			421.941i			0.666573i
$634$		0			0
$635$	−88.0839	−	88.0839i	−0.138715	−	0.138715i
$636$		0			0
$637$	1185.29	+	1185.29i	1.86074	+	1.86074i
$638$		0			0
$639$			1125.77i			1.76177i
$640$		0			0
$641$	−537.182			−0.838037			−0.419019	−	0.907978i	$-0.637626\pi$
$641$	−537.182			−0.838037			−0.419019	+	0.907978i	$0.637626\pi$
$642$		0			0
$643$	54.4743	−	54.4743i	0.0847190	−	0.0847190i	−0.663477	−	0.748196i	$-0.730920\pi$
$643$	54.4743	−	54.4743i	0.0847190	−	0.0847190i	0.748196	+	0.663477i	$0.230920\pi$
$644$		0			0
$645$	166.242	−	166.242i	0.257739	−	0.257739i
$646$		0			0
$647$	−1094.96			−1.69237			−0.846184	−	0.532891i	$-0.821106\pi$
$647$	−1094.96			−1.69237			−0.846184	+	0.532891i	$0.821106\pi$
$648$		0			0
$649$			301.770i			0.464977i
$650$		0			0
$651$	−2439.72	−	2439.72i	−3.74764	−	3.74764i
$652$		0			0
$653$	195.649	+	195.649i	0.299616	+	0.299616i	0.840863	−	0.541247i	$-0.182048\pi$
$653$	195.649	+	195.649i	0.299616	+	0.299616i	−0.541247	+	0.840863i	$0.682048\pi$
$654$		0			0
$655$			177.601i			0.271146i
$656$		0			0
$657$	−514.929			−0.783758
$658$		0			0
$659$	−344.936	+	344.936i	−0.523424	+	0.523424i	−0.918604	−	0.395180i	$-0.870682\pi$
$659$	−344.936	+	344.936i	−0.523424	+	0.523424i	0.395180	+	0.918604i	$0.370682\pi$
$660$		0			0
$661$	62.4130	−	62.4130i	0.0944220	−	0.0944220i	−0.658318	−	0.752740i	$-0.728732\pi$
$661$	62.4130	−	62.4130i	0.0944220	−	0.0944220i	0.752740	+	0.658318i	$0.228732\pi$
$662$		0			0
$663$	3.46397			0.00522469
$664$		0			0
$665$		−	269.898i		−	0.405862i
$666$		0			0
$667$	262.632	+	262.632i	0.393750	+	0.393750i
$668$		0			0
$669$	−412.329	−	412.329i	−0.616336	−	0.616336i
$670$		0			0
$671$			116.118i			0.173053i
$672$		0			0
$673$	−99.0512			−0.147179			−0.0735893	−	0.997289i	$-0.523445\pi$
$673$	−99.0512			−0.147179			−0.0735893	+	0.997289i	$0.523445\pi$
$674$		0			0
$675$	18.6134	−	18.6134i	0.0275754	−	0.0275754i
$676$		0			0
$677$	−832.146	+	832.146i	−1.22917	+	1.22917i	−0.264887	+	0.964279i	$0.585335\pi$
$677$	−832.146	+	832.146i	−1.22917	+	1.22917i	−0.964279	+	0.264887i	$0.914665\pi$
$678$		0			0
$679$	−329.500			−0.485273
$680$		0			0
$681$			1035.49i			1.52054i
$682$		0			0
$683$	325.018	+	325.018i	0.475868	+	0.475868i	0.903807	−	0.427939i	$-0.140760\pi$
$683$	325.018	+	325.018i	0.475868	+	0.475868i	−0.427939	+	0.903807i	$0.640760\pi$
$684$		0			0
$685$	−16.7649	−	16.7649i	−0.0244743	−	0.0244743i
$686$		0			0
$687$		−	188.308i		−	0.274102i
$688$		0			0
$689$	168.508			0.244569
$690$		0			0
$691$	−642.205	+	642.205i	−0.929385	+	0.929385i	−0.997666	−	0.0682812i	$-0.978249\pi$
$691$	−642.205	+	642.205i	−0.929385	+	0.929385i	0.0682812	+	0.997666i	$0.478249\pi$
$692$		0			0
$693$	653.219	−	653.219i	0.942595	−	0.942595i
$694$		0			0
$695$	472.588			0.679982
$696$		0			0
$697$		−	1.91632i		−	0.00274938i
$698$		0			0
$699$	−9.18325	−	9.18325i	−0.0131377	−	0.0131377i
$700$		0			0
$701$	546.577	+	546.577i	0.779710	+	0.779710i	0.979781	−	0.200071i	$-0.0641173\pi$
$701$	546.577	+	546.577i	0.779710	+	0.779710i	−0.200071	+	0.979781i	$0.564117\pi$
$702$		0			0
$703$		−	258.777i		−	0.368104i
$704$		0			0
$705$	−664.930			−0.943163
$706$		0			0
$707$	−977.472	+	977.472i	−1.38256	+	1.38256i
$708$		0			0
$709$	−127.872	+	127.872i	−0.180355	+	0.180355i	−0.791510	−	0.611156i	$-0.790705\pi$
$709$	−127.872	+	127.872i	−0.180355	+	0.180355i	0.611156	+	0.791510i	$0.290705\pi$
$710$		0			0
$711$	788.493			1.10899
$712$		0			0
$713$		−	778.478i		−	1.09183i
$714$		0			0
$715$	−152.250	−	152.250i	−0.212937	−	0.212937i
$716$		0			0
$717$	84.3262	+	84.3262i	0.117610	+	0.117610i
$718$		0			0
$719$		−	548.411i		−	0.762741i	−0.924422	−	0.381371i	$-0.875452\pi$
$719$		−	548.411i		−	0.762741i	0.924422	−	0.381371i	$-0.124548\pi$
$720$		0			0
$721$	334.417			0.463824
$722$		0			0
$723$	−676.131	+	676.131i	−0.935174	+	0.935174i
$724$		0			0
$725$	−101.888	+	101.888i	−0.140535	+	0.140535i
$726$		0			0
$727$	928.624			1.27734			0.638669	−	0.769482i	$-0.279485\pi$
$727$	928.624			1.27734			0.638669	+	0.769482i	$0.279485\pi$
$728$		0			0
$729$		−	908.909i		−	1.24679i
$730$		0			0
$731$	−0.967580	−	0.967580i	−0.00132364	−	0.00132364i
$732$		0			0
$733$	854.928	+	854.928i	1.16634	+	1.16634i	0.983061	+	0.183280i	$0.0586716\pi$
$733$	854.928	+	854.928i	1.16634	+	1.16634i	0.183280	+	0.983061i	$0.441328\pi$
$734$		0			0
$735$		−	1184.91i		−	1.61212i
$736$		0			0
$737$	−186.612			−0.253205
$738$		0			0
$739$	912.143	−	912.143i	1.23429	−	1.23429i	0.271994	−	0.962299i	$-0.412317\pi$
$739$	912.143	−	912.143i	1.23429	−	1.23429i	0.962299	−	0.271994i	$-0.0876832\pi$
$740$		0			0
$741$	397.687	−	397.687i	0.536689	−	0.536689i
$742$		0			0
$743$	752.683			1.01303			0.506516	−	0.862230i	$-0.330933\pi$
$743$	752.683			1.01303			0.506516	+	0.862230i	$0.330933\pi$
$744$		0			0
$745$			44.0638i			0.0591461i
$746$		0			0
$747$	−1122.13	−	1122.13i	−1.50219	−	1.50219i
$748$		0			0
$749$	−297.777	−	297.777i	−0.397567	−	0.397567i
$750$		0			0
$751$			72.6596i			0.0967505i	0.998829	+	0.0483752i	$0.0154043\pi$
$751$			72.6596i			0.0967505i	−0.998829	+	0.0483752i	$0.984596\pi$
$752$		0			0
$753$	−574.984			−0.763591
$754$		0			0
$755$	−239.778	+	239.778i	−0.317587	+	0.317587i
$756$		0			0
$757$	325.499	−	325.499i	0.429985	−	0.429985i	−0.458638	−	0.888623i	$-0.651662\pi$
$757$	325.499	−	325.499i	0.429985	−	0.429985i	0.888623	+	0.458638i	$0.151662\pi$
$758$		0			0
$759$	392.317			0.516887
$760$		0			0
$761$			385.629i			0.506740i	0.967369	+	0.253370i	$0.0815391\pi$
$761$			385.629i			0.506740i	−0.967369	+	0.253370i	$0.918461\pi$
$762$		0			0
$763$	−805.143	−	805.143i	−1.05523	−	1.05523i
$764$		0			0
$765$	−0.919877	−	0.919877i	−0.00120245	−	0.00120245i
$766$		0			0
$767$			602.155i			0.785078i
$768$		0			0
$769$	−394.931			−0.513564			−0.256782	−	0.966469i	$-0.582662\pi$
$769$	−394.931			−0.513564			−0.256782	+	0.966469i	$0.582662\pi$
$770$		0			0
$771$	67.8491	−	67.8491i	0.0880014	−	0.0880014i
$772$		0			0
$773$	348.687	−	348.687i	0.451083	−	0.451083i	−0.444631	−	0.895714i	$-0.646665\pi$
$773$	348.687	−	348.687i	0.451083	−	0.451083i	0.895714	+	0.444631i	$0.146665\pi$
$774$		0			0
$775$	302.011			0.389692
$776$		0			0
$777$		−	1596.42i		−	2.05460i
$778$		0			0
$779$	−220.006	−	220.006i	−0.282421	−	0.282421i
$780$		0			0
$781$	−542.064	−	542.064i	−0.694064	−	0.694064i
$782$		0			0
$783$		−	151.719i		−	0.193766i
$784$		0			0
$785$	−173.419			−0.220916
$786$		0			0
$787$	107.998	−	107.998i	0.137228	−	0.137228i	−0.635156	−	0.772384i	$-0.719064\pi$
$787$	107.998	−	107.998i	0.137228	−	0.137228i	0.772384	+	0.635156i	$0.219064\pi$
$788$		0			0
$789$	745.727	−	745.727i	0.945155	−	0.945155i
$790$		0			0
$791$	604.397			0.764092
$792$		0			0
$793$			231.704i			0.292186i
$794$		0			0
$795$	−84.2264	−	84.2264i	−0.105945	−	0.105945i
$796$		0			0
$797$	306.658	+	306.658i	0.384765	+	0.384765i	0.872815	−	0.488050i	$-0.162292\pi$
$797$	306.658	+	306.658i	0.384765	+	0.384765i	−0.488050	+	0.872815i	$0.662292\pi$
$798$		0			0
$799$			3.87010i			0.00484368i
$800$		0			0
$801$	950.564			1.18672
$802$		0			0
$803$	247.941	−	247.941i	0.308768	−	0.308768i
$804$		0			0
$805$	265.643	−	265.643i	0.329991	−	0.329991i
$806$		0			0
$807$	1096.10			1.35824
$808$		0			0
$809$		−	84.8058i		−	0.104828i	−0.998625	−	0.0524140i	$-0.983308\pi$
$809$		−	84.8058i		−	0.104828i	0.998625	−	0.0524140i	$-0.0166915\pi$
$810$		0			0
$811$	777.010	+	777.010i	0.958089	+	0.958089i	0.999156	−	0.0410678i	$-0.0130760\pi$
$811$	777.010	+	777.010i	0.958089	+	0.958089i	−0.0410678	+	0.999156i	$0.513076\pi$
$812$		0			0
$813$	−375.775	−	375.775i	−0.462208	−	0.462208i
$814$		0			0
$815$			157.379i			0.193103i
$816$		0			0
$817$	−222.169			−0.271933
$818$		0			0
$819$	1303.44	−	1303.44i	1.59150	−	1.59150i
$820$		0			0
$821$	−87.3696	+	87.3696i	−0.106418	+	0.106418i	−0.758311	−	0.651893i	$-0.773975\pi$
$821$	−87.3696	+	87.3696i	−0.106418	+	0.106418i	0.651893	+	0.758311i	$0.273975\pi$
$822$		0			0
$823$	−657.759			−0.799221			−0.399610	−	0.916685i	$-0.630855\pi$
$823$	−657.759			−0.799221			−0.399610	+	0.916685i	$0.630855\pi$
$824$		0			0
$825$			152.200i			0.184485i
$826$		0			0
$827$	103.692	+	103.692i	0.125383	+	0.125383i	0.767014	−	0.641631i	$-0.221742\pi$
$827$	103.692	+	103.692i	0.125383	+	0.125383i	−0.641631	+	0.767014i	$0.721742\pi$
$828$		0			0
$829$	−138.573	−	138.573i	−0.167157	−	0.167157i	0.618572	−	0.785728i	$-0.287712\pi$
$829$	−138.573	−	138.573i	−0.167157	−	0.167157i	−0.785728	+	0.618572i	$0.787712\pi$
$830$		0			0
$831$			2098.56i			2.52534i
$832$		0			0
$833$	−6.89653			−0.00827914
$834$		0			0
$835$	−338.739	+	338.739i	−0.405675	+	0.405675i
$836$		0			0
$837$	−224.858	+	224.858i	−0.268648	+	0.268648i
$838$		0			0
$839$	563.984			0.672210			0.336105	−	0.941825i	$-0.390890\pi$
$839$	563.984			0.672210			0.336105	+	0.941825i	$0.390890\pi$
$840$		0			0
$841$		−	10.5045i		−	0.0124904i
$842$		0			0
$843$	1195.63	+	1195.63i	1.41831	+	1.41831i
$844$		0			0
$845$	−36.5875	−	36.5875i	−0.0432988	−	0.0432988i
$846$		0			0
$847$		−	948.264i		−	1.11956i
$848$		0			0
$849$	−1191.95			−1.40395
$850$		0			0
$851$	254.697	−	254.697i	0.299292	−	0.299292i
$852$		0			0
$853$	332.898	−	332.898i	0.390267	−	0.390267i	−0.484516	−	0.874783i	$-0.661004\pi$
$853$	332.898	−	332.898i	0.390267	−	0.390267i	0.874783	+	0.484516i	$0.161004\pi$
$854$		0			0
$855$	−211.216			−0.247036
$856$		0			0
$857$			1027.39i			1.19882i	0.800440	+	0.599412i	$0.204599\pi$
$857$			1027.39i			1.19882i	−0.800440	+	0.599412i	$0.795401\pi$
$858$		0			0
$859$	−822.293	−	822.293i	−0.957268	−	0.957268i	0.0418560	−	0.999124i	$-0.486673\pi$
$859$	−822.293	−	822.293i	−0.957268	−	0.957268i	−0.999124	+	0.0418560i	$0.986673\pi$
$860$		0			0
$861$	−1357.24	−	1357.24i	−1.57635	−	1.57635i
$862$		0			0
$863$		−	1045.44i		−	1.21140i	−0.795694	−	0.605699i	$-0.792894\pi$
$863$		−	1045.44i		−	1.21140i	0.795694	−	0.605699i	$-0.207106\pi$
$864$		0			0
$865$	−193.744			−0.223982
$866$		0			0
$867$	895.457	−	895.457i	1.03282	−	1.03282i
$868$		0			0
$869$	−379.663	+	379.663i	−0.436897	+	0.436897i
$870$		0			0
$871$	−372.367			−0.427517
$872$		0			0
$873$			257.859i			0.295372i
$874$		0			0
$875$	103.056	+	103.056i	0.117779	+	0.117779i
$876$		0			0
$877$	−408.516	−	408.516i	−0.465811	−	0.465811i	0.434743	−	0.900554i	$-0.356839\pi$
$877$	−408.516	−	408.516i	−0.465811	−	0.465811i	−0.900554	+	0.434743i	$0.856839\pi$
$878$		0			0
$879$			862.875i			0.981655i
$880$		0			0
$881$	1034.62			1.17437			0.587185	−	0.809453i	$-0.300236\pi$
$881$	1034.62			1.17437			0.587185	+	0.809453i	$0.300236\pi$
$882$		0			0
$883$	22.1691	−	22.1691i	0.0251065	−	0.0251065i	−0.694442	−	0.719549i	$-0.744349\pi$
$883$	22.1691	−	22.1691i	0.0251065	−	0.0251065i	0.719549	+	0.694442i	$0.244349\pi$
$884$		0			0
$885$	300.979	−	300.979i	0.340089	−	0.340089i
$886$		0			0
$887$	−357.676			−0.403242			−0.201621	−	0.979464i	$-0.564621\pi$
$887$	−357.676			−0.403242			−0.201621	+	0.979464i	$0.564621\pi$
$888$		0			0
$889$			726.208i			0.816881i
$890$		0			0
$891$	337.671	+	337.671i	0.378980	+	0.378980i
$892$		0			0
$893$	444.313	+	444.313i	0.497551	+	0.497551i
$894$		0			0
$895$			48.1760i			0.0538279i
$896$		0			0
$897$	782.833			0.872723
$898$		0			0
$899$	1230.85	−	1230.85i	1.36914	−	1.36914i
$900$		0			0
$901$	−0.490224	+	0.490224i	−0.000544089	+	0.000544089i
$902$		0			0
$903$	−1370.58			−1.51781
$904$		0			0
$905$			307.667i			0.339964i
$906$		0			0
$907$	168.013	+	168.013i	0.185241	+	0.185241i	0.793635	−	0.608394i	$-0.208186\pi$
$907$	168.013	+	168.013i	0.185241	+	0.185241i	−0.608394	+	0.793635i	$0.708186\pi$
$908$		0			0
$909$	764.947	+	764.947i	0.841526	+	0.841526i
$910$		0			0
$911$			63.0075i			0.0691630i	0.999402	+	0.0345815i	$0.0110098\pi$
$911$			63.0075i			0.0691630i	−0.999402	+	0.0345815i	$0.988990\pi$
$912$		0			0
$913$	1080.63			1.18360
$914$		0			0
$915$	115.814	−	115.814i	0.126573	−	0.126573i
$916$		0			0
$917$	732.114	−	732.114i	0.798380	−	0.798380i
$918$		0			0
$919$	−1204.21			−1.31035			−0.655175	−	0.755477i	$-0.727405\pi$
$919$	−1204.21			−1.31035			−0.655175	+	0.755477i	$0.727405\pi$
$920$		0			0
$921$			2167.12i			2.35301i
$922$		0			0
$923$	−1081.64	−	1081.64i	−1.17187	−	1.17187i
$924$		0			0
$925$	98.8101	+	98.8101i	0.106822	+	0.106822i
$926$		0			0
$927$		−	261.707i		−	0.282316i
$928$		0			0
$929$	1090.56			1.17391			0.586954	−	0.809621i	$-0.300327\pi$
$929$	1090.56			1.17391			0.586954	+	0.809621i	$0.300327\pi$
$930$		0			0
$931$	−791.767	+	791.767i	−0.850448	+	0.850448i
$932$		0			0
$933$	1533.72	−	1533.72i	1.64386	−	1.64386i
$934$		0			0
$935$	0.885851			0.000947434
$936$		0			0
$937$		−	1483.09i		−	1.58280i	−0.611296	−	0.791402i	$-0.709351\pi$
$937$		−	1483.09i		−	1.58280i	0.611296	−	0.791402i	$-0.290649\pi$
$938$		0			0
$939$	1244.73	+	1244.73i	1.32559	+	1.32559i
$940$		0			0
$941$	593.649	+	593.649i	0.630870	+	0.630870i	0.948286	−	0.317416i	$-0.102815\pi$
$941$	593.649	+	593.649i	0.630870	+	0.630870i	−0.317416	+	0.948286i	$0.602815\pi$
$942$		0			0
$943$		−	433.075i		−	0.459252i
$944$		0			0
$945$	−153.458			−0.162390
$946$		0			0
$947$	1027.33	−	1027.33i	1.08483	−	1.08483i	0.0887735	−	0.996052i	$-0.471705\pi$
$947$	1027.33	−	1027.33i	1.08483	−	1.08483i	0.996052	−	0.0887735i	$-0.0282947\pi$
$948$		0			0
$949$	494.743	−	494.743i	0.521331	−	0.521331i
$950$		0			0
$951$	1362.34			1.43253
$952$		0			0
$953$		−	1207.29i		−	1.26683i	−0.773811	−	0.633417i	$-0.781652\pi$
$953$		−	1207.29i		−	1.26683i	0.773811	−	0.633417i	$-0.218348\pi$
$954$		0			0
$955$	−358.524	−	358.524i	−0.375418	−	0.375418i
$956$		0			0
$957$	620.295	+	620.295i	0.648166	+	0.648166i
$958$		0			0
$959$			138.218i			0.144127i
$960$		0			0
$961$	−2687.43			−2.79649
$962$		0			0
$963$	−233.034	+	233.034i	−0.241987	+	0.241987i
$964$		0			0
$965$	−325.379	+	325.379i	−0.337181	+	0.337181i
$966$		0			0
$967$	−890.860			−0.921262			−0.460631	−	0.887592i	$-0.652377\pi$
$967$	−890.860			−0.921262			−0.460631	+	0.887592i	$0.652377\pi$
$968$		0			0
$969$			2.31390i			0.00238793i
$970$		0			0
$971$	−1036.95	−	1036.95i	−1.06792	−	1.06792i	−0.997519	−	0.0704020i	$-0.977572\pi$
$971$	−1036.95	−	1036.95i	−1.06792	−	1.06792i	−0.0704020	−	0.997519i	$-0.522428\pi$
$972$		0			0
$973$	−1948.12	−	1948.12i	−2.00218	−	2.00218i
$974$		0			0
$975$			303.701i			0.311488i
$976$		0			0
$977$	−595.913			−0.609941			−0.304971	−	0.952362i	$-0.598647\pi$
$977$	−595.913			−0.609941			−0.304971	+	0.952362i	$0.598647\pi$
$978$		0			0
$979$	−457.701	+	457.701i	−0.467519	+	0.467519i
$980$		0			0
$981$	−630.087	+	630.087i	−0.642290	+	0.642290i
$982$		0			0
$983$	110.830			0.112746			0.0563731	−	0.998410i	$-0.482046\pi$
$983$	110.830			0.112746			0.0563731	+	0.998410i	$0.482046\pi$
$984$		0			0
$985$		−	261.372i		−	0.265352i
$986$		0			0
$987$	2741.01	+	2741.01i	2.77711	+	2.77711i
$988$		0			0
$989$	−218.666	−	218.666i	−0.221098	−	0.221098i
$990$		0			0
$991$			900.246i			0.908421i	0.890894	+	0.454211i	$0.150079\pi$
$991$			900.246i			0.908421i	−0.890894	+	0.454211i	$0.849921\pi$
$992$		0			0
$993$	−138.837			−0.139816
$994$		0			0
$995$	−161.638	+	161.638i	−0.162450	+	0.162450i
$996$		0			0
$997$	−716.305	+	716.305i	−0.718460	+	0.718460i	−0.968290	−	0.249830i	$-0.919625\pi$
$997$	−716.305	+	716.305i	−0.718460	+	0.718460i	0.249830	+	0.968290i	$0.419625\pi$
$998$		0			0
$999$	−147.135			−0.147283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.r.a.111.3		32
4.3	odd	2		80.3.r.a.51.15	yes	32
8.3	odd	2		640.3.r.a.351.3		32
8.5	even	2		640.3.r.b.351.14		32
16.3	odd	4		640.3.r.b.31.14		32
16.5	even	4		80.3.r.a.11.15	✓	32
16.11	odd	4	inner	320.3.r.a.271.3		32
16.13	even	4		640.3.r.a.31.3		32
20.3	even	4		400.3.k.h.99.10		32
20.7	even	4		400.3.k.g.99.7		32
20.19	odd	2		400.3.r.f.51.2		32
80.37	odd	4		400.3.k.h.299.10		32
80.53	odd	4		400.3.k.g.299.7		32
80.69	even	4		400.3.r.f.251.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.15	✓	32	16.5	even	4
80.3.r.a.51.15	yes	32	4.3	odd	2
320.3.r.a.111.3		32	1.1	even	1	trivial
320.3.r.a.271.3		32	16.11	odd	4	inner
400.3.k.g.99.7		32	20.7	even	4
400.3.k.g.299.7		32	80.53	odd	4
400.3.k.h.99.10		32	20.3	even	4
400.3.k.h.299.10		32	80.37	odd	4
400.3.r.f.51.2		32	20.19	odd	2
400.3.r.f.251.2		32	80.69	even	4
640.3.r.a.31.3		32	16.13	even	4
640.3.r.a.351.3		32	8.3	odd	2
640.3.r.b.31.14		32	16.3	odd	4
640.3.r.b.351.14		32	8.5	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.r (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.09850 + 3.09850i) q^{3} +(-1.58114 + 1.58114i) q^{5} +13.0357 q^{7} -10.2014i q^{9} +O(q^{10})\)	\(q+(-3.09850 + 3.09850i) q^{3} +(-1.58114 + 1.58114i) q^{5} +13.0357 q^{7} -10.2014i q^{9} +(4.91205 + 4.91205i) q^{11} +(9.80153 + 9.80153i) q^{13} -9.79833i q^{15} -0.0570293 q^{17} +(-6.54734 + 6.54734i) q^{19} +(-40.3912 + 40.3912i) q^{21} -12.8882 q^{23} -5.00000i q^{25} +(3.72268 + 3.72268i) q^{27} +(-20.3776 - 20.3776i) q^{29} +60.4022i q^{31} -30.4400 q^{33} +(-20.6113 + 20.6113i) q^{35} +(-19.7620 + 19.7620i) q^{37} -60.7401 q^{39} +33.6023i q^{41} +(16.9664 + 16.9664i) q^{43} +(16.1299 + 16.1299i) q^{45} -67.8616i q^{47} +120.930 q^{49} +(0.176706 - 0.176706i) q^{51} +(8.59600 - 8.59600i) q^{53} -15.5333 q^{55} -40.5739i q^{57} +(30.7174 + 30.7174i) q^{59} +(11.8198 + 11.8198i) q^{61} -132.983i q^{63} -30.9952 q^{65} +(-18.9954 + 18.9954i) q^{67} +(39.9342 - 39.9342i) q^{69} -110.354 q^{71} -50.4761i q^{73} +(15.4925 + 15.4925i) q^{75} +(64.0320 + 64.0320i) q^{77} +77.2923i q^{79} +68.7435 q^{81} +(109.998 - 109.998i) q^{83} +(0.0901713 - 0.0901713i) q^{85} +126.280 q^{87} +93.1793i q^{89} +(127.770 + 127.770i) q^{91} +(-187.157 - 187.157i) q^{93} -20.7045i q^{95} -25.2768 q^{97} +(50.1100 - 50.1100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more