LMFDB - Embedded newform 1740.3.bl.a.481.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1740,3,Mod(481,1740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1740, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1740.481");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1740.bl (of order $4$, degree $2$, 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:	$47.4115659987$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			481.14
Character	$\chi$	$=$	1740.481
Dual form			1740.3.bl.a.1201.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 1.22474i) q^{3} +2.23607i q^{5} +4.92030 q^{7} -3.00000i q^{9} +(-4.50909 + 4.50909i) q^{11} +2.37920i q^{13} +(-2.73861 - 2.73861i) q^{15} +(9.67426 - 9.67426i) q^{17} +(3.07195 - 3.07195i) q^{19} +(-6.02611 + 6.02611i) q^{21} +20.3604 q^{23} -5.00000 q^{25} +(3.67423 + 3.67423i) q^{27} +(-4.95885 - 28.5729i) q^{29} +(31.2749 - 31.2749i) q^{31} -11.0450i q^{33} +11.0021i q^{35} +(5.24068 + 5.24068i) q^{37} +(-2.91392 - 2.91392i) q^{39} +(47.2943 + 47.2943i) q^{41} +(-51.9205 + 51.9205i) q^{43} +6.70820 q^{45} +(-4.56954 - 4.56954i) q^{47} -24.7907 q^{49} +23.6970i q^{51} +17.4977 q^{53} +(-10.0826 - 10.0826i) q^{55} +7.52470i q^{57} +60.6038 q^{59} +(77.4847 - 77.4847i) q^{61} -14.7609i q^{63} -5.32006 q^{65} +24.2525i q^{67} +(-24.9362 + 24.9362i) q^{69} -63.5896i q^{71} +(-32.9786 - 32.9786i) q^{73} +(6.12372 - 6.12372i) q^{75} +(-22.1861 + 22.1861i) q^{77} +(24.8475 - 24.8475i) q^{79} -9.00000 q^{81} +79.9020 q^{83} +(21.6323 + 21.6323i) q^{85} +(41.0678 + 28.9212i) q^{87} +(-63.0239 + 63.0239i) q^{89} +11.7064i q^{91} +76.6077i q^{93} +(6.86908 + 6.86908i) q^{95} +(-47.9182 - 47.9182i) q^{97} +(13.5273 + 13.5273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 56 q^{17} + 24 q^{19} + 144 q^{23} - 400 q^{25} - 64 q^{29} - 128 q^{31} - 48 q^{37} + 48 q^{39} + 56 q^{41} - 88 q^{43} - 56 q^{47} + 448 q^{49} - 64 q^{53} - 80 q^{55} - 16 q^{59} + 248 q^{61}+ \cdots - 312 q^{97}+O(q^{100}) $ 80 * q - 56 * q^17 + 24 * q^19 + 144 * q^23 - 400 * q^25 - 64 * q^29 - 128 * q^31 - 48 * q^37 + 48 * q^39 + 56 * q^41 - 88 * q^43 - 56 * q^47 + 448 * q^49 - 64 * q^53 - 80 * q^55 - 16 * q^59 + 248 * q^61 + 216 * q^69 + 128 * q^73 - 360 * q^77 + 136 * q^79 - 720 * q^81 - 160 * q^83 - 120 * q^85 - 24 * q^87 - 88 * q^89 - 80 * q^95 - 312 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1740\mathbb{Z}\right)^\times$.

$n$	$581$	$697$	$871$	$901$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		0			0
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$		0			0
$7$	4.92030			0.702900			0.351450	−	0.936207i	$-0.385689\pi$
$7$	4.92030			0.702900			0.351450	+	0.936207i	$0.385689\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−4.50909	+	4.50909i	−0.409917	+	0.409917i	−0.881710	−	0.471792i	$-0.843607\pi$
$11$	−4.50909	+	4.50909i	−0.409917	+	0.409917i	0.471792	+	0.881710i	$0.343607\pi$
$12$		0			0
$13$			2.37920i			0.183016i	0.995804	+	0.0915078i	$0.0291686\pi$
$13$			2.37920i			0.183016i	−0.995804	+	0.0915078i	$0.970831\pi$
$14$		0			0
$15$	−2.73861	−	2.73861i	−0.182574	−	0.182574i
$16$		0			0
$17$	9.67426	−	9.67426i	0.569074	−	0.569074i	−0.362795	−	0.931869i	$-0.618177\pi$
$17$	9.67426	−	9.67426i	0.569074	−	0.569074i	0.931869	+	0.362795i	$0.118177\pi$
$18$		0			0
$19$	3.07195	−	3.07195i	0.161681	−	0.161681i	−0.621630	−	0.783311i	$-0.713529\pi$
$19$	3.07195	−	3.07195i	0.161681	−	0.161681i	0.783311	+	0.621630i	$0.213529\pi$
$20$		0			0
$21$	−6.02611	+	6.02611i	−0.286958	+	0.286958i
$22$		0			0
$23$	20.3604			0.885233			0.442617	−	0.896711i	$-0.354050\pi$
$23$	20.3604			0.885233			0.442617	+	0.896711i	$0.354050\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$		0			0
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$		0			0
$29$	−4.95885	−	28.5729i	−0.170995	−	0.985272i
$29$	−4.95885	−	28.5729i	−0.170995	−	0.985272i
$30$		0			0
$31$	31.2749	−	31.2749i	1.00887	−	1.00887i	0.00890884	−	0.999960i	$-0.497164\pi$
$31$	31.2749	−	31.2749i	1.00887	−	1.00887i	0.999960	−	0.00890884i	$-0.00283581\pi$
$32$		0			0
$33$		−	11.0450i		−	0.334696i
$34$		0			0
$35$			11.0021i			0.314346i
$36$		0			0
$37$	5.24068	+	5.24068i	0.141640	+	0.141640i	0.774371	−	0.632731i	$-0.218066\pi$
$37$	5.24068	+	5.24068i	0.141640	+	0.141640i	−0.632731	+	0.774371i	$0.718066\pi$
$38$		0			0
$39$	−2.91392	−	2.91392i	−0.0747158	−	0.0747158i
$40$		0			0
$41$	47.2943	+	47.2943i	1.15352	+	1.15352i	0.985842	+	0.167677i	$0.0536264\pi$
$41$	47.2943	+	47.2943i	1.15352	+	1.15352i	0.167677	+	0.985842i	$0.446374\pi$
$42$		0			0
$43$	−51.9205	+	51.9205i	−1.20745	+	1.20745i	−0.235606	+	0.971849i	$0.575707\pi$
$43$	−51.9205	+	51.9205i	−1.20745	+	1.20745i	−0.971849	+	0.235606i	$0.924293\pi$
$44$		0			0
$45$	6.70820			0.149071
$46$		0			0
$47$	−4.56954	−	4.56954i	−0.0972242	−	0.0972242i	0.656822	−	0.754046i	$-0.271900\pi$
$47$	−4.56954	−	4.56954i	−0.0972242	−	0.0972242i	−0.754046	+	0.656822i	$0.771900\pi$
$48$		0			0
$49$	−24.7907			−0.505932
$50$		0			0
$51$			23.6970i			0.464647i
$52$		0			0
$53$	17.4977			0.330145			0.165072	−	0.986281i	$-0.447214\pi$
$53$	17.4977			0.330145			0.165072	+	0.986281i	$0.447214\pi$
$54$		0			0
$55$	−10.0826	−	10.0826i	−0.183321	−	0.183321i
$56$		0			0
$57$			7.52470i			0.132012i
$58$		0			0
$59$	60.6038			1.02718			0.513592	−	0.858035i	$-0.328315\pi$
$59$	60.6038			1.02718			0.513592	+	0.858035i	$0.328315\pi$
$60$		0			0
$61$	77.4847	−	77.4847i	1.27024	−	1.27024i	0.324280	−	0.945961i	$-0.394878\pi$
$61$	77.4847	−	77.4847i	1.27024	−	1.27024i	0.945961	−	0.324280i	$-0.105122\pi$
$62$		0			0
$63$		−	14.7609i		−	0.234300i
$64$		0			0
$65$	−5.32006			−0.0818470
$66$		0			0
$67$			24.2525i			0.361977i	0.983485	+	0.180989i	$0.0579297\pi$
$67$			24.2525i			0.361977i	−0.983485	+	0.180989i	$0.942070\pi$
$68$		0			0
$69$	−24.9362	+	24.9362i	−0.361395	+	0.361395i
$70$		0			0
$71$		−	63.5896i		−	0.895628i	−0.894127	−	0.447814i	$-0.852203\pi$
$71$		−	63.5896i		−	0.895628i	0.894127	−	0.447814i	$-0.147797\pi$
$72$		0			0
$73$	−32.9786	−	32.9786i	−0.451762	−	0.451762i	0.444177	−	0.895939i	$-0.353496\pi$
$73$	−32.9786	−	32.9786i	−0.451762	−	0.451762i	−0.895939	+	0.444177i	$0.853496\pi$
$74$		0			0
$75$	6.12372	−	6.12372i	0.0816497	−	0.0816497i
$76$		0			0
$77$	−22.1861	+	22.1861i	−0.288131	+	0.288131i
$78$		0			0
$79$	24.8475	−	24.8475i	0.314525	−	0.314525i	−0.532135	−	0.846660i	$-0.678610\pi$
$79$	24.8475	−	24.8475i	0.314525	−	0.314525i	0.846660	+	0.532135i	$0.178610\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	79.9020			0.962675			0.481337	−	0.876535i	$-0.340151\pi$
$83$	79.9020			0.962675			0.481337	+	0.876535i	$0.340151\pi$
$84$		0			0
$85$	21.6323	+	21.6323i	0.254498	+	0.254498i
$86$		0			0
$87$	41.0678	+	28.9212i	0.472044	+	0.332427i
$88$		0			0
$89$	−63.0239	+	63.0239i	−0.708134	+	0.708134i	−0.966143	−	0.258009i	$-0.916934\pi$
$89$	−63.0239	+	63.0239i	−0.708134	+	0.708134i	0.258009	+	0.966143i	$0.416934\pi$
$90$		0			0
$91$			11.7064i			0.128642i
$92$		0			0
$93$			76.6077i			0.823738i
$94$		0			0
$95$	6.86908	+	6.86908i	0.0723062	+	0.0723062i
$96$		0			0
$97$	−47.9182	−	47.9182i	−0.494002	−	0.494002i	0.415563	−	0.909565i	$-0.363585\pi$
$97$	−47.9182	−	47.9182i	−0.494002	−	0.494002i	−0.909565	+	0.415563i	$0.863585\pi$
$98$		0			0
$99$	13.5273	+	13.5273i	0.136639	+	0.136639i
$100$		0			0
$101$	−52.0598	+	52.0598i	−0.515443	+	0.515443i	−0.916189	−	0.400746i	$-0.868751\pi$
$101$	−52.0598	+	52.0598i	−0.515443	+	0.515443i	0.400746	+	0.916189i	$0.368751\pi$
$102$		0			0
$103$	−104.648			−1.01600			−0.508002	−	0.861356i	$-0.669616\pi$
$103$	−104.648			−1.01600			−0.508002	+	0.861356i	$0.669616\pi$
$104$		0			0
$105$	−13.4748	−	13.4748i	−0.128331	−	0.128331i
$106$		0			0
$107$	131.814			1.23191			0.615953	−	0.787783i	$-0.288771\pi$
$107$	131.814			1.23191			0.615953	+	0.787783i	$0.288771\pi$
$108$		0			0
$109$			88.8610i			0.815239i	0.913152	+	0.407619i	$0.133641\pi$
$109$			88.8610i			0.815239i	−0.913152	+	0.407619i	$0.866359\pi$
$110$		0			0
$111$	−12.8370			−0.115649
$112$		0			0
$113$	80.6690	+	80.6690i	0.713885	+	0.713885i	0.967346	−	0.253461i	$-0.0815688\pi$
$113$	80.6690	+	80.6690i	0.713885	+	0.713885i	−0.253461	+	0.967346i	$0.581569\pi$
$114$		0			0
$115$			45.5272i			0.395888i
$116$		0			0
$117$	7.13761			0.0610052
$118$		0			0
$119$	47.6002	−	47.6002i	0.400002	−	0.400002i
$120$		0			0
$121$			80.3362i			0.663935i
$122$		0			0
$123$	−115.847			−0.941844
$124$		0			0
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	117.138	−	117.138i	0.922350	−	0.922350i	−0.0748454	−	0.997195i	$-0.523846\pi$
$127$	117.138	−	117.138i	0.922350	−	0.922350i	0.997195	+	0.0748454i	$0.0238463\pi$
$128$		0			0
$129$		−	127.179i		−	0.985883i
$130$		0			0
$131$	138.116	+	138.116i	1.05432	+	1.05432i	0.998437	+	0.0558855i	$0.0177982\pi$
$131$	138.116	+	138.116i	1.05432	+	1.05432i	0.0558855	+	0.998437i	$0.482202\pi$
$132$		0			0
$133$	15.1149	−	15.1149i	0.113646	−	0.113646i
$134$		0			0
$135$	−8.21584	+	8.21584i	−0.0608581	+	0.0608581i
$136$		0			0
$137$	82.3268	−	82.3268i	0.600926	−	0.600926i	−0.339632	−	0.940558i	$-0.610303\pi$
$137$	82.3268	−	82.3268i	0.600926	−	0.600926i	0.940558	+	0.339632i	$0.110303\pi$
$138$		0			0
$139$	−173.281			−1.24662			−0.623312	−	0.781974i	$-0.714213\pi$
$139$	−173.281			−1.24662			−0.623312	+	0.781974i	$0.714213\pi$
$140$		0			0
$141$	11.1930			0.0793832
$142$		0			0
$143$	−10.7280	−	10.7280i	−0.0750213	−	0.0750213i
$144$		0			0
$145$	63.8909	−	11.0883i	0.440627	−	0.0764712i
$146$		0			0
$147$	30.3622	−	30.3622i	0.206546	−	0.206546i
$148$		0			0
$149$			202.897i			1.36173i	0.732411	+	0.680863i	$0.238395\pi$
$149$			202.897i			1.36173i	−0.732411	+	0.680863i	$0.761605\pi$
$150$		0			0
$151$			109.215i			0.723278i	0.932318	+	0.361639i	$0.117783\pi$
$151$			109.215i			0.723278i	−0.932318	+	0.361639i	$0.882217\pi$
$152$		0			0
$153$	−29.0228	−	29.0228i	−0.189691	−	0.189691i
$154$		0			0
$155$	69.9329	+	69.9329i	0.451180	+	0.451180i
$156$		0			0
$157$	210.737	+	210.737i	1.34228	+	1.34228i	0.893789	+	0.448488i	$0.148037\pi$
$157$	210.737	+	210.737i	1.34228	+	1.34228i	0.448488	+	0.893789i	$0.351963\pi$
$158$		0			0
$159$	−21.4302	+	21.4302i	−0.134781	+	0.134781i
$160$		0			0
$161$	100.179			0.622230
$162$		0			0
$163$	226.000	+	226.000i	1.38651	+	1.38651i	0.832538	+	0.553967i	$0.186887\pi$
$163$	226.000	+	226.000i	1.38651	+	1.38651i	0.553967	+	0.832538i	$0.313113\pi$
$164$		0			0
$165$	24.6973			0.149681
$166$		0			0
$167$			29.6838i			0.177747i	0.996043	+	0.0888736i	$0.0283267\pi$
$167$			29.6838i			0.177747i	−0.996043	+	0.0888736i	$0.971673\pi$
$168$		0			0
$169$	163.339			0.966505
$170$		0			0
$171$	−9.21584	−	9.21584i	−0.0538938	−	0.0538938i
$172$		0			0
$173$			84.1834i			0.486609i	0.969950	+	0.243305i	$0.0782315\pi$
$173$			84.1834i			0.486609i	−0.969950	+	0.243305i	$0.921769\pi$
$174$		0			0
$175$	−24.6015			−0.140580
$176$		0			0
$177$	−74.2242	+	74.2242i	−0.419346	+	0.419346i
$178$		0			0
$179$		−	15.5114i		−	0.0866560i	−0.999061	−	0.0433280i	$-0.986204\pi$
$179$		−	15.5114i		−	0.0866560i	0.999061	−	0.0433280i	$-0.0137960\pi$
$180$		0			0
$181$	−266.702			−1.47349			−0.736745	−	0.676171i	$-0.763638\pi$
$181$	−266.702			−1.47349			−0.736745	+	0.676171i	$0.763638\pi$
$182$		0			0
$183$			189.798i			1.03715i
$184$		0			0
$185$	−11.7185	+	11.7185i	−0.0633434	+	0.0633434i
$186$		0			0
$187$			87.2443i			0.466547i
$188$		0			0
$189$	18.0783	+	18.0783i	0.0956526	+	0.0956526i
$190$		0			0
$191$	−246.554	+	246.554i	−1.29086	+	1.29086i	−0.356601	+	0.934257i	$0.616064\pi$
$191$	−246.554	+	246.554i	−1.29086	+	1.29086i	−0.934257	+	0.356601i	$0.883936\pi$
$192$		0			0
$193$	−45.3461	+	45.3461i	−0.234954	+	0.234954i	−0.814757	−	0.579803i	$-0.803130\pi$
$193$	−45.3461	+	45.3461i	−0.234954	+	0.234954i	0.579803	+	0.814757i	$0.303130\pi$
$194$		0			0
$195$	6.51571	−	6.51571i	0.0334139	−	0.0334139i
$196$		0			0
$197$	170.640			0.866194			0.433097	−	0.901347i	$-0.357421\pi$
$197$	170.640			0.866194			0.433097	+	0.901347i	$0.357421\pi$
$198$		0			0
$199$	151.175			0.759675			0.379837	−	0.925053i	$-0.375980\pi$
$199$	151.175			0.759675			0.379837	+	0.925053i	$0.375980\pi$
$200$		0			0
$201$	−29.7031	−	29.7031i	−0.147777	−	0.147777i
$202$		0			0
$203$	−24.3990	−	140.587i	−0.120192	−	0.692548i
$204$		0			0
$205$	−105.753	+	105.753i	−0.515869	+	0.515869i
$206$		0			0
$207$		−	61.0811i		−	0.295078i
$208$		0			0
$209$			27.7034i			0.132552i
$210$		0			0
$211$	45.9441	+	45.9441i	0.217745	+	0.217745i	0.807547	−	0.589803i	$-0.200795\pi$
$211$	45.9441	+	45.9441i	0.217745	+	0.217745i	−0.589803	+	0.807547i	$0.700795\pi$
$212$		0			0
$213$	77.8810	+	77.8810i	0.365639	+	0.365639i
$214$		0			0
$215$	−116.098	−	116.098i	−0.539990	−	0.539990i
$216$		0			0
$217$	153.882	−	153.882i	0.709134	−	0.709134i
$218$		0			0
$219$	80.7807			0.368862
$220$		0			0
$221$	23.0170	+	23.0170i	0.104149	+	0.104149i
$222$		0			0
$223$	294.316			1.31980			0.659900	−	0.751353i	$-0.270598\pi$
$223$	294.316			1.31980			0.659900	+	0.751353i	$0.270598\pi$
$224$		0			0
$225$			15.0000i			0.0666667i
$226$		0			0
$227$	60.0133			0.264376			0.132188	−	0.991225i	$-0.457800\pi$
$227$	60.0133			0.264376			0.132188	+	0.991225i	$0.457800\pi$
$228$		0			0
$229$	−9.15393	−	9.15393i	−0.0399735	−	0.0399735i	0.686837	−	0.726811i	$-0.258998\pi$
$229$	−9.15393	−	9.15393i	−0.0399735	−	0.0399735i	−0.726811	+	0.686837i	$0.758998\pi$
$230$		0			0
$231$		−	54.3446i		−	0.235258i
$232$		0			0
$233$	44.6616			0.191681			0.0958403	−	0.995397i	$-0.469446\pi$
$233$	44.6616			0.191681			0.0958403	+	0.995397i	$0.469446\pi$
$234$		0			0
$235$	10.2178	−	10.2178i	0.0434800	−	0.0434800i
$236$		0			0
$237$			60.8636i			0.256808i
$238$		0			0
$239$	296.259			1.23958			0.619788	−	0.784769i	$-0.287219\pi$
$239$	296.259			1.23958			0.619788	+	0.784769i	$0.287219\pi$
$240$		0			0
$241$		−	8.66869i		−	0.0359697i	−0.999838	−	0.0179848i	$-0.994275\pi$
$241$		−	8.66869i		−	0.0359697i	0.999838	−	0.0179848i	$-0.00572506\pi$
$242$		0			0
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		0			0
$245$		−	55.4336i		−	0.226260i
$246$		0			0
$247$	7.30878	+	7.30878i	0.0295902	+	0.0295902i
$248$		0			0
$249$	−97.8596	+	97.8596i	−0.393010	+	0.393010i
$250$		0			0
$251$	93.3466	−	93.3466i	0.371899	−	0.371899i	−0.496270	−	0.868168i	$-0.665297\pi$
$251$	93.3466	−	93.3466i	0.371899	−	0.371899i	0.868168	+	0.496270i	$0.165297\pi$
$252$		0			0
$253$	−91.8067	+	91.8067i	−0.362873	+	0.362873i
$254$		0			0
$255$	−52.9881			−0.207796
$256$		0			0
$257$	292.353			1.13756			0.568780	−	0.822490i	$-0.307416\pi$
$257$	292.353			1.13756			0.568780	+	0.822490i	$0.307416\pi$
$258$		0			0
$259$	25.7857	+	25.7857i	0.0995588	+	0.0995588i
$260$		0			0
$261$	−85.7187	+	14.8765i	−0.328424	+	0.0569983i
$262$		0			0
$263$	212.322	−	212.322i	0.807306	−	0.807306i	−0.176919	−	0.984225i	$-0.556613\pi$
$263$	212.322	−	212.322i	0.807306	−	0.807306i	0.984225	+	0.176919i	$0.0566131\pi$
$264$		0			0
$265$			39.1260i			0.147645i
$266$		0			0
$267$		−	154.376i		−	0.578189i
$268$		0			0
$269$	−234.025	−	234.025i	−0.869982	−	0.869982i	0.122488	−	0.992470i	$-0.460913\pi$
$269$	−234.025	−	234.025i	−0.869982	−	0.869982i	−0.992470	+	0.122488i	$0.960913\pi$
$270$		0			0
$271$	−234.006	−	234.006i	−0.863491	−	0.863491i	0.128251	−	0.991742i	$-0.459064\pi$
$271$	−234.006	−	234.006i	−0.863491	−	0.863491i	−0.991742	+	0.128251i	$0.959064\pi$
$272$		0			0
$273$	−14.3373	−	14.3373i	−0.0525177	−	0.0525177i
$274$		0			0
$275$	22.5455	−	22.5455i	0.0819835	−	0.0819835i
$276$		0			0
$277$	−293.821			−1.06073			−0.530364	−	0.847770i	$-0.677945\pi$
$277$	−293.821			−1.06073			−0.530364	+	0.847770i	$0.677945\pi$
$278$		0			0
$279$	−93.8248	−	93.8248i	−0.336290	−	0.336290i
$280$		0			0
$281$	89.8185			0.319639			0.159819	−	0.987146i	$-0.448909\pi$
$281$	89.8185			0.319639			0.159819	+	0.987146i	$0.448909\pi$
$282$		0			0
$283$		−	520.527i		−	1.83932i	−0.392717	−	0.919659i	$-0.628465\pi$
$283$		−	520.527i		−	1.83932i	0.392717	−	0.919659i	$-0.371535\pi$
$284$		0			0
$285$	−16.8258			−0.0590377
$286$		0			0
$287$	232.702	+	232.702i	0.810808	+	0.810808i
$288$		0			0
$289$			101.817i			0.352309i
$290$		0			0
$291$	117.375			0.403351
$292$		0			0
$293$	−145.401	+	145.401i	−0.496248	+	0.496248i	−0.910268	−	0.414020i	$-0.864124\pi$
$293$	−145.401	+	145.401i	−0.496248	+	0.496248i	0.414020	+	0.910268i	$0.364124\pi$
$294$		0			0
$295$			135.514i			0.459370i
$296$		0			0
$297$	−33.1349			−0.111565
$298$		0			0
$299$			48.4414i			0.162011i
$300$		0			0
$301$	−255.465	+	255.465i	−0.848720	+	0.848720i
$302$		0			0
$303$		−	127.520i		−	0.420858i
$304$		0			0
$305$	173.261	+	173.261i	0.568069	+	0.568069i
$306$		0			0
$307$	79.7749	−	79.7749i	0.259853	−	0.259853i	−0.565141	−	0.824994i	$-0.691178\pi$
$307$	79.7749	−	79.7749i	0.259853	−	0.259853i	0.824994	+	0.565141i	$0.191178\pi$
$308$		0			0
$309$	128.168	−	128.168i	0.414782	−	0.414782i
$310$		0			0
$311$	46.8626	−	46.8626i	0.150684	−	0.150684i	−0.627740	−	0.778423i	$-0.716020\pi$
$311$	46.8626	−	46.8626i	0.150684	−	0.150684i	0.778423	+	0.627740i	$0.216020\pi$
$312$		0			0
$313$	−463.099			−1.47955			−0.739775	−	0.672854i	$-0.765068\pi$
$313$	−463.099			−1.47955			−0.739775	+	0.672854i	$0.765068\pi$
$314$		0			0
$315$	33.0064			0.104782
$316$		0			0
$317$	179.937	+	179.937i	0.567624	+	0.567624i	0.931462	−	0.363838i	$-0.118534\pi$
$317$	179.937	+	179.937i	0.567624	+	0.567624i	−0.363838	+	0.931462i	$0.618534\pi$
$318$		0			0
$319$	151.198	+	106.478i	0.473974	+	0.333786i
$320$		0			0
$321$	−161.438	+	161.438i	−0.502923	+	0.502923i
$322$		0			0
$323$		−	59.4376i		−	0.184017i
$324$		0			0
$325$		−	11.8960i		−	0.0366031i
$326$		0			0
$327$	−108.832	−	108.832i	−0.332820	−	0.332820i
$328$		0			0
$329$	−22.4835	−	22.4835i	−0.0683389	−	0.0683389i
$330$		0			0
$331$	172.849	+	172.849i	0.522203	+	0.522203i	0.918236	−	0.396033i	$-0.129614\pi$
$331$	172.849	+	172.849i	0.522203	+	0.522203i	−0.396033	+	0.918236i	$0.629614\pi$
$332$		0			0
$333$	15.7220	−	15.7220i	0.0472134	−	0.0472134i
$334$		0			0
$335$	−54.2302			−0.161881
$336$		0			0
$337$	−330.702	−	330.702i	−0.981312	−	0.981312i	0.0185162	−	0.999829i	$-0.494106\pi$
$337$	−330.702	−	330.702i	−0.981312	−	0.981312i	−0.999829	+	0.0185162i	$0.994106\pi$
$338$		0			0
$339$	−197.598			−0.582885
$340$		0			0
$341$			282.043i			0.827106i
$342$		0			0
$343$	−363.072			−1.05852
$344$		0			0
$345$	−55.7591	−	55.7591i	−0.161621	−	0.161621i
$346$		0			0
$347$		−	260.678i		−	0.751233i	−0.926775	−	0.375617i	$-0.877431\pi$
$347$		−	260.678i		−	0.751233i	0.926775	−	0.375617i	$-0.122569\pi$
$348$		0			0
$349$	−400.297			−1.14698			−0.573491	−	0.819212i	$-0.694411\pi$
$349$	−400.297			−1.14698			−0.573491	+	0.819212i	$0.694411\pi$
$350$		0			0
$351$	−8.74175	+	8.74175i	−0.0249053	+	0.0249053i
$352$		0			0
$353$			175.144i			0.496159i	0.968740	+	0.248080i	$0.0797994\pi$
$353$			175.144i			0.496159i	−0.968740	+	0.248080i	$0.920201\pi$
$354$		0			0
$355$	142.191			0.400537
$356$		0			0
$357$			116.596i			0.326600i
$358$		0			0
$359$	474.271	−	474.271i	1.32109	−	1.32109i	0.408196	−	0.912894i	$-0.366158\pi$
$359$	474.271	−	474.271i	1.32109	−	1.32109i	0.912894	−	0.408196i	$-0.133842\pi$
$360$		0			0
$361$			342.126i			0.947718i
$362$		0			0
$363$	−98.3913	−	98.3913i	−0.271050	−	0.271050i
$364$		0			0
$365$	73.7424	−	73.7424i	0.202034	−	0.202034i
$366$		0			0
$367$	333.007	−	333.007i	0.907377	−	0.907377i	−0.0886830	−	0.996060i	$-0.528266\pi$
$367$	333.007	−	333.007i	0.907377	−	0.907377i	0.996060	+	0.0886830i	$0.0282658\pi$
$368$		0			0
$369$	141.883	−	141.883i	0.384506	−	0.384506i
$370$		0			0
$371$	86.0938			0.232059
$372$		0			0
$373$	192.387			0.515782			0.257891	−	0.966174i	$-0.416972\pi$
$373$	192.387			0.515782			0.257891	+	0.966174i	$0.416972\pi$
$374$		0			0
$375$	13.6931	+	13.6931i	0.0365148	+	0.0365148i
$376$		0			0
$377$	67.9807	−	11.7981i	0.180320	−	0.0312947i
$378$		0			0
$379$	−485.470	+	485.470i	−1.28092	+	1.28092i	−0.340783	+	0.940142i	$0.610692\pi$
$379$	−485.470	+	485.470i	−1.28092	+	1.28092i	−0.940142	+	0.340783i	$0.889308\pi$
$380$		0			0
$381$			286.929i			0.753095i
$382$		0			0
$383$		−	527.240i		−	1.37661i	−0.725424	−	0.688303i	$-0.758356\pi$
$383$		−	527.240i		−	1.37661i	0.725424	−	0.688303i	$-0.241644\pi$
$384$		0			0
$385$	−49.6096	−	49.6096i	−0.128856	−	0.128856i
$386$		0			0
$387$	155.762	+	155.762i	0.402485	+	0.402485i
$388$		0			0
$389$	−476.398	−	476.398i	−1.22467	−	1.22467i	−0.965952	−	0.258720i	$-0.916699\pi$
$389$	−476.398	−	476.398i	−1.22467	−	1.22467i	−0.258720	−	0.965952i	$-0.583301\pi$
$390$		0			0
$391$	196.971	−	196.971i	0.503763	−	0.503763i
$392$		0			0
$393$	−338.314			−0.860851
$394$		0			0
$395$	55.5606	+	55.5606i	0.140660	+	0.140660i
$396$		0			0
$397$	65.9474			0.166114			0.0830572	−	0.996545i	$-0.473532\pi$
$397$	65.9474			0.166114			0.0830572	+	0.996545i	$0.473532\pi$
$398$		0			0
$399$			37.0238i			0.0927915i
$400$		0			0
$401$	−713.760			−1.77995			−0.889975	−	0.456010i	$-0.849278\pi$
$401$	−713.760			−1.77995			−0.889975	+	0.456010i	$0.849278\pi$
$402$		0			0
$403$	74.4094	+	74.4094i	0.184639	+	0.184639i
$404$		0			0
$405$		−	20.1246i		−	0.0496904i
$406$		0			0
$407$	−47.2614			−0.116121
$408$		0			0
$409$	−18.6013	+	18.6013i	−0.0454798	+	0.0454798i	−0.729481	−	0.684001i	$-0.760238\pi$
$409$	−18.6013	+	18.6013i	−0.0454798	+	0.0454798i	0.684001	+	0.729481i	$0.260238\pi$
$410$		0			0
$411$			201.659i			0.490654i
$412$		0			0
$413$	298.189			0.722007
$414$		0			0
$415$			178.666i			0.430521i
$416$		0			0
$417$	212.225	−	212.225i	0.508932	−	0.508932i
$418$		0			0
$419$			743.747i			1.77505i	0.460756	+	0.887527i	$0.347578\pi$
$419$			743.747i			1.77505i	−0.460756	+	0.887527i	$0.652422\pi$
$420$		0			0
$421$	−379.300	−	379.300i	−0.900951	−	0.900951i	0.0945677	−	0.995518i	$-0.469853\pi$
$421$	−379.300	−	379.300i	−0.900951	−	0.900951i	−0.995518	+	0.0945677i	$0.969853\pi$
$422$		0			0
$423$	−13.7086	+	13.7086i	−0.0324081	+	0.0324081i
$424$		0			0
$425$	−48.3713	+	48.3713i	−0.113815	+	0.113815i
$426$		0			0
$427$	381.248	−	381.248i	0.892852	−	0.892852i
$428$		0			0
$429$	26.2782			0.0612546
$430$		0			0
$431$	−330.017			−0.765701			−0.382851	−	0.923810i	$-0.625058\pi$
$431$	−330.017			−0.765701			−0.382851	+	0.923810i	$0.625058\pi$
$432$		0			0
$433$	−2.11830	−	2.11830i	−0.00489215	−	0.00489215i	0.704656	−	0.709549i	$-0.251101\pi$
$433$	−2.11830	−	2.11830i	−0.00489215	−	0.00489215i	−0.709549	+	0.704656i	$0.751101\pi$
$434$		0			0
$435$	−64.6697	+	91.8304i	−0.148666	+	0.211104i
$436$		0			0
$437$	62.5460	−	62.5460i	0.143126	−	0.143126i
$438$		0			0
$439$		−	240.917i		−	0.548785i	−0.961618	−	0.274393i	$-0.911523\pi$
$439$		−	240.917i		−	0.548785i	0.961618	−	0.274393i	$-0.0884768\pi$
$440$		0			0
$441$			74.3720i			0.168644i
$442$		0			0
$443$	298.890	+	298.890i	0.674695	+	0.674695i	0.958795	−	0.284100i	$-0.0916947\pi$
$443$	298.890	+	298.890i	0.674695	+	0.674695i	−0.284100	+	0.958795i	$0.591695\pi$
$444$		0			0
$445$	−140.926	−	140.926i	−0.316687	−	0.316687i
$446$		0			0
$447$	−248.497	−	248.497i	−0.555922	−	0.555922i
$448$		0			0
$449$	472.057	−	472.057i	1.05135	−	1.05135i	0.0527436	−	0.998608i	$-0.483203\pi$
$449$	472.057	−	472.057i	1.05135	−	1.05135i	0.998608	−	0.0527436i	$-0.0167966\pi$
$450$		0			0
$451$	−426.508			−0.945695
$452$		0			0
$453$	−133.760	−	133.760i	−0.295277	−	0.295277i
$454$		0			0
$455$	−26.1763			−0.0575303
$456$		0			0
$457$			375.045i			0.820668i	0.911935	+	0.410334i	$0.134588\pi$
$457$			375.045i			0.820668i	−0.911935	+	0.410334i	$0.865412\pi$
$458$		0			0
$459$	71.0910			0.154882
$460$		0			0
$461$	280.910	+	280.910i	0.609350	+	0.609350i	0.942776	−	0.333426i	$-0.108205\pi$
$461$	280.910	+	280.910i	0.609350	+	0.609350i	−0.333426	+	0.942776i	$0.608205\pi$
$462$		0			0
$463$		−	296.343i		−	0.640050i	−0.947409	−	0.320025i	$-0.896309\pi$
$463$		−	296.343i		−	0.640050i	0.947409	−	0.320025i	$-0.103691\pi$
$464$		0			0
$465$	−171.300			−0.368387
$466$		0			0
$467$	572.365	−	572.365i	1.22562	−	1.22562i	0.260018	−	0.965604i	$-0.416272\pi$
$467$	572.365	−	572.365i	1.22562	−	1.22562i	0.965604	−	0.260018i	$-0.0837284\pi$
$468$		0			0
$469$			119.329i			0.254434i
$470$		0			0
$471$	−516.199			−1.09596
$472$		0			0
$473$		−	468.229i		−	0.989914i
$474$		0			0
$475$	−15.3597	+	15.3597i	−0.0323363	+	0.0323363i
$476$		0			0
$477$		−	52.4930i		−	0.110048i
$478$		0			0
$479$	468.571	+	468.571i	0.978227	+	0.978227i	0.999768	−	0.0215412i	$-0.00685732\pi$
$479$	468.571	+	468.571i	0.978227	+	0.978227i	−0.0215412	+	0.999768i	$0.506857\pi$
$480$		0			0
$481$	−12.4686	+	12.4686i	−0.0259223	+	0.0259223i
$482$		0			0
$483$	−122.694	+	122.694i	−0.254024	+	0.254024i
$484$		0			0
$485$	107.148	−	107.148i	0.220924	−	0.220924i
$486$		0			0
$487$	−42.2851			−0.0868278			−0.0434139	−	0.999057i	$-0.513823\pi$
$487$	−42.2851			−0.0868278			−0.0434139	+	0.999057i	$0.513823\pi$
$488$		0			0
$489$	−553.586			−1.13208
$490$		0			0
$491$	−370.462	−	370.462i	−0.754505	−	0.754505i	0.220812	−	0.975317i	$-0.429129\pi$
$491$	−370.462	−	370.462i	−0.754505	−	0.754505i	−0.975317	+	0.220812i	$0.929129\pi$
$492$		0			0
$493$	−324.395	−	228.448i	−0.658001	−	0.463384i
$494$		0			0
$495$	−30.2479	+	30.2479i	−0.0611069	+	0.0611069i
$496$		0			0
$497$		−	312.880i		−	0.629537i
$498$		0			0
$499$		−	692.143i		−	1.38706i	−0.720427	−	0.693530i	$-0.756054\pi$
$499$		−	692.143i		−	1.38706i	0.720427	−	0.693530i	$-0.243946\pi$
$500$		0			0
$501$	−36.3550	−	36.3550i	−0.0725650	−	0.0725650i
$502$		0			0
$503$	277.112	+	277.112i	0.550919	+	0.550919i	0.926706	−	0.375787i	$-0.122628\pi$
$503$	277.112	+	277.112i	0.550919	+	0.550919i	−0.375787	+	0.926706i	$0.622628\pi$
$504$		0			0
$505$	−116.409	−	116.409i	−0.230513	−	0.230513i
$506$		0			0
$507$	−200.049	+	200.049i	−0.394574	+	0.394574i
$508$		0			0
$509$	383.380			0.753202			0.376601	−	0.926376i	$-0.377093\pi$
$509$	383.380			0.753202			0.376601	+	0.926376i	$0.377093\pi$
$510$		0			0
$511$	−162.265	−	162.265i	−0.317543	−	0.317543i
$512$		0			0
$513$	22.5741			0.0440041
$514$		0			0
$515$		−	234.001i		−	0.454371i
$516$		0			0
$517$	41.2089			0.0797078
$518$		0			0
$519$	−103.103	−	103.103i	−0.198657	−	0.198657i
$520$		0			0
$521$			789.828i			1.51598i	0.652264	+	0.757992i	$0.273819\pi$
$521$			789.828i			1.51598i	−0.652264	+	0.757992i	$0.726181\pi$
$522$		0			0
$523$	31.2758			0.0598008			0.0299004	−	0.999553i	$-0.490481\pi$
$523$	31.2758			0.0598008			0.0299004	+	0.999553i	$0.490481\pi$
$524$		0			0
$525$	30.1306	−	30.1306i	0.0573915	−	0.0573915i
$526$		0			0
$527$		−	605.124i		−	1.14824i
$528$		0			0
$529$	−114.456			−0.216362
$530$		0			0
$531$		−	181.811i		−	0.342395i
$532$		0			0
$533$	−112.523	+	112.523i	−0.211112	+	0.211112i
$534$		0			0
$535$			294.745i			0.550925i
$536$		0			0
$537$	18.9975	+	18.9975i	0.0353772	+	0.0353772i
$538$		0			0
$539$	111.783	−	111.783i	0.207390	−	0.207390i
$540$		0			0
$541$	−249.049	+	249.049i	−0.460349	+	0.460349i	−0.898770	−	0.438421i	$-0.855538\pi$
$541$	−249.049	+	249.049i	−0.460349	+	0.460349i	0.438421	+	0.898770i	$0.355538\pi$
$542$		0			0
$543$	326.641	−	326.641i	0.601549	−	0.601549i
$544$		0			0
$545$	−198.699			−0.364586
$546$		0			0
$547$	−395.722			−0.723440			−0.361720	−	0.932287i	$-0.617810\pi$
$547$	−395.722			−0.723440			−0.361720	+	0.932287i	$0.617810\pi$
$548$		0			0
$549$	−232.454	−	232.454i	−0.423414	−	0.423414i
$550$		0			0
$551$	−103.008	−	72.5411i	−0.186947	−	0.131654i
$552$		0			0
$553$	122.257	−	122.257i	0.221079	−	0.221079i
$554$		0			0
$555$		−	28.7044i		−	0.0517196i
$556$		0			0
$557$			519.056i			0.931879i	0.884817	+	0.465939i	$0.154284\pi$
$557$			519.056i			0.931879i	−0.884817	+	0.465939i	$0.845716\pi$
$558$		0			0
$559$	−123.529	−	123.529i	−0.220983	−	0.220983i
$560$		0			0
$561$	−106.852	−	106.852i	−0.190467	−	0.190467i
$562$		0			0
$563$	598.061	+	598.061i	1.06227	+	1.06227i	0.997928	+	0.0643470i	$0.0204965\pi$
$563$	598.061	+	598.061i	1.06227	+	1.06227i	0.0643470	+	0.997928i	$0.479504\pi$
$564$		0			0
$565$	−180.381	+	180.381i	−0.319259	+	0.319259i
$566$		0			0
$567$	−44.2827			−0.0781000
$568$		0			0
$569$	−774.320	−	774.320i	−1.36084	−	1.36084i	−0.872844	−	0.488000i	$-0.837727\pi$
$569$	−774.320	−	774.320i	−1.36084	−	1.36084i	−0.488000	−	0.872844i	$-0.662273\pi$
$570$		0			0
$571$	−273.896			−0.479679			−0.239839	−	0.970813i	$-0.577095\pi$
$571$	−273.896			−0.479679			−0.239839	+	0.970813i	$0.577095\pi$
$572$		0			0
$573$		−	603.931i		−	1.05398i
$574$		0			0
$575$	−101.802			−0.177047
$576$		0			0
$577$	−51.2109	−	51.2109i	−0.0887537	−	0.0887537i	0.661336	−	0.750090i	$-0.269990\pi$
$577$	−51.2109	−	51.2109i	−0.0887537	−	0.0887537i	−0.750090	+	0.661336i	$0.769990\pi$
$578$		0			0
$579$		−	111.075i		−	0.191839i
$580$		0			0
$581$	393.142			0.676664
$582$		0			0
$583$	−78.8986	+	78.8986i	−0.135332	+	0.135332i
$584$		0			0
$585$			15.9602i			0.0272823i
$586$		0			0
$587$	17.1834			0.0292733			0.0146366	−	0.999893i	$-0.495341\pi$
$587$	17.1834			0.0292733			0.0146366	+	0.999893i	$0.495341\pi$
$588$		0			0
$589$		−	192.150i		−	0.326231i
$590$		0			0
$591$	−208.991	+	208.991i	−0.353622	+	0.353622i
$592$		0			0
$593$		−	821.772i		−	1.38579i	−0.721039	−	0.692894i	$-0.756335\pi$
$593$		−	821.772i		−	1.38579i	0.721039	−	0.692894i	$-0.243665\pi$
$594$		0			0
$595$	106.437	+	106.437i	0.178886	+	0.178886i
$596$		0			0
$597$	−185.151	+	185.151i	−0.310136	+	0.310136i
$598$		0			0
$599$	705.424	−	705.424i	1.17767	−	1.17767i	0.197333	−	0.980336i	$-0.436772\pi$
$599$	705.424	−	705.424i	1.17767	−	1.17767i	0.980336	−	0.197333i	$-0.0632281\pi$
$600$		0			0
$601$	−438.379	+	438.379i	−0.729415	+	0.729415i	−0.970503	−	0.241088i	$-0.922496\pi$
$601$	−438.379	+	438.379i	−0.729415	+	0.729415i	0.241088	+	0.970503i	$0.422496\pi$
$602$		0			0
$603$	72.7574			0.120659
$604$		0			0
$605$	−179.637			−0.296921
$606$		0			0
$607$	−640.898	−	640.898i	−1.05585	−	1.05585i	−0.998346	−	0.0574999i	$-0.981687\pi$
$607$	−640.898	−	640.898i	−1.05585	−	1.05585i	−0.0574999	−	0.998346i	$-0.518313\pi$
$608$		0			0
$609$	202.066	+	142.301i	0.331800	+	0.233663i
$610$		0			0
$611$	10.8719	−	10.8719i	0.0177935	−	0.0177935i
$612$		0			0
$613$			744.442i			1.21442i	0.794540	+	0.607212i	$0.207712\pi$
$613$			744.442i			1.21442i	−0.794540	+	0.607212i	$0.792288\pi$
$614$		0			0
$615$		−	259.041i		−	0.421205i
$616$		0			0
$617$	294.924	+	294.924i	0.477998	+	0.477998i	0.904491	−	0.426493i	$-0.140251\pi$
$617$	294.924	+	294.924i	0.477998	+	0.477998i	−0.426493	+	0.904491i	$0.640251\pi$
$618$		0			0
$619$	232.097	+	232.097i	0.374955	+	0.374955i	0.869278	−	0.494323i	$-0.164584\pi$
$619$	232.097	+	232.097i	0.374955	+	0.374955i	−0.494323	+	0.869278i	$0.664584\pi$
$620$		0			0
$621$	74.8087	+	74.8087i	0.120465	+	0.120465i
$622$		0			0
$623$	−310.096	+	310.096i	−0.497747	+	0.497747i
$624$		0			0
$625$	25.0000			0.0400000
$626$		0			0
$627$	−33.9296	−	33.9296i	−0.0541142	−	0.0541142i
$628$		0			0
$629$	101.399			0.161207
$630$		0			0
$631$		−	633.231i		−	1.00354i	−0.865002	−	0.501768i	$-0.832683\pi$
$631$		−	633.231i		−	1.00354i	0.865002	−	0.501768i	$-0.167317\pi$
$632$		0			0
$633$	−112.540			−0.177788
$634$		0			0
$635$	261.929	+	261.929i	0.412487	+	0.412487i
$636$		0			0
$637$		−	58.9820i		−	0.0925934i
$638$		0			0
$639$	−190.769			−0.298543
$640$		0			0
$641$	238.969	−	238.969i	0.372806	−	0.372806i	−0.495692	−	0.868498i	$-0.665086\pi$
$641$	238.969	−	238.969i	0.372806	−	0.372806i	0.868498	+	0.495692i	$0.165086\pi$
$642$		0			0
$643$			23.5789i			0.0366702i	0.999832	+	0.0183351i	$0.00583657\pi$
$643$			23.5789i			0.0366702i	−0.999832	+	0.0183351i	$0.994163\pi$
$644$		0			0
$645$	284.381			0.440900
$646$		0			0
$647$		−	437.536i		−	0.676254i	−0.941100	−	0.338127i	$-0.890207\pi$
$647$		−	437.536i		−	0.676254i	0.941100	−	0.338127i	$-0.109793\pi$
$648$		0			0
$649$	−273.268	+	273.268i	−0.421061	+	0.421061i
$650$		0			0
$651$			376.933i			0.579005i
$652$		0			0
$653$	13.4869	+	13.4869i	0.0206538	+	0.0206538i	0.717358	−	0.696704i	$-0.245351\pi$
$653$	13.4869	+	13.4869i	0.0206538	+	0.0206538i	−0.696704	+	0.717358i	$0.745351\pi$
$654$		0			0
$655$	−308.837	+	308.837i	−0.471507	+	0.471507i
$656$		0			0
$657$	−98.9358	+	98.9358i	−0.150587	+	0.150587i
$658$		0			0
$659$	−20.4878	+	20.4878i	−0.0310892	+	0.0310892i	−0.722480	−	0.691391i	$-0.756998\pi$
$659$	−20.4878	+	20.4878i	−0.0310892	+	0.0310892i	0.691391	+	0.722480i	$0.256998\pi$
$660$		0			0
$661$	−460.347			−0.696441			−0.348220	−	0.937413i	$-0.613214\pi$
$661$	−460.347			−0.696441			−0.348220	+	0.937413i	$0.613214\pi$
$662$		0			0
$663$	−56.3799			−0.0850376
$664$		0			0
$665$	33.7979	+	33.7979i	0.0508240	+	0.0508240i
$666$		0			0
$667$	−100.964	−	581.754i	−0.151370	−	0.872195i
$668$		0			0
$669$	−360.462	+	360.462i	−0.538806	+	0.538806i
$670$		0			0
$671$			698.771i			1.04139i
$672$		0			0
$673$			132.957i			0.197559i	0.995109	+	0.0987795i	$0.0314939\pi$
$673$			132.957i			0.197559i	−0.995109	+	0.0987795i	$0.968506\pi$
$674$		0			0
$675$	−18.3712	−	18.3712i	−0.0272166	−	0.0272166i
$676$		0			0
$677$	−599.109	−	599.109i	−0.884947	−	0.884947i	0.109085	−	0.994032i	$-0.465208\pi$
$677$	−599.109	−	599.109i	−0.884947	−	0.884947i	−0.994032	+	0.109085i	$0.965208\pi$
$678$		0			0
$679$	−235.772	−	235.772i	−0.347234	−	0.347234i
$680$		0			0
$681$	−73.5010	+	73.5010i	−0.107931	+	0.107931i
$682$		0			0
$683$	−1337.94			−1.95891			−0.979456	−	0.201658i	$-0.935367\pi$
$683$	−1337.94			−1.95891			−0.979456	+	0.201658i	$0.935367\pi$
$684$		0			0
$685$	184.088	+	184.088i	0.268742	+	0.268742i
$686$		0			0
$687$	22.4225			0.0326382
$688$		0			0
$689$			41.6305i			0.0604216i
$690$		0			0
$691$	198.701			0.287555			0.143778	−	0.989610i	$-0.454075\pi$
$691$	198.701			0.287555			0.143778	+	0.989610i	$0.454075\pi$
$692$		0			0
$693$	66.5582	+	66.5582i	0.0960436	+	0.0960436i
$694$		0			0
$695$		−	387.467i		−	0.557507i
$696$		0			0
$697$	915.074			1.31287
$698$		0			0
$699$	−54.6991	+	54.6991i	−0.0782533	+	0.0782533i
$700$		0			0
$701$			60.4021i			0.0861656i	0.999072	+	0.0430828i	$0.0137179\pi$
$701$			60.4021i			0.0861656i	−0.999072	+	0.0430828i	$0.986282\pi$
$702$		0			0
$703$	32.1982			0.0458012
$704$		0			0
$705$			25.0284i			0.0355013i
$706$		0			0
$707$	−256.150	+	256.150i	−0.362305	+	0.362305i
$708$		0			0
$709$		−	209.910i		−	0.296065i	−0.988982	−	0.148033i	$-0.952706\pi$
$709$		−	209.910i		−	0.296065i	0.988982	−	0.148033i	$-0.0472941\pi$
$710$		0			0
$711$	−74.5424	−	74.5424i	−0.104842	−	0.104842i
$712$		0			0
$713$	636.769	−	636.769i	0.893084	−	0.893084i
$714$		0			0
$715$	23.9886	−	23.9886i	0.0335505	−	0.0335505i
$716$		0			0
$717$	−362.841	+	362.841i	−0.506055	+	0.506055i
$718$		0			0
$719$	−339.437			−0.472096			−0.236048	−	0.971741i	$-0.575852\pi$
$719$	−339.437			−0.472096			−0.236048	+	0.971741i	$0.575852\pi$
$720$		0			0
$721$	−514.901			−0.714149
$722$		0			0
$723$	10.6169	+	10.6169i	0.0146846	+	0.0146846i
$724$		0			0
$725$	24.7942	+	142.864i	0.0341990	+	0.197054i
$726$		0			0
$727$	516.525	−	516.525i	0.710489	−	0.710489i	−0.256149	−	0.966637i	$-0.582454\pi$
$727$	516.525	−	516.525i	0.710489	−	0.710489i	0.966637	+	0.256149i	$0.0824536\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$			1004.59i			1.37426i
$732$		0			0
$733$	−223.530	−	223.530i	−0.304953	−	0.304953i	0.537995	−	0.842948i	$-0.319182\pi$
$733$	−223.530	−	223.530i	−0.304953	−	0.304953i	−0.842948	+	0.537995i	$0.819182\pi$
$734$		0			0
$735$	67.8920	+	67.8920i	0.0923701	+	0.0923701i
$736$		0			0
$737$	−109.357	−	109.357i	−0.148381	−	0.148381i
$738$		0			0
$739$	918.763	−	918.763i	1.24325	−	1.24325i	0.284608	−	0.958644i	$-0.408136\pi$
$739$	918.763	−	918.763i	1.24325	−	1.24325i	0.958644	−	0.284608i	$-0.0918636\pi$
$740$		0			0
$741$	−17.9028			−0.0241603
$742$		0			0
$743$	−310.585	−	310.585i	−0.418014	−	0.418014i	0.466505	−	0.884519i	$-0.345513\pi$
$743$	−310.585	−	310.585i	−0.418014	−	0.418014i	−0.884519	+	0.466505i	$0.845513\pi$
$744$		0			0
$745$	−453.692			−0.608982
$746$		0			0
$747$		−	239.706i		−	0.320892i
$748$		0			0
$749$	648.564			0.865906
$750$		0			0
$751$	−183.665	−	183.665i	−0.244561	−	0.244561i	0.574173	−	0.818734i	$-0.305324\pi$
$751$	−183.665	−	183.665i	−0.244561	−	0.244561i	−0.818734	+	0.574173i	$0.805324\pi$
$752$		0			0
$753$			228.651i			0.303654i
$754$		0			0
$755$	−244.212			−0.323460
$756$		0			0
$757$	651.311	−	651.311i	0.860384	−	0.860384i	−0.130999	−	0.991383i	$-0.541818\pi$
$757$	651.311	−	651.311i	0.860384	−	0.860384i	0.991383	+	0.130999i	$0.0418184\pi$
$758$		0			0
$759$		−	224.880i		−	0.296284i
$760$		0			0
$761$	−143.381			−0.188411			−0.0942055	−	0.995553i	$-0.530031\pi$
$761$	−143.381			−0.188411			−0.0942055	+	0.995553i	$0.530031\pi$
$762$		0			0
$763$			437.223i			0.573031i
$764$		0			0
$765$	64.8969	−	64.8969i	0.0848325	−	0.0848325i
$766$		0			0
$767$			144.189i			0.187991i
$768$		0			0
$769$	−420.214	−	420.214i	−0.546442	−	0.546442i	0.378968	−	0.925410i	$-0.376279\pi$
$769$	−420.214	−	420.214i	−0.546442	−	0.546442i	−0.925410	+	0.378968i	$0.876279\pi$
$770$		0			0
$771$	−358.058	+	358.058i	−0.464407	+	0.464407i
$772$		0			0
$773$	569.353	−	569.353i	0.736550	−	0.736550i	−0.235359	−	0.971909i	$-0.575627\pi$
$773$	569.353	−	569.353i	0.736550	−	0.736550i	0.971909	+	0.235359i	$0.0756265\pi$
$774$		0			0
$775$	−156.375	+	156.375i	−0.201774	+	0.201774i
$776$		0			0
$777$	−63.1619			−0.0812894
$778$		0			0
$779$	290.571			0.373005
$780$		0			0
$781$	286.731	+	286.731i	0.367134	+	0.367134i
$782$		0			0
$783$	86.7635	−	123.203i	0.110809	−	0.157348i
$784$		0			0
$785$	−471.223	+	471.223i	−0.600285	+	0.600285i
$786$		0			0
$787$		−	474.180i		−	0.602516i	−0.953543	−	0.301258i	$-0.902593\pi$
$787$		−	474.180i		−	0.602516i	0.953543	−	0.301258i	$-0.0974066\pi$
$788$		0			0
$789$			520.079i			0.659163i
$790$		0			0
$791$	396.916	+	396.916i	0.501790	+	0.501790i
$792$		0			0
$793$	184.352	+	184.352i	0.232474	+	0.232474i
$794$		0			0
$795$	−47.9193	−	47.9193i	−0.0602759	−	0.0602759i
$796$		0			0
$797$	138.576	−	138.576i	0.173872	−	0.173872i	−0.614806	−	0.788678i	$-0.710766\pi$
$797$	138.576	−	138.576i	0.173872	−	0.173872i	0.788678	+	0.614806i	$0.210766\pi$
$798$		0			0
$799$	−88.4138			−0.110656
$800$		0			0
$801$	189.072	+	189.072i	0.236045	+	0.236045i
$802$		0			0
$803$	297.407			0.370370
$804$		0			0
$805$			224.007i			0.278270i
$806$		0			0
$807$	573.242			0.710337
$808$		0			0
$809$	197.806	+	197.806i	0.244507	+	0.244507i	0.818712	−	0.574205i	$-0.194689\pi$
$809$	197.806	+	197.806i	0.244507	+	0.244507i	−0.574205	+	0.818712i	$0.694689\pi$
$810$		0			0
$811$		−	564.175i		−	0.695653i	−0.937559	−	0.347827i	$-0.886920\pi$
$811$		−	564.175i		−	0.695653i	0.937559	−	0.347827i	$-0.113080\pi$
$812$		0			0
$813$	573.195			0.705037
$814$		0			0
$815$	−505.352	+	505.352i	−0.620064	+	0.620064i
$816$		0			0
$817$			318.994i			0.390446i
$818$		0			0
$819$	35.1192			0.0428805
$820$		0			0
$821$			215.716i			0.262748i	0.991333	+	0.131374i	$0.0419389\pi$
$821$			215.716i			0.262748i	−0.991333	+	0.131374i	$0.958061\pi$
$822$		0			0
$823$	−907.469	+	907.469i	−1.10264	+	1.10264i	−0.108544	+	0.994092i	$0.534619\pi$
$823$	−907.469	+	907.469i	−1.10264	+	1.10264i	−0.994092	+	0.108544i	$0.965381\pi$
$824$		0			0
$825$			55.2249i			0.0669392i
$826$		0			0
$827$	328.919	+	328.919i	0.397725	+	0.397725i	0.877430	−	0.479705i	$-0.159256\pi$
$827$	328.919	+	328.919i	0.397725	+	0.397725i	−0.479705	+	0.877430i	$0.659256\pi$
$828$		0			0
$829$	−60.3347	+	60.3347i	−0.0727801	+	0.0727801i	−0.742560	−	0.669780i	$-0.766389\pi$
$829$	−60.3347	+	60.3347i	−0.0727801	+	0.0727801i	0.669780	+	0.742560i	$0.266389\pi$
$830$		0			0
$831$	359.856	−	359.856i	0.433040	−	0.433040i
$832$		0			0
$833$	−239.831	+	239.831i	−0.287913	+	0.287913i
$834$		0			0
$835$	−66.3749			−0.0794909
$836$		0			0
$837$	229.823			0.274579
$838$		0			0
$839$	862.434	+	862.434i	1.02793	+	1.02793i	0.999599	+	0.0283323i	$0.00901967\pi$
$839$	862.434	+	862.434i	1.02793	+	1.02793i	0.0283323	+	0.999599i	$0.490980\pi$
$840$		0			0
$841$	−791.820	+	283.377i	−0.941522	+	0.336953i
$842$		0			0
$843$	−110.005	+	110.005i	−0.130492	+	0.130492i
$844$		0			0
$845$			365.238i			0.432234i
$846$		0			0
$847$			395.278i			0.466680i
$848$		0			0
$849$	637.513	+	637.513i	0.750899	+	0.750899i
$850$		0			0
$851$	106.702	+	106.702i	0.125384	+	0.125384i
$852$		0			0
$853$	904.743	+	904.743i	1.06066	+	1.06066i	0.998037	+	0.0626230i	$0.0199466\pi$
$853$	904.743	+	904.743i	1.06066	+	1.06066i	0.0626230	+	0.998037i	$0.480053\pi$
$854$		0			0
$855$	20.6073	−	20.6073i	0.0241021	−	0.0241021i
$856$		0			0
$857$	−785.849			−0.916977			−0.458488	−	0.888700i	$-0.651609\pi$
$857$	−785.849			−0.916977			−0.458488	+	0.888700i	$0.651609\pi$
$858$		0			0
$859$	591.335	+	591.335i	0.688399	+	0.688399i	0.961878	−	0.273479i	$-0.0881743\pi$
$859$	591.335	+	591.335i	0.688399	+	0.688399i	−0.273479	+	0.961878i	$0.588174\pi$
$860$		0			0
$861$	−570.001			−0.662022
$862$		0			0
$863$		−	27.6383i		−	0.0320258i	−0.999872	−	0.0160129i	$-0.994903\pi$
$863$		−	27.6383i		−	0.0320258i	0.999872	−	0.0160129i	$-0.00509729\pi$
$864$		0			0
$865$	−188.240			−0.217618
$866$		0			0
$867$	−124.700	−	124.700i	−0.143830	−	0.143830i
$868$		0			0
$869$			224.079i			0.257858i
$870$		0			0
$871$	−57.7015			−0.0662474
$872$		0			0
$873$	−143.755	+	143.755i	−0.164667	+	0.164667i
$874$		0			0
$875$		−	55.0106i		−	0.0628693i
$876$		0			0
$877$	−975.866			−1.11273			−0.556366	−	0.830937i	$-0.687805\pi$
$877$	−975.866			−1.11273			−0.556366	+	0.830937i	$0.687805\pi$
$878$		0			0
$879$		−	356.158i		−	0.405185i
$880$		0			0
$881$	124.169	−	124.169i	0.140941	−	0.140941i	−0.633116	−	0.774057i	$-0.718224\pi$
$881$	124.169	−	124.169i	0.140941	−	0.140941i	0.774057	+	0.633116i	$0.218224\pi$
$882$		0			0
$883$		−	988.891i		−	1.11992i	−0.828519	−	0.559961i	$-0.810816\pi$
$883$		−	988.891i		−	1.11992i	0.828519	−	0.559961i	$-0.189184\pi$
$884$		0			0
$885$	−165.970	−	165.970i	−0.187537	−	0.187537i
$886$		0			0
$887$	765.335	−	765.335i	0.862835	−	0.862835i	−0.128832	−	0.991666i	$-0.541123\pi$
$887$	765.335	−	765.335i	0.862835	−	0.862835i	0.991666	+	0.128832i	$0.0411227\pi$
$888$		0			0
$889$	576.356	−	576.356i	0.648319	−	0.648319i
$890$		0			0
$891$	40.5818	−	40.5818i	0.0455464	−	0.0455464i
$892$		0			0
$893$	−28.0748			−0.0314387
$894$		0			0
$895$	34.6846			0.0387537
$896$		0			0
$897$	−59.3284	−	59.3284i	−0.0661409	−	0.0661409i
$898$		0			0
$899$	−1048.70	−	738.528i	−1.16652	−	0.821499i
$900$		0			0
$901$	169.277	−	169.277i	0.187877	−	0.187877i
$902$		0			0
$903$		−	625.758i		−	0.692977i
$904$		0			0
$905$		−	596.363i		−	0.658964i
$906$		0			0
$907$	−778.395	−	778.395i	−0.858208	−	0.858208i	0.132919	−	0.991127i	$-0.457565\pi$
$907$	−778.395	−	778.395i	−0.858208	−	0.858208i	−0.991127	+	0.132919i	$0.957565\pi$
$908$		0			0
$909$	156.179	+	156.179i	0.171814	+	0.171814i
$910$		0			0
$911$	−230.510	−	230.510i	−0.253029	−	0.253029i	0.569182	−	0.822211i	$-0.307260\pi$
$911$	−230.510	−	230.510i	−0.253029	−	0.253029i	−0.822211	+	0.569182i	$0.807260\pi$
$912$		0			0
$913$	−360.286	+	360.286i	−0.394617	+	0.394617i
$914$		0			0
$915$	−424.401			−0.463827
$916$		0			0
$917$	679.573	+	679.573i	0.741083	+	0.741083i
$918$		0			0
$919$	502.790			0.547105			0.273553	−	0.961857i	$-0.411801\pi$
$919$	502.790			0.547105			0.273553	+	0.961857i	$0.411801\pi$
$920$		0			0
$921$			195.408i			0.212169i
$922$		0			0
$923$	151.292			0.163914
$924$		0			0
$925$	−26.2034	−	26.2034i	−0.0283280	−	0.0283280i
$926$		0			0
$927$			313.945i			0.338668i
$928$		0			0
$929$	592.492			0.637773			0.318887	−	0.947793i	$-0.396691\pi$
$929$	592.492			0.637773			0.318887	+	0.947793i	$0.396691\pi$
$930$		0			0
$931$	−76.1556	+	76.1556i	−0.0817998	+	0.0817998i
$932$		0			0
$933$			114.790i			0.123033i
$934$		0			0
$935$	−195.084			−0.208646
$936$		0			0
$937$		−	56.7969i		−	0.0606157i	−0.999541	−	0.0303078i	$-0.990351\pi$
$937$		−	56.7969i		−	0.0606157i	0.999541	−	0.0303078i	$-0.00964876\pi$
$938$		0			0
$939$	567.178	−	567.178i	0.604024	−	0.604024i
$940$		0			0
$941$			391.645i			0.416201i	0.978107	+	0.208100i	$0.0667280\pi$
$941$			391.645i			0.416201i	−0.978107	+	0.208100i	$0.933272\pi$
$942$		0			0
$943$	962.928	+	962.928i	1.02113	+	1.02113i
$944$		0			0
$945$	−40.4244	+	40.4244i	−0.0427771	+	0.0427771i
$946$		0			0
$947$	742.514	−	742.514i	0.784070	−	0.784070i	−0.196445	−	0.980515i	$-0.562940\pi$
$947$	742.514	−	742.514i	0.784070	−	0.784070i	0.980515	+	0.196445i	$0.0629397\pi$
$948$		0			0
$949$	78.4628	−	78.4628i	0.0826794	−	0.0826794i
$950$		0			0
$951$	−440.753			−0.463463
$952$		0			0
$953$	−1029.42			−1.08019			−0.540096	−	0.841603i	$-0.681612\pi$
$953$	−1029.42			−1.08019			−0.540096	+	0.841603i	$0.681612\pi$
$954$		0			0
$955$	−551.311	−	551.311i	−0.577289	−	0.577289i
$956$		0			0
$957$	−315.587	+	54.7704i	−0.329767	+	0.0572313i
$958$		0			0
$959$	405.073	−	405.073i	0.422391	−	0.422391i
$960$		0			0
$961$		−	995.244i		−	1.03563i
$962$		0			0
$963$		−	395.442i		−	0.410635i
$964$		0			0
$965$	−101.397	−	101.397i	−0.105075	−	0.105075i
$966$		0			0
$967$	216.951	+	216.951i	0.224355	+	0.224355i	0.810329	−	0.585975i	$-0.199288\pi$
$967$	216.951	+	216.951i	0.224355	+	0.224355i	−0.585975	+	0.810329i	$0.699288\pi$
$968$		0			0
$969$	72.7959	+	72.7959i	0.0751248	+	0.0751248i
$970$		0			0
$971$	−375.130	+	375.130i	−0.386334	+	0.386334i	−0.873378	−	0.487044i	$-0.838075\pi$
$971$	−375.130	+	375.130i	−0.386334	+	0.386334i	0.487044	+	0.873378i	$0.338075\pi$
$972$		0			0
$973$	−852.592			−0.876251
$974$		0			0
$975$	14.5696	+	14.5696i	0.0149432	+	0.0149432i
$976$		0			0
$977$	1650.72			1.68958			0.844790	−	0.535097i	$-0.179725\pi$
$977$	1650.72			1.68958			0.844790	+	0.535097i	$0.179725\pi$
$978$		0			0
$979$		−	568.361i		−	0.580553i
$980$		0			0
$981$	266.583			0.271746
$982$		0			0
$983$	34.2313	+	34.2313i	0.0348233	+	0.0348233i	0.724304	−	0.689481i	$-0.242161\pi$
$983$	34.2313	+	34.2313i	0.0348233	+	0.0348233i	−0.689481	+	0.724304i	$0.742161\pi$
$984$		0			0
$985$			381.563i			0.387374i
$986$		0			0
$987$	55.0731			0.0557985
$988$		0			0
$989$	−1057.12	+	1057.12i	−1.06888	+	1.06888i
$990$		0			0
$991$			645.719i			0.651583i	0.945442	+	0.325792i	$0.105631\pi$
$991$			645.719i			0.651583i	−0.945442	+	0.325792i	$0.894369\pi$
$992$		0			0
$993$	−423.392			−0.426377
$994$		0			0
$995$			338.038i			0.339737i
$996$		0			0
$997$	945.951	−	945.951i	0.948798	−	0.948798i	−0.0499539	−	0.998752i	$-0.515907\pi$
$997$	945.951	−	945.951i	0.948798	−	0.948798i	0.998752	+	0.0499539i	$0.0159075\pi$
$998$		0			0
$999$			38.5110i			0.0385495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1740.3.bl.a.481.14	✓	80
29.12	odd	4	inner	1740.3.bl.a.1201.14	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1740.3.bl.a.481.14	✓	80	1.1	even	1	trivial
1740.3.bl.a.1201.14	yes	80	29.12	odd	4	inner

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:	\( N \)	\(=\)	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1740.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{3} +2.23607i q^{5} +4.92030 q^{7} -3.00000i q^{9} +(-4.50909 + 4.50909i) q^{11} +2.37920i q^{13} +(-2.73861 - 2.73861i) q^{15} +(9.67426 - 9.67426i) q^{17} +(3.07195 - 3.07195i) q^{19} +(-6.02611 + 6.02611i) q^{21} +20.3604 q^{23} -5.00000 q^{25} +(3.67423 + 3.67423i) q^{27} +(-4.95885 - 28.5729i) q^{29} +(31.2749 - 31.2749i) q^{31} -11.0450i q^{33} +11.0021i q^{35} +(5.24068 + 5.24068i) q^{37} +(-2.91392 - 2.91392i) q^{39} +(47.2943 + 47.2943i) q^{41} +(-51.9205 + 51.9205i) q^{43} +6.70820 q^{45} +(-4.56954 - 4.56954i) q^{47} -24.7907 q^{49} +23.6970i q^{51} +17.4977 q^{53} +(-10.0826 - 10.0826i) q^{55} +7.52470i q^{57} +60.6038 q^{59} +(77.4847 - 77.4847i) q^{61} -14.7609i q^{63} -5.32006 q^{65} +24.2525i q^{67} +(-24.9362 + 24.9362i) q^{69} -63.5896i q^{71} +(-32.9786 - 32.9786i) q^{73} +(6.12372 - 6.12372i) q^{75} +(-22.1861 + 22.1861i) q^{77} +(24.8475 - 24.8475i) q^{79} -9.00000 q^{81} +79.9020 q^{83} +(21.6323 + 21.6323i) q^{85} +(41.0678 + 28.9212i) q^{87} +(-63.0239 + 63.0239i) q^{89} +11.7064i q^{91} +76.6077i q^{93} +(6.86908 + 6.86908i) q^{95} +(-47.9182 - 47.9182i) q^{97} +(13.5273 + 13.5273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 56 q^{17} + 24 q^{19} + 144 q^{23} - 400 q^{25} - 64 q^{29} - 128 q^{31} - 48 q^{37} + 48 q^{39} + 56 q^{41} - 88 q^{43} - 56 q^{47} + 448 q^{49} - 64 q^{53} - 80 q^{55} - 16 q^{59} + 248 q^{61}+ \cdots - 312 q^{97}+O(q^{100}) \) 80 * q - 56 * q^17 + 24 * q^19 + 144 * q^23 - 400 * q^25 - 64 * q^29 - 128 * q^31 - 48 * q^37 + 48 * q^39 + 56 * q^41 - 88 * q^43 - 56 * q^47 + 448 * q^49 - 64 * q^53 - 80 * q^55 - 16 * q^59 + 248 * q^61 + 216 * q^69 + 128 * q^73 - 360 * q^77 + 136 * q^79 - 720 * q^81 - 160 * q^83 - 120 * q^85 - 24 * q^87 - 88 * q^89 - 80 * q^95 - 312 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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