LMFDB - Embedded newform 5550.2.a.bw.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5550,2,Mod(1,5550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5550, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("5550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5550.a (trivial)

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:	yes
Analytic conductor:	$44.3169731218$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1110)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	5550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -6.12311 q^{11} +1.00000 q^{12} -5.68466 q^{13} -1.00000 q^{14} +1.00000 q^{16} +5.00000 q^{17} -1.00000 q^{18} +0.561553 q^{19} +1.00000 q^{21} +6.12311 q^{22} +6.56155 q^{23} -1.00000 q^{24} +5.68466 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.68466 q^{29} -3.56155 q^{31} -1.00000 q^{32} -6.12311 q^{33} -5.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} -0.561553 q^{38} -5.68466 q^{39} +8.68466 q^{41} -1.00000 q^{42} +12.6847 q^{43} -6.12311 q^{44} -6.56155 q^{46} +8.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +5.00000 q^{51} -5.68466 q^{52} -5.24621 q^{53} -1.00000 q^{54} -1.00000 q^{56} +0.561553 q^{57} +6.68466 q^{58} +4.24621 q^{59} -13.8078 q^{61} +3.56155 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.12311 q^{66} -13.1231 q^{67} +5.00000 q^{68} +6.56155 q^{69} +1.12311 q^{71} -1.00000 q^{72} +6.56155 q^{73} +1.00000 q^{74} +0.561553 q^{76} -6.12311 q^{77} +5.68466 q^{78} +14.2462 q^{79} +1.00000 q^{81} -8.68466 q^{82} +7.43845 q^{83} +1.00000 q^{84} -12.6847 q^{86} -6.68466 q^{87} +6.12311 q^{88} +5.68466 q^{89} -5.68466 q^{91} +6.56155 q^{92} -3.56155 q^{93} -8.00000 q^{94} -1.00000 q^{96} -3.31534 q^{97} +6.00000 q^{98} -6.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - 4 q^{11} + 2 q^{12} + q^{13} - 2 q^{14} + 2 q^{16} + 10 q^{17} - 2 q^{18} - 3 q^{19} + 2 q^{21} + 4 q^{22} + 9 q^{23} - 2 q^{24} - q^{26} + 2 q^{27} + 2 q^{28} - q^{29} - 3 q^{31} - 2 q^{32} - 4 q^{33} - 10 q^{34} + 2 q^{36} - 2 q^{37} + 3 q^{38} + q^{39} + 5 q^{41} - 2 q^{42} + 13 q^{43} - 4 q^{44} - 9 q^{46} + 16 q^{47} + 2 q^{48} - 12 q^{49} + 10 q^{51} + q^{52} + 6 q^{53} - 2 q^{54} - 2 q^{56} - 3 q^{57} + q^{58} - 8 q^{59} - 7 q^{61} + 3 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{66} - 18 q^{67} + 10 q^{68} + 9 q^{69} - 6 q^{71} - 2 q^{72} + 9 q^{73} + 2 q^{74} - 3 q^{76} - 4 q^{77} - q^{78} + 12 q^{79} + 2 q^{81} - 5 q^{82} + 19 q^{83} + 2 q^{84} - 13 q^{86} - q^{87} + 4 q^{88} - q^{89} + q^{91} + 9 q^{92} - 3 q^{93} - 16 q^{94} - 2 q^{96} - 19 q^{97} + 12 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - 4 * q^11 + 2 * q^12 + q^13 - 2 * q^14 + 2 * q^16 + 10 * q^17 - 2 * q^18 - 3 * q^19 + 2 * q^21 + 4 * q^22 + 9 * q^23 - 2 * q^24 - q^26 + 2 * q^27 + 2 * q^28 - q^29 - 3 * q^31 - 2 * q^32 - 4 * q^33 - 10 * q^34 + 2 * q^36 - 2 * q^37 + 3 * q^38 + q^39 + 5 * q^41 - 2 * q^42 + 13 * q^43 - 4 * q^44 - 9 * q^46 + 16 * q^47 + 2 * q^48 - 12 * q^49 + 10 * q^51 + q^52 + 6 * q^53 - 2 * q^54 - 2 * q^56 - 3 * q^57 + q^58 - 8 * q^59 - 7 * q^61 + 3 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^66 - 18 * q^67 + 10 * q^68 + 9 * q^69 - 6 * q^71 - 2 * q^72 + 9 * q^73 + 2 * q^74 - 3 * q^76 - 4 * q^77 - q^78 + 12 * q^79 + 2 * q^81 - 5 * q^82 + 19 * q^83 + 2 * q^84 - 13 * q^86 - q^87 + 4 * q^88 - q^89 + q^91 + 9 * q^92 - 3 * q^93 - 16 * q^94 - 2 * q^96 - 19 * q^97 + 12 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−6.12311	−1.84619	−0.923093	−	0.384577i	$-0.874347\pi$
$11$	−6.12311	−1.84619	−0.923093	+	0.384577i	$0.874347\pi$
$12$	1.00000	0.288675
$13$	−5.68466	−1.57664	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	−5.68466	−1.57664	−0.788320	+	0.615265i	$0.789049\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	5.00000	1.21268	0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000	1.21268	0.606339	+	0.795206i	$0.292637\pi$
$18$	−1.00000	−0.235702
$19$	0.561553	0.128829	0.0644145	−	0.997923i	$-0.479482\pi$
$19$	0.561553	0.128829	0.0644145	+	0.997923i	$0.479482\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	6.12311	1.30545
$23$	6.56155	1.36818	0.684089	−	0.729398i	$-0.260200\pi$
$23$	6.56155	1.36818	0.684089	+	0.729398i	$0.260200\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	5.68466	1.11485
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−6.68466	−1.24131	−0.620655	−	0.784084i	$-0.713133\pi$
$29$	−6.68466	−1.24131	−0.620655	+	0.784084i	$0.713133\pi$
$30$	0	0
$31$	−3.56155	−0.639674	−0.319837	−	0.947473i	$-0.603628\pi$
$31$	−3.56155	−0.639674	−0.319837	+	0.947473i	$0.603628\pi$
$32$	−1.00000	−0.176777
$33$	−6.12311	−1.06590
$34$	−5.00000	−0.857493
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−0.561553	−0.0910959
$39$	−5.68466	−0.910274
$40$	0	0
$41$	8.68466	1.35632	0.678158	−	0.734916i	$-0.262779\pi$
$41$	8.68466	1.35632	0.678158	+	0.734916i	$0.262779\pi$
$42$	−1.00000	−0.154303
$43$	12.6847	1.93439	0.967196	−	0.254031i	$-0.0817565\pi$
$43$	12.6847	1.93439	0.967196	+	0.254031i	$0.0817565\pi$
$44$	−6.12311	−0.923093
$45$	0	0
$46$	−6.56155	−0.967448
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	0	0
$51$	5.00000	0.700140
$52$	−5.68466	−0.788320
$53$	−5.24621	−0.720623	−0.360311	−	0.932832i	$-0.617330\pi$
$53$	−5.24621	−0.720623	−0.360311	+	0.932832i	$0.617330\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0.561553	0.0743795
$58$	6.68466	0.877739
$59$	4.24621	0.552810	0.276405	−	0.961041i	$-0.410857\pi$
$59$	4.24621	0.552810	0.276405	+	0.961041i	$0.410857\pi$
$60$	0	0
$61$	−13.8078	−1.76790	−0.883952	−	0.467579i	$-0.845126\pi$
$61$	−13.8078	−1.76790	−0.883952	+	0.467579i	$0.845126\pi$
$62$	3.56155	0.452318
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	6.12311	0.753702
$67$	−13.1231	−1.60324	−0.801621	−	0.597832i	$-0.796029\pi$
$67$	−13.1231	−1.60324	−0.801621	+	0.597832i	$0.796029\pi$
$68$	5.00000	0.606339
$69$	6.56155	0.789918
$70$	0	0
$71$	1.12311	0.133288	0.0666441	−	0.997777i	$-0.478771\pi$
$71$	1.12311	0.133288	0.0666441	+	0.997777i	$0.478771\pi$
$72$	−1.00000	−0.117851
$73$	6.56155	0.767972	0.383986	−	0.923339i	$-0.374551\pi$
$73$	6.56155	0.767972	0.383986	+	0.923339i	$0.374551\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	0.561553	0.0644145
$77$	−6.12311	−0.697793
$78$	5.68466	0.643661
$79$	14.2462	1.60282	0.801412	−	0.598113i	$-0.204082\pi$
$79$	14.2462	1.60282	0.801412	+	0.598113i	$0.204082\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−8.68466	−0.959060
$83$	7.43845	0.816476	0.408238	−	0.912876i	$-0.366143\pi$
$83$	7.43845	0.816476	0.408238	+	0.912876i	$0.366143\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	−12.6847	−1.36782
$87$	−6.68466	−0.716671
$88$	6.12311	0.652725
$89$	5.68466	0.602573	0.301286	−	0.953534i	$-0.402584\pi$
$89$	5.68466	0.602573	0.301286	+	0.953534i	$0.402584\pi$
$90$	0	0
$91$	−5.68466	−0.595914
$92$	6.56155	0.684089
$93$	−3.56155	−0.369316
$94$	−8.00000	−0.825137
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−3.31534	−0.336622	−0.168311	−	0.985734i	$-0.553831\pi$
$97$	−3.31534	−0.336622	−0.168311	+	0.985734i	$0.553831\pi$
$98$	6.00000	0.606092
$99$	−6.12311	−0.615395
$100$	0	0
$101$	10.8769	1.08229	0.541146	−	0.840929i	$-0.317991\pi$
$101$	10.8769	1.08229	0.541146	+	0.840929i	$0.317991\pi$
$102$	−5.00000	−0.495074
$103$	16.4924	1.62505	0.812523	−	0.582929i	$-0.198093\pi$
$103$	16.4924	1.62505	0.812523	+	0.582929i	$0.198093\pi$
$104$	5.68466	0.557427
$105$	0	0
$106$	5.24621	0.509557
$107$	10.8078	1.04483	0.522413	−	0.852693i	$-0.325032\pi$
$107$	10.8078	1.04483	0.522413	+	0.852693i	$0.325032\pi$
$108$	1.00000	0.0962250
$109$	−2.12311	−0.203357	−0.101678	−	0.994817i	$-0.532421\pi$
$109$	−2.12311	−0.203357	−0.101678	+	0.994817i	$0.532421\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	1.00000	0.0944911
$113$	10.6847	1.00513	0.502564	−	0.864540i	$-0.332390\pi$
$113$	10.6847	1.00513	0.502564	+	0.864540i	$0.332390\pi$
$114$	−0.561553	−0.0525942
$115$	0	0
$116$	−6.68466	−0.620655
$117$	−5.68466	−0.525547
$118$	−4.24621	−0.390895
$119$	5.00000	0.458349
$120$	0	0
$121$	26.4924	2.40840
$122$	13.8078	1.25010
$123$	8.68466	0.783069
$124$	−3.56155	−0.319837
$125$	0	0
$126$	−1.00000	−0.0890871
$127$	−14.5616	−1.29213	−0.646064	−	0.763283i	$-0.723586\pi$
$127$	−14.5616	−1.29213	−0.646064	+	0.763283i	$0.723586\pi$
$128$	−1.00000	−0.0883883
$129$	12.6847	1.11682
$130$	0	0
$131$	7.12311	0.622349	0.311174	−	0.950353i	$-0.399278\pi$
$131$	7.12311	0.622349	0.311174	+	0.950353i	$0.399278\pi$
$132$	−6.12311	−0.532948
$133$	0.561553	0.0486928
$134$	13.1231	1.13366
$135$	0	0
$136$	−5.00000	−0.428746
$137$	4.24621	0.362778	0.181389	−	0.983411i	$-0.441941\pi$
$137$	4.24621	0.362778	0.181389	+	0.983411i	$0.441941\pi$
$138$	−6.56155	−0.558556
$139$	13.8078	1.17116	0.585580	−	0.810615i	$-0.300867\pi$
$139$	13.8078	1.17116	0.585580	+	0.810615i	$0.300867\pi$
$140$	0	0
$141$	8.00000	0.673722
$142$	−1.12311	−0.0942489
$143$	34.8078	2.91077
$144$	1.00000	0.0833333
$145$	0	0
$146$	−6.56155	−0.543038
$147$	−6.00000	−0.494872
$148$	−1.00000	−0.0821995
$149$	7.75379	0.635215	0.317608	−	0.948222i	$-0.397121\pi$
$149$	7.75379	0.635215	0.317608	+	0.948222i	$0.397121\pi$
$150$	0	0
$151$	−15.4384	−1.25636	−0.628182	−	0.778067i	$-0.716200\pi$
$151$	−15.4384	−1.25636	−0.628182	+	0.778067i	$0.716200\pi$
$152$	−0.561553	−0.0455479
$153$	5.00000	0.404226
$154$	6.12311	0.493414
$155$	0	0
$156$	−5.68466	−0.455137
$157$	18.0540	1.44086	0.720432	−	0.693526i	$-0.243944\pi$
$157$	18.0540	1.44086	0.720432	+	0.693526i	$0.243944\pi$
$158$	−14.2462	−1.13337
$159$	−5.24621	−0.416052
$160$	0	0
$161$	6.56155	0.517123
$162$	−1.00000	−0.0785674
$163$	−19.4924	−1.52676	−0.763382	−	0.645947i	$-0.776463\pi$
$163$	−19.4924	−1.52676	−0.763382	+	0.645947i	$0.776463\pi$
$164$	8.68466	0.678158
$165$	0	0
$166$	−7.43845	−0.577335
$167$	−19.0540	−1.47444	−0.737220	−	0.675652i	$-0.763862\pi$
$167$	−19.0540	−1.47444	−0.737220	+	0.675652i	$0.763862\pi$
$168$	−1.00000	−0.0771517
$169$	19.3153	1.48580
$170$	0	0
$171$	0.561553	0.0429430
$172$	12.6847	0.967196
$173$	2.12311	0.161417	0.0807084	−	0.996738i	$-0.474282\pi$
$173$	2.12311	0.161417	0.0807084	+	0.996738i	$0.474282\pi$
$174$	6.68466	0.506763
$175$	0	0
$176$	−6.12311	−0.461546
$177$	4.24621	0.319165
$178$	−5.68466	−0.426083
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	0	0
$181$	20.2462	1.50489	0.752445	−	0.658656i	$-0.228875\pi$
$181$	20.2462	1.50489	0.752445	+	0.658656i	$0.228875\pi$
$182$	5.68466	0.421375
$183$	−13.8078	−1.02070
$184$	−6.56155	−0.483724
$185$	0	0
$186$	3.56155	0.261146
$187$	−30.6155	−2.23883
$188$	8.00000	0.583460
$189$	1.00000	0.0727393
$190$	0	0
$191$	14.3693	1.03973	0.519864	−	0.854249i	$-0.325983\pi$
$191$	14.3693	1.03973	0.519864	+	0.854249i	$0.325983\pi$
$192$	1.00000	0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	3.31534	0.238028
$195$	0	0
$196$	−6.00000	−0.428571
$197$	2.31534	0.164961	0.0824806	−	0.996593i	$-0.473716\pi$
$197$	2.31534	0.164961	0.0824806	+	0.996593i	$0.473716\pi$
$198$	6.12311	0.435150
$199$	−16.4924	−1.16912	−0.584558	−	0.811352i	$-0.698732\pi$
$199$	−16.4924	−1.16912	−0.584558	+	0.811352i	$0.698732\pi$
$200$	0	0
$201$	−13.1231	−0.925633
$202$	−10.8769	−0.765296
$203$	−6.68466	−0.469171
$204$	5.00000	0.350070
$205$	0	0
$206$	−16.4924	−1.14908
$207$	6.56155	0.456059
$208$	−5.68466	−0.394160
$209$	−3.43845	−0.237842
$210$	0	0
$211$	4.43845	0.305555	0.152778	−	0.988261i	$-0.451178\pi$
$211$	4.43845	0.305555	0.152778	+	0.988261i	$0.451178\pi$
$212$	−5.24621	−0.360311
$213$	1.12311	0.0769539
$214$	−10.8078	−0.738804
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−3.56155	−0.241774
$218$	2.12311	0.143795
$219$	6.56155	0.443389
$220$	0	0
$221$	−28.4233	−1.91196
$222$	1.00000	0.0671156
$223$	19.8078	1.32643	0.663213	−	0.748431i	$-0.269192\pi$
$223$	19.8078	1.32643	0.663213	+	0.748431i	$0.269192\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−10.6847	−0.710733
$227$	10.9309	0.725507	0.362754	−	0.931885i	$-0.381837\pi$
$227$	10.9309	0.725507	0.362754	+	0.931885i	$0.381837\pi$
$228$	0.561553	0.0371897
$229$	−5.12311	−0.338544	−0.169272	−	0.985569i	$-0.554142\pi$
$229$	−5.12311	−0.338544	−0.169272	+	0.985569i	$0.554142\pi$
$230$	0	0
$231$	−6.12311	−0.402871
$232$	6.68466	0.438869
$233$	−11.3693	−0.744829	−0.372414	−	0.928067i	$-0.621470\pi$
$233$	−11.3693	−0.744829	−0.372414	+	0.928067i	$0.621470\pi$
$234$	5.68466	0.371618
$235$	0	0
$236$	4.24621	0.276405
$237$	14.2462	0.925391
$238$	−5.00000	−0.324102
$239$	7.80776	0.505042	0.252521	−	0.967591i	$-0.418740\pi$
$239$	7.80776	0.505042	0.252521	+	0.967591i	$0.418740\pi$
$240$	0	0
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	−26.4924	−1.70300
$243$	1.00000	0.0641500
$244$	−13.8078	−0.883952
$245$	0	0
$246$	−8.68466	−0.553714
$247$	−3.19224	−0.203117
$248$	3.56155	0.226159
$249$	7.43845	0.471392
$250$	0	0
$251$	25.6155	1.61684	0.808419	−	0.588608i	$-0.200324\pi$
$251$	25.6155	1.61684	0.808419	+	0.588608i	$0.200324\pi$
$252$	1.00000	0.0629941
$253$	−40.1771	−2.52591
$254$	14.5616	0.913673
$255$	0	0
$256$	1.00000	0.0625000
$257$	−10.8078	−0.674170	−0.337085	−	0.941474i	$-0.609441\pi$
$257$	−10.8078	−0.674170	−0.337085	+	0.941474i	$0.609441\pi$
$258$	−12.6847	−0.789712
$259$	−1.00000	−0.0621370
$260$	0	0
$261$	−6.68466	−0.413770
$262$	−7.12311	−0.440067
$263$	6.43845	0.397012	0.198506	−	0.980100i	$-0.436391\pi$
$263$	6.43845	0.397012	0.198506	+	0.980100i	$0.436391\pi$
$264$	6.12311	0.376851
$265$	0	0
$266$	−0.561553	−0.0344310
$267$	5.68466	0.347895
$268$	−13.1231	−0.801621
$269$	−16.8078	−1.02479	−0.512394	−	0.858751i	$-0.671241\pi$
$269$	−16.8078	−1.02479	−0.512394	+	0.858751i	$0.671241\pi$
$270$	0	0
$271$	−16.4924	−1.00184	−0.500922	−	0.865493i	$-0.667006\pi$
$271$	−16.4924	−1.00184	−0.500922	+	0.865493i	$0.667006\pi$
$272$	5.00000	0.303170
$273$	−5.68466	−0.344051
$274$	−4.24621	−0.256523
$275$	0	0
$276$	6.56155	0.394959
$277$	−27.6847	−1.66341	−0.831705	−	0.555218i	$-0.812635\pi$
$277$	−27.6847	−1.66341	−0.831705	+	0.555218i	$0.812635\pi$
$278$	−13.8078	−0.828135
$279$	−3.56155	−0.213225
$280$	0	0
$281$	22.1771	1.32297	0.661487	−	0.749957i	$-0.269926\pi$
$281$	22.1771	1.32297	0.661487	+	0.749957i	$0.269926\pi$
$282$	−8.00000	−0.476393
$283$	−9.93087	−0.590329	−0.295164	−	0.955446i	$-0.595374\pi$
$283$	−9.93087	−0.590329	−0.295164	+	0.955446i	$0.595374\pi$
$284$	1.12311	0.0666441
$285$	0	0
$286$	−34.8078	−2.05823
$287$	8.68466	0.512639
$288$	−1.00000	−0.0589256
$289$	8.00000	0.470588
$290$	0	0
$291$	−3.31534	−0.194349
$292$	6.56155	0.383986
$293$	16.6155	0.970690	0.485345	−	0.874323i	$-0.338694\pi$
$293$	16.6155	0.970690	0.485345	+	0.874323i	$0.338694\pi$
$294$	6.00000	0.349927
$295$	0	0
$296$	1.00000	0.0581238
$297$	−6.12311	−0.355299
$298$	−7.75379	−0.449165
$299$	−37.3002	−2.15713
$300$	0	0
$301$	12.6847	0.731132
$302$	15.4384	0.888383
$303$	10.8769	0.624861
$304$	0.561553	0.0322073
$305$	0	0
$306$	−5.00000	−0.285831
$307$	0.246211	0.0140520	0.00702601	−	0.999975i	$-0.497764\pi$
$307$	0.246211	0.0140520	0.00702601	+	0.999975i	$0.497764\pi$
$308$	−6.12311	−0.348896
$309$	16.4924	0.938221
$310$	0	0
$311$	−21.1771	−1.20084	−0.600421	−	0.799684i	$-0.705000\pi$
$311$	−21.1771	−1.20084	−0.600421	+	0.799684i	$0.705000\pi$
$312$	5.68466	0.321830
$313$	24.8769	1.40613	0.703063	−	0.711128i	$-0.251815\pi$
$313$	24.8769	1.40613	0.703063	+	0.711128i	$0.251815\pi$
$314$	−18.0540	−1.01884
$315$	0	0
$316$	14.2462	0.801412
$317$	−16.9309	−0.950932	−0.475466	−	0.879734i	$-0.657721\pi$
$317$	−16.9309	−0.950932	−0.475466	+	0.879734i	$0.657721\pi$
$318$	5.24621	0.294193
$319$	40.9309	2.29169
$320$	0	0
$321$	10.8078	0.603231
$322$	−6.56155	−0.365661
$323$	2.80776	0.156228
$324$	1.00000	0.0555556
$325$	0	0
$326$	19.4924	1.07959
$327$	−2.12311	−0.117408
$328$	−8.68466	−0.479530
$329$	8.00000	0.441054
$330$	0	0
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	7.43845	0.408238
$333$	−1.00000	−0.0547997
$334$	19.0540	1.04259
$335$	0	0
$336$	1.00000	0.0545545
$337$	−4.56155	−0.248484	−0.124242	−	0.992252i	$-0.539650\pi$
$337$	−4.56155	−0.248484	−0.124242	+	0.992252i	$0.539650\pi$
$338$	−19.3153	−1.05062
$339$	10.6847	0.580311
$340$	0	0
$341$	21.8078	1.18096
$342$	−0.561553	−0.0303653
$343$	−13.0000	−0.701934
$344$	−12.6847	−0.683911
$345$	0	0
$346$	−2.12311	−0.114139
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	−6.68466	−0.358335
$349$	14.2462	0.762582	0.381291	−	0.924455i	$-0.375480\pi$
$349$	14.2462	0.762582	0.381291	+	0.924455i	$0.375480\pi$
$350$	0	0
$351$	−5.68466	−0.303425
$352$	6.12311	0.326363
$353$	29.8078	1.58651	0.793254	−	0.608891i	$-0.208385\pi$
$353$	29.8078	1.58651	0.793254	+	0.608891i	$0.208385\pi$
$354$	−4.24621	−0.225684
$355$	0	0
$356$	5.68466	0.301286
$357$	5.00000	0.264628
$358$	4.00000	0.211407
$359$	−20.8769	−1.10184	−0.550920	−	0.834558i	$-0.685723\pi$
$359$	−20.8769	−1.10184	−0.550920	+	0.834558i	$0.685723\pi$
$360$	0	0
$361$	−18.6847	−0.983403
$362$	−20.2462	−1.06412
$363$	26.4924	1.39049
$364$	−5.68466	−0.297957
$365$	0	0
$366$	13.8078	0.721743
$367$	17.0000	0.887393	0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000	0.887393	0.443696	+	0.896177i	$0.353667\pi$
$368$	6.56155	0.342045
$369$	8.68466	0.452105
$370$	0	0
$371$	−5.24621	−0.272370
$372$	−3.56155	−0.184658
$373$	30.4924	1.57884	0.789419	−	0.613855i	$-0.210382\pi$
$373$	30.4924	1.57884	0.789419	+	0.613855i	$0.210382\pi$
$374$	30.6155	1.58309
$375$	0	0
$376$	−8.00000	−0.412568
$377$	38.0000	1.95710
$378$	−1.00000	−0.0514344
$379$	−2.87689	−0.147776	−0.0738881	−	0.997267i	$-0.523541\pi$
$379$	−2.87689	−0.147776	−0.0738881	+	0.997267i	$0.523541\pi$
$380$	0	0
$381$	−14.5616	−0.746011
$382$	−14.3693	−0.735198
$383$	27.6847	1.41462	0.707310	−	0.706904i	$-0.249909\pi$
$383$	27.6847	1.41462	0.707310	+	0.706904i	$0.249909\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−14.0000	−0.712581
$387$	12.6847	0.644797
$388$	−3.31534	−0.168311
$389$	20.9309	1.06124	0.530619	−	0.847611i	$-0.321960\pi$
$389$	20.9309	1.06124	0.530619	+	0.847611i	$0.321960\pi$
$390$	0	0
$391$	32.8078	1.65916
$392$	6.00000	0.303046
$393$	7.12311	0.359313
$394$	−2.31534	−0.116645
$395$	0	0
$396$	−6.12311	−0.307698
$397$	−27.1231	−1.36127	−0.680635	−	0.732623i	$-0.738296\pi$
$397$	−27.1231	−1.36127	−0.680635	+	0.732623i	$0.738296\pi$
$398$	16.4924	0.826690
$399$	0.561553	0.0281128
$400$	0	0
$401$	−14.8078	−0.739464	−0.369732	−	0.929138i	$-0.620551\pi$
$401$	−14.8078	−0.739464	−0.369732	+	0.929138i	$0.620551\pi$
$402$	13.1231	0.654521
$403$	20.2462	1.00854
$404$	10.8769	0.541146
$405$	0	0
$406$	6.68466	0.331754
$407$	6.12311	0.303511
$408$	−5.00000	−0.247537
$409$	−0.876894	−0.0433596	−0.0216798	−	0.999765i	$-0.506901\pi$
$409$	−0.876894	−0.0433596	−0.0216798	+	0.999765i	$0.506901\pi$
$410$	0	0
$411$	4.24621	0.209450
$412$	16.4924	0.812523
$413$	4.24621	0.208942
$414$	−6.56155	−0.322483
$415$	0	0
$416$	5.68466	0.278713
$417$	13.8078	0.676169
$418$	3.43845	0.168180
$419$	−10.5616	−0.515966	−0.257983	−	0.966150i	$-0.583058\pi$
$419$	−10.5616	−0.515966	−0.257983	+	0.966150i	$0.583058\pi$
$420$	0	0
$421$	30.9848	1.51011	0.755054	−	0.655662i	$-0.227610\pi$
$421$	30.9848	1.51011	0.755054	+	0.655662i	$0.227610\pi$
$422$	−4.43845	−0.216060
$423$	8.00000	0.388973
$424$	5.24621	0.254779
$425$	0	0
$426$	−1.12311	−0.0544146
$427$	−13.8078	−0.668205
$428$	10.8078	0.522413
$429$	34.8078	1.68053
$430$	0	0
$431$	−29.0000	−1.39688	−0.698440	−	0.715668i	$-0.746122\pi$
$431$	−29.0000	−1.39688	−0.698440	+	0.715668i	$0.746122\pi$
$432$	1.00000	0.0481125
$433$	30.4233	1.46205	0.731025	−	0.682351i	$-0.239042\pi$
$433$	30.4233	1.46205	0.731025	+	0.682351i	$0.239042\pi$
$434$	3.56155	0.170960
$435$	0	0
$436$	−2.12311	−0.101678
$437$	3.68466	0.176261
$438$	−6.56155	−0.313523
$439$	−14.0540	−0.670760	−0.335380	−	0.942083i	$-0.608865\pi$
$439$	−14.0540	−0.670760	−0.335380	+	0.942083i	$0.608865\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	28.4233	1.35196
$443$	−33.8617	−1.60882	−0.804410	−	0.594075i	$-0.797518\pi$
$443$	−33.8617	−1.60882	−0.804410	+	0.594075i	$0.797518\pi$
$444$	−1.00000	−0.0474579
$445$	0	0
$446$	−19.8078	−0.937925
$447$	7.75379	0.366742
$448$	1.00000	0.0472456
$449$	−1.61553	−0.0762415	−0.0381207	−	0.999273i	$-0.512137\pi$
$449$	−1.61553	−0.0762415	−0.0381207	+	0.999273i	$0.512137\pi$
$450$	0	0
$451$	−53.1771	−2.50401
$452$	10.6847	0.502564
$453$	−15.4384	−0.725362
$454$	−10.9309	−0.513011
$455$	0	0
$456$	−0.561553	−0.0262971
$457$	30.9309	1.44689	0.723443	−	0.690385i	$-0.242559\pi$
$457$	30.9309	1.44689	0.723443	+	0.690385i	$0.242559\pi$
$458$	5.12311	0.239387
$459$	5.00000	0.233380
$460$	0	0
$461$	0.438447	0.0204205	0.0102103	−	0.999948i	$-0.496750\pi$
$461$	0.438447	0.0204205	0.0102103	+	0.999948i	$0.496750\pi$
$462$	6.12311	0.284873
$463$	−4.87689	−0.226649	−0.113324	−	0.993558i	$-0.536150\pi$
$463$	−4.87689	−0.226649	−0.113324	+	0.993558i	$0.536150\pi$
$464$	−6.68466	−0.310327
$465$	0	0
$466$	11.3693	0.526673
$467$	−2.43845	−0.112838	−0.0564189	−	0.998407i	$-0.517968\pi$
$467$	−2.43845	−0.112838	−0.0564189	+	0.998407i	$0.517968\pi$
$468$	−5.68466	−0.262773
$469$	−13.1231	−0.605969
$470$	0	0
$471$	18.0540	0.831883
$472$	−4.24621	−0.195448
$473$	−77.6695	−3.57125
$474$	−14.2462	−0.654350
$475$	0	0
$476$	5.00000	0.229175
$477$	−5.24621	−0.240208
$478$	−7.80776	−0.357119
$479$	−6.56155	−0.299805	−0.149903	−	0.988701i	$-0.547896\pi$
$479$	−6.56155	−0.299805	−0.149903	+	0.988701i	$0.547896\pi$
$480$	0	0
$481$	5.68466	0.259198
$482$	2.00000	0.0910975
$483$	6.56155	0.298561
$484$	26.4924	1.20420
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−16.7386	−0.758500	−0.379250	−	0.925294i	$-0.623818\pi$
$487$	−16.7386	−0.758500	−0.379250	+	0.925294i	$0.623818\pi$
$488$	13.8078	0.625048
$489$	−19.4924	−0.881478
$490$	0	0
$491$	−12.1771	−0.549544	−0.274772	−	0.961509i	$-0.588602\pi$
$491$	−12.1771	−0.549544	−0.274772	+	0.961509i	$0.588602\pi$
$492$	8.68466	0.391535
$493$	−33.4233	−1.50531
$494$	3.19224	0.143625
$495$	0	0
$496$	−3.56155	−0.159918
$497$	1.12311	0.0503782
$498$	−7.43845	−0.333325
$499$	32.8078	1.46868	0.734339	−	0.678783i	$-0.237492\pi$
$499$	32.8078	1.46868	0.734339	+	0.678783i	$0.237492\pi$
$500$	0	0
$501$	−19.0540	−0.851269
$502$	−25.6155	−1.14328
$503$	18.2462	0.813558	0.406779	−	0.913527i	$-0.366652\pi$
$503$	18.2462	0.813558	0.406779	+	0.913527i	$0.366652\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	40.1771	1.78609
$507$	19.3153	0.857824
$508$	−14.5616	−0.646064
$509$	23.0540	1.02185	0.510925	−	0.859625i	$-0.329303\pi$
$509$	23.0540	1.02185	0.510925	+	0.859625i	$0.329303\pi$
$510$	0	0
$511$	6.56155	0.290266
$512$	−1.00000	−0.0441942
$513$	0.561553	0.0247932
$514$	10.8078	0.476710
$515$	0	0
$516$	12.6847	0.558411
$517$	−48.9848	−2.15435
$518$	1.00000	0.0439375
$519$	2.12311	0.0931940
$520$	0	0
$521$	−18.4384	−0.807803	−0.403902	−	0.914802i	$-0.632346\pi$
$521$	−18.4384	−0.807803	−0.403902	+	0.914802i	$0.632346\pi$
$522$	6.68466	0.292580
$523$	−30.7386	−1.34411	−0.672053	−	0.740503i	$-0.734587\pi$
$523$	−30.7386	−1.34411	−0.672053	+	0.740503i	$0.734587\pi$
$524$	7.12311	0.311174
$525$	0	0
$526$	−6.43845	−0.280730
$527$	−17.8078	−0.775718
$528$	−6.12311	−0.266474
$529$	20.0540	0.871912
$530$	0	0
$531$	4.24621	0.184270
$532$	0.561553	0.0243464
$533$	−49.3693	−2.13842
$534$	−5.68466	−0.245999
$535$	0	0
$536$	13.1231	0.566832
$537$	−4.00000	−0.172613
$538$	16.8078	0.724634
$539$	36.7386	1.58244
$540$	0	0
$541$	−20.4233	−0.878066	−0.439033	−	0.898471i	$-0.644679\pi$
$541$	−20.4233	−0.878066	−0.439033	+	0.898471i	$0.644679\pi$
$542$	16.4924	0.708410
$543$	20.2462	0.868848
$544$	−5.00000	−0.214373
$545$	0	0
$546$	5.68466	0.243281
$547$	39.7386	1.69910	0.849551	−	0.527507i	$-0.176873\pi$
$547$	39.7386	1.69910	0.849551	+	0.527507i	$0.176873\pi$
$548$	4.24621	0.181389
$549$	−13.8078	−0.589301
$550$	0	0
$551$	−3.75379	−0.159917
$552$	−6.56155	−0.279278
$553$	14.2462	0.605811
$554$	27.6847	1.17621
$555$	0	0
$556$	13.8078	0.585580
$557$	−7.61553	−0.322680	−0.161340	−	0.986899i	$-0.551582\pi$
$557$	−7.61553	−0.322680	−0.161340	+	0.986899i	$0.551582\pi$
$558$	3.56155	0.150773
$559$	−72.1080	−3.04984
$560$	0	0
$561$	−30.6155	−1.29259
$562$	−22.1771	−0.935484
$563$	−4.93087	−0.207811	−0.103906	−	0.994587i	$-0.533134\pi$
$563$	−4.93087	−0.207811	−0.103906	+	0.994587i	$0.533134\pi$
$564$	8.00000	0.336861
$565$	0	0
$566$	9.93087	0.417426
$567$	1.00000	0.0419961
$568$	−1.12311	−0.0471245
$569$	2.31534	0.0970642	0.0485321	−	0.998822i	$-0.484546\pi$
$569$	2.31534	0.0970642	0.0485321	+	0.998822i	$0.484546\pi$
$570$	0	0
$571$	−5.80776	−0.243047	−0.121524	−	0.992589i	$-0.538778\pi$
$571$	−5.80776	−0.243047	−0.121524	+	0.992589i	$0.538778\pi$
$572$	34.8078	1.45539
$573$	14.3693	0.600287
$574$	−8.68466	−0.362491
$575$	0	0
$576$	1.00000	0.0416667
$577$	14.4924	0.603327	0.301664	−	0.953414i	$-0.402458\pi$
$577$	14.4924	0.603327	0.301664	+	0.953414i	$0.402458\pi$
$578$	−8.00000	−0.332756
$579$	14.0000	0.581820
$580$	0	0
$581$	7.43845	0.308599
$582$	3.31534	0.137425
$583$	32.1231	1.33040
$584$	−6.56155	−0.271519
$585$	0	0
$586$	−16.6155	−0.686381
$587$	12.3002	0.507683	0.253842	−	0.967246i	$-0.418306\pi$
$587$	12.3002	0.507683	0.253842	+	0.967246i	$0.418306\pi$
$588$	−6.00000	−0.247436
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	2.31534	0.0952404
$592$	−1.00000	−0.0410997
$593$	−4.87689	−0.200270	−0.100135	−	0.994974i	$-0.531927\pi$
$593$	−4.87689	−0.200270	−0.100135	+	0.994974i	$0.531927\pi$
$594$	6.12311	0.251234
$595$	0	0
$596$	7.75379	0.317608
$597$	−16.4924	−0.674990
$598$	37.3002	1.52532
$599$	26.7386	1.09251	0.546255	−	0.837619i	$-0.316053\pi$
$599$	26.7386	1.09251	0.546255	+	0.837619i	$0.316053\pi$
$600$	0	0
$601$	−42.8617	−1.74837	−0.874183	−	0.485596i	$-0.838603\pi$
$601$	−42.8617	−1.74837	−0.874183	+	0.485596i	$0.838603\pi$
$602$	−12.6847	−0.516988
$603$	−13.1231	−0.534414
$604$	−15.4384	−0.628182
$605$	0	0
$606$	−10.8769	−0.441844
$607$	26.4924	1.07529	0.537647	−	0.843170i	$-0.319313\pi$
$607$	26.4924	1.07529	0.537647	+	0.843170i	$0.319313\pi$
$608$	−0.561553	−0.0227740
$609$	−6.68466	−0.270876
$610$	0	0
$611$	−45.4773	−1.83981
$612$	5.00000	0.202113
$613$	−8.43845	−0.340826	−0.170413	−	0.985373i	$-0.554510\pi$
$613$	−8.43845	−0.340826	−0.170413	+	0.985373i	$0.554510\pi$
$614$	−0.246211	−0.00993628
$615$	0	0
$616$	6.12311	0.246707
$617$	−14.4924	−0.583443	−0.291721	−	0.956503i	$-0.594228\pi$
$617$	−14.4924	−0.583443	−0.291721	+	0.956503i	$0.594228\pi$
$618$	−16.4924	−0.663423
$619$	−35.8078	−1.43924	−0.719618	−	0.694370i	$-0.755683\pi$
$619$	−35.8078	−1.43924	−0.719618	+	0.694370i	$0.755683\pi$
$620$	0	0
$621$	6.56155	0.263306
$622$	21.1771	0.849124
$623$	5.68466	0.227751
$624$	−5.68466	−0.227568
$625$	0	0
$626$	−24.8769	−0.994281
$627$	−3.43845	−0.137318
$628$	18.0540	0.720432
$629$	−5.00000	−0.199363
$630$	0	0
$631$	15.3153	0.609694	0.304847	−	0.952401i	$-0.401395\pi$
$631$	15.3153	0.609694	0.304847	+	0.952401i	$0.401395\pi$
$632$	−14.2462	−0.566684
$633$	4.43845	0.176412
$634$	16.9309	0.672411
$635$	0	0
$636$	−5.24621	−0.208026
$637$	34.1080	1.35141
$638$	−40.9309	−1.62047
$639$	1.12311	0.0444294
$640$	0	0
$641$	1.94602	0.0768634	0.0384317	−	0.999261i	$-0.487764\pi$
$641$	1.94602	0.0768634	0.0384317	+	0.999261i	$0.487764\pi$
$642$	−10.8078	−0.426548
$643$	34.1231	1.34568	0.672842	−	0.739786i	$-0.265073\pi$
$643$	34.1231	1.34568	0.672842	+	0.739786i	$0.265073\pi$
$644$	6.56155	0.258561
$645$	0	0
$646$	−2.80776	−0.110470
$647$	36.8078	1.44706	0.723531	−	0.690292i	$-0.242518\pi$
$647$	36.8078	1.44706	0.723531	+	0.690292i	$0.242518\pi$
$648$	−1.00000	−0.0392837
$649$	−26.0000	−1.02059
$650$	0	0
$651$	−3.56155	−0.139588
$652$	−19.4924	−0.763382
$653$	28.4924	1.11499	0.557497	−	0.830179i	$-0.311762\pi$
$653$	28.4924	1.11499	0.557497	+	0.830179i	$0.311762\pi$
$654$	2.12311	0.0830200
$655$	0	0
$656$	8.68466	0.339079
$657$	6.56155	0.255991
$658$	−8.00000	−0.311872
$659$	−18.2462	−0.710771	−0.355386	−	0.934720i	$-0.615650\pi$
$659$	−18.2462	−0.710771	−0.355386	+	0.934720i	$0.615650\pi$
$660$	0	0
$661$	32.8617	1.27817	0.639087	−	0.769135i	$-0.279312\pi$
$661$	32.8617	1.27817	0.639087	+	0.769135i	$0.279312\pi$
$662$	12.0000	0.466393
$663$	−28.4233	−1.10387
$664$	−7.43845	−0.288668
$665$	0	0
$666$	1.00000	0.0387492
$667$	−43.8617	−1.69833
$668$	−19.0540	−0.737220
$669$	19.8078	0.765812
$670$	0	0
$671$	84.5464	3.26388
$672$	−1.00000	−0.0385758
$673$	18.5616	0.715495	0.357748	−	0.933818i	$-0.383545\pi$
$673$	18.5616	0.715495	0.357748	+	0.933818i	$0.383545\pi$
$674$	4.56155	0.175704
$675$	0	0
$676$	19.3153	0.742898
$677$	−35.9309	−1.38094	−0.690468	−	0.723363i	$-0.742595\pi$
$677$	−35.9309	−1.38094	−0.690468	+	0.723363i	$0.742595\pi$
$678$	−10.6847	−0.410342
$679$	−3.31534	−0.127231
$680$	0	0
$681$	10.9309	0.418872
$682$	−21.8078	−0.835062
$683$	30.4384	1.16469	0.582347	−	0.812940i	$-0.302134\pi$
$683$	30.4384	1.16469	0.582347	+	0.812940i	$0.302134\pi$
$684$	0.561553	0.0214715
$685$	0	0
$686$	13.0000	0.496342
$687$	−5.12311	−0.195459
$688$	12.6847	0.483598
$689$	29.8229	1.13616
$690$	0	0
$691$	−5.31534	−0.202205	−0.101103	−	0.994876i	$-0.532237\pi$
$691$	−5.31534	−0.202205	−0.101103	+	0.994876i	$0.532237\pi$
$692$	2.12311	0.0807084
$693$	−6.12311	−0.232598
$694$	−28.0000	−1.06287
$695$	0	0
$696$	6.68466	0.253381
$697$	43.4233	1.64477
$698$	−14.2462	−0.539227
$699$	−11.3693	−0.430027
$700$	0	0
$701$	9.36932	0.353874	0.176937	−	0.984222i	$-0.443381\pi$
$701$	9.36932	0.353874	0.176937	+	0.984222i	$0.443381\pi$
$702$	5.68466	0.214554
$703$	−0.561553	−0.0211794
$704$	−6.12311	−0.230773
$705$	0	0
$706$	−29.8078	−1.12183
$707$	10.8769	0.409068
$708$	4.24621	0.159582
$709$	−4.50758	−0.169286	−0.0846428	−	0.996411i	$-0.526975\pi$
$709$	−4.50758	−0.169286	−0.0846428	+	0.996411i	$0.526975\pi$
$710$	0	0
$711$	14.2462	0.534275
$712$	−5.68466	−0.213042
$713$	−23.3693	−0.875188
$714$	−5.00000	−0.187120
$715$	0	0
$716$	−4.00000	−0.149487
$717$	7.80776	0.291586
$718$	20.8769	0.779119
$719$	−2.00000	−0.0745874	−0.0372937	−	0.999304i	$-0.511874\pi$
$719$	−2.00000	−0.0745874	−0.0372937	+	0.999304i	$0.511874\pi$
$720$	0	0
$721$	16.4924	0.614210
$722$	18.6847	0.695371
$723$	−2.00000	−0.0743808
$724$	20.2462	0.752445
$725$	0	0
$726$	−26.4924	−0.983226
$727$	−50.9848	−1.89092	−0.945462	−	0.325734i	$-0.894389\pi$
$727$	−50.9848	−1.89092	−0.945462	+	0.325734i	$0.894389\pi$
$728$	5.68466	0.210687
$729$	1.00000	0.0370370
$730$	0	0
$731$	63.4233	2.34580
$732$	−13.8078	−0.510350
$733$	22.3002	0.823676	0.411838	−	0.911257i	$-0.364887\pi$
$733$	22.3002	0.823676	0.411838	+	0.911257i	$0.364887\pi$
$734$	−17.0000	−0.627481
$735$	0	0
$736$	−6.56155	−0.241862
$737$	80.3542	2.95988
$738$	−8.68466	−0.319687
$739$	−39.1771	−1.44115	−0.720576	−	0.693376i	$-0.756123\pi$
$739$	−39.1771	−1.44115	−0.720576	+	0.693376i	$0.756123\pi$
$740$	0	0
$741$	−3.19224	−0.117270
$742$	5.24621	0.192594
$743$	−21.4233	−0.785944	−0.392972	−	0.919550i	$-0.628553\pi$
$743$	−21.4233	−0.785944	−0.392972	+	0.919550i	$0.628553\pi$
$744$	3.56155	0.130573
$745$	0	0
$746$	−30.4924	−1.11641
$747$	7.43845	0.272159
$748$	−30.6155	−1.11941
$749$	10.8078	0.394907
$750$	0	0
$751$	22.7386	0.829745	0.414872	−	0.909880i	$-0.363826\pi$
$751$	22.7386	0.829745	0.414872	+	0.909880i	$0.363826\pi$
$752$	8.00000	0.291730
$753$	25.6155	0.933482
$754$	−38.0000	−1.38388
$755$	0	0
$756$	1.00000	0.0363696
$757$	14.9460	0.543223	0.271611	−	0.962407i	$-0.412444\pi$
$757$	14.9460	0.543223	0.271611	+	0.962407i	$0.412444\pi$
$758$	2.87689	0.104494
$759$	−40.1771	−1.45834
$760$	0	0
$761$	17.3153	0.627681	0.313840	−	0.949476i	$-0.398384\pi$
$761$	17.3153	0.627681	0.313840	+	0.949476i	$0.398384\pi$
$762$	14.5616	0.527509
$763$	−2.12311	−0.0768616
$764$	14.3693	0.519864
$765$	0	0
$766$	−27.6847	−1.00029
$767$	−24.1383	−0.871582
$768$	1.00000	0.0360844
$769$	−9.50758	−0.342852	−0.171426	−	0.985197i	$-0.554837\pi$
$769$	−9.50758	−0.342852	−0.171426	+	0.985197i	$0.554837\pi$
$770$	0	0
$771$	−10.8078	−0.389232
$772$	14.0000	0.503871
$773$	3.49242	0.125614	0.0628069	−	0.998026i	$-0.479995\pi$
$773$	3.49242	0.125614	0.0628069	+	0.998026i	$0.479995\pi$
$774$	−12.6847	−0.455941
$775$	0	0
$776$	3.31534	0.119014
$777$	−1.00000	−0.0358748
$778$	−20.9309	−0.750408
$779$	4.87689	0.174733
$780$	0	0
$781$	−6.87689	−0.246075
$782$	−32.8078	−1.17320
$783$	−6.68466	−0.238890
$784$	−6.00000	−0.214286
$785$	0	0
$786$	−7.12311	−0.254073
$787$	−26.8769	−0.958058	−0.479029	−	0.877799i	$-0.659011\pi$
$787$	−26.8769	−0.958058	−0.479029	+	0.877799i	$0.659011\pi$
$788$	2.31534	0.0824806
$789$	6.43845	0.229215
$790$	0	0
$791$	10.6847	0.379903
$792$	6.12311	0.217575
$793$	78.4924	2.78735
$794$	27.1231	0.962563
$795$	0	0
$796$	−16.4924	−0.584558
$797$	25.6155	0.907349	0.453674	−	0.891168i	$-0.350113\pi$
$797$	25.6155	0.907349	0.453674	+	0.891168i	$0.350113\pi$
$798$	−0.561553	−0.0198788
$799$	40.0000	1.41510
$800$	0	0
$801$	5.68466	0.200858
$802$	14.8078	0.522880
$803$	−40.1771	−1.41782
$804$	−13.1231	−0.462816
$805$	0	0
$806$	−20.2462	−0.713142
$807$	−16.8078	−0.591661
$808$	−10.8769	−0.382648
$809$	−25.4384	−0.894368	−0.447184	−	0.894442i	$-0.647573\pi$
$809$	−25.4384	−0.894368	−0.447184	+	0.894442i	$0.647573\pi$
$810$	0	0
$811$	2.73863	0.0961664	0.0480832	−	0.998843i	$-0.484689\pi$
$811$	2.73863	0.0961664	0.0480832	+	0.998843i	$0.484689\pi$
$812$	−6.68466	−0.234586
$813$	−16.4924	−0.578415
$814$	−6.12311	−0.214615
$815$	0	0
$816$	5.00000	0.175035
$817$	7.12311	0.249206
$818$	0.876894	0.0306599
$819$	−5.68466	−0.198638
$820$	0	0
$821$	23.4384	0.818007	0.409004	−	0.912533i	$-0.365876\pi$
$821$	23.4384	0.818007	0.409004	+	0.912533i	$0.365876\pi$
$822$	−4.24621	−0.148104
$823$	−31.5464	−1.09964	−0.549819	−	0.835284i	$-0.685303\pi$
$823$	−31.5464	−1.09964	−0.549819	+	0.835284i	$0.685303\pi$
$824$	−16.4924	−0.574541
$825$	0	0
$826$	−4.24621	−0.147745
$827$	10.4384	0.362980	0.181490	−	0.983393i	$-0.441908\pi$
$827$	10.4384	0.362980	0.181490	+	0.983393i	$0.441908\pi$
$828$	6.56155	0.228030
$829$	−22.1231	−0.768367	−0.384184	−	0.923257i	$-0.625517\pi$
$829$	−22.1231	−0.768367	−0.384184	+	0.923257i	$0.625517\pi$
$830$	0	0
$831$	−27.6847	−0.960370
$832$	−5.68466	−0.197080
$833$	−30.0000	−1.03944
$834$	−13.8078	−0.478124
$835$	0	0
$836$	−3.43845	−0.118921
$837$	−3.56155	−0.123105
$838$	10.5616	0.364843
$839$	28.2462	0.975168	0.487584	−	0.873076i	$-0.337878\pi$
$839$	28.2462	0.975168	0.487584	+	0.873076i	$0.337878\pi$
$840$	0	0
$841$	15.6847	0.540850
$842$	−30.9848	−1.06781
$843$	22.1771	0.763819
$844$	4.43845	0.152778
$845$	0	0
$846$	−8.00000	−0.275046
$847$	26.4924	0.910290
$848$	−5.24621	−0.180156
$849$	−9.93087	−0.340827
$850$	0	0
$851$	−6.56155	−0.224927
$852$	1.12311	0.0384770
$853$	−7.93087	−0.271548	−0.135774	−	0.990740i	$-0.543352\pi$
$853$	−7.93087	−0.271548	−0.135774	+	0.990740i	$0.543352\pi$
$854$	13.8078	0.472492
$855$	0	0
$856$	−10.8078	−0.369402
$857$	8.75379	0.299024	0.149512	−	0.988760i	$-0.452230\pi$
$857$	8.75379	0.299024	0.149512	+	0.988760i	$0.452230\pi$
$858$	−34.8078	−1.18832
$859$	−2.80776	−0.0957997	−0.0478998	−	0.998852i	$-0.515253\pi$
$859$	−2.80776	−0.0957997	−0.0478998	+	0.998852i	$0.515253\pi$
$860$	0	0
$861$	8.68466	0.295972
$862$	29.0000	0.987744
$863$	−20.1922	−0.687352	−0.343676	−	0.939088i	$-0.611672\pi$
$863$	−20.1922	−0.687352	−0.343676	+	0.939088i	$0.611672\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−30.4233	−1.03383
$867$	8.00000	0.271694
$868$	−3.56155	−0.120887
$869$	−87.2311	−2.95911
$870$	0	0
$871$	74.6004	2.52774
$872$	2.12311	0.0718974
$873$	−3.31534	−0.112207
$874$	−3.68466	−0.124635
$875$	0	0
$876$	6.56155	0.221694
$877$	−46.9309	−1.58474	−0.792371	−	0.610039i	$-0.791154\pi$
$877$	−46.9309	−1.58474	−0.792371	+	0.610039i	$0.791154\pi$
$878$	14.0540	0.474299
$879$	16.6155	0.560428
$880$	0	0
$881$	34.9309	1.17685	0.588425	−	0.808551i	$-0.299748\pi$
$881$	34.9309	1.17685	0.588425	+	0.808551i	$0.299748\pi$
$882$	6.00000	0.202031
$883$	14.3693	0.483566	0.241783	−	0.970330i	$-0.422268\pi$
$883$	14.3693	0.483566	0.241783	+	0.970330i	$0.422268\pi$
$884$	−28.4233	−0.955979
$885$	0	0
$886$	33.8617	1.13761
$887$	17.8078	0.597926	0.298963	−	0.954265i	$-0.403359\pi$
$887$	17.8078	0.597926	0.298963	+	0.954265i	$0.403359\pi$
$888$	1.00000	0.0335578
$889$	−14.5616	−0.488379
$890$	0	0
$891$	−6.12311	−0.205132
$892$	19.8078	0.663213
$893$	4.49242	0.150333
$894$	−7.75379	−0.259325
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	−37.3002	−1.24542
$898$	1.61553	0.0539109
$899$	23.8078	0.794033
$900$	0	0
$901$	−26.2311	−0.873883
$902$	53.1771	1.77060
$903$	12.6847	0.422119
$904$	−10.6847	−0.355366
$905$	0	0
$906$	15.4384	0.512908
$907$	−45.4384	−1.50876	−0.754379	−	0.656439i	$-0.772062\pi$
$907$	−45.4384	−1.50876	−0.754379	+	0.656439i	$0.772062\pi$
$908$	10.9309	0.362754
$909$	10.8769	0.360764
$910$	0	0
$911$	20.4924	0.678944	0.339472	−	0.940616i	$-0.389752\pi$
$911$	20.4924	0.678944	0.339472	+	0.940616i	$0.389752\pi$
$912$	0.561553	0.0185949
$913$	−45.5464	−1.50737
$914$	−30.9309	−1.02310
$915$	0	0
$916$	−5.12311	−0.169272
$917$	7.12311	0.235226
$918$	−5.00000	−0.165025
$919$	6.73863	0.222287	0.111144	−	0.993804i	$-0.464549\pi$
$919$	6.73863	0.222287	0.111144	+	0.993804i	$0.464549\pi$
$920$	0	0
$921$	0.246211	0.00811294
$922$	−0.438447	−0.0144395
$923$	−6.38447	−0.210147
$924$	−6.12311	−0.201435
$925$	0	0
$926$	4.87689	0.160265
$927$	16.4924	0.541682
$928$	6.68466	0.219435
$929$	−5.80776	−0.190547	−0.0952733	−	0.995451i	$-0.530372\pi$
$929$	−5.80776	−0.190547	−0.0952733	+	0.995451i	$0.530372\pi$
$930$	0	0
$931$	−3.36932	−0.110425
$932$	−11.3693	−0.372414
$933$	−21.1771	−0.693307
$934$	2.43845	0.0797884
$935$	0	0
$936$	5.68466	0.185809
$937$	0.630683	0.0206035	0.0103018	−	0.999947i	$-0.496721\pi$
$937$	0.630683	0.0206035	0.0103018	+	0.999947i	$0.496721\pi$
$938$	13.1231	0.428485
$939$	24.8769	0.811827
$940$	0	0
$941$	−8.24621	−0.268819	−0.134409	−	0.990926i	$-0.542914\pi$
$941$	−8.24621	−0.268819	−0.134409	+	0.990926i	$0.542914\pi$
$942$	−18.0540	−0.588230
$943$	56.9848	1.85568
$944$	4.24621	0.138202
$945$	0	0
$946$	77.6695	2.52525
$947$	−16.3002	−0.529685	−0.264842	−	0.964292i	$-0.585320\pi$
$947$	−16.3002	−0.529685	−0.264842	+	0.964292i	$0.585320\pi$
$948$	14.2462	0.462695
$949$	−37.3002	−1.21082
$950$	0	0
$951$	−16.9309	−0.549021
$952$	−5.00000	−0.162051
$953$	1.61553	0.0523321	0.0261660	−	0.999658i	$-0.491670\pi$
$953$	1.61553	0.0523321	0.0261660	+	0.999658i	$0.491670\pi$
$954$	5.24621	0.169852
$955$	0	0
$956$	7.80776	0.252521
$957$	40.9309	1.32311
$958$	6.56155	0.211994
$959$	4.24621	0.137117
$960$	0	0
$961$	−18.3153	−0.590817
$962$	−5.68466	−0.183281
$963$	10.8078	0.348275
$964$	−2.00000	−0.0644157
$965$	0	0
$966$	−6.56155	−0.211115
$967$	−32.6307	−1.04933	−0.524666	−	0.851308i	$-0.675810\pi$
$967$	−32.6307	−1.04933	−0.524666	+	0.851308i	$0.675810\pi$
$968$	−26.4924	−0.851499
$969$	2.80776	0.0901984
$970$	0	0
$971$	−15.8078	−0.507295	−0.253648	−	0.967297i	$-0.581630\pi$
$971$	−15.8078	−0.507295	−0.253648	+	0.967297i	$0.581630\pi$
$972$	1.00000	0.0320750
$973$	13.8078	0.442657
$974$	16.7386	0.536340
$975$	0	0
$976$	−13.8078	−0.441976
$977$	12.5076	0.400153	0.200076	−	0.979780i	$-0.435881\pi$
$977$	12.5076	0.400153	0.200076	+	0.979780i	$0.435881\pi$
$978$	19.4924	0.623299
$979$	−34.8078	−1.11246
$980$	0	0
$981$	−2.12311	−0.0677855
$982$	12.1771	0.388586
$983$	24.9309	0.795171	0.397586	−	0.917565i	$-0.369848\pi$
$983$	24.9309	0.795171	0.397586	+	0.917565i	$0.369848\pi$
$984$	−8.68466	−0.276857
$985$	0	0
$986$	33.4233	1.06441
$987$	8.00000	0.254643
$988$	−3.19224	−0.101559
$989$	83.2311	2.64659
$990$	0	0
$991$	3.42329	0.108744	0.0543722	−	0.998521i	$-0.482684\pi$
$991$	3.42329	0.108744	0.0543722	+	0.998521i	$0.482684\pi$
$992$	3.56155	0.113079
$993$	−12.0000	−0.380808
$994$	−1.12311	−0.0356227
$995$	0	0
$996$	7.43845	0.235696
$997$	−19.3002	−0.611243	−0.305622	−	0.952153i	$-0.598864\pi$
$997$	−19.3002	−0.611243	−0.305622	+	0.952153i	$0.598864\pi$
$998$	−32.8078	−1.03851
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5550.2.a.bw.1.1		2
5.4	even	2		1110.2.a.r.1.1	✓	2
15.14	odd	2		3330.2.a.bc.1.2		2
20.19	odd	2		8880.2.a.bp.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.a.r.1.1	✓	2	5.4	even	2
3330.2.a.bc.1.2		2	15.14	odd	2
5550.2.a.bw.1.1		2	1.1	even	1	trivial
8880.2.a.bp.1.2		2	20.19	odd	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:	\( N \)	\(=\)	\( 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5550.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -6.12311 q^{11} +1.00000 q^{12} -5.68466 q^{13} -1.00000 q^{14} +1.00000 q^{16} +5.00000 q^{17} -1.00000 q^{18} +0.561553 q^{19} +1.00000 q^{21} +6.12311 q^{22} +6.56155 q^{23} -1.00000 q^{24} +5.68466 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.68466 q^{29} -3.56155 q^{31} -1.00000 q^{32} -6.12311 q^{33} -5.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} -0.561553 q^{38} -5.68466 q^{39} +8.68466 q^{41} -1.00000 q^{42} +12.6847 q^{43} -6.12311 q^{44} -6.56155 q^{46} +8.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +5.00000 q^{51} -5.68466 q^{52} -5.24621 q^{53} -1.00000 q^{54} -1.00000 q^{56} +0.561553 q^{57} +6.68466 q^{58} +4.24621 q^{59} -13.8078 q^{61} +3.56155 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.12311 q^{66} -13.1231 q^{67} +5.00000 q^{68} +6.56155 q^{69} +1.12311 q^{71} -1.00000 q^{72} +6.56155 q^{73} +1.00000 q^{74} +0.561553 q^{76} -6.12311 q^{77} +5.68466 q^{78} +14.2462 q^{79} +1.00000 q^{81} -8.68466 q^{82} +7.43845 q^{83} +1.00000 q^{84} -12.6847 q^{86} -6.68466 q^{87} +6.12311 q^{88} +5.68466 q^{89} -5.68466 q^{91} +6.56155 q^{92} -3.56155 q^{93} -8.00000 q^{94} -1.00000 q^{96} -3.31534 q^{97} +6.00000 q^{98} -6.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - 4 q^{11} + 2 q^{12} + q^{13} - 2 q^{14} + 2 q^{16} + 10 q^{17} - 2 q^{18} - 3 q^{19} + 2 q^{21} + 4 q^{22} + 9 q^{23} - 2 q^{24} - q^{26} + 2 q^{27} + 2 q^{28} - q^{29} - 3 q^{31} - 2 q^{32} - 4 q^{33} - 10 q^{34} + 2 q^{36} - 2 q^{37} + 3 q^{38} + q^{39} + 5 q^{41} - 2 q^{42} + 13 q^{43} - 4 q^{44} - 9 q^{46} + 16 q^{47} + 2 q^{48} - 12 q^{49} + 10 q^{51} + q^{52} + 6 q^{53} - 2 q^{54} - 2 q^{56} - 3 q^{57} + q^{58} - 8 q^{59} - 7 q^{61} + 3 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{66} - 18 q^{67} + 10 q^{68} + 9 q^{69} - 6 q^{71} - 2 q^{72} + 9 q^{73} + 2 q^{74} - 3 q^{76} - 4 q^{77} - q^{78} + 12 q^{79} + 2 q^{81} - 5 q^{82} + 19 q^{83} + 2 q^{84} - 13 q^{86} - q^{87} + 4 q^{88} - q^{89} + q^{91} + 9 q^{92} - 3 q^{93} - 16 q^{94} - 2 q^{96} - 19 q^{97} + 12 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - 4 * q^11 + 2 * q^12 + q^13 - 2 * q^14 + 2 * q^16 + 10 * q^17 - 2 * q^18 - 3 * q^19 + 2 * q^21 + 4 * q^22 + 9 * q^23 - 2 * q^24 - q^26 + 2 * q^27 + 2 * q^28 - q^29 - 3 * q^31 - 2 * q^32 - 4 * q^33 - 10 * q^34 + 2 * q^36 - 2 * q^37 + 3 * q^38 + q^39 + 5 * q^41 - 2 * q^42 + 13 * q^43 - 4 * q^44 - 9 * q^46 + 16 * q^47 + 2 * q^48 - 12 * q^49 + 10 * q^51 + q^52 + 6 * q^53 - 2 * q^54 - 2 * q^56 - 3 * q^57 + q^58 - 8 * q^59 - 7 * q^61 + 3 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^66 - 18 * q^67 + 10 * q^68 + 9 * q^69 - 6 * q^71 - 2 * q^72 + 9 * q^73 + 2 * q^74 - 3 * q^76 - 4 * q^77 - q^78 + 12 * q^79 + 2 * q^81 - 5 * q^82 + 19 * q^83 + 2 * q^84 - 13 * q^86 - q^87 + 4 * q^88 - q^89 + q^91 + 9 * q^92 - 3 * q^93 - 16 * q^94 - 2 * q^96 - 19 * q^97 + 12 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more