LMFDB - Embedded newform 275.2.b.e.199.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(199,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.199"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.4
Root			$1.61803i$ of defining polynomial
Character	$\chi$	$=$	275.199
Dual form			275.2.b.e.199.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.61803i q^{2} -2.61803i q^{3} -0.618034 q^{4} +4.23607 q^{6} -2.85410i q^{7} +2.23607i q^{8} -3.85410 q^{9} +1.00000 q^{11} +1.61803i q^{12} -6.23607i q^{13} +4.61803 q^{14} -4.85410 q^{16} -0.618034i q^{17} -6.23607i q^{18} +6.70820 q^{19} -7.47214 q^{21} +1.61803i q^{22} +4.09017i q^{23} +5.85410 q^{24} +10.0902 q^{26} +2.23607i q^{27} +1.76393i q^{28} +1.38197 q^{29} -3.00000 q^{31} -3.38197i q^{32} -2.61803i q^{33} +1.00000 q^{34} +2.38197 q^{36} +10.2361i q^{37} +10.8541i q^{38} -16.3262 q^{39} -3.00000 q^{41} -12.0902i q^{42} +6.00000i q^{43} -0.618034 q^{44} -6.61803 q^{46} +11.9443i q^{47} +12.7082i q^{48} -1.14590 q^{49} -1.61803 q^{51} +3.85410i q^{52} -9.32624i q^{53} -3.61803 q^{54} +6.38197 q^{56} -17.5623i q^{57} +2.23607i q^{58} -0.527864 q^{59} +0.0901699 q^{61} -4.85410i q^{62} +11.0000i q^{63} -4.23607 q^{64} +4.23607 q^{66} +8.00000i q^{67} +0.381966i q^{68} +10.7082 q^{69} +8.18034 q^{71} -8.61803i q^{72} -10.3820i q^{73} -16.5623 q^{74} -4.14590 q^{76} -2.85410i q^{77} -26.4164i q^{78} -5.85410 q^{79} -5.70820 q^{81} -4.85410i q^{82} +10.1459i q^{83} +4.61803 q^{84} -9.70820 q^{86} -3.61803i q^{87} +2.23607i q^{88} +6.90983 q^{89} -17.7984 q^{91} -2.52786i q^{92} +7.85410i q^{93} -19.3262 q^{94} -8.85410 q^{96} +1.61803i q^{97} -1.85410i q^{98} -3.85410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 8 q^{6} - 2 q^{9} + 4 q^{11} + 14 q^{14} - 6 q^{16} - 12 q^{21} + 10 q^{24} + 18 q^{26} + 10 q^{29} - 12 q^{31} + 4 q^{34} + 14 q^{36} - 34 q^{39} - 12 q^{41} + 2 q^{44} - 22 q^{46} - 18 q^{49}+ \cdots - 2 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 8 * q^6 - 2 * q^9 + 4 * q^11 + 14 * q^14 - 6 * q^16 - 12 * q^21 + 10 * q^24 + 18 * q^26 + 10 * q^29 - 12 * q^31 + 4 * q^34 + 14 * q^36 - 34 * q^39 - 12 * q^41 + 2 * q^44 - 22 * q^46 - 18 * q^49 - 2 * q^51 - 10 * q^54 + 30 * q^56 - 20 * q^59 - 22 * q^61 - 8 * q^64 + 8 * q^66 + 16 * q^69 - 12 * q^71 - 26 * q^74 - 30 * q^76 - 10 * q^79 + 4 * q^81 + 14 * q^84 - 12 * q^86 + 50 * q^89 - 22 * q^91 - 46 * q^94 - 22 * q^96 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.61803i	1.14412i	0.820211	+	0.572061i	$0.193856\pi$
$2$	1.61803i	1.14412i	−0.820211	+	0.572061i	$0.806144\pi$
$3$	− 2.61803i	− 1.51152i	−0.654847	−	0.755761i	$-0.727267\pi$
$3$	− 2.61803i	− 1.51152i	0.654847	−	0.755761i	$-0.272733\pi$
$4$	−0.618034	−0.309017
$5$	0	0
$5$	0	0
$6$	4.23607	1.72937
$7$	− 2.85410i	− 1.07875i	−0.842066	−	0.539375i	$-0.818661\pi$
$7$	− 2.85410i	− 1.07875i	0.842066	−	0.539375i	$-0.181339\pi$
$8$	2.23607i	0.790569i
$9$	−3.85410	−1.28470
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.61803i	0.467086i
$13$	− 6.23607i	− 1.72957i	−0.502139	−	0.864787i	$-0.667453\pi$
$13$	− 6.23607i	− 1.72957i	0.502139	−	0.864787i	$-0.332547\pi$
$14$	4.61803	1.23422
$15$	0	0
$16$	−4.85410	−1.21353
$17$	− 0.618034i	− 0.149895i	−0.997187	−	0.0749476i	$-0.976121\pi$
$17$	− 0.618034i	− 0.149895i	0.997187	−	0.0749476i	$-0.0238790\pi$
$18$	− 6.23607i	− 1.46986i
$19$	6.70820	1.53897	0.769484	−	0.638666i	$-0.220514\pi$
$19$	6.70820	1.53897	0.769484	+	0.638666i	$0.220514\pi$
$20$	0	0
$21$	−7.47214	−1.63055
$22$	1.61803i	0.344966i
$23$	4.09017i	0.852859i	0.904521	+	0.426430i	$0.140229\pi$
$23$	4.09017i	0.852859i	−0.904521	+	0.426430i	$0.859771\pi$
$24$	5.85410	1.19496
$25$	0	0
$26$	10.0902	1.97885
$27$	2.23607i	0.430331i
$28$	1.76393i	0.333352i
$29$	1.38197	0.256625	0.128312	−	0.991734i	$-0.459044\pi$
$29$	1.38197	0.256625	0.128312	+	0.991734i	$0.459044\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	− 3.38197i	− 0.597853i
$33$	− 2.61803i	− 0.455741i
$34$	1.00000	0.171499
$35$	0	0
$36$	2.38197	0.396994
$37$	10.2361i	1.68280i	0.540413	+	0.841400i	$0.318268\pi$
$37$	10.2361i	1.68280i	−0.540413	+	0.841400i	$0.681732\pi$
$38$	10.8541i	1.76077i
$39$	−16.3262	−2.61429
$40$	0	0
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	− 12.0902i	− 1.86555i
$43$	6.00000i	0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$	6.00000i	0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	−0.618034	−0.0931721
$45$	0	0
$46$	−6.61803	−0.975776
$47$	11.9443i	1.74225i	0.491060	+	0.871126i	$0.336609\pi$
$47$	11.9443i	1.74225i	−0.491060	+	0.871126i	$0.663391\pi$
$48$	12.7082i	1.83427i
$49$	−1.14590	−0.163700
$50$	0	0
$51$	−1.61803	−0.226570
$52$	3.85410i	0.534468i
$53$	− 9.32624i	− 1.28106i	−0.767934	−	0.640529i	$-0.778715\pi$
$53$	− 9.32624i	− 1.28106i	0.767934	−	0.640529i	$-0.221285\pi$
$54$	−3.61803	−0.492352
$55$	0	0
$56$	6.38197	0.852826
$57$	− 17.5623i	− 2.32618i
$58$	2.23607i	0.293610i
$59$	−0.527864	−0.0687220	−0.0343610	−	0.999409i	$-0.510940\pi$
$59$	−0.527864	−0.0687220	−0.0343610	+	0.999409i	$0.510940\pi$
$60$	0	0
$61$	0.0901699	0.0115451	0.00577254	−	0.999983i	$-0.498163\pi$
$61$	0.0901699	0.0115451	0.00577254	+	0.999983i	$0.498163\pi$
$62$	− 4.85410i	− 0.616472i
$63$	11.0000i	1.38587i
$64$	−4.23607	−0.529508
$65$	0	0
$66$	4.23607	0.521424
$67$	8.00000i	0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$	8.00000i	0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$	0.381966i	0.0463202i
$69$	10.7082	1.28912
$70$	0	0
$71$	8.18034	0.970828	0.485414	−	0.874284i	$-0.338669\pi$
$71$	8.18034	0.970828	0.485414	+	0.874284i	$0.338669\pi$
$72$	− 8.61803i	− 1.01565i
$73$	− 10.3820i	− 1.21512i	−0.794275	−	0.607559i	$-0.792149\pi$
$73$	− 10.3820i	− 1.21512i	0.794275	−	0.607559i	$-0.207851\pi$
$74$	−16.5623	−1.92533
$75$	0	0
$76$	−4.14590	−0.475567
$77$	− 2.85410i	− 0.325255i
$78$	− 26.4164i	− 2.99107i
$79$	−5.85410	−0.658638	−0.329319	−	0.944219i	$-0.606819\pi$
$79$	−5.85410	−0.658638	−0.329319	+	0.944219i	$0.606819\pi$
$80$	0	0
$81$	−5.70820	−0.634245
$82$	− 4.85410i	− 0.536046i
$83$	10.1459i	1.11366i	0.830627	+	0.556828i	$0.187982\pi$
$83$	10.1459i	1.11366i	−0.830627	+	0.556828i	$0.812018\pi$
$84$	4.61803	0.503869
$85$	0	0
$86$	−9.70820	−1.04686
$87$	− 3.61803i	− 0.387894i
$88$	2.23607i	0.238366i
$89$	6.90983	0.732441	0.366220	−	0.930528i	$-0.380652\pi$
$89$	6.90983	0.732441	0.366220	+	0.930528i	$0.380652\pi$
$90$	0	0
$91$	−17.7984	−1.86578
$92$	− 2.52786i	− 0.263548i
$93$	7.85410i	0.814432i
$94$	−19.3262	−1.99335
$95$	0	0
$96$	−8.85410	−0.903668
$97$	1.61803i	0.164286i	0.996621	+	0.0821432i	$0.0261765\pi$
$97$	1.61803i	0.164286i	−0.996621	+	0.0821432i	$0.973824\pi$
$98$	− 1.85410i	− 0.187293i
$99$	−3.85410	−0.387352
$100$	0	0
$101$	−6.09017	−0.605995	−0.302997	−	0.952991i	$-0.597987\pi$
$101$	−6.09017	−0.605995	−0.302997	+	0.952991i	$0.597987\pi$
$102$	− 2.61803i	− 0.259224i
$103$	− 5.38197i	− 0.530301i	−0.964207	−	0.265150i	$-0.914578\pi$
$103$	− 5.38197i	− 0.530301i	0.964207	−	0.265150i	$-0.0854216\pi$
$104$	13.9443	1.36735
$105$	0	0
$106$	15.0902	1.46569
$107$	− 4.23607i	− 0.409516i	−0.978813	−	0.204758i	$-0.934359\pi$
$107$	− 4.23607i	− 0.409516i	0.978813	−	0.204758i	$-0.0656408\pi$
$108$	− 1.38197i	− 0.132980i
$109$	3.09017	0.295985	0.147992	−	0.988989i	$-0.452719\pi$
$109$	3.09017	0.295985	0.147992	+	0.988989i	$0.452719\pi$
$110$	0	0
$111$	26.7984	2.54359
$112$	13.8541i	1.30909i
$113$	11.6525i	1.09617i	0.836422	+	0.548086i	$0.184643\pi$
$113$	11.6525i	1.09617i	−0.836422	+	0.548086i	$0.815357\pi$
$114$	28.4164	2.66144
$115$	0	0
$116$	−0.854102	−0.0793014
$117$	24.0344i	2.22198i
$118$	− 0.854102i	− 0.0786265i
$119$	−1.76393	−0.161699
$120$	0	0
$121$	1.00000	0.0909091
$122$	0.145898i	0.0132090i
$123$	7.85410i	0.708181i
$124$	1.85410	0.166503
$125$	0	0
$126$	−17.7984	−1.58561
$127$	− 0.618034i	− 0.0548416i	−0.999624	−	0.0274208i	$-0.991271\pi$
$127$	− 0.618034i	− 0.0548416i	0.999624	−	0.0274208i	$-0.00872941\pi$
$128$	− 13.6180i	− 1.20368i
$129$	15.7082	1.38303
$130$	0	0
$131$	10.0902	0.881582	0.440791	−	0.897610i	$-0.354698\pi$
$131$	10.0902	0.881582	0.440791	+	0.897610i	$0.354698\pi$
$132$	1.61803i	0.140832i
$133$	− 19.1459i	− 1.66016i
$134$	−12.9443	−1.11821
$135$	0	0
$136$	1.38197	0.118503
$137$	5.56231i	0.475220i	0.971361	+	0.237610i	$0.0763640\pi$
$137$	5.56231i	0.475220i	−0.971361	+	0.237610i	$0.923636\pi$
$138$	17.3262i	1.47491i
$139$	3.29180	0.279206	0.139603	−	0.990208i	$-0.455417\pi$
$139$	3.29180	0.279206	0.139603	+	0.990208i	$0.455417\pi$
$140$	0	0
$141$	31.2705	2.63345
$142$	13.2361i	1.11075i
$143$	− 6.23607i	− 0.521486i
$144$	18.7082	1.55902
$145$	0	0
$146$	16.7984	1.39024
$147$	3.00000i	0.247436i
$148$	− 6.32624i	− 0.520014i
$149$	8.94427	0.732743	0.366372	−	0.930469i	$-0.380600\pi$
$149$	8.94427	0.732743	0.366372	+	0.930469i	$0.380600\pi$
$150$	0	0
$151$	−3.00000	−0.244137	−0.122068	−	0.992522i	$-0.538953\pi$
$151$	−3.00000	−0.244137	−0.122068	+	0.992522i	$0.538953\pi$
$152$	15.0000i	1.21666i
$153$	2.38197i	0.192571i
$154$	4.61803	0.372132
$155$	0	0
$156$	10.0902	0.807860
$157$	− 5.41641i	− 0.432276i	−0.976363	−	0.216138i	$-0.930654\pi$
$157$	− 5.41641i	− 0.432276i	0.976363	−	0.216138i	$-0.0693462\pi$
$158$	− 9.47214i	− 0.753563i
$159$	−24.4164	−1.93635
$160$	0	0
$161$	11.6738	0.920021
$162$	− 9.23607i	− 0.725654i
$163$	6.85410i	0.536855i	0.963300	+	0.268427i	$0.0865039\pi$
$163$	6.85410i	0.536855i	−0.963300	+	0.268427i	$0.913496\pi$
$164$	1.85410	0.144781
$165$	0	0
$166$	−16.4164	−1.27416
$167$	− 5.29180i	− 0.409491i	−0.978815	−	0.204746i	$-0.934363\pi$
$167$	− 5.29180i	− 0.409491i	0.978815	−	0.204746i	$-0.0656368\pi$
$168$	− 16.7082i	− 1.28907i
$169$	−25.8885	−1.99143
$170$	0	0
$171$	−25.8541	−1.97711
$172$	− 3.70820i	− 0.282748i
$173$	5.47214i	0.416039i	0.978125	+	0.208019i	$0.0667017\pi$
$173$	5.47214i	0.416039i	−0.978125	+	0.208019i	$0.933298\pi$
$174$	5.85410	0.443798
$175$	0	0
$176$	−4.85410	−0.365892
$177$	1.38197i	0.103875i
$178$	11.1803i	0.838002i
$179$	13.6180	1.01786	0.508930	−	0.860808i	$-0.330041\pi$
$179$	13.6180	1.01786	0.508930	+	0.860808i	$0.330041\pi$
$180$	0	0
$181$	−6.09017	−0.452679	−0.226339	−	0.974049i	$-0.572676\pi$
$181$	−6.09017	−0.452679	−0.226339	+	0.974049i	$0.572676\pi$
$182$	− 28.7984i	− 2.13468i
$183$	− 0.236068i	− 0.0174506i
$184$	−9.14590	−0.674245
$185$	0	0
$186$	−12.7082	−0.931811
$187$	− 0.618034i	− 0.0451951i
$188$	− 7.38197i	− 0.538385i
$189$	6.38197	0.464220
$190$	0	0
$191$	−21.0902	−1.52603	−0.763016	−	0.646380i	$-0.776282\pi$
$191$	−21.0902	−1.52603	−0.763016	+	0.646380i	$0.776282\pi$
$192$	11.0902i	0.800364i
$193$	− 12.9443i	− 0.931749i	−0.884851	−	0.465875i	$-0.845740\pi$
$193$	− 12.9443i	− 0.931749i	0.884851	−	0.465875i	$-0.154260\pi$
$194$	−2.61803	−0.187964
$195$	0	0
$196$	0.708204	0.0505860
$197$	− 20.0902i	− 1.43137i	−0.698426	−	0.715683i	$-0.746116\pi$
$197$	− 20.0902i	− 1.43137i	0.698426	−	0.715683i	$-0.253884\pi$
$198$	− 6.23607i	− 0.443178i
$199$	3.09017	0.219056	0.109528	−	0.993984i	$-0.465066\pi$
$199$	3.09017	0.219056	0.109528	+	0.993984i	$0.465066\pi$
$200$	0	0
$201$	20.9443	1.47730
$202$	− 9.85410i	− 0.693332i
$203$	− 3.94427i	− 0.276834i
$204$	1.00000	0.0700140
$205$	0	0
$206$	8.70820	0.606729
$207$	− 15.7639i	− 1.09567i
$208$	30.2705i	2.09888i
$209$	6.70820	0.464016
$210$	0	0
$211$	17.0000	1.17033	0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000	1.17033	0.585164	+	0.810915i	$0.301030\pi$
$212$	5.76393i	0.395868i
$213$	− 21.4164i	− 1.46743i
$214$	6.85410	0.468537
$215$	0	0
$216$	−5.00000	−0.340207
$217$	8.56231i	0.581247i
$218$	5.00000i	0.338643i
$219$	−27.1803	−1.83668
$220$	0	0
$221$	−3.85410	−0.259255
$222$	43.3607i	2.91018i
$223$	− 16.8885i	− 1.13094i	−0.824769	−	0.565470i	$-0.808695\pi$
$223$	− 16.8885i	− 1.13094i	0.824769	−	0.565470i	$-0.191305\pi$
$224$	−9.65248	−0.644933
$225$	0	0
$226$	−18.8541	−1.25416
$227$	− 24.0344i	− 1.59522i	−0.603172	−	0.797611i	$-0.706097\pi$
$227$	− 24.0344i	− 1.59522i	0.603172	−	0.797611i	$-0.293903\pi$
$228$	10.8541i	0.718830i
$229$	−12.0344	−0.795258	−0.397629	−	0.917546i	$-0.630167\pi$
$229$	−12.0344	−0.795258	−0.397629	+	0.917546i	$0.630167\pi$
$230$	0	0
$231$	−7.47214	−0.491630
$232$	3.09017i	0.202880i
$233$	− 15.5066i	− 1.01587i	−0.861395	−	0.507935i	$-0.830409\pi$
$233$	− 15.5066i	− 1.01587i	0.861395	−	0.507935i	$-0.169591\pi$
$234$	−38.8885	−2.54222
$235$	0	0
$236$	0.326238	0.0212363
$237$	15.3262i	0.995546i
$238$	− 2.85410i	− 0.185004i
$239$	−6.38197	−0.412815	−0.206408	−	0.978466i	$-0.566177\pi$
$239$	−6.38197	−0.412815	−0.206408	+	0.978466i	$0.566177\pi$
$240$	0	0
$241$	21.2705	1.37015	0.685077	−	0.728471i	$-0.259769\pi$
$241$	21.2705	1.37015	0.685077	+	0.728471i	$0.259769\pi$
$242$	1.61803i	0.104011i
$243$	21.6525i	1.38901i
$244$	−0.0557281	−0.00356763
$245$	0	0
$246$	−12.7082	−0.810245
$247$	− 41.8328i	− 2.66176i
$248$	− 6.70820i	− 0.425971i
$249$	26.5623	1.68332
$250$	0	0
$251$	−27.2705	−1.72130	−0.860650	−	0.509198i	$-0.829942\pi$
$251$	−27.2705	−1.72130	−0.860650	+	0.509198i	$0.829942\pi$
$252$	− 6.79837i	− 0.428257i
$253$	4.09017i	0.257147i
$254$	1.00000	0.0627456
$255$	0	0
$256$	13.5623	0.847644
$257$	− 10.9443i	− 0.682685i	−0.939939	−	0.341342i	$-0.889118\pi$
$257$	− 10.9443i	− 0.682685i	0.939939	−	0.341342i	$-0.110882\pi$
$258$	25.4164i	1.58236i
$259$	29.2148	1.81532
$260$	0	0
$261$	−5.32624	−0.329686
$262$	16.3262i	1.00864i
$263$	21.0000i	1.29492i	0.762101	+	0.647458i	$0.224168\pi$
$263$	21.0000i	1.29492i	−0.762101	+	0.647458i	$0.775832\pi$
$264$	5.85410	0.360295
$265$	0	0
$266$	30.9787	1.89943
$267$	− 18.0902i	− 1.10710i
$268$	− 4.94427i	− 0.302019i
$269$	−30.3262	−1.84902	−0.924512	−	0.381154i	$-0.875527\pi$
$269$	−30.3262	−1.84902	−0.924512	+	0.381154i	$0.875527\pi$
$270$	0	0
$271$	13.1803	0.800649	0.400324	−	0.916374i	$-0.368897\pi$
$271$	13.1803	0.800649	0.400324	+	0.916374i	$0.368897\pi$
$272$	3.00000i	0.181902i
$273$	46.5967i	2.82016i
$274$	−9.00000	−0.543710
$275$	0	0
$276$	−6.61803	−0.398359
$277$	− 11.4721i	− 0.689294i	−0.938732	−	0.344647i	$-0.887999\pi$
$277$	− 11.4721i	− 0.689294i	0.938732	−	0.344647i	$-0.112001\pi$
$278$	5.32624i	0.319447i
$279$	11.5623	0.692217
$280$	0	0
$281$	−25.3607	−1.51289	−0.756446	−	0.654057i	$-0.773066\pi$
$281$	−25.3607	−1.51289	−0.756446	+	0.654057i	$0.773066\pi$
$282$	50.5967i	3.01299i
$283$	7.38197i	0.438812i	0.975634	+	0.219406i	$0.0704120\pi$
$283$	7.38197i	0.438812i	−0.975634	+	0.219406i	$0.929588\pi$
$284$	−5.05573	−0.300002
$285$	0	0
$286$	10.0902	0.596644
$287$	8.56231i	0.505417i
$288$	13.0344i	0.768062i
$289$	16.6180	0.977531
$290$	0	0
$291$	4.23607	0.248323
$292$	6.41641i	0.375492i
$293$	23.8885i	1.39558i	0.716301	+	0.697792i	$0.245834\pi$
$293$	23.8885i	1.39558i	−0.716301	+	0.697792i	$0.754166\pi$
$294$	−4.85410	−0.283097
$295$	0	0
$296$	−22.8885	−1.33037
$297$	2.23607i	0.129750i
$298$	14.4721i	0.838348i
$299$	25.5066	1.47508
$300$	0	0
$301$	17.1246	0.987046
$302$	− 4.85410i	− 0.279322i
$303$	15.9443i	0.915974i
$304$	−32.5623	−1.86758
$305$	0	0
$306$	−3.85410	−0.220324
$307$	33.4508i	1.90914i	0.297985	+	0.954570i	$0.403685\pi$
$307$	33.4508i	1.90914i	−0.297985	+	0.954570i	$0.596315\pi$
$308$	1.76393i	0.100509i
$309$	−14.0902	−0.801562
$310$	0	0
$311$	−19.1803	−1.08762	−0.543809	−	0.839209i	$-0.683018\pi$
$311$	−19.1803	−1.08762	−0.543809	+	0.839209i	$0.683018\pi$
$312$	− 36.5066i	− 2.06678i
$313$	3.23607i	0.182913i	0.995809	+	0.0914567i	$0.0291523\pi$
$313$	3.23607i	0.182913i	−0.995809	+	0.0914567i	$0.970848\pi$
$314$	8.76393	0.494577
$315$	0	0
$316$	3.61803	0.203530
$317$	16.6180i	0.933362i	0.884426	+	0.466681i	$0.154550\pi$
$317$	16.6180i	0.933362i	−0.884426	+	0.466681i	$0.845450\pi$
$318$	− 39.5066i	− 2.21542i
$319$	1.38197	0.0773752
$320$	0	0
$321$	−11.0902	−0.618993
$322$	18.8885i	1.05262i
$323$	− 4.14590i	− 0.230684i
$324$	3.52786	0.195992
$325$	0	0
$326$	−11.0902	−0.614228
$327$	− 8.09017i	− 0.447387i
$328$	− 6.70820i	− 0.370399i
$329$	34.0902	1.87945
$330$	0	0
$331$	−19.1803	−1.05425	−0.527123	−	0.849789i	$-0.676729\pi$
$331$	−19.1803	−1.05425	−0.527123	+	0.849789i	$0.676729\pi$
$332$	− 6.27051i	− 0.344139i
$333$	− 39.4508i	− 2.16189i
$334$	8.56231	0.468509
$335$	0	0
$336$	36.2705	1.97872
$337$	1.41641i	0.0771567i	0.999256	+	0.0385783i	$0.0122829\pi$
$337$	1.41641i	0.0771567i	−0.999256	+	0.0385783i	$0.987717\pi$
$338$	− 41.8885i	− 2.27844i
$339$	30.5066	1.65689
$340$	0	0
$341$	−3.00000	−0.162459
$342$	− 41.8328i	− 2.26206i
$343$	− 16.7082i	− 0.902158i
$344$	−13.4164	−0.723364
$345$	0	0
$346$	−8.85410	−0.475999
$347$	20.5623i	1.10384i	0.833896	+	0.551921i	$0.186105\pi$
$347$	20.5623i	1.10384i	−0.833896	+	0.551921i	$0.813895\pi$
$348$	2.23607i	0.119866i
$349$	−21.8328	−1.16868	−0.584342	−	0.811508i	$-0.698647\pi$
$349$	−21.8328	−1.16868	−0.584342	+	0.811508i	$0.698647\pi$
$350$	0	0
$351$	13.9443	0.744290
$352$	− 3.38197i	− 0.180259i
$353$	− 21.3607i	− 1.13691i	−0.822713	−	0.568457i	$-0.807541\pi$
$353$	− 21.3607i	− 1.13691i	0.822713	−	0.568457i	$-0.192459\pi$
$354$	−2.23607	−0.118846
$355$	0	0
$356$	−4.27051	−0.226337
$357$	4.61803i	0.244412i
$358$	22.0344i	1.16456i
$359$	4.47214	0.236030	0.118015	−	0.993012i	$-0.462347\pi$
$359$	4.47214	0.236030	0.118015	+	0.993012i	$0.462347\pi$
$360$	0	0
$361$	26.0000	1.36842
$362$	− 9.85410i	− 0.517920i
$363$	− 2.61803i	− 0.137411i
$364$	11.0000	0.576557
$365$	0	0
$366$	0.381966	0.0199657
$367$	7.14590i	0.373013i	0.982454	+	0.186506i	$0.0597165\pi$
$367$	7.14590i	0.373013i	−0.982454	+	0.186506i	$0.940283\pi$
$368$	− 19.8541i	− 1.03497i
$369$	11.5623	0.601910
$370$	0	0
$371$	−26.6180	−1.38194
$372$	− 4.85410i	− 0.251673i
$373$	− 2.81966i	− 0.145996i	−0.997332	−	0.0729982i	$-0.976743\pi$
$373$	− 2.81966i	− 0.145996i	0.997332	−	0.0729982i	$-0.0232567\pi$
$374$	1.00000	0.0517088
$375$	0	0
$376$	−26.7082	−1.37737
$377$	− 8.61803i	− 0.443851i
$378$	10.3262i	0.531124i
$379$	17.7639	0.912472	0.456236	−	0.889859i	$-0.349197\pi$
$379$	17.7639	0.912472	0.456236	+	0.889859i	$0.349197\pi$
$380$	0	0
$381$	−1.61803	−0.0828944
$382$	− 34.1246i	− 1.74597i
$383$	− 5.05573i	− 0.258336i	−0.991623	−	0.129168i	$-0.958769\pi$
$383$	− 5.05573i	− 0.258336i	0.991623	−	0.129168i	$-0.0412306\pi$
$384$	−35.6525	−1.81938
$385$	0	0
$386$	20.9443	1.06604
$387$	− 23.1246i	− 1.17549i
$388$	− 1.00000i	− 0.0507673i
$389$	−5.52786	−0.280274	−0.140137	−	0.990132i	$-0.544754\pi$
$389$	−5.52786	−0.280274	−0.140137	+	0.990132i	$0.544754\pi$
$390$	0	0
$391$	2.52786	0.127840
$392$	− 2.56231i	− 0.129416i
$393$	− 26.4164i	− 1.33253i
$394$	32.5066	1.63766
$395$	0	0
$396$	2.38197	0.119698
$397$	14.9098i	0.748303i	0.927368	+	0.374151i	$0.122066\pi$
$397$	14.9098i	0.748303i	−0.927368	+	0.374151i	$0.877934\pi$
$398$	5.00000i	0.250627i
$399$	−50.1246	−2.50937
$400$	0	0
$401$	34.3607	1.71589	0.857945	−	0.513741i	$-0.171741\pi$
$401$	34.3607	1.71589	0.857945	+	0.513741i	$0.171741\pi$
$402$	33.8885i	1.69021i
$403$	18.7082i	0.931922i
$404$	3.76393	0.187263
$405$	0	0
$406$	6.38197	0.316732
$407$	10.2361i	0.507383i
$408$	− 3.61803i	− 0.179119i
$409$	−20.1246	−0.995098	−0.497549	−	0.867436i	$-0.665767\pi$
$409$	−20.1246	−0.995098	−0.497549	+	0.867436i	$0.665767\pi$
$410$	0	0
$411$	14.5623	0.718306
$412$	3.32624i	0.163872i
$413$	1.50658i	0.0741338i
$414$	25.5066	1.25358
$415$	0	0
$416$	−21.0902	−1.03403
$417$	− 8.61803i	− 0.422027i
$418$	10.8541i	0.530891i
$419$	−21.1803	−1.03473	−0.517364	−	0.855766i	$-0.673087\pi$
$419$	−21.1803	−1.03473	−0.517364	+	0.855766i	$0.673087\pi$
$420$	0	0
$421$	−12.2705	−0.598028	−0.299014	−	0.954249i	$-0.596658\pi$
$421$	−12.2705	−0.598028	−0.299014	+	0.954249i	$0.596658\pi$
$422$	27.5066i	1.33900i
$423$	− 46.0344i	− 2.23827i
$424$	20.8541	1.01276
$425$	0	0
$426$	34.6525	1.67892
$427$	− 0.257354i	− 0.0124542i
$428$	2.61803i	0.126547i
$429$	−16.3262	−0.788238
$430$	0	0
$431$	0.819660	0.0394816	0.0197408	−	0.999805i	$-0.493716\pi$
$431$	0.819660	0.0394816	0.0197408	+	0.999805i	$0.493716\pi$
$432$	− 10.8541i	− 0.522218i
$433$	18.8885i	0.907725i	0.891072	+	0.453863i	$0.149954\pi$
$433$	18.8885i	0.907725i	−0.891072	+	0.453863i	$0.850046\pi$
$434$	−13.8541	−0.665018
$435$	0	0
$436$	−1.90983	−0.0914643
$437$	27.4377i	1.31252i
$438$	− 43.9787i	− 2.10138i
$439$	0.729490	0.0348167	0.0174083	−	0.999848i	$-0.494458\pi$
$439$	0.729490	0.0348167	0.0174083	+	0.999848i	$0.494458\pi$
$440$	0	0
$441$	4.41641	0.210305
$442$	− 6.23607i	− 0.296620i
$443$	36.6525i	1.74141i	0.491804	+	0.870706i	$0.336338\pi$
$443$	36.6525i	1.74141i	−0.491804	+	0.870706i	$0.663662\pi$
$444$	−16.5623	−0.786012
$445$	0	0
$446$	27.3262	1.29393
$447$	− 23.4164i	− 1.10756i
$448$	12.0902i	0.571207i
$449$	15.3262	0.723290	0.361645	−	0.932316i	$-0.382215\pi$
$449$	15.3262	0.723290	0.361645	+	0.932316i	$0.382215\pi$
$450$	0	0
$451$	−3.00000	−0.141264
$452$	− 7.20163i	− 0.338736i
$453$	7.85410i	0.369018i
$454$	38.8885	1.82513
$455$	0	0
$456$	39.2705	1.83901
$457$	− 7.97871i	− 0.373228i	−0.982433	−	0.186614i	$-0.940249\pi$
$457$	− 7.97871i	− 0.373228i	0.982433	−	0.186614i	$-0.0597514\pi$
$458$	− 19.4721i	− 0.909873i
$459$	1.38197	0.0645046
$460$	0	0
$461$	−9.18034	−0.427571	−0.213786	−	0.976881i	$-0.568579\pi$
$461$	−9.18034	−0.427571	−0.213786	+	0.976881i	$0.568579\pi$
$462$	− 12.0902i	− 0.562486i
$463$	− 11.3607i	− 0.527976i	−0.964526	−	0.263988i	$-0.914962\pi$
$463$	− 11.3607i	− 0.527976i	0.964526	−	0.263988i	$-0.0850379\pi$
$464$	−6.70820	−0.311421
$465$	0	0
$466$	25.0902	1.16228
$467$	37.4721i	1.73400i	0.498305	+	0.867002i	$0.333956\pi$
$467$	37.4721i	1.73400i	−0.498305	+	0.867002i	$0.666044\pi$
$468$	− 14.8541i	− 0.686631i
$469$	22.8328	1.05432
$470$	0	0
$471$	−14.1803	−0.653396
$472$	− 1.18034i	− 0.0543295i
$473$	6.00000i	0.275880i
$474$	−24.7984	−1.13903
$475$	0	0
$476$	1.09017	0.0499679
$477$	35.9443i	1.64578i
$478$	− 10.3262i	− 0.472311i
$479$	−28.4164	−1.29838	−0.649189	−	0.760627i	$-0.724892\pi$
$479$	−28.4164	−1.29838	−0.649189	+	0.760627i	$0.724892\pi$
$480$	0	0
$481$	63.8328	2.91053
$482$	34.4164i	1.56762i
$483$	− 30.5623i	− 1.39063i
$484$	−0.618034	−0.0280925
$485$	0	0
$486$	−35.0344	−1.58919
$487$	− 30.4164i	− 1.37830i	−0.724619	−	0.689150i	$-0.757984\pi$
$487$	− 30.4164i	− 1.37830i	0.724619	−	0.689150i	$-0.242016\pi$
$488$	0.201626i	0.00912719i
$489$	17.9443	0.811468
$490$	0	0
$491$	−6.81966	−0.307767	−0.153883	−	0.988089i	$-0.549178\pi$
$491$	−6.81966	−0.307767	−0.153883	+	0.988089i	$0.549178\pi$
$492$	− 4.85410i	− 0.218840i
$493$	− 0.854102i	− 0.0384668i
$494$	67.6869	3.04538
$495$	0	0
$496$	14.5623	0.653867
$497$	− 23.3475i	− 1.04728i
$498$	42.9787i	1.92592i
$499$	−29.7984	−1.33396	−0.666979	−	0.745076i	$-0.732413\pi$
$499$	−29.7984	−1.33396	−0.666979	+	0.745076i	$0.732413\pi$
$500$	0	0
$501$	−13.8541	−0.618956
$502$	− 44.1246i	− 1.96938i
$503$	6.65248i	0.296619i	0.988941	+	0.148310i	$0.0473832\pi$
$503$	6.65248i	0.296619i	−0.988941	+	0.148310i	$0.952617\pi$
$504$	−24.5967	−1.09563
$505$	0	0
$506$	−6.61803	−0.294207
$507$	67.7771i	3.01009i
$508$	0.381966i	0.0169470i
$509$	−16.3820	−0.726118	−0.363059	−	0.931766i	$-0.618268\pi$
$509$	−16.3820	−0.726118	−0.363059	+	0.931766i	$0.618268\pi$
$510$	0	0
$511$	−29.6312	−1.31081
$512$	− 5.29180i	− 0.233867i
$513$	15.0000i	0.662266i
$514$	17.7082	0.781075
$515$	0	0
$516$	−9.70820	−0.427380
$517$	11.9443i	0.525308i
$518$	47.2705i	2.07695i
$519$	14.3262	0.628852
$520$	0	0
$521$	−1.81966	−0.0797208	−0.0398604	−	0.999205i	$-0.512691\pi$
$521$	−1.81966	−0.0797208	−0.0398604	+	0.999205i	$0.512691\pi$
$522$	− 8.61803i	− 0.377201i
$523$	− 22.9443i	− 1.00328i	−0.865076	−	0.501641i	$-0.832730\pi$
$523$	− 22.9443i	− 1.00328i	0.865076	−	0.501641i	$-0.167270\pi$
$524$	−6.23607	−0.272424
$525$	0	0
$526$	−33.9787	−1.48154
$527$	1.85410i	0.0807660i
$528$	12.7082i	0.553054i
$529$	6.27051	0.272631
$530$	0	0
$531$	2.03444	0.0882873
$532$	11.8328i	0.513018i
$533$	18.7082i	0.810342i
$534$	29.2705	1.26666
$535$	0	0
$536$	−17.8885	−0.772667
$537$	− 35.6525i	− 1.53852i
$538$	− 49.0689i	− 2.11551i
$539$	−1.14590	−0.0493573
$540$	0	0
$541$	−42.2705	−1.81735	−0.908676	−	0.417503i	$-0.862905\pi$
$541$	−42.2705	−1.81735	−0.908676	+	0.417503i	$0.862905\pi$
$542$	21.3262i	0.916040i
$543$	15.9443i	0.684234i
$544$	−2.09017	−0.0896153
$545$	0	0
$546$	−75.3951	−3.22661
$547$	− 21.1459i	− 0.904133i	−0.891984	−	0.452067i	$-0.850687\pi$
$547$	− 21.1459i	− 0.904133i	0.891984	−	0.452067i	$-0.149313\pi$
$548$	− 3.43769i	− 0.146851i
$549$	−0.347524	−0.0148320
$550$	0	0
$551$	9.27051	0.394937
$552$	23.9443i	1.01914i
$553$	16.7082i	0.710505i
$554$	18.5623	0.788637
$555$	0	0
$556$	−2.03444	−0.0862796
$557$	− 9.76393i	− 0.413711i	−0.978371	−	0.206856i	$-0.933677\pi$
$557$	− 9.76393i	− 0.413711i	0.978371	−	0.206856i	$-0.0663230\pi$
$558$	18.7082i	0.791981i
$559$	37.4164	1.58255
$560$	0	0
$561$	−1.61803	−0.0683134
$562$	− 41.0344i	− 1.73093i
$563$	13.0344i	0.549336i	0.961539	+	0.274668i	$0.0885680\pi$
$563$	13.0344i	0.549336i	−0.961539	+	0.274668i	$0.911432\pi$
$564$	−19.3262	−0.813781
$565$	0	0
$566$	−11.9443	−0.502055
$567$	16.2918i	0.684191i
$568$	18.2918i	0.767507i
$569$	−26.3820	−1.10599	−0.552995	−	0.833185i	$-0.686515\pi$
$569$	−26.3820	−1.10599	−0.552995	+	0.833185i	$0.686515\pi$
$570$	0	0
$571$	36.2705	1.51787	0.758937	−	0.651164i	$-0.225719\pi$
$571$	36.2705	1.51787	0.758937	+	0.651164i	$0.225719\pi$
$572$	3.85410i	0.161148i
$573$	55.2148i	2.30663i
$574$	−13.8541	−0.578259
$575$	0	0
$576$	16.3262	0.680260
$577$	15.5623i	0.647867i	0.946080	+	0.323934i	$0.105005\pi$
$577$	15.5623i	0.647867i	−0.946080	+	0.323934i	$0.894995\pi$
$578$	26.8885i	1.11842i
$579$	−33.8885	−1.40836
$580$	0	0
$581$	28.9574	1.20136
$582$	6.85410i	0.284112i
$583$	− 9.32624i	− 0.386253i
$584$	23.2148	0.960635
$585$	0	0
$586$	−38.6525	−1.59672
$587$	− 4.03444i	− 0.166519i	−0.996528	−	0.0832596i	$-0.973467\pi$
$587$	− 4.03444i	− 0.166519i	0.996528	−	0.0832596i	$-0.0265331\pi$
$588$	− 1.85410i	− 0.0764619i
$589$	−20.1246	−0.829220
$590$	0	0
$591$	−52.5967	−2.16354
$592$	− 49.6869i	− 2.04212i
$593$	− 9.00000i	− 0.369586i	−0.982777	−	0.184793i	$-0.940839\pi$
$593$	− 9.00000i	− 0.369586i	0.982777	−	0.184793i	$-0.0591614\pi$
$594$	−3.61803	−0.148450
$595$	0	0
$596$	−5.52786	−0.226430
$597$	− 8.09017i	− 0.331109i
$598$	41.2705i	1.68768i
$599$	−0.326238	−0.0133297	−0.00666486	−	0.999978i	$-0.502122\pi$
$599$	−0.326238	−0.0133297	−0.00666486	+	0.999978i	$0.502122\pi$
$600$	0	0
$601$	−22.2705	−0.908433	−0.454217	−	0.890891i	$-0.650081\pi$
$601$	−22.2705	−0.908433	−0.454217	+	0.890891i	$0.650081\pi$
$602$	27.7082i	1.12930i
$603$	− 30.8328i	− 1.25561i
$604$	1.85410	0.0754423
$605$	0	0
$606$	−25.7984	−1.04799
$607$	3.52786i	0.143192i	0.997434	+	0.0715958i	$0.0228092\pi$
$607$	3.52786i	0.143192i	−0.997434	+	0.0715958i	$0.977191\pi$
$608$	− 22.6869i	− 0.920076i
$609$	−10.3262	−0.418440
$610$	0	0
$611$	74.4853	3.01335
$612$	− 1.47214i	− 0.0595076i
$613$	− 6.43769i	− 0.260016i	−0.991513	−	0.130008i	$-0.958500\pi$
$613$	− 6.43769i	− 0.260016i	0.991513	−	0.130008i	$-0.0415003\pi$
$614$	−54.1246	−2.18429
$615$	0	0
$616$	6.38197	0.257137
$617$	− 38.1803i	− 1.53708i	−0.639800	−	0.768541i	$-0.720983\pi$
$617$	− 38.1803i	− 1.53708i	0.639800	−	0.768541i	$-0.279017\pi$
$618$	− 22.7984i	− 0.917085i
$619$	22.8885	0.919968	0.459984	−	0.887927i	$-0.347855\pi$
$619$	22.8885	0.919968	0.459984	+	0.887927i	$0.347855\pi$
$620$	0	0
$621$	−9.14590	−0.367012
$622$	− 31.0344i	− 1.24437i
$623$	− 19.7214i	− 0.790120i
$624$	79.2492	3.17251
$625$	0	0
$626$	−5.23607	−0.209275
$627$	− 17.5623i	− 0.701371i
$628$	3.34752i	0.133581i
$629$	6.32624	0.252244
$630$	0	0
$631$	36.2705	1.44391	0.721953	−	0.691942i	$-0.243245\pi$
$631$	36.2705	1.44391	0.721953	+	0.691942i	$0.243245\pi$
$632$	− 13.0902i	− 0.520699i
$633$	− 44.5066i	− 1.76898i
$634$	−26.8885	−1.06788
$635$	0	0
$636$	15.0902	0.598364
$637$	7.14590i	0.283131i
$638$	2.23607i	0.0885268i
$639$	−31.5279	−1.24722
$640$	0	0
$641$	−3.00000	−0.118493	−0.0592464	−	0.998243i	$-0.518870\pi$
$641$	−3.00000	−0.118493	−0.0592464	+	0.998243i	$0.518870\pi$
$642$	− 17.9443i	− 0.708204i
$643$	− 10.5836i	− 0.417376i	−0.977982	−	0.208688i	$-0.933081\pi$
$643$	− 10.5836i	− 0.417376i	0.977982	−	0.208688i	$-0.0669193\pi$
$644$	−7.21478	−0.284302
$645$	0	0
$646$	6.70820	0.263931
$647$	12.3475i	0.485431i	0.970097	+	0.242716i	$0.0780382\pi$
$647$	12.3475i	0.485431i	−0.970097	+	0.242716i	$0.921962\pi$
$648$	− 12.7639i	− 0.501415i
$649$	−0.527864	−0.0207205
$650$	0	0
$651$	22.4164	0.878568
$652$	− 4.23607i	− 0.165897i
$653$	− 7.74265i	− 0.302993i	−0.988458	−	0.151497i	$-0.951591\pi$
$653$	− 7.74265i	− 0.302993i	0.988458	−	0.151497i	$-0.0484093\pi$
$654$	13.0902	0.511866
$655$	0	0
$656$	14.5623	0.568563
$657$	40.0132i	1.56106i
$658$	55.1591i	2.15032i
$659$	−9.27051	−0.361128	−0.180564	−	0.983563i	$-0.557792\pi$
$659$	−9.27051	−0.361128	−0.180564	+	0.983563i	$0.557792\pi$
$660$	0	0
$661$	−49.1803	−1.91289	−0.956447	−	0.291907i	$-0.905710\pi$
$661$	−49.1803	−1.91289	−0.956447	+	0.291907i	$0.905710\pi$
$662$	− 31.0344i	− 1.20619i
$663$	10.0902i	0.391870i
$664$	−22.6869	−0.880423
$665$	0	0
$666$	63.8328	2.47347
$667$	5.65248i	0.218865i
$668$	3.27051i	0.126540i
$669$	−44.2148	−1.70944
$670$	0	0
$671$	0.0901699	0.00348097
$672$	25.2705i	0.974831i
$673$	− 2.41641i	− 0.0931457i	−0.998915	−	0.0465728i	$-0.985170\pi$
$673$	− 2.41641i	− 0.0931457i	0.998915	−	0.0465728i	$-0.0148300\pi$
$674$	−2.29180	−0.0882767
$675$	0	0
$676$	16.0000	0.615385
$677$	28.6525i	1.10120i	0.834768	+	0.550602i	$0.185602\pi$
$677$	28.6525i	1.10120i	−0.834768	+	0.550602i	$0.814398\pi$
$678$	49.3607i	1.89569i
$679$	4.61803	0.177224
$680$	0	0
$681$	−62.9230	−2.41121
$682$	− 4.85410i	− 0.185873i
$683$	43.3607i	1.65915i	0.558395	+	0.829575i	$0.311417\pi$
$683$	43.3607i	1.65915i	−0.558395	+	0.829575i	$0.688583\pi$
$684$	15.9787	0.610961
$685$	0	0
$686$	27.0344	1.03218
$687$	31.5066i	1.20205i
$688$	− 29.1246i	− 1.11037i
$689$	−58.1591	−2.21568
$690$	0	0
$691$	30.0902	1.14468	0.572342	−	0.820015i	$-0.306035\pi$
$691$	30.0902	1.14468	0.572342	+	0.820015i	$0.306035\pi$
$692$	− 3.38197i	− 0.128563i
$693$	11.0000i	0.417855i
$694$	−33.2705	−1.26293
$695$	0	0
$696$	8.09017	0.306657
$697$	1.85410i	0.0702291i
$698$	− 35.3262i	− 1.33712i
$699$	−40.5967	−1.53551
$700$	0	0
$701$	−0.360680	−0.0136227	−0.00681134	−	0.999977i	$-0.502168\pi$
$701$	−0.360680	−0.0136227	−0.00681134	+	0.999977i	$0.502168\pi$
$702$	22.5623i	0.851559i
$703$	68.6656i	2.58977i
$704$	−4.23607	−0.159653
$705$	0	0
$706$	34.5623	1.30077
$707$	17.3820i	0.653716i
$708$	− 0.854102i	− 0.0320991i
$709$	41.3050	1.55124	0.775620	−	0.631200i	$-0.217437\pi$
$709$	41.3050	1.55124	0.775620	+	0.631200i	$0.217437\pi$
$710$	0	0
$711$	22.5623	0.846153
$712$	15.4508i	0.579045i
$713$	− 12.2705i	− 0.459534i
$714$	−7.47214	−0.279638
$715$	0	0
$716$	−8.41641	−0.314536
$717$	16.7082i	0.623979i
$718$	7.23607i	0.270048i
$719$	15.6525	0.583739	0.291869	−	0.956458i	$-0.405723\pi$
$719$	15.6525	0.583739	0.291869	+	0.956458i	$0.405723\pi$
$720$	0	0
$721$	−15.3607	−0.572062
$722$	42.0689i	1.56564i
$723$	− 55.6869i	− 2.07102i
$724$	3.76393	0.139885
$725$	0	0
$726$	4.23607	0.157215
$727$	− 41.2705i	− 1.53064i	−0.643651	−	0.765319i	$-0.722581\pi$
$727$	− 41.2705i	− 1.53064i	0.643651	−	0.765319i	$-0.277419\pi$
$728$	− 39.7984i	− 1.47503i
$729$	39.5623	1.46527
$730$	0	0
$731$	3.70820	0.137153
$732$	0.145898i	0.00539255i
$733$	− 45.8328i	− 1.69287i	−0.532489	−	0.846437i	$-0.678743\pi$
$733$	− 45.8328i	− 1.69287i	0.532489	−	0.846437i	$-0.321257\pi$
$734$	−11.5623	−0.426772
$735$	0	0
$736$	13.8328	0.509884
$737$	8.00000i	0.294684i
$738$	18.7082i	0.688659i
$739$	29.1459	1.07215	0.536075	−	0.844171i	$-0.319907\pi$
$739$	29.1459	1.07215	0.536075	+	0.844171i	$0.319907\pi$
$740$	0	0
$741$	−109.520	−4.02331
$742$	− 43.0689i	− 1.58111i
$743$	− 18.6738i	− 0.685074i	−0.939504	−	0.342537i	$-0.888714\pi$
$743$	− 18.6738i	− 0.685074i	0.939504	−	0.342537i	$-0.111286\pi$
$744$	−17.5623	−0.643865
$745$	0	0
$746$	4.56231	0.167038
$747$	− 39.1033i	− 1.43072i
$748$	0.381966i	0.0139661i
$749$	−12.0902	−0.441765
$750$	0	0
$751$	11.2705	0.411267	0.205633	−	0.978629i	$-0.434075\pi$
$751$	11.2705	0.411267	0.205633	+	0.978629i	$0.434075\pi$
$752$	− 57.9787i	− 2.11427i
$753$	71.3951i	2.60178i
$754$	13.9443	0.507820
$755$	0	0
$756$	−3.94427	−0.143452
$757$	− 21.4721i	− 0.780418i	−0.920726	−	0.390209i	$-0.872403\pi$
$757$	− 21.4721i	− 0.780418i	0.920726	−	0.390209i	$-0.127597\pi$
$758$	28.7426i	1.04398i
$759$	10.7082	0.388683
$760$	0	0
$761$	12.0000	0.435000	0.217500	−	0.976060i	$-0.430210\pi$
$761$	12.0000	0.435000	0.217500	+	0.976060i	$0.430210\pi$
$762$	− 2.61803i	− 0.0948414i
$763$	− 8.81966i	− 0.319293i
$764$	13.0344	0.471570
$765$	0	0
$766$	8.18034	0.295568
$767$	3.29180i	0.118860i
$768$	− 35.5066i	− 1.28123i
$769$	5.00000	0.180305	0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000	0.180305	0.0901523	+	0.995928i	$0.471265\pi$
$770$	0	0
$771$	−28.6525	−1.03189
$772$	8.00000i	0.287926i
$773$	− 33.7984i	− 1.21564i	−0.794074	−	0.607822i	$-0.792044\pi$
$773$	− 33.7984i	− 1.21564i	0.794074	−	0.607822i	$-0.207956\pi$
$774$	37.4164	1.34491
$775$	0	0
$776$	−3.61803	−0.129880
$777$	− 76.4853i	− 2.74389i
$778$	− 8.94427i	− 0.320668i
$779$	−20.1246	−0.721039
$780$	0	0
$781$	8.18034	0.292716
$782$	4.09017i	0.146264i
$783$	3.09017i	0.110434i
$784$	5.56231	0.198654
$785$	0	0
$786$	42.7426	1.52458
$787$	21.2918i	0.758971i	0.925198	+	0.379485i	$0.123899\pi$
$787$	21.2918i	0.758971i	−0.925198	+	0.379485i	$0.876101\pi$
$788$	12.4164i	0.442316i
$789$	54.9787	1.95729
$790$	0	0
$791$	33.2574	1.18250
$792$	− 8.61803i	− 0.306229i
$793$	− 0.562306i	− 0.0199681i
$794$	−24.1246	−0.856150
$795$	0	0
$796$	−1.90983	−0.0676921
$797$	3.20163i	0.113407i	0.998391	+	0.0567037i	$0.0180590\pi$
$797$	3.20163i	0.113407i	−0.998391	+	0.0567037i	$0.981941\pi$
$798$	− 81.1033i	− 2.87103i
$799$	7.38197	0.261155
$800$	0	0
$801$	−26.6312	−0.940967
$802$	55.5967i	1.96319i
$803$	− 10.3820i	− 0.366372i
$804$	−12.9443	−0.456509
$805$	0	0
$806$	−30.2705	−1.06623
$807$	79.3951i	2.79484i
$808$	− 13.6180i	− 0.479081i
$809$	16.5836	0.583048	0.291524	−	0.956564i	$-0.405838\pi$
$809$	16.5836	0.583048	0.291524	+	0.956564i	$0.405838\pi$
$810$	0	0
$811$	17.0000	0.596951	0.298475	−	0.954417i	$-0.403522\pi$
$811$	17.0000	0.596951	0.298475	+	0.954417i	$0.403522\pi$
$812$	2.43769i	0.0855463i
$813$	− 34.5066i	− 1.21020i
$814$	−16.5623	−0.580509
$815$	0	0
$816$	7.85410	0.274949
$817$	40.2492i	1.40814i
$818$	− 32.5623i	− 1.13851i
$819$	68.5967	2.39696
$820$	0	0
$821$	4.36068	0.152189	0.0760944	−	0.997101i	$-0.475755\pi$
$821$	4.36068	0.152189	0.0760944	+	0.997101i	$0.475755\pi$
$822$	23.5623i	0.821830i
$823$	− 27.4164i	− 0.955676i	−0.878448	−	0.477838i	$-0.841421\pi$
$823$	− 27.4164i	− 0.955676i	0.878448	−	0.477838i	$-0.158579\pi$
$824$	12.0344	0.419240
$825$	0	0
$826$	−2.43769	−0.0848182
$827$	32.0689i	1.11514i	0.830128	+	0.557572i	$0.188267\pi$
$827$	32.0689i	1.11514i	−0.830128	+	0.557572i	$0.811733\pi$
$828$	9.74265i	0.338580i
$829$	36.1033	1.25392	0.626960	−	0.779051i	$-0.284299\pi$
$829$	36.1033	1.25392	0.626960	+	0.779051i	$0.284299\pi$
$830$	0	0
$831$	−30.0344	−1.04188
$832$	26.4164i	0.915824i
$833$	0.708204i	0.0245378i
$834$	13.9443	0.482851
$835$	0	0
$836$	−4.14590	−0.143389
$837$	− 6.70820i	− 0.231869i
$838$	− 34.2705i	− 1.18386i
$839$	48.3394	1.66886	0.834431	−	0.551113i	$-0.185797\pi$
$839$	48.3394	1.66886	0.834431	+	0.551113i	$0.185797\pi$
$840$	0	0
$841$	−27.0902	−0.934144
$842$	− 19.8541i	− 0.684218i
$843$	66.3951i	2.28677i
$844$	−10.5066	−0.361651
$845$	0	0
$846$	74.4853	2.56086
$847$	− 2.85410i	− 0.0980681i
$848$	45.2705i	1.55460i
$849$	19.3262	0.663275
$850$	0	0
$851$	−41.8673	−1.43519
$852$	13.2361i	0.453460i
$853$	− 49.8541i	− 1.70697i	−0.521116	−	0.853486i	$-0.674484\pi$
$853$	− 49.8541i	− 1.70697i	0.521116	−	0.853486i	$-0.325516\pi$
$854$	0.416408	0.0142492
$855$	0	0
$856$	9.47214	0.323751
$857$	− 53.1803i	− 1.81661i	−0.418313	−	0.908303i	$-0.637379\pi$
$857$	− 53.1803i	− 1.81661i	0.418313	−	0.908303i	$-0.362621\pi$
$858$	− 26.4164i	− 0.901841i
$859$	−16.1803	−0.552066	−0.276033	−	0.961148i	$-0.589020\pi$
$859$	−16.1803	−0.552066	−0.276033	+	0.961148i	$0.589020\pi$
$860$	0	0
$861$	22.4164	0.763949
$862$	1.32624i	0.0451718i
$863$	0.596748i	0.0203135i	0.999948	+	0.0101568i	$0.00323305\pi$
$863$	0.596748i	0.0203135i	−0.999948	+	0.0101568i	$0.996767\pi$
$864$	7.56231	0.257275
$865$	0	0
$866$	−30.5623	−1.03855
$867$	− 43.5066i	− 1.47756i
$868$	− 5.29180i	− 0.179615i
$869$	−5.85410	−0.198587
$870$	0	0
$871$	49.8885	1.69041
$872$	6.90983i	0.233996i
$873$	− 6.23607i	− 0.211059i
$874$	−44.3951	−1.50169
$875$	0	0
$876$	16.7984	0.567564
$877$	4.58359i	0.154777i	0.997001	+	0.0773885i	$0.0246582\pi$
$877$	4.58359i	0.154777i	−0.997001	+	0.0773885i	$0.975342\pi$
$878$	1.18034i	0.0398345i
$879$	62.5410	2.10946
$880$	0	0
$881$	10.0902	0.339946	0.169973	−	0.985449i	$-0.445632\pi$
$881$	10.0902	0.339946	0.169973	+	0.985449i	$0.445632\pi$
$882$	7.14590i	0.240615i
$883$	31.6525i	1.06519i	0.846370	+	0.532595i	$0.178783\pi$
$883$	31.6525i	1.06519i	−0.846370	+	0.532595i	$0.821217\pi$
$884$	2.38197	0.0801142
$885$	0	0
$886$	−59.3050	−1.99239
$887$	28.7771i	0.966240i	0.875554	+	0.483120i	$0.160497\pi$
$887$	28.7771i	0.966240i	−0.875554	+	0.483120i	$0.839503\pi$
$888$	59.9230i	2.01088i
$889$	−1.76393	−0.0591604
$890$	0	0
$891$	−5.70820	−0.191232
$892$	10.4377i	0.349480i
$893$	80.1246i	2.68127i
$894$	37.8885	1.26718
$895$	0	0
$896$	−38.8673	−1.29846
$897$	− 66.7771i	− 2.22962i
$898$	24.7984i	0.827532i
$899$	−4.14590	−0.138273
$900$	0	0
$901$	−5.76393	−0.192024
$902$	− 4.85410i	− 0.161624i
$903$	− 44.8328i	− 1.49194i
$904$	−26.0557	−0.866601
$905$	0	0
$906$	−12.7082	−0.422202
$907$	14.8328i	0.492516i	0.969204	+	0.246258i	$0.0792010\pi$
$907$	14.8328i	0.492516i	−0.969204	+	0.246258i	$0.920799\pi$
$908$	14.8541i	0.492951i
$909$	23.4721	0.778522
$910$	0	0
$911$	−18.0000	−0.596367	−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000	−0.596367	−0.298183	+	0.954509i	$0.596381\pi$
$912$	85.2492i	2.82288i
$913$	10.1459i	0.335780i
$914$	12.9098	0.427019
$915$	0	0
$916$	7.43769	0.245748
$917$	− 28.7984i	− 0.951006i
$918$	2.23607i	0.0738012i
$919$	−23.4164	−0.772436	−0.386218	−	0.922408i	$-0.626219\pi$
$919$	−23.4164	−0.772436	−0.386218	+	0.922408i	$0.626219\pi$
$920$	0	0
$921$	87.5755	2.88571
$922$	− 14.8541i	− 0.489194i
$923$	− 51.0132i	− 1.67912i
$924$	4.61803	0.151922
$925$	0	0
$926$	18.3820	0.604069
$927$	20.7426i	0.681278i
$928$	− 4.67376i	− 0.153424i
$929$	−54.5967	−1.79126	−0.895631	−	0.444799i	$-0.853275\pi$
$929$	−54.5967	−1.79126	−0.895631	+	0.444799i	$0.853275\pi$
$930$	0	0
$931$	−7.68692	−0.251929
$932$	9.58359i	0.313921i
$933$	50.2148i	1.64396i
$934$	−60.6312	−1.98391
$935$	0	0
$936$	−53.7426	−1.75663
$937$	− 38.8328i	− 1.26861i	−0.773082	−	0.634306i	$-0.781286\pi$
$937$	− 38.8328i	− 1.26861i	0.773082	−	0.634306i	$-0.218714\pi$
$938$	36.9443i	1.20627i
$939$	8.47214	0.276478
$940$	0	0
$941$	41.7214	1.36008	0.680039	−	0.733176i	$-0.261963\pi$
$941$	41.7214	1.36008	0.680039	+	0.733176i	$0.261963\pi$
$942$	− 22.9443i	− 0.747565i
$943$	− 12.2705i	− 0.399583i
$944$	2.56231	0.0833960
$945$	0	0
$946$	−9.70820	−0.315641
$947$	− 39.3607i	− 1.27905i	−0.768770	−	0.639525i	$-0.779131\pi$
$947$	− 39.3607i	− 1.27905i	0.768770	−	0.639525i	$-0.220869\pi$
$948$	− 9.47214i	− 0.307641i
$949$	−64.7426	−2.10164
$950$	0	0
$951$	43.5066	1.41080
$952$	− 3.94427i	− 0.127835i
$953$	− 8.47214i	− 0.274439i	−0.990541	−	0.137220i	$-0.956183\pi$
$953$	− 8.47214i	− 0.274439i	0.990541	−	0.137220i	$-0.0438166\pi$
$954$	−58.1591	−1.88297
$955$	0	0
$956$	3.94427	0.127567
$957$	− 3.61803i	− 0.116954i
$958$	− 45.9787i	− 1.48550i
$959$	15.8754	0.512643
$960$	0	0
$961$	−22.0000	−0.709677
$962$	103.284i	3.33000i
$963$	16.3262i	0.526106i
$964$	−13.1459	−0.423401
$965$	0	0
$966$	49.4508	1.59106
$967$	37.2705i	1.19854i	0.800547	+	0.599269i	$0.204542\pi$
$967$	37.2705i	1.19854i	−0.800547	+	0.599269i	$0.795458\pi$
$968$	2.23607i	0.0718699i
$969$	−10.8541	−0.348684
$970$	0	0
$971$	23.9098	0.767303	0.383651	−	0.923478i	$-0.374666\pi$
$971$	23.9098	0.767303	0.383651	+	0.923478i	$0.374666\pi$
$972$	− 13.3820i	− 0.429227i
$973$	− 9.39512i	− 0.301194i
$974$	49.2148	1.57694
$975$	0	0
$976$	−0.437694	−0.0140102
$977$	57.0689i	1.82580i	0.408188	+	0.912898i	$0.366161\pi$
$977$	57.0689i	1.82580i	−0.408188	+	0.912898i	$0.633839\pi$
$978$	29.0344i	0.928419i
$979$	6.90983	0.220839
$980$	0	0
$981$	−11.9098	−0.380252
$982$	− 11.0344i	− 0.352123i
$983$	1.52786i	0.0487313i	0.999703	+	0.0243656i	$0.00775659\pi$
$983$	1.52786i	0.0487313i	−0.999703	+	0.0243656i	$0.992243\pi$
$984$	−17.5623	−0.559866
$985$	0	0
$986$	1.38197	0.0440108
$987$	− 89.2492i	− 2.84083i
$988$	25.8541i	0.822529i
$989$	−24.5410	−0.780359
$990$	0	0
$991$	21.2705	0.675680	0.337840	−	0.941204i	$-0.390304\pi$
$991$	21.2705	0.675680	0.337840	+	0.941204i	$0.390304\pi$
$992$	10.1459i	0.322133i
$993$	50.2148i	1.59352i
$994$	37.7771	1.19822
$995$	0	0
$996$	−16.4164	−0.520174
$997$	32.1459i	1.01807i	0.860746	+	0.509035i	$0.169998\pi$
$997$	32.1459i	1.01807i	−0.860746	+	0.509035i	$0.830002\pi$
$998$	− 48.2148i	− 1.52621i
$999$	−22.8885	−0.724161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.b.e.199.4		4
3.2	odd	2		2475.2.c.p.199.1		4
4.3	odd	2		4400.2.b.x.4049.4		4
5.2	odd	4		275.2.a.d.1.1	✓	2
5.3	odd	4		275.2.a.g.1.2	yes	2
5.4	even	2	inner	275.2.b.e.199.1		4
15.2	even	4		2475.2.a.s.1.2		2
15.8	even	4		2475.2.a.n.1.1		2
15.14	odd	2		2475.2.c.p.199.4		4
20.3	even	4		4400.2.a.bg.1.1		2
20.7	even	4		4400.2.a.bv.1.2		2
20.19	odd	2		4400.2.b.x.4049.1		4
55.32	even	4		3025.2.a.m.1.2		2
55.43	even	4		3025.2.a.i.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.a.d.1.1	✓	2	5.2	odd	4
275.2.a.g.1.2	yes	2	5.3	odd	4
275.2.b.e.199.1		4	5.4	even	2	inner
275.2.b.e.199.4		4	1.1	even	1	trivial
2475.2.a.n.1.1		2	15.8	even	4
2475.2.a.s.1.2		2	15.2	even	4
2475.2.c.p.199.1		4	3.2	odd	2
2475.2.c.p.199.4		4	15.14	odd	2
3025.2.a.i.1.1		2	55.43	even	4
3025.2.a.m.1.2		2	55.32	even	4
4400.2.a.bg.1.1		2	20.3	even	4
4400.2.a.bv.1.2		2	20.7	even	4
4400.2.b.x.4049.1		4	20.19	odd	2
4400.2.b.x.4049.4		4	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.61803i q^{2} -2.61803i q^{3} -0.618034 q^{4} +4.23607 q^{6} -2.85410i q^{7} +2.23607i q^{8} -3.85410 q^{9} +1.00000 q^{11} +1.61803i q^{12} -6.23607i q^{13} +4.61803 q^{14} -4.85410 q^{16} -0.618034i q^{17} -6.23607i q^{18} +6.70820 q^{19} -7.47214 q^{21} +1.61803i q^{22} +4.09017i q^{23} +5.85410 q^{24} +10.0902 q^{26} +2.23607i q^{27} +1.76393i q^{28} +1.38197 q^{29} -3.00000 q^{31} -3.38197i q^{32} -2.61803i q^{33} +1.00000 q^{34} +2.38197 q^{36} +10.2361i q^{37} +10.8541i q^{38} -16.3262 q^{39} -3.00000 q^{41} -12.0902i q^{42} +6.00000i q^{43} -0.618034 q^{44} -6.61803 q^{46} +11.9443i q^{47} +12.7082i q^{48} -1.14590 q^{49} -1.61803 q^{51} +3.85410i q^{52} -9.32624i q^{53} -3.61803 q^{54} +6.38197 q^{56} -17.5623i q^{57} +2.23607i q^{58} -0.527864 q^{59} +0.0901699 q^{61} -4.85410i q^{62} +11.0000i q^{63} -4.23607 q^{64} +4.23607 q^{66} +8.00000i q^{67} +0.381966i q^{68} +10.7082 q^{69} +8.18034 q^{71} -8.61803i q^{72} -10.3820i q^{73} -16.5623 q^{74} -4.14590 q^{76} -2.85410i q^{77} -26.4164i q^{78} -5.85410 q^{79} -5.70820 q^{81} -4.85410i q^{82} +10.1459i q^{83} +4.61803 q^{84} -9.70820 q^{86} -3.61803i q^{87} +2.23607i q^{88} +6.90983 q^{89} -17.7984 q^{91} -2.52786i q^{92} +7.85410i q^{93} -19.3262 q^{94} -8.85410 q^{96} +1.61803i q^{97} -1.85410i q^{98} -3.85410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 8 q^{6} - 2 q^{9} + 4 q^{11} + 14 q^{14} - 6 q^{16} - 12 q^{21} + 10 q^{24} + 18 q^{26} + 10 q^{29} - 12 q^{31} + 4 q^{34} + 14 q^{36} - 34 q^{39} - 12 q^{41} + 2 q^{44} - 22 q^{46} - 18 q^{49}+ \cdots - 2 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 8 * q^6 - 2 * q^9 + 4 * q^11 + 14 * q^14 - 6 * q^16 - 12 * q^21 + 10 * q^24 + 18 * q^26 + 10 * q^29 - 12 * q^31 + 4 * q^34 + 14 * q^36 - 34 * q^39 - 12 * q^41 + 2 * q^44 - 22 * q^46 - 18 * q^49 - 2 * q^51 - 10 * q^54 + 30 * q^56 - 20 * q^59 - 22 * q^61 - 8 * q^64 + 8 * q^66 + 16 * q^69 - 12 * q^71 - 26 * q^74 - 30 * q^76 - 10 * q^79 + 4 * q^81 + 14 * q^84 - 12 * q^86 + 50 * q^89 - 22 * q^91 - 46 * q^94 - 22 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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