LMFDB - Embedded newform 2850.2.a.bd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(1,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, 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("2850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.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:	$22.7573645761$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	2850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.732051 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.732051 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.73205 q^{11} -1.00000 q^{12} -2.73205 q^{13} -0.732051 q^{14} +1.00000 q^{16} -6.19615 q^{17} -1.00000 q^{18} -1.00000 q^{19} -0.732051 q^{21} -3.73205 q^{22} +5.92820 q^{23} +1.00000 q^{24} +2.73205 q^{26} -1.00000 q^{27} +0.732051 q^{28} -1.73205 q^{29} -2.46410 q^{31} -1.00000 q^{32} -3.73205 q^{33} +6.19615 q^{34} +1.00000 q^{36} -2.00000 q^{37} +1.00000 q^{38} +2.73205 q^{39} -2.92820 q^{41} +0.732051 q^{42} -8.19615 q^{43} +3.73205 q^{44} -5.92820 q^{46} +3.46410 q^{47} -1.00000 q^{48} -6.46410 q^{49} +6.19615 q^{51} -2.73205 q^{52} -1.73205 q^{53} +1.00000 q^{54} -0.732051 q^{56} +1.00000 q^{57} +1.73205 q^{58} -8.19615 q^{59} +10.6603 q^{61} +2.46410 q^{62} +0.732051 q^{63} +1.00000 q^{64} +3.73205 q^{66} -0.267949 q^{67} -6.19615 q^{68} -5.92820 q^{69} +12.1962 q^{71} -1.00000 q^{72} -2.46410 q^{73} +2.00000 q^{74} -1.00000 q^{76} +2.73205 q^{77} -2.73205 q^{78} -5.53590 q^{79} +1.00000 q^{81} +2.92820 q^{82} +3.73205 q^{83} -0.732051 q^{84} +8.19615 q^{86} +1.73205 q^{87} -3.73205 q^{88} +10.8564 q^{89} -2.00000 q^{91} +5.92820 q^{92} +2.46410 q^{93} -3.46410 q^{94} +1.00000 q^{96} -15.1244 q^{97} +6.46410 q^{98} +3.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 2 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{19} + 2 q^{21} - 4 q^{22} - 2 q^{23} + 2 q^{24} + 2 q^{26} - 2 q^{27} - 2 q^{28} + 2 q^{31} - 2 q^{32} - 4 q^{33} + 2 q^{34} + 2 q^{36} - 4 q^{37} + 2 q^{38} + 2 q^{39} + 8 q^{41} - 2 q^{42} - 6 q^{43} + 4 q^{44} + 2 q^{46} - 2 q^{48} - 6 q^{49} + 2 q^{51} - 2 q^{52} + 2 q^{54} + 2 q^{56} + 2 q^{57} - 6 q^{59} + 4 q^{61} - 2 q^{62} - 2 q^{63} + 2 q^{64} + 4 q^{66} - 4 q^{67} - 2 q^{68} + 2 q^{69} + 14 q^{71} - 2 q^{72} + 2 q^{73} + 4 q^{74} - 2 q^{76} + 2 q^{77} - 2 q^{78} - 18 q^{79} + 2 q^{81} - 8 q^{82} + 4 q^{83} + 2 q^{84} + 6 q^{86} - 4 q^{88} - 6 q^{89} - 4 q^{91} - 2 q^{92} - 2 q^{93} + 2 q^{96} - 6 q^{97} + 6 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 - 2 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^19 + 2 * q^21 - 4 * q^22 - 2 * q^23 + 2 * q^24 + 2 * q^26 - 2 * q^27 - 2 * q^28 + 2 * q^31 - 2 * q^32 - 4 * q^33 + 2 * q^34 + 2 * q^36 - 4 * q^37 + 2 * q^38 + 2 * q^39 + 8 * q^41 - 2 * q^42 - 6 * q^43 + 4 * q^44 + 2 * q^46 - 2 * q^48 - 6 * q^49 + 2 * q^51 - 2 * q^52 + 2 * q^54 + 2 * q^56 + 2 * q^57 - 6 * q^59 + 4 * q^61 - 2 * q^62 - 2 * q^63 + 2 * q^64 + 4 * q^66 - 4 * q^67 - 2 * q^68 + 2 * q^69 + 14 * q^71 - 2 * q^72 + 2 * q^73 + 4 * q^74 - 2 * q^76 + 2 * q^77 - 2 * q^78 - 18 * q^79 + 2 * q^81 - 8 * q^82 + 4 * q^83 + 2 * q^84 + 6 * q^86 - 4 * q^88 - 6 * q^89 - 4 * q^91 - 2 * q^92 - 2 * q^93 + 2 * q^96 - 6 * q^97 + 6 * 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
$7$	0.732051	0.276689	0.138345	−	0.990384i	$-0.455822\pi$
$7$	0.732051	0.276689	0.138345	+	0.990384i	$0.455822\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	3.73205	1.12526	0.562628	−	0.826710i	$-0.309790\pi$
$11$	3.73205	1.12526	0.562628	+	0.826710i	$0.309790\pi$
$12$	−1.00000	−0.288675
$13$	−2.73205	−0.757735	−0.378867	−	0.925451i	$-0.623686\pi$
$13$	−2.73205	−0.757735	−0.378867	+	0.925451i	$0.623686\pi$
$14$	−0.732051	−0.195649
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.19615	−1.50279	−0.751394	−	0.659854i	$-0.770618\pi$
$17$	−6.19615	−1.50279	−0.751394	+	0.659854i	$0.770618\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	−0.732051	−0.159747
$22$	−3.73205	−0.795676
$23$	5.92820	1.23612	0.618058	−	0.786133i	$-0.287920\pi$
$23$	5.92820	1.23612	0.618058	+	0.786133i	$0.287920\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	2.73205	0.535799
$27$	−1.00000	−0.192450
$28$	0.732051	0.138345
$29$	−1.73205	−0.321634	−0.160817	−	0.986984i	$-0.551413\pi$
$29$	−1.73205	−0.321634	−0.160817	+	0.986984i	$0.551413\pi$
$30$	0	0
$31$	−2.46410	−0.442566	−0.221283	−	0.975210i	$-0.571024\pi$
$31$	−2.46410	−0.442566	−0.221283	+	0.975210i	$0.571024\pi$
$32$	−1.00000	−0.176777
$33$	−3.73205	−0.649667
$34$	6.19615	1.06263
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	1.00000	0.162221
$39$	2.73205	0.437478
$40$	0	0
$41$	−2.92820	−0.457309	−0.228654	−	0.973508i	$-0.573433\pi$
$41$	−2.92820	−0.457309	−0.228654	+	0.973508i	$0.573433\pi$
$42$	0.732051	0.112958
$43$	−8.19615	−1.24990	−0.624951	−	0.780664i	$-0.714881\pi$
$43$	−8.19615	−1.24990	−0.624951	+	0.780664i	$0.714881\pi$
$44$	3.73205	0.562628
$45$	0	0
$46$	−5.92820	−0.874066
$47$	3.46410	0.505291	0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410	0.505291	0.252646	+	0.967559i	$0.418699\pi$
$48$	−1.00000	−0.144338
$49$	−6.46410	−0.923443
$50$	0	0
$51$	6.19615	0.867635
$52$	−2.73205	−0.378867
$53$	−1.73205	−0.237915	−0.118958	−	0.992899i	$-0.537955\pi$
$53$	−1.73205	−0.237915	−0.118958	+	0.992899i	$0.537955\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−0.732051	−0.0978244
$57$	1.00000	0.132453
$58$	1.73205	0.227429
$59$	−8.19615	−1.06705	−0.533524	−	0.845785i	$-0.679133\pi$
$59$	−8.19615	−1.06705	−0.533524	+	0.845785i	$0.679133\pi$
$60$	0	0
$61$	10.6603	1.36491	0.682453	−	0.730930i	$-0.260913\pi$
$61$	10.6603	1.36491	0.682453	+	0.730930i	$0.260913\pi$
$62$	2.46410	0.312941
$63$	0.732051	0.0922297
$64$	1.00000	0.125000
$65$	0	0
$66$	3.73205	0.459384
$67$	−0.267949	−0.0327352	−0.0163676	−	0.999866i	$-0.505210\pi$
$67$	−0.267949	−0.0327352	−0.0163676	+	0.999866i	$0.505210\pi$
$68$	−6.19615	−0.751394
$69$	−5.92820	−0.713672
$70$	0	0
$71$	12.1962	1.44742	0.723708	−	0.690106i	$-0.242436\pi$
$71$	12.1962	1.44742	0.723708	+	0.690106i	$0.242436\pi$
$72$	−1.00000	−0.117851
$73$	−2.46410	−0.288401	−0.144201	−	0.989548i	$-0.546061\pi$
$73$	−2.46410	−0.288401	−0.144201	+	0.989548i	$0.546061\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	2.73205	0.311346
$78$	−2.73205	−0.309344
$79$	−5.53590	−0.622837	−0.311419	−	0.950273i	$-0.600804\pi$
$79$	−5.53590	−0.622837	−0.311419	+	0.950273i	$0.600804\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.92820	0.323366
$83$	3.73205	0.409646	0.204823	−	0.978799i	$-0.434338\pi$
$83$	3.73205	0.409646	0.204823	+	0.978799i	$0.434338\pi$
$84$	−0.732051	−0.0798733
$85$	0	0
$86$	8.19615	0.883814
$87$	1.73205	0.185695
$88$	−3.73205	−0.397838
$89$	10.8564	1.15078	0.575388	−	0.817880i	$-0.304851\pi$
$89$	10.8564	1.15078	0.575388	+	0.817880i	$0.304851\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	5.92820	0.618058
$93$	2.46410	0.255515
$94$	−3.46410	−0.357295
$95$	0	0
$96$	1.00000	0.102062
$97$	−15.1244	−1.53565	−0.767823	−	0.640662i	$-0.778660\pi$
$97$	−15.1244	−1.53565	−0.767823	+	0.640662i	$0.778660\pi$
$98$	6.46410	0.652973
$99$	3.73205	0.375085
$100$	0	0
$101$	9.26795	0.922195	0.461098	−	0.887349i	$-0.347456\pi$
$101$	9.26795	0.922195	0.461098	+	0.887349i	$0.347456\pi$
$102$	−6.19615	−0.613511
$103$	−3.53590	−0.348402	−0.174201	−	0.984710i	$-0.555734\pi$
$103$	−3.53590	−0.348402	−0.174201	+	0.984710i	$0.555734\pi$
$104$	2.73205	0.267900
$105$	0	0
$106$	1.73205	0.168232
$107$	2.19615	0.212310	0.106155	−	0.994350i	$-0.466146\pi$
$107$	2.19615	0.212310	0.106155	+	0.994350i	$0.466146\pi$
$108$	−1.00000	−0.0962250
$109$	2.39230	0.229141	0.114571	−	0.993415i	$-0.463451\pi$
$109$	2.39230	0.229141	0.114571	+	0.993415i	$0.463451\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	0.732051	0.0691723
$113$	−13.3923	−1.25984	−0.629921	−	0.776659i	$-0.716913\pi$
$113$	−13.3923	−1.25984	−0.629921	+	0.776659i	$0.716913\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	−1.73205	−0.160817
$117$	−2.73205	−0.252578
$118$	8.19615	0.754517
$119$	−4.53590	−0.415805
$120$	0	0
$121$	2.92820	0.266200
$122$	−10.6603	−0.965134
$123$	2.92820	0.264027
$124$	−2.46410	−0.221283
$125$	0	0
$126$	−0.732051	−0.0652163
$127$	−5.00000	−0.443678	−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000	−0.443678	−0.221839	+	0.975083i	$0.571206\pi$
$128$	−1.00000	−0.0883883
$129$	8.19615	0.721631
$130$	0	0
$131$	10.2679	0.897115	0.448557	−	0.893754i	$-0.351938\pi$
$131$	10.2679	0.897115	0.448557	+	0.893754i	$0.351938\pi$
$132$	−3.73205	−0.324833
$133$	−0.732051	−0.0634769
$134$	0.267949	0.0231473
$135$	0	0
$136$	6.19615	0.531316
$137$	−12.3923	−1.05875	−0.529373	−	0.848389i	$-0.677573\pi$
$137$	−12.3923	−1.05875	−0.529373	+	0.848389i	$0.677573\pi$
$138$	5.92820	0.504642
$139$	−21.1244	−1.79174	−0.895872	−	0.444312i	$-0.853448\pi$
$139$	−21.1244	−1.79174	−0.895872	+	0.444312i	$0.853448\pi$
$140$	0	0
$141$	−3.46410	−0.291730
$142$	−12.1962	−1.02348
$143$	−10.1962	−0.852645
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.46410	0.203931
$147$	6.46410	0.533150
$148$	−2.00000	−0.164399
$149$	−21.8564	−1.79055	−0.895273	−	0.445517i	$-0.853020\pi$
$149$	−21.8564	−1.79055	−0.895273	+	0.445517i	$0.853020\pi$
$150$	0	0
$151$	−11.4641	−0.932935	−0.466468	−	0.884538i	$-0.654474\pi$
$151$	−11.4641	−0.932935	−0.466468	+	0.884538i	$0.654474\pi$
$152$	1.00000	0.0811107
$153$	−6.19615	−0.500929
$154$	−2.73205	−0.220155
$155$	0	0
$156$	2.73205	0.218739
$157$	13.8564	1.10586	0.552931	−	0.833227i	$-0.313509\pi$
$157$	13.8564	1.10586	0.552931	+	0.833227i	$0.313509\pi$
$158$	5.53590	0.440412
$159$	1.73205	0.137361
$160$	0	0
$161$	4.33975	0.342020
$162$	−1.00000	−0.0785674
$163$	−2.00000	−0.156652	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000	−0.156652	−0.0783260	+	0.996928i	$0.524958\pi$
$164$	−2.92820	−0.228654
$165$	0	0
$166$	−3.73205	−0.289663
$167$	−8.92820	−0.690885	−0.345443	−	0.938440i	$-0.612271\pi$
$167$	−8.92820	−0.690885	−0.345443	+	0.938440i	$0.612271\pi$
$168$	0.732051	0.0564789
$169$	−5.53590	−0.425838
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	−8.19615	−0.624951
$173$	13.5885	1.03311	0.516556	−	0.856254i	$-0.327214\pi$
$173$	13.5885	1.03311	0.516556	+	0.856254i	$0.327214\pi$
$174$	−1.73205	−0.131306
$175$	0	0
$176$	3.73205	0.281314
$177$	8.19615	0.616061
$178$	−10.8564	−0.813722
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	−16.5885	−1.23301	−0.616505	−	0.787351i	$-0.711452\pi$
$181$	−16.5885	−1.23301	−0.616505	+	0.787351i	$0.711452\pi$
$182$	2.00000	0.148250
$183$	−10.6603	−0.788029
$184$	−5.92820	−0.437033
$185$	0	0
$186$	−2.46410	−0.180677
$187$	−23.1244	−1.69102
$188$	3.46410	0.252646
$189$	−0.732051	−0.0532489
$190$	0	0
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	−1.00000	−0.0721688
$193$	22.0526	1.58738	0.793689	−	0.608324i	$-0.208158\pi$
$193$	22.0526	1.58738	0.793689	+	0.608324i	$0.208158\pi$
$194$	15.1244	1.08587
$195$	0	0
$196$	−6.46410	−0.461722
$197$	24.5885	1.75186	0.875928	−	0.482443i	$-0.160250\pi$
$197$	24.5885	1.75186	0.875928	+	0.482443i	$0.160250\pi$
$198$	−3.73205	−0.265225
$199$	−14.0000	−0.992434	−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000	−0.992434	−0.496217	+	0.868199i	$0.665278\pi$
$200$	0	0
$201$	0.267949	0.0188997
$202$	−9.26795	−0.652091
$203$	−1.26795	−0.0889926
$204$	6.19615	0.433817
$205$	0	0
$206$	3.53590	0.246358
$207$	5.92820	0.412039
$208$	−2.73205	−0.189434
$209$	−3.73205	−0.258151
$210$	0	0
$211$	−10.2679	−0.706875	−0.353437	−	0.935458i	$-0.614987\pi$
$211$	−10.2679	−0.706875	−0.353437	+	0.935458i	$0.614987\pi$
$212$	−1.73205	−0.118958
$213$	−12.1962	−0.835667
$214$	−2.19615	−0.150126
$215$	0	0
$216$	1.00000	0.0680414
$217$	−1.80385	−0.122453
$218$	−2.39230	−0.162027
$219$	2.46410	0.166509
$220$	0	0
$221$	16.9282	1.13871
$222$	−2.00000	−0.134231
$223$	−3.53590	−0.236781	−0.118391	−	0.992967i	$-0.537774\pi$
$223$	−3.53590	−0.236781	−0.118391	+	0.992967i	$0.537774\pi$
$224$	−0.732051	−0.0489122
$225$	0	0
$226$	13.3923	0.890843
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	1.00000	0.0662266
$229$	−6.26795	−0.414198	−0.207099	−	0.978320i	$-0.566402\pi$
$229$	−6.26795	−0.414198	−0.207099	+	0.978320i	$0.566402\pi$
$230$	0	0
$231$	−2.73205	−0.179756
$232$	1.73205	0.113715
$233$	−21.1244	−1.38390	−0.691951	−	0.721944i	$-0.743249\pi$
$233$	−21.1244	−1.38390	−0.691951	+	0.721944i	$0.743249\pi$
$234$	2.73205	0.178600
$235$	0	0
$236$	−8.19615	−0.533524
$237$	5.53590	0.359595
$238$	4.53590	0.294019
$239$	−14.0000	−0.905585	−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000	−0.905585	−0.452792	+	0.891616i	$0.649572\pi$
$240$	0	0
$241$	−30.1962	−1.94511	−0.972553	−	0.232683i	$-0.925249\pi$
$241$	−30.1962	−1.94511	−0.972553	+	0.232683i	$0.925249\pi$
$242$	−2.92820	−0.188232
$243$	−1.00000	−0.0641500
$244$	10.6603	0.682453
$245$	0	0
$246$	−2.92820	−0.186695
$247$	2.73205	0.173836
$248$	2.46410	0.156471
$249$	−3.73205	−0.236509
$250$	0	0
$251$	11.4641	0.723608	0.361804	−	0.932254i	$-0.382161\pi$
$251$	11.4641	0.723608	0.361804	+	0.932254i	$0.382161\pi$
$252$	0.732051	0.0461149
$253$	22.1244	1.39095
$254$	5.00000	0.313728
$255$	0	0
$256$	1.00000	0.0625000
$257$	9.00000	0.561405	0.280702	−	0.959795i	$-0.409433\pi$
$257$	9.00000	0.561405	0.280702	+	0.959795i	$0.409433\pi$
$258$	−8.19615	−0.510270
$259$	−1.46410	−0.0909748
$260$	0	0
$261$	−1.73205	−0.107211
$262$	−10.2679	−0.634356
$263$	15.0000	0.924940	0.462470	−	0.886635i	$-0.346963\pi$
$263$	15.0000	0.924940	0.462470	+	0.886635i	$0.346963\pi$
$264$	3.73205	0.229692
$265$	0	0
$266$	0.732051	0.0448849
$267$	−10.8564	−0.664401
$268$	−0.267949	−0.0163676
$269$	−20.5359	−1.25210	−0.626048	−	0.779785i	$-0.715329\pi$
$269$	−20.5359	−1.25210	−0.626048	+	0.779785i	$0.715329\pi$
$270$	0	0
$271$	−15.8038	−0.960015	−0.480008	−	0.877264i	$-0.659366\pi$
$271$	−15.8038	−0.960015	−0.480008	+	0.877264i	$0.659366\pi$
$272$	−6.19615	−0.375697
$273$	2.00000	0.121046
$274$	12.3923	0.748647
$275$	0	0
$276$	−5.92820	−0.356836
$277$	11.1962	0.672712	0.336356	−	0.941735i	$-0.390806\pi$
$277$	11.1962	0.672712	0.336356	+	0.941735i	$0.390806\pi$
$278$	21.1244	1.26695
$279$	−2.46410	−0.147522
$280$	0	0
$281$	17.7846	1.06094	0.530470	−	0.847703i	$-0.322015\pi$
$281$	17.7846	1.06094	0.530470	+	0.847703i	$0.322015\pi$
$282$	3.46410	0.206284
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	12.1962	0.723708
$285$	0	0
$286$	10.1962	0.602911
$287$	−2.14359	−0.126532
$288$	−1.00000	−0.0589256
$289$	21.3923	1.25837
$290$	0	0
$291$	15.1244	0.886605
$292$	−2.46410	−0.144201
$293$	−27.7321	−1.62012	−0.810062	−	0.586344i	$-0.800567\pi$
$293$	−27.7321	−1.62012	−0.810062	+	0.586344i	$0.800567\pi$
$294$	−6.46410	−0.376994
$295$	0	0
$296$	2.00000	0.116248
$297$	−3.73205	−0.216556
$298$	21.8564	1.26611
$299$	−16.1962	−0.936648
$300$	0	0
$301$	−6.00000	−0.345834
$302$	11.4641	0.659685
$303$	−9.26795	−0.532430
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	6.19615	0.354210
$307$	−20.2679	−1.15675	−0.578376	−	0.815770i	$-0.696314\pi$
$307$	−20.2679	−1.15675	−0.578376	+	0.815770i	$0.696314\pi$
$308$	2.73205	0.155673
$309$	3.53590	0.201150
$310$	0	0
$311$	−29.3205	−1.66261	−0.831307	−	0.555814i	$-0.812407\pi$
$311$	−29.3205	−1.66261	−0.831307	+	0.555814i	$0.812407\pi$
$312$	−2.73205	−0.154672
$313$	−3.92820	−0.222035	−0.111018	−	0.993818i	$-0.535411\pi$
$313$	−3.92820	−0.222035	−0.111018	+	0.993818i	$0.535411\pi$
$314$	−13.8564	−0.781962
$315$	0	0
$316$	−5.53590	−0.311419
$317$	−1.73205	−0.0972817	−0.0486408	−	0.998816i	$-0.515489\pi$
$317$	−1.73205	−0.0972817	−0.0486408	+	0.998816i	$0.515489\pi$
$318$	−1.73205	−0.0971286
$319$	−6.46410	−0.361920
$320$	0	0
$321$	−2.19615	−0.122577
$322$	−4.33975	−0.241845
$323$	6.19615	0.344763
$324$	1.00000	0.0555556
$325$	0	0
$326$	2.00000	0.110770
$327$	−2.39230	−0.132295
$328$	2.92820	0.161683
$329$	2.53590	0.139809
$330$	0	0
$331$	−22.2679	−1.22396	−0.611979	−	0.790874i	$-0.709626\pi$
$331$	−22.2679	−1.22396	−0.611979	+	0.790874i	$0.709626\pi$
$332$	3.73205	0.204823
$333$	−2.00000	−0.109599
$334$	8.92820	0.488530
$335$	0	0
$336$	−0.732051	−0.0399366
$337$	10.5359	0.573927	0.286963	−	0.957942i	$-0.407354\pi$
$337$	10.5359	0.573927	0.286963	+	0.957942i	$0.407354\pi$
$338$	5.53590	0.301113
$339$	13.3923	0.727370
$340$	0	0
$341$	−9.19615	−0.498000
$342$	1.00000	0.0540738
$343$	−9.85641	−0.532196
$344$	8.19615	0.441907
$345$	0	0
$346$	−13.5885	−0.730520
$347$	−20.7846	−1.11578	−0.557888	−	0.829916i	$-0.688388\pi$
$347$	−20.7846	−1.11578	−0.557888	+	0.829916i	$0.688388\pi$
$348$	1.73205	0.0928477
$349$	−17.0526	−0.912803	−0.456401	−	0.889774i	$-0.650862\pi$
$349$	−17.0526	−0.912803	−0.456401	+	0.889774i	$0.650862\pi$
$350$	0	0
$351$	2.73205	0.145826
$352$	−3.73205	−0.198919
$353$	16.0526	0.854391	0.427196	−	0.904159i	$-0.359502\pi$
$353$	16.0526	0.854391	0.427196	+	0.904159i	$0.359502\pi$
$354$	−8.19615	−0.435621
$355$	0	0
$356$	10.8564	0.575388
$357$	4.53590	0.240065
$358$	12.0000	0.634220
$359$	−16.9282	−0.893436	−0.446718	−	0.894675i	$-0.647407\pi$
$359$	−16.9282	−0.893436	−0.446718	+	0.894675i	$0.647407\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	16.5885	0.871870
$363$	−2.92820	−0.153691
$364$	−2.00000	−0.104828
$365$	0	0
$366$	10.6603	0.557220
$367$	−13.2679	−0.692581	−0.346291	−	0.938127i	$-0.612559\pi$
$367$	−13.2679	−0.692581	−0.346291	+	0.938127i	$0.612559\pi$
$368$	5.92820	0.309029
$369$	−2.92820	−0.152436
$370$	0	0
$371$	−1.26795	−0.0658286
$372$	2.46410	0.127758
$373$	−31.5167	−1.63187	−0.815935	−	0.578143i	$-0.803778\pi$
$373$	−31.5167	−1.63187	−0.815935	+	0.578143i	$0.803778\pi$
$374$	23.1244	1.19573
$375$	0	0
$376$	−3.46410	−0.178647
$377$	4.73205	0.243713
$378$	0.732051	0.0376526
$379$	−0.392305	−0.0201513	−0.0100757	−	0.999949i	$-0.503207\pi$
$379$	−0.392305	−0.0201513	−0.0100757	+	0.999949i	$0.503207\pi$
$380$	0	0
$381$	5.00000	0.256158
$382$	−3.00000	−0.153493
$383$	−19.5167	−0.997255	−0.498627	−	0.866816i	$-0.666162\pi$
$383$	−19.5167	−0.997255	−0.498627	+	0.866816i	$0.666162\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−22.0526	−1.12245
$387$	−8.19615	−0.416634
$388$	−15.1244	−0.767823
$389$	21.7128	1.10088	0.550442	−	0.834874i	$-0.314459\pi$
$389$	21.7128	1.10088	0.550442	+	0.834874i	$0.314459\pi$
$390$	0	0
$391$	−36.7321	−1.85762
$392$	6.46410	0.326486
$393$	−10.2679	−0.517950
$394$	−24.5885	−1.23875
$395$	0	0
$396$	3.73205	0.187543
$397$	11.7321	0.588815	0.294407	−	0.955680i	$-0.404878\pi$
$397$	11.7321	0.588815	0.294407	+	0.955680i	$0.404878\pi$
$398$	14.0000	0.701757
$399$	0.732051	0.0366484
$400$	0	0
$401$	16.8564	0.841769	0.420884	−	0.907114i	$-0.361720\pi$
$401$	16.8564	0.841769	0.420884	+	0.907114i	$0.361720\pi$
$402$	−0.267949	−0.0133641
$403$	6.73205	0.335347
$404$	9.26795	0.461098
$405$	0	0
$406$	1.26795	0.0629273
$407$	−7.46410	−0.369982
$408$	−6.19615	−0.306755
$409$	1.60770	0.0794954	0.0397477	−	0.999210i	$-0.487345\pi$
$409$	1.60770	0.0794954	0.0397477	+	0.999210i	$0.487345\pi$
$410$	0	0
$411$	12.3923	0.611267
$412$	−3.53590	−0.174201
$413$	−6.00000	−0.295241
$414$	−5.92820	−0.291355
$415$	0	0
$416$	2.73205	0.133950
$417$	21.1244	1.03446
$418$	3.73205	0.182541
$419$	13.8564	0.676930	0.338465	−	0.940979i	$-0.390092\pi$
$419$	13.8564	0.676930	0.338465	+	0.940979i	$0.390092\pi$
$420$	0	0
$421$	6.78461	0.330662	0.165331	−	0.986238i	$-0.447131\pi$
$421$	6.78461	0.330662	0.165331	+	0.986238i	$0.447131\pi$
$422$	10.2679	0.499836
$423$	3.46410	0.168430
$424$	1.73205	0.0841158
$425$	0	0
$426$	12.1962	0.590906
$427$	7.80385	0.377655
$428$	2.19615	0.106155
$429$	10.1962	0.492275
$430$	0	0
$431$	−29.3205	−1.41232	−0.706160	−	0.708053i	$-0.749574\pi$
$431$	−29.3205	−1.41232	−0.706160	+	0.708053i	$0.749574\pi$
$432$	−1.00000	−0.0481125
$433$	24.1962	1.16279	0.581396	−	0.813620i	$-0.302507\pi$
$433$	24.1962	1.16279	0.581396	+	0.813620i	$0.302507\pi$
$434$	1.80385	0.0865875
$435$	0	0
$436$	2.39230	0.114571
$437$	−5.92820	−0.283584
$438$	−2.46410	−0.117739
$439$	25.7846	1.23063	0.615316	−	0.788280i	$-0.289028\pi$
$439$	25.7846	1.23063	0.615316	+	0.788280i	$0.289028\pi$
$440$	0	0
$441$	−6.46410	−0.307814
$442$	−16.9282	−0.805193
$443$	3.33975	0.158676	0.0793381	−	0.996848i	$-0.474719\pi$
$443$	3.33975	0.158676	0.0793381	+	0.996848i	$0.474719\pi$
$444$	2.00000	0.0949158
$445$	0	0
$446$	3.53590	0.167430
$447$	21.8564	1.03377
$448$	0.732051	0.0345861
$449$	24.4641	1.15453	0.577266	−	0.816556i	$-0.304120\pi$
$449$	24.4641	1.15453	0.577266	+	0.816556i	$0.304120\pi$
$450$	0	0
$451$	−10.9282	−0.514589
$452$	−13.3923	−0.629921
$453$	11.4641	0.538630
$454$	6.00000	0.281594
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	5.07180	0.237249	0.118624	−	0.992939i	$-0.462152\pi$
$457$	5.07180	0.237249	0.118624	+	0.992939i	$0.462152\pi$
$458$	6.26795	0.292882
$459$	6.19615	0.289212
$460$	0	0
$461$	−17.8564	−0.831656	−0.415828	−	0.909443i	$-0.636508\pi$
$461$	−17.8564	−0.831656	−0.415828	+	0.909443i	$0.636508\pi$
$462$	2.73205	0.127107
$463$	35.3205	1.64148	0.820742	−	0.571300i	$-0.193561\pi$
$463$	35.3205	1.64148	0.820742	+	0.571300i	$0.193561\pi$
$464$	−1.73205	−0.0804084
$465$	0	0
$466$	21.1244	0.978567
$467$	−7.19615	−0.332998	−0.166499	−	0.986042i	$-0.553246\pi$
$467$	−7.19615	−0.332998	−0.166499	+	0.986042i	$0.553246\pi$
$468$	−2.73205	−0.126289
$469$	−0.196152	−0.00905748
$470$	0	0
$471$	−13.8564	−0.638470
$472$	8.19615	0.377258
$473$	−30.5885	−1.40646
$474$	−5.53590	−0.254272
$475$	0	0
$476$	−4.53590	−0.207903
$477$	−1.73205	−0.0793052
$478$	14.0000	0.640345
$479$	3.14359	0.143634	0.0718172	−	0.997418i	$-0.477120\pi$
$479$	3.14359	0.143634	0.0718172	+	0.997418i	$0.477120\pi$
$480$	0	0
$481$	5.46410	0.249142
$482$	30.1962	1.37540
$483$	−4.33975	−0.197465
$484$	2.92820	0.133100
$485$	0	0
$486$	1.00000	0.0453609
$487$	−2.14359	−0.0971355	−0.0485677	−	0.998820i	$-0.515466\pi$
$487$	−2.14359	−0.0971355	−0.0485677	+	0.998820i	$0.515466\pi$
$488$	−10.6603	−0.482567
$489$	2.00000	0.0904431
$490$	0	0
$491$	−2.92820	−0.132148	−0.0660740	−	0.997815i	$-0.521047\pi$
$491$	−2.92820	−0.132148	−0.0660740	+	0.997815i	$0.521047\pi$
$492$	2.92820	0.132014
$493$	10.7321	0.483347
$494$	−2.73205	−0.122921
$495$	0	0
$496$	−2.46410	−0.110641
$497$	8.92820	0.400485
$498$	3.73205	0.167237
$499$	41.3731	1.85211	0.926056	−	0.377385i	$-0.123177\pi$
$499$	41.3731	1.85211	0.926056	+	0.377385i	$0.123177\pi$
$500$	0	0
$501$	8.92820	0.398883
$502$	−11.4641	−0.511668
$503$	17.8564	0.796178	0.398089	−	0.917347i	$-0.369674\pi$
$503$	17.8564	0.796178	0.398089	+	0.917347i	$0.369674\pi$
$504$	−0.732051	−0.0326081
$505$	0	0
$506$	−22.1244	−0.983548
$507$	5.53590	0.245858
$508$	−5.00000	−0.221839
$509$	13.8756	0.615027	0.307514	−	0.951544i	$-0.400503\pi$
$509$	13.8756	0.615027	0.307514	+	0.951544i	$0.400503\pi$
$510$	0	0
$511$	−1.80385	−0.0797975
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−9.00000	−0.396973
$515$	0	0
$516$	8.19615	0.360815
$517$	12.9282	0.568582
$518$	1.46410	0.0643289
$519$	−13.5885	−0.596467
$520$	0	0
$521$	24.1769	1.05921	0.529605	−	0.848244i	$-0.322340\pi$
$521$	24.1769	1.05921	0.529605	+	0.848244i	$0.322340\pi$
$522$	1.73205	0.0758098
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	10.2679	0.448557
$525$	0	0
$526$	−15.0000	−0.654031
$527$	15.2679	0.665082
$528$	−3.73205	−0.162417
$529$	12.1436	0.527982
$530$	0	0
$531$	−8.19615	−0.355683
$532$	−0.732051	−0.0317384
$533$	8.00000	0.346518
$534$	10.8564	0.469803
$535$	0	0
$536$	0.267949	0.0115736
$537$	12.0000	0.517838
$538$	20.5359	0.885365
$539$	−24.1244	−1.03911
$540$	0	0
$541$	17.1962	0.739320	0.369660	−	0.929167i	$-0.379474\pi$
$541$	17.1962	0.739320	0.369660	+	0.929167i	$0.379474\pi$
$542$	15.8038	0.678833
$543$	16.5885	0.711879
$544$	6.19615	0.265658
$545$	0	0
$546$	−2.00000	−0.0855921
$547$	43.4449	1.85757	0.928784	−	0.370621i	$-0.120855\pi$
$547$	43.4449	1.85757	0.928784	+	0.370621i	$0.120855\pi$
$548$	−12.3923	−0.529373
$549$	10.6603	0.454969
$550$	0	0
$551$	1.73205	0.0737878
$552$	5.92820	0.252321
$553$	−4.05256	−0.172332
$554$	−11.1962	−0.475679
$555$	0	0
$556$	−21.1244	−0.895872
$557$	3.80385	0.161174	0.0805871	−	0.996748i	$-0.474320\pi$
$557$	3.80385	0.161174	0.0805871	+	0.996748i	$0.474320\pi$
$558$	2.46410	0.104314
$559$	22.3923	0.947094
$560$	0	0
$561$	23.1244	0.976311
$562$	−17.7846	−0.750198
$563$	7.66025	0.322841	0.161421	−	0.986886i	$-0.448392\pi$
$563$	7.66025	0.322841	0.161421	+	0.986886i	$0.448392\pi$
$564$	−3.46410	−0.145865
$565$	0	0
$566$	−4.00000	−0.168133
$567$	0.732051	0.0307432
$568$	−12.1962	−0.511739
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	0	0
$571$	−6.19615	−0.259301	−0.129650	−	0.991560i	$-0.541386\pi$
$571$	−6.19615	−0.259301	−0.129650	+	0.991560i	$0.541386\pi$
$572$	−10.1962	−0.426323
$573$	−3.00000	−0.125327
$574$	2.14359	0.0894719
$575$	0	0
$576$	1.00000	0.0416667
$577$	−17.2487	−0.718073	−0.359037	−	0.933323i	$-0.616895\pi$
$577$	−17.2487	−0.718073	−0.359037	+	0.933323i	$0.616895\pi$
$578$	−21.3923	−0.889803
$579$	−22.0526	−0.916473
$580$	0	0
$581$	2.73205	0.113345
$582$	−15.1244	−0.626925
$583$	−6.46410	−0.267716
$584$	2.46410	0.101965
$585$	0	0
$586$	27.7321	1.14560
$587$	−12.2679	−0.506352	−0.253176	−	0.967420i	$-0.581475\pi$
$587$	−12.2679	−0.506352	−0.253176	+	0.967420i	$0.581475\pi$
$588$	6.46410	0.266575
$589$	2.46410	0.101532
$590$	0	0
$591$	−24.5885	−1.01143
$592$	−2.00000	−0.0821995
$593$	−27.6077	−1.13371	−0.566856	−	0.823817i	$-0.691840\pi$
$593$	−27.6077	−1.13371	−0.566856	+	0.823817i	$0.691840\pi$
$594$	3.73205	0.153128
$595$	0	0
$596$	−21.8564	−0.895273
$597$	14.0000	0.572982
$598$	16.1962	0.662310
$599$	−3.66025	−0.149554	−0.0747770	−	0.997200i	$-0.523824\pi$
$599$	−3.66025	−0.149554	−0.0747770	+	0.997200i	$0.523824\pi$
$600$	0	0
$601$	−10.0526	−0.410052	−0.205026	−	0.978756i	$-0.565728\pi$
$601$	−10.0526	−0.410052	−0.205026	+	0.978756i	$0.565728\pi$
$602$	6.00000	0.244542
$603$	−0.267949	−0.0109117
$604$	−11.4641	−0.466468
$605$	0	0
$606$	9.26795	0.376485
$607$	−11.7846	−0.478323	−0.239161	−	0.970980i	$-0.576872\pi$
$607$	−11.7846	−0.478323	−0.239161	+	0.970980i	$0.576872\pi$
$608$	1.00000	0.0405554
$609$	1.26795	0.0513799
$610$	0	0
$611$	−9.46410	−0.382877
$612$	−6.19615	−0.250465
$613$	38.7846	1.56650	0.783248	−	0.621710i	$-0.213562\pi$
$613$	38.7846	1.56650	0.783248	+	0.621710i	$0.213562\pi$
$614$	20.2679	0.817948
$615$	0	0
$616$	−2.73205	−0.110077
$617$	46.3923	1.86768	0.933842	−	0.357686i	$-0.116434\pi$
$617$	46.3923	1.86768	0.933842	+	0.357686i	$0.116434\pi$
$618$	−3.53590	−0.142235
$619$	−0.196152	−0.00788403	−0.00394202	−	0.999992i	$-0.501255\pi$
$619$	−0.196152	−0.00788403	−0.00394202	+	0.999992i	$0.501255\pi$
$620$	0	0
$621$	−5.92820	−0.237891
$622$	29.3205	1.17565
$623$	7.94744	0.318408
$624$	2.73205	0.109370
$625$	0	0
$626$	3.92820	0.157003
$627$	3.73205	0.149044
$628$	13.8564	0.552931
$629$	12.3923	0.494114
$630$	0	0
$631$	2.92820	0.116570	0.0582850	−	0.998300i	$-0.481437\pi$
$631$	2.92820	0.116570	0.0582850	+	0.998300i	$0.481437\pi$
$632$	5.53590	0.220206
$633$	10.2679	0.408114
$634$	1.73205	0.0687885
$635$	0	0
$636$	1.73205	0.0686803
$637$	17.6603	0.699725
$638$	6.46410	0.255916
$639$	12.1962	0.482472
$640$	0	0
$641$	10.5359	0.416143	0.208071	−	0.978114i	$-0.433281\pi$
$641$	10.5359	0.416143	0.208071	+	0.978114i	$0.433281\pi$
$642$	2.19615	0.0866752
$643$	27.0718	1.06761	0.533804	−	0.845608i	$-0.320762\pi$
$643$	27.0718	1.06761	0.533804	+	0.845608i	$0.320762\pi$
$644$	4.33975	0.171010
$645$	0	0
$646$	−6.19615	−0.243784
$647$	9.39230	0.369250	0.184625	−	0.982809i	$-0.440893\pi$
$647$	9.39230	0.369250	0.184625	+	0.982809i	$0.440893\pi$
$648$	−1.00000	−0.0392837
$649$	−30.5885	−1.20070
$650$	0	0
$651$	1.80385	0.0706984
$652$	−2.00000	−0.0783260
$653$	−17.4641	−0.683423	−0.341712	−	0.939805i	$-0.611007\pi$
$653$	−17.4641	−0.683423	−0.341712	+	0.939805i	$0.611007\pi$
$654$	2.39230	0.0935465
$655$	0	0
$656$	−2.92820	−0.114327
$657$	−2.46410	−0.0961338
$658$	−2.53590	−0.0988596
$659$	7.41154	0.288713	0.144356	−	0.989526i	$-0.453889\pi$
$659$	7.41154	0.288713	0.144356	+	0.989526i	$0.453889\pi$
$660$	0	0
$661$	−22.6410	−0.880633	−0.440317	−	0.897843i	$-0.645134\pi$
$661$	−22.6410	−0.880633	−0.440317	+	0.897843i	$0.645134\pi$
$662$	22.2679	0.865468
$663$	−16.9282	−0.657437
$664$	−3.73205	−0.144832
$665$	0	0
$666$	2.00000	0.0774984
$667$	−10.2679	−0.397577
$668$	−8.92820	−0.345443
$669$	3.53590	0.136706
$670$	0	0
$671$	39.7846	1.53587
$672$	0.732051	0.0282395
$673$	6.98076	0.269089	0.134544	−	0.990908i	$-0.457043\pi$
$673$	6.98076	0.269089	0.134544	+	0.990908i	$0.457043\pi$
$674$	−10.5359	−0.405828
$675$	0	0
$676$	−5.53590	−0.212919
$677$	−8.66025	−0.332841	−0.166420	−	0.986055i	$-0.553221\pi$
$677$	−8.66025	−0.332841	−0.166420	+	0.986055i	$0.553221\pi$
$678$	−13.3923	−0.514328
$679$	−11.0718	−0.424897
$680$	0	0
$681$	6.00000	0.229920
$682$	9.19615	0.352139
$683$	46.9808	1.79767	0.898834	−	0.438288i	$-0.144415\pi$
$683$	46.9808	1.79767	0.898834	+	0.438288i	$0.144415\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	9.85641	0.376319
$687$	6.26795	0.239137
$688$	−8.19615	−0.312475
$689$	4.73205	0.180277
$690$	0	0
$691$	−22.1962	−0.844381	−0.422191	−	0.906507i	$-0.638739\pi$
$691$	−22.1962	−0.844381	−0.422191	+	0.906507i	$0.638739\pi$
$692$	13.5885	0.516556
$693$	2.73205	0.103782
$694$	20.7846	0.788973
$695$	0	0
$696$	−1.73205	−0.0656532
$697$	18.1436	0.687238
$698$	17.0526	0.645449
$699$	21.1244	0.798997
$700$	0	0
$701$	3.60770	0.136261	0.0681304	−	0.997676i	$-0.478297\pi$
$701$	3.60770	0.136261	0.0681304	+	0.997676i	$0.478297\pi$
$702$	−2.73205	−0.103115
$703$	2.00000	0.0754314
$704$	3.73205	0.140657
$705$	0	0
$706$	−16.0526	−0.604146
$707$	6.78461	0.255162
$708$	8.19615	0.308030
$709$	47.3013	1.77644	0.888218	−	0.459422i	$-0.151943\pi$
$709$	47.3013	1.77644	0.888218	+	0.459422i	$0.151943\pi$
$710$	0	0
$711$	−5.53590	−0.207612
$712$	−10.8564	−0.406861
$713$	−14.6077	−0.547062
$714$	−4.53590	−0.169752
$715$	0	0
$716$	−12.0000	−0.448461
$717$	14.0000	0.522840
$718$	16.9282	0.631755
$719$	12.1769	0.454122	0.227061	−	0.973881i	$-0.427088\pi$
$719$	12.1769	0.454122	0.227061	+	0.973881i	$0.427088\pi$
$720$	0	0
$721$	−2.58846	−0.0963992
$722$	−1.00000	−0.0372161
$723$	30.1962	1.12301
$724$	−16.5885	−0.616505
$725$	0	0
$726$	2.92820	0.108676
$727$	−38.1051	−1.41324	−0.706620	−	0.707593i	$-0.749781\pi$
$727$	−38.1051	−1.41324	−0.706620	+	0.707593i	$0.749781\pi$
$728$	2.00000	0.0741249
$729$	1.00000	0.0370370
$730$	0	0
$731$	50.7846	1.87834
$732$	−10.6603	−0.394014
$733$	−20.5167	−0.757800	−0.378900	−	0.925438i	$-0.623698\pi$
$733$	−20.5167	−0.757800	−0.378900	+	0.925438i	$0.623698\pi$
$734$	13.2679	0.489729
$735$	0	0
$736$	−5.92820	−0.218516
$737$	−1.00000	−0.0368355
$738$	2.92820	0.107789
$739$	−53.1769	−1.95614	−0.978072	−	0.208266i	$-0.933218\pi$
$739$	−53.1769	−1.95614	−0.978072	+	0.208266i	$0.933218\pi$
$740$	0	0
$741$	−2.73205	−0.100364
$742$	1.26795	0.0465479
$743$	−5.07180	−0.186066	−0.0930331	−	0.995663i	$-0.529656\pi$
$743$	−5.07180	−0.186066	−0.0930331	+	0.995663i	$0.529656\pi$
$744$	−2.46410	−0.0903383
$745$	0	0
$746$	31.5167	1.15391
$747$	3.73205	0.136549
$748$	−23.1244	−0.845510
$749$	1.60770	0.0587439
$750$	0	0
$751$	7.46410	0.272369	0.136184	−	0.990683i	$-0.456516\pi$
$751$	7.46410	0.272369	0.136184	+	0.990683i	$0.456516\pi$
$752$	3.46410	0.126323
$753$	−11.4641	−0.417775
$754$	−4.73205	−0.172331
$755$	0	0
$756$	−0.732051	−0.0266244
$757$	−13.5885	−0.493881	−0.246940	−	0.969031i	$-0.579425\pi$
$757$	−13.5885	−0.493881	−0.246940	+	0.969031i	$0.579425\pi$
$758$	0.392305	0.0142492
$759$	−22.1244	−0.803063
$760$	0	0
$761$	1.26795	0.0459631	0.0229816	−	0.999736i	$-0.492684\pi$
$761$	1.26795	0.0459631	0.0229816	+	0.999736i	$0.492684\pi$
$762$	−5.00000	−0.181131
$763$	1.75129	0.0634009
$764$	3.00000	0.108536
$765$	0	0
$766$	19.5167	0.705166
$767$	22.3923	0.808539
$768$	−1.00000	−0.0360844
$769$	−34.7128	−1.25178	−0.625888	−	0.779913i	$-0.715263\pi$
$769$	−34.7128	−1.25178	−0.625888	+	0.779913i	$0.715263\pi$
$770$	0	0
$771$	−9.00000	−0.324127
$772$	22.0526	0.793689
$773$	−45.3205	−1.63007	−0.815033	−	0.579415i	$-0.803281\pi$
$773$	−45.3205	−1.63007	−0.815033	+	0.579415i	$0.803281\pi$
$774$	8.19615	0.294605
$775$	0	0
$776$	15.1244	0.542933
$777$	1.46410	0.0525244
$778$	−21.7128	−0.778442
$779$	2.92820	0.104914
$780$	0	0
$781$	45.5167	1.62871
$782$	36.7321	1.31354
$783$	1.73205	0.0618984
$784$	−6.46410	−0.230861
$785$	0	0
$786$	10.2679	0.366246
$787$	2.12436	0.0757251	0.0378626	−	0.999283i	$-0.487945\pi$
$787$	2.12436	0.0757251	0.0378626	+	0.999283i	$0.487945\pi$
$788$	24.5885	0.875928
$789$	−15.0000	−0.534014
$790$	0	0
$791$	−9.80385	−0.348585
$792$	−3.73205	−0.132613
$793$	−29.1244	−1.03424
$794$	−11.7321	−0.416355
$795$	0	0
$796$	−14.0000	−0.496217
$797$	20.0000	0.708436	0.354218	−	0.935163i	$-0.384747\pi$
$797$	20.0000	0.708436	0.354218	+	0.935163i	$0.384747\pi$
$798$	−0.732051	−0.0259143
$799$	−21.4641	−0.759345
$800$	0	0
$801$	10.8564	0.383592
$802$	−16.8564	−0.595220
$803$	−9.19615	−0.324525
$804$	0.267949	0.00944984
$805$	0	0
$806$	−6.73205	−0.237126
$807$	20.5359	0.722898
$808$	−9.26795	−0.326045
$809$	37.5167	1.31902	0.659508	−	0.751698i	$-0.270765\pi$
$809$	37.5167	1.31902	0.659508	+	0.751698i	$0.270765\pi$
$810$	0	0
$811$	18.3731	0.645166	0.322583	−	0.946541i	$-0.395449\pi$
$811$	18.3731	0.645166	0.322583	+	0.946541i	$0.395449\pi$
$812$	−1.26795	−0.0444963
$813$	15.8038	0.554265
$814$	7.46410	0.261617
$815$	0	0
$816$	6.19615	0.216909
$817$	8.19615	0.286747
$818$	−1.60770	−0.0562117
$819$	−2.00000	−0.0698857
$820$	0	0
$821$	2.48334	0.0866691	0.0433346	−	0.999061i	$-0.486202\pi$
$821$	2.48334	0.0866691	0.0433346	+	0.999061i	$0.486202\pi$
$822$	−12.3923	−0.432231
$823$	−6.78461	−0.236497	−0.118248	−	0.992984i	$-0.537728\pi$
$823$	−6.78461	−0.236497	−0.118248	+	0.992984i	$0.537728\pi$
$824$	3.53590	0.123179
$825$	0	0
$826$	6.00000	0.208767
$827$	6.73205	0.234096	0.117048	−	0.993126i	$-0.462657\pi$
$827$	6.73205	0.234096	0.117048	+	0.993126i	$0.462657\pi$
$828$	5.92820	0.206019
$829$	6.19615	0.215201	0.107601	−	0.994194i	$-0.465683\pi$
$829$	6.19615	0.215201	0.107601	+	0.994194i	$0.465683\pi$
$830$	0	0
$831$	−11.1962	−0.388390
$832$	−2.73205	−0.0947168
$833$	40.0526	1.38774
$834$	−21.1244	−0.731477
$835$	0	0
$836$	−3.73205	−0.129076
$837$	2.46410	0.0851718
$838$	−13.8564	−0.478662
$839$	−46.5885	−1.60841	−0.804206	−	0.594351i	$-0.797409\pi$
$839$	−46.5885	−1.60841	−0.804206	+	0.594351i	$0.797409\pi$
$840$	0	0
$841$	−26.0000	−0.896552
$842$	−6.78461	−0.233813
$843$	−17.7846	−0.612534
$844$	−10.2679	−0.353437
$845$	0	0
$846$	−3.46410	−0.119098
$847$	2.14359	0.0736547
$848$	−1.73205	−0.0594789
$849$	−4.00000	−0.137280
$850$	0	0
$851$	−11.8564	−0.406432
$852$	−12.1962	−0.417833
$853$	−4.53590	−0.155306	−0.0776531	−	0.996980i	$-0.524743\pi$
$853$	−4.53590	−0.155306	−0.0776531	+	0.996980i	$0.524743\pi$
$854$	−7.80385	−0.267042
$855$	0	0
$856$	−2.19615	−0.0750629
$857$	−42.9282	−1.46640	−0.733200	−	0.680013i	$-0.761974\pi$
$857$	−42.9282	−1.46640	−0.733200	+	0.680013i	$0.761974\pi$
$858$	−10.1962	−0.348091
$859$	56.9282	1.94237	0.971183	−	0.238337i	$-0.0766021\pi$
$859$	56.9282	1.94237	0.971183	+	0.238337i	$0.0766021\pi$
$860$	0	0
$861$	2.14359	0.0730535
$862$	29.3205	0.998660
$863$	−55.3205	−1.88313	−0.941566	−	0.336829i	$-0.890646\pi$
$863$	−55.3205	−1.88313	−0.941566	+	0.336829i	$0.890646\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−24.1962	−0.822219
$867$	−21.3923	−0.726521
$868$	−1.80385	−0.0612266
$869$	−20.6603	−0.700851
$870$	0	0
$871$	0.732051	0.0248046
$872$	−2.39230	−0.0810137
$873$	−15.1244	−0.511882
$874$	5.92820	0.200524
$875$	0	0
$876$	2.46410	0.0832543
$877$	31.1769	1.05277	0.526385	−	0.850246i	$-0.323547\pi$
$877$	31.1769	1.05277	0.526385	+	0.850246i	$0.323547\pi$
$878$	−25.7846	−0.870188
$879$	27.7321	0.935379
$880$	0	0
$881$	−26.5359	−0.894017	−0.447009	−	0.894530i	$-0.647511\pi$
$881$	−26.5359	−0.894017	−0.447009	+	0.894530i	$0.647511\pi$
$882$	6.46410	0.217658
$883$	27.2679	0.917640	0.458820	−	0.888529i	$-0.348272\pi$
$883$	27.2679	0.917640	0.458820	+	0.888529i	$0.348272\pi$
$884$	16.9282	0.569357
$885$	0	0
$886$	−3.33975	−0.112201
$887$	−7.60770	−0.255441	−0.127721	−	0.991810i	$-0.540766\pi$
$887$	−7.60770	−0.255441	−0.127721	+	0.991810i	$0.540766\pi$
$888$	−2.00000	−0.0671156
$889$	−3.66025	−0.122761
$890$	0	0
$891$	3.73205	0.125028
$892$	−3.53590	−0.118391
$893$	−3.46410	−0.115922
$894$	−21.8564	−0.730988
$895$	0	0
$896$	−0.732051	−0.0244561
$897$	16.1962	0.540774
$898$	−24.4641	−0.816378
$899$	4.26795	0.142344
$900$	0	0
$901$	10.7321	0.357536
$902$	10.9282	0.363869
$903$	6.00000	0.199667
$904$	13.3923	0.445421
$905$	0	0
$906$	−11.4641	−0.380869
$907$	49.3205	1.63766	0.818830	−	0.574036i	$-0.194623\pi$
$907$	49.3205	1.63766	0.818830	+	0.574036i	$0.194623\pi$
$908$	−6.00000	−0.199117
$909$	9.26795	0.307398
$910$	0	0
$911$	34.1051	1.12995	0.564976	−	0.825107i	$-0.308885\pi$
$911$	34.1051	1.12995	0.564976	+	0.825107i	$0.308885\pi$
$912$	1.00000	0.0331133
$913$	13.9282	0.460956
$914$	−5.07180	−0.167760
$915$	0	0
$916$	−6.26795	−0.207099
$917$	7.51666	0.248222
$918$	−6.19615	−0.204504
$919$	−4.48334	−0.147892	−0.0739459	−	0.997262i	$-0.523559\pi$
$919$	−4.48334	−0.147892	−0.0739459	+	0.997262i	$0.523559\pi$
$920$	0	0
$921$	20.2679	0.667852
$922$	17.8564	0.588069
$923$	−33.3205	−1.09676
$924$	−2.73205	−0.0898779
$925$	0	0
$926$	−35.3205	−1.16070
$927$	−3.53590	−0.116134
$928$	1.73205	0.0568574
$929$	42.9282	1.40843	0.704214	−	0.709987i	$-0.251299\pi$
$929$	42.9282	1.40843	0.704214	+	0.709987i	$0.251299\pi$
$930$	0	0
$931$	6.46410	0.211852
$932$	−21.1244	−0.691951
$933$	29.3205	0.959910
$934$	7.19615	0.235465
$935$	0	0
$936$	2.73205	0.0892999
$937$	−13.2154	−0.431728	−0.215864	−	0.976423i	$-0.569257\pi$
$937$	−13.2154	−0.431728	−0.215864	+	0.976423i	$0.569257\pi$
$938$	0.196152	0.00640460
$939$	3.92820	0.128192
$940$	0	0
$941$	−12.2679	−0.399924	−0.199962	−	0.979804i	$-0.564082\pi$
$941$	−12.2679	−0.399924	−0.199962	+	0.979804i	$0.564082\pi$
$942$	13.8564	0.451466
$943$	−17.3590	−0.565286
$944$	−8.19615	−0.266762
$945$	0	0
$946$	30.5885	0.994517
$947$	5.85641	0.190308	0.0951538	−	0.995463i	$-0.469666\pi$
$947$	5.85641	0.190308	0.0951538	+	0.995463i	$0.469666\pi$
$948$	5.53590	0.179798
$949$	6.73205	0.218532
$950$	0	0
$951$	1.73205	0.0561656
$952$	4.53590	0.147009
$953$	5.24871	0.170022	0.0850112	−	0.996380i	$-0.472907\pi$
$953$	5.24871	0.170022	0.0850112	+	0.996380i	$0.472907\pi$
$954$	1.73205	0.0560772
$955$	0	0
$956$	−14.0000	−0.452792
$957$	6.46410	0.208955
$958$	−3.14359	−0.101565
$959$	−9.07180	−0.292944
$960$	0	0
$961$	−24.9282	−0.804136
$962$	−5.46410	−0.176170
$963$	2.19615	0.0707700
$964$	−30.1962	−0.972553
$965$	0	0
$966$	4.33975	0.139629
$967$	−18.1051	−0.582221	−0.291111	−	0.956689i	$-0.594025\pi$
$967$	−18.1051	−0.582221	−0.291111	+	0.956689i	$0.594025\pi$
$968$	−2.92820	−0.0941160
$969$	−6.19615	−0.199049
$970$	0	0
$971$	−37.7654	−1.21195	−0.605974	−	0.795484i	$-0.707217\pi$
$971$	−37.7654	−1.21195	−0.605974	+	0.795484i	$0.707217\pi$
$972$	−1.00000	−0.0320750
$973$	−15.4641	−0.495756
$974$	2.14359	0.0686852
$975$	0	0
$976$	10.6603	0.341226
$977$	1.46410	0.0468408	0.0234204	−	0.999726i	$-0.492544\pi$
$977$	1.46410	0.0468408	0.0234204	+	0.999726i	$0.492544\pi$
$978$	−2.00000	−0.0639529
$979$	40.5167	1.29492
$980$	0	0
$981$	2.39230	0.0763804
$982$	2.92820	0.0934427
$983$	30.3397	0.967688	0.483844	−	0.875154i	$-0.339240\pi$
$983$	30.3397	0.967688	0.483844	+	0.875154i	$0.339240\pi$
$984$	−2.92820	−0.0933477
$985$	0	0
$986$	−10.7321	−0.341778
$987$	−2.53590	−0.0807185
$988$	2.73205	0.0869181
$989$	−48.5885	−1.54502
$990$	0	0
$991$	−40.3205	−1.28082	−0.640412	−	0.768032i	$-0.721236\pi$
$991$	−40.3205	−1.28082	−0.640412	+	0.768032i	$0.721236\pi$
$992$	2.46410	0.0782353
$993$	22.2679	0.706652
$994$	−8.92820	−0.283185
$995$	0	0
$996$	−3.73205	−0.118255
$997$	63.0526	1.99689	0.998447	−	0.0557047i	$-0.0177405\pi$
$997$	63.0526	1.99689	0.998447	+	0.0557047i	$0.0177405\pi$
$998$	−41.3731	−1.30964
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.a.bd.1.2	✓	2
3.2	odd	2		8550.2.a.by.1.2		2
5.2	odd	4		2850.2.d.x.799.2		4
5.3	odd	4		2850.2.d.x.799.3		4
5.4	even	2		2850.2.a.bi.1.1	yes	2
15.14	odd	2		8550.2.a.bs.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2850.2.a.bd.1.2	✓	2	1.1	even	1	trivial
2850.2.a.bi.1.1	yes	2	5.4	even	2
2850.2.d.x.799.2		4	5.2	odd	4
2850.2.d.x.799.3		4	5.3	odd	4
8550.2.a.bs.1.1		2	15.14	odd	2
8550.2.a.by.1.2		2	3.2	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:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.732051 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.732051 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.73205 q^{11} -1.00000 q^{12} -2.73205 q^{13} -0.732051 q^{14} +1.00000 q^{16} -6.19615 q^{17} -1.00000 q^{18} -1.00000 q^{19} -0.732051 q^{21} -3.73205 q^{22} +5.92820 q^{23} +1.00000 q^{24} +2.73205 q^{26} -1.00000 q^{27} +0.732051 q^{28} -1.73205 q^{29} -2.46410 q^{31} -1.00000 q^{32} -3.73205 q^{33} +6.19615 q^{34} +1.00000 q^{36} -2.00000 q^{37} +1.00000 q^{38} +2.73205 q^{39} -2.92820 q^{41} +0.732051 q^{42} -8.19615 q^{43} +3.73205 q^{44} -5.92820 q^{46} +3.46410 q^{47} -1.00000 q^{48} -6.46410 q^{49} +6.19615 q^{51} -2.73205 q^{52} -1.73205 q^{53} +1.00000 q^{54} -0.732051 q^{56} +1.00000 q^{57} +1.73205 q^{58} -8.19615 q^{59} +10.6603 q^{61} +2.46410 q^{62} +0.732051 q^{63} +1.00000 q^{64} +3.73205 q^{66} -0.267949 q^{67} -6.19615 q^{68} -5.92820 q^{69} +12.1962 q^{71} -1.00000 q^{72} -2.46410 q^{73} +2.00000 q^{74} -1.00000 q^{76} +2.73205 q^{77} -2.73205 q^{78} -5.53590 q^{79} +1.00000 q^{81} +2.92820 q^{82} +3.73205 q^{83} -0.732051 q^{84} +8.19615 q^{86} +1.73205 q^{87} -3.73205 q^{88} +10.8564 q^{89} -2.00000 q^{91} +5.92820 q^{92} +2.46410 q^{93} -3.46410 q^{94} +1.00000 q^{96} -15.1244 q^{97} +6.46410 q^{98} +3.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{19} + 2 q^{21} - 4 q^{22} - 2 q^{23} + 2 q^{24} + 2 q^{26} - 2 q^{27} - 2 q^{28} + 2 q^{31} - 2 q^{32} - 4 q^{33} + 2 q^{34} + 2 q^{36} - 4 q^{37} + 2 q^{38} + 2 q^{39} + 8 q^{41} - 2 q^{42} - 6 q^{43} + 4 q^{44} + 2 q^{46} - 2 q^{48} - 6 q^{49} + 2 q^{51} - 2 q^{52} + 2 q^{54} + 2 q^{56} + 2 q^{57} - 6 q^{59} + 4 q^{61} - 2 q^{62} - 2 q^{63} + 2 q^{64} + 4 q^{66} - 4 q^{67} - 2 q^{68} + 2 q^{69} + 14 q^{71} - 2 q^{72} + 2 q^{73} + 4 q^{74} - 2 q^{76} + 2 q^{77} - 2 q^{78} - 18 q^{79} + 2 q^{81} - 8 q^{82} + 4 q^{83} + 2 q^{84} + 6 q^{86} - 4 q^{88} - 6 q^{89} - 4 q^{91} - 2 q^{92} - 2 q^{93} + 2 q^{96} - 6 q^{97} + 6 q^{98} + 4 q^{99}+O(q^{100}) \) 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 - 2 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^19 + 2 * q^21 - 4 * q^22 - 2 * q^23 + 2 * q^24 + 2 * q^26 - 2 * q^27 - 2 * q^28 + 2 * q^31 - 2 * q^32 - 4 * q^33 + 2 * q^34 + 2 * q^36 - 4 * q^37 + 2 * q^38 + 2 * q^39 + 8 * q^41 - 2 * q^42 - 6 * q^43 + 4 * q^44 + 2 * q^46 - 2 * q^48 - 6 * q^49 + 2 * q^51 - 2 * q^52 + 2 * q^54 + 2 * q^56 + 2 * q^57 - 6 * q^59 + 4 * q^61 - 2 * q^62 - 2 * q^63 + 2 * q^64 + 4 * q^66 - 4 * q^67 - 2 * q^68 + 2 * q^69 + 14 * q^71 - 2 * q^72 + 2 * q^73 + 4 * q^74 - 2 * q^76 + 2 * q^77 - 2 * q^78 - 18 * q^79 + 2 * q^81 - 8 * q^82 + 4 * q^83 + 2 * q^84 + 6 * q^86 - 4 * q^88 - 6 * q^89 - 4 * q^91 - 2 * q^92 - 2 * q^93 + 2 * q^96 - 6 * q^97 + 6 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more