LMFDB - Embedded newform 2850.2.a.bc.1.1

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(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
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			1.1
Root			$-2.44949$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.44949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.44949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.44949 q^{11} -1.00000 q^{12} +2.44949 q^{13} +4.44949 q^{14} +1.00000 q^{16} -4.44949 q^{17} -1.00000 q^{18} +1.00000 q^{19} +4.44949 q^{21} -3.44949 q^{22} +1.00000 q^{23} +1.00000 q^{24} -2.44949 q^{26} -1.00000 q^{27} -4.44949 q^{28} -4.34847 q^{29} -3.00000 q^{31} -1.00000 q^{32} -3.44949 q^{33} +4.44949 q^{34} +1.00000 q^{36} +7.79796 q^{37} -1.00000 q^{38} -2.44949 q^{39} -0.898979 q^{41} -4.44949 q^{42} +2.44949 q^{43} +3.44949 q^{44} -1.00000 q^{46} +7.79796 q^{47} -1.00000 q^{48} +12.7980 q^{49} +4.44949 q^{51} +2.44949 q^{52} +7.44949 q^{53} +1.00000 q^{54} +4.44949 q^{56} -1.00000 q^{57} +4.34847 q^{58} +6.44949 q^{59} -9.44949 q^{61} +3.00000 q^{62} -4.44949 q^{63} +1.00000 q^{64} +3.44949 q^{66} -15.2474 q^{67} -4.44949 q^{68} -1.00000 q^{69} -1.55051 q^{71} -1.00000 q^{72} +1.00000 q^{73} -7.79796 q^{74} +1.00000 q^{76} -15.3485 q^{77} +2.44949 q^{78} -5.00000 q^{79} +1.00000 q^{81} +0.898979 q^{82} -8.34847 q^{83} +4.44949 q^{84} -2.44949 q^{86} +4.34847 q^{87} -3.44949 q^{88} +2.10102 q^{89} -10.8990 q^{91} +1.00000 q^{92} +3.00000 q^{93} -7.79796 q^{94} +1.00000 q^{96} -1.55051 q^{97} -12.7980 q^{98} +3.44949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 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 - 4 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} - 2 q^{12} + 4 q^{14} + 2 q^{16} - 4 q^{17} - 2 q^{18} + 2 q^{19} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 2 q^{24} - 2 q^{27} - 4 q^{28} + 6 q^{29} - 6 q^{31} - 2 q^{32} - 2 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} - 2 q^{38} + 8 q^{41} - 4 q^{42} + 2 q^{44} - 2 q^{46} - 4 q^{47} - 2 q^{48} + 6 q^{49} + 4 q^{51} + 10 q^{53} + 2 q^{54} + 4 q^{56} - 2 q^{57} - 6 q^{58} + 8 q^{59} - 14 q^{61} + 6 q^{62} - 4 q^{63} + 2 q^{64} + 2 q^{66} - 6 q^{67} - 4 q^{68} - 2 q^{69} - 8 q^{71} - 2 q^{72} + 2 q^{73} + 4 q^{74} + 2 q^{76} - 16 q^{77} - 10 q^{79} + 2 q^{81} - 8 q^{82} - 2 q^{83} + 4 q^{84} - 6 q^{87} - 2 q^{88} + 14 q^{89} - 12 q^{91} + 2 q^{92} + 6 q^{93} + 4 q^{94} + 2 q^{96} - 8 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 - 2 * q^12 + 4 * q^14 + 2 * q^16 - 4 * q^17 - 2 * q^18 + 2 * q^19 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 2 * q^24 - 2 * q^27 - 4 * q^28 + 6 * q^29 - 6 * q^31 - 2 * q^32 - 2 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 - 2 * q^38 + 8 * q^41 - 4 * q^42 + 2 * q^44 - 2 * q^46 - 4 * q^47 - 2 * q^48 + 6 * q^49 + 4 * q^51 + 10 * q^53 + 2 * q^54 + 4 * q^56 - 2 * q^57 - 6 * q^58 + 8 * q^59 - 14 * q^61 + 6 * q^62 - 4 * q^63 + 2 * q^64 + 2 * q^66 - 6 * q^67 - 4 * q^68 - 2 * q^69 - 8 * q^71 - 2 * q^72 + 2 * q^73 + 4 * q^74 + 2 * q^76 - 16 * q^77 - 10 * q^79 + 2 * q^81 - 8 * q^82 - 2 * q^83 + 4 * q^84 - 6 * q^87 - 2 * q^88 + 14 * q^89 - 12 * q^91 + 2 * q^92 + 6 * q^93 + 4 * q^94 + 2 * q^96 - 8 * q^97 - 6 * q^98 + 2 * 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
$7$	−4.44949	−1.68175	−0.840875	−	0.541230i	$-0.817959\pi$
$7$	−4.44949	−1.68175	−0.840875	+	0.541230i	$0.817959\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	3.44949	1.04006	0.520030	−	0.854148i	$-0.325921\pi$
$11$	3.44949	1.04006	0.520030	+	0.854148i	$0.325921\pi$
$12$	−1.00000	−0.288675
$13$	2.44949	0.679366	0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949	0.679366	0.339683	+	0.940540i	$0.389680\pi$
$14$	4.44949	1.18918
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.44949	−1.07916	−0.539580	−	0.841934i	$-0.681417\pi$
$17$	−4.44949	−1.07916	−0.539580	+	0.841934i	$0.681417\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	4.44949	0.970958
$22$	−3.44949	−0.735434
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−2.44949	−0.480384
$27$	−1.00000	−0.192450
$28$	−4.44949	−0.840875
$29$	−4.34847	−0.807490	−0.403745	−	0.914871i	$-0.632292\pi$
$29$	−4.34847	−0.807490	−0.403745	+	0.914871i	$0.632292\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	−1.00000	−0.176777
$33$	−3.44949	−0.600479
$34$	4.44949	0.763081
$35$	0	0
$36$	1.00000	0.166667
$37$	7.79796	1.28198	0.640988	−	0.767551i	$-0.278525\pi$
$37$	7.79796	1.28198	0.640988	+	0.767551i	$0.278525\pi$
$38$	−1.00000	−0.162221
$39$	−2.44949	−0.392232
$40$	0	0
$41$	−0.898979	−0.140397	−0.0701985	−	0.997533i	$-0.522363\pi$
$41$	−0.898979	−0.140397	−0.0701985	+	0.997533i	$0.522363\pi$
$42$	−4.44949	−0.686571
$43$	2.44949	0.373544	0.186772	−	0.982403i	$-0.440197\pi$
$43$	2.44949	0.373544	0.186772	+	0.982403i	$0.440197\pi$
$44$	3.44949	0.520030
$45$	0	0
$46$	−1.00000	−0.147442
$47$	7.79796	1.13745	0.568725	−	0.822528i	$-0.307437\pi$
$47$	7.79796	1.13745	0.568725	+	0.822528i	$0.307437\pi$
$48$	−1.00000	−0.144338
$49$	12.7980	1.82828
$50$	0	0
$51$	4.44949	0.623053
$52$	2.44949	0.339683
$53$	7.44949	1.02327	0.511633	−	0.859204i	$-0.329041\pi$
$53$	7.44949	1.02327	0.511633	+	0.859204i	$0.329041\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	4.44949	0.594588
$57$	−1.00000	−0.132453
$58$	4.34847	0.570982
$59$	6.44949	0.839652	0.419826	−	0.907605i	$-0.362091\pi$
$59$	6.44949	0.839652	0.419826	+	0.907605i	$0.362091\pi$
$60$	0	0
$61$	−9.44949	−1.20988	−0.604942	−	0.796270i	$-0.706804\pi$
$61$	−9.44949	−1.20988	−0.604942	+	0.796270i	$0.706804\pi$
$62$	3.00000	0.381000
$63$	−4.44949	−0.560583
$64$	1.00000	0.125000
$65$	0	0
$66$	3.44949	0.424603
$67$	−15.2474	−1.86277	−0.931386	−	0.364033i	$-0.881400\pi$
$67$	−15.2474	−1.86277	−0.931386	+	0.364033i	$0.881400\pi$
$68$	−4.44949	−0.539580
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−1.55051	−0.184012	−0.0920059	−	0.995758i	$-0.529328\pi$
$71$	−1.55051	−0.184012	−0.0920059	+	0.995758i	$0.529328\pi$
$72$	−1.00000	−0.117851
$73$	1.00000	0.117041	0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000	0.117041	0.0585206	+	0.998286i	$0.481362\pi$
$74$	−7.79796	−0.906494
$75$	0	0
$76$	1.00000	0.114708
$77$	−15.3485	−1.74912
$78$	2.44949	0.277350
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0.898979	0.0992757
$83$	−8.34847	−0.916364	−0.458182	−	0.888859i	$-0.651499\pi$
$83$	−8.34847	−0.916364	−0.458182	+	0.888859i	$0.651499\pi$
$84$	4.44949	0.485479
$85$	0	0
$86$	−2.44949	−0.264135
$87$	4.34847	0.466205
$88$	−3.44949	−0.367717
$89$	2.10102	0.222708	0.111354	−	0.993781i	$-0.464481\pi$
$89$	2.10102	0.222708	0.111354	+	0.993781i	$0.464481\pi$
$90$	0	0
$91$	−10.8990	−1.14252
$92$	1.00000	0.104257
$93$	3.00000	0.311086
$94$	−7.79796	−0.804298
$95$	0	0
$96$	1.00000	0.102062
$97$	−1.55051	−0.157430	−0.0787152	−	0.996897i	$-0.525082\pi$
$97$	−1.55051	−0.157430	−0.0787152	+	0.996897i	$0.525082\pi$
$98$	−12.7980	−1.29279
$99$	3.44949	0.346687
$100$	0	0
$101$	−1.55051	−0.154282	−0.0771408	−	0.997020i	$-0.524579\pi$
$101$	−1.55051	−0.154282	−0.0771408	+	0.997020i	$0.524579\pi$
$102$	−4.44949	−0.440565
$103$	−1.89898	−0.187112	−0.0935560	−	0.995614i	$-0.529823\pi$
$103$	−1.89898	−0.187112	−0.0935560	+	0.995614i	$0.529823\pi$
$104$	−2.44949	−0.240192
$105$	0	0
$106$	−7.44949	−0.723558
$107$	−17.3485	−1.67714	−0.838570	−	0.544794i	$-0.816608\pi$
$107$	−17.3485	−1.67714	−0.838570	+	0.544794i	$0.816608\pi$
$108$	−1.00000	−0.0962250
$109$	−2.89898	−0.277672	−0.138836	−	0.990315i	$-0.544336\pi$
$109$	−2.89898	−0.277672	−0.138836	+	0.990315i	$0.544336\pi$
$110$	0	0
$111$	−7.79796	−0.740150
$112$	−4.44949	−0.420437
$113$	16.7980	1.58022	0.790110	−	0.612966i	$-0.210024\pi$
$113$	16.7980	1.58022	0.790110	+	0.612966i	$0.210024\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	−4.34847	−0.403745
$117$	2.44949	0.226455
$118$	−6.44949	−0.593724
$119$	19.7980	1.81488
$120$	0	0
$121$	0.898979	0.0817254
$122$	9.44949	0.855517
$123$	0.898979	0.0810583
$124$	−3.00000	−0.269408
$125$	0	0
$126$	4.44949	0.396392
$127$	−0.101021	−0.00896412	−0.00448206	−	0.999990i	$-0.501427\pi$
$127$	−0.101021	−0.00896412	−0.00448206	+	0.999990i	$0.501427\pi$
$128$	−1.00000	−0.0883883
$129$	−2.44949	−0.215666
$130$	0	0
$131$	9.24745	0.807953	0.403977	−	0.914769i	$-0.367628\pi$
$131$	9.24745	0.807953	0.403977	+	0.914769i	$0.367628\pi$
$132$	−3.44949	−0.300240
$133$	−4.44949	−0.385820
$134$	15.2474	1.31718
$135$	0	0
$136$	4.44949	0.381541
$137$	4.89898	0.418548	0.209274	−	0.977857i	$-0.432890\pi$
$137$	4.89898	0.418548	0.209274	+	0.977857i	$0.432890\pi$
$138$	1.00000	0.0851257
$139$	−22.2474	−1.88700	−0.943502	−	0.331367i	$-0.892490\pi$
$139$	−22.2474	−1.88700	−0.943502	+	0.331367i	$0.892490\pi$
$140$	0	0
$141$	−7.79796	−0.656707
$142$	1.55051	0.130116
$143$	8.44949	0.706582
$144$	1.00000	0.0833333
$145$	0	0
$146$	−1.00000	−0.0827606
$147$	−12.7980	−1.05556
$148$	7.79796	0.640988
$149$	5.79796	0.474987	0.237494	−	0.971389i	$-0.423674\pi$
$149$	5.79796	0.474987	0.237494	+	0.971389i	$0.423674\pi$
$150$	0	0
$151$	−23.7980	−1.93665	−0.968325	−	0.249692i	$-0.919671\pi$
$151$	−23.7980	−1.93665	−0.968325	+	0.249692i	$0.919671\pi$
$152$	−1.00000	−0.0811107
$153$	−4.44949	−0.359720
$154$	15.3485	1.23681
$155$	0	0
$156$	−2.44949	−0.196116
$157$	4.89898	0.390981	0.195491	−	0.980706i	$-0.437370\pi$
$157$	4.89898	0.390981	0.195491	+	0.980706i	$0.437370\pi$
$158$	5.00000	0.397779
$159$	−7.44949	−0.590783
$160$	0	0
$161$	−4.44949	−0.350669
$162$	−1.00000	−0.0785674
$163$	−19.7980	−1.55070	−0.775348	−	0.631534i	$-0.782425\pi$
$163$	−19.7980	−1.55070	−0.775348	+	0.631534i	$0.782425\pi$
$164$	−0.898979	−0.0701985
$165$	0	0
$166$	8.34847	0.647967
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	−4.44949	−0.343286
$169$	−7.00000	−0.538462
$170$	0	0
$171$	1.00000	0.0764719
$172$	2.44949	0.186772
$173$	1.65153	0.125564	0.0627818	−	0.998027i	$-0.480003\pi$
$173$	1.65153	0.125564	0.0627818	+	0.998027i	$0.480003\pi$
$174$	−4.34847	−0.329657
$175$	0	0
$176$	3.44949	0.260015
$177$	−6.44949	−0.484773
$178$	−2.10102	−0.157478
$179$	25.7980	1.92823	0.964115	−	0.265485i	$-0.0855321\pi$
$179$	25.7980	1.92823	0.964115	+	0.265485i	$0.0855321\pi$
$180$	0	0
$181$	−14.4495	−1.07402	−0.537011	−	0.843575i	$-0.680447\pi$
$181$	−14.4495	−1.07402	−0.537011	+	0.843575i	$0.680447\pi$
$182$	10.8990	0.807886
$183$	9.44949	0.698526
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−3.00000	−0.219971
$187$	−15.3485	−1.12239
$188$	7.79796	0.568725
$189$	4.44949	0.323653
$190$	0	0
$191$	−0.101021	−0.00730959	−0.00365479	−	0.999993i	$-0.501163\pi$
$191$	−0.101021	−0.00730959	−0.00365479	+	0.999993i	$0.501163\pi$
$192$	−1.00000	−0.0721688
$193$	15.3485	1.10481	0.552403	−	0.833577i	$-0.313711\pi$
$193$	15.3485	1.10481	0.552403	+	0.833577i	$0.313711\pi$
$194$	1.55051	0.111320
$195$	0	0
$196$	12.7980	0.914140
$197$	−27.3485	−1.94850	−0.974249	−	0.225475i	$-0.927606\pi$
$197$	−27.3485	−1.94850	−0.974249	+	0.225475i	$0.927606\pi$
$198$	−3.44949	−0.245145
$199$	−10.0000	−0.708881	−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000	−0.708881	−0.354441	+	0.935079i	$0.615329\pi$
$200$	0	0
$201$	15.2474	1.07547
$202$	1.55051	0.109094
$203$	19.3485	1.35800
$204$	4.44949	0.311527
$205$	0	0
$206$	1.89898	0.132308
$207$	1.00000	0.0695048
$208$	2.44949	0.169842
$209$	3.44949	0.238606
$210$	0	0
$211$	−3.65153	−0.251382	−0.125691	−	0.992069i	$-0.540115\pi$
$211$	−3.65153	−0.251382	−0.125691	+	0.992069i	$0.540115\pi$
$212$	7.44949	0.511633
$213$	1.55051	0.106239
$214$	17.3485	1.18592
$215$	0	0
$216$	1.00000	0.0680414
$217$	13.3485	0.906153
$218$	2.89898	0.196344
$219$	−1.00000	−0.0675737
$220$	0	0
$221$	−10.8990	−0.733145
$222$	7.79796	0.523365
$223$	−16.1010	−1.07820	−0.539102	−	0.842240i	$-0.681236\pi$
$223$	−16.1010	−1.07820	−0.539102	+	0.842240i	$0.681236\pi$
$224$	4.44949	0.297294
$225$	0	0
$226$	−16.7980	−1.11738
$227$	−29.5959	−1.96435	−0.982175	−	0.187969i	$-0.939810\pi$
$227$	−29.5959	−1.96435	−0.982175	+	0.187969i	$0.939810\pi$
$228$	−1.00000	−0.0662266
$229$	7.24745	0.478925	0.239462	−	0.970906i	$-0.423029\pi$
$229$	7.24745	0.478925	0.239462	+	0.970906i	$0.423029\pi$
$230$	0	0
$231$	15.3485	1.00986
$232$	4.34847	0.285491
$233$	−6.24745	−0.409284	−0.204642	−	0.978837i	$-0.565603\pi$
$233$	−6.24745	−0.409284	−0.204642	+	0.978837i	$0.565603\pi$
$234$	−2.44949	−0.160128
$235$	0	0
$236$	6.44949	0.419826
$237$	5.00000	0.324785
$238$	−19.7980	−1.28331
$239$	−8.69694	−0.562558	−0.281279	−	0.959626i	$-0.590759\pi$
$239$	−8.69694	−0.562558	−0.281279	+	0.959626i	$0.590759\pi$
$240$	0	0
$241$	−4.44949	−0.286617	−0.143308	−	0.989678i	$-0.545774\pi$
$241$	−4.44949	−0.286617	−0.143308	+	0.989678i	$0.545774\pi$
$242$	−0.898979	−0.0577886
$243$	−1.00000	−0.0641500
$244$	−9.44949	−0.604942
$245$	0	0
$246$	−0.898979	−0.0573168
$247$	2.44949	0.155857
$248$	3.00000	0.190500
$249$	8.34847	0.529063
$250$	0	0
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	−4.44949	−0.280292
$253$	3.44949	0.216868
$254$	0.101021	0.00633859
$255$	0	0
$256$	1.00000	0.0625000
$257$	21.4949	1.34081	0.670407	−	0.741993i	$-0.266119\pi$
$257$	21.4949	1.34081	0.670407	+	0.741993i	$0.266119\pi$
$258$	2.44949	0.152499
$259$	−34.6969	−2.15596
$260$	0	0
$261$	−4.34847	−0.269163
$262$	−9.24745	−0.571309
$263$	6.79796	0.419180	0.209590	−	0.977789i	$-0.432787\pi$
$263$	6.79796	0.419180	0.209590	+	0.977789i	$0.432787\pi$
$264$	3.44949	0.212301
$265$	0	0
$266$	4.44949	0.272816
$267$	−2.10102	−0.128580
$268$	−15.2474	−0.931386
$269$	−2.89898	−0.176754	−0.0883769	−	0.996087i	$-0.528168\pi$
$269$	−2.89898	−0.176754	−0.0883769	+	0.996087i	$0.528168\pi$
$270$	0	0
$271$	22.9444	1.39377	0.696886	−	0.717182i	$-0.254568\pi$
$271$	22.9444	1.39377	0.696886	+	0.717182i	$0.254568\pi$
$272$	−4.44949	−0.269790
$273$	10.8990	0.659636
$274$	−4.89898	−0.295958
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	−21.0454	−1.26450	−0.632248	−	0.774766i	$-0.717868\pi$
$277$	−21.0454	−1.26450	−0.632248	+	0.774766i	$0.717868\pi$
$278$	22.2474	1.33431
$279$	−3.00000	−0.179605
$280$	0	0
$281$	7.00000	0.417585	0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000	0.417585	0.208792	+	0.977960i	$0.433047\pi$
$282$	7.79796	0.464362
$283$	−29.7980	−1.77130	−0.885652	−	0.464349i	$-0.846288\pi$
$283$	−29.7980	−1.77130	−0.885652	+	0.464349i	$0.846288\pi$
$284$	−1.55051	−0.0920059
$285$	0	0
$286$	−8.44949	−0.499629
$287$	4.00000	0.236113
$288$	−1.00000	−0.0589256
$289$	2.79796	0.164586
$290$	0	0
$291$	1.55051	0.0908925
$292$	1.00000	0.0585206
$293$	23.2474	1.35813	0.679065	−	0.734078i	$-0.262385\pi$
$293$	23.2474	1.35813	0.679065	+	0.734078i	$0.262385\pi$
$294$	12.7980	0.746392
$295$	0	0
$296$	−7.79796	−0.453247
$297$	−3.44949	−0.200160
$298$	−5.79796	−0.335867
$299$	2.44949	0.141658
$300$	0	0
$301$	−10.8990	−0.628207
$302$	23.7980	1.36942
$303$	1.55051	0.0890745
$304$	1.00000	0.0573539
$305$	0	0
$306$	4.44949	0.254360
$307$	16.3485	0.933056	0.466528	−	0.884506i	$-0.345505\pi$
$307$	16.3485	0.933056	0.466528	+	0.884506i	$0.345505\pi$
$308$	−15.3485	−0.874560
$309$	1.89898	0.108029
$310$	0	0
$311$	−23.7980	−1.34946	−0.674729	−	0.738065i	$-0.735740\pi$
$311$	−23.7980	−1.34946	−0.674729	+	0.738065i	$0.735740\pi$
$312$	2.44949	0.138675
$313$	−31.8990	−1.80304	−0.901518	−	0.432741i	$-0.857547\pi$
$313$	−31.8990	−1.80304	−0.901518	+	0.432741i	$0.857547\pi$
$314$	−4.89898	−0.276465
$315$	0	0
$316$	−5.00000	−0.281272
$317$	−15.2474	−0.856382	−0.428191	−	0.903688i	$-0.640849\pi$
$317$	−15.2474	−0.856382	−0.428191	+	0.903688i	$0.640849\pi$
$318$	7.44949	0.417747
$319$	−15.0000	−0.839839
$320$	0	0
$321$	17.3485	0.968297
$322$	4.44949	0.247960
$323$	−4.44949	−0.247576
$324$	1.00000	0.0555556
$325$	0	0
$326$	19.7980	1.09651
$327$	2.89898	0.160314
$328$	0.898979	0.0496378
$329$	−34.6969	−1.91290
$330$	0	0
$331$	−22.3485	−1.22838	−0.614191	−	0.789157i	$-0.710518\pi$
$331$	−22.3485	−1.22838	−0.614191	+	0.789157i	$0.710518\pi$
$332$	−8.34847	−0.458182
$333$	7.79796	0.427326
$334$	18.0000	0.984916
$335$	0	0
$336$	4.44949	0.242740
$337$	24.8990	1.35633	0.678167	−	0.734908i	$-0.262775\pi$
$337$	24.8990	1.35633	0.678167	+	0.734908i	$0.262775\pi$
$338$	7.00000	0.380750
$339$	−16.7980	−0.912340
$340$	0	0
$341$	−10.3485	−0.560401
$342$	−1.00000	−0.0540738
$343$	−25.7980	−1.39296
$344$	−2.44949	−0.132068
$345$	0	0
$346$	−1.65153	−0.0887868
$347$	23.5959	1.26670	0.633348	−	0.773867i	$-0.281680\pi$
$347$	23.5959	1.26670	0.633348	+	0.773867i	$0.281680\pi$
$348$	4.34847	0.233102
$349$	−25.9444	−1.38877	−0.694386	−	0.719603i	$-0.744324\pi$
$349$	−25.9444	−1.38877	−0.694386	+	0.719603i	$0.744324\pi$
$350$	0	0
$351$	−2.44949	−0.130744
$352$	−3.44949	−0.183858
$353$	18.2474	0.971214	0.485607	−	0.874177i	$-0.338599\pi$
$353$	18.2474	0.971214	0.485607	+	0.874177i	$0.338599\pi$
$354$	6.44949	0.342787
$355$	0	0
$356$	2.10102	0.111354
$357$	−19.7980	−1.04782
$358$	−25.7980	−1.36346
$359$	−22.8990	−1.20856	−0.604281	−	0.796771i	$-0.706540\pi$
$359$	−22.8990	−1.20856	−0.604281	+	0.796771i	$0.706540\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	14.4495	0.759448
$363$	−0.898979	−0.0471842
$364$	−10.8990	−0.571262
$365$	0	0
$366$	−9.44949	−0.493933
$367$	5.55051	0.289734	0.144867	−	0.989451i	$-0.453725\pi$
$367$	5.55051	0.289734	0.144867	+	0.989451i	$0.453725\pi$
$368$	1.00000	0.0521286
$369$	−0.898979	−0.0467990
$370$	0	0
$371$	−33.1464	−1.72088
$372$	3.00000	0.155543
$373$	22.4495	1.16239	0.581195	−	0.813764i	$-0.302585\pi$
$373$	22.4495	1.16239	0.581195	+	0.813764i	$0.302585\pi$
$374$	15.3485	0.793650
$375$	0	0
$376$	−7.79796	−0.402149
$377$	−10.6515	−0.548582
$378$	−4.44949	−0.228857
$379$	−1.30306	−0.0669338	−0.0334669	−	0.999440i	$-0.510655\pi$
$379$	−1.30306	−0.0669338	−0.0334669	+	0.999440i	$0.510655\pi$
$380$	0	0
$381$	0.101021	0.00517544
$382$	0.101021	0.00516866
$383$	−16.2474	−0.830206	−0.415103	−	0.909774i	$-0.636254\pi$
$383$	−16.2474	−0.830206	−0.415103	+	0.909774i	$0.636254\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−15.3485	−0.781217
$387$	2.44949	0.124515
$388$	−1.55051	−0.0787152
$389$	21.5959	1.09496	0.547478	−	0.836820i	$-0.315588\pi$
$389$	21.5959	1.09496	0.547478	+	0.836820i	$0.315588\pi$
$390$	0	0
$391$	−4.44949	−0.225020
$392$	−12.7980	−0.646395
$393$	−9.24745	−0.466472
$394$	27.3485	1.37780
$395$	0	0
$396$	3.44949	0.173343
$397$	−23.9444	−1.20173	−0.600867	−	0.799349i	$-0.705178\pi$
$397$	−23.9444	−1.20173	−0.600867	+	0.799349i	$0.705178\pi$
$398$	10.0000	0.501255
$399$	4.44949	0.222753
$400$	0	0
$401$	11.2020	0.559403	0.279702	−	0.960087i	$-0.409764\pi$
$401$	11.2020	0.559403	0.279702	+	0.960087i	$0.409764\pi$
$402$	−15.2474	−0.760474
$403$	−7.34847	−0.366053
$404$	−1.55051	−0.0771408
$405$	0	0
$406$	−19.3485	−0.960248
$407$	26.8990	1.33333
$408$	−4.44949	−0.220283
$409$	−22.8990	−1.13228	−0.566141	−	0.824309i	$-0.691564\pi$
$409$	−22.8990	−1.13228	−0.566141	+	0.824309i	$0.691564\pi$
$410$	0	0
$411$	−4.89898	−0.241649
$412$	−1.89898	−0.0935560
$413$	−28.6969	−1.41208
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	−2.44949	−0.120096
$417$	22.2474	1.08946
$418$	−3.44949	−0.168720
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	3.65153	0.177754
$423$	7.79796	0.379150
$424$	−7.44949	−0.361779
$425$	0	0
$426$	−1.55051	−0.0751225
$427$	42.0454	2.03472
$428$	−17.3485	−0.838570
$429$	−8.44949	−0.407945
$430$	0	0
$431$	−5.10102	−0.245708	−0.122854	−	0.992425i	$-0.539205\pi$
$431$	−5.10102	−0.245708	−0.122854	+	0.992425i	$0.539205\pi$
$432$	−1.00000	−0.0481125
$433$	−4.65153	−0.223538	−0.111769	−	0.993734i	$-0.535652\pi$
$433$	−4.65153	−0.223538	−0.111769	+	0.993734i	$0.535652\pi$
$434$	−13.3485	−0.640747
$435$	0	0
$436$	−2.89898	−0.138836
$437$	1.00000	0.0478365
$438$	1.00000	0.0477818
$439$	−12.1010	−0.577550	−0.288775	−	0.957397i	$-0.593248\pi$
$439$	−12.1010	−0.577550	−0.288775	+	0.957397i	$0.593248\pi$
$440$	0	0
$441$	12.7980	0.609427
$442$	10.8990	0.518412
$443$	−21.2474	−1.00950	−0.504748	−	0.863267i	$-0.668415\pi$
$443$	−21.2474	−1.00950	−0.504748	+	0.863267i	$0.668415\pi$
$444$	−7.79796	−0.370075
$445$	0	0
$446$	16.1010	0.762405
$447$	−5.79796	−0.274234
$448$	−4.44949	−0.210219
$449$	−15.0000	−0.707894	−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000	−0.707894	−0.353947	+	0.935266i	$0.615161\pi$
$450$	0	0
$451$	−3.10102	−0.146021
$452$	16.7980	0.790110
$453$	23.7980	1.11813
$454$	29.5959	1.38901
$455$	0	0
$456$	1.00000	0.0468293
$457$	24.8990	1.16473	0.582363	−	0.812929i	$-0.302128\pi$
$457$	24.8990	1.16473	0.582363	+	0.812929i	$0.302128\pi$
$458$	−7.24745	−0.338651
$459$	4.44949	0.207684
$460$	0	0
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	−15.3485	−0.714075
$463$	14.6969	0.683025	0.341512	−	0.939877i	$-0.389061\pi$
$463$	14.6969	0.683025	0.341512	+	0.939877i	$0.389061\pi$
$464$	−4.34847	−0.201873
$465$	0	0
$466$	6.24745	0.289407
$467$	6.34847	0.293772	0.146886	−	0.989153i	$-0.453075\pi$
$467$	6.34847	0.293772	0.146886	+	0.989153i	$0.453075\pi$
$468$	2.44949	0.113228
$469$	67.8434	3.13272
$470$	0	0
$471$	−4.89898	−0.225733
$472$	−6.44949	−0.296862
$473$	8.44949	0.388508
$474$	−5.00000	−0.229658
$475$	0	0
$476$	19.7980	0.907438
$477$	7.44949	0.341089
$478$	8.69694	0.397789
$479$	16.5959	0.758287	0.379143	−	0.925338i	$-0.376219\pi$
$479$	16.5959	0.758287	0.379143	+	0.925338i	$0.376219\pi$
$480$	0	0
$481$	19.1010	0.870932
$482$	4.44949	0.202669
$483$	4.44949	0.202459
$484$	0.898979	0.0408627
$485$	0	0
$486$	1.00000	0.0453609
$487$	32.0000	1.45006	0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000	1.45006	0.725029	+	0.688718i	$0.241826\pi$
$488$	9.44949	0.427758
$489$	19.7980	0.895295
$490$	0	0
$491$	43.5959	1.96746	0.983728	−	0.179664i	$-0.0575009\pi$
$491$	43.5959	1.96746	0.983728	+	0.179664i	$0.0575009\pi$
$492$	0.898979	0.0405291
$493$	19.3485	0.871411
$494$	−2.44949	−0.110208
$495$	0	0
$496$	−3.00000	−0.134704
$497$	6.89898	0.309462
$498$	−8.34847	−0.374104
$499$	−23.8434	−1.06738	−0.533688	−	0.845682i	$-0.679194\pi$
$499$	−23.8434	−1.06738	−0.533688	+	0.845682i	$0.679194\pi$
$500$	0	0
$501$	18.0000	0.804181
$502$	18.0000	0.803379
$503$	−29.7980	−1.32863	−0.664313	−	0.747455i	$-0.731276\pi$
$503$	−29.7980	−1.32863	−0.664313	+	0.747455i	$0.731276\pi$
$504$	4.44949	0.198196
$505$	0	0
$506$	−3.44949	−0.153349
$507$	7.00000	0.310881
$508$	−0.101021	−0.00448206
$509$	−30.1464	−1.33622	−0.668108	−	0.744064i	$-0.732896\pi$
$509$	−30.1464	−1.33622	−0.668108	+	0.744064i	$0.732896\pi$
$510$	0	0
$511$	−4.44949	−0.196834
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−21.4949	−0.948099
$515$	0	0
$516$	−2.44949	−0.107833
$517$	26.8990	1.18302
$518$	34.6969	1.52450
$519$	−1.65153	−0.0724942
$520$	0	0
$521$	15.6969	0.687695	0.343848	−	0.939025i	$-0.388270\pi$
$521$	15.6969	0.687695	0.343848	+	0.939025i	$0.388270\pi$
$522$	4.34847	0.190327
$523$	33.3939	1.46021	0.730106	−	0.683334i	$-0.239471\pi$
$523$	33.3939	1.46021	0.730106	+	0.683334i	$0.239471\pi$
$524$	9.24745	0.403977
$525$	0	0
$526$	−6.79796	−0.296405
$527$	13.3485	0.581468
$528$	−3.44949	−0.150120
$529$	−22.0000	−0.956522
$530$	0	0
$531$	6.44949	0.279884
$532$	−4.44949	−0.192910
$533$	−2.20204	−0.0953810
$534$	2.10102	0.0909200
$535$	0	0
$536$	15.2474	0.658589
$537$	−25.7980	−1.11326
$538$	2.89898	0.124984
$539$	44.1464	1.90152
$540$	0	0
$541$	22.1464	0.952149	0.476075	−	0.879405i	$-0.342059\pi$
$541$	22.1464	0.952149	0.476075	+	0.879405i	$0.342059\pi$
$542$	−22.9444	−0.985546
$543$	14.4495	0.620087
$544$	4.44949	0.190770
$545$	0	0
$546$	−10.8990	−0.466433
$547$	46.6413	1.99424	0.997120	−	0.0758461i	$-0.0241658\pi$
$547$	46.6413	1.99424	0.997120	+	0.0758461i	$0.0241658\pi$
$548$	4.89898	0.209274
$549$	−9.44949	−0.403294
$550$	0	0
$551$	−4.34847	−0.185251
$552$	1.00000	0.0425628
$553$	22.2474	0.946058
$554$	21.0454	0.894134
$555$	0	0
$556$	−22.2474	−0.943502
$557$	−27.3485	−1.15879	−0.579396	−	0.815046i	$-0.696711\pi$
$557$	−27.3485	−1.15879	−0.579396	+	0.815046i	$0.696711\pi$
$558$	3.00000	0.127000
$559$	6.00000	0.253773
$560$	0	0
$561$	15.3485	0.648013
$562$	−7.00000	−0.295277
$563$	−6.24745	−0.263299	−0.131649	−	0.991296i	$-0.542027\pi$
$563$	−6.24745	−0.263299	−0.131649	+	0.991296i	$0.542027\pi$
$564$	−7.79796	−0.328353
$565$	0	0
$566$	29.7980	1.25250
$567$	−4.44949	−0.186861
$568$	1.55051	0.0650580
$569$	−33.1918	−1.39147	−0.695737	−	0.718297i	$-0.744922\pi$
$569$	−33.1918	−1.39147	−0.695737	+	0.718297i	$0.744922\pi$
$570$	0	0
$571$	−10.2474	−0.428842	−0.214421	−	0.976741i	$-0.568787\pi$
$571$	−10.2474	−0.428842	−0.214421	+	0.976741i	$0.568787\pi$
$572$	8.44949	0.353291
$573$	0.101021	0.00422019
$574$	−4.00000	−0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	−0.101021	−0.00420554	−0.00210277	−	0.999998i	$-0.500669\pi$
$577$	−0.101021	−0.00420554	−0.00210277	+	0.999998i	$0.500669\pi$
$578$	−2.79796	−0.116380
$579$	−15.3485	−0.637861
$580$	0	0
$581$	37.1464	1.54109
$582$	−1.55051	−0.0642707
$583$	25.6969	1.06426
$584$	−1.00000	−0.0413803
$585$	0	0
$586$	−23.2474	−0.960343
$587$	33.4495	1.38061	0.690304	−	0.723519i	$-0.257477\pi$
$587$	33.4495	1.38061	0.690304	+	0.723519i	$0.257477\pi$
$588$	−12.7980	−0.527779
$589$	−3.00000	−0.123613
$590$	0	0
$591$	27.3485	1.12497
$592$	7.79796	0.320494
$593$	−8.49490	−0.348844	−0.174422	−	0.984671i	$-0.555806\pi$
$593$	−8.49490	−0.348844	−0.174422	+	0.984671i	$0.555806\pi$
$594$	3.44949	0.141534
$595$	0	0
$596$	5.79796	0.237494
$597$	10.0000	0.409273
$598$	−2.44949	−0.100167
$599$	16.4495	0.672108	0.336054	−	0.941843i	$-0.390908\pi$
$599$	16.4495	0.672108	0.336054	+	0.941843i	$0.390908\pi$
$600$	0	0
$601$	17.1464	0.699417	0.349709	−	0.936858i	$-0.386281\pi$
$601$	17.1464	0.699417	0.349709	+	0.936858i	$0.386281\pi$
$602$	10.8990	0.444209
$603$	−15.2474	−0.620924
$604$	−23.7980	−0.968325
$605$	0	0
$606$	−1.55051	−0.0629852
$607$	−46.1918	−1.87487	−0.937434	−	0.348162i	$-0.886806\pi$
$607$	−46.1918	−1.87487	−0.937434	+	0.348162i	$0.886806\pi$
$608$	−1.00000	−0.0405554
$609$	−19.3485	−0.784040
$610$	0	0
$611$	19.1010	0.772745
$612$	−4.44949	−0.179860
$613$	−37.1918	−1.50216	−0.751082	−	0.660209i	$-0.770468\pi$
$613$	−37.1918	−1.50216	−0.751082	+	0.660209i	$0.770468\pi$
$614$	−16.3485	−0.659771
$615$	0	0
$616$	15.3485	0.618407
$617$	−28.2929	−1.13903	−0.569514	−	0.821982i	$-0.692868\pi$
$617$	−28.2929	−1.13903	−0.569514	+	0.821982i	$0.692868\pi$
$618$	−1.89898	−0.0763882
$619$	45.1464	1.81459	0.907294	−	0.420497i	$-0.138144\pi$
$619$	45.1464	1.81459	0.907294	+	0.420497i	$0.138144\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	23.7980	0.954211
$623$	−9.34847	−0.374539
$624$	−2.44949	−0.0980581
$625$	0	0
$626$	31.8990	1.27494
$627$	−3.44949	−0.137759
$628$	4.89898	0.195491
$629$	−34.6969	−1.38346
$630$	0	0
$631$	−28.0000	−1.11466	−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000	−1.11466	−0.557331	+	0.830290i	$0.688175\pi$
$632$	5.00000	0.198889
$633$	3.65153	0.145135
$634$	15.2474	0.605554
$635$	0	0
$636$	−7.44949	−0.295391
$637$	31.3485	1.24207
$638$	15.0000	0.593856
$639$	−1.55051	−0.0613372
$640$	0	0
$641$	37.7980	1.49293	0.746465	−	0.665425i	$-0.231750\pi$
$641$	37.7980	1.49293	0.746465	+	0.665425i	$0.231750\pi$
$642$	−17.3485	−0.684689
$643$	0.202041	0.00796772	0.00398386	−	0.999992i	$-0.498732\pi$
$643$	0.202041	0.00796772	0.00398386	+	0.999992i	$0.498732\pi$
$644$	−4.44949	−0.175334
$645$	0	0
$646$	4.44949	0.175063
$647$	−25.8990	−1.01819	−0.509097	−	0.860709i	$-0.670021\pi$
$647$	−25.8990	−1.01819	−0.509097	+	0.860709i	$0.670021\pi$
$648$	−1.00000	−0.0392837
$649$	22.2474	0.873289
$650$	0	0
$651$	−13.3485	−0.523168
$652$	−19.7980	−0.775348
$653$	14.6969	0.575136	0.287568	−	0.957760i	$-0.407153\pi$
$653$	14.6969	0.575136	0.287568	+	0.957760i	$0.407153\pi$
$654$	−2.89898	−0.113359
$655$	0	0
$656$	−0.898979	−0.0350993
$657$	1.00000	0.0390137
$658$	34.6969	1.35263
$659$	−18.0454	−0.702949	−0.351475	−	0.936197i	$-0.614320\pi$
$659$	−18.0454	−0.702949	−0.351475	+	0.936197i	$0.614320\pi$
$660$	0	0
$661$	23.5959	0.917775	0.458887	−	0.888494i	$-0.348248\pi$
$661$	23.5959	0.917775	0.458887	+	0.888494i	$0.348248\pi$
$662$	22.3485	0.868598
$663$	10.8990	0.423281
$664$	8.34847	0.323983
$665$	0	0
$666$	−7.79796	−0.302165
$667$	−4.34847	−0.168373
$668$	−18.0000	−0.696441
$669$	16.1010	0.622501
$670$	0	0
$671$	−32.5959	−1.25835
$672$	−4.44949	−0.171643
$673$	45.3485	1.74806	0.874028	−	0.485876i	$-0.161499\pi$
$673$	45.3485	1.74806	0.874028	+	0.485876i	$0.161499\pi$
$674$	−24.8990	−0.959073
$675$	0	0
$676$	−7.00000	−0.269231
$677$	−22.3485	−0.858921	−0.429461	−	0.903086i	$-0.641296\pi$
$677$	−22.3485	−0.858921	−0.429461	+	0.903086i	$0.641296\pi$
$678$	16.7980	0.645122
$679$	6.89898	0.264759
$680$	0	0
$681$	29.5959	1.13412
$682$	10.3485	0.396263
$683$	35.6413	1.36378	0.681889	−	0.731456i	$-0.261159\pi$
$683$	35.6413	1.36378	0.681889	+	0.731456i	$0.261159\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	25.7980	0.984971
$687$	−7.24745	−0.276507
$688$	2.44949	0.0933859
$689$	18.2474	0.695172
$690$	0	0
$691$	9.75255	0.371005	0.185502	−	0.982644i	$-0.440609\pi$
$691$	9.75255	0.371005	0.185502	+	0.982644i	$0.440609\pi$
$692$	1.65153	0.0627818
$693$	−15.3485	−0.583040
$694$	−23.5959	−0.895689
$695$	0	0
$696$	−4.34847	−0.164828
$697$	4.00000	0.151511
$698$	25.9444	0.982010
$699$	6.24745	0.236300
$700$	0	0
$701$	−32.4949	−1.22732	−0.613658	−	0.789572i	$-0.710302\pi$
$701$	−32.4949	−1.22732	−0.613658	+	0.789572i	$0.710302\pi$
$702$	2.44949	0.0924500
$703$	7.79796	0.294106
$704$	3.44949	0.130008
$705$	0	0
$706$	−18.2474	−0.686752
$707$	6.89898	0.259463
$708$	−6.44949	−0.242387
$709$	−12.7526	−0.478932	−0.239466	−	0.970905i	$-0.576972\pi$
$709$	−12.7526	−0.478932	−0.239466	+	0.970905i	$0.576972\pi$
$710$	0	0
$711$	−5.00000	−0.187515
$712$	−2.10102	−0.0787391
$713$	−3.00000	−0.112351
$714$	19.7980	0.740920
$715$	0	0
$716$	25.7980	0.964115
$717$	8.69694	0.324793
$718$	22.8990	0.854582
$719$	−19.2020	−0.716115	−0.358058	−	0.933699i	$-0.616561\pi$
$719$	−19.2020	−0.716115	−0.358058	+	0.933699i	$0.616561\pi$
$720$	0	0
$721$	8.44949	0.314675
$722$	−1.00000	−0.0372161
$723$	4.44949	0.165478
$724$	−14.4495	−0.537011
$725$	0	0
$726$	0.898979	0.0333643
$727$	−22.4949	−0.834290	−0.417145	−	0.908840i	$-0.636969\pi$
$727$	−22.4949	−0.834290	−0.417145	+	0.908840i	$0.636969\pi$
$728$	10.8990	0.403943
$729$	1.00000	0.0370370
$730$	0	0
$731$	−10.8990	−0.403113
$732$	9.44949	0.349263
$733$	−4.14643	−0.153152	−0.0765759	−	0.997064i	$-0.524399\pi$
$733$	−4.14643	−0.153152	−0.0765759	+	0.997064i	$0.524399\pi$
$734$	−5.55051	−0.204873
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−52.5959	−1.93740
$738$	0.898979	0.0330919
$739$	32.8990	1.21021	0.605104	−	0.796146i	$-0.293131\pi$
$739$	32.8990	1.21021	0.605104	+	0.796146i	$0.293131\pi$
$740$	0	0
$741$	−2.44949	−0.0899843
$742$	33.1464	1.21684
$743$	53.3939	1.95883	0.979416	−	0.201854i	$-0.0646966\pi$
$743$	53.3939	1.95883	0.979416	+	0.201854i	$0.0646966\pi$
$744$	−3.00000	−0.109985
$745$	0	0
$746$	−22.4495	−0.821934
$747$	−8.34847	−0.305455
$748$	−15.3485	−0.561196
$749$	77.1918	2.82053
$750$	0	0
$751$	−23.7980	−0.868400	−0.434200	−	0.900817i	$-0.642969\pi$
$751$	−23.7980	−0.868400	−0.434200	+	0.900817i	$0.642969\pi$
$752$	7.79796	0.284362
$753$	18.0000	0.655956
$754$	10.6515	0.387906
$755$	0	0
$756$	4.44949	0.161826
$757$	−48.1464	−1.74991	−0.874956	−	0.484203i	$-0.839110\pi$
$757$	−48.1464	−1.74991	−0.874956	+	0.484203i	$0.839110\pi$
$758$	1.30306	0.0473293
$759$	−3.44949	−0.125209
$760$	0	0
$761$	51.3485	1.86138	0.930690	−	0.365808i	$-0.119207\pi$
$761$	51.3485	1.86138	0.930690	+	0.365808i	$0.119207\pi$
$762$	−0.101021	−0.00365959
$763$	12.8990	0.466974
$764$	−0.101021	−0.00365479
$765$	0	0
$766$	16.2474	0.587044
$767$	15.7980	0.570431
$768$	−1.00000	−0.0360844
$769$	−7.89898	−0.284844	−0.142422	−	0.989806i	$-0.545489\pi$
$769$	−7.89898	−0.284844	−0.142422	+	0.989806i	$0.545489\pi$
$770$	0	0
$771$	−21.4949	−0.774120
$772$	15.3485	0.552403
$773$	−18.4949	−0.665215	−0.332608	−	0.943065i	$-0.607928\pi$
$773$	−18.4949	−0.665215	−0.332608	+	0.943065i	$0.607928\pi$
$774$	−2.44949	−0.0880451
$775$	0	0
$776$	1.55051	0.0556601
$777$	34.6969	1.24475
$778$	−21.5959	−0.774251
$779$	−0.898979	−0.0322093
$780$	0	0
$781$	−5.34847	−0.191383
$782$	4.44949	0.159113
$783$	4.34847	0.155402
$784$	12.7980	0.457070
$785$	0	0
$786$	9.24745	0.329846
$787$	33.4495	1.19235	0.596173	−	0.802856i	$-0.296687\pi$
$787$	33.4495	1.19235	0.596173	+	0.802856i	$0.296687\pi$
$788$	−27.3485	−0.974249
$789$	−6.79796	−0.242014
$790$	0	0
$791$	−74.7423	−2.65753
$792$	−3.44949	−0.122572
$793$	−23.1464	−0.821954
$794$	23.9444	0.849755
$795$	0	0
$796$	−10.0000	−0.354441
$797$	−3.50510	−0.124157	−0.0620786	−	0.998071i	$-0.519773\pi$
$797$	−3.50510	−0.124157	−0.0620786	+	0.998071i	$0.519773\pi$
$798$	−4.44949	−0.157510
$799$	−34.6969	−1.22749
$800$	0	0
$801$	2.10102	0.0742359
$802$	−11.2020	−0.395558
$803$	3.44949	0.121730
$804$	15.2474	0.537736
$805$	0	0
$806$	7.34847	0.258839
$807$	2.89898	0.102049
$808$	1.55051	0.0545468
$809$	−3.55051	−0.124829	−0.0624146	−	0.998050i	$-0.519880\pi$
$809$	−3.55051	−0.124829	−0.0624146	+	0.998050i	$0.519880\pi$
$810$	0	0
$811$	−19.4495	−0.682964	−0.341482	−	0.939888i	$-0.610929\pi$
$811$	−19.4495	−0.682964	−0.341482	+	0.939888i	$0.610929\pi$
$812$	19.3485	0.678998
$813$	−22.9444	−0.804695
$814$	−26.8990	−0.942809
$815$	0	0
$816$	4.44949	0.155763
$817$	2.44949	0.0856968
$818$	22.8990	0.800644
$819$	−10.8990	−0.380841
$820$	0	0
$821$	−23.1464	−0.807816	−0.403908	−	0.914800i	$-0.632348\pi$
$821$	−23.1464	−0.807816	−0.403908	+	0.914800i	$0.632348\pi$
$822$	4.89898	0.170872
$823$	31.7980	1.10841	0.554204	−	0.832381i	$-0.313023\pi$
$823$	31.7980	1.10841	0.554204	+	0.832381i	$0.313023\pi$
$824$	1.89898	0.0661541
$825$	0	0
$826$	28.6969	0.998494
$827$	−0.247449	−0.00860463	−0.00430232	−	0.999991i	$-0.501369\pi$
$827$	−0.247449	−0.00860463	−0.00430232	+	0.999991i	$0.501369\pi$
$828$	1.00000	0.0347524
$829$	−39.6413	−1.37680	−0.688400	−	0.725331i	$-0.741687\pi$
$829$	−39.6413	−1.37680	−0.688400	+	0.725331i	$0.741687\pi$
$830$	0	0
$831$	21.0454	0.730057
$832$	2.44949	0.0849208
$833$	−56.9444	−1.97301
$834$	−22.2474	−0.770366
$835$	0	0
$836$	3.44949	0.119303
$837$	3.00000	0.103695
$838$	0	0
$839$	10.6515	0.367732	0.183866	−	0.982951i	$-0.441139\pi$
$839$	10.6515	0.367732	0.183866	+	0.982951i	$0.441139\pi$
$840$	0	0
$841$	−10.0908	−0.347959
$842$	−22.0000	−0.758170
$843$	−7.00000	−0.241093
$844$	−3.65153	−0.125691
$845$	0	0
$846$	−7.79796	−0.268099
$847$	−4.00000	−0.137442
$848$	7.44949	0.255817
$849$	29.7980	1.02266
$850$	0	0
$851$	7.79796	0.267311
$852$	1.55051	0.0531196
$853$	−1.10102	−0.0376982	−0.0188491	−	0.999822i	$-0.506000\pi$
$853$	−1.10102	−0.0376982	−0.0188491	+	0.999822i	$0.506000\pi$
$854$	−42.0454	−1.43876
$855$	0	0
$856$	17.3485	0.592958
$857$	36.4949	1.24664	0.623321	−	0.781966i	$-0.285783\pi$
$857$	36.4949	1.24664	0.623321	+	0.781966i	$0.285783\pi$
$858$	8.44949	0.288461
$859$	−4.20204	−0.143372	−0.0716859	−	0.997427i	$-0.522838\pi$
$859$	−4.20204	−0.143372	−0.0716859	+	0.997427i	$0.522838\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	5.10102	0.173741
$863$	17.3031	0.589003	0.294502	−	0.955651i	$-0.404846\pi$
$863$	17.3031	0.589003	0.294502	+	0.955651i	$0.404846\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	4.65153	0.158065
$867$	−2.79796	−0.0950237
$868$	13.3485	0.453077
$869$	−17.2474	−0.585080
$870$	0	0
$871$	−37.3485	−1.26550
$872$	2.89898	0.0981718
$873$	−1.55051	−0.0524768
$874$	−1.00000	−0.0338255
$875$	0	0
$876$	−1.00000	−0.0337869
$877$	9.10102	0.307320	0.153660	−	0.988124i	$-0.450894\pi$
$877$	9.10102	0.307320	0.153660	+	0.988124i	$0.450894\pi$
$878$	12.1010	0.408390
$879$	−23.2474	−0.784117
$880$	0	0
$881$	50.6969	1.70802	0.854012	−	0.520254i	$-0.174163\pi$
$881$	50.6969	1.70802	0.854012	+	0.520254i	$0.174163\pi$
$882$	−12.7980	−0.430930
$883$	−34.6515	−1.16612	−0.583058	−	0.812430i	$-0.698144\pi$
$883$	−34.6515	−1.16612	−0.583058	+	0.812430i	$0.698144\pi$
$884$	−10.8990	−0.366572
$885$	0	0
$886$	21.2474	0.713822
$887$	4.89898	0.164492	0.0822458	−	0.996612i	$-0.473791\pi$
$887$	4.89898	0.164492	0.0822458	+	0.996612i	$0.473791\pi$
$888$	7.79796	0.261682
$889$	0.449490	0.0150754
$890$	0	0
$891$	3.44949	0.115562
$892$	−16.1010	−0.539102
$893$	7.79796	0.260949
$894$	5.79796	0.193913
$895$	0	0
$896$	4.44949	0.148647
$897$	−2.44949	−0.0817861
$898$	15.0000	0.500556
$899$	13.0454	0.435089
$900$	0	0
$901$	−33.1464	−1.10427
$902$	3.10102	0.103253
$903$	10.8990	0.362695
$904$	−16.7980	−0.558692
$905$	0	0
$906$	−23.7980	−0.790634
$907$	22.0000	0.730498	0.365249	−	0.930910i	$-0.380984\pi$
$907$	22.0000	0.730498	0.365249	+	0.930910i	$0.380984\pi$
$908$	−29.5959	−0.982175
$909$	−1.55051	−0.0514272
$910$	0	0
$911$	6.49490	0.215186	0.107593	−	0.994195i	$-0.465686\pi$
$911$	6.49490	0.215186	0.107593	+	0.994195i	$0.465686\pi$
$912$	−1.00000	−0.0331133
$913$	−28.7980	−0.953073
$914$	−24.8990	−0.823585
$915$	0	0
$916$	7.24745	0.239462
$917$	−41.1464	−1.35877
$918$	−4.44949	−0.146855
$919$	23.8434	0.786520	0.393260	−	0.919427i	$-0.371347\pi$
$919$	23.8434	0.786520	0.393260	+	0.919427i	$0.371347\pi$
$920$	0	0
$921$	−16.3485	−0.538700
$922$	−12.0000	−0.395199
$923$	−3.79796	−0.125011
$924$	15.3485	0.504928
$925$	0	0
$926$	−14.6969	−0.482971
$927$	−1.89898	−0.0623707
$928$	4.34847	0.142745
$929$	−31.5959	−1.03663	−0.518314	−	0.855190i	$-0.673440\pi$
$929$	−31.5959	−1.03663	−0.518314	+	0.855190i	$0.673440\pi$
$930$	0	0
$931$	12.7980	0.419436
$932$	−6.24745	−0.204642
$933$	23.7980	0.779110
$934$	−6.34847	−0.207728
$935$	0	0
$936$	−2.44949	−0.0800641
$937$	19.3939	0.633570	0.316785	−	0.948497i	$-0.397397\pi$
$937$	19.3939	0.633570	0.316785	+	0.948497i	$0.397397\pi$
$938$	−67.8434	−2.21516
$939$	31.8990	1.04098
$940$	0	0
$941$	36.6413	1.19447	0.597237	−	0.802065i	$-0.296265\pi$
$941$	36.6413	1.19447	0.597237	+	0.802065i	$0.296265\pi$
$942$	4.89898	0.159617
$943$	−0.898979	−0.0292748
$944$	6.44949	0.209913
$945$	0	0
$946$	−8.44949	−0.274717
$947$	−8.00000	−0.259965	−0.129983	−	0.991516i	$-0.541492\pi$
$947$	−8.00000	−0.259965	−0.129983	+	0.991516i	$0.541492\pi$
$948$	5.00000	0.162392
$949$	2.44949	0.0795138
$950$	0	0
$951$	15.2474	0.494432
$952$	−19.7980	−0.641656
$953$	15.4949	0.501929	0.250964	−	0.967996i	$-0.419252\pi$
$953$	15.4949	0.501929	0.250964	+	0.967996i	$0.419252\pi$
$954$	−7.44949	−0.241186
$955$	0	0
$956$	−8.69694	−0.281279
$957$	15.0000	0.484881
$958$	−16.5959	−0.536190
$959$	−21.7980	−0.703893
$960$	0	0
$961$	−22.0000	−0.709677
$962$	−19.1010	−0.615842
$963$	−17.3485	−0.559047
$964$	−4.44949	−0.143308
$965$	0	0
$966$	−4.44949	−0.143160
$967$	34.8990	1.12228	0.561138	−	0.827722i	$-0.310364\pi$
$967$	34.8990	1.12228	0.561138	+	0.827722i	$0.310364\pi$
$968$	−0.898979	−0.0288943
$969$	4.44949	0.142938
$970$	0	0
$971$	41.6413	1.33633	0.668167	−	0.744011i	$-0.267079\pi$
$971$	41.6413	1.33633	0.668167	+	0.744011i	$0.267079\pi$
$972$	−1.00000	−0.0320750
$973$	98.9898	3.17347
$974$	−32.0000	−1.02535
$975$	0	0
$976$	−9.44949	−0.302471
$977$	−19.5959	−0.626929	−0.313464	−	0.949600i	$-0.601490\pi$
$977$	−19.5959	−0.626929	−0.313464	+	0.949600i	$0.601490\pi$
$978$	−19.7980	−0.633069
$979$	7.24745	0.231629
$980$	0	0
$981$	−2.89898	−0.0925573
$982$	−43.5959	−1.39120
$983$	−50.4495	−1.60909	−0.804544	−	0.593892i	$-0.797590\pi$
$983$	−50.4495	−1.60909	−0.804544	+	0.593892i	$0.797590\pi$
$984$	−0.898979	−0.0286584
$985$	0	0
$986$	−19.3485	−0.616181
$987$	34.6969	1.10442
$988$	2.44949	0.0779287
$989$	2.44949	0.0778892
$990$	0	0
$991$	44.1010	1.40092	0.700458	−	0.713694i	$-0.252979\pi$
$991$	44.1010	1.40092	0.700458	+	0.713694i	$0.252979\pi$
$992$	3.00000	0.0952501
$993$	22.3485	0.709207
$994$	−6.89898	−0.218822
$995$	0	0
$996$	8.34847	0.264531
$997$	−39.4495	−1.24938	−0.624689	−	0.780874i	$-0.714774\pi$
$997$	−39.4495	−1.24938	−0.624689	+	0.780874i	$0.714774\pi$
$998$	23.8434	0.754749
$999$	−7.79796	−0.246717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.a.bc.1.1	✓	2
3.2	odd	2		8550.2.a.bv.1.1		2
5.2	odd	4		2850.2.d.w.799.1		4
5.3	odd	4		2850.2.d.w.799.4		4
5.4	even	2		2850.2.a.bj.1.2	yes	2
15.14	odd	2		8550.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2850.2.a.bc.1.1	✓	2	1.1	even	1	trivial
2850.2.a.bj.1.2	yes	2	5.4	even	2
2850.2.d.w.799.1		4	5.2	odd	4
2850.2.d.w.799.4		4	5.3	odd	4
8550.2.a.bu.1.2		2	15.14	odd	2
8550.2.a.bv.1.1		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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.44949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.44949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.44949 q^{11} -1.00000 q^{12} +2.44949 q^{13} +4.44949 q^{14} +1.00000 q^{16} -4.44949 q^{17} -1.00000 q^{18} +1.00000 q^{19} +4.44949 q^{21} -3.44949 q^{22} +1.00000 q^{23} +1.00000 q^{24} -2.44949 q^{26} -1.00000 q^{27} -4.44949 q^{28} -4.34847 q^{29} -3.00000 q^{31} -1.00000 q^{32} -3.44949 q^{33} +4.44949 q^{34} +1.00000 q^{36} +7.79796 q^{37} -1.00000 q^{38} -2.44949 q^{39} -0.898979 q^{41} -4.44949 q^{42} +2.44949 q^{43} +3.44949 q^{44} -1.00000 q^{46} +7.79796 q^{47} -1.00000 q^{48} +12.7980 q^{49} +4.44949 q^{51} +2.44949 q^{52} +7.44949 q^{53} +1.00000 q^{54} +4.44949 q^{56} -1.00000 q^{57} +4.34847 q^{58} +6.44949 q^{59} -9.44949 q^{61} +3.00000 q^{62} -4.44949 q^{63} +1.00000 q^{64} +3.44949 q^{66} -15.2474 q^{67} -4.44949 q^{68} -1.00000 q^{69} -1.55051 q^{71} -1.00000 q^{72} +1.00000 q^{73} -7.79796 q^{74} +1.00000 q^{76} -15.3485 q^{77} +2.44949 q^{78} -5.00000 q^{79} +1.00000 q^{81} +0.898979 q^{82} -8.34847 q^{83} +4.44949 q^{84} -2.44949 q^{86} +4.34847 q^{87} -3.44949 q^{88} +2.10102 q^{89} -10.8990 q^{91} +1.00000 q^{92} +3.00000 q^{93} -7.79796 q^{94} +1.00000 q^{96} -1.55051 q^{97} -12.7980 q^{98} +3.44949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} - 2 q^{12} + 4 q^{14} + 2 q^{16} - 4 q^{17} - 2 q^{18} + 2 q^{19} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 2 q^{24} - 2 q^{27} - 4 q^{28} + 6 q^{29} - 6 q^{31} - 2 q^{32} - 2 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} - 2 q^{38} + 8 q^{41} - 4 q^{42} + 2 q^{44} - 2 q^{46} - 4 q^{47} - 2 q^{48} + 6 q^{49} + 4 q^{51} + 10 q^{53} + 2 q^{54} + 4 q^{56} - 2 q^{57} - 6 q^{58} + 8 q^{59} - 14 q^{61} + 6 q^{62} - 4 q^{63} + 2 q^{64} + 2 q^{66} - 6 q^{67} - 4 q^{68} - 2 q^{69} - 8 q^{71} - 2 q^{72} + 2 q^{73} + 4 q^{74} + 2 q^{76} - 16 q^{77} - 10 q^{79} + 2 q^{81} - 8 q^{82} - 2 q^{83} + 4 q^{84} - 6 q^{87} - 2 q^{88} + 14 q^{89} - 12 q^{91} + 2 q^{92} + 6 q^{93} + 4 q^{94} + 2 q^{96} - 8 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 - 2 * q^12 + 4 * q^14 + 2 * q^16 - 4 * q^17 - 2 * q^18 + 2 * q^19 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 2 * q^24 - 2 * q^27 - 4 * q^28 + 6 * q^29 - 6 * q^31 - 2 * q^32 - 2 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 - 2 * q^38 + 8 * q^41 - 4 * q^42 + 2 * q^44 - 2 * q^46 - 4 * q^47 - 2 * q^48 + 6 * q^49 + 4 * q^51 + 10 * q^53 + 2 * q^54 + 4 * q^56 - 2 * q^57 - 6 * q^58 + 8 * q^59 - 14 * q^61 + 6 * q^62 - 4 * q^63 + 2 * q^64 + 2 * q^66 - 6 * q^67 - 4 * q^68 - 2 * q^69 - 8 * q^71 - 2 * q^72 + 2 * q^73 + 4 * q^74 + 2 * q^76 - 16 * q^77 - 10 * q^79 + 2 * q^81 - 8 * q^82 - 2 * q^83 + 4 * q^84 - 6 * q^87 - 2 * q^88 + 14 * q^89 - 12 * q^91 + 2 * q^92 + 6 * q^93 + 4 * q^94 + 2 * q^96 - 8 * q^97 - 6 * q^98 + 2 * q^99

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