LMFDB - Embedded newform 2850.2.a.bc.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(\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			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.449490 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.449490 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.44949 q^{11} -1.00000 q^{12} -2.44949 q^{13} -0.449490 q^{14} +1.00000 q^{16} +0.449490 q^{17} -1.00000 q^{18} +1.00000 q^{19} -0.449490 q^{21} +1.44949 q^{22} +1.00000 q^{23} +1.00000 q^{24} +2.44949 q^{26} -1.00000 q^{27} +0.449490 q^{28} +10.3485 q^{29} -3.00000 q^{31} -1.00000 q^{32} +1.44949 q^{33} -0.449490 q^{34} +1.00000 q^{36} -11.7980 q^{37} -1.00000 q^{38} +2.44949 q^{39} +8.89898 q^{41} +0.449490 q^{42} -2.44949 q^{43} -1.44949 q^{44} -1.00000 q^{46} -11.7980 q^{47} -1.00000 q^{48} -6.79796 q^{49} -0.449490 q^{51} -2.44949 q^{52} +2.55051 q^{53} +1.00000 q^{54} -0.449490 q^{56} -1.00000 q^{57} -10.3485 q^{58} +1.55051 q^{59} -4.55051 q^{61} +3.00000 q^{62} +0.449490 q^{63} +1.00000 q^{64} -1.44949 q^{66} +9.24745 q^{67} +0.449490 q^{68} -1.00000 q^{69} -6.44949 q^{71} -1.00000 q^{72} +1.00000 q^{73} +11.7980 q^{74} +1.00000 q^{76} -0.651531 q^{77} -2.44949 q^{78} -5.00000 q^{79} +1.00000 q^{81} -8.89898 q^{82} +6.34847 q^{83} -0.449490 q^{84} +2.44949 q^{86} -10.3485 q^{87} +1.44949 q^{88} +11.8990 q^{89} -1.10102 q^{91} +1.00000 q^{92} +3.00000 q^{93} +11.7980 q^{94} +1.00000 q^{96} -6.44949 q^{97} +6.79796 q^{98} -1.44949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	0.449490	0.169891	0.0849456	−	0.996386i	$-0.472928\pi$
$7$	0.449490	0.169891	0.0849456	+	0.996386i	$0.472928\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.44949	−0.437038	−0.218519	−	0.975833i	$-0.570122\pi$
$11$	−1.44949	−0.437038	−0.218519	+	0.975833i	$0.570122\pi$
$12$	−1.00000	−0.288675
$13$	−2.44949	−0.679366	−0.339683	−	0.940540i	$-0.610320\pi$
$13$	−2.44949	−0.679366	−0.339683	+	0.940540i	$0.610320\pi$
$14$	−0.449490	−0.120131
$15$	0	0
$16$	1.00000	0.250000
$17$	0.449490	0.109017	0.0545086	−	0.998513i	$-0.482641\pi$
$17$	0.449490	0.109017	0.0545086	+	0.998513i	$0.482641\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−0.449490	−0.0980867
$22$	1.44949	0.309032
$23$	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
$28$	0.449490	0.0849456
$29$	10.3485	1.92166	0.960831	−	0.277134i	$-0.0893846\pi$
$29$	10.3485	1.92166	0.960831	+	0.277134i	$0.0893846\pi$
$30$	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
$33$	1.44949	0.252324
$34$	−0.449490	−0.0770869
$35$	0	0
$36$	1.00000	0.166667
$37$	−11.7980	−1.93957	−0.969786	−	0.243956i	$-0.921555\pi$
$37$	−11.7980	−1.93957	−0.969786	+	0.243956i	$0.921555\pi$
$38$	−1.00000	−0.162221
$39$	2.44949	0.392232
$40$	0	0
$41$	8.89898	1.38979	0.694894	−	0.719113i	$-0.255451\pi$
$41$	8.89898	1.38979	0.694894	+	0.719113i	$0.255451\pi$
$42$	0.449490	0.0693578
$43$	−2.44949	−0.373544	−0.186772	−	0.982403i	$-0.559803\pi$
$43$	−2.44949	−0.373544	−0.186772	+	0.982403i	$0.559803\pi$
$44$	−1.44949	−0.218519
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−11.7980	−1.72091	−0.860455	−	0.509527i	$-0.829820\pi$
$47$	−11.7980	−1.72091	−0.860455	+	0.509527i	$0.829820\pi$
$48$	−1.00000	−0.144338
$49$	−6.79796	−0.971137
$50$	0	0
$51$	−0.449490	−0.0629412
$52$	−2.44949	−0.339683
$53$	2.55051	0.350340	0.175170	−	0.984538i	$-0.443953\pi$
$53$	2.55051	0.350340	0.175170	+	0.984538i	$0.443953\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−0.449490	−0.0600656
$57$	−1.00000	−0.132453
$58$	−10.3485	−1.35882
$59$	1.55051	0.201859	0.100930	−	0.994894i	$-0.467818\pi$
$59$	1.55051	0.201859	0.100930	+	0.994894i	$0.467818\pi$
$60$	0	0
$61$	−4.55051	−0.582633	−0.291317	−	0.956627i	$-0.594093\pi$
$61$	−4.55051	−0.582633	−0.291317	+	0.956627i	$0.594093\pi$
$62$	3.00000	0.381000
$63$	0.449490	0.0566304
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.44949	−0.178420
$67$	9.24745	1.12976	0.564878	−	0.825175i	$-0.308923\pi$
$67$	9.24745	1.12976	0.564878	+	0.825175i	$0.308923\pi$
$68$	0.449490	0.0545086
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−6.44949	−0.765414	−0.382707	−	0.923870i	$-0.625008\pi$
$71$	−6.44949	−0.765414	−0.382707	+	0.923870i	$0.625008\pi$
$72$	−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	$0.481362\pi$
$74$	11.7980	1.37148
$75$	0	0
$76$	1.00000	0.114708
$77$	−0.651531	−0.0742488
$78$	−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
$82$	−8.89898	−0.982728
$83$	6.34847	0.696835	0.348418	−	0.937339i	$-0.386719\pi$
$83$	6.34847	0.696835	0.348418	+	0.937339i	$0.386719\pi$
$84$	−0.449490	−0.0490434
$85$	0	0
$86$	2.44949	0.264135
$87$	−10.3485	−1.10947
$88$	1.44949	0.154516
$89$	11.8990	1.26129	0.630645	−	0.776072i	$-0.282791\pi$
$89$	11.8990	1.26129	0.630645	+	0.776072i	$0.282791\pi$
$90$	0	0
$91$	−1.10102	−0.115418
$92$	1.00000	0.104257
$93$	3.00000	0.311086
$94$	11.7980	1.21687
$95$	0	0
$96$	1.00000	0.102062
$97$	−6.44949	−0.654846	−0.327423	−	0.944878i	$-0.606180\pi$
$97$	−6.44949	−0.654846	−0.327423	+	0.944878i	$0.606180\pi$
$98$	6.79796	0.686698
$99$	−1.44949	−0.145679
$100$	0	0
$101$	−6.44949	−0.641748	−0.320874	−	0.947122i	$-0.603977\pi$
$101$	−6.44949	−0.641748	−0.320874	+	0.947122i	$0.603977\pi$
$102$	0.449490	0.0445061
$103$	7.89898	0.778310	0.389155	−	0.921172i	$-0.372767\pi$
$103$	7.89898	0.778310	0.389155	+	0.921172i	$0.372767\pi$
$104$	2.44949	0.240192
$105$	0	0
$106$	−2.55051	−0.247727
$107$	−2.65153	−0.256333	−0.128167	−	0.991753i	$-0.540909\pi$
$107$	−2.65153	−0.256333	−0.128167	+	0.991753i	$0.540909\pi$
$108$	−1.00000	−0.0962250
$109$	6.89898	0.660802	0.330401	−	0.943841i	$-0.392816\pi$
$109$	6.89898	0.660802	0.330401	+	0.943841i	$0.392816\pi$
$110$	0	0
$111$	11.7980	1.11981
$112$	0.449490	0.0424728
$113$	−2.79796	−0.263210	−0.131605	−	0.991302i	$-0.542013\pi$
$113$	−2.79796	−0.263210	−0.131605	+	0.991302i	$0.542013\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	10.3485	0.960831
$117$	−2.44949	−0.226455
$118$	−1.55051	−0.142736
$119$	0.202041	0.0185211
$120$	0	0
$121$	−8.89898	−0.808998
$122$	4.55051	0.411984
$123$	−8.89898	−0.802394
$124$	−3.00000	−0.269408
$125$	0	0
$126$	−0.449490	−0.0400437
$127$	−9.89898	−0.878392	−0.439196	−	0.898391i	$-0.644737\pi$
$127$	−9.89898	−0.878392	−0.439196	+	0.898391i	$0.644737\pi$
$128$	−1.00000	−0.0883883
$129$	2.44949	0.215666
$130$	0	0
$131$	−15.2474	−1.33218	−0.666088	−	0.745873i	$-0.732032\pi$
$131$	−15.2474	−1.33218	−0.666088	+	0.745873i	$0.732032\pi$
$132$	1.44949	0.126162
$133$	0.449490	0.0389757
$134$	−9.24745	−0.798858
$135$	0	0
$136$	−0.449490	−0.0385434
$137$	−4.89898	−0.418548	−0.209274	−	0.977857i	$-0.567110\pi$
$137$	−4.89898	−0.418548	−0.209274	+	0.977857i	$0.567110\pi$
$138$	1.00000	0.0851257
$139$	2.24745	0.190626	0.0953131	−	0.995447i	$-0.469615\pi$
$139$	2.24745	0.190626	0.0953131	+	0.995447i	$0.469615\pi$
$140$	0	0
$141$	11.7980	0.993567
$142$	6.44949	0.541229
$143$	3.55051	0.296909
$144$	1.00000	0.0833333
$145$	0	0
$146$	−1.00000	−0.0827606
$147$	6.79796	0.560686
$148$	−11.7980	−0.969786
$149$	−13.7980	−1.13037	−0.565186	−	0.824963i	$-0.691196\pi$
$149$	−13.7980	−1.13037	−0.565186	+	0.824963i	$0.691196\pi$
$150$	0	0
$151$	−4.20204	−0.341957	−0.170979	−	0.985275i	$-0.554693\pi$
$151$	−4.20204	−0.341957	−0.170979	+	0.985275i	$0.554693\pi$
$152$	−1.00000	−0.0811107
$153$	0.449490	0.0363391
$154$	0.651531	0.0525018
$155$	0	0
$156$	2.44949	0.196116
$157$	−4.89898	−0.390981	−0.195491	−	0.980706i	$-0.562630\pi$
$157$	−4.89898	−0.390981	−0.195491	+	0.980706i	$0.562630\pi$
$158$	5.00000	0.397779
$159$	−2.55051	−0.202269
$160$	0	0
$161$	0.449490	0.0354248
$162$	−1.00000	−0.0785674
$163$	−0.202041	−0.0158251	−0.00791254	−	0.999969i	$-0.502519\pi$
$163$	−0.202041	−0.0158251	−0.00791254	+	0.999969i	$0.502519\pi$
$164$	8.89898	0.694894
$165$	0	0
$166$	−6.34847	−0.492737
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	0.449490	0.0346789
$169$	−7.00000	−0.538462
$170$	0	0
$171$	1.00000	0.0764719
$172$	−2.44949	−0.186772
$173$	16.3485	1.24295	0.621476	−	0.783434i	$-0.286534\pi$
$173$	16.3485	1.24295	0.621476	+	0.783434i	$0.286534\pi$
$174$	10.3485	0.784515
$175$	0	0
$176$	−1.44949	−0.109259
$177$	−1.55051	−0.116543
$178$	−11.8990	−0.891866
$179$	6.20204	0.463562	0.231781	−	0.972768i	$-0.425545\pi$
$179$	6.20204	0.463562	0.231781	+	0.972768i	$0.425545\pi$
$180$	0	0
$181$	−9.55051	−0.709884	−0.354942	−	0.934888i	$-0.615499\pi$
$181$	−9.55051	−0.709884	−0.354942	+	0.934888i	$0.615499\pi$
$182$	1.10102	0.0816131
$183$	4.55051	0.336383
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−3.00000	−0.219971
$187$	−0.651531	−0.0476446
$188$	−11.7980	−0.860455
$189$	−0.449490	−0.0326956
$190$	0	0
$191$	−9.89898	−0.716265	−0.358133	−	0.933671i	$-0.616586\pi$
$191$	−9.89898	−0.716265	−0.358133	+	0.933671i	$0.616586\pi$
$192$	−1.00000	−0.0721688
$193$	0.651531	0.0468982	0.0234491	−	0.999725i	$-0.492535\pi$
$193$	0.651531	0.0468982	0.0234491	+	0.999725i	$0.492535\pi$
$194$	6.44949	0.463046
$195$	0	0
$196$	−6.79796	−0.485568
$197$	−12.6515	−0.901384	−0.450692	−	0.892679i	$-0.648823\pi$
$197$	−12.6515	−0.901384	−0.450692	+	0.892679i	$0.648823\pi$
$198$	1.44949	0.103011
$199$	−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
$201$	−9.24745	−0.652265
$202$	6.44949	0.453785
$203$	4.65153	0.326473
$204$	−0.449490	−0.0314706
$205$	0	0
$206$	−7.89898	−0.550348
$207$	1.00000	0.0695048
$208$	−2.44949	−0.169842
$209$	−1.44949	−0.100263
$210$	0	0
$211$	−18.3485	−1.26316	−0.631580	−	0.775310i	$-0.717593\pi$
$211$	−18.3485	−1.26316	−0.631580	+	0.775310i	$0.717593\pi$
$212$	2.55051	0.175170
$213$	6.44949	0.441912
$214$	2.65153	0.181255
$215$	0	0
$216$	1.00000	0.0680414
$217$	−1.34847	−0.0915401
$218$	−6.89898	−0.467258
$219$	−1.00000	−0.0675737
$220$	0	0
$221$	−1.10102	−0.0740627
$222$	−11.7980	−0.791827
$223$	−25.8990	−1.73432	−0.867162	−	0.498026i	$-0.834058\pi$
$223$	−25.8990	−1.73432	−0.867162	+	0.498026i	$0.834058\pi$
$224$	−0.449490	−0.0300328
$225$	0	0
$226$	2.79796	0.186117
$227$	9.59592	0.636903	0.318452	−	0.947939i	$-0.396837\pi$
$227$	9.59592	0.636903	0.318452	+	0.947939i	$0.396837\pi$
$228$	−1.00000	−0.0662266
$229$	−17.2474	−1.13974	−0.569872	−	0.821734i	$-0.693007\pi$
$229$	−17.2474	−1.13974	−0.569872	+	0.821734i	$0.693007\pi$
$230$	0	0
$231$	0.651531	0.0428676
$232$	−10.3485	−0.679410
$233$	18.2474	1.19543	0.597715	−	0.801709i	$-0.296075\pi$
$233$	18.2474	1.19543	0.597715	+	0.801709i	$0.296075\pi$
$234$	2.44949	0.160128
$235$	0	0
$236$	1.55051	0.100930
$237$	5.00000	0.324785
$238$	−0.202041	−0.0130964
$239$	20.6969	1.33877	0.669387	−	0.742914i	$-0.266557\pi$
$239$	20.6969	1.33877	0.669387	+	0.742914i	$0.266557\pi$
$240$	0	0
$241$	0.449490	0.0289542	0.0144771	−	0.999895i	$-0.495392\pi$
$241$	0.449490	0.0289542	0.0144771	+	0.999895i	$0.495392\pi$
$242$	8.89898	0.572048
$243$	−1.00000	−0.0641500
$244$	−4.55051	−0.291317
$245$	0	0
$246$	8.89898	0.567378
$247$	−2.44949	−0.155857
$248$	3.00000	0.190500
$249$	−6.34847	−0.402318
$250$	0	0
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	0.449490	0.0283152
$253$	−1.44949	−0.0911286
$254$	9.89898	0.621117
$255$	0	0
$256$	1.00000	0.0625000
$257$	−27.4949	−1.71508	−0.857542	−	0.514413i	$-0.828010\pi$
$257$	−27.4949	−1.71508	−0.857542	+	0.514413i	$0.828010\pi$
$258$	−2.44949	−0.152499
$259$	−5.30306	−0.329516
$260$	0	0
$261$	10.3485	0.640554
$262$	15.2474	0.941991
$263$	−12.7980	−0.789156	−0.394578	−	0.918862i	$-0.629109\pi$
$263$	−12.7980	−0.789156	−0.394578	+	0.918862i	$0.629109\pi$
$264$	−1.44949	−0.0892099
$265$	0	0
$266$	−0.449490	−0.0275600
$267$	−11.8990	−0.728206
$268$	9.24745	0.564878
$269$	6.89898	0.420638	0.210319	−	0.977633i	$-0.432550\pi$
$269$	6.89898	0.420638	0.210319	+	0.977633i	$0.432550\pi$
$270$	0	0
$271$	−30.9444	−1.87974	−0.939869	−	0.341536i	$-0.889053\pi$
$271$	−30.9444	−1.87974	−0.939869	+	0.341536i	$0.889053\pi$
$272$	0.449490	0.0272543
$273$	1.10102	0.0666368
$274$	4.89898	0.295958
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	23.0454	1.38466	0.692332	−	0.721579i	$-0.256583\pi$
$277$	23.0454	1.38466	0.692332	+	0.721579i	$0.256583\pi$
$278$	−2.24745	−0.134793
$279$	−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	$0.433047\pi$
$282$	−11.7980	−0.702558
$283$	−10.2020	−0.606448	−0.303224	−	0.952919i	$-0.598063\pi$
$283$	−10.2020	−0.606448	−0.303224	+	0.952919i	$0.598063\pi$
$284$	−6.44949	−0.382707
$285$	0	0
$286$	−3.55051	−0.209946
$287$	4.00000	0.236113
$288$	−1.00000	−0.0589256
$289$	−16.7980	−0.988115
$290$	0	0
$291$	6.44949	0.378076
$292$	1.00000	0.0585206
$293$	−1.24745	−0.0728767	−0.0364384	−	0.999336i	$-0.511601\pi$
$293$	−1.24745	−0.0728767	−0.0364384	+	0.999336i	$0.511601\pi$
$294$	−6.79796	−0.396465
$295$	0	0
$296$	11.7980	0.685742
$297$	1.44949	0.0841079
$298$	13.7980	0.799294
$299$	−2.44949	−0.141658
$300$	0	0
$301$	−1.10102	−0.0634618
$302$	4.20204	0.241800
$303$	6.44949	0.370514
$304$	1.00000	0.0573539
$305$	0	0
$306$	−0.449490	−0.0256956
$307$	1.65153	0.0942578	0.0471289	−	0.998889i	$-0.484993\pi$
$307$	1.65153	0.0942578	0.0471289	+	0.998889i	$0.484993\pi$
$308$	−0.651531	−0.0371244
$309$	−7.89898	−0.449357
$310$	0	0
$311$	−4.20204	−0.238276	−0.119138	−	0.992878i	$-0.538013\pi$
$311$	−4.20204	−0.238276	−0.119138	+	0.992878i	$0.538013\pi$
$312$	−2.44949	−0.138675
$313$	−22.1010	−1.24922	−0.624612	−	0.780935i	$-0.714743\pi$
$313$	−22.1010	−1.24922	−0.624612	+	0.780935i	$0.714743\pi$
$314$	4.89898	0.276465
$315$	0	0
$316$	−5.00000	−0.281272
$317$	9.24745	0.519388	0.259694	−	0.965691i	$-0.416378\pi$
$317$	9.24745	0.519388	0.259694	+	0.965691i	$0.416378\pi$
$318$	2.55051	0.143026
$319$	−15.0000	−0.839839
$320$	0	0
$321$	2.65153	0.147994
$322$	−0.449490	−0.0250491
$323$	0.449490	0.0250103
$324$	1.00000	0.0555556
$325$	0	0
$326$	0.202041	0.0111900
$327$	−6.89898	−0.381514
$328$	−8.89898	−0.491364
$329$	−5.30306	−0.292367
$330$	0	0
$331$	−7.65153	−0.420566	−0.210283	−	0.977641i	$-0.567439\pi$
$331$	−7.65153	−0.420566	−0.210283	+	0.977641i	$0.567439\pi$
$332$	6.34847	0.348418
$333$	−11.7980	−0.646524
$334$	18.0000	0.984916
$335$	0	0
$336$	−0.449490	−0.0245217
$337$	15.1010	0.822605	0.411303	−	0.911499i	$-0.365074\pi$
$337$	15.1010	0.822605	0.411303	+	0.911499i	$0.365074\pi$
$338$	7.00000	0.380750
$339$	2.79796	0.151964
$340$	0	0
$341$	4.34847	0.235483
$342$	−1.00000	−0.0540738
$343$	−6.20204	−0.334879
$344$	2.44949	0.132068
$345$	0	0
$346$	−16.3485	−0.878899
$347$	−15.5959	−0.837233	−0.418616	−	0.908163i	$-0.637485\pi$
$347$	−15.5959	−0.837233	−0.418616	+	0.908163i	$0.637485\pi$
$348$	−10.3485	−0.554736
$349$	27.9444	1.49583	0.747914	−	0.663795i	$-0.231055\pi$
$349$	27.9444	1.49583	0.747914	+	0.663795i	$0.231055\pi$
$350$	0	0
$351$	2.44949	0.130744
$352$	1.44949	0.0772581
$353$	−6.24745	−0.332518	−0.166259	−	0.986082i	$-0.553169\pi$
$353$	−6.24745	−0.332518	−0.166259	+	0.986082i	$0.553169\pi$
$354$	1.55051	0.0824087
$355$	0	0
$356$	11.8990	0.630645
$357$	−0.202041	−0.0106931
$358$	−6.20204	−0.327788
$359$	−13.1010	−0.691445	−0.345723	−	0.938337i	$-0.612366\pi$
$359$	−13.1010	−0.691445	−0.345723	+	0.938337i	$0.612366\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	9.55051	0.501964
$363$	8.89898	0.467075
$364$	−1.10102	−0.0577092
$365$	0	0
$366$	−4.55051	−0.237859
$367$	10.4495	0.545459	0.272729	−	0.962091i	$-0.412074\pi$
$367$	10.4495	0.545459	0.272729	+	0.962091i	$0.412074\pi$
$368$	1.00000	0.0521286
$369$	8.89898	0.463262
$370$	0	0
$371$	1.14643	0.0595196
$372$	3.00000	0.155543
$373$	17.5505	0.908731	0.454365	−	0.890815i	$-0.349866\pi$
$373$	17.5505	0.908731	0.454365	+	0.890815i	$0.349866\pi$
$374$	0.651531	0.0336899
$375$	0	0
$376$	11.7980	0.608433
$377$	−25.3485	−1.30551
$378$	0.449490	0.0231193
$379$	−30.6969	−1.57680	−0.788398	−	0.615166i	$-0.789089\pi$
$379$	−30.6969	−1.57680	−0.788398	+	0.615166i	$0.789089\pi$
$380$	0	0
$381$	9.89898	0.507140
$382$	9.89898	0.506476
$383$	8.24745	0.421425	0.210712	−	0.977548i	$-0.432422\pi$
$383$	8.24745	0.421425	0.210712	+	0.977548i	$0.432422\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−0.651531	−0.0331620
$387$	−2.44949	−0.124515
$388$	−6.44949	−0.327423
$389$	−17.5959	−0.892148	−0.446074	−	0.894996i	$-0.647178\pi$
$389$	−17.5959	−0.892148	−0.446074	+	0.894996i	$0.647178\pi$
$390$	0	0
$391$	0.449490	0.0227317
$392$	6.79796	0.343349
$393$	15.2474	0.769132
$394$	12.6515	0.637375
$395$	0	0
$396$	−1.44949	−0.0728396
$397$	29.9444	1.50287	0.751433	−	0.659810i	$-0.229363\pi$
$397$	29.9444	1.50287	0.751433	+	0.659810i	$0.229363\pi$
$398$	10.0000	0.501255
$399$	−0.449490	−0.0225026
$400$	0	0
$401$	30.7980	1.53798	0.768988	−	0.639263i	$-0.220760\pi$
$401$	30.7980	1.53798	0.768988	+	0.639263i	$0.220760\pi$
$402$	9.24745	0.461221
$403$	7.34847	0.366053
$404$	−6.44949	−0.320874
$405$	0	0
$406$	−4.65153	−0.230852
$407$	17.1010	0.847666
$408$	0.449490	0.0222531
$409$	−13.1010	−0.647804	−0.323902	−	0.946091i	$-0.604995\pi$
$409$	−13.1010	−0.647804	−0.323902	+	0.946091i	$0.604995\pi$
$410$	0	0
$411$	4.89898	0.241649
$412$	7.89898	0.389155
$413$	0.696938	0.0342941
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	2.44949	0.120096
$417$	−2.24745	−0.110058
$418$	1.44949	0.0708969
$419$	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	$0.319894\pi$
$422$	18.3485	0.893190
$423$	−11.7980	−0.573636
$424$	−2.55051	−0.123864
$425$	0	0
$426$	−6.44949	−0.312479
$427$	−2.04541	−0.0989842
$428$	−2.65153	−0.128167
$429$	−3.55051	−0.171420
$430$	0	0
$431$	−14.8990	−0.717659	−0.358829	−	0.933403i	$-0.616824\pi$
$431$	−14.8990	−0.717659	−0.358829	+	0.933403i	$0.616824\pi$
$432$	−1.00000	−0.0481125
$433$	−19.3485	−0.929828	−0.464914	−	0.885356i	$-0.653915\pi$
$433$	−19.3485	−0.929828	−0.464914	+	0.885356i	$0.653915\pi$
$434$	1.34847	0.0647286
$435$	0	0
$436$	6.89898	0.330401
$437$	1.00000	0.0478365
$438$	1.00000	0.0477818
$439$	−21.8990	−1.04518	−0.522591	−	0.852584i	$-0.675034\pi$
$439$	−21.8990	−1.04518	−0.522591	+	0.852584i	$0.675034\pi$
$440$	0	0
$441$	−6.79796	−0.323712
$442$	1.10102	0.0523702
$443$	3.24745	0.154291	0.0771455	−	0.997020i	$-0.475419\pi$
$443$	3.24745	0.154291	0.0771455	+	0.997020i	$0.475419\pi$
$444$	11.7980	0.559906
$445$	0	0
$446$	25.8990	1.22635
$447$	13.7980	0.652621
$448$	0.449490	0.0212364
$449$	−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
$451$	−12.8990	−0.607389
$452$	−2.79796	−0.131605
$453$	4.20204	0.197429
$454$	−9.59592	−0.450359
$455$	0	0
$456$	1.00000	0.0468293
$457$	15.1010	0.706396	0.353198	−	0.935549i	$-0.385094\pi$
$457$	15.1010	0.706396	0.353198	+	0.935549i	$0.385094\pi$
$458$	17.2474	0.805920
$459$	−0.449490	−0.0209804
$460$	0	0
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	−0.651531	−0.0303120
$463$	−14.6969	−0.683025	−0.341512	−	0.939877i	$-0.610939\pi$
$463$	−14.6969	−0.683025	−0.341512	+	0.939877i	$0.610939\pi$
$464$	10.3485	0.480416
$465$	0	0
$466$	−18.2474	−0.845297
$467$	−8.34847	−0.386321	−0.193161	−	0.981167i	$-0.561874\pi$
$467$	−8.34847	−0.386321	−0.193161	+	0.981167i	$0.561874\pi$
$468$	−2.44949	−0.113228
$469$	4.15663	0.191935
$470$	0	0
$471$	4.89898	0.225733
$472$	−1.55051	−0.0713680
$473$	3.55051	0.163253
$474$	−5.00000	−0.229658
$475$	0	0
$476$	0.202041	0.00926054
$477$	2.55051	0.116780
$478$	−20.6969	−0.946656
$479$	−22.5959	−1.03243	−0.516217	−	0.856458i	$-0.672660\pi$
$479$	−22.5959	−1.03243	−0.516217	+	0.856458i	$0.672660\pi$
$480$	0	0
$481$	28.8990	1.31768
$482$	−0.449490	−0.0204737
$483$	−0.449490	−0.0204525
$484$	−8.89898	−0.404499
$485$	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	$0.241826\pi$
$488$	4.55051	0.205992
$489$	0.202041	0.00913661
$490$	0	0
$491$	4.40408	0.198753	0.0993767	−	0.995050i	$-0.468315\pi$
$491$	4.40408	0.198753	0.0993767	+	0.995050i	$0.468315\pi$
$492$	−8.89898	−0.401197
$493$	4.65153	0.209494
$494$	2.44949	0.110208
$495$	0	0
$496$	−3.00000	−0.134704
$497$	−2.89898	−0.130037
$498$	6.34847	0.284482
$499$	39.8434	1.78363	0.891817	−	0.452396i	$-0.149431\pi$
$499$	39.8434	1.78363	0.891817	+	0.452396i	$0.149431\pi$
$500$	0	0
$501$	18.0000	0.804181
$502$	18.0000	0.803379
$503$	−10.2020	−0.454887	−0.227443	−	0.973791i	$-0.573037\pi$
$503$	−10.2020	−0.454887	−0.227443	+	0.973791i	$0.573037\pi$
$504$	−0.449490	−0.0200219
$505$	0	0
$506$	1.44949	0.0644377
$507$	7.00000	0.310881
$508$	−9.89898	−0.439196
$509$	4.14643	0.183787	0.0918936	−	0.995769i	$-0.470708\pi$
$509$	4.14643	0.183787	0.0918936	+	0.995769i	$0.470708\pi$
$510$	0	0
$511$	0.449490	0.0198843
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	27.4949	1.21275
$515$	0	0
$516$	2.44949	0.107833
$517$	17.1010	0.752102
$518$	5.30306	0.233003
$519$	−16.3485	−0.717618
$520$	0	0
$521$	−13.6969	−0.600074	−0.300037	−	0.953928i	$-0.596999\pi$
$521$	−13.6969	−0.600074	−0.300037	+	0.953928i	$0.596999\pi$
$522$	−10.3485	−0.452940
$523$	−25.3939	−1.11040	−0.555198	−	0.831718i	$-0.687358\pi$
$523$	−25.3939	−1.11040	−0.555198	+	0.831718i	$0.687358\pi$
$524$	−15.2474	−0.666088
$525$	0	0
$526$	12.7980	0.558018
$527$	−1.34847	−0.0587402
$528$	1.44949	0.0630809
$529$	−22.0000	−0.956522
$530$	0	0
$531$	1.55051	0.0672864
$532$	0.449490	0.0194879
$533$	−21.7980	−0.944174
$534$	11.8990	0.514919
$535$	0	0
$536$	−9.24745	−0.399429
$537$	−6.20204	−0.267638
$538$	−6.89898	−0.297436
$539$	9.85357	0.424423
$540$	0	0
$541$	−12.1464	−0.522216	−0.261108	−	0.965310i	$-0.584088\pi$
$541$	−12.1464	−0.522216	−0.261108	+	0.965310i	$0.584088\pi$
$542$	30.9444	1.32918
$543$	9.55051	0.409852
$544$	−0.449490	−0.0192717
$545$	0	0
$546$	−1.10102	−0.0471193
$547$	−36.6413	−1.56667	−0.783335	−	0.621600i	$-0.786483\pi$
$547$	−36.6413	−1.56667	−0.783335	+	0.621600i	$0.786483\pi$
$548$	−4.89898	−0.209274
$549$	−4.55051	−0.194211
$550$	0	0
$551$	10.3485	0.440860
$552$	1.00000	0.0425628
$553$	−2.24745	−0.0955712
$554$	−23.0454	−0.979106
$555$	0	0
$556$	2.24745	0.0953131
$557$	−12.6515	−0.536063	−0.268031	−	0.963410i	$-0.586373\pi$
$557$	−12.6515	−0.536063	−0.268031	+	0.963410i	$0.586373\pi$
$558$	3.00000	0.127000
$559$	6.00000	0.253773
$560$	0	0
$561$	0.651531	0.0275077
$562$	−7.00000	−0.295277
$563$	18.2474	0.769038	0.384519	−	0.923117i	$-0.374367\pi$
$563$	18.2474	0.769038	0.384519	+	0.923117i	$0.374367\pi$
$564$	11.7980	0.496784
$565$	0	0
$566$	10.2020	0.428824
$567$	0.449490	0.0188768
$568$	6.44949	0.270615
$569$	45.1918	1.89454	0.947270	−	0.320436i	$-0.103829\pi$
$569$	45.1918	1.89454	0.947270	+	0.320436i	$0.103829\pi$
$570$	0	0
$571$	14.2474	0.596237	0.298119	−	0.954529i	$-0.403641\pi$
$571$	14.2474	0.596237	0.298119	+	0.954529i	$0.403641\pi$
$572$	3.55051	0.148454
$573$	9.89898	0.413536
$574$	−4.00000	−0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	−9.89898	−0.412100	−0.206050	−	0.978541i	$-0.566061\pi$
$577$	−9.89898	−0.412100	−0.206050	+	0.978541i	$0.566061\pi$
$578$	16.7980	0.698703
$579$	−0.651531	−0.0270767
$580$	0	0
$581$	2.85357	0.118386
$582$	−6.44949	−0.267340
$583$	−3.69694	−0.153112
$584$	−1.00000	−0.0413803
$585$	0	0
$586$	1.24745	0.0515316
$587$	28.5505	1.17841	0.589203	−	0.807985i	$-0.299442\pi$
$587$	28.5505	1.17841	0.589203	+	0.807985i	$0.299442\pi$
$588$	6.79796	0.280343
$589$	−3.00000	−0.123613
$590$	0	0
$591$	12.6515	0.520414
$592$	−11.7980	−0.484893
$593$	40.4949	1.66293	0.831463	−	0.555580i	$-0.187504\pi$
$593$	40.4949	1.66293	0.831463	+	0.555580i	$0.187504\pi$
$594$	−1.44949	−0.0594733
$595$	0	0
$596$	−13.7980	−0.565186
$597$	10.0000	0.409273
$598$	2.44949	0.100167
$599$	11.5505	0.471941	0.235971	−	0.971760i	$-0.424173\pi$
$599$	11.5505	0.471941	0.235971	+	0.971760i	$0.424173\pi$
$600$	0	0
$601$	−17.1464	−0.699417	−0.349709	−	0.936858i	$-0.613719\pi$
$601$	−17.1464	−0.699417	−0.349709	+	0.936858i	$0.613719\pi$
$602$	1.10102	0.0448742
$603$	9.24745	0.376585
$604$	−4.20204	−0.170979
$605$	0	0
$606$	−6.44949	−0.261993
$607$	32.1918	1.30663	0.653313	−	0.757088i	$-0.273379\pi$
$607$	32.1918	1.30663	0.653313	+	0.757088i	$0.273379\pi$
$608$	−1.00000	−0.0405554
$609$	−4.65153	−0.188490
$610$	0	0
$611$	28.8990	1.16913
$612$	0.449490	0.0181695
$613$	41.1918	1.66372	0.831861	−	0.554984i	$-0.187275\pi$
$613$	41.1918	1.66372	0.831861	+	0.554984i	$0.187275\pi$
$614$	−1.65153	−0.0666504
$615$	0	0
$616$	0.651531	0.0262509
$617$	40.2929	1.62213	0.811065	−	0.584957i	$-0.198888\pi$
$617$	40.2929	1.62213	0.811065	+	0.584957i	$0.198888\pi$
$618$	7.89898	0.317744
$619$	10.8536	0.436242	0.218121	−	0.975922i	$-0.430007\pi$
$619$	10.8536	0.436242	0.218121	+	0.975922i	$0.430007\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	4.20204	0.168486
$623$	5.34847	0.214282
$624$	2.44949	0.0980581
$625$	0	0
$626$	22.1010	0.883334
$627$	1.44949	0.0578870
$628$	−4.89898	−0.195491
$629$	−5.30306	−0.211447
$630$	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
$633$	18.3485	0.729286
$634$	−9.24745	−0.367263
$635$	0	0
$636$	−2.55051	−0.101134
$637$	16.6515	0.659758
$638$	15.0000	0.593856
$639$	−6.44949	−0.255138
$640$	0	0
$641$	18.2020	0.718937	0.359469	−	0.933157i	$-0.382958\pi$
$641$	18.2020	0.718937	0.359469	+	0.933157i	$0.382958\pi$
$642$	−2.65153	−0.104648
$643$	19.7980	0.780755	0.390378	−	0.920655i	$-0.372344\pi$
$643$	19.7980	0.780755	0.390378	+	0.920655i	$0.372344\pi$
$644$	0.449490	0.0177124
$645$	0	0
$646$	−0.449490	−0.0176849
$647$	−16.1010	−0.632996	−0.316498	−	0.948593i	$-0.602507\pi$
$647$	−16.1010	−0.632996	−0.316498	+	0.948593i	$0.602507\pi$
$648$	−1.00000	−0.0392837
$649$	−2.24745	−0.0882201
$650$	0	0
$651$	1.34847	0.0528507
$652$	−0.202041	−0.00791254
$653$	−14.6969	−0.575136	−0.287568	−	0.957760i	$-0.592847\pi$
$653$	−14.6969	−0.575136	−0.287568	+	0.957760i	$0.592847\pi$
$654$	6.89898	0.269771
$655$	0	0
$656$	8.89898	0.347447
$657$	1.00000	0.0390137
$658$	5.30306	0.206735
$659$	26.0454	1.01459	0.507293	−	0.861774i	$-0.330646\pi$
$659$	26.0454	1.01459	0.507293	+	0.861774i	$0.330646\pi$
$660$	0	0
$661$	−15.5959	−0.606611	−0.303305	−	0.952893i	$-0.598090\pi$
$661$	−15.5959	−0.606611	−0.303305	+	0.952893i	$0.598090\pi$
$662$	7.65153	0.297385
$663$	1.10102	0.0427601
$664$	−6.34847	−0.246368
$665$	0	0
$666$	11.7980	0.457162
$667$	10.3485	0.400694
$668$	−18.0000	−0.696441
$669$	25.8990	1.00131
$670$	0	0
$671$	6.59592	0.254633
$672$	0.449490	0.0173394
$673$	30.6515	1.18153	0.590765	−	0.806844i	$-0.298826\pi$
$673$	30.6515	1.18153	0.590765	+	0.806844i	$0.298826\pi$
$674$	−15.1010	−0.581670
$675$	0	0
$676$	−7.00000	−0.269231
$677$	−7.65153	−0.294072	−0.147036	−	0.989131i	$-0.546973\pi$
$677$	−7.65153	−0.294072	−0.147036	+	0.989131i	$0.546973\pi$
$678$	−2.79796	−0.107455
$679$	−2.89898	−0.111253
$680$	0	0
$681$	−9.59592	−0.367716
$682$	−4.34847	−0.166511
$683$	−47.6413	−1.82294	−0.911472	−	0.411361i	$-0.865053\pi$
$683$	−47.6413	−1.82294	−0.911472	+	0.411361i	$0.865053\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	6.20204	0.236795
$687$	17.2474	0.658031
$688$	−2.44949	−0.0933859
$689$	−6.24745	−0.238009
$690$	0	0
$691$	34.2474	1.30283	0.651417	−	0.758720i	$-0.274175\pi$
$691$	34.2474	1.30283	0.651417	+	0.758720i	$0.274175\pi$
$692$	16.3485	0.621476
$693$	−0.651531	−0.0247496
$694$	15.5959	0.592013
$695$	0	0
$696$	10.3485	0.392258
$697$	4.00000	0.151511
$698$	−27.9444	−1.05771
$699$	−18.2474	−0.690182
$700$	0	0
$701$	16.4949	0.623004	0.311502	−	0.950246i	$-0.399168\pi$
$701$	16.4949	0.623004	0.311502	+	0.950246i	$0.399168\pi$
$702$	−2.44949	−0.0924500
$703$	−11.7980	−0.444968
$704$	−1.44949	−0.0546297
$705$	0	0
$706$	6.24745	0.235126
$707$	−2.89898	−0.109027
$708$	−1.55051	−0.0582717
$709$	−37.2474	−1.39886	−0.699429	−	0.714702i	$-0.746562\pi$
$709$	−37.2474	−1.39886	−0.699429	+	0.714702i	$0.746562\pi$
$710$	0	0
$711$	−5.00000	−0.187515
$712$	−11.8990	−0.445933
$713$	−3.00000	−0.112351
$714$	0.202041	0.00756120
$715$	0	0
$716$	6.20204	0.231781
$717$	−20.6969	−0.772941
$718$	13.1010	0.488926
$719$	−38.7980	−1.44692	−0.723460	−	0.690366i	$-0.757449\pi$
$719$	−38.7980	−1.44692	−0.723460	+	0.690366i	$0.757449\pi$
$720$	0	0
$721$	3.55051	0.132228
$722$	−1.00000	−0.0372161
$723$	−0.449490	−0.0167167
$724$	−9.55051	−0.354942
$725$	0	0
$726$	−8.89898	−0.330272
$727$	26.4949	0.982641	0.491321	−	0.870979i	$-0.336514\pi$
$727$	26.4949	0.982641	0.491321	+	0.870979i	$0.336514\pi$
$728$	1.10102	0.0408065
$729$	1.00000	0.0370370
$730$	0	0
$731$	−1.10102	−0.0407227
$732$	4.55051	0.168192
$733$	30.1464	1.11348	0.556742	−	0.830686i	$-0.312051\pi$
$733$	30.1464	1.11348	0.556742	+	0.830686i	$0.312051\pi$
$734$	−10.4495	−0.385698
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−13.4041	−0.493746
$738$	−8.89898	−0.327576
$739$	23.1010	0.849785	0.424892	−	0.905244i	$-0.360312\pi$
$739$	23.1010	0.849785	0.424892	+	0.905244i	$0.360312\pi$
$740$	0	0
$741$	2.44949	0.0899843
$742$	−1.14643	−0.0420867
$743$	−5.39388	−0.197882	−0.0989411	−	0.995093i	$-0.531546\pi$
$743$	−5.39388	−0.197882	−0.0989411	+	0.995093i	$0.531546\pi$
$744$	−3.00000	−0.109985
$745$	0	0
$746$	−17.5505	−0.642570
$747$	6.34847	0.232278
$748$	−0.651531	−0.0238223
$749$	−1.19184	−0.0435487
$750$	0	0
$751$	−4.20204	−0.153335	−0.0766673	−	0.997057i	$-0.524428\pi$
$751$	−4.20204	−0.153335	−0.0766673	+	0.997057i	$0.524428\pi$
$752$	−11.7980	−0.430227
$753$	18.0000	0.655956
$754$	25.3485	0.923137
$755$	0	0
$756$	−0.449490	−0.0163478
$757$	−13.8536	−0.503517	−0.251758	−	0.967790i	$-0.581009\pi$
$757$	−13.8536	−0.503517	−0.251758	+	0.967790i	$0.581009\pi$
$758$	30.6969	1.11496
$759$	1.44949	0.0526131
$760$	0	0
$761$	36.6515	1.32862	0.664308	−	0.747459i	$-0.268726\pi$
$761$	36.6515	1.32862	0.664308	+	0.747459i	$0.268726\pi$
$762$	−9.89898	−0.358602
$763$	3.10102	0.112264
$764$	−9.89898	−0.358133
$765$	0	0
$766$	−8.24745	−0.297992
$767$	−3.79796	−0.137136
$768$	−1.00000	−0.0360844
$769$	1.89898	0.0684790	0.0342395	−	0.999414i	$-0.489099\pi$
$769$	1.89898	0.0684790	0.0342395	+	0.999414i	$0.489099\pi$
$770$	0	0
$771$	27.4949	0.990205
$772$	0.651531	0.0234491
$773$	30.4949	1.09683	0.548413	−	0.836208i	$-0.315232\pi$
$773$	30.4949	1.09683	0.548413	+	0.836208i	$0.315232\pi$
$774$	2.44949	0.0880451
$775$	0	0
$776$	6.44949	0.231523
$777$	5.30306	0.190246
$778$	17.5959	0.630844
$779$	8.89898	0.318839
$780$	0	0
$781$	9.34847	0.334515
$782$	−0.449490	−0.0160737
$783$	−10.3485	−0.369824
$784$	−6.79796	−0.242784
$785$	0	0
$786$	−15.2474	−0.543858
$787$	28.5505	1.01772	0.508858	−	0.860851i	$-0.330068\pi$
$787$	28.5505	1.01772	0.508858	+	0.860851i	$0.330068\pi$
$788$	−12.6515	−0.450692
$789$	12.7980	0.455619
$790$	0	0
$791$	−1.25765	−0.0447170
$792$	1.44949	0.0515054
$793$	11.1464	0.395821
$794$	−29.9444	−1.06269
$795$	0	0
$796$	−10.0000	−0.354441
$797$	−52.4949	−1.85946	−0.929732	−	0.368236i	$-0.879962\pi$
$797$	−52.4949	−1.85946	−0.929732	+	0.368236i	$0.879962\pi$
$798$	0.449490	0.0159118
$799$	−5.30306	−0.187609
$800$	0	0
$801$	11.8990	0.420430
$802$	−30.7980	−1.08751
$803$	−1.44949	−0.0511514
$804$	−9.24745	−0.326132
$805$	0	0
$806$	−7.34847	−0.258839
$807$	−6.89898	−0.242856
$808$	6.44949	0.226892
$809$	−8.44949	−0.297068	−0.148534	−	0.988907i	$-0.547455\pi$
$809$	−8.44949	−0.297068	−0.148534	+	0.988907i	$0.547455\pi$
$810$	0	0
$811$	−14.5505	−0.510938	−0.255469	−	0.966817i	$-0.582230\pi$
$811$	−14.5505	−0.510938	−0.255469	+	0.966817i	$0.582230\pi$
$812$	4.65153	0.163237
$813$	30.9444	1.08527
$814$	−17.1010	−0.599390
$815$	0	0
$816$	−0.449490	−0.0157353
$817$	−2.44949	−0.0856968
$818$	13.1010	0.458066
$819$	−1.10102	−0.0384728
$820$	0	0
$821$	11.1464	0.389013	0.194507	−	0.980901i	$-0.437689\pi$
$821$	11.1464	0.389013	0.194507	+	0.980901i	$0.437689\pi$
$822$	−4.89898	−0.170872
$823$	12.2020	0.425336	0.212668	−	0.977124i	$-0.431785\pi$
$823$	12.2020	0.425336	0.212668	+	0.977124i	$0.431785\pi$
$824$	−7.89898	−0.275174
$825$	0	0
$826$	−0.696938	−0.0242496
$827$	24.2474	0.843166	0.421583	−	0.906790i	$-0.361475\pi$
$827$	24.2474	0.843166	0.421583	+	0.906790i	$0.361475\pi$
$828$	1.00000	0.0347524
$829$	43.6413	1.51573	0.757863	−	0.652414i	$-0.226244\pi$
$829$	43.6413	1.51573	0.757863	+	0.652414i	$0.226244\pi$
$830$	0	0
$831$	−23.0454	−0.799436
$832$	−2.44949	−0.0849208
$833$	−3.05561	−0.105871
$834$	2.24745	0.0778228
$835$	0	0
$836$	−1.44949	−0.0501317
$837$	3.00000	0.103695
$838$	0	0
$839$	25.3485	0.875126	0.437563	−	0.899188i	$-0.355842\pi$
$839$	25.3485	0.875126	0.437563	+	0.899188i	$0.355842\pi$
$840$	0	0
$841$	78.0908	2.69279
$842$	−22.0000	−0.758170
$843$	−7.00000	−0.241093
$844$	−18.3485	−0.631580
$845$	0	0
$846$	11.7980	0.405622
$847$	−4.00000	−0.137442
$848$	2.55051	0.0875849
$849$	10.2020	0.350133
$850$	0	0
$851$	−11.7980	−0.404429
$852$	6.44949	0.220956
$853$	−10.8990	−0.373174	−0.186587	−	0.982438i	$-0.559743\pi$
$853$	−10.8990	−0.373174	−0.186587	+	0.982438i	$0.559743\pi$
$854$	2.04541	0.0699924
$855$	0	0
$856$	2.65153	0.0906275
$857$	−12.4949	−0.426818	−0.213409	−	0.976963i	$-0.568457\pi$
$857$	−12.4949	−0.426818	−0.213409	+	0.976963i	$0.568457\pi$
$858$	3.55051	0.121212
$859$	−23.7980	−0.811976	−0.405988	−	0.913878i	$-0.633073\pi$
$859$	−23.7980	−0.811976	−0.405988	+	0.913878i	$0.633073\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	14.8990	0.507461
$863$	46.6969	1.58958	0.794791	−	0.606883i	$-0.207580\pi$
$863$	46.6969	1.58958	0.794791	+	0.606883i	$0.207580\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	19.3485	0.657488
$867$	16.7980	0.570489
$868$	−1.34847	−0.0457700
$869$	7.24745	0.245853
$870$	0	0
$871$	−22.6515	−0.767518
$872$	−6.89898	−0.233629
$873$	−6.44949	−0.218282
$874$	−1.00000	−0.0338255
$875$	0	0
$876$	−1.00000	−0.0337869
$877$	18.8990	0.638173	0.319087	−	0.947726i	$-0.396624\pi$
$877$	18.8990	0.638173	0.319087	+	0.947726i	$0.396624\pi$
$878$	21.8990	0.739055
$879$	1.24745	0.0420754
$880$	0	0
$881$	21.3031	0.717718	0.358859	−	0.933392i	$-0.383166\pi$
$881$	21.3031	0.717718	0.358859	+	0.933392i	$0.383166\pi$
$882$	6.79796	0.228899
$883$	−49.3485	−1.66071	−0.830354	−	0.557236i	$-0.811862\pi$
$883$	−49.3485	−1.66071	−0.830354	+	0.557236i	$0.811862\pi$
$884$	−1.10102	−0.0370313
$885$	0	0
$886$	−3.24745	−0.109100
$887$	−4.89898	−0.164492	−0.0822458	−	0.996612i	$-0.526209\pi$
$887$	−4.89898	−0.164492	−0.0822458	+	0.996612i	$0.526209\pi$
$888$	−11.7980	−0.395914
$889$	−4.44949	−0.149231
$890$	0	0
$891$	−1.44949	−0.0485597
$892$	−25.8990	−0.867162
$893$	−11.7980	−0.394804
$894$	−13.7980	−0.461473
$895$	0	0
$896$	−0.449490	−0.0150164
$897$	2.44949	0.0817861
$898$	15.0000	0.500556
$899$	−31.0454	−1.03542
$900$	0	0
$901$	1.14643	0.0381931
$902$	12.8990	0.429489
$903$	1.10102	0.0366397
$904$	2.79796	0.0930587
$905$	0	0
$906$	−4.20204	−0.139603
$907$	22.0000	0.730498	0.365249	−	0.930910i	$-0.380984\pi$
$907$	22.0000	0.730498	0.365249	+	0.930910i	$0.380984\pi$
$908$	9.59592	0.318452
$909$	−6.44949	−0.213916
$910$	0	0
$911$	−42.4949	−1.40792	−0.703959	−	0.710240i	$-0.748586\pi$
$911$	−42.4949	−1.40792	−0.703959	+	0.710240i	$0.748586\pi$
$912$	−1.00000	−0.0331133
$913$	−9.20204	−0.304543
$914$	−15.1010	−0.499497
$915$	0	0
$916$	−17.2474	−0.569872
$917$	−6.85357	−0.226325
$918$	0.449490	0.0148354
$919$	−39.8434	−1.31431	−0.657156	−	0.753755i	$-0.728241\pi$
$919$	−39.8434	−1.31431	−0.657156	+	0.753755i	$0.728241\pi$
$920$	0	0
$921$	−1.65153	−0.0544198
$922$	−12.0000	−0.395199
$923$	15.7980	0.519996
$924$	0.651531	0.0214338
$925$	0	0
$926$	14.6969	0.482971
$927$	7.89898	0.259437
$928$	−10.3485	−0.339705
$929$	7.59592	0.249214	0.124607	−	0.992206i	$-0.460233\pi$
$929$	7.59592	0.249214	0.124607	+	0.992206i	$0.460233\pi$
$930$	0	0
$931$	−6.79796	−0.222794
$932$	18.2474	0.597715
$933$	4.20204	0.137569
$934$	8.34847	0.273170
$935$	0	0
$936$	2.44949	0.0800641
$937$	−39.3939	−1.28694	−0.643471	−	0.765471i	$-0.722506\pi$
$937$	−39.3939	−1.28694	−0.643471	+	0.765471i	$0.722506\pi$
$938$	−4.15663	−0.135719
$939$	22.1010	0.721240
$940$	0	0
$941$	−46.6413	−1.52046	−0.760232	−	0.649652i	$-0.774915\pi$
$941$	−46.6413	−1.52046	−0.760232	+	0.649652i	$0.774915\pi$
$942$	−4.89898	−0.159617
$943$	8.89898	0.289791
$944$	1.55051	0.0504648
$945$	0	0
$946$	−3.55051	−0.115437
$947$	−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
$951$	−9.24745	−0.299869
$952$	−0.202041	−0.00654819
$953$	−33.4949	−1.08501	−0.542503	−	0.840054i	$-0.682523\pi$
$953$	−33.4949	−1.08501	−0.542503	+	0.840054i	$0.682523\pi$
$954$	−2.55051	−0.0825758
$955$	0	0
$956$	20.6969	0.669387
$957$	15.0000	0.484881
$958$	22.5959	0.730041
$959$	−2.20204	−0.0711076
$960$	0	0
$961$	−22.0000	−0.709677
$962$	−28.8990	−0.931740
$963$	−2.65153	−0.0854444
$964$	0.449490	0.0144771
$965$	0	0
$966$	0.449490	0.0144621
$967$	25.1010	0.807194	0.403597	−	0.914937i	$-0.367760\pi$
$967$	25.1010	0.807194	0.403597	+	0.914937i	$0.367760\pi$
$968$	8.89898	0.286024
$969$	−0.449490	−0.0144397
$970$	0	0
$971$	−41.6413	−1.33633	−0.668167	−	0.744011i	$-0.732921\pi$
$971$	−41.6413	−1.33633	−0.668167	+	0.744011i	$0.732921\pi$
$972$	−1.00000	−0.0320750
$973$	1.01021	0.0323857
$974$	−32.0000	−1.02535
$975$	0	0
$976$	−4.55051	−0.145658
$977$	19.5959	0.626929	0.313464	−	0.949600i	$-0.398510\pi$
$977$	19.5959	0.626929	0.313464	+	0.949600i	$0.398510\pi$
$978$	−0.202041	−0.00646056
$979$	−17.2474	−0.551231
$980$	0	0
$981$	6.89898	0.220267
$982$	−4.40408	−0.140540
$983$	−45.5505	−1.45284	−0.726418	−	0.687253i	$-0.758816\pi$
$983$	−45.5505	−1.45284	−0.726418	+	0.687253i	$0.758816\pi$
$984$	8.89898	0.283689
$985$	0	0
$986$	−4.65153	−0.148135
$987$	5.30306	0.168798
$988$	−2.44949	−0.0779287
$989$	−2.44949	−0.0778892
$990$	0	0
$991$	53.8990	1.71216	0.856079	−	0.516845i	$-0.172894\pi$
$991$	53.8990	1.71216	0.856079	+	0.516845i	$0.172894\pi$
$992$	3.00000	0.0952501
$993$	7.65153	0.242814
$994$	2.89898	0.0919500
$995$	0	0
$996$	−6.34847	−0.201159
$997$	−34.5505	−1.09423	−0.547113	−	0.837059i	$-0.684273\pi$
$997$	−34.5505	−1.09423	−0.547113	+	0.837059i	$0.684273\pi$
$998$	−39.8434	−1.26122
$999$	11.7980	0.373271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.a.bc.1.2	✓	2
3.2	odd	2		8550.2.a.bv.1.2		2
5.2	odd	4		2850.2.d.w.799.2		4
5.3	odd	4		2850.2.d.w.799.3		4
5.4	even	2		2850.2.a.bj.1.1	yes	2
15.14	odd	2		8550.2.a.bu.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2850.2.a.bc.1.2	✓	2	1.1	even	1	trivial
2850.2.a.bj.1.1	yes	2	5.4	even	2
2850.2.d.w.799.2		4	5.2	odd	4
2850.2.d.w.799.3		4	5.3	odd	4
8550.2.a.bu.1.1		2	15.14	odd	2
8550.2.a.bv.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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.449490 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.449490 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.44949 q^{11} -1.00000 q^{12} -2.44949 q^{13} -0.449490 q^{14} +1.00000 q^{16} +0.449490 q^{17} -1.00000 q^{18} +1.00000 q^{19} -0.449490 q^{21} +1.44949 q^{22} +1.00000 q^{23} +1.00000 q^{24} +2.44949 q^{26} -1.00000 q^{27} +0.449490 q^{28} +10.3485 q^{29} -3.00000 q^{31} -1.00000 q^{32} +1.44949 q^{33} -0.449490 q^{34} +1.00000 q^{36} -11.7980 q^{37} -1.00000 q^{38} +2.44949 q^{39} +8.89898 q^{41} +0.449490 q^{42} -2.44949 q^{43} -1.44949 q^{44} -1.00000 q^{46} -11.7980 q^{47} -1.00000 q^{48} -6.79796 q^{49} -0.449490 q^{51} -2.44949 q^{52} +2.55051 q^{53} +1.00000 q^{54} -0.449490 q^{56} -1.00000 q^{57} -10.3485 q^{58} +1.55051 q^{59} -4.55051 q^{61} +3.00000 q^{62} +0.449490 q^{63} +1.00000 q^{64} -1.44949 q^{66} +9.24745 q^{67} +0.449490 q^{68} -1.00000 q^{69} -6.44949 q^{71} -1.00000 q^{72} +1.00000 q^{73} +11.7980 q^{74} +1.00000 q^{76} -0.651531 q^{77} -2.44949 q^{78} -5.00000 q^{79} +1.00000 q^{81} -8.89898 q^{82} +6.34847 q^{83} -0.449490 q^{84} +2.44949 q^{86} -10.3485 q^{87} +1.44949 q^{88} +11.8990 q^{89} -1.10102 q^{91} +1.00000 q^{92} +3.00000 q^{93} +11.7980 q^{94} +1.00000 q^{96} -6.44949 q^{97} +6.79796 q^{98} -1.44949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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