LMFDB - Embedded newform 273.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(1,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, 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("273.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} -2.41421 q^{6} +1.00000 q^{7} +4.41421 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} -2.41421 q^{6} +1.00000 q^{7} +4.41421 q^{8} +1.00000 q^{9} +2.00000 q^{11} -3.82843 q^{12} -1.00000 q^{13} +2.41421 q^{14} +3.00000 q^{16} -0.828427 q^{17} +2.41421 q^{18} -5.65685 q^{19} -1.00000 q^{21} +4.82843 q^{22} +1.17157 q^{23} -4.41421 q^{24} -5.00000 q^{25} -2.41421 q^{26} -1.00000 q^{27} +3.82843 q^{28} -3.65685 q^{29} +1.65685 q^{31} -1.58579 q^{32} -2.00000 q^{33} -2.00000 q^{34} +3.82843 q^{36} -7.65685 q^{37} -13.6569 q^{38} +1.00000 q^{39} +5.65685 q^{41} -2.41421 q^{42} +9.65685 q^{43} +7.65685 q^{44} +2.82843 q^{46} +3.17157 q^{47} -3.00000 q^{48} +1.00000 q^{49} -12.0711 q^{50} +0.828427 q^{51} -3.82843 q^{52} +3.65685 q^{53} -2.41421 q^{54} +4.41421 q^{56} +5.65685 q^{57} -8.82843 q^{58} -10.4853 q^{59} -0.343146 q^{61} +4.00000 q^{62} +1.00000 q^{63} -9.82843 q^{64} -4.82843 q^{66} +4.00000 q^{67} -3.17157 q^{68} -1.17157 q^{69} +14.0000 q^{71} +4.41421 q^{72} -7.65685 q^{73} -18.4853 q^{74} +5.00000 q^{75} -21.6569 q^{76} +2.00000 q^{77} +2.41421 q^{78} -11.3137 q^{79} +1.00000 q^{81} +13.6569 q^{82} +16.1421 q^{83} -3.82843 q^{84} +23.3137 q^{86} +3.65685 q^{87} +8.82843 q^{88} +15.3137 q^{89} -1.00000 q^{91} +4.48528 q^{92} -1.65685 q^{93} +7.65685 q^{94} +1.58579 q^{96} -2.00000 q^{97} +2.41421 q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} - 10 q^{25} - 2 q^{26} - 2 q^{27} + 2 q^{28} + 4 q^{29} - 8 q^{31} - 6 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 16 q^{38} + 2 q^{39} - 2 q^{42} + 8 q^{43} + 4 q^{44} + 12 q^{47} - 6 q^{48} + 2 q^{49} - 10 q^{50} - 4 q^{51} - 2 q^{52} - 4 q^{53} - 2 q^{54} + 6 q^{56} - 12 q^{58} - 4 q^{59} - 12 q^{61} + 8 q^{62} + 2 q^{63} - 14 q^{64} - 4 q^{66} + 8 q^{67} - 12 q^{68} - 8 q^{69} + 28 q^{71} + 6 q^{72} - 4 q^{73} - 20 q^{74} + 10 q^{75} - 32 q^{76} + 4 q^{77} + 2 q^{78} + 2 q^{81} + 16 q^{82} + 4 q^{83} - 2 q^{84} + 24 q^{86} - 4 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{91} - 8 q^{92} + 8 q^{93} + 4 q^{94} + 6 q^{96} - 4 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 - 10 * q^25 - 2 * q^26 - 2 * q^27 + 2 * q^28 + 4 * q^29 - 8 * q^31 - 6 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 16 * q^38 + 2 * q^39 - 2 * q^42 + 8 * q^43 + 4 * q^44 + 12 * q^47 - 6 * q^48 + 2 * q^49 - 10 * q^50 - 4 * q^51 - 2 * q^52 - 4 * q^53 - 2 * q^54 + 6 * q^56 - 12 * q^58 - 4 * q^59 - 12 * q^61 + 8 * q^62 + 2 * q^63 - 14 * q^64 - 4 * q^66 + 8 * q^67 - 12 * q^68 - 8 * q^69 + 28 * q^71 + 6 * q^72 - 4 * q^73 - 20 * q^74 + 10 * q^75 - 32 * q^76 + 4 * q^77 + 2 * q^78 + 2 * q^81 + 16 * q^82 + 4 * q^83 - 2 * q^84 + 24 * q^86 - 4 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^91 - 8 * q^92 + 8 * q^93 + 4 * q^94 + 6 * q^96 - 4 * q^97 + 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.41421	1.70711	0.853553	−	0.521005i	$-0.174443\pi$
$2$	2.41421	1.70711	0.853553	+	0.521005i	$0.174443\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.82843	1.91421
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	−2.41421	−0.985599
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	4.41421	1.56066
$9$	1.00000	0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−3.82843	−1.10517
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.41421	0.645226
$15$	0	0
$16$	3.00000	0.750000
$17$	−0.828427	−0.200923	−0.100462	−	0.994941i	$-0.532032\pi$
$17$	−0.828427	−0.200923	−0.100462	+	0.994941i	$0.532032\pi$
$18$	2.41421	0.569036
$19$	−5.65685	−1.29777	−0.648886	−	0.760886i	$-0.724765\pi$
$19$	−5.65685	−1.29777	−0.648886	+	0.760886i	$0.724765\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	4.82843	1.02942
$23$	1.17157	0.244290	0.122145	−	0.992512i	$-0.461023\pi$
$23$	1.17157	0.244290	0.122145	+	0.992512i	$0.461023\pi$
$24$	−4.41421	−0.901048
$25$	−5.00000	−1.00000
$26$	−2.41421	−0.473466
$27$	−1.00000	−0.192450
$28$	3.82843	0.723505
$29$	−3.65685	−0.679061	−0.339530	−	0.940595i	$-0.610268\pi$
$29$	−3.65685	−0.679061	−0.339530	+	0.940595i	$0.610268\pi$
$30$	0	0
$31$	1.65685	0.297580	0.148790	−	0.988869i	$-0.452462\pi$
$31$	1.65685	0.297580	0.148790	+	0.988869i	$0.452462\pi$
$32$	−1.58579	−0.280330
$33$	−2.00000	−0.348155
$34$	−2.00000	−0.342997
$35$	0	0
$36$	3.82843	0.638071
$37$	−7.65685	−1.25878	−0.629390	−	0.777090i	$-0.716695\pi$
$37$	−7.65685	−1.25878	−0.629390	+	0.777090i	$0.716695\pi$
$38$	−13.6569	−2.21543
$39$	1.00000	0.160128
$40$	0	0
$41$	5.65685	0.883452	0.441726	−	0.897150i	$-0.354366\pi$
$41$	5.65685	0.883452	0.441726	+	0.897150i	$0.354366\pi$
$42$	−2.41421	−0.372521
$43$	9.65685	1.47266	0.736328	−	0.676625i	$-0.236558\pi$
$43$	9.65685	1.47266	0.736328	+	0.676625i	$0.236558\pi$
$44$	7.65685	1.15431
$45$	0	0
$46$	2.82843	0.417029
$47$	3.17157	0.462621	0.231311	−	0.972880i	$-0.425699\pi$
$47$	3.17157	0.462621	0.231311	+	0.972880i	$0.425699\pi$
$48$	−3.00000	−0.433013
$49$	1.00000	0.142857
$50$	−12.0711	−1.70711
$51$	0.828427	0.116003
$52$	−3.82843	−0.530907
$53$	3.65685	0.502308	0.251154	−	0.967947i	$-0.419190\pi$
$53$	3.65685	0.502308	0.251154	+	0.967947i	$0.419190\pi$
$54$	−2.41421	−0.328533
$55$	0	0
$56$	4.41421	0.589874
$57$	5.65685	0.749269
$58$	−8.82843	−1.15923
$59$	−10.4853	−1.36507	−0.682534	−	0.730854i	$-0.739122\pi$
$59$	−10.4853	−1.36507	−0.682534	+	0.730854i	$0.739122\pi$
$60$	0	0
$61$	−0.343146	−0.0439353	−0.0219677	−	0.999759i	$-0.506993\pi$
$61$	−0.343146	−0.0439353	−0.0219677	+	0.999759i	$0.506993\pi$
$62$	4.00000	0.508001
$63$	1.00000	0.125988
$64$	−9.82843	−1.22855
$65$	0	0
$66$	−4.82843	−0.594338
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−3.17157	−0.384610
$69$	−1.17157	−0.141041
$70$	0	0
$71$	14.0000	1.66149	0.830747	−	0.556650i	$-0.187914\pi$
$71$	14.0000	1.66149	0.830747	+	0.556650i	$0.187914\pi$
$72$	4.41421	0.520220
$73$	−7.65685	−0.896167	−0.448084	−	0.893992i	$-0.647893\pi$
$73$	−7.65685	−0.896167	−0.448084	+	0.893992i	$0.647893\pi$
$74$	−18.4853	−2.14887
$75$	5.00000	0.577350
$76$	−21.6569	−2.48421
$77$	2.00000	0.227921
$78$	2.41421	0.273356
$79$	−11.3137	−1.27289	−0.636446	−	0.771321i	$-0.719596\pi$
$79$	−11.3137	−1.27289	−0.636446	+	0.771321i	$0.719596\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	13.6569	1.50815
$83$	16.1421	1.77183	0.885915	−	0.463848i	$-0.153532\pi$
$83$	16.1421	1.77183	0.885915	+	0.463848i	$0.153532\pi$
$84$	−3.82843	−0.417716
$85$	0	0
$86$	23.3137	2.51398
$87$	3.65685	0.392056
$88$	8.82843	0.941113
$89$	15.3137	1.62325	0.811625	−	0.584179i	$-0.198583\pi$
$89$	15.3137	1.62325	0.811625	+	0.584179i	$0.198583\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	4.48528	0.467623
$93$	−1.65685	−0.171808
$94$	7.65685	0.789744
$95$	0	0
$96$	1.58579	0.161849
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	2.41421	0.243872
$99$	2.00000	0.201008
$100$	−19.1421	−1.91421
$101$	4.82843	0.480446	0.240223	−	0.970718i	$-0.422779\pi$
$101$	4.82843	0.480446	0.240223	+	0.970718i	$0.422779\pi$
$102$	2.00000	0.198030
$103$	13.6569	1.34565	0.672825	−	0.739802i	$-0.265081\pi$
$103$	13.6569	1.34565	0.672825	+	0.739802i	$0.265081\pi$
$104$	−4.41421	−0.432849
$105$	0	0
$106$	8.82843	0.857493
$107$	2.82843	0.273434	0.136717	−	0.990610i	$-0.456345\pi$
$107$	2.82843	0.273434	0.136717	+	0.990610i	$0.456345\pi$
$108$	−3.82843	−0.368391
$109$	−11.6569	−1.11652	−0.558262	−	0.829665i	$-0.688532\pi$
$109$	−11.6569	−1.11652	−0.558262	+	0.829665i	$0.688532\pi$
$110$	0	0
$111$	7.65685	0.726756
$112$	3.00000	0.283473
$113$	0.343146	0.0322804	0.0161402	−	0.999870i	$-0.494862\pi$
$113$	0.343146	0.0322804	0.0161402	+	0.999870i	$0.494862\pi$
$114$	13.6569	1.27908
$115$	0	0
$116$	−14.0000	−1.29987
$117$	−1.00000	−0.0924500
$118$	−25.3137	−2.33032
$119$	−0.828427	−0.0759418
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−0.828427	−0.0750023
$123$	−5.65685	−0.510061
$124$	6.34315	0.569631
$125$	0	0
$126$	2.41421	0.215075
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−20.5563	−1.81694
$129$	−9.65685	−0.850239
$130$	0	0
$131$	16.9706	1.48272	0.741362	−	0.671105i	$-0.234180\pi$
$131$	16.9706	1.48272	0.741362	+	0.671105i	$0.234180\pi$
$132$	−7.65685	−0.666444
$133$	−5.65685	−0.490511
$134$	9.65685	0.834225
$135$	0	0
$136$	−3.65685	−0.313573
$137$	−22.1421	−1.89173	−0.945865	−	0.324560i	$-0.894784\pi$
$137$	−22.1421	−1.89173	−0.945865	+	0.324560i	$0.894784\pi$
$138$	−2.82843	−0.240772
$139$	−17.6569	−1.49763	−0.748817	−	0.662776i	$-0.769378\pi$
$139$	−17.6569	−1.49763	−0.748817	+	0.662776i	$0.769378\pi$
$140$	0	0
$141$	−3.17157	−0.267095
$142$	33.7990	2.83635
$143$	−2.00000	−0.167248
$144$	3.00000	0.250000
$145$	0	0
$146$	−18.4853	−1.52985
$147$	−1.00000	−0.0824786
$148$	−29.3137	−2.40957
$149$	4.48528	0.367449	0.183724	−	0.982978i	$-0.441185\pi$
$149$	4.48528	0.367449	0.183724	+	0.982978i	$0.441185\pi$
$150$	12.0711	0.985599
$151$	0.686292	0.0558496	0.0279248	−	0.999610i	$-0.491110\pi$
$151$	0.686292	0.0558496	0.0279248	+	0.999610i	$0.491110\pi$
$152$	−24.9706	−2.02538
$153$	−0.828427	−0.0669744
$154$	4.82843	0.389086
$155$	0	0
$156$	3.82843	0.306519
$157$	9.31371	0.743315	0.371657	−	0.928370i	$-0.378790\pi$
$157$	9.31371	0.743315	0.371657	+	0.928370i	$0.378790\pi$
$158$	−27.3137	−2.17296
$159$	−3.65685	−0.290007
$160$	0	0
$161$	1.17157	0.0923329
$162$	2.41421	0.189679
$163$	−11.3137	−0.886158	−0.443079	−	0.896483i	$-0.646114\pi$
$163$	−11.3137	−0.886158	−0.443079	+	0.896483i	$0.646114\pi$
$164$	21.6569	1.69112
$165$	0	0
$166$	38.9706	3.02470
$167$	11.1716	0.864482	0.432241	−	0.901758i	$-0.357723\pi$
$167$	11.1716	0.864482	0.432241	+	0.901758i	$0.357723\pi$
$168$	−4.41421	−0.340564
$169$	1.00000	0.0769231
$170$	0	0
$171$	−5.65685	−0.432590
$172$	36.9706	2.81898
$173$	−14.4853	−1.10130	−0.550648	−	0.834738i	$-0.685619\pi$
$173$	−14.4853	−1.10130	−0.550648	+	0.834738i	$0.685619\pi$
$174$	8.82843	0.669281
$175$	−5.00000	−0.377964
$176$	6.00000	0.452267
$177$	10.4853	0.788122
$178$	36.9706	2.77106
$179$	10.1421	0.758059	0.379029	−	0.925385i	$-0.376258\pi$
$179$	10.1421	0.758059	0.379029	+	0.925385i	$0.376258\pi$
$180$	0	0
$181$	−4.34315	−0.322823	−0.161412	−	0.986887i	$-0.551605\pi$
$181$	−4.34315	−0.322823	−0.161412	+	0.986887i	$0.551605\pi$
$182$	−2.41421	−0.178953
$183$	0.343146	0.0253661
$184$	5.17157	0.381253
$185$	0	0
$186$	−4.00000	−0.293294
$187$	−1.65685	−0.121161
$188$	12.1421	0.885556
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−26.8284	−1.94124	−0.970618	−	0.240624i	$-0.922648\pi$
$191$	−26.8284	−1.94124	−0.970618	+	0.240624i	$0.922648\pi$
$192$	9.82843	0.709306
$193$	26.9706	1.94138	0.970692	−	0.240328i	$-0.0772549\pi$
$193$	26.9706	1.94138	0.970692	+	0.240328i	$0.0772549\pi$
$194$	−4.82843	−0.346661
$195$	0	0
$196$	3.82843	0.273459
$197$	2.82843	0.201517	0.100759	−	0.994911i	$-0.467873\pi$
$197$	2.82843	0.201517	0.100759	+	0.994911i	$0.467873\pi$
$198$	4.82843	0.343141
$199$	16.9706	1.20301	0.601506	−	0.798869i	$-0.294568\pi$
$199$	16.9706	1.20301	0.601506	+	0.798869i	$0.294568\pi$
$200$	−22.0711	−1.56066
$201$	−4.00000	−0.282138
$202$	11.6569	0.820173
$203$	−3.65685	−0.256661
$204$	3.17157	0.222055
$205$	0	0
$206$	32.9706	2.29717
$207$	1.17157	0.0814299
$208$	−3.00000	−0.208013
$209$	−11.3137	−0.782586
$210$	0	0
$211$	−6.34315	−0.436680	−0.218340	−	0.975873i	$-0.570064\pi$
$211$	−6.34315	−0.436680	−0.218340	+	0.975873i	$0.570064\pi$
$212$	14.0000	0.961524
$213$	−14.0000	−0.959264
$214$	6.82843	0.466782
$215$	0	0
$216$	−4.41421	−0.300349
$217$	1.65685	0.112475
$218$	−28.1421	−1.90603
$219$	7.65685	0.517402
$220$	0	0
$221$	0.828427	0.0557260
$222$	18.4853	1.24065
$223$	17.6569	1.18239	0.591195	−	0.806529i	$-0.298656\pi$
$223$	17.6569	1.18239	0.591195	+	0.806529i	$0.298656\pi$
$224$	−1.58579	−0.105955
$225$	−5.00000	−0.333333
$226$	0.828427	0.0551062
$227$	−2.48528	−0.164954	−0.0824770	−	0.996593i	$-0.526283\pi$
$227$	−2.48528	−0.164954	−0.0824770	+	0.996593i	$0.526283\pi$
$228$	21.6569	1.43426
$229$	−19.6569	−1.29896	−0.649481	−	0.760378i	$-0.725014\pi$
$229$	−19.6569	−1.29896	−0.649481	+	0.760378i	$0.725014\pi$
$230$	0	0
$231$	−2.00000	−0.131590
$232$	−16.1421	−1.05978
$233$	1.31371	0.0860639	0.0430320	−	0.999074i	$-0.486298\pi$
$233$	1.31371	0.0860639	0.0430320	+	0.999074i	$0.486298\pi$
$234$	−2.41421	−0.157822
$235$	0	0
$236$	−40.1421	−2.61303
$237$	11.3137	0.734904
$238$	−2.00000	−0.129641
$239$	−12.3431	−0.798412	−0.399206	−	0.916861i	$-0.630714\pi$
$239$	−12.3431	−0.798412	−0.399206	+	0.916861i	$0.630714\pi$
$240$	0	0
$241$	−23.6569	−1.52387	−0.761936	−	0.647652i	$-0.775751\pi$
$241$	−23.6569	−1.52387	−0.761936	+	0.647652i	$0.775751\pi$
$242$	−16.8995	−1.08634
$243$	−1.00000	−0.0641500
$244$	−1.31371	−0.0841016
$245$	0	0
$246$	−13.6569	−0.870729
$247$	5.65685	0.359937
$248$	7.31371	0.464421
$249$	−16.1421	−1.02297
$250$	0	0
$251$	−22.6274	−1.42823	−0.714115	−	0.700028i	$-0.753171\pi$
$251$	−22.6274	−1.42823	−0.714115	+	0.700028i	$0.753171\pi$
$252$	3.82843	0.241168
$253$	2.34315	0.147312
$254$	38.6274	2.42370
$255$	0	0
$256$	−29.9706	−1.87316
$257$	3.17157	0.197837	0.0989186	−	0.995096i	$-0.468462\pi$
$257$	3.17157	0.197837	0.0989186	+	0.995096i	$0.468462\pi$
$258$	−23.3137	−1.45145
$259$	−7.65685	−0.475774
$260$	0	0
$261$	−3.65685	−0.226354
$262$	40.9706	2.53117
$263$	4.48528	0.276574	0.138287	−	0.990392i	$-0.455840\pi$
$263$	4.48528	0.276574	0.138287	+	0.990392i	$0.455840\pi$
$264$	−8.82843	−0.543352
$265$	0	0
$266$	−13.6569	−0.837355
$267$	−15.3137	−0.937184
$268$	15.3137	0.935434
$269$	10.4853	0.639299	0.319649	−	0.947536i	$-0.396435\pi$
$269$	10.4853	0.639299	0.319649	+	0.947536i	$0.396435\pi$
$270$	0	0
$271$	22.6274	1.37452	0.687259	−	0.726413i	$-0.258814\pi$
$271$	22.6274	1.37452	0.687259	+	0.726413i	$0.258814\pi$
$272$	−2.48528	−0.150692
$273$	1.00000	0.0605228
$274$	−53.4558	−3.22939
$275$	−10.0000	−0.603023
$276$	−4.48528	−0.269982
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−42.6274	−2.55662
$279$	1.65685	0.0991933
$280$	0	0
$281$	16.4853	0.983429	0.491715	−	0.870756i	$-0.336370\pi$
$281$	16.4853	0.983429	0.491715	+	0.870756i	$0.336370\pi$
$282$	−7.65685	−0.455959
$283$	−25.6569	−1.52514	−0.762571	−	0.646905i	$-0.776063\pi$
$283$	−25.6569	−1.52514	−0.762571	+	0.646905i	$0.776063\pi$
$284$	53.5980	3.18045
$285$	0	0
$286$	−4.82843	−0.285511
$287$	5.65685	0.333914
$288$	−1.58579	−0.0934434
$289$	−16.3137	−0.959630
$290$	0	0
$291$	2.00000	0.117242
$292$	−29.3137	−1.71546
$293$	−7.31371	−0.427271	−0.213636	−	0.976913i	$-0.568531\pi$
$293$	−7.31371	−0.427271	−0.213636	+	0.976913i	$0.568531\pi$
$294$	−2.41421	−0.140800
$295$	0	0
$296$	−33.7990	−1.96453
$297$	−2.00000	−0.116052
$298$	10.8284	0.627274
$299$	−1.17157	−0.0677538
$300$	19.1421	1.10517
$301$	9.65685	0.556612
$302$	1.65685	0.0953412
$303$	−4.82843	−0.277386
$304$	−16.9706	−0.973329
$305$	0	0
$306$	−2.00000	−0.114332
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	7.65685	0.436290
$309$	−13.6569	−0.776911
$310$	0	0
$311$	−31.3137	−1.77564	−0.887819	−	0.460193i	$-0.847780\pi$
$311$	−31.3137	−1.77564	−0.887819	+	0.460193i	$0.847780\pi$
$312$	4.41421	0.249906
$313$	−10.9706	−0.620093	−0.310046	−	0.950721i	$-0.600345\pi$
$313$	−10.9706	−0.620093	−0.310046	+	0.950721i	$0.600345\pi$
$314$	22.4853	1.26892
$315$	0	0
$316$	−43.3137	−2.43659
$317$	−0.485281	−0.0272561	−0.0136281	−	0.999907i	$-0.504338\pi$
$317$	−0.485281	−0.0272561	−0.0136281	+	0.999907i	$0.504338\pi$
$318$	−8.82843	−0.495074
$319$	−7.31371	−0.409489
$320$	0	0
$321$	−2.82843	−0.157867
$322$	2.82843	0.157622
$323$	4.68629	0.260752
$324$	3.82843	0.212690
$325$	5.00000	0.277350
$326$	−27.3137	−1.51277
$327$	11.6569	0.644626
$328$	24.9706	1.37877
$329$	3.17157	0.174854
$330$	0	0
$331$	26.6274	1.46358	0.731788	−	0.681533i	$-0.238686\pi$
$331$	26.6274	1.46358	0.731788	+	0.681533i	$0.238686\pi$
$332$	61.7990	3.39166
$333$	−7.65685	−0.419593
$334$	26.9706	1.47576
$335$	0	0
$336$	−3.00000	−0.163663
$337$	17.3137	0.943138	0.471569	−	0.881829i	$-0.343688\pi$
$337$	17.3137	0.943138	0.471569	+	0.881829i	$0.343688\pi$
$338$	2.41421	0.131316
$339$	−0.343146	−0.0186371
$340$	0	0
$341$	3.31371	0.179447
$342$	−13.6569	−0.738478
$343$	1.00000	0.0539949
$344$	42.6274	2.29832
$345$	0	0
$346$	−34.9706	−1.88003
$347$	−1.17157	−0.0628933	−0.0314467	−	0.999505i	$-0.510011\pi$
$347$	−1.17157	−0.0628933	−0.0314467	+	0.999505i	$0.510011\pi$
$348$	14.0000	0.750479
$349$	−13.3137	−0.712666	−0.356333	−	0.934359i	$-0.615973\pi$
$349$	−13.3137	−0.712666	−0.356333	+	0.934359i	$0.615973\pi$
$350$	−12.0711	−0.645226
$351$	1.00000	0.0533761
$352$	−3.17157	−0.169045
$353$	11.3137	0.602168	0.301084	−	0.953598i	$-0.402652\pi$
$353$	11.3137	0.602168	0.301084	+	0.953598i	$0.402652\pi$
$354$	25.3137	1.34541
$355$	0	0
$356$	58.6274	3.10725
$357$	0.828427	0.0438450
$358$	24.4853	1.29409
$359$	25.3137	1.33601	0.668003	−	0.744158i	$-0.267149\pi$
$359$	25.3137	1.33601	0.668003	+	0.744158i	$0.267149\pi$
$360$	0	0
$361$	13.0000	0.684211
$362$	−10.4853	−0.551094
$363$	7.00000	0.367405
$364$	−3.82843	−0.200664
$365$	0	0
$366$	0.828427	0.0433026
$367$	−22.6274	−1.18114	−0.590571	−	0.806986i	$-0.701097\pi$
$367$	−22.6274	−1.18114	−0.590571	+	0.806986i	$0.701097\pi$
$368$	3.51472	0.183217
$369$	5.65685	0.294484
$370$	0	0
$371$	3.65685	0.189854
$372$	−6.34315	−0.328877
$373$	−25.3137	−1.31069	−0.655347	−	0.755328i	$-0.727478\pi$
$373$	−25.3137	−1.31069	−0.655347	+	0.755328i	$0.727478\pi$
$374$	−4.00000	−0.206835
$375$	0	0
$376$	14.0000	0.721995
$377$	3.65685	0.188338
$378$	−2.41421	−0.124174
$379$	27.3137	1.40301	0.701505	−	0.712664i	$-0.252512\pi$
$379$	27.3137	1.40301	0.701505	+	0.712664i	$0.252512\pi$
$380$	0	0
$381$	−16.0000	−0.819705
$382$	−64.7696	−3.31390
$383$	15.1716	0.775231	0.387616	−	0.921821i	$-0.373299\pi$
$383$	15.1716	0.775231	0.387616	+	0.921821i	$0.373299\pi$
$384$	20.5563	1.04901
$385$	0	0
$386$	65.1127	3.31415
$387$	9.65685	0.490885
$388$	−7.65685	−0.388718
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	0	0
$391$	−0.970563	−0.0490835
$392$	4.41421	0.222951
$393$	−16.9706	−0.856052
$394$	6.82843	0.344011
$395$	0	0
$396$	7.65685	0.384771
$397$	−20.3431	−1.02099	−0.510497	−	0.859880i	$-0.670538\pi$
$397$	−20.3431	−1.02099	−0.510497	+	0.859880i	$0.670538\pi$
$398$	40.9706	2.05367
$399$	5.65685	0.283197
$400$	−15.0000	−0.750000
$401$	−35.1127	−1.75344	−0.876722	−	0.480997i	$-0.840275\pi$
$401$	−35.1127	−1.75344	−0.876722	+	0.480997i	$0.840275\pi$
$402$	−9.65685	−0.481640
$403$	−1.65685	−0.0825338
$404$	18.4853	0.919677
$405$	0	0
$406$	−8.82843	−0.438147
$407$	−15.3137	−0.759072
$408$	3.65685	0.181041
$409$	9.31371	0.460533	0.230267	−	0.973128i	$-0.426040\pi$
$409$	9.31371	0.460533	0.230267	+	0.973128i	$0.426040\pi$
$410$	0	0
$411$	22.1421	1.09219
$412$	52.2843	2.57586
$413$	−10.4853	−0.515947
$414$	2.82843	0.139010
$415$	0	0
$416$	1.58579	0.0777496
$417$	17.6569	0.864660
$418$	−27.3137	−1.33596
$419$	−33.9411	−1.65813	−0.829066	−	0.559150i	$-0.811127\pi$
$419$	−33.9411	−1.65813	−0.829066	+	0.559150i	$0.811127\pi$
$420$	0	0
$421$	16.6274	0.810371	0.405185	−	0.914235i	$-0.367207\pi$
$421$	16.6274	0.810371	0.405185	+	0.914235i	$0.367207\pi$
$422$	−15.3137	−0.745460
$423$	3.17157	0.154207
$424$	16.1421	0.783931
$425$	4.14214	0.200923
$426$	−33.7990	−1.63757
$427$	−0.343146	−0.0166060
$428$	10.8284	0.523412
$429$	2.00000	0.0965609
$430$	0	0
$431$	−14.9706	−0.721107	−0.360553	−	0.932739i	$-0.617412\pi$
$431$	−14.9706	−0.721107	−0.360553	+	0.932739i	$0.617412\pi$
$432$	−3.00000	−0.144338
$433$	19.6569	0.944648	0.472324	−	0.881425i	$-0.343415\pi$
$433$	19.6569	0.944648	0.472324	+	0.881425i	$0.343415\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	−44.6274	−2.13727
$437$	−6.62742	−0.317032
$438$	18.4853	0.883261
$439$	−3.31371	−0.158155	−0.0790773	−	0.996868i	$-0.525197\pi$
$439$	−3.31371	−0.158155	−0.0790773	+	0.996868i	$0.525197\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	2.00000	0.0951303
$443$	−38.1421	−1.81219	−0.906094	−	0.423077i	$-0.860950\pi$
$443$	−38.1421	−1.81219	−0.906094	+	0.423077i	$0.860950\pi$
$444$	29.3137	1.39117
$445$	0	0
$446$	42.6274	2.01847
$447$	−4.48528	−0.212147
$448$	−9.82843	−0.464350
$449$	23.7990	1.12314	0.561572	−	0.827428i	$-0.310197\pi$
$449$	23.7990	1.12314	0.561572	+	0.827428i	$0.310197\pi$
$450$	−12.0711	−0.569036
$451$	11.3137	0.532742
$452$	1.31371	0.0617916
$453$	−0.686292	−0.0322448
$454$	−6.00000	−0.281594
$455$	0	0
$456$	24.9706	1.16935
$457$	42.2843	1.97797	0.988987	−	0.148000i	$-0.0472835\pi$
$457$	42.2843	1.97797	0.988987	+	0.148000i	$0.0472835\pi$
$458$	−47.4558	−2.21747
$459$	0.828427	0.0386677
$460$	0	0
$461$	18.3431	0.854325	0.427163	−	0.904175i	$-0.359513\pi$
$461$	18.3431	0.854325	0.427163	+	0.904175i	$0.359513\pi$
$462$	−4.82843	−0.224639
$463$	27.3137	1.26938	0.634688	−	0.772769i	$-0.281129\pi$
$463$	27.3137	1.26938	0.634688	+	0.772769i	$0.281129\pi$
$464$	−10.9706	−0.509296
$465$	0	0
$466$	3.17157	0.146920
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	−3.82843	−0.176969
$469$	4.00000	0.184703
$470$	0	0
$471$	−9.31371	−0.429153
$472$	−46.2843	−2.13041
$473$	19.3137	0.888045
$474$	27.3137	1.25456
$475$	28.2843	1.29777
$476$	−3.17157	−0.145369
$477$	3.65685	0.167436
$478$	−29.7990	−1.36297
$479$	−6.48528	−0.296320	−0.148160	−	0.988963i	$-0.547335\pi$
$479$	−6.48528	−0.296320	−0.148160	+	0.988963i	$0.547335\pi$
$480$	0	0
$481$	7.65685	0.349123
$482$	−57.1127	−2.60141
$483$	−1.17157	−0.0533084
$484$	−26.7990	−1.21814
$485$	0	0
$486$	−2.41421	−0.109511
$487$	31.3137	1.41896	0.709480	−	0.704726i	$-0.248930\pi$
$487$	31.3137	1.41896	0.709480	+	0.704726i	$0.248930\pi$
$488$	−1.51472	−0.0685681
$489$	11.3137	0.511624
$490$	0	0
$491$	−23.5147	−1.06120	−0.530602	−	0.847621i	$-0.678034\pi$
$491$	−23.5147	−1.06120	−0.530602	+	0.847621i	$0.678034\pi$
$492$	−21.6569	−0.976366
$493$	3.02944	0.136439
$494$	13.6569	0.614451
$495$	0	0
$496$	4.97056	0.223185
$497$	14.0000	0.627986
$498$	−38.9706	−1.74631
$499$	−7.31371	−0.327407	−0.163703	−	0.986510i	$-0.552344\pi$
$499$	−7.31371	−0.327407	−0.163703	+	0.986510i	$0.552344\pi$
$500$	0	0
$501$	−11.1716	−0.499109
$502$	−54.6274	−2.43814
$503$	40.2843	1.79619	0.898093	−	0.439805i	$-0.144952\pi$
$503$	40.2843	1.79619	0.898093	+	0.439805i	$0.144952\pi$
$504$	4.41421	0.196625
$505$	0	0
$506$	5.65685	0.251478
$507$	−1.00000	−0.0444116
$508$	61.2548	2.71774
$509$	−8.00000	−0.354594	−0.177297	−	0.984157i	$-0.556735\pi$
$509$	−8.00000	−0.354594	−0.177297	+	0.984157i	$0.556735\pi$
$510$	0	0
$511$	−7.65685	−0.338719
$512$	−31.2426	−1.38074
$513$	5.65685	0.249756
$514$	7.65685	0.337729
$515$	0	0
$516$	−36.9706	−1.62754
$517$	6.34315	0.278971
$518$	−18.4853	−0.812197
$519$	14.4853	0.635833
$520$	0	0
$521$	−5.79899	−0.254058	−0.127029	−	0.991899i	$-0.540544\pi$
$521$	−5.79899	−0.254058	−0.127029	+	0.991899i	$0.540544\pi$
$522$	−8.82843	−0.386410
$523$	1.65685	0.0724492	0.0362246	−	0.999344i	$-0.488467\pi$
$523$	1.65685	0.0724492	0.0362246	+	0.999344i	$0.488467\pi$
$524$	64.9706	2.83825
$525$	5.00000	0.218218
$526$	10.8284	0.472142
$527$	−1.37258	−0.0597907
$528$	−6.00000	−0.261116
$529$	−21.6274	−0.940322
$530$	0	0
$531$	−10.4853	−0.455022
$532$	−21.6569	−0.938944
$533$	−5.65685	−0.245026
$534$	−36.9706	−1.59987
$535$	0	0
$536$	17.6569	0.762660
$537$	−10.1421	−0.437665
$538$	25.3137	1.09135
$539$	2.00000	0.0861461
$540$	0	0
$541$	5.31371	0.228454	0.114227	−	0.993455i	$-0.463561\pi$
$541$	5.31371	0.228454	0.114227	+	0.993455i	$0.463561\pi$
$542$	54.6274	2.34645
$543$	4.34315	0.186382
$544$	1.31371	0.0563248
$545$	0	0
$546$	2.41421	0.103319
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−84.7696	−3.62118
$549$	−0.343146	−0.0146451
$550$	−24.1421	−1.02942
$551$	20.6863	0.881266
$552$	−5.17157	−0.220117
$553$	−11.3137	−0.481108
$554$	−24.1421	−1.02570
$555$	0	0
$556$	−67.5980	−2.86679
$557$	44.4853	1.88490	0.942451	−	0.334344i	$-0.108515\pi$
$557$	44.4853	1.88490	0.942451	+	0.334344i	$0.108515\pi$
$558$	4.00000	0.169334
$559$	−9.65685	−0.408441
$560$	0	0
$561$	1.65685	0.0699524
$562$	39.7990	1.67882
$563$	−6.34315	−0.267332	−0.133666	−	0.991026i	$-0.542675\pi$
$563$	−6.34315	−0.267332	−0.133666	+	0.991026i	$0.542675\pi$
$564$	−12.1421	−0.511276
$565$	0	0
$566$	−61.9411	−2.60358
$567$	1.00000	0.0419961
$568$	61.7990	2.59303
$569$	1.31371	0.0550735	0.0275368	−	0.999621i	$-0.491234\pi$
$569$	1.31371	0.0550735	0.0275368	+	0.999621i	$0.491234\pi$
$570$	0	0
$571$	10.6274	0.444744	0.222372	−	0.974962i	$-0.428620\pi$
$571$	10.6274	0.444744	0.222372	+	0.974962i	$0.428620\pi$
$572$	−7.65685	−0.320149
$573$	26.8284	1.12077
$574$	13.6569	0.570026
$575$	−5.85786	−0.244290
$576$	−9.82843	−0.409518
$577$	10.9706	0.456711	0.228355	−	0.973578i	$-0.426665\pi$
$577$	10.9706	0.456711	0.228355	+	0.973578i	$0.426665\pi$
$578$	−39.3848	−1.63819
$579$	−26.9706	−1.12086
$580$	0	0
$581$	16.1421	0.669689
$582$	4.82843	0.200145
$583$	7.31371	0.302903
$584$	−33.7990	−1.39861
$585$	0	0
$586$	−17.6569	−0.729398
$587$	25.1127	1.03651	0.518256	−	0.855226i	$-0.326581\pi$
$587$	25.1127	1.03651	0.518256	+	0.855226i	$0.326581\pi$
$588$	−3.82843	−0.157882
$589$	−9.37258	−0.386191
$590$	0	0
$591$	−2.82843	−0.116346
$592$	−22.9706	−0.944084
$593$	−25.6569	−1.05360	−0.526800	−	0.849989i	$-0.676608\pi$
$593$	−25.6569	−1.05360	−0.526800	+	0.849989i	$0.676608\pi$
$594$	−4.82843	−0.198113
$595$	0	0
$596$	17.1716	0.703375
$597$	−16.9706	−0.694559
$598$	−2.82843	−0.115663
$599$	−20.4853	−0.837006	−0.418503	−	0.908215i	$-0.637445\pi$
$599$	−20.4853	−0.837006	−0.418503	+	0.908215i	$0.637445\pi$
$600$	22.0711	0.901048
$601$	−10.9706	−0.447499	−0.223749	−	0.974647i	$-0.571830\pi$
$601$	−10.9706	−0.447499	−0.223749	+	0.974647i	$0.571830\pi$
$602$	23.3137	0.950196
$603$	4.00000	0.162893
$604$	2.62742	0.106908
$605$	0	0
$606$	−11.6569	−0.473527
$607$	−22.6274	−0.918419	−0.459209	−	0.888328i	$-0.651867\pi$
$607$	−22.6274	−0.918419	−0.459209	+	0.888328i	$0.651867\pi$
$608$	8.97056	0.363804
$609$	3.65685	0.148183
$610$	0	0
$611$	−3.17157	−0.128308
$612$	−3.17157	−0.128203
$613$	10.6863	0.431615	0.215808	−	0.976436i	$-0.430762\pi$
$613$	10.6863	0.431615	0.215808	+	0.976436i	$0.430762\pi$
$614$	9.65685	0.389719
$615$	0	0
$616$	8.82843	0.355707
$617$	−36.7696	−1.48029	−0.740143	−	0.672449i	$-0.765242\pi$
$617$	−36.7696	−1.48029	−0.740143	+	0.672449i	$0.765242\pi$
$618$	−32.9706	−1.32627
$619$	−36.0000	−1.44696	−0.723481	−	0.690344i	$-0.757459\pi$
$619$	−36.0000	−1.44696	−0.723481	+	0.690344i	$0.757459\pi$
$620$	0	0
$621$	−1.17157	−0.0470136
$622$	−75.5980	−3.03120
$623$	15.3137	0.613531
$624$	3.00000	0.120096
$625$	25.0000	1.00000
$626$	−26.4853	−1.05856
$627$	11.3137	0.451826
$628$	35.6569	1.42286
$629$	6.34315	0.252918
$630$	0	0
$631$	44.0000	1.75161	0.875806	−	0.482663i	$-0.160330\pi$
$631$	44.0000	1.75161	0.875806	+	0.482663i	$0.160330\pi$
$632$	−49.9411	−1.98655
$633$	6.34315	0.252117
$634$	−1.17157	−0.0465291
$635$	0	0
$636$	−14.0000	−0.555136
$637$	−1.00000	−0.0396214
$638$	−17.6569	−0.699042
$639$	14.0000	0.553831
$640$	0	0
$641$	−19.6569	−0.776399	−0.388200	−	0.921575i	$-0.626903\pi$
$641$	−19.6569	−0.776399	−0.388200	+	0.921575i	$0.626903\pi$
$642$	−6.82843	−0.269497
$643$	7.31371	0.288425	0.144212	−	0.989547i	$-0.453935\pi$
$643$	7.31371	0.288425	0.144212	+	0.989547i	$0.453935\pi$
$644$	4.48528	0.176745
$645$	0	0
$646$	11.3137	0.445132
$647$	12.2843	0.482945	0.241472	−	0.970408i	$-0.422370\pi$
$647$	12.2843	0.482945	0.241472	+	0.970408i	$0.422370\pi$
$648$	4.41421	0.173407
$649$	−20.9706	−0.823167
$650$	12.0711	0.473466
$651$	−1.65685	−0.0649372
$652$	−43.3137	−1.69630
$653$	41.5980	1.62785	0.813927	−	0.580967i	$-0.197325\pi$
$653$	41.5980	1.62785	0.813927	+	0.580967i	$0.197325\pi$
$654$	28.1421	1.10044
$655$	0	0
$656$	16.9706	0.662589
$657$	−7.65685	−0.298722
$658$	7.65685	0.298495
$659$	−29.4558	−1.14744	−0.573718	−	0.819053i	$-0.694500\pi$
$659$	−29.4558	−1.14744	−0.573718	+	0.819053i	$0.694500\pi$
$660$	0	0
$661$	9.31371	0.362261	0.181131	−	0.983459i	$-0.442024\pi$
$661$	9.31371	0.362261	0.181131	+	0.983459i	$0.442024\pi$
$662$	64.2843	2.49848
$663$	−0.828427	−0.0321734
$664$	71.2548	2.76522
$665$	0	0
$666$	−18.4853	−0.716290
$667$	−4.28427	−0.165888
$668$	42.7696	1.65480
$669$	−17.6569	−0.682653
$670$	0	0
$671$	−0.686292	−0.0264940
$672$	1.58579	0.0611730
$673$	0.627417	0.0241851	0.0120926	−	0.999927i	$-0.496151\pi$
$673$	0.627417	0.0241851	0.0120926	+	0.999927i	$0.496151\pi$
$674$	41.7990	1.61004
$675$	5.00000	0.192450
$676$	3.82843	0.147247
$677$	14.4853	0.556715	0.278357	−	0.960478i	$-0.410210\pi$
$677$	14.4853	0.556715	0.278357	+	0.960478i	$0.410210\pi$
$678$	−0.828427	−0.0318156
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	2.48528	0.0952362
$682$	8.00000	0.306336
$683$	−24.3431	−0.931465	−0.465732	−	0.884926i	$-0.654209\pi$
$683$	−24.3431	−0.931465	−0.465732	+	0.884926i	$0.654209\pi$
$684$	−21.6569	−0.828071
$685$	0	0
$686$	2.41421	0.0921751
$687$	19.6569	0.749956
$688$	28.9706	1.10449
$689$	−3.65685	−0.139315
$690$	0	0
$691$	−23.3137	−0.886895	−0.443448	−	0.896300i	$-0.646245\pi$
$691$	−23.3137	−0.886895	−0.443448	+	0.896300i	$0.646245\pi$
$692$	−55.4558	−2.10811
$693$	2.00000	0.0759737
$694$	−2.82843	−0.107366
$695$	0	0
$696$	16.1421	0.611866
$697$	−4.68629	−0.177506
$698$	−32.1421	−1.21660
$699$	−1.31371	−0.0496890
$700$	−19.1421	−0.723505
$701$	−0.627417	−0.0236972	−0.0118486	−	0.999930i	$-0.503772\pi$
$701$	−0.627417	−0.0236972	−0.0118486	+	0.999930i	$0.503772\pi$
$702$	2.41421	0.0911186
$703$	43.3137	1.63361
$704$	−19.6569	−0.740846
$705$	0	0
$706$	27.3137	1.02796
$707$	4.82843	0.181592
$708$	40.1421	1.50863
$709$	2.97056	0.111562	0.0557809	−	0.998443i	$-0.482235\pi$
$709$	2.97056	0.111562	0.0557809	+	0.998443i	$0.482235\pi$
$710$	0	0
$711$	−11.3137	−0.424297
$712$	67.5980	2.53334
$713$	1.94113	0.0726957
$714$	2.00000	0.0748481
$715$	0	0
$716$	38.8284	1.45109
$717$	12.3431	0.460963
$718$	61.1127	2.28071
$719$	30.3431	1.13161	0.565804	−	0.824540i	$-0.308566\pi$
$719$	30.3431	1.13161	0.565804	+	0.824540i	$0.308566\pi$
$720$	0	0
$721$	13.6569	0.508608
$722$	31.3848	1.16802
$723$	23.6569	0.879808
$724$	−16.6274	−0.617953
$725$	18.2843	0.679061
$726$	16.8995	0.627199
$727$	−30.6274	−1.13591	−0.567954	−	0.823060i	$-0.692265\pi$
$727$	−30.6274	−1.13591	−0.567954	+	0.823060i	$0.692265\pi$
$728$	−4.41421	−0.163602
$729$	1.00000	0.0370370
$730$	0	0
$731$	−8.00000	−0.295891
$732$	1.31371	0.0485561
$733$	−18.2843	−0.675345	−0.337672	−	0.941264i	$-0.609640\pi$
$733$	−18.2843	−0.675345	−0.337672	+	0.941264i	$0.609640\pi$
$734$	−54.6274	−2.01633
$735$	0	0
$736$	−1.85786	−0.0684818
$737$	8.00000	0.294684
$738$	13.6569	0.502716
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	0	0
$741$	−5.65685	−0.207810
$742$	8.82843	0.324102
$743$	−24.6274	−0.903492	−0.451746	−	0.892147i	$-0.649199\pi$
$743$	−24.6274	−0.903492	−0.451746	+	0.892147i	$0.649199\pi$
$744$	−7.31371	−0.268134
$745$	0	0
$746$	−61.1127	−2.23749
$747$	16.1421	0.590610
$748$	−6.34315	−0.231928
$749$	2.82843	0.103348
$750$	0	0
$751$	28.2843	1.03211	0.516054	−	0.856556i	$-0.327400\pi$
$751$	28.2843	1.03211	0.516054	+	0.856556i	$0.327400\pi$
$752$	9.51472	0.346966
$753$	22.6274	0.824589
$754$	8.82843	0.321512
$755$	0	0
$756$	−3.82843	−0.139239
$757$	−20.6274	−0.749716	−0.374858	−	0.927082i	$-0.622309\pi$
$757$	−20.6274	−0.749716	−0.374858	+	0.927082i	$0.622309\pi$
$758$	65.9411	2.39509
$759$	−2.34315	−0.0850508
$760$	0	0
$761$	−48.9706	−1.77518	−0.887591	−	0.460633i	$-0.847622\pi$
$761$	−48.9706	−1.77518	−0.887591	+	0.460633i	$0.847622\pi$
$762$	−38.6274	−1.39932
$763$	−11.6569	−0.422006
$764$	−102.711	−3.71594
$765$	0	0
$766$	36.6274	1.32340
$767$	10.4853	0.378602
$768$	29.9706	1.08147
$769$	−39.9411	−1.44031	−0.720157	−	0.693811i	$-0.755930\pi$
$769$	−39.9411	−1.44031	−0.720157	+	0.693811i	$0.755930\pi$
$770$	0	0
$771$	−3.17157	−0.114221
$772$	103.255	3.71622
$773$	20.0000	0.719350	0.359675	−	0.933078i	$-0.382888\pi$
$773$	20.0000	0.719350	0.359675	+	0.933078i	$0.382888\pi$
$774$	23.3137	0.837994
$775$	−8.28427	−0.297580
$776$	−8.82843	−0.316922
$777$	7.65685	0.274688
$778$	53.1127	1.90418
$779$	−32.0000	−1.14652
$780$	0	0
$781$	28.0000	1.00192
$782$	−2.34315	−0.0837907
$783$	3.65685	0.130685
$784$	3.00000	0.107143
$785$	0	0
$786$	−40.9706	−1.46137
$787$	−7.31371	−0.260706	−0.130353	−	0.991468i	$-0.541611\pi$
$787$	−7.31371	−0.260706	−0.130353	+	0.991468i	$0.541611\pi$
$788$	10.8284	0.385747
$789$	−4.48528	−0.159680
$790$	0	0
$791$	0.343146	0.0122009
$792$	8.82843	0.313704
$793$	0.343146	0.0121855
$794$	−49.1127	−1.74294
$795$	0	0
$796$	64.9706	2.30282
$797$	−16.1421	−0.571784	−0.285892	−	0.958262i	$-0.592290\pi$
$797$	−16.1421	−0.571784	−0.285892	+	0.958262i	$0.592290\pi$
$798$	13.6569	0.483447
$799$	−2.62742	−0.0929513
$800$	7.92893	0.280330
$801$	15.3137	0.541083
$802$	−84.7696	−2.99332
$803$	−15.3137	−0.540409
$804$	−15.3137	−0.540073
$805$	0	0
$806$	−4.00000	−0.140894
$807$	−10.4853	−0.369099
$808$	21.3137	0.749814
$809$	−2.97056	−0.104439	−0.0522197	−	0.998636i	$-0.516630\pi$
$809$	−2.97056	−0.104439	−0.0522197	+	0.998636i	$0.516630\pi$
$810$	0	0
$811$	−28.2843	−0.993195	−0.496598	−	0.867981i	$-0.665417\pi$
$811$	−28.2843	−0.993195	−0.496598	+	0.867981i	$0.665417\pi$
$812$	−14.0000	−0.491304
$813$	−22.6274	−0.793578
$814$	−36.9706	−1.29582
$815$	0	0
$816$	2.48528	0.0870023
$817$	−54.6274	−1.91117
$818$	22.4853	0.786179
$819$	−1.00000	−0.0349428
$820$	0	0
$821$	−21.4558	−0.748814	−0.374407	−	0.927264i	$-0.622154\pi$
$821$	−21.4558	−0.748814	−0.374407	+	0.927264i	$0.622154\pi$
$822$	53.4558	1.86449
$823$	22.6274	0.788742	0.394371	−	0.918951i	$-0.370962\pi$
$823$	22.6274	0.788742	0.394371	+	0.918951i	$0.370962\pi$
$824$	60.2843	2.10010
$825$	10.0000	0.348155
$826$	−25.3137	−0.880777
$827$	−22.0000	−0.765015	−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000	−0.765015	−0.382507	+	0.923952i	$0.624939\pi$
$828$	4.48528	0.155874
$829$	−41.3137	−1.43488	−0.717442	−	0.696618i	$-0.754687\pi$
$829$	−41.3137	−1.43488	−0.717442	+	0.696618i	$0.754687\pi$
$830$	0	0
$831$	10.0000	0.346896
$832$	9.82843	0.340739
$833$	−0.828427	−0.0287033
$834$	42.6274	1.47607
$835$	0	0
$836$	−43.3137	−1.49804
$837$	−1.65685	−0.0572693
$838$	−81.9411	−2.83061
$839$	−49.7990	−1.71925	−0.859626	−	0.510924i	$-0.829303\pi$
$839$	−49.7990	−1.71925	−0.859626	+	0.510924i	$0.829303\pi$
$840$	0	0
$841$	−15.6274	−0.538876
$842$	40.1421	1.38339
$843$	−16.4853	−0.567783
$844$	−24.2843	−0.835899
$845$	0	0
$846$	7.65685	0.263248
$847$	−7.00000	−0.240523
$848$	10.9706	0.376731
$849$	25.6569	0.880541
$850$	10.0000	0.342997
$851$	−8.97056	−0.307507
$852$	−53.5980	−1.83624
$853$	6.97056	0.238668	0.119334	−	0.992854i	$-0.461924\pi$
$853$	6.97056	0.238668	0.119334	+	0.992854i	$0.461924\pi$
$854$	−0.828427	−0.0283482
$855$	0	0
$856$	12.4853	0.426738
$857$	37.1127	1.26775	0.633873	−	0.773437i	$-0.281464\pi$
$857$	37.1127	1.26775	0.633873	+	0.773437i	$0.281464\pi$
$858$	4.82843	0.164840
$859$	−28.9706	−0.988463	−0.494231	−	0.869330i	$-0.664550\pi$
$859$	−28.9706	−0.988463	−0.494231	+	0.869330i	$0.664550\pi$
$860$	0	0
$861$	−5.65685	−0.192785
$862$	−36.1421	−1.23101
$863$	−43.2548	−1.47241	−0.736206	−	0.676758i	$-0.763384\pi$
$863$	−43.2548	−1.47241	−0.736206	+	0.676758i	$0.763384\pi$
$864$	1.58579	0.0539496
$865$	0	0
$866$	47.4558	1.61262
$867$	16.3137	0.554043
$868$	6.34315	0.215300
$869$	−22.6274	−0.767583
$870$	0	0
$871$	−4.00000	−0.135535
$872$	−51.4558	−1.74251
$873$	−2.00000	−0.0676897
$874$	−16.0000	−0.541208
$875$	0	0
$876$	29.3137	0.990418
$877$	18.6863	0.630991	0.315496	−	0.948927i	$-0.397829\pi$
$877$	18.6863	0.630991	0.315496	+	0.948927i	$0.397829\pi$
$878$	−8.00000	−0.269987
$879$	7.31371	0.246685
$880$	0	0
$881$	34.7696	1.17142	0.585708	−	0.810522i	$-0.300817\pi$
$881$	34.7696	1.17142	0.585708	+	0.810522i	$0.300817\pi$
$882$	2.41421	0.0812908
$883$	−8.28427	−0.278788	−0.139394	−	0.990237i	$-0.544515\pi$
$883$	−8.28427	−0.278788	−0.139394	+	0.990237i	$0.544515\pi$
$884$	3.17157	0.106672
$885$	0	0
$886$	−92.0833	−3.09360
$887$	48.9706	1.64427	0.822135	−	0.569292i	$-0.192783\pi$
$887$	48.9706	1.64427	0.822135	+	0.569292i	$0.192783\pi$
$888$	33.7990	1.13422
$889$	16.0000	0.536623
$890$	0	0
$891$	2.00000	0.0670025
$892$	67.5980	2.26335
$893$	−17.9411	−0.600377
$894$	−10.8284	−0.362157
$895$	0	0
$896$	−20.5563	−0.686739
$897$	1.17157	0.0391177
$898$	57.4558	1.91733
$899$	−6.05887	−0.202075
$900$	−19.1421	−0.638071
$901$	−3.02944	−0.100925
$902$	27.3137	0.909447
$903$	−9.65685	−0.321360
$904$	1.51472	0.0503788
$905$	0	0
$906$	−1.65685	−0.0550453
$907$	−49.6569	−1.64883	−0.824414	−	0.565987i	$-0.808495\pi$
$907$	−49.6569	−1.64883	−0.824414	+	0.565987i	$0.808495\pi$
$908$	−9.51472	−0.315757
$909$	4.82843	0.160149
$910$	0	0
$911$	7.11270	0.235654	0.117827	−	0.993034i	$-0.462407\pi$
$911$	7.11270	0.235654	0.117827	+	0.993034i	$0.462407\pi$
$912$	16.9706	0.561951
$913$	32.2843	1.06845
$914$	102.083	3.37661
$915$	0	0
$916$	−75.2548	−2.48649
$917$	16.9706	0.560417
$918$	2.00000	0.0660098
$919$	−40.9706	−1.35149	−0.675747	−	0.737134i	$-0.736179\pi$
$919$	−40.9706	−1.35149	−0.675747	+	0.737134i	$0.736179\pi$
$920$	0	0
$921$	−4.00000	−0.131804
$922$	44.2843	1.45842
$923$	−14.0000	−0.460816
$924$	−7.65685	−0.251892
$925$	38.2843	1.25878
$926$	65.9411	2.16696
$927$	13.6569	0.448550
$928$	5.79899	0.190361
$929$	0.970563	0.0318431	0.0159216	−	0.999873i	$-0.494932\pi$
$929$	0.970563	0.0318431	0.0159216	+	0.999873i	$0.494932\pi$
$930$	0	0
$931$	−5.65685	−0.185396
$932$	5.02944	0.164745
$933$	31.3137	1.02516
$934$	−19.3137	−0.631964
$935$	0	0
$936$	−4.41421	−0.144283
$937$	14.9706	0.489067	0.244533	−	0.969641i	$-0.421365\pi$
$937$	14.9706	0.489067	0.244533	+	0.969641i	$0.421365\pi$
$938$	9.65685	0.315307
$939$	10.9706	0.358011
$940$	0	0
$941$	41.6569	1.35797	0.678987	−	0.734150i	$-0.262419\pi$
$941$	41.6569	1.35797	0.678987	+	0.734150i	$0.262419\pi$
$942$	−22.4853	−0.732610
$943$	6.62742	0.215818
$944$	−31.4558	−1.02380
$945$	0	0
$946$	46.6274	1.51599
$947$	6.97056	0.226513	0.113256	−	0.993566i	$-0.463872\pi$
$947$	6.97056	0.226513	0.113256	+	0.993566i	$0.463872\pi$
$948$	43.3137	1.40676
$949$	7.65685	0.248552
$950$	68.2843	2.21543
$951$	0.485281	0.0157363
$952$	−3.65685	−0.118519
$953$	−28.3431	−0.918125	−0.459062	−	0.888404i	$-0.651815\pi$
$953$	−28.3431	−0.918125	−0.459062	+	0.888404i	$0.651815\pi$
$954$	8.82843	0.285831
$955$	0	0
$956$	−47.2548	−1.52833
$957$	7.31371	0.236419
$958$	−15.6569	−0.505850
$959$	−22.1421	−0.715007
$960$	0	0
$961$	−28.2548	−0.911446
$962$	18.4853	0.595989
$963$	2.82843	0.0911448
$964$	−90.5685	−2.91702
$965$	0	0
$966$	−2.82843	−0.0910032
$967$	5.94113	0.191054	0.0955269	−	0.995427i	$-0.469546\pi$
$967$	5.94113	0.191054	0.0955269	+	0.995427i	$0.469546\pi$
$968$	−30.8995	−0.993147
$969$	−4.68629	−0.150545
$970$	0	0
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	−3.82843	−0.122797
$973$	−17.6569	−0.566053
$974$	75.5980	2.42232
$975$	−5.00000	−0.160128
$976$	−1.02944	−0.0329515
$977$	42.1421	1.34825	0.674123	−	0.738619i	$-0.264522\pi$
$977$	42.1421	1.34825	0.674123	+	0.738619i	$0.264522\pi$
$978$	27.3137	0.873396
$979$	30.6274	0.978856
$980$	0	0
$981$	−11.6569	−0.372175
$982$	−56.7696	−1.81159
$983$	49.1127	1.56645	0.783226	−	0.621737i	$-0.213573\pi$
$983$	49.1127	1.56645	0.783226	+	0.621737i	$0.213573\pi$
$984$	−24.9706	−0.796032
$985$	0	0
$986$	7.31371	0.232916
$987$	−3.17157	−0.100952
$988$	21.6569	0.688996
$989$	11.3137	0.359755
$990$	0	0
$991$	−53.6569	−1.70447	−0.852233	−	0.523162i	$-0.824752\pi$
$991$	−53.6569	−1.70447	−0.852233	+	0.523162i	$0.824752\pi$
$992$	−2.62742	−0.0834206
$993$	−26.6274	−0.844996
$994$	33.7990	1.07204
$995$	0	0
$996$	−61.7990	−1.95818
$997$	10.6863	0.338438	0.169219	−	0.985578i	$-0.445875\pi$
$997$	10.6863	0.338438	0.169219	+	0.985578i	$0.445875\pi$
$998$	−17.6569	−0.558918
$999$	7.65685	0.242252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.a.c.1.2	✓	2
3.2	odd	2		819.2.a.g.1.1		2
4.3	odd	2		4368.2.a.bj.1.1		2
5.4	even	2		6825.2.a.m.1.1		2
7.6	odd	2		1911.2.a.k.1.2		2
13.12	even	2		3549.2.a.f.1.1		2
21.20	even	2		5733.2.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.c.1.2	✓	2	1.1	even	1	trivial
819.2.a.g.1.1		2	3.2	odd	2
1911.2.a.k.1.2		2	7.6	odd	2
3549.2.a.f.1.1		2	13.12	even	2
4368.2.a.bj.1.1		2	4.3	odd	2
5733.2.a.n.1.1		2	21.20	even	2
6825.2.a.m.1.1		2	5.4	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} -2.41421 q^{6} +1.00000 q^{7} +4.41421 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} -2.41421 q^{6} +1.00000 q^{7} +4.41421 q^{8} +1.00000 q^{9} +2.00000 q^{11} -3.82843 q^{12} -1.00000 q^{13} +2.41421 q^{14} +3.00000 q^{16} -0.828427 q^{17} +2.41421 q^{18} -5.65685 q^{19} -1.00000 q^{21} +4.82843 q^{22} +1.17157 q^{23} -4.41421 q^{24} -5.00000 q^{25} -2.41421 q^{26} -1.00000 q^{27} +3.82843 q^{28} -3.65685 q^{29} +1.65685 q^{31} -1.58579 q^{32} -2.00000 q^{33} -2.00000 q^{34} +3.82843 q^{36} -7.65685 q^{37} -13.6569 q^{38} +1.00000 q^{39} +5.65685 q^{41} -2.41421 q^{42} +9.65685 q^{43} +7.65685 q^{44} +2.82843 q^{46} +3.17157 q^{47} -3.00000 q^{48} +1.00000 q^{49} -12.0711 q^{50} +0.828427 q^{51} -3.82843 q^{52} +3.65685 q^{53} -2.41421 q^{54} +4.41421 q^{56} +5.65685 q^{57} -8.82843 q^{58} -10.4853 q^{59} -0.343146 q^{61} +4.00000 q^{62} +1.00000 q^{63} -9.82843 q^{64} -4.82843 q^{66} +4.00000 q^{67} -3.17157 q^{68} -1.17157 q^{69} +14.0000 q^{71} +4.41421 q^{72} -7.65685 q^{73} -18.4853 q^{74} +5.00000 q^{75} -21.6569 q^{76} +2.00000 q^{77} +2.41421 q^{78} -11.3137 q^{79} +1.00000 q^{81} +13.6569 q^{82} +16.1421 q^{83} -3.82843 q^{84} +23.3137 q^{86} +3.65685 q^{87} +8.82843 q^{88} +15.3137 q^{89} -1.00000 q^{91} +4.48528 q^{92} -1.65685 q^{93} +7.65685 q^{94} +1.58579 q^{96} -2.00000 q^{97} +2.41421 q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} - 10 q^{25} - 2 q^{26} - 2 q^{27} + 2 q^{28} + 4 q^{29} - 8 q^{31} - 6 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 16 q^{38} + 2 q^{39} - 2 q^{42} + 8 q^{43} + 4 q^{44} + 12 q^{47} - 6 q^{48} + 2 q^{49} - 10 q^{50} - 4 q^{51} - 2 q^{52} - 4 q^{53} - 2 q^{54} + 6 q^{56} - 12 q^{58} - 4 q^{59} - 12 q^{61} + 8 q^{62} + 2 q^{63} - 14 q^{64} - 4 q^{66} + 8 q^{67} - 12 q^{68} - 8 q^{69} + 28 q^{71} + 6 q^{72} - 4 q^{73} - 20 q^{74} + 10 q^{75} - 32 q^{76} + 4 q^{77} + 2 q^{78} + 2 q^{81} + 16 q^{82} + 4 q^{83} - 2 q^{84} + 24 q^{86} - 4 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{91} - 8 q^{92} + 8 q^{93} + 4 q^{94} + 6 q^{96} - 4 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 - 10 * q^25 - 2 * q^26 - 2 * q^27 + 2 * q^28 + 4 * q^29 - 8 * q^31 - 6 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 16 * q^38 + 2 * q^39 - 2 * q^42 + 8 * q^43 + 4 * q^44 + 12 * q^47 - 6 * q^48 + 2 * q^49 - 10 * q^50 - 4 * q^51 - 2 * q^52 - 4 * q^53 - 2 * q^54 + 6 * q^56 - 12 * q^58 - 4 * q^59 - 12 * q^61 + 8 * q^62 + 2 * q^63 - 14 * q^64 - 4 * q^66 + 8 * q^67 - 12 * q^68 - 8 * q^69 + 28 * q^71 + 6 * q^72 - 4 * q^73 - 20 * q^74 + 10 * q^75 - 32 * q^76 + 4 * q^77 + 2 * q^78 + 2 * q^81 + 16 * q^82 + 4 * q^83 - 2 * q^84 + 24 * q^86 - 4 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^91 - 8 * q^92 + 8 * q^93 + 4 * q^94 + 6 * q^96 - 4 * q^97 + 2 * q^98 + 4 * q^99

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