LMFDB - Embedded newform 8022.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	7.7.118870813.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 $ x^7 - 9x^5 - 3x^4 + 20x^3 + 7x^2 - 13*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.52532$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.58265 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.58265 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.58265 q^{10} +2.43459 q^{11} +1.00000 q^{12} +2.21415 q^{13} +1.00000 q^{14} -3.58265 q^{15} +1.00000 q^{16} -5.32904 q^{17} +1.00000 q^{18} -4.95539 q^{19} -3.58265 q^{20} +1.00000 q^{21} +2.43459 q^{22} +2.78063 q^{23} +1.00000 q^{24} +7.83541 q^{25} +2.21415 q^{26} +1.00000 q^{27} +1.00000 q^{28} -3.20548 q^{29} -3.58265 q^{30} -8.14486 q^{31} +1.00000 q^{32} +2.43459 q^{33} -5.32904 q^{34} -3.58265 q^{35} +1.00000 q^{36} -2.90646 q^{37} -4.95539 q^{38} +2.21415 q^{39} -3.58265 q^{40} -10.0487 q^{41} +1.00000 q^{42} -0.360753 q^{43} +2.43459 q^{44} -3.58265 q^{45} +2.78063 q^{46} +4.29971 q^{47} +1.00000 q^{48} +1.00000 q^{49} +7.83541 q^{50} -5.32904 q^{51} +2.21415 q^{52} +2.73826 q^{53} +1.00000 q^{54} -8.72230 q^{55} +1.00000 q^{56} -4.95539 q^{57} -3.20548 q^{58} +14.5207 q^{59} -3.58265 q^{60} -11.3279 q^{61} -8.14486 q^{62} +1.00000 q^{63} +1.00000 q^{64} -7.93252 q^{65} +2.43459 q^{66} -14.7901 q^{67} -5.32904 q^{68} +2.78063 q^{69} -3.58265 q^{70} +5.84436 q^{71} +1.00000 q^{72} +1.87603 q^{73} -2.90646 q^{74} +7.83541 q^{75} -4.95539 q^{76} +2.43459 q^{77} +2.21415 q^{78} +7.01184 q^{79} -3.58265 q^{80} +1.00000 q^{81} -10.0487 q^{82} -0.953479 q^{83} +1.00000 q^{84} +19.0921 q^{85} -0.360753 q^{86} -3.20548 q^{87} +2.43459 q^{88} -7.53346 q^{89} -3.58265 q^{90} +2.21415 q^{91} +2.78063 q^{92} -8.14486 q^{93} +4.29971 q^{94} +17.7534 q^{95} +1.00000 q^{96} -11.1858 q^{97} +1.00000 q^{98} +2.43459 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} - 8 q^{5} + 7 q^{6} + 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 - 8 * q^5 + 7 * q^6 + 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} - 8 q^{5} + 7 q^{6} + 7 q^{7} + 7 q^{8} + 7 q^{9} - 8 q^{10} - 9 q^{11} + 7 q^{12} - 15 q^{13} + 7 q^{14} - 8 q^{15} + 7 q^{16} - 16 q^{17} + 7 q^{18} - 18 q^{19} - 8 q^{20} + 7 q^{21} - 9 q^{22} - 3 q^{23} + 7 q^{24} - 5 q^{25} - 15 q^{26} + 7 q^{27} + 7 q^{28} - 5 q^{29} - 8 q^{30} - 22 q^{31} + 7 q^{32} - 9 q^{33} - 16 q^{34} - 8 q^{35} + 7 q^{36} - 6 q^{37} - 18 q^{38} - 15 q^{39} - 8 q^{40} - 20 q^{41} + 7 q^{42} - 19 q^{43} - 9 q^{44} - 8 q^{45} - 3 q^{46} - 13 q^{47} + 7 q^{48} + 7 q^{49} - 5 q^{50} - 16 q^{51} - 15 q^{52} - 4 q^{53} + 7 q^{54} - 21 q^{55} + 7 q^{56} - 18 q^{57} - 5 q^{58} - 14 q^{59} - 8 q^{60} - 25 q^{61} - 22 q^{62} + 7 q^{63} + 7 q^{64} + 16 q^{65} - 9 q^{66} - 27 q^{67} - 16 q^{68} - 3 q^{69} - 8 q^{70} + 9 q^{71} + 7 q^{72} - 15 q^{73} - 6 q^{74} - 5 q^{75} - 18 q^{76} - 9 q^{77} - 15 q^{78} - 9 q^{79} - 8 q^{80} + 7 q^{81} - 20 q^{82} - 12 q^{83} + 7 q^{84} + 18 q^{85} - 19 q^{86} - 5 q^{87} - 9 q^{88} - 19 q^{89} - 8 q^{90} - 15 q^{91} - 3 q^{92} - 22 q^{93} - 13 q^{94} + 16 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} - 9 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 - 8 * q^5 + 7 * q^6 + 7 * q^7 + 7 * q^8 + 7 * q^9 - 8 * q^10 - 9 * q^11 + 7 * q^12 - 15 * q^13 + 7 * q^14 - 8 * q^15 + 7 * q^16 - 16 * q^17 + 7 * q^18 - 18 * q^19 - 8 * q^20 + 7 * q^21 - 9 * q^22 - 3 * q^23 + 7 * q^24 - 5 * q^25 - 15 * q^26 + 7 * q^27 + 7 * q^28 - 5 * q^29 - 8 * q^30 - 22 * q^31 + 7 * q^32 - 9 * q^33 - 16 * q^34 - 8 * q^35 + 7 * q^36 - 6 * q^37 - 18 * q^38 - 15 * q^39 - 8 * q^40 - 20 * q^41 + 7 * q^42 - 19 * q^43 - 9 * q^44 - 8 * q^45 - 3 * q^46 - 13 * q^47 + 7 * q^48 + 7 * q^49 - 5 * q^50 - 16 * q^51 - 15 * q^52 - 4 * q^53 + 7 * q^54 - 21 * q^55 + 7 * q^56 - 18 * q^57 - 5 * q^58 - 14 * q^59 - 8 * q^60 - 25 * q^61 - 22 * q^62 + 7 * q^63 + 7 * q^64 + 16 * q^65 - 9 * q^66 - 27 * q^67 - 16 * q^68 - 3 * q^69 - 8 * q^70 + 9 * q^71 + 7 * q^72 - 15 * q^73 - 6 * q^74 - 5 * q^75 - 18 * q^76 - 9 * q^77 - 15 * q^78 - 9 * q^79 - 8 * q^80 + 7 * q^81 - 20 * q^82 - 12 * q^83 + 7 * q^84 + 18 * q^85 - 19 * q^86 - 5 * q^87 - 9 * q^88 - 19 * q^89 - 8 * q^90 - 15 * q^91 - 3 * q^92 - 22 * q^93 - 13 * q^94 + 16 * q^95 + 7 * q^96 - 18 * q^97 + 7 * q^98 - 9 * 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
$5$	−3.58265	−1.60221	−0.801106	−	0.598523i	$-0.795755\pi$
$5$	−3.58265	−1.60221	−0.801106	+	0.598523i	$0.795755\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.58265	−1.13293
$11$	2.43459	0.734057	0.367029	−	0.930210i	$-0.380375\pi$
$11$	2.43459	0.734057	0.367029	+	0.930210i	$0.380375\pi$
$12$	1.00000	0.288675
$13$	2.21415	0.614094	0.307047	−	0.951694i	$-0.400659\pi$
$13$	2.21415	0.614094	0.307047	+	0.951694i	$0.400659\pi$
$14$	1.00000	0.267261
$15$	−3.58265	−0.925037
$16$	1.00000	0.250000
$17$	−5.32904	−1.29248	−0.646241	−	0.763134i	$-0.723660\pi$
$17$	−5.32904	−1.29248	−0.646241	+	0.763134i	$0.723660\pi$
$18$	1.00000	0.235702
$19$	−4.95539	−1.13684	−0.568422	−	0.822737i	$-0.692446\pi$
$19$	−4.95539	−1.13684	−0.568422	+	0.822737i	$0.692446\pi$
$20$	−3.58265	−0.801106
$21$	1.00000	0.218218
$22$	2.43459	0.519057
$23$	2.78063	0.579801	0.289900	−	0.957057i	$-0.406378\pi$
$23$	2.78063	0.579801	0.289900	+	0.957057i	$0.406378\pi$
$24$	1.00000	0.204124
$25$	7.83541	1.56708
$26$	2.21415	0.434230
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−3.20548	−0.595242	−0.297621	−	0.954684i	$-0.596193\pi$
$29$	−3.20548	−0.595242	−0.297621	+	0.954684i	$0.596193\pi$
$30$	−3.58265	−0.654100
$31$	−8.14486	−1.46286	−0.731430	−	0.681916i	$-0.761147\pi$
$31$	−8.14486	−1.46286	−0.731430	+	0.681916i	$0.761147\pi$
$32$	1.00000	0.176777
$33$	2.43459	0.423808
$34$	−5.32904	−0.913922
$35$	−3.58265	−0.605579
$36$	1.00000	0.166667
$37$	−2.90646	−0.477820	−0.238910	−	0.971042i	$-0.576790\pi$
$37$	−2.90646	−0.477820	−0.238910	+	0.971042i	$0.576790\pi$
$38$	−4.95539	−0.803870
$39$	2.21415	0.354547
$40$	−3.58265	−0.566467
$41$	−10.0487	−1.56934	−0.784672	−	0.619911i	$-0.787169\pi$
$41$	−10.0487	−1.56934	−0.784672	+	0.619911i	$0.787169\pi$
$42$	1.00000	0.154303
$43$	−0.360753	−0.0550143	−0.0275072	−	0.999622i	$-0.508757\pi$
$43$	−0.360753	−0.0550143	−0.0275072	+	0.999622i	$0.508757\pi$
$44$	2.43459	0.367029
$45$	−3.58265	−0.534070
$46$	2.78063	0.409981
$47$	4.29971	0.627176	0.313588	−	0.949559i	$-0.398469\pi$
$47$	4.29971	0.627176	0.313588	+	0.949559i	$0.398469\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	7.83541	1.10809
$51$	−5.32904	−0.746214
$52$	2.21415	0.307047
$53$	2.73826	0.376129	0.188064	−	0.982157i	$-0.439779\pi$
$53$	2.73826	0.376129	0.188064	+	0.982157i	$0.439779\pi$
$54$	1.00000	0.136083
$55$	−8.72230	−1.17612
$56$	1.00000	0.133631
$57$	−4.95539	−0.656357
$58$	−3.20548	−0.420900
$59$	14.5207	1.89044	0.945219	−	0.326436i	$-0.105848\pi$
$59$	14.5207	1.89044	0.945219	+	0.326436i	$0.105848\pi$
$60$	−3.58265	−0.462519
$61$	−11.3279	−1.45039	−0.725197	−	0.688541i	$-0.758251\pi$
$61$	−11.3279	−1.45039	−0.725197	+	0.688541i	$0.758251\pi$
$62$	−8.14486	−1.03440
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−7.93252	−0.983908
$66$	2.43459	0.299678
$67$	−14.7901	−1.80690	−0.903452	−	0.428690i	$-0.858975\pi$
$67$	−14.7901	−1.80690	−0.903452	+	0.428690i	$0.858975\pi$
$68$	−5.32904	−0.646241
$69$	2.78063	0.334748
$70$	−3.58265	−0.428209
$71$	5.84436	0.693598	0.346799	−	0.937940i	$-0.387269\pi$
$71$	5.84436	0.693598	0.346799	+	0.937940i	$0.387269\pi$
$72$	1.00000	0.117851
$73$	1.87603	0.219573	0.109787	−	0.993955i	$-0.464983\pi$
$73$	1.87603	0.219573	0.109787	+	0.993955i	$0.464983\pi$
$74$	−2.90646	−0.337870
$75$	7.83541	0.904755
$76$	−4.95539	−0.568422
$77$	2.43459	0.277448
$78$	2.21415	0.250703
$79$	7.01184	0.788893	0.394447	−	0.918919i	$-0.370936\pi$
$79$	7.01184	0.788893	0.394447	+	0.918919i	$0.370936\pi$
$80$	−3.58265	−0.400553
$81$	1.00000	0.111111
$82$	−10.0487	−1.10969
$83$	−0.953479	−0.104658	−0.0523290	−	0.998630i	$-0.516664\pi$
$83$	−0.953479	−0.104658	−0.0523290	+	0.998630i	$0.516664\pi$
$84$	1.00000	0.109109
$85$	19.0921	2.07083
$86$	−0.360753	−0.0389010
$87$	−3.20548	−0.343663
$88$	2.43459	0.259528
$89$	−7.53346	−0.798545	−0.399273	−	0.916832i	$-0.630737\pi$
$89$	−7.53346	−0.798545	−0.399273	+	0.916832i	$0.630737\pi$
$90$	−3.58265	−0.377645
$91$	2.21415	0.232106
$92$	2.78063	0.289900
$93$	−8.14486	−0.844583
$94$	4.29971	0.443481
$95$	17.7534	1.82146
$96$	1.00000	0.102062
$97$	−11.1858	−1.13574	−0.567872	−	0.823117i	$-0.692233\pi$
$97$	−11.1858	−1.13574	−0.567872	+	0.823117i	$0.692233\pi$
$98$	1.00000	0.101015
$99$	2.43459	0.244686
$100$	7.83541	0.783541
$101$	11.2629	1.12070	0.560352	−	0.828255i	$-0.310666\pi$
$101$	11.2629	1.12070	0.560352	+	0.828255i	$0.310666\pi$
$102$	−5.32904	−0.527653
$103$	−0.712397	−0.0701946	−0.0350973	−	0.999384i	$-0.511174\pi$
$103$	−0.712397	−0.0701946	−0.0350973	+	0.999384i	$0.511174\pi$
$104$	2.21415	0.217115
$105$	−3.58265	−0.349631
$106$	2.73826	0.265963
$107$	1.33155	0.128725	0.0643627	−	0.997927i	$-0.479499\pi$
$107$	1.33155	0.128725	0.0643627	+	0.997927i	$0.479499\pi$
$108$	1.00000	0.0962250
$109$	−9.77823	−0.936585	−0.468292	−	0.883574i	$-0.655131\pi$
$109$	−9.77823	−0.936585	−0.468292	+	0.883574i	$0.655131\pi$
$110$	−8.72230	−0.831639
$111$	−2.90646	−0.275869
$112$	1.00000	0.0944911
$113$	15.5768	1.46534	0.732671	−	0.680584i	$-0.238274\pi$
$113$	15.5768	1.46534	0.732671	+	0.680584i	$0.238274\pi$
$114$	−4.95539	−0.464114
$115$	−9.96203	−0.928964
$116$	−3.20548	−0.297621
$117$	2.21415	0.204698
$118$	14.5207	1.33674
$119$	−5.32904	−0.488512
$120$	−3.58265	−0.327050
$121$	−5.07276	−0.461160
$122$	−11.3279	−1.02558
$123$	−10.0487	−0.906062
$124$	−8.14486	−0.731430
$125$	−10.1583	−0.908584
$126$	1.00000	0.0890871
$127$	−12.5561	−1.11417	−0.557085	−	0.830455i	$-0.688080\pi$
$127$	−12.5561	−1.11417	−0.557085	+	0.830455i	$0.688080\pi$
$128$	1.00000	0.0883883
$129$	−0.360753	−0.0317625
$130$	−7.93252	−0.695728
$131$	−11.5905	−1.01267	−0.506335	−	0.862337i	$-0.669000\pi$
$131$	−11.5905	−1.01267	−0.506335	+	0.862337i	$0.669000\pi$
$132$	2.43459	0.211904
$133$	−4.95539	−0.429686
$134$	−14.7901	−1.27767
$135$	−3.58265	−0.308346
$136$	−5.32904	−0.456961
$137$	−4.05458	−0.346406	−0.173203	−	0.984886i	$-0.555412\pi$
$137$	−4.05458	−0.346406	−0.173203	+	0.984886i	$0.555412\pi$
$138$	2.78063	0.236703
$139$	−0.221442	−0.0187825	−0.00939123	−	0.999956i	$-0.502989\pi$
$139$	−0.221442	−0.0187825	−0.00939123	+	0.999956i	$0.502989\pi$
$140$	−3.58265	−0.302789
$141$	4.29971	0.362100
$142$	5.84436	0.490448
$143$	5.39055	0.450780
$144$	1.00000	0.0833333
$145$	11.4841	0.953704
$146$	1.87603	0.155262
$147$	1.00000	0.0824786
$148$	−2.90646	−0.238910
$149$	11.8240	0.968660	0.484330	−	0.874885i	$-0.339063\pi$
$149$	11.8240	0.968660	0.484330	+	0.874885i	$0.339063\pi$
$150$	7.83541	0.639758
$151$	−12.3016	−1.00109	−0.500546	−	0.865710i	$-0.666867\pi$
$151$	−12.3016	−1.00109	−0.500546	+	0.865710i	$0.666867\pi$
$152$	−4.95539	−0.401935
$153$	−5.32904	−0.430827
$154$	2.43459	0.196185
$155$	29.1802	2.34381
$156$	2.21415	0.177274
$157$	−5.71912	−0.456436	−0.228218	−	0.973610i	$-0.573290\pi$
$157$	−5.71912	−0.456436	−0.228218	+	0.973610i	$0.573290\pi$
$158$	7.01184	0.557832
$159$	2.73826	0.217158
$160$	−3.58265	−0.283234
$161$	2.78063	0.219144
$162$	1.00000	0.0785674
$163$	−5.46689	−0.428200	−0.214100	−	0.976812i	$-0.568682\pi$
$163$	−5.46689	−0.428200	−0.214100	+	0.976812i	$0.568682\pi$
$164$	−10.0487	−0.784672
$165$	−8.72230	−0.679030
$166$	−0.953479	−0.0740043
$167$	−13.8085	−1.06853	−0.534265	−	0.845317i	$-0.679412\pi$
$167$	−13.8085	−1.06853	−0.534265	+	0.845317i	$0.679412\pi$
$168$	1.00000	0.0771517
$169$	−8.09755	−0.622889
$170$	19.0921	1.46430
$171$	−4.95539	−0.378948
$172$	−0.360753	−0.0275072
$173$	−9.26423	−0.704347	−0.352173	−	0.935935i	$-0.614557\pi$
$173$	−9.26423	−0.704347	−0.352173	+	0.935935i	$0.614557\pi$
$174$	−3.20548	−0.243007
$175$	7.83541	0.592301
$176$	2.43459	0.183514
$177$	14.5207	1.09145
$178$	−7.53346	−0.564657
$179$	−15.1901	−1.13536	−0.567679	−	0.823250i	$-0.692159\pi$
$179$	−15.1901	−1.13536	−0.567679	+	0.823250i	$0.692159\pi$
$180$	−3.58265	−0.267035
$181$	−21.8546	−1.62444	−0.812219	−	0.583352i	$-0.801741\pi$
$181$	−21.8546	−1.62444	−0.812219	+	0.583352i	$0.801741\pi$
$182$	2.21415	0.164124
$183$	−11.3279	−0.837386
$184$	2.78063	0.204991
$185$	10.4129	0.765568
$186$	−8.14486	−0.597210
$187$	−12.9740	−0.948755
$188$	4.29971	0.313588
$189$	1.00000	0.0727393
$190$	17.7534	1.28797
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	1.00000	0.0721688
$193$	17.7955	1.28095	0.640474	−	0.767980i	$-0.278738\pi$
$193$	17.7955	1.28095	0.640474	+	0.767980i	$0.278738\pi$
$194$	−11.1858	−0.803092
$195$	−7.93252	−0.568060
$196$	1.00000	0.0714286
$197$	−7.18202	−0.511698	−0.255849	−	0.966717i	$-0.582355\pi$
$197$	−7.18202	−0.511698	−0.255849	+	0.966717i	$0.582355\pi$
$198$	2.43459	0.173019
$199$	−0.605928	−0.0429531	−0.0214765	−	0.999769i	$-0.506837\pi$
$199$	−0.605928	−0.0429531	−0.0214765	+	0.999769i	$0.506837\pi$
$200$	7.83541	0.554047
$201$	−14.7901	−1.04322
$202$	11.2629	0.792457
$203$	−3.20548	−0.224980
$204$	−5.32904	−0.373107
$205$	36.0010	2.51442
$206$	−0.712397	−0.0496351
$207$	2.78063	0.193267
$208$	2.21415	0.153523
$209$	−12.0643	−0.834508
$210$	−3.58265	−0.247227
$211$	12.9055	0.888449	0.444225	−	0.895915i	$-0.353479\pi$
$211$	12.9055	0.888449	0.444225	+	0.895915i	$0.353479\pi$
$212$	2.73826	0.188064
$213$	5.84436	0.400449
$214$	1.33155	0.0910226
$215$	1.29245	0.0881445
$216$	1.00000	0.0680414
$217$	−8.14486	−0.552909
$218$	−9.77823	−0.662265
$219$	1.87603	0.126771
$220$	−8.72230	−0.588058
$221$	−11.7993	−0.793705
$222$	−2.90646	−0.195069
$223$	−24.6060	−1.64774	−0.823871	−	0.566777i	$-0.808190\pi$
$223$	−24.6060	−1.64774	−0.823871	+	0.566777i	$0.808190\pi$
$224$	1.00000	0.0668153
$225$	7.83541	0.522360
$226$	15.5768	1.03615
$227$	12.0053	0.796823	0.398412	−	0.917207i	$-0.369562\pi$
$227$	12.0053	0.796823	0.398412	+	0.917207i	$0.369562\pi$
$228$	−4.95539	−0.328178
$229$	−5.60221	−0.370204	−0.185102	−	0.982719i	$-0.559262\pi$
$229$	−5.60221	−0.370204	−0.185102	+	0.982719i	$0.559262\pi$
$230$	−9.96203	−0.656877
$231$	2.43459	0.160184
$232$	−3.20548	−0.210450
$233$	−19.8447	−1.30007	−0.650034	−	0.759905i	$-0.725245\pi$
$233$	−19.8447	−1.30007	−0.650034	+	0.759905i	$0.725245\pi$
$234$	2.21415	0.144743
$235$	−15.4044	−1.00487
$236$	14.5207	0.945219
$237$	7.01184	0.455468
$238$	−5.32904	−0.345430
$239$	0.515631	0.0333534	0.0166767	−	0.999861i	$-0.494691\pi$
$239$	0.515631	0.0333534	0.0166767	+	0.999861i	$0.494691\pi$
$240$	−3.58265	−0.231259
$241$	22.9546	1.47863	0.739317	−	0.673358i	$-0.235149\pi$
$241$	22.9546	1.47863	0.739317	+	0.673358i	$0.235149\pi$
$242$	−5.07276	−0.326089
$243$	1.00000	0.0641500
$244$	−11.3279	−0.725197
$245$	−3.58265	−0.228887
$246$	−10.0487	−0.640682
$247$	−10.9720	−0.698129
$248$	−8.14486	−0.517199
$249$	−0.953479	−0.0604243
$250$	−10.1583	−0.642466
$251$	1.55602	0.0982148	0.0491074	−	0.998794i	$-0.484362\pi$
$251$	1.55602	0.0982148	0.0491074	+	0.998794i	$0.484362\pi$
$252$	1.00000	0.0629941
$253$	6.76970	0.425607
$254$	−12.5561	−0.787837
$255$	19.0921	1.19559
$256$	1.00000	0.0625000
$257$	−10.2909	−0.641927	−0.320964	−	0.947092i	$-0.604007\pi$
$257$	−10.2909	−0.641927	−0.320964	+	0.947092i	$0.604007\pi$
$258$	−0.360753	−0.0224595
$259$	−2.90646	−0.180599
$260$	−7.93252	−0.491954
$261$	−3.20548	−0.198414
$262$	−11.5905	−0.716066
$263$	1.18170	0.0728668	0.0364334	−	0.999336i	$-0.488400\pi$
$263$	1.18170	0.0728668	0.0364334	+	0.999336i	$0.488400\pi$
$264$	2.43459	0.149839
$265$	−9.81024	−0.602638
$266$	−4.95539	−0.303834
$267$	−7.53346	−0.461040
$268$	−14.7901	−0.903452
$269$	−20.8240	−1.26966	−0.634832	−	0.772650i	$-0.718931\pi$
$269$	−20.8240	−1.26966	−0.634832	+	0.772650i	$0.718931\pi$
$270$	−3.58265	−0.218033
$271$	−10.7360	−0.652165	−0.326082	−	0.945341i	$-0.605729\pi$
$271$	−10.7360	−0.652165	−0.326082	+	0.945341i	$0.605729\pi$
$272$	−5.32904	−0.323120
$273$	2.21415	0.134006
$274$	−4.05458	−0.244946
$275$	19.0760	1.15033
$276$	2.78063	0.167374
$277$	−20.9347	−1.25784	−0.628922	−	0.777468i	$-0.716504\pi$
$277$	−20.9347	−1.25784	−0.628922	+	0.777468i	$0.716504\pi$
$278$	−0.221442	−0.0132812
$279$	−8.14486	−0.487620
$280$	−3.58265	−0.214104
$281$	−10.3790	−0.619159	−0.309580	−	0.950874i	$-0.600188\pi$
$281$	−10.3790	−0.619159	−0.309580	+	0.950874i	$0.600188\pi$
$282$	4.29971	0.256044
$283$	14.3809	0.854859	0.427429	−	0.904049i	$-0.359419\pi$
$283$	14.3809	0.854859	0.427429	+	0.904049i	$0.359419\pi$
$284$	5.84436	0.346799
$285$	17.7534	1.05162
$286$	5.39055	0.318750
$287$	−10.0487	−0.593157
$288$	1.00000	0.0589256
$289$	11.3986	0.670508
$290$	11.4841	0.674371
$291$	−11.1858	−0.655722
$292$	1.87603	0.109787
$293$	−10.7922	−0.630489	−0.315244	−	0.949011i	$-0.602086\pi$
$293$	−10.7922	−0.630489	−0.315244	+	0.949011i	$0.602086\pi$
$294$	1.00000	0.0583212
$295$	−52.0228	−3.02888
$296$	−2.90646	−0.168935
$297$	2.43459	0.141269
$298$	11.8240	0.684946
$299$	6.15672	0.356052
$300$	7.83541	0.452377
$301$	−0.360753	−0.0207935
$302$	−12.3016	−0.707878
$303$	11.2629	0.647038
$304$	−4.95539	−0.284211
$305$	40.5841	2.32384
$306$	−5.32904	−0.304641
$307$	30.1133	1.71866	0.859330	−	0.511422i	$-0.170881\pi$
$307$	30.1133	1.71866	0.859330	+	0.511422i	$0.170881\pi$
$308$	2.43459	0.138724
$309$	−0.712397	−0.0405269
$310$	29.1802	1.65733
$311$	19.2751	1.09299	0.546494	−	0.837463i	$-0.315962\pi$
$311$	19.2751	1.09299	0.546494	+	0.837463i	$0.315962\pi$
$312$	2.21415	0.125351
$313$	18.3636	1.03797	0.518987	−	0.854782i	$-0.326309\pi$
$313$	18.3636	1.03797	0.518987	+	0.854782i	$0.326309\pi$
$314$	−5.71912	−0.322749
$315$	−3.58265	−0.201860
$316$	7.01184	0.394447
$317$	−1.36946	−0.0769167	−0.0384584	−	0.999260i	$-0.512245\pi$
$317$	−1.36946	−0.0769167	−0.0384584	+	0.999260i	$0.512245\pi$
$318$	2.73826	0.153554
$319$	−7.80404	−0.436942
$320$	−3.58265	−0.200276
$321$	1.33155	0.0743197
$322$	2.78063	0.154958
$323$	26.4074	1.46935
$324$	1.00000	0.0555556
$325$	17.3487	0.962335
$326$	−5.46689	−0.302783
$327$	−9.77823	−0.540737
$328$	−10.0487	−0.554847
$329$	4.29971	0.237050
$330$	−8.72230	−0.480147
$331$	3.56644	0.196030	0.0980148	−	0.995185i	$-0.468751\pi$
$331$	3.56644	0.196030	0.0980148	+	0.995185i	$0.468751\pi$
$332$	−0.953479	−0.0523290
$333$	−2.90646	−0.159273
$334$	−13.8085	−0.755566
$335$	52.9879	2.89504
$336$	1.00000	0.0545545
$337$	−24.5920	−1.33961	−0.669805	−	0.742537i	$-0.733622\pi$
$337$	−24.5920	−1.33961	−0.669805	+	0.742537i	$0.733622\pi$
$338$	−8.09755	−0.440449
$339$	15.5768	0.846015
$340$	19.0921	1.03541
$341$	−19.8294	−1.07382
$342$	−4.95539	−0.267957
$343$	1.00000	0.0539949
$344$	−0.360753	−0.0194505
$345$	−9.96203	−0.536337
$346$	−9.26423	−0.498048
$347$	33.5832	1.80284	0.901419	−	0.432948i	$-0.142526\pi$
$347$	33.5832	1.80284	0.901419	+	0.432948i	$0.142526\pi$
$348$	−3.20548	−0.171832
$349$	12.0992	0.647655	0.323828	−	0.946116i	$-0.395030\pi$
$349$	12.0992	0.647655	0.323828	+	0.946116i	$0.395030\pi$
$350$	7.83541	0.418820
$351$	2.21415	0.118182
$352$	2.43459	0.129764
$353$	11.4680	0.610381	0.305191	−	0.952291i	$-0.401280\pi$
$353$	11.4680	0.610381	0.305191	+	0.952291i	$0.401280\pi$
$354$	14.5207	0.771768
$355$	−20.9383	−1.11129
$356$	−7.53346	−0.399273
$357$	−5.32904	−0.282043
$358$	−15.1901	−0.802820
$359$	22.0386	1.16315	0.581577	−	0.813491i	$-0.302436\pi$
$359$	22.0386	1.16315	0.581577	+	0.813491i	$0.302436\pi$
$360$	−3.58265	−0.188822
$361$	5.55585	0.292413
$362$	−21.8546	−1.14865
$363$	−5.07276	−0.266251
$364$	2.21415	0.116053
$365$	−6.72118	−0.351803
$366$	−11.3279	−0.592121
$367$	−21.1932	−1.10627	−0.553137	−	0.833090i	$-0.686569\pi$
$367$	−21.1932	−1.10627	−0.553137	+	0.833090i	$0.686569\pi$
$368$	2.78063	0.144950
$369$	−10.0487	−0.523115
$370$	10.4129	0.541338
$371$	2.73826	0.142163
$372$	−8.14486	−0.422291
$373$	−11.6020	−0.600726	−0.300363	−	0.953825i	$-0.597108\pi$
$373$	−11.6020	−0.600726	−0.300363	+	0.953825i	$0.597108\pi$
$374$	−12.9740	−0.670871
$375$	−10.1583	−0.524571
$376$	4.29971	0.221740
$377$	−7.09740	−0.365535
$378$	1.00000	0.0514344
$379$	0.286800	0.0147319	0.00736595	−	0.999973i	$-0.497655\pi$
$379$	0.286800	0.0147319	0.00736595	+	0.999973i	$0.497655\pi$
$380$	17.7534	0.910732
$381$	−12.5561	−0.643266
$382$	1.00000	0.0511645
$383$	17.4403	0.891157	0.445579	−	0.895243i	$-0.352998\pi$
$383$	17.4403	0.891157	0.445579	+	0.895243i	$0.352998\pi$
$384$	1.00000	0.0510310
$385$	−8.72230	−0.444530
$386$	17.7955	0.905767
$387$	−0.360753	−0.0183381
$388$	−11.1858	−0.567872
$389$	1.27467	0.0646281	0.0323141	−	0.999478i	$-0.489712\pi$
$389$	1.27467	0.0646281	0.0323141	+	0.999478i	$0.489712\pi$
$390$	−7.93252	−0.401679
$391$	−14.8181	−0.749382
$392$	1.00000	0.0505076
$393$	−11.5905	−0.584666
$394$	−7.18202	−0.361825
$395$	−25.1210	−1.26397
$396$	2.43459	0.122343
$397$	29.1401	1.46250	0.731251	−	0.682109i	$-0.238937\pi$
$397$	29.1401	1.46250	0.731251	+	0.682109i	$0.238937\pi$
$398$	−0.605928	−0.0303724
$399$	−4.95539	−0.248080
$400$	7.83541	0.391770
$401$	−23.0304	−1.15008	−0.575041	−	0.818125i	$-0.695014\pi$
$401$	−23.0304	−1.15008	−0.575041	+	0.818125i	$0.695014\pi$
$402$	−14.7901	−0.737665
$403$	−18.0339	−0.898334
$404$	11.2629	0.560352
$405$	−3.58265	−0.178023
$406$	−3.20548	−0.159085
$407$	−7.07606	−0.350747
$408$	−5.32904	−0.263827
$409$	−14.8353	−0.733558	−0.366779	−	0.930308i	$-0.619539\pi$
$409$	−14.8353	−0.733558	−0.366779	+	0.930308i	$0.619539\pi$
$410$	36.0010	1.77797
$411$	−4.05458	−0.199998
$412$	−0.712397	−0.0350973
$413$	14.5207	0.714519
$414$	2.78063	0.136660
$415$	3.41598	0.167684
$416$	2.21415	0.108558
$417$	−0.221442	−0.0108441
$418$	−12.0643	−0.590087
$419$	−9.70024	−0.473888	−0.236944	−	0.971523i	$-0.576146\pi$
$419$	−9.70024	−0.473888	−0.236944	+	0.971523i	$0.576146\pi$
$420$	−3.58265	−0.174816
$421$	−28.9523	−1.41105	−0.705524	−	0.708686i	$-0.749288\pi$
$421$	−28.9523	−1.41105	−0.705524	+	0.708686i	$0.749288\pi$
$422$	12.9055	0.628228
$423$	4.29971	0.209059
$424$	2.73826	0.132982
$425$	−41.7552	−2.02542
$426$	5.84436	0.283160
$427$	−11.3279	−0.548198
$428$	1.33155	0.0643627
$429$	5.39055	0.260258
$430$	1.29245	0.0623276
$431$	20.1335	0.969796	0.484898	−	0.874571i	$-0.338857\pi$
$431$	20.1335	0.969796	0.484898	+	0.874571i	$0.338857\pi$
$432$	1.00000	0.0481125
$433$	−34.1349	−1.64042	−0.820210	−	0.572062i	$-0.806144\pi$
$433$	−34.1349	−1.64042	−0.820210	+	0.572062i	$0.806144\pi$
$434$	−8.14486	−0.390966
$435$	11.4841	0.550621
$436$	−9.77823	−0.468292
$437$	−13.7791	−0.659143
$438$	1.87603	0.0896404
$439$	13.8004	0.658655	0.329327	−	0.944216i	$-0.393178\pi$
$439$	13.8004	0.658655	0.329327	+	0.944216i	$0.393178\pi$
$440$	−8.72230	−0.415819
$441$	1.00000	0.0476190
$442$	−11.7993	−0.561234
$443$	−38.6651	−1.83704	−0.918518	−	0.395379i	$-0.870613\pi$
$443$	−38.6651	−1.83704	−0.918518	+	0.395379i	$0.870613\pi$
$444$	−2.90646	−0.137935
$445$	26.9898	1.27944
$446$	−24.6060	−1.16513
$447$	11.8240	0.559256
$448$	1.00000	0.0472456
$449$	−22.9062	−1.08101	−0.540506	−	0.841340i	$-0.681767\pi$
$449$	−22.9062	−1.08101	−0.540506	+	0.841340i	$0.681767\pi$
$450$	7.83541	0.369365
$451$	−24.4645	−1.15199
$452$	15.5768	0.732671
$453$	−12.3016	−0.577980
$454$	12.0053	0.563439
$455$	−7.93252	−0.371882
$456$	−4.95539	−0.232057
$457$	6.15151	0.287755	0.143878	−	0.989595i	$-0.454043\pi$
$457$	6.15151	0.287755	0.143878	+	0.989595i	$0.454043\pi$
$458$	−5.60221	−0.261774
$459$	−5.32904	−0.248738
$460$	−9.96203	−0.464482
$461$	−14.6859	−0.683991	−0.341995	−	0.939702i	$-0.611103\pi$
$461$	−14.6859	−0.683991	−0.341995	+	0.939702i	$0.611103\pi$
$462$	2.43459	0.113268
$463$	17.4277	0.809933	0.404967	−	0.914331i	$-0.367283\pi$
$463$	17.4277	0.809933	0.404967	+	0.914331i	$0.367283\pi$
$464$	−3.20548	−0.148811
$465$	29.1802	1.35320
$466$	−19.8447	−0.919287
$467$	11.3694	0.526114	0.263057	−	0.964780i	$-0.415269\pi$
$467$	11.3694	0.526114	0.263057	+	0.964780i	$0.415269\pi$
$468$	2.21415	0.102349
$469$	−14.7901	−0.682945
$470$	−15.4044	−0.710550
$471$	−5.71912	−0.263523
$472$	14.5207	0.668371
$473$	−0.878287	−0.0403837
$474$	7.01184	0.322064
$475$	−38.8275	−1.78153
$476$	−5.32904	−0.244256
$477$	2.73826	0.125376
$478$	0.515631	0.0235844
$479$	20.2914	0.927138	0.463569	−	0.886061i	$-0.346569\pi$
$479$	20.2914	0.927138	0.463569	+	0.886061i	$0.346569\pi$
$480$	−3.58265	−0.163525
$481$	−6.43534	−0.293426
$482$	22.9546	1.04555
$483$	2.78063	0.126523
$484$	−5.07276	−0.230580
$485$	40.0748	1.81970
$486$	1.00000	0.0453609
$487$	16.3203	0.739545	0.369772	−	0.929122i	$-0.379436\pi$
$487$	16.3203	0.739545	0.369772	+	0.929122i	$0.379436\pi$
$488$	−11.3279	−0.512792
$489$	−5.46689	−0.247221
$490$	−3.58265	−0.161848
$491$	−34.6681	−1.56455	−0.782275	−	0.622934i	$-0.785941\pi$
$491$	−34.6681	−1.56455	−0.782275	+	0.622934i	$0.785941\pi$
$492$	−10.0487	−0.453031
$493$	17.0821	0.769340
$494$	−10.9720	−0.493652
$495$	−8.72230	−0.392038
$496$	−8.14486	−0.365715
$497$	5.84436	0.262155
$498$	−0.953479	−0.0427264
$499$	23.8409	1.06727	0.533633	−	0.845716i	$-0.320826\pi$
$499$	23.8409	1.06727	0.533633	+	0.845716i	$0.320826\pi$
$500$	−10.1583	−0.454292
$501$	−13.8085	−0.616917
$502$	1.55602	0.0694484
$503$	29.4286	1.31216	0.656078	−	0.754693i	$-0.272214\pi$
$503$	29.4286	1.31216	0.656078	+	0.754693i	$0.272214\pi$
$504$	1.00000	0.0445435
$505$	−40.3512	−1.79560
$506$	6.76970	0.300950
$507$	−8.09755	−0.359625
$508$	−12.5561	−0.557085
$509$	−1.01413	−0.0449506	−0.0224753	−	0.999747i	$-0.507155\pi$
$509$	−1.01413	−0.0449506	−0.0224753	+	0.999747i	$0.507155\pi$
$510$	19.0921	0.845412
$511$	1.87603	0.0829908
$512$	1.00000	0.0441942
$513$	−4.95539	−0.218786
$514$	−10.2909	−0.453911
$515$	2.55227	0.112467
$516$	−0.360753	−0.0158813
$517$	10.4680	0.460384
$518$	−2.90646	−0.127703
$519$	−9.26423	−0.406655
$520$	−7.93252	−0.347864
$521$	−19.1769	−0.840153	−0.420077	−	0.907489i	$-0.637997\pi$
$521$	−19.1769	−0.840153	−0.420077	+	0.907489i	$0.637997\pi$
$522$	−3.20548	−0.140300
$523$	−18.9543	−0.828812	−0.414406	−	0.910092i	$-0.636011\pi$
$523$	−18.9543	−0.828812	−0.414406	+	0.910092i	$0.636011\pi$
$524$	−11.5905	−0.506335
$525$	7.83541	0.341965
$526$	1.18170	0.0515246
$527$	43.4043	1.89072
$528$	2.43459	0.105952
$529$	−15.2681	−0.663831
$530$	−9.81024	−0.426129
$531$	14.5207	0.630146
$532$	−4.95539	−0.214843
$533$	−22.2493	−0.963725
$534$	−7.53346	−0.326005
$535$	−4.77047	−0.206245
$536$	−14.7901	−0.638837
$537$	−15.1901	−0.655499
$538$	−20.8240	−0.897788
$539$	2.43459	0.104865
$540$	−3.58265	−0.154173
$541$	2.29283	0.0985765	0.0492882	−	0.998785i	$-0.484305\pi$
$541$	2.29283	0.0985765	0.0492882	+	0.998785i	$0.484305\pi$
$542$	−10.7360	−0.461150
$543$	−21.8546	−0.937870
$544$	−5.32904	−0.228481
$545$	35.0320	1.50061
$546$	2.21415	0.0947568
$547$	12.0934	0.517076	0.258538	−	0.966001i	$-0.416759\pi$
$547$	12.0934	0.517076	0.258538	+	0.966001i	$0.416759\pi$
$548$	−4.05458	−0.173203
$549$	−11.3279	−0.483465
$550$	19.0760	0.813404
$551$	15.8844	0.676697
$552$	2.78063	0.118351
$553$	7.01184	0.298174
$554$	−20.9347	−0.889430
$555$	10.4129	0.442001
$556$	−0.221442	−0.00939123
$557$	11.3331	0.480199	0.240099	−	0.970748i	$-0.422820\pi$
$557$	11.3331	0.480199	0.240099	+	0.970748i	$0.422820\pi$
$558$	−8.14486	−0.344800
$559$	−0.798760	−0.0337840
$560$	−3.58265	−0.151395
$561$	−12.9740	−0.547764
$562$	−10.3790	−0.437812
$563$	−18.0958	−0.762649	−0.381324	−	0.924441i	$-0.624532\pi$
$563$	−18.0958	−0.762649	−0.381324	+	0.924441i	$0.624532\pi$
$564$	4.29971	0.181050
$565$	−55.8062	−2.34779
$566$	14.3809	0.604476
$567$	1.00000	0.0419961
$568$	5.84436	0.245224
$569$	−37.5249	−1.57313	−0.786564	−	0.617509i	$-0.788142\pi$
$569$	−37.5249	−1.57313	−0.786564	+	0.617509i	$0.788142\pi$
$570$	17.7534	0.743609
$571$	9.63326	0.403139	0.201570	−	0.979474i	$-0.435396\pi$
$571$	9.63326	0.403139	0.201570	+	0.979474i	$0.435396\pi$
$572$	5.39055	0.225390
$573$	1.00000	0.0417756
$574$	−10.0487	−0.419425
$575$	21.7873	0.908595
$576$	1.00000	0.0416667
$577$	−1.98242	−0.0825293	−0.0412646	−	0.999148i	$-0.513139\pi$
$577$	−1.98242	−0.0825293	−0.0412646	+	0.999148i	$0.513139\pi$
$578$	11.3986	0.474121
$579$	17.7955	0.739556
$580$	11.4841	0.476852
$581$	−0.953479	−0.0395570
$582$	−11.1858	−0.463665
$583$	6.66655	0.276100
$584$	1.87603	0.0776308
$585$	−7.93252	−0.327969
$586$	−10.7922	−0.445823
$587$	22.6264	0.933892	0.466946	−	0.884286i	$-0.345354\pi$
$587$	22.6264	0.933892	0.466946	+	0.884286i	$0.345354\pi$
$588$	1.00000	0.0412393
$589$	40.3609	1.66304
$590$	−52.0228	−2.14174
$591$	−7.18202	−0.295429
$592$	−2.90646	−0.119455
$593$	31.4547	1.29169	0.645844	−	0.763469i	$-0.276506\pi$
$593$	31.4547	1.29169	0.645844	+	0.763469i	$0.276506\pi$
$594$	2.43459	0.0998926
$595$	19.0921	0.782699
$596$	11.8240	0.484330
$597$	−0.605928	−0.0247990
$598$	6.15672	0.251767
$599$	19.1964	0.784344	0.392172	−	0.919892i	$-0.371724\pi$
$599$	19.1964	0.784344	0.392172	+	0.919892i	$0.371724\pi$
$600$	7.83541	0.319879
$601$	−46.6402	−1.90249	−0.951246	−	0.308434i	$-0.900195\pi$
$601$	−46.6402	−1.90249	−0.951246	+	0.308434i	$0.900195\pi$
$602$	−0.360753	−0.0147032
$603$	−14.7901	−0.602301
$604$	−12.3016	−0.500546
$605$	18.1739	0.738875
$606$	11.2629	0.457525
$607$	31.1174	1.26302	0.631508	−	0.775370i	$-0.282436\pi$
$607$	31.1174	1.26302	0.631508	+	0.775370i	$0.282436\pi$
$608$	−4.95539	−0.200967
$609$	−3.20548	−0.129893
$610$	40.5841	1.64320
$611$	9.52018	0.385145
$612$	−5.32904	−0.215414
$613$	−29.0798	−1.17452	−0.587261	−	0.809397i	$-0.699794\pi$
$613$	−29.0798	−1.17452	−0.587261	+	0.809397i	$0.699794\pi$
$614$	30.1133	1.21528
$615$	36.0010	1.45170
$616$	2.43459	0.0980925
$617$	6.14184	0.247261	0.123631	−	0.992328i	$-0.460546\pi$
$617$	6.14184	0.247261	0.123631	+	0.992328i	$0.460546\pi$
$618$	−0.712397	−0.0286568
$619$	35.2063	1.41506	0.707530	−	0.706683i	$-0.249809\pi$
$619$	35.2063	1.41506	0.707530	+	0.706683i	$0.249809\pi$
$620$	29.1802	1.17191
$621$	2.78063	0.111583
$622$	19.2751	0.772860
$623$	−7.53346	−0.301822
$624$	2.21415	0.0886368
$625$	−2.78345	−0.111338
$626$	18.3636	0.733959
$627$	−12.0643	−0.481804
$628$	−5.71912	−0.228218
$629$	15.4887	0.617573
$630$	−3.58265	−0.142736
$631$	4.42418	0.176124	0.0880620	−	0.996115i	$-0.471933\pi$
$631$	4.42418	0.176124	0.0880620	+	0.996115i	$0.471933\pi$
$632$	7.01184	0.278916
$633$	12.9055	0.512946
$634$	−1.36946	−0.0543883
$635$	44.9840	1.78514
$636$	2.73826	0.108579
$637$	2.21415	0.0877277
$638$	−7.80404	−0.308965
$639$	5.84436	0.231199
$640$	−3.58265	−0.141617
$641$	26.0045	1.02712	0.513558	−	0.858055i	$-0.328327\pi$
$641$	26.0045	1.02712	0.513558	+	0.858055i	$0.328327\pi$
$642$	1.33155	0.0525519
$643$	28.1195	1.10892	0.554462	−	0.832209i	$-0.312924\pi$
$643$	28.1195	1.10892	0.554462	+	0.832209i	$0.312924\pi$
$644$	2.78063	0.109572
$645$	1.29245	0.0508903
$646$	26.4074	1.03899
$647$	11.2582	0.442604	0.221302	−	0.975205i	$-0.428969\pi$
$647$	11.2582	0.442604	0.221302	+	0.975205i	$0.428969\pi$
$648$	1.00000	0.0392837
$649$	35.3521	1.38769
$650$	17.3487	0.680474
$651$	−8.14486	−0.319222
$652$	−5.46689	−0.214100
$653$	35.1778	1.37661	0.688306	−	0.725420i	$-0.258354\pi$
$653$	35.1778	1.37661	0.688306	+	0.725420i	$0.258354\pi$
$654$	−9.77823	−0.382359
$655$	41.5249	1.62251
$656$	−10.0487	−0.392336
$657$	1.87603	0.0731910
$658$	4.29971	0.167620
$659$	−46.7606	−1.82153	−0.910766	−	0.412922i	$-0.864508\pi$
$659$	−46.7606	−1.82153	−0.910766	+	0.412922i	$0.864508\pi$
$660$	−8.72230	−0.339515
$661$	42.3794	1.64837	0.824185	−	0.566321i	$-0.191634\pi$
$661$	42.3794	1.64837	0.824185	+	0.566321i	$0.191634\pi$
$662$	3.56644	0.138614
$663$	−11.7993	−0.458246
$664$	−0.953479	−0.0370022
$665$	17.7534	0.688449
$666$	−2.90646	−0.112623
$667$	−8.91324	−0.345122
$668$	−13.8085	−0.534265
$669$	−24.6060	−0.951324
$670$	52.9879	2.04710
$671$	−27.5789	−1.06467
$672$	1.00000	0.0385758
$673$	40.8330	1.57400	0.786998	−	0.616955i	$-0.211634\pi$
$673$	40.8330	1.57400	0.786998	+	0.616955i	$0.211634\pi$
$674$	−24.5920	−0.947248
$675$	7.83541	0.301585
$676$	−8.09755	−0.311444
$677$	48.4793	1.86321	0.931605	−	0.363473i	$-0.118409\pi$
$677$	48.4793	1.86321	0.931605	+	0.363473i	$0.118409\pi$
$678$	15.5768	0.598223
$679$	−11.1858	−0.429271
$680$	19.0921	0.732148
$681$	12.0053	0.460046
$682$	−19.8294	−0.759308
$683$	15.8685	0.607192	0.303596	−	0.952801i	$-0.401813\pi$
$683$	15.8685	0.607192	0.303596	+	0.952801i	$0.401813\pi$
$684$	−4.95539	−0.189474
$685$	14.5262	0.555016
$686$	1.00000	0.0381802
$687$	−5.60221	−0.213737
$688$	−0.360753	−0.0137536
$689$	6.06291	0.230978
$690$	−9.96203	−0.379248
$691$	−19.4880	−0.741360	−0.370680	−	0.928761i	$-0.620875\pi$
$691$	−19.4880	−0.741360	−0.370680	+	0.928761i	$0.620875\pi$
$692$	−9.26423	−0.352173
$693$	2.43459	0.0924825
$694$	33.5832	1.27480
$695$	0.793349	0.0300935
$696$	−3.20548	−0.121503
$697$	53.5500	2.02835
$698$	12.0992	0.457961
$699$	−19.8447	−0.750594
$700$	7.83541	0.296150
$701$	−7.11238	−0.268631	−0.134315	−	0.990939i	$-0.542884\pi$
$701$	−7.11238	−0.268631	−0.134315	+	0.990939i	$0.542884\pi$
$702$	2.21415	0.0835676
$703$	14.4027	0.543206
$704$	2.43459	0.0917572
$705$	−15.4044	−0.580161
$706$	11.4680	0.431605
$707$	11.2629	0.423586
$708$	14.5207	0.545723
$709$	18.4624	0.693370	0.346685	−	0.937982i	$-0.387307\pi$
$709$	18.4624	0.693370	0.346685	+	0.937982i	$0.387307\pi$
$710$	−20.9383	−0.785801
$711$	7.01184	0.262964
$712$	−7.53346	−0.282328
$713$	−22.6478	−0.848168
$714$	−5.32904	−0.199434
$715$	−19.3125	−0.722245
$716$	−15.1901	−0.567679
$717$	0.515631	0.0192566
$718$	22.0386	0.822474
$719$	36.5779	1.36413	0.682064	−	0.731293i	$-0.261083\pi$
$719$	36.5779	1.36413	0.682064	+	0.731293i	$0.261083\pi$
$720$	−3.58265	−0.133518
$721$	−0.712397	−0.0265311
$722$	5.55585	0.206767
$723$	22.9546	0.853690
$724$	−21.8546	−0.812219
$725$	−25.1162	−0.932793
$726$	−5.07276	−0.188268
$727$	−11.8339	−0.438896	−0.219448	−	0.975624i	$-0.570426\pi$
$727$	−11.8339	−0.438896	−0.219448	+	0.975624i	$0.570426\pi$
$728$	2.21415	0.0820618
$729$	1.00000	0.0370370
$730$	−6.72118	−0.248762
$731$	1.92247	0.0711050
$732$	−11.3279	−0.418693
$733$	10.1794	0.375986	0.187993	−	0.982170i	$-0.439802\pi$
$733$	10.1794	0.375986	0.187993	+	0.982170i	$0.439802\pi$
$734$	−21.1932	−0.782254
$735$	−3.58265	−0.132148
$736$	2.78063	0.102495
$737$	−36.0080	−1.32637
$738$	−10.0487	−0.369898
$739$	44.7129	1.64479	0.822396	−	0.568915i	$-0.192637\pi$
$739$	44.7129	1.64479	0.822396	+	0.568915i	$0.192637\pi$
$740$	10.4129	0.382784
$741$	−10.9720	−0.403065
$742$	2.73826	0.100525
$743$	−20.6523	−0.757660	−0.378830	−	0.925466i	$-0.623674\pi$
$743$	−20.6523	−0.757660	−0.378830	+	0.925466i	$0.623674\pi$
$744$	−8.14486	−0.298605
$745$	−42.3613	−1.55200
$746$	−11.6020	−0.424778
$747$	−0.953479	−0.0348860
$748$	−12.9740	−0.474378
$749$	1.33155	0.0486536
$750$	−10.1583	−0.370928
$751$	−0.324616	−0.0118454	−0.00592270	−	0.999982i	$-0.501885\pi$
$751$	−0.324616	−0.0118454	−0.00592270	+	0.999982i	$0.501885\pi$
$752$	4.29971	0.156794
$753$	1.55602	0.0567044
$754$	−7.09740	−0.258472
$755$	44.0724	1.60396
$756$	1.00000	0.0363696
$757$	29.5021	1.07227	0.536136	−	0.844131i	$-0.319883\pi$
$757$	29.5021	1.07227	0.536136	+	0.844131i	$0.319883\pi$
$758$	0.286800	0.0104170
$759$	6.76970	0.245724
$760$	17.7534	0.643985
$761$	−49.7231	−1.80246	−0.901231	−	0.433339i	$-0.857335\pi$
$761$	−49.7231	−1.80246	−0.901231	+	0.433339i	$0.857335\pi$
$762$	−12.5561	−0.454858
$763$	−9.77823	−0.353996
$764$	1.00000	0.0361787
$765$	19.0921	0.690276
$766$	17.4403	0.630143
$767$	32.1510	1.16091
$768$	1.00000	0.0360844
$769$	−37.5862	−1.35539	−0.677696	−	0.735342i	$-0.737021\pi$
$769$	−37.5862	−1.35539	−0.677696	+	0.735342i	$0.737021\pi$
$770$	−8.72230	−0.314330
$771$	−10.2909	−0.370617
$772$	17.7955	0.640474
$773$	36.8812	1.32652	0.663262	−	0.748387i	$-0.269171\pi$
$773$	36.8812	1.32652	0.663262	+	0.748387i	$0.269171\pi$
$774$	−0.360753	−0.0129670
$775$	−63.8183	−2.29242
$776$	−11.1858	−0.401546
$777$	−2.90646	−0.104269
$778$	1.27467	0.0456990
$779$	49.7952	1.78410
$780$	−7.93252	−0.284030
$781$	14.2286	0.509141
$782$	−14.8181	−0.529893
$783$	−3.20548	−0.114554
$784$	1.00000	0.0357143
$785$	20.4896	0.731306
$786$	−11.5905	−0.413421
$787$	33.0186	1.17699	0.588494	−	0.808502i	$-0.299721\pi$
$787$	33.0186	1.17699	0.588494	+	0.808502i	$0.299721\pi$
$788$	−7.18202	−0.255849
$789$	1.18170	0.0420697
$790$	−25.1210	−0.893764
$791$	15.5768	0.553847
$792$	2.43459	0.0865095
$793$	−25.0817	−0.890679
$794$	29.1401	1.03414
$795$	−9.81024	−0.347933
$796$	−0.605928	−0.0214765
$797$	18.0345	0.638814	0.319407	−	0.947618i	$-0.396516\pi$
$797$	18.0345	0.638814	0.319407	+	0.947618i	$0.396516\pi$
$798$	−4.95539	−0.175419
$799$	−22.9133	−0.810614
$800$	7.83541	0.277023
$801$	−7.53346	−0.266182
$802$	−23.0304	−0.813230
$803$	4.56738	0.161179
$804$	−14.7901	−0.521608
$805$	−9.96203	−0.351115
$806$	−18.0339	−0.635218
$807$	−20.8240	−0.733041
$808$	11.2629	0.396228
$809$	38.8507	1.36592	0.682959	−	0.730457i	$-0.260693\pi$
$809$	38.8507	1.36592	0.682959	+	0.730457i	$0.260693\pi$
$810$	−3.58265	−0.125882
$811$	20.8823	0.733278	0.366639	−	0.930363i	$-0.380508\pi$
$811$	20.8823	0.733278	0.366639	+	0.930363i	$0.380508\pi$
$812$	−3.20548	−0.112490
$813$	−10.7360	−0.376528
$814$	−7.07606	−0.248016
$815$	19.5860	0.686067
$816$	−5.32904	−0.186554
$817$	1.78767	0.0625427
$818$	−14.8353	−0.518704
$819$	2.21415	0.0773686
$820$	36.0010	1.25721
$821$	14.9300	0.521062	0.260531	−	0.965465i	$-0.416102\pi$
$821$	14.9300	0.521062	0.260531	+	0.965465i	$0.416102\pi$
$822$	−4.05458	−0.141420
$823$	25.9732	0.905370	0.452685	−	0.891670i	$-0.350466\pi$
$823$	25.9732	0.905370	0.452685	+	0.891670i	$0.350466\pi$
$824$	−0.712397	−0.0248175
$825$	19.0760	0.664142
$826$	14.5207	0.505241
$827$	1.50790	0.0524349	0.0262174	−	0.999656i	$-0.491654\pi$
$827$	1.50790	0.0524349	0.0262174	+	0.999656i	$0.491654\pi$
$828$	2.78063	0.0966335
$829$	21.0359	0.730606	0.365303	−	0.930889i	$-0.380965\pi$
$829$	21.0359	0.730606	0.365303	+	0.930889i	$0.380965\pi$
$830$	3.41598	0.118571
$831$	−20.9347	−0.726217
$832$	2.21415	0.0767617
$833$	−5.32904	−0.184640
$834$	−0.221442	−0.00766790
$835$	49.4709	1.71201
$836$	−12.0643	−0.417254
$837$	−8.14486	−0.281528
$838$	−9.70024	−0.335089
$839$	−0.737529	−0.0254623	−0.0127312	−	0.999919i	$-0.504053\pi$
$839$	−0.737529	−0.0254623	−0.0127312	+	0.999919i	$0.504053\pi$
$840$	−3.58265	−0.123613
$841$	−18.7249	−0.645687
$842$	−28.9523	−0.997761
$843$	−10.3790	−0.357472
$844$	12.9055	0.444225
$845$	29.0107	0.997999
$846$	4.29971	0.147827
$847$	−5.07276	−0.174302
$848$	2.73826	0.0940322
$849$	14.3809	0.493553
$850$	−41.7552	−1.43219
$851$	−8.08179	−0.277040
$852$	5.84436	0.200224
$853$	14.5734	0.498984	0.249492	−	0.968377i	$-0.419736\pi$
$853$	14.5734	0.498984	0.249492	+	0.968377i	$0.419736\pi$
$854$	−11.3279	−0.387634
$855$	17.7534	0.607155
$856$	1.33155	0.0455113
$857$	−29.6595	−1.01315	−0.506574	−	0.862196i	$-0.669088\pi$
$857$	−29.6595	−1.01315	−0.506574	+	0.862196i	$0.669088\pi$
$858$	5.39055	0.184030
$859$	−27.4486	−0.936535	−0.468267	−	0.883587i	$-0.655122\pi$
$859$	−27.4486	−0.936535	−0.468267	+	0.883587i	$0.655122\pi$
$860$	1.29245	0.0440723
$861$	−10.0487	−0.342459
$862$	20.1335	0.685749
$863$	48.2804	1.64349	0.821743	−	0.569859i	$-0.193002\pi$
$863$	48.2804	1.64349	0.821743	+	0.569859i	$0.193002\pi$
$864$	1.00000	0.0340207
$865$	33.1905	1.12851
$866$	−34.1349	−1.15995
$867$	11.3986	0.387118
$868$	−8.14486	−0.276455
$869$	17.0710	0.579093
$870$	11.4841	0.389348
$871$	−32.7476	−1.10961
$872$	−9.77823	−0.331133
$873$	−11.1858	−0.378581
$874$	−13.7791	−0.466085
$875$	−10.1583	−0.343412
$876$	1.87603	0.0633853
$877$	−9.45466	−0.319261	−0.159631	−	0.987177i	$-0.551030\pi$
$877$	−9.45466	−0.319261	−0.159631	+	0.987177i	$0.551030\pi$
$878$	13.8004	0.465739
$879$	−10.7922	−0.364013
$880$	−8.72230	−0.294029
$881$	−3.19012	−0.107478	−0.0537390	−	0.998555i	$-0.517114\pi$
$881$	−3.19012	−0.107478	−0.0537390	+	0.998555i	$0.517114\pi$
$882$	1.00000	0.0336718
$883$	14.4132	0.485044	0.242522	−	0.970146i	$-0.422025\pi$
$883$	14.4132	0.485044	0.242522	+	0.970146i	$0.422025\pi$
$884$	−11.7993	−0.396852
$885$	−52.0228	−1.74873
$886$	−38.6651	−1.29898
$887$	−13.4775	−0.452531	−0.226266	−	0.974066i	$-0.572652\pi$
$887$	−13.4775	−0.452531	−0.226266	+	0.974066i	$0.572652\pi$
$888$	−2.90646	−0.0975345
$889$	−12.5561	−0.421117
$890$	26.9898	0.904699
$891$	2.43459	0.0815619
$892$	−24.6060	−0.823871
$893$	−21.3067	−0.713002
$894$	11.8240	0.395454
$895$	54.4207	1.81908
$896$	1.00000	0.0334077
$897$	6.15672	0.205567
$898$	−22.9062	−0.764391
$899$	26.1082	0.870757
$900$	7.83541	0.261180
$901$	−14.5923	−0.486140
$902$	−24.4645	−0.814579
$903$	−0.360753	−0.0120051
$904$	15.5768	0.518076
$905$	78.2974	2.60269
$906$	−12.3016	−0.408694
$907$	−5.51903	−0.183257	−0.0916283	−	0.995793i	$-0.529207\pi$
$907$	−5.51903	−0.183257	−0.0916283	+	0.995793i	$0.529207\pi$
$908$	12.0053	0.398412
$909$	11.2629	0.373568
$910$	−7.93252	−0.262961
$911$	−15.7121	−0.520564	−0.260282	−	0.965533i	$-0.583816\pi$
$911$	−15.7121	−0.520564	−0.260282	+	0.965533i	$0.583816\pi$
$912$	−4.95539	−0.164089
$913$	−2.32133	−0.0768249
$914$	6.15151	0.203474
$915$	40.5841	1.34167
$916$	−5.60221	−0.185102
$917$	−11.5905	−0.382754
$918$	−5.32904	−0.175884
$919$	−49.8713	−1.64510	−0.822551	−	0.568691i	$-0.807450\pi$
$919$	−49.8713	−1.64510	−0.822551	+	0.568691i	$0.807450\pi$
$920$	−9.96203	−0.328438
$921$	30.1133	0.992268
$922$	−14.6859	−0.483654
$923$	12.9403	0.425934
$924$	2.43459	0.0800922
$925$	−22.7733	−0.748782
$926$	17.4277	0.572709
$927$	−0.712397	−0.0233982
$928$	−3.20548	−0.105225
$929$	21.2632	0.697622	0.348811	−	0.937193i	$-0.386586\pi$
$929$	21.2632	0.697622	0.348811	+	0.937193i	$0.386586\pi$
$930$	29.1802	0.956857
$931$	−4.95539	−0.162406
$932$	−19.8447	−0.650034
$933$	19.2751	0.631037
$934$	11.3694	0.372019
$935$	46.4815	1.52011
$936$	2.21415	0.0723717
$937$	−60.7253	−1.98381	−0.991905	−	0.126984i	$-0.959470\pi$
$937$	−60.7253	−1.98381	−0.991905	+	0.126984i	$0.959470\pi$
$938$	−14.7901	−0.482915
$939$	18.3636	0.599275
$940$	−15.4044	−0.502435
$941$	26.3413	0.858701	0.429350	−	0.903138i	$-0.358743\pi$
$941$	26.3413	0.858701	0.429350	+	0.903138i	$0.358743\pi$
$942$	−5.71912	−0.186339
$943$	−27.9417	−0.909908
$944$	14.5207	0.472610
$945$	−3.58265	−0.116544
$946$	−0.878287	−0.0285556
$947$	−25.8973	−0.841549	−0.420774	−	0.907165i	$-0.638242\pi$
$947$	−25.8973	−0.841549	−0.420774	+	0.907165i	$0.638242\pi$
$948$	7.01184	0.227734
$949$	4.15381	0.134839
$950$	−38.8275	−1.25973
$951$	−1.36946	−0.0444079
$952$	−5.32904	−0.172715
$953$	−12.0930	−0.391732	−0.195866	−	0.980631i	$-0.562752\pi$
$953$	−12.0930	−0.391732	−0.195866	+	0.980631i	$0.562752\pi$
$954$	2.73826	0.0886544
$955$	−3.58265	−0.115932
$956$	0.515631	0.0166767
$957$	−7.80404	−0.252269
$958$	20.2914	0.655586
$959$	−4.05458	−0.130929
$960$	−3.58265	−0.115630
$961$	35.3388	1.13996
$962$	−6.43534	−0.207484
$963$	1.33155	0.0429085
$964$	22.9546	0.739317
$965$	−63.7551	−2.05235
$966$	2.78063	0.0894652
$967$	34.2433	1.10119	0.550596	−	0.834772i	$-0.314401\pi$
$967$	34.2433	1.10119	0.550596	+	0.834772i	$0.314401\pi$
$968$	−5.07276	−0.163045
$969$	26.4074	0.848329
$970$	40.0748	1.28672
$971$	−51.7628	−1.66115	−0.830574	−	0.556908i	$-0.811988\pi$
$971$	−51.7628	−1.66115	−0.830574	+	0.556908i	$0.811988\pi$
$972$	1.00000	0.0320750
$973$	−0.221442	−0.00709910
$974$	16.3203	0.522937
$975$	17.3487	0.555604
$976$	−11.3279	−0.362599
$977$	13.6967	0.438196	0.219098	−	0.975703i	$-0.429689\pi$
$977$	13.6967	0.438196	0.219098	+	0.975703i	$0.429689\pi$
$978$	−5.46689	−0.174812
$979$	−18.3409	−0.586178
$980$	−3.58265	−0.114444
$981$	−9.77823	−0.312195
$982$	−34.6681	−1.10630
$983$	19.1142	0.609648	0.304824	−	0.952409i	$-0.401402\pi$
$983$	19.1142	0.609648	0.304824	+	0.952409i	$0.401402\pi$
$984$	−10.0487	−0.320341
$985$	25.7307	0.819848
$986$	17.0821	0.544005
$987$	4.29971	0.136861
$988$	−10.9720	−0.349064
$989$	−1.00312	−0.0318974
$990$	−8.72230	−0.277213
$991$	17.9240	0.569374	0.284687	−	0.958621i	$-0.408110\pi$
$991$	17.9240	0.569374	0.284687	+	0.958621i	$0.408110\pi$
$992$	−8.14486	−0.258600
$993$	3.56644	0.113178
$994$	5.84436	0.185372
$995$	2.17083	0.0688199
$996$	−0.953479	−0.0302121
$997$	−26.6015	−0.842477	−0.421238	−	0.906950i	$-0.638404\pi$
$997$	−26.6015	−0.842477	−0.421238	+	0.906950i	$0.638404\pi$
$998$	23.8409	0.754672
$999$	−2.90646	−0.0919564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.l.1.1	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.l.1.1	✓	7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.58265 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.58265 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.58265 q^{10} +2.43459 q^{11} +1.00000 q^{12} +2.21415 q^{13} +1.00000 q^{14} -3.58265 q^{15} +1.00000 q^{16} -5.32904 q^{17} +1.00000 q^{18} -4.95539 q^{19} -3.58265 q^{20} +1.00000 q^{21} +2.43459 q^{22} +2.78063 q^{23} +1.00000 q^{24} +7.83541 q^{25} +2.21415 q^{26} +1.00000 q^{27} +1.00000 q^{28} -3.20548 q^{29} -3.58265 q^{30} -8.14486 q^{31} +1.00000 q^{32} +2.43459 q^{33} -5.32904 q^{34} -3.58265 q^{35} +1.00000 q^{36} -2.90646 q^{37} -4.95539 q^{38} +2.21415 q^{39} -3.58265 q^{40} -10.0487 q^{41} +1.00000 q^{42} -0.360753 q^{43} +2.43459 q^{44} -3.58265 q^{45} +2.78063 q^{46} +4.29971 q^{47} +1.00000 q^{48} +1.00000 q^{49} +7.83541 q^{50} -5.32904 q^{51} +2.21415 q^{52} +2.73826 q^{53} +1.00000 q^{54} -8.72230 q^{55} +1.00000 q^{56} -4.95539 q^{57} -3.20548 q^{58} +14.5207 q^{59} -3.58265 q^{60} -11.3279 q^{61} -8.14486 q^{62} +1.00000 q^{63} +1.00000 q^{64} -7.93252 q^{65} +2.43459 q^{66} -14.7901 q^{67} -5.32904 q^{68} +2.78063 q^{69} -3.58265 q^{70} +5.84436 q^{71} +1.00000 q^{72} +1.87603 q^{73} -2.90646 q^{74} +7.83541 q^{75} -4.95539 q^{76} +2.43459 q^{77} +2.21415 q^{78} +7.01184 q^{79} -3.58265 q^{80} +1.00000 q^{81} -10.0487 q^{82} -0.953479 q^{83} +1.00000 q^{84} +19.0921 q^{85} -0.360753 q^{86} -3.20548 q^{87} +2.43459 q^{88} -7.53346 q^{89} -3.58265 q^{90} +2.21415 q^{91} +2.78063 q^{92} -8.14486 q^{93} +4.29971 q^{94} +17.7534 q^{95} +1.00000 q^{96} -11.1858 q^{97} +1.00000 q^{98} +2.43459 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} - 8 q^{5} + 7 q^{6} + 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 - 8 * q^5 + 7 * q^6 + 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} - 8 q^{5} + 7 q^{6} + 7 q^{7} + 7 q^{8} + 7 q^{9} - 8 q^{10} - 9 q^{11} + 7 q^{12} - 15 q^{13} + 7 q^{14} - 8 q^{15} + 7 q^{16} - 16 q^{17} + 7 q^{18} - 18 q^{19} - 8 q^{20} + 7 q^{21} - 9 q^{22} - 3 q^{23} + 7 q^{24} - 5 q^{25} - 15 q^{26} + 7 q^{27} + 7 q^{28} - 5 q^{29} - 8 q^{30} - 22 q^{31} + 7 q^{32} - 9 q^{33} - 16 q^{34} - 8 q^{35} + 7 q^{36} - 6 q^{37} - 18 q^{38} - 15 q^{39} - 8 q^{40} - 20 q^{41} + 7 q^{42} - 19 q^{43} - 9 q^{44} - 8 q^{45} - 3 q^{46} - 13 q^{47} + 7 q^{48} + 7 q^{49} - 5 q^{50} - 16 q^{51} - 15 q^{52} - 4 q^{53} + 7 q^{54} - 21 q^{55} + 7 q^{56} - 18 q^{57} - 5 q^{58} - 14 q^{59} - 8 q^{60} - 25 q^{61} - 22 q^{62} + 7 q^{63} + 7 q^{64} + 16 q^{65} - 9 q^{66} - 27 q^{67} - 16 q^{68} - 3 q^{69} - 8 q^{70} + 9 q^{71} + 7 q^{72} - 15 q^{73} - 6 q^{74} - 5 q^{75} - 18 q^{76} - 9 q^{77} - 15 q^{78} - 9 q^{79} - 8 q^{80} + 7 q^{81} - 20 q^{82} - 12 q^{83} + 7 q^{84} + 18 q^{85} - 19 q^{86} - 5 q^{87} - 9 q^{88} - 19 q^{89} - 8 q^{90} - 15 q^{91} - 3 q^{92} - 22 q^{93} - 13 q^{94} + 16 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} - 9 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 - 8 * q^5 + 7 * q^6 + 7 * q^7 + 7 * q^8 + 7 * q^9 - 8 * q^10 - 9 * q^11 + 7 * q^12 - 15 * q^13 + 7 * q^14 - 8 * q^15 + 7 * q^16 - 16 * q^17 + 7 * q^18 - 18 * q^19 - 8 * q^20 + 7 * q^21 - 9 * q^22 - 3 * q^23 + 7 * q^24 - 5 * q^25 - 15 * q^26 + 7 * q^27 + 7 * q^28 - 5 * q^29 - 8 * q^30 - 22 * q^31 + 7 * q^32 - 9 * q^33 - 16 * q^34 - 8 * q^35 + 7 * q^36 - 6 * q^37 - 18 * q^38 - 15 * q^39 - 8 * q^40 - 20 * q^41 + 7 * q^42 - 19 * q^43 - 9 * q^44 - 8 * q^45 - 3 * q^46 - 13 * q^47 + 7 * q^48 + 7 * q^49 - 5 * q^50 - 16 * q^51 - 15 * q^52 - 4 * q^53 + 7 * q^54 - 21 * q^55 + 7 * q^56 - 18 * q^57 - 5 * q^58 - 14 * q^59 - 8 * q^60 - 25 * q^61 - 22 * q^62 + 7 * q^63 + 7 * q^64 + 16 * q^65 - 9 * q^66 - 27 * q^67 - 16 * q^68 - 3 * q^69 - 8 * q^70 + 9 * q^71 + 7 * q^72 - 15 * q^73 - 6 * q^74 - 5 * q^75 - 18 * q^76 - 9 * q^77 - 15 * q^78 - 9 * q^79 - 8 * q^80 + 7 * q^81 - 20 * q^82 - 12 * q^83 + 7 * q^84 + 18 * q^85 - 19 * q^86 - 5 * q^87 - 9 * q^88 - 19 * q^89 - 8 * q^90 - 15 * q^91 - 3 * q^92 - 22 * q^93 - 13 * q^94 + 16 * q^95 + 7 * q^96 - 18 * q^97 + 7 * q^98 - 9 * q^99

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