LMFDB - Embedded newform 9282.2.a.bs.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.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:	$74.1171431562$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.1462249.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 7x^{2} + 15x + 2 $ x^5 - 2x^4 - 7x^3 + 7x^2 + 15x + 2
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			1.5
Root			$-1.71772$ of defining polynomial
Character	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.717722 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.717722 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.717722 q^{10} -6.48452 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} -0.717722 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.03303 q^{19} +0.717722 q^{20} -1.00000 q^{21} -6.48452 q^{22} -2.21681 q^{23} -1.00000 q^{24} -4.48488 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -5.86566 q^{29} -0.717722 q^{30} +7.23187 q^{31} +1.00000 q^{32} +6.48452 q^{33} +1.00000 q^{34} +0.717722 q^{35} +1.00000 q^{36} +1.59942 q^{37} +4.03303 q^{38} -1.00000 q^{39} +0.717722 q^{40} -9.50614 q^{41} -1.00000 q^{42} -2.34190 q^{43} -6.48452 q^{44} +0.717722 q^{45} -2.21681 q^{46} +11.5406 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.48488 q^{50} -1.00000 q^{51} +1.00000 q^{52} -11.5901 q^{53} -1.00000 q^{54} -4.65408 q^{55} +1.00000 q^{56} -4.03303 q^{57} -5.86566 q^{58} -3.41077 q^{59} -0.717722 q^{60} +12.3374 q^{61} +7.23187 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.717722 q^{65} +6.48452 q^{66} -3.67352 q^{67} +1.00000 q^{68} +2.21681 q^{69} +0.717722 q^{70} -1.04411 q^{71} +1.00000 q^{72} -2.74735 q^{73} +1.59942 q^{74} +4.48488 q^{75} +4.03303 q^{76} -6.48452 q^{77} -1.00000 q^{78} -3.50614 q^{79} +0.717722 q^{80} +1.00000 q^{81} -9.50614 q^{82} -15.7278 q^{83} -1.00000 q^{84} +0.717722 q^{85} -2.34190 q^{86} +5.86566 q^{87} -6.48452 q^{88} +8.63768 q^{89} +0.717722 q^{90} +1.00000 q^{91} -2.21681 q^{92} -7.23187 q^{93} +11.5406 q^{94} +2.89460 q^{95} -1.00000 q^{96} +2.60124 q^{97} +1.00000 q^{98} -6.48452 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9} - 7 q^{10} - 9 q^{11} - 5 q^{12} + 5 q^{13} + 5 q^{14} + 7 q^{15} + 5 q^{16} + 5 q^{17} + 5 q^{18} - q^{19} - 7 q^{20} - 5 q^{21} - 9 q^{22} - 6 q^{23} - 5 q^{24} + 2 q^{25} + 5 q^{26} - 5 q^{27} + 5 q^{28} - 10 q^{29} + 7 q^{30} - 7 q^{31} + 5 q^{32} + 9 q^{33} + 5 q^{34} - 7 q^{35} + 5 q^{36} - 3 q^{37} - q^{38} - 5 q^{39} - 7 q^{40} - 19 q^{41} - 5 q^{42} - 3 q^{43} - 9 q^{44} - 7 q^{45} - 6 q^{46} - 2 q^{47} - 5 q^{48} + 5 q^{49} + 2 q^{50} - 5 q^{51} + 5 q^{52} + 5 q^{53} - 5 q^{54} + 14 q^{55} + 5 q^{56} + q^{57} - 10 q^{58} - 12 q^{59} + 7 q^{60} - 21 q^{61} - 7 q^{62} + 5 q^{63} + 5 q^{64} - 7 q^{65} + 9 q^{66} + 12 q^{67} + 5 q^{68} + 6 q^{69} - 7 q^{70} + 4 q^{71} + 5 q^{72} + 6 q^{73} - 3 q^{74} - 2 q^{75} - q^{76} - 9 q^{77} - 5 q^{78} + 11 q^{79} - 7 q^{80} + 5 q^{81} - 19 q^{82} - 23 q^{83} - 5 q^{84} - 7 q^{85} - 3 q^{86} + 10 q^{87} - 9 q^{88} - 12 q^{89} - 7 q^{90} + 5 q^{91} - 6 q^{92} + 7 q^{93} - 2 q^{94} + 15 q^{95} - 5 q^{96} - 9 q^{97} + 5 q^{98} - 9 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9 - 7 * q^10 - 9 * q^11 - 5 * q^12 + 5 * q^13 + 5 * q^14 + 7 * q^15 + 5 * q^16 + 5 * q^17 + 5 * q^18 - q^19 - 7 * q^20 - 5 * q^21 - 9 * q^22 - 6 * q^23 - 5 * q^24 + 2 * q^25 + 5 * q^26 - 5 * q^27 + 5 * q^28 - 10 * q^29 + 7 * q^30 - 7 * q^31 + 5 * q^32 + 9 * q^33 + 5 * q^34 - 7 * q^35 + 5 * q^36 - 3 * q^37 - q^38 - 5 * q^39 - 7 * q^40 - 19 * q^41 - 5 * q^42 - 3 * q^43 - 9 * q^44 - 7 * q^45 - 6 * q^46 - 2 * q^47 - 5 * q^48 + 5 * q^49 + 2 * q^50 - 5 * q^51 + 5 * q^52 + 5 * q^53 - 5 * q^54 + 14 * q^55 + 5 * q^56 + q^57 - 10 * q^58 - 12 * q^59 + 7 * q^60 - 21 * q^61 - 7 * q^62 + 5 * q^63 + 5 * q^64 - 7 * q^65 + 9 * q^66 + 12 * q^67 + 5 * q^68 + 6 * q^69 - 7 * q^70 + 4 * q^71 + 5 * q^72 + 6 * q^73 - 3 * q^74 - 2 * q^75 - q^76 - 9 * q^77 - 5 * q^78 + 11 * q^79 - 7 * q^80 + 5 * q^81 - 19 * q^82 - 23 * q^83 - 5 * q^84 - 7 * q^85 - 3 * q^86 + 10 * q^87 - 9 * q^88 - 12 * q^89 - 7 * q^90 + 5 * q^91 - 6 * q^92 + 7 * q^93 - 2 * q^94 + 15 * q^95 - 5 * q^96 - 9 * q^97 + 5 * 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
$5$	0.717722	0.320975	0.160487	−	0.987038i	$-0.448693\pi$
$5$	0.717722	0.320975	0.160487	+	0.987038i	$0.448693\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.717722	0.226964
$11$	−6.48452	−1.95515	−0.977577	−	0.210576i	$-0.932466\pi$
$11$	−6.48452	−1.95515	−0.977577	+	0.210576i	$0.932466\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.00000	0.267261
$15$	−0.717722	−0.185315
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	4.03303	0.925242	0.462621	−	0.886556i	$-0.346909\pi$
$19$	4.03303	0.925242	0.462621	+	0.886556i	$0.346909\pi$
$20$	0.717722	0.160487
$21$	−1.00000	−0.218218
$22$	−6.48452	−1.38250
$23$	−2.21681	−0.462237	−0.231118	−	0.972926i	$-0.574238\pi$
$23$	−2.21681	−0.462237	−0.231118	+	0.972926i	$0.574238\pi$
$24$	−1.00000	−0.204124
$25$	−4.48488	−0.896975
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−5.86566	−1.08923	−0.544613	−	0.838688i	$-0.683323\pi$
$29$	−5.86566	−1.08923	−0.544613	+	0.838688i	$0.683323\pi$
$30$	−0.717722	−0.131037
$31$	7.23187	1.29888	0.649441	−	0.760412i	$-0.275003\pi$
$31$	7.23187	1.29888	0.649441	+	0.760412i	$0.275003\pi$
$32$	1.00000	0.176777
$33$	6.48452	1.12881
$34$	1.00000	0.171499
$35$	0.717722	0.121317
$36$	1.00000	0.166667
$37$	1.59942	0.262942	0.131471	−	0.991320i	$-0.458030\pi$
$37$	1.59942	0.262942	0.131471	+	0.991320i	$0.458030\pi$
$38$	4.03303	0.654245
$39$	−1.00000	−0.160128
$40$	0.717722	0.113482
$41$	−9.50614	−1.48461	−0.742305	−	0.670062i	$-0.766267\pi$
$41$	−9.50614	−1.48461	−0.742305	+	0.670062i	$0.766267\pi$
$42$	−1.00000	−0.154303
$43$	−2.34190	−0.357136	−0.178568	−	0.983928i	$-0.557146\pi$
$43$	−2.34190	−0.357136	−0.178568	+	0.983928i	$0.557146\pi$
$44$	−6.48452	−0.977577
$45$	0.717722	0.106992
$46$	−2.21681	−0.326851
$47$	11.5406	1.68338	0.841688	−	0.539965i	$-0.181562\pi$
$47$	11.5406	1.68338	0.841688	+	0.539965i	$0.181562\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.48488	−0.634257
$51$	−1.00000	−0.140028
$52$	1.00000	0.138675
$53$	−11.5901	−1.59202	−0.796010	−	0.605284i	$-0.793060\pi$
$53$	−11.5901	−1.59202	−0.796010	+	0.605284i	$0.793060\pi$
$54$	−1.00000	−0.136083
$55$	−4.65408	−0.627556
$56$	1.00000	0.133631
$57$	−4.03303	−0.534189
$58$	−5.86566	−0.770199
$59$	−3.41077	−0.444045	−0.222022	−	0.975042i	$-0.571266\pi$
$59$	−3.41077	−0.444045	−0.222022	+	0.975042i	$0.571266\pi$
$60$	−0.717722	−0.0926575
$61$	12.3374	1.57965	0.789823	−	0.613335i	$-0.210173\pi$
$61$	12.3374	1.57965	0.789823	+	0.613335i	$0.210173\pi$
$62$	7.23187	0.918448
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0.717722	0.0890224
$66$	6.48452	0.798189
$67$	−3.67352	−0.448792	−0.224396	−	0.974498i	$-0.572041\pi$
$67$	−3.67352	−0.448792	−0.224396	+	0.974498i	$0.572041\pi$
$68$	1.00000	0.121268
$69$	2.21681	0.266872
$70$	0.717722	0.0857842
$71$	−1.04411	−0.123913	−0.0619567	−	0.998079i	$-0.519734\pi$
$71$	−1.04411	−0.123913	−0.0619567	+	0.998079i	$0.519734\pi$
$72$	1.00000	0.117851
$73$	−2.74735	−0.321553	−0.160777	−	0.986991i	$-0.551400\pi$
$73$	−2.74735	−0.321553	−0.160777	+	0.986991i	$0.551400\pi$
$74$	1.59942	0.185928
$75$	4.48488	0.517869
$76$	4.03303	0.462621
$77$	−6.48452	−0.738979
$78$	−1.00000	−0.113228
$79$	−3.50614	−0.394472	−0.197236	−	0.980356i	$-0.563196\pi$
$79$	−3.50614	−0.394472	−0.197236	+	0.980356i	$0.563196\pi$
$80$	0.717722	0.0802437
$81$	1.00000	0.111111
$82$	−9.50614	−1.04978
$83$	−15.7278	−1.72635	−0.863176	−	0.504903i	$-0.831528\pi$
$83$	−15.7278	−1.72635	−0.863176	+	0.504903i	$0.831528\pi$
$84$	−1.00000	−0.109109
$85$	0.717722	0.0778479
$86$	−2.34190	−0.252533
$87$	5.86566	0.628865
$88$	−6.48452	−0.691252
$89$	8.63768	0.915592	0.457796	−	0.889057i	$-0.348639\pi$
$89$	8.63768	0.915592	0.457796	+	0.889057i	$0.348639\pi$
$90$	0.717722	0.0756545
$91$	1.00000	0.104828
$92$	−2.21681	−0.231118
$93$	−7.23187	−0.749910
$94$	11.5406	1.19033
$95$	2.89460	0.296979
$96$	−1.00000	−0.102062
$97$	2.60124	0.264116	0.132058	−	0.991242i	$-0.457841\pi$
$97$	2.60124	0.264116	0.132058	+	0.991242i	$0.457841\pi$
$98$	1.00000	0.101015
$99$	−6.48452	−0.651718
$100$	−4.48488	−0.448488
$101$	−10.3255	−1.02743	−0.513713	−	0.857962i	$-0.671730\pi$
$101$	−10.3255	−1.02743	−0.513713	+	0.857962i	$0.671730\pi$
$102$	−1.00000	−0.0990148
$103$	−5.39584	−0.531668	−0.265834	−	0.964019i	$-0.585647\pi$
$103$	−5.39584	−0.531668	−0.265834	+	0.964019i	$0.585647\pi$
$104$	1.00000	0.0980581
$105$	−0.717722	−0.0700425
$106$	−11.5901	−1.12573
$107$	−8.91123	−0.861482	−0.430741	−	0.902476i	$-0.641748\pi$
$107$	−8.91123	−0.861482	−0.430741	+	0.902476i	$0.641748\pi$
$108$	−1.00000	−0.0962250
$109$	−12.6259	−1.20934	−0.604672	−	0.796475i	$-0.706696\pi$
$109$	−12.6259	−1.20934	−0.604672	+	0.796475i	$0.706696\pi$
$110$	−4.65408	−0.443749
$111$	−1.59942	−0.151810
$112$	1.00000	0.0944911
$113$	2.34034	0.220161	0.110081	−	0.993923i	$-0.464889\pi$
$113$	2.34034	0.220161	0.110081	+	0.993923i	$0.464889\pi$
$114$	−4.03303	−0.377728
$115$	−1.59105	−0.148366
$116$	−5.86566	−0.544613
$117$	1.00000	0.0924500
$118$	−3.41077	−0.313987
$119$	1.00000	0.0916698
$120$	−0.717722	−0.0655187
$121$	31.0489	2.82263
$122$	12.3374	1.11698
$123$	9.50614	0.857140
$124$	7.23187	0.649441
$125$	−6.80750	−0.608881
$126$	1.00000	0.0890871
$127$	−1.07942	−0.0957833	−0.0478916	−	0.998853i	$-0.515250\pi$
$127$	−1.07942	−0.0957833	−0.0478916	+	0.998853i	$0.515250\pi$
$128$	1.00000	0.0883883
$129$	2.34190	0.206193
$130$	0.717722	0.0629484
$131$	−9.20077	−0.803875	−0.401938	−	0.915667i	$-0.631663\pi$
$131$	−9.20077	−0.803875	−0.401938	+	0.915667i	$0.631663\pi$
$132$	6.48452	0.564405
$133$	4.03303	0.349708
$134$	−3.67352	−0.317344
$135$	−0.717722	−0.0617717
$136$	1.00000	0.0857493
$137$	0.898092	0.0767291	0.0383646	−	0.999264i	$-0.487785\pi$
$137$	0.898092	0.0767291	0.0383646	+	0.999264i	$0.487785\pi$
$138$	2.21681	0.188707
$139$	−15.1188	−1.28236	−0.641180	−	0.767391i	$-0.721555\pi$
$139$	−15.1188	−1.28236	−0.641180	+	0.767391i	$0.721555\pi$
$140$	0.717722	0.0606586
$141$	−11.5406	−0.971897
$142$	−1.04411	−0.0876200
$143$	−6.48452	−0.542262
$144$	1.00000	0.0833333
$145$	−4.20991	−0.349614
$146$	−2.74735	−0.227372
$147$	−1.00000	−0.0824786
$148$	1.59942	0.131471
$149$	−4.64508	−0.380540	−0.190270	−	0.981732i	$-0.560936\pi$
$149$	−4.64508	−0.380540	−0.190270	+	0.981732i	$0.560936\pi$
$150$	4.48488	0.366189
$151$	13.9907	1.13854	0.569272	−	0.822149i	$-0.307225\pi$
$151$	13.9907	1.13854	0.569272	+	0.822149i	$0.307225\pi$
$152$	4.03303	0.327122
$153$	1.00000	0.0808452
$154$	−6.48452	−0.522537
$155$	5.19047	0.416908
$156$	−1.00000	−0.0800641
$157$	−17.3708	−1.38634	−0.693171	−	0.720773i	$-0.743787\pi$
$157$	−17.3708	−1.38634	−0.693171	+	0.720773i	$0.743787\pi$
$158$	−3.50614	−0.278934
$159$	11.5901	0.919153
$160$	0.717722	0.0567409
$161$	−2.21681	−0.174709
$162$	1.00000	0.0785674
$163$	−2.15326	−0.168656	−0.0843280	−	0.996438i	$-0.526874\pi$
$163$	−2.15326	−0.168656	−0.0843280	+	0.996438i	$0.526874\pi$
$164$	−9.50614	−0.742305
$165$	4.65408	0.362319
$166$	−15.7278	−1.22072
$167$	−8.24497	−0.638015	−0.319008	−	0.947752i	$-0.603350\pi$
$167$	−8.24497	−0.638015	−0.319008	+	0.947752i	$0.603350\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	0.717722	0.0550467
$171$	4.03303	0.308414
$172$	−2.34190	−0.178568
$173$	−9.24486	−0.702874	−0.351437	−	0.936212i	$-0.614307\pi$
$173$	−9.24486	−0.702874	−0.351437	+	0.936212i	$0.614307\pi$
$174$	5.86566	0.444674
$175$	−4.48488	−0.339025
$176$	−6.48452	−0.488789
$177$	3.41077	0.256369
$178$	8.63768	0.647422
$179$	5.76898	0.431194	0.215597	−	0.976482i	$-0.430830\pi$
$179$	5.76898	0.431194	0.215597	+	0.976482i	$0.430830\pi$
$180$	0.717722	0.0534958
$181$	−7.17189	−0.533082	−0.266541	−	0.963824i	$-0.585881\pi$
$181$	−7.17189	−0.533082	−0.266541	+	0.963824i	$0.585881\pi$
$182$	1.00000	0.0741249
$183$	−12.3374	−0.912009
$184$	−2.21681	−0.163425
$185$	1.14794	0.0843979
$186$	−7.23187	−0.530266
$187$	−6.48452	−0.474195
$188$	11.5406	0.841688
$189$	−1.00000	−0.0727393
$190$	2.89460	0.209996
$191$	3.99197	0.288849	0.144424	−	0.989516i	$-0.453867\pi$
$191$	3.99197	0.288849	0.144424	+	0.989516i	$0.453867\pi$
$192$	−1.00000	−0.0721688
$193$	2.85840	0.205752	0.102876	−	0.994694i	$-0.467196\pi$
$193$	2.85840	0.205752	0.102876	+	0.994694i	$0.467196\pi$
$194$	2.60124	0.186758
$195$	−0.717722	−0.0513971
$196$	1.00000	0.0714286
$197$	21.7861	1.55220	0.776098	−	0.630613i	$-0.217196\pi$
$197$	21.7861	1.55220	0.776098	+	0.630613i	$0.217196\pi$
$198$	−6.48452	−0.460834
$199$	−8.86895	−0.628703	−0.314351	−	0.949307i	$-0.601787\pi$
$199$	−8.86895	−0.628703	−0.314351	+	0.949307i	$0.601787\pi$
$200$	−4.48488	−0.317129
$201$	3.67352	0.259110
$202$	−10.3255	−0.726500
$203$	−5.86566	−0.411688
$204$	−1.00000	−0.0700140
$205$	−6.82276	−0.476523
$206$	−5.39584	−0.375946
$207$	−2.21681	−0.154079
$208$	1.00000	0.0693375
$209$	−26.1523	−1.80899
$210$	−0.717722	−0.0495275
$211$	12.7084	0.874881	0.437440	−	0.899247i	$-0.355885\pi$
$211$	12.7084	0.874881	0.437440	+	0.899247i	$0.355885\pi$
$212$	−11.5901	−0.796010
$213$	1.04411	0.0715414
$214$	−8.91123	−0.609159
$215$	−1.68083	−0.114632
$216$	−1.00000	−0.0680414
$217$	7.23187	0.490931
$218$	−12.6259	−0.855135
$219$	2.74735	0.185649
$220$	−4.65408	−0.313778
$221$	1.00000	0.0672673
$222$	−1.59942	−0.107346
$223$	2.60318	0.174322	0.0871609	−	0.996194i	$-0.472221\pi$
$223$	2.60318	0.174322	0.0871609	+	0.996194i	$0.472221\pi$
$224$	1.00000	0.0668153
$225$	−4.48488	−0.298992
$226$	2.34034	0.155677
$227$	3.17820	0.210944	0.105472	−	0.994422i	$-0.466365\pi$
$227$	3.17820	0.210944	0.105472	+	0.994422i	$0.466365\pi$
$228$	−4.03303	−0.267094
$229$	7.76241	0.512955	0.256477	−	0.966550i	$-0.417438\pi$
$229$	7.76241	0.512955	0.256477	+	0.966550i	$0.417438\pi$
$230$	−1.59105	−0.104911
$231$	6.48452	0.426650
$232$	−5.86566	−0.385099
$233$	−25.6117	−1.67788	−0.838938	−	0.544227i	$-0.816823\pi$
$233$	−25.6117	−1.67788	−0.838938	+	0.544227i	$0.816823\pi$
$234$	1.00000	0.0653720
$235$	8.28297	0.540321
$236$	−3.41077	−0.222022
$237$	3.50614	0.227748
$238$	1.00000	0.0648204
$239$	−15.5006	−1.00265	−0.501324	−	0.865260i	$-0.667153\pi$
$239$	−15.5006	−1.00265	−0.501324	+	0.865260i	$0.667153\pi$
$240$	−0.717722	−0.0463287
$241$	−23.6493	−1.52339	−0.761694	−	0.647937i	$-0.775632\pi$
$241$	−23.6493	−1.52339	−0.761694	+	0.647937i	$0.775632\pi$
$242$	31.0489	1.99590
$243$	−1.00000	−0.0641500
$244$	12.3374	0.789823
$245$	0.717722	0.0458536
$246$	9.50614	0.606089
$247$	4.03303	0.256616
$248$	7.23187	0.459224
$249$	15.7278	0.996710
$250$	−6.80750	−0.430544
$251$	6.37144	0.402162	0.201081	−	0.979575i	$-0.435555\pi$
$251$	6.37144	0.402162	0.201081	+	0.979575i	$0.435555\pi$
$252$	1.00000	0.0629941
$253$	14.3749	0.903744
$254$	−1.07942	−0.0677290
$255$	−0.717722	−0.0449455
$256$	1.00000	0.0625000
$257$	−11.3529	−0.708174	−0.354087	−	0.935213i	$-0.615208\pi$
$257$	−11.3529	−0.708174	−0.354087	+	0.935213i	$0.615208\pi$
$258$	2.34190	0.145800
$259$	1.59942	0.0993829
$260$	0.717722	0.0445112
$261$	−5.86566	−0.363075
$262$	−9.20077	−0.568426
$263$	22.1382	1.36510	0.682551	−	0.730838i	$-0.260871\pi$
$263$	22.1382	1.36510	0.682551	+	0.730838i	$0.260871\pi$
$264$	6.48452	0.399094
$265$	−8.31845	−0.510998
$266$	4.03303	0.247281
$267$	−8.63768	−0.528617
$268$	−3.67352	−0.224396
$269$	−5.15256	−0.314157	−0.157079	−	0.987586i	$-0.550208\pi$
$269$	−5.15256	−0.314157	−0.157079	+	0.987586i	$0.550208\pi$
$270$	−0.717722	−0.0436792
$271$	19.5766	1.18919	0.594597	−	0.804024i	$-0.297312\pi$
$271$	19.5766	1.18919	0.594597	+	0.804024i	$0.297312\pi$
$272$	1.00000	0.0606339
$273$	−1.00000	−0.0605228
$274$	0.898092	0.0542557
$275$	29.0822	1.75373
$276$	2.21681	0.133436
$277$	−12.6030	−0.757243	−0.378622	−	0.925552i	$-0.623602\pi$
$277$	−12.6030	−0.757243	−0.378622	+	0.925552i	$0.623602\pi$
$278$	−15.1188	−0.906765
$279$	7.23187	0.432961
$280$	0.717722	0.0428921
$281$	3.17318	0.189296	0.0946481	−	0.995511i	$-0.469827\pi$
$281$	3.17318	0.189296	0.0946481	+	0.995511i	$0.469827\pi$
$282$	−11.5406	−0.687235
$283$	−4.76715	−0.283378	−0.141689	−	0.989911i	$-0.545253\pi$
$283$	−4.76715	−0.283378	−0.141689	+	0.989911i	$0.545253\pi$
$284$	−1.04411	−0.0619567
$285$	−2.89460	−0.171461
$286$	−6.48452	−0.383437
$287$	−9.50614	−0.561130
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−4.20991	−0.247214
$291$	−2.60124	−0.152487
$292$	−2.74735	−0.160777
$293$	−4.56787	−0.266858	−0.133429	−	0.991058i	$-0.542599\pi$
$293$	−4.56787	−0.266858	−0.133429	+	0.991058i	$0.542599\pi$
$294$	−1.00000	−0.0583212
$295$	−2.44799	−0.142527
$296$	1.59942	0.0929642
$297$	6.48452	0.376270
$298$	−4.64508	−0.269082
$299$	−2.21681	−0.128201
$300$	4.48488	0.258934
$301$	−2.34190	−0.134985
$302$	13.9907	0.805072
$303$	10.3255	0.593185
$304$	4.03303	0.231310
$305$	8.85484	0.507027
$306$	1.00000	0.0571662
$307$	−5.45088	−0.311098	−0.155549	−	0.987828i	$-0.549715\pi$
$307$	−5.45088	−0.311098	−0.155549	+	0.987828i	$0.549715\pi$
$308$	−6.48452	−0.369490
$309$	5.39584	0.306959
$310$	5.19047	0.294799
$311$	−26.2043	−1.48591	−0.742955	−	0.669342i	$-0.766576\pi$
$311$	−26.2043	−1.48591	−0.742955	+	0.669342i	$0.766576\pi$
$312$	−1.00000	−0.0566139
$313$	20.1730	1.14024	0.570122	−	0.821560i	$-0.306896\pi$
$313$	20.1730	1.14024	0.570122	+	0.821560i	$0.306896\pi$
$314$	−17.3708	−0.980292
$315$	0.717722	0.0404390
$316$	−3.50614	−0.197236
$317$	8.65797	0.486280	0.243140	−	0.969991i	$-0.421823\pi$
$317$	8.65797	0.486280	0.243140	+	0.969991i	$0.421823\pi$
$318$	11.5901	0.649939
$319$	38.0359	2.12960
$320$	0.717722	0.0401219
$321$	8.91123	0.497377
$322$	−2.21681	−0.123538
$323$	4.03303	0.224404
$324$	1.00000	0.0555556
$325$	−4.48488	−0.248776
$326$	−2.15326	−0.119258
$327$	12.6259	0.698215
$328$	−9.50614	−0.524889
$329$	11.5406	0.636256
$330$	4.65408	0.256199
$331$	5.17392	0.284384	0.142192	−	0.989839i	$-0.454585\pi$
$331$	5.17392	0.284384	0.142192	+	0.989839i	$0.454585\pi$
$332$	−15.7278	−0.863176
$333$	1.59942	0.0876475
$334$	−8.24497	−0.451145
$335$	−2.63656	−0.144051
$336$	−1.00000	−0.0545545
$337$	−24.5758	−1.33873	−0.669365	−	0.742933i	$-0.733434\pi$
$337$	−24.5758	−1.33873	−0.669365	+	0.742933i	$0.733434\pi$
$338$	1.00000	0.0543928
$339$	−2.34034	−0.127110
$340$	0.717722	0.0389239
$341$	−46.8952	−2.53952
$342$	4.03303	0.218082
$343$	1.00000	0.0539949
$344$	−2.34190	−0.126267
$345$	1.59105	0.0856594
$346$	−9.24486	−0.497007
$347$	2.15308	0.115583	0.0577916	−	0.998329i	$-0.481594\pi$
$347$	2.15308	0.115583	0.0577916	+	0.998329i	$0.481594\pi$
$348$	5.86566	0.314432
$349$	−29.8434	−1.59748	−0.798741	−	0.601676i	$-0.794500\pi$
$349$	−29.8434	−1.59748	−0.798741	+	0.601676i	$0.794500\pi$
$350$	−4.48488	−0.239727
$351$	−1.00000	−0.0533761
$352$	−6.48452	−0.345626
$353$	7.87549	0.419170	0.209585	−	0.977790i	$-0.432789\pi$
$353$	7.87549	0.419170	0.209585	+	0.977790i	$0.432789\pi$
$354$	3.41077	0.181281
$355$	−0.749382	−0.0397731
$356$	8.63768	0.457796
$357$	−1.00000	−0.0529256
$358$	5.76898	0.304900
$359$	−18.1552	−0.958195	−0.479098	−	0.877762i	$-0.659036\pi$
$359$	−18.1552	−0.958195	−0.479098	+	0.877762i	$0.659036\pi$
$360$	0.717722	0.0378273
$361$	−2.73463	−0.143928
$362$	−7.17189	−0.376946
$363$	−31.0489	−1.62965
$364$	1.00000	0.0524142
$365$	−1.97183	−0.103211
$366$	−12.3374	−0.644888
$367$	21.4845	1.12148	0.560740	−	0.827992i	$-0.310517\pi$
$367$	21.4845	1.12148	0.560740	+	0.827992i	$0.310517\pi$
$368$	−2.21681	−0.115559
$369$	−9.50614	−0.494870
$370$	1.14794	0.0596783
$371$	−11.5901	−0.601727
$372$	−7.23187	−0.374955
$373$	−27.4244	−1.41998	−0.709991	−	0.704211i	$-0.751301\pi$
$373$	−27.4244	−1.41998	−0.709991	+	0.704211i	$0.751301\pi$
$374$	−6.48452	−0.335306
$375$	6.80750	0.351538
$376$	11.5406	0.595163
$377$	−5.86566	−0.302097
$378$	−1.00000	−0.0514344
$379$	4.23719	0.217650	0.108825	−	0.994061i	$-0.465291\pi$
$379$	4.23719	0.217650	0.108825	+	0.994061i	$0.465291\pi$
$380$	2.89460	0.148490
$381$	1.07942	0.0553005
$382$	3.99197	0.204247
$383$	18.2546	0.932768	0.466384	−	0.884582i	$-0.345557\pi$
$383$	18.2546	0.932768	0.466384	+	0.884582i	$0.345557\pi$
$384$	−1.00000	−0.0510310
$385$	−4.65408	−0.237194
$386$	2.85840	0.145489
$387$	−2.34190	−0.119045
$388$	2.60124	0.132058
$389$	−31.1786	−1.58082	−0.790409	−	0.612580i	$-0.790132\pi$
$389$	−31.1786	−1.58082	−0.790409	+	0.612580i	$0.790132\pi$
$390$	−0.717722	−0.0363433
$391$	−2.21681	−0.112109
$392$	1.00000	0.0505076
$393$	9.20077	0.464118
$394$	21.7861	1.09757
$395$	−2.51643	−0.126616
$396$	−6.48452	−0.325859
$397$	−36.2110	−1.81738	−0.908688	−	0.417475i	$-0.862915\pi$
$397$	−36.2110	−1.81738	−0.908688	+	0.417475i	$0.862915\pi$
$398$	−8.86895	−0.444560
$399$	−4.03303	−0.201904
$400$	−4.48488	−0.224244
$401$	−27.7637	−1.38645	−0.693226	−	0.720720i	$-0.743811\pi$
$401$	−27.7637	−1.38645	−0.693226	+	0.720720i	$0.743811\pi$
$402$	3.67352	0.183218
$403$	7.23187	0.360245
$404$	−10.3255	−0.513713
$405$	0.717722	0.0356639
$406$	−5.86566	−0.291108
$407$	−10.3714	−0.514093
$408$	−1.00000	−0.0495074
$409$	−14.4271	−0.713375	−0.356687	−	0.934224i	$-0.616094\pi$
$409$	−14.4271	−0.713375	−0.356687	+	0.934224i	$0.616094\pi$
$410$	−6.82276	−0.336952
$411$	−0.898092	−0.0442996
$412$	−5.39584	−0.265834
$413$	−3.41077	−0.167833
$414$	−2.21681	−0.108950
$415$	−11.2882	−0.554116
$416$	1.00000	0.0490290
$417$	15.1188	0.740370
$418$	−26.1523	−1.27915
$419$	27.4378	1.34042	0.670212	−	0.742170i	$-0.266203\pi$
$419$	27.4378	1.34042	0.670212	+	0.742170i	$0.266203\pi$
$420$	−0.717722	−0.0350212
$421$	15.9426	0.776995	0.388497	−	0.921450i	$-0.372994\pi$
$421$	15.9426	0.776995	0.388497	+	0.921450i	$0.372994\pi$
$422$	12.7084	0.618634
$423$	11.5406	0.561125
$424$	−11.5901	−0.562864
$425$	−4.48488	−0.217548
$426$	1.04411	0.0505874
$427$	12.3374	0.597050
$428$	−8.91123	−0.430741
$429$	6.48452	0.313075
$430$	−1.68083	−0.0810569
$431$	20.0108	0.963886	0.481943	−	0.876203i	$-0.339931\pi$
$431$	20.0108	0.963886	0.481943	+	0.876203i	$0.339931\pi$
$432$	−1.00000	−0.0481125
$433$	31.8302	1.52966	0.764831	−	0.644231i	$-0.222823\pi$
$433$	31.8302	1.52966	0.764831	+	0.644231i	$0.222823\pi$
$434$	7.23187	0.347141
$435$	4.20991	0.201850
$436$	−12.6259	−0.604672
$437$	−8.94047	−0.427681
$438$	2.74735	0.131274
$439$	−41.2350	−1.96804	−0.984020	−	0.178057i	$-0.943019\pi$
$439$	−41.2350	−1.96804	−0.984020	+	0.178057i	$0.943019\pi$
$440$	−4.65408	−0.221874
$441$	1.00000	0.0476190
$442$	1.00000	0.0475651
$443$	−0.767952	−0.0364865	−0.0182433	−	0.999834i	$-0.505807\pi$
$443$	−0.767952	−0.0364865	−0.0182433	+	0.999834i	$0.505807\pi$
$444$	−1.59942	−0.0759049
$445$	6.19945	0.293882
$446$	2.60318	0.123264
$447$	4.64508	0.219705
$448$	1.00000	0.0472456
$449$	5.51938	0.260475	0.130238	−	0.991483i	$-0.458426\pi$
$449$	5.51938	0.260475	0.130238	+	0.991483i	$0.458426\pi$
$450$	−4.48488	−0.211419
$451$	61.6427	2.90264
$452$	2.34034	0.110081
$453$	−13.9907	−0.657338
$454$	3.17820	0.149160
$455$	0.717722	0.0336473
$456$	−4.03303	−0.188864
$457$	−16.4385	−0.768960	−0.384480	−	0.923133i	$-0.625619\pi$
$457$	−16.4385	−0.768960	−0.384480	+	0.923133i	$0.625619\pi$
$458$	7.76241	0.362714
$459$	−1.00000	−0.0466760
$460$	−1.59105	−0.0741832
$461$	35.7815	1.66651	0.833255	−	0.552889i	$-0.186475\pi$
$461$	35.7815	1.66651	0.833255	+	0.552889i	$0.186475\pi$
$462$	6.48452	0.301687
$463$	8.65855	0.402397	0.201199	−	0.979550i	$-0.435516\pi$
$463$	8.65855	0.402397	0.201199	+	0.979550i	$0.435516\pi$
$464$	−5.86566	−0.272306
$465$	−5.19047	−0.240702
$466$	−25.6117	−1.18644
$467$	15.3181	0.708838	0.354419	−	0.935087i	$-0.384679\pi$
$467$	15.3181	0.708838	0.354419	+	0.935087i	$0.384679\pi$
$468$	1.00000	0.0462250
$469$	−3.67352	−0.169627
$470$	8.28297	0.382065
$471$	17.3708	0.800405
$472$	−3.41077	−0.156994
$473$	15.1861	0.698257
$474$	3.50614	0.161042
$475$	−18.0877	−0.829919
$476$	1.00000	0.0458349
$477$	−11.5901	−0.530673
$478$	−15.5006	−0.708979
$479$	−12.5484	−0.573351	−0.286676	−	0.958028i	$-0.592550\pi$
$479$	−12.5484	−0.573351	−0.286676	+	0.958028i	$0.592550\pi$
$480$	−0.717722	−0.0327594
$481$	1.59942	0.0729271
$482$	−23.6493	−1.07720
$483$	2.21681	0.100868
$484$	31.0489	1.41132
$485$	1.86697	0.0847746
$486$	−1.00000	−0.0453609
$487$	20.1213	0.911785	0.455893	−	0.890035i	$-0.349320\pi$
$487$	20.1213	0.911785	0.455893	+	0.890035i	$0.349320\pi$
$488$	12.3374	0.558489
$489$	2.15326	0.0973736
$490$	0.717722	0.0324234
$491$	3.81247	0.172054	0.0860272	−	0.996293i	$-0.472583\pi$
$491$	3.81247	0.172054	0.0860272	+	0.996293i	$0.472583\pi$
$492$	9.50614	0.428570
$493$	−5.86566	−0.264176
$494$	4.03303	0.181455
$495$	−4.65408	−0.209185
$496$	7.23187	0.324720
$497$	−1.04411	−0.0468348
$498$	15.7278	0.704780
$499$	−35.2043	−1.57596	−0.787980	−	0.615701i	$-0.788873\pi$
$499$	−35.2043	−1.57596	−0.787980	+	0.615701i	$0.788873\pi$
$500$	−6.80750	−0.304441
$501$	8.24497	0.368358
$502$	6.37144	0.284371
$503$	1.97159	0.0879088	0.0439544	−	0.999034i	$-0.486004\pi$
$503$	1.97159	0.0879088	0.0439544	+	0.999034i	$0.486004\pi$
$504$	1.00000	0.0445435
$505$	−7.41084	−0.329778
$506$	14.3749	0.639044
$507$	−1.00000	−0.0444116
$508$	−1.07942	−0.0478916
$509$	−3.12133	−0.138350	−0.0691752	−	0.997605i	$-0.522037\pi$
$509$	−3.12133	−0.138350	−0.0691752	+	0.997605i	$0.522037\pi$
$510$	−0.717722	−0.0317813
$511$	−2.74735	−0.121536
$512$	1.00000	0.0441942
$513$	−4.03303	−0.178063
$514$	−11.3529	−0.500754
$515$	−3.87271	−0.170652
$516$	2.34190	0.103096
$517$	−74.8355	−3.29126
$518$	1.59942	0.0702743
$519$	9.24486	0.405804
$520$	0.717722	0.0314742
$521$	22.9026	1.00338	0.501691	−	0.865047i	$-0.332712\pi$
$521$	22.9026	1.00338	0.501691	+	0.865047i	$0.332712\pi$
$522$	−5.86566	−0.256733
$523$	27.0299	1.18193	0.590967	−	0.806696i	$-0.298746\pi$
$523$	27.0299	1.18193	0.590967	+	0.806696i	$0.298746\pi$
$524$	−9.20077	−0.401938
$525$	4.48488	0.195736
$526$	22.1382	0.965273
$527$	7.23187	0.315025
$528$	6.48452	0.282202
$529$	−18.0858	−0.786337
$530$	−8.31845	−0.361330
$531$	−3.41077	−0.148015
$532$	4.03303	0.174854
$533$	−9.50614	−0.411757
$534$	−8.63768	−0.373789
$535$	−6.39579	−0.276514
$536$	−3.67352	−0.158672
$537$	−5.76898	−0.248950
$538$	−5.15256	−0.222143
$539$	−6.48452	−0.279308
$540$	−0.717722	−0.0308858
$541$	11.7956	0.507132	0.253566	−	0.967318i	$-0.418396\pi$
$541$	11.7956	0.507132	0.253566	+	0.967318i	$0.418396\pi$
$542$	19.5766	0.840887
$543$	7.17189	0.307775
$544$	1.00000	0.0428746
$545$	−9.06189	−0.388169
$546$	−1.00000	−0.0427960
$547$	0.836646	0.0357724	0.0178862	−	0.999840i	$-0.494306\pi$
$547$	0.836646	0.0357724	0.0178862	+	0.999840i	$0.494306\pi$
$548$	0.898092	0.0383646
$549$	12.3374	0.526548
$550$	29.0822	1.24007
$551$	−23.6564	−1.00780
$552$	2.21681	0.0943537
$553$	−3.50614	−0.149096
$554$	−12.6030	−0.535452
$555$	−1.14794	−0.0487272
$556$	−15.1188	−0.641180
$557$	22.2816	0.944100	0.472050	−	0.881572i	$-0.343514\pi$
$557$	22.2816	0.944100	0.472050	+	0.881572i	$0.343514\pi$
$558$	7.23187	0.306149
$559$	−2.34190	−0.0990518
$560$	0.717722	0.0303293
$561$	6.48452	0.273776
$562$	3.17318	0.133853
$563$	32.1093	1.35325	0.676624	−	0.736329i	$-0.263442\pi$
$563$	32.1093	1.35325	0.676624	+	0.736329i	$0.263442\pi$
$564$	−11.5406	−0.485949
$565$	1.67972	0.0706662
$566$	−4.76715	−0.200378
$567$	1.00000	0.0419961
$568$	−1.04411	−0.0438100
$569$	1.14370	0.0479463	0.0239731	−	0.999713i	$-0.492368\pi$
$569$	1.14370	0.0479463	0.0239731	+	0.999713i	$0.492368\pi$
$570$	−2.89460	−0.121241
$571$	13.4419	0.562525	0.281262	−	0.959631i	$-0.409247\pi$
$571$	13.4419	0.562525	0.281262	+	0.959631i	$0.409247\pi$
$572$	−6.48452	−0.271131
$573$	−3.99197	−0.166767
$574$	−9.50614	−0.396779
$575$	9.94211	0.414615
$576$	1.00000	0.0416667
$577$	18.8098	0.783061	0.391530	−	0.920165i	$-0.371946\pi$
$577$	18.8098	0.783061	0.391530	+	0.920165i	$0.371946\pi$
$578$	1.00000	0.0415945
$579$	−2.85840	−0.118791
$580$	−4.20991	−0.174807
$581$	−15.7278	−0.652500
$582$	−2.60124	−0.107825
$583$	75.1560	3.11264
$584$	−2.74735	−0.113686
$585$	0.717722	0.0296741
$586$	−4.56787	−0.188697
$587$	27.7247	1.14432	0.572161	−	0.820141i	$-0.306105\pi$
$587$	27.7247	1.14432	0.572161	+	0.820141i	$0.306105\pi$
$588$	−1.00000	−0.0412393
$589$	29.1664	1.20178
$590$	−2.44799	−0.100782
$591$	−21.7861	−0.896160
$592$	1.59942	0.0657356
$593$	6.65969	0.273481	0.136740	−	0.990607i	$-0.456337\pi$
$593$	6.65969	0.273481	0.136740	+	0.990607i	$0.456337\pi$
$594$	6.48452	0.266063
$595$	0.717722	0.0294237
$596$	−4.64508	−0.190270
$597$	8.86895	0.362982
$598$	−2.21681	−0.0906521
$599$	−9.78619	−0.399853	−0.199926	−	0.979811i	$-0.564070\pi$
$599$	−9.78619	−0.399853	−0.199926	+	0.979811i	$0.564070\pi$
$600$	4.48488	0.183094
$601$	−30.7810	−1.25558	−0.627792	−	0.778381i	$-0.716041\pi$
$601$	−30.7810	−1.25558	−0.627792	+	0.778381i	$0.716041\pi$
$602$	−2.34190	−0.0954487
$603$	−3.67352	−0.149597
$604$	13.9907	0.569272
$605$	22.2845	0.905994
$606$	10.3255	0.419445
$607$	−28.7972	−1.16884	−0.584420	−	0.811451i	$-0.698678\pi$
$607$	−28.7972	−1.16884	−0.584420	+	0.811451i	$0.698678\pi$
$608$	4.03303	0.163561
$609$	5.86566	0.237688
$610$	8.85484	0.358522
$611$	11.5406	0.466884
$612$	1.00000	0.0404226
$613$	−3.54593	−0.143219	−0.0716094	−	0.997433i	$-0.522814\pi$
$613$	−3.54593	−0.143219	−0.0716094	+	0.997433i	$0.522814\pi$
$614$	−5.45088	−0.219979
$615$	6.82276	0.275120
$616$	−6.48452	−0.261269
$617$	−9.25726	−0.372683	−0.186342	−	0.982485i	$-0.559663\pi$
$617$	−9.25726	−0.372683	−0.186342	+	0.982485i	$0.559663\pi$
$618$	5.39584	0.217053
$619$	27.8380	1.11890	0.559451	−	0.828863i	$-0.311012\pi$
$619$	27.8380	1.11890	0.559451	+	0.828863i	$0.311012\pi$
$620$	5.19047	0.208454
$621$	2.21681	0.0889575
$622$	−26.2043	−1.05070
$623$	8.63768	0.346061
$624$	−1.00000	−0.0400320
$625$	17.5385	0.701539
$626$	20.1730	0.806274
$627$	26.1523	1.04442
$628$	−17.3708	−0.693171
$629$	1.59942	0.0637729
$630$	0.717722	0.0285947
$631$	−21.8869	−0.871305	−0.435653	−	0.900115i	$-0.643482\pi$
$631$	−21.8869	−0.871305	−0.435653	+	0.900115i	$0.643482\pi$
$632$	−3.50614	−0.139467
$633$	−12.7084	−0.505113
$634$	8.65797	0.343852
$635$	−0.774725	−0.0307440
$636$	11.5901	0.459576
$637$	1.00000	0.0396214
$638$	38.0359	1.50586
$639$	−1.04411	−0.0413044
$640$	0.717722	0.0283704
$641$	−24.0103	−0.948349	−0.474174	−	0.880431i	$-0.657253\pi$
$641$	−24.0103	−0.948349	−0.474174	+	0.880431i	$0.657253\pi$
$642$	8.91123	0.351698
$643$	−9.05207	−0.356979	−0.178489	−	0.983942i	$-0.557121\pi$
$643$	−9.05207	−0.356979	−0.178489	+	0.983942i	$0.557121\pi$
$644$	−2.21681	−0.0873545
$645$	1.68083	0.0661827
$646$	4.03303	0.158678
$647$	−19.0168	−0.747628	−0.373814	−	0.927504i	$-0.621950\pi$
$647$	−19.0168	−0.747628	−0.373814	+	0.927504i	$0.621950\pi$
$648$	1.00000	0.0392837
$649$	22.1172	0.868176
$650$	−4.48488	−0.175911
$651$	−7.23187	−0.283439
$652$	−2.15326	−0.0843280
$653$	−30.6684	−1.20015	−0.600073	−	0.799945i	$-0.704862\pi$
$653$	−30.6684	−1.20015	−0.600073	+	0.799945i	$0.704862\pi$
$654$	12.6259	0.493712
$655$	−6.60359	−0.258024
$656$	−9.50614	−0.371152
$657$	−2.74735	−0.107184
$658$	11.5406	0.449901
$659$	−0.126309	−0.00492031	−0.00246016	−	0.999997i	$-0.500783\pi$
$659$	−0.126309	−0.00492031	−0.00246016	+	0.999997i	$0.500783\pi$
$660$	4.65408	0.181160
$661$	−29.4690	−1.14621	−0.573105	−	0.819482i	$-0.694261\pi$
$661$	−29.4690	−1.14621	−0.573105	+	0.819482i	$0.694261\pi$
$662$	5.17392	0.201090
$663$	−1.00000	−0.0388368
$664$	−15.7278	−0.610358
$665$	2.89460	0.112248
$666$	1.59942	0.0619761
$667$	13.0030	0.503480
$668$	−8.24497	−0.319008
$669$	−2.60318	−0.100645
$670$	−2.63656	−0.101859
$671$	−80.0022	−3.08845
$672$	−1.00000	−0.0385758
$673$	−19.9121	−0.767553	−0.383777	−	0.923426i	$-0.625377\pi$
$673$	−19.9121	−0.767553	−0.383777	+	0.923426i	$0.625377\pi$
$674$	−24.5758	−0.946626
$675$	4.48488	0.172623
$676$	1.00000	0.0384615
$677$	20.7167	0.796206	0.398103	−	0.917341i	$-0.369669\pi$
$677$	20.7167	0.796206	0.398103	+	0.917341i	$0.369669\pi$
$678$	−2.34034	−0.0898804
$679$	2.60124	0.0998265
$680$	0.717722	0.0275234
$681$	−3.17820	−0.121789
$682$	−46.8952	−1.79571
$683$	44.3808	1.69818	0.849092	−	0.528246i	$-0.177150\pi$
$683$	44.3808	1.69818	0.849092	+	0.528246i	$0.177150\pi$
$684$	4.03303	0.154207
$685$	0.644580	0.0246281
$686$	1.00000	0.0381802
$687$	−7.76241	−0.296154
$688$	−2.34190	−0.0892841
$689$	−11.5901	−0.441547
$690$	1.59105	0.0605703
$691$	12.6372	0.480741	0.240371	−	0.970681i	$-0.422731\pi$
$691$	12.6372	0.480741	0.240371	+	0.970681i	$0.422731\pi$
$692$	−9.24486	−0.351437
$693$	−6.48452	−0.246326
$694$	2.15308	0.0817296
$695$	−10.8511	−0.411605
$696$	5.86566	0.222337
$697$	−9.50614	−0.360071
$698$	−29.8434	−1.12959
$699$	25.6117	0.968722
$700$	−4.48488	−0.169512
$701$	12.8589	0.485673	0.242836	−	0.970067i	$-0.421922\pi$
$701$	12.8589	0.485673	0.242836	+	0.970067i	$0.421922\pi$
$702$	−1.00000	−0.0377426
$703$	6.45050	0.243285
$704$	−6.48452	−0.244394
$705$	−8.28297	−0.311955
$706$	7.87549	0.296398
$707$	−10.3255	−0.388330
$708$	3.41077	0.128185
$709$	−18.9484	−0.711622	−0.355811	−	0.934558i	$-0.615795\pi$
$709$	−18.9484	−0.711622	−0.355811	+	0.934558i	$0.615795\pi$
$710$	−0.749382	−0.0281238
$711$	−3.50614	−0.131491
$712$	8.63768	0.323711
$713$	−16.0317	−0.600391
$714$	−1.00000	−0.0374241
$715$	−4.65408	−0.174053
$716$	5.76898	0.215597
$717$	15.5006	0.578879
$718$	−18.1552	−0.677546
$719$	−15.2267	−0.567861	−0.283931	−	0.958845i	$-0.591639\pi$
$719$	−15.2267	−0.567861	−0.283931	+	0.958845i	$0.591639\pi$
$720$	0.717722	0.0267479
$721$	−5.39584	−0.200952
$722$	−2.73463	−0.101772
$723$	23.6493	0.879528
$724$	−7.17189	−0.266541
$725$	26.3067	0.977008
$726$	−31.0489	−1.15233
$727$	23.7861	0.882178	0.441089	−	0.897463i	$-0.354592\pi$
$727$	23.7861	0.882178	0.441089	+	0.897463i	$0.354592\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	−1.97183	−0.0729809
$731$	−2.34190	−0.0866183
$732$	−12.3374	−0.456004
$733$	0.319899	0.0118157	0.00590787	−	0.999983i	$-0.498119\pi$
$733$	0.319899	0.0118157	0.00590787	+	0.999983i	$0.498119\pi$
$734$	21.4845	0.793006
$735$	−0.717722	−0.0264736
$736$	−2.21681	−0.0817127
$737$	23.8210	0.877457
$738$	−9.50614	−0.349926
$739$	−15.3314	−0.563973	−0.281987	−	0.959418i	$-0.590993\pi$
$739$	−15.3314	−0.563973	−0.281987	+	0.959418i	$0.590993\pi$
$740$	1.14794	0.0421990
$741$	−4.03303	−0.148157
$742$	−11.5901	−0.425485
$743$	−16.7037	−0.612798	−0.306399	−	0.951903i	$-0.599124\pi$
$743$	−16.7037	−0.612798	−0.306399	+	0.951903i	$0.599124\pi$
$744$	−7.23187	−0.265133
$745$	−3.33388	−0.122144
$746$	−27.4244	−1.00408
$747$	−15.7278	−0.575451
$748$	−6.48452	−0.237097
$749$	−8.91123	−0.325609
$750$	6.80750	0.248575
$751$	9.07503	0.331152	0.165576	−	0.986197i	$-0.447052\pi$
$751$	9.07503	0.331152	0.165576	+	0.986197i	$0.447052\pi$
$752$	11.5406	0.420844
$753$	−6.37144	−0.232188
$754$	−5.86566	−0.213615
$755$	10.0414	0.365444
$756$	−1.00000	−0.0363696
$757$	−30.6400	−1.11363	−0.556814	−	0.830637i	$-0.687976\pi$
$757$	−30.6400	−1.11363	−0.556814	+	0.830637i	$0.687976\pi$
$758$	4.23719	0.153902
$759$	−14.3749	−0.521777
$760$	2.89460	0.104998
$761$	−35.8580	−1.29985	−0.649926	−	0.759998i	$-0.725200\pi$
$761$	−35.8580	−1.29985	−0.649926	+	0.759998i	$0.725200\pi$
$762$	1.07942	0.0391034
$763$	−12.6259	−0.457089
$764$	3.99197	0.144424
$765$	0.717722	0.0259493
$766$	18.2546	0.659566
$767$	−3.41077	−0.123156
$768$	−1.00000	−0.0360844
$769$	−53.7119	−1.93690	−0.968450	−	0.249207i	$-0.919830\pi$
$769$	−53.7119	−1.93690	−0.968450	+	0.249207i	$0.919830\pi$
$770$	−4.65408	−0.167721
$771$	11.3529	0.408864
$772$	2.85840	0.102876
$773$	39.0698	1.40524	0.702622	−	0.711563i	$-0.252012\pi$
$773$	39.0698	1.40524	0.702622	+	0.711563i	$0.252012\pi$
$774$	−2.34190	−0.0841778
$775$	−32.4340	−1.16506
$776$	2.60124	0.0933791
$777$	−1.59942	−0.0573787
$778$	−31.1786	−1.11781
$779$	−38.3386	−1.37362
$780$	−0.717722	−0.0256986
$781$	6.77056	0.242270
$782$	−2.21681	−0.0792729
$783$	5.86566	0.209622
$784$	1.00000	0.0357143
$785$	−12.4674	−0.444981
$786$	9.20077	0.328181
$787$	−41.2340	−1.46983	−0.734916	−	0.678158i	$-0.762778\pi$
$787$	−41.2340	−1.46983	−0.734916	+	0.678158i	$0.762778\pi$
$788$	21.7861	0.776098
$789$	−22.1382	−0.788142
$790$	−2.51643	−0.0895307
$791$	2.34034	0.0832131
$792$	−6.48452	−0.230417
$793$	12.3374	0.438115
$794$	−36.2110	−1.28508
$795$	8.31845	0.295025
$796$	−8.86895	−0.314351
$797$	3.45793	0.122486	0.0612431	−	0.998123i	$-0.480494\pi$
$797$	3.45793	0.122486	0.0612431	+	0.998123i	$0.480494\pi$
$798$	−4.03303	−0.142768
$799$	11.5406	0.408279
$800$	−4.48488	−0.158564
$801$	8.63768	0.305197
$802$	−27.7637	−0.980370
$803$	17.8152	0.628686
$804$	3.67352	0.129555
$805$	−1.59105	−0.0560772
$806$	7.23187	0.254732
$807$	5.15256	0.181379
$808$	−10.3255	−0.363250
$809$	−9.38318	−0.329895	−0.164948	−	0.986302i	$-0.552745\pi$
$809$	−9.38318	−0.329895	−0.164948	+	0.986302i	$0.552745\pi$
$810$	0.717722	0.0252182
$811$	−15.0031	−0.526831	−0.263416	−	0.964682i	$-0.584849\pi$
$811$	−15.0031	−0.526831	−0.263416	+	0.964682i	$0.584849\pi$
$812$	−5.86566	−0.205844
$813$	−19.5766	−0.686582
$814$	−10.3714	−0.363519
$815$	−1.54544	−0.0541343
$816$	−1.00000	−0.0350070
$817$	−9.44496	−0.330437
$818$	−14.4271	−0.504432
$819$	1.00000	0.0349428
$820$	−6.82276	−0.238261
$821$	14.9371	0.521309	0.260654	−	0.965432i	$-0.416062\pi$
$821$	14.9371	0.521309	0.260654	+	0.965432i	$0.416062\pi$
$822$	−0.898092	−0.0313245
$823$	−31.8699	−1.11091	−0.555457	−	0.831545i	$-0.687457\pi$
$823$	−31.8699	−1.11091	−0.555457	+	0.831545i	$0.687457\pi$
$824$	−5.39584	−0.187973
$825$	−29.0822	−1.01251
$826$	−3.41077	−0.118676
$827$	1.34646	0.0468211	0.0234105	−	0.999726i	$-0.492548\pi$
$827$	1.34646	0.0468211	0.0234105	+	0.999726i	$0.492548\pi$
$828$	−2.21681	−0.0770394
$829$	25.3789	0.881445	0.440722	−	0.897643i	$-0.354722\pi$
$829$	25.3789	0.881445	0.440722	+	0.897643i	$0.354722\pi$
$830$	−11.2882	−0.391819
$831$	12.6030	0.437194
$832$	1.00000	0.0346688
$833$	1.00000	0.0346479
$834$	15.1188	0.523521
$835$	−5.91760	−0.204787
$836$	−26.1523	−0.904495
$837$	−7.23187	−0.249970
$838$	27.4378	0.947823
$839$	−15.3511	−0.529979	−0.264989	−	0.964251i	$-0.585368\pi$
$839$	−15.3511	−0.529979	−0.264989	+	0.964251i	$0.585368\pi$
$840$	−0.717722	−0.0247638
$841$	5.40594	0.186412
$842$	15.9426	0.549418
$843$	−3.17318	−0.109290
$844$	12.7084	0.437440
$845$	0.717722	0.0246904
$846$	11.5406	0.396775
$847$	31.0489	1.06685
$848$	−11.5901	−0.398005
$849$	4.76715	0.163608
$850$	−4.48488	−0.153830
$851$	−3.54560	−0.121542
$852$	1.04411	0.0357707
$853$	−49.9456	−1.71010	−0.855052	−	0.518542i	$-0.826475\pi$
$853$	−49.9456	−1.71010	−0.855052	+	0.518542i	$0.826475\pi$
$854$	12.3374	0.422178
$855$	2.89460	0.0989931
$856$	−8.91123	−0.304580
$857$	−16.2922	−0.556531	−0.278266	−	0.960504i	$-0.589760\pi$
$857$	−16.2922	−0.556531	−0.278266	+	0.960504i	$0.589760\pi$
$858$	6.48452	0.221378
$859$	44.6166	1.52230	0.761150	−	0.648576i	$-0.224635\pi$
$859$	44.6166	1.52230	0.761150	+	0.648576i	$0.224635\pi$
$860$	−1.68083	−0.0573159
$861$	9.50614	0.323968
$862$	20.0108	0.681570
$863$	−30.5302	−1.03926	−0.519630	−	0.854391i	$-0.673930\pi$
$863$	−30.5302	−1.03926	−0.519630	+	0.854391i	$0.673930\pi$
$864$	−1.00000	−0.0340207
$865$	−6.63524	−0.225605
$866$	31.8302	1.08163
$867$	−1.00000	−0.0339618
$868$	7.23187	0.245466
$869$	22.7356	0.771253
$870$	4.20991	0.142729
$871$	−3.67352	−0.124472
$872$	−12.6259	−0.427567
$873$	2.60124	0.0880387
$874$	−8.94047	−0.302416
$875$	−6.80750	−0.230136
$876$	2.74735	0.0928244
$877$	−14.6145	−0.493496	−0.246748	−	0.969080i	$-0.579362\pi$
$877$	−14.6145	−0.493496	−0.246748	+	0.969080i	$0.579362\pi$
$878$	−41.2350	−1.39161
$879$	4.56787	0.154070
$880$	−4.65408	−0.156889
$881$	36.6939	1.23625	0.618125	−	0.786080i	$-0.287893\pi$
$881$	36.6939	1.23625	0.618125	+	0.786080i	$0.287893\pi$
$882$	1.00000	0.0336718
$883$	52.8134	1.77731	0.888656	−	0.458574i	$-0.151639\pi$
$883$	52.8134	1.77731	0.888656	+	0.458574i	$0.151639\pi$
$884$	1.00000	0.0336336
$885$	2.44799	0.0822881
$886$	−0.767952	−0.0257999
$887$	−18.1244	−0.608558	−0.304279	−	0.952583i	$-0.598416\pi$
$887$	−18.1244	−0.608558	−0.304279	+	0.952583i	$0.598416\pi$
$888$	−1.59942	−0.0536729
$889$	−1.07942	−0.0362027
$890$	6.19945	0.207806
$891$	−6.48452	−0.217239
$892$	2.60318	0.0871609
$893$	46.5438	1.55753
$894$	4.64508	0.155355
$895$	4.14052	0.138402
$896$	1.00000	0.0334077
$897$	2.21681	0.0740171
$898$	5.51938	0.184184
$899$	−42.4197	−1.41477
$900$	−4.48488	−0.149496
$901$	−11.5901	−0.386121
$902$	61.6427	2.05248
$903$	2.34190	0.0779335
$904$	2.34034	0.0778387
$905$	−5.14742	−0.171106
$906$	−13.9907	−0.464808
$907$	−29.5670	−0.981757	−0.490878	−	0.871228i	$-0.663324\pi$
$907$	−29.5670	−0.981757	−0.490878	+	0.871228i	$0.663324\pi$
$908$	3.17820	0.105472
$909$	−10.3255	−0.342475
$910$	0.717722	0.0237922
$911$	32.0319	1.06126	0.530632	−	0.847602i	$-0.321955\pi$
$911$	32.0319	1.06126	0.530632	+	0.847602i	$0.321955\pi$
$912$	−4.03303	−0.133547
$913$	101.987	3.37529
$914$	−16.4385	−0.543737
$915$	−8.85484	−0.292732
$916$	7.76241	0.256477
$917$	−9.20077	−0.303836
$918$	−1.00000	−0.0330049
$919$	46.7831	1.54323	0.771616	−	0.636088i	$-0.219449\pi$
$919$	46.7831	1.54323	0.771616	+	0.636088i	$0.219449\pi$
$920$	−1.59105	−0.0524554
$921$	5.45088	0.179612
$922$	35.7815	1.17840
$923$	−1.04411	−0.0343674
$924$	6.48452	0.213325
$925$	−7.17318	−0.235853
$926$	8.65855	0.284538
$927$	−5.39584	−0.177223
$928$	−5.86566	−0.192550
$929$	50.9822	1.67267	0.836335	−	0.548218i	$-0.184694\pi$
$929$	50.9822	1.67267	0.836335	+	0.548218i	$0.184694\pi$
$930$	−5.19047	−0.170202
$931$	4.03303	0.132177
$932$	−25.6117	−0.838938
$933$	26.2043	0.857890
$934$	15.3181	0.501224
$935$	−4.65408	−0.152205
$936$	1.00000	0.0326860
$937$	−18.8769	−0.616682	−0.308341	−	0.951276i	$-0.599774\pi$
$937$	−18.8769	−0.616682	−0.308341	+	0.951276i	$0.599774\pi$
$938$	−3.67352	−0.119945
$939$	−20.1730	−0.658320
$940$	8.28297	0.270161
$941$	−53.1133	−1.73144	−0.865721	−	0.500526i	$-0.833140\pi$
$941$	−53.1133	−1.73144	−0.865721	+	0.500526i	$0.833140\pi$
$942$	17.3708	0.565972
$943$	21.0733	0.686241
$944$	−3.41077	−0.111011
$945$	−0.717722	−0.0233475
$946$	15.1861	0.493742
$947$	−12.4957	−0.406056	−0.203028	−	0.979173i	$-0.565078\pi$
$947$	−12.4957	−0.406056	−0.203028	+	0.979173i	$0.565078\pi$
$948$	3.50614	0.113874
$949$	−2.74735	−0.0891828
$950$	−18.0877	−0.586841
$951$	−8.65797	−0.280754
$952$	1.00000	0.0324102
$953$	2.84541	0.0921717	0.0460859	−	0.998937i	$-0.485325\pi$
$953$	2.84541	0.0921717	0.0460859	+	0.998937i	$0.485325\pi$
$954$	−11.5901	−0.375242
$955$	2.86512	0.0927132
$956$	−15.5006	−0.501324
$957$	−38.0359	−1.22953
$958$	−12.5484	−0.405421
$959$	0.898092	0.0290009
$960$	−0.717722	−0.0231644
$961$	21.2999	0.687094
$962$	1.59942	0.0515672
$963$	−8.91123	−0.287161
$964$	−23.6493	−0.761694
$965$	2.05153	0.0660412
$966$	2.21681	0.0713247
$967$	21.9381	0.705483	0.352741	−	0.935721i	$-0.385250\pi$
$967$	21.9381	0.705483	0.352741	+	0.935721i	$0.385250\pi$
$968$	31.0489	0.997951
$969$	−4.03303	−0.129560
$970$	1.86697	0.0599447
$971$	−36.5605	−1.17328	−0.586640	−	0.809848i	$-0.699550\pi$
$971$	−36.5605	−1.17328	−0.586640	+	0.809848i	$0.699550\pi$
$972$	−1.00000	−0.0320750
$973$	−15.1188	−0.484686
$974$	20.1213	0.644730
$975$	4.48488	0.143631
$976$	12.3374	0.394911
$977$	−16.0743	−0.514263	−0.257132	−	0.966376i	$-0.582777\pi$
$977$	−16.0743	−0.514263	−0.257132	+	0.966376i	$0.582777\pi$
$978$	2.15326	0.0688535
$979$	−56.0112	−1.79012
$980$	0.717722	0.0229268
$981$	−12.6259	−0.403114
$982$	3.81247	0.121661
$983$	60.0402	1.91498	0.957492	−	0.288460i	$-0.0931433\pi$
$983$	60.0402	1.91498	0.957492	+	0.288460i	$0.0931433\pi$
$984$	9.50614	0.303045
$985$	15.6364	0.498216
$986$	−5.86566	−0.186801
$987$	−11.5406	−0.367343
$988$	4.03303	0.128308
$989$	5.19154	0.165081
$990$	−4.65408	−0.147916
$991$	7.64471	0.242842	0.121421	−	0.992601i	$-0.461255\pi$
$991$	7.64471	0.242842	0.121421	+	0.992601i	$0.461255\pi$
$992$	7.23187	0.229612
$993$	−5.17392	−0.164189
$994$	−1.04411	−0.0331172
$995$	−6.36544	−0.201798
$996$	15.7278	0.498355
$997$	−5.86883	−0.185868	−0.0929339	−	0.995672i	$-0.529625\pi$
$997$	−5.86883	−0.185868	−0.0929339	+	0.995672i	$0.529625\pi$
$998$	−35.2043	−1.11437
$999$	−1.59942	−0.0506033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.bs.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.bs.1.5	✓	5	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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.717722 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.717722 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.717722 q^{10} -6.48452 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} -0.717722 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.03303 q^{19} +0.717722 q^{20} -1.00000 q^{21} -6.48452 q^{22} -2.21681 q^{23} -1.00000 q^{24} -4.48488 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -5.86566 q^{29} -0.717722 q^{30} +7.23187 q^{31} +1.00000 q^{32} +6.48452 q^{33} +1.00000 q^{34} +0.717722 q^{35} +1.00000 q^{36} +1.59942 q^{37} +4.03303 q^{38} -1.00000 q^{39} +0.717722 q^{40} -9.50614 q^{41} -1.00000 q^{42} -2.34190 q^{43} -6.48452 q^{44} +0.717722 q^{45} -2.21681 q^{46} +11.5406 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.48488 q^{50} -1.00000 q^{51} +1.00000 q^{52} -11.5901 q^{53} -1.00000 q^{54} -4.65408 q^{55} +1.00000 q^{56} -4.03303 q^{57} -5.86566 q^{58} -3.41077 q^{59} -0.717722 q^{60} +12.3374 q^{61} +7.23187 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.717722 q^{65} +6.48452 q^{66} -3.67352 q^{67} +1.00000 q^{68} +2.21681 q^{69} +0.717722 q^{70} -1.04411 q^{71} +1.00000 q^{72} -2.74735 q^{73} +1.59942 q^{74} +4.48488 q^{75} +4.03303 q^{76} -6.48452 q^{77} -1.00000 q^{78} -3.50614 q^{79} +0.717722 q^{80} +1.00000 q^{81} -9.50614 q^{82} -15.7278 q^{83} -1.00000 q^{84} +0.717722 q^{85} -2.34190 q^{86} +5.86566 q^{87} -6.48452 q^{88} +8.63768 q^{89} +0.717722 q^{90} +1.00000 q^{91} -2.21681 q^{92} -7.23187 q^{93} +11.5406 q^{94} +2.89460 q^{95} -1.00000 q^{96} +2.60124 q^{97} +1.00000 q^{98} -6.48452 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9} - 7 q^{10} - 9 q^{11} - 5 q^{12} + 5 q^{13} + 5 q^{14} + 7 q^{15} + 5 q^{16} + 5 q^{17} + 5 q^{18} - q^{19} - 7 q^{20} - 5 q^{21} - 9 q^{22} - 6 q^{23} - 5 q^{24} + 2 q^{25} + 5 q^{26} - 5 q^{27} + 5 q^{28} - 10 q^{29} + 7 q^{30} - 7 q^{31} + 5 q^{32} + 9 q^{33} + 5 q^{34} - 7 q^{35} + 5 q^{36} - 3 q^{37} - q^{38} - 5 q^{39} - 7 q^{40} - 19 q^{41} - 5 q^{42} - 3 q^{43} - 9 q^{44} - 7 q^{45} - 6 q^{46} - 2 q^{47} - 5 q^{48} + 5 q^{49} + 2 q^{50} - 5 q^{51} + 5 q^{52} + 5 q^{53} - 5 q^{54} + 14 q^{55} + 5 q^{56} + q^{57} - 10 q^{58} - 12 q^{59} + 7 q^{60} - 21 q^{61} - 7 q^{62} + 5 q^{63} + 5 q^{64} - 7 q^{65} + 9 q^{66} + 12 q^{67} + 5 q^{68} + 6 q^{69} - 7 q^{70} + 4 q^{71} + 5 q^{72} + 6 q^{73} - 3 q^{74} - 2 q^{75} - q^{76} - 9 q^{77} - 5 q^{78} + 11 q^{79} - 7 q^{80} + 5 q^{81} - 19 q^{82} - 23 q^{83} - 5 q^{84} - 7 q^{85} - 3 q^{86} + 10 q^{87} - 9 q^{88} - 12 q^{89} - 7 q^{90} + 5 q^{91} - 6 q^{92} + 7 q^{93} - 2 q^{94} + 15 q^{95} - 5 q^{96} - 9 q^{97} + 5 q^{98} - 9 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9 - 7 * q^10 - 9 * q^11 - 5 * q^12 + 5 * q^13 + 5 * q^14 + 7 * q^15 + 5 * q^16 + 5 * q^17 + 5 * q^18 - q^19 - 7 * q^20 - 5 * q^21 - 9 * q^22 - 6 * q^23 - 5 * q^24 + 2 * q^25 + 5 * q^26 - 5 * q^27 + 5 * q^28 - 10 * q^29 + 7 * q^30 - 7 * q^31 + 5 * q^32 + 9 * q^33 + 5 * q^34 - 7 * q^35 + 5 * q^36 - 3 * q^37 - q^38 - 5 * q^39 - 7 * q^40 - 19 * q^41 - 5 * q^42 - 3 * q^43 - 9 * q^44 - 7 * q^45 - 6 * q^46 - 2 * q^47 - 5 * q^48 + 5 * q^49 + 2 * q^50 - 5 * q^51 + 5 * q^52 + 5 * q^53 - 5 * q^54 + 14 * q^55 + 5 * q^56 + q^57 - 10 * q^58 - 12 * q^59 + 7 * q^60 - 21 * q^61 - 7 * q^62 + 5 * q^63 + 5 * q^64 - 7 * q^65 + 9 * q^66 + 12 * q^67 + 5 * q^68 + 6 * q^69 - 7 * q^70 + 4 * q^71 + 5 * q^72 + 6 * q^73 - 3 * q^74 - 2 * q^75 - q^76 - 9 * q^77 - 5 * q^78 + 11 * q^79 - 7 * q^80 + 5 * q^81 - 19 * q^82 - 23 * q^83 - 5 * q^84 - 7 * q^85 - 3 * q^86 + 10 * q^87 - 9 * q^88 - 12 * q^89 - 7 * q^90 + 5 * q^91 - 6 * q^92 + 7 * q^93 - 2 * q^94 + 15 * q^95 - 5 * q^96 - 9 * q^97 + 5 * q^98 - 9 * q^99

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