LMFDB - Embedded newform 8030.2.a.z.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 11x^{5} + 17x^{4} + 25x^{3} - 9x^{2} - 14x - 3 $ x^7 - 2x^6 - 11x^5 + 17x^4 + 25x^3 - 9x^2 - 14x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.335989$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.335989 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.335989 q^{6} -3.89614 q^{7} -1.00000 q^{8} -2.88711 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.335989 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.335989 q^{6} -3.89614 q^{7} -1.00000 q^{8} -2.88711 q^{9} -1.00000 q^{10} -1.00000 q^{11} +0.335989 q^{12} +1.74566 q^{13} +3.89614 q^{14} +0.335989 q^{15} +1.00000 q^{16} +0.959044 q^{17} +2.88711 q^{18} -0.980111 q^{19} +1.00000 q^{20} -1.30906 q^{21} +1.00000 q^{22} +6.94577 q^{23} -0.335989 q^{24} +1.00000 q^{25} -1.74566 q^{26} -1.97801 q^{27} -3.89614 q^{28} -4.84932 q^{29} -0.335989 q^{30} +5.52406 q^{31} -1.00000 q^{32} -0.335989 q^{33} -0.959044 q^{34} -3.89614 q^{35} -2.88711 q^{36} +11.5299 q^{37} +0.980111 q^{38} +0.586522 q^{39} -1.00000 q^{40} +3.60586 q^{41} +1.30906 q^{42} -10.3853 q^{43} -1.00000 q^{44} -2.88711 q^{45} -6.94577 q^{46} -0.509239 q^{47} +0.335989 q^{48} +8.17988 q^{49} -1.00000 q^{50} +0.322228 q^{51} +1.74566 q^{52} -13.9395 q^{53} +1.97801 q^{54} -1.00000 q^{55} +3.89614 q^{56} -0.329307 q^{57} +4.84932 q^{58} +8.18800 q^{59} +0.335989 q^{60} -1.07784 q^{61} -5.52406 q^{62} +11.2486 q^{63} +1.00000 q^{64} +1.74566 q^{65} +0.335989 q^{66} -5.45954 q^{67} +0.959044 q^{68} +2.33370 q^{69} +3.89614 q^{70} -1.51738 q^{71} +2.88711 q^{72} +1.00000 q^{73} -11.5299 q^{74} +0.335989 q^{75} -0.980111 q^{76} +3.89614 q^{77} -0.586522 q^{78} +1.12029 q^{79} +1.00000 q^{80} +7.99675 q^{81} -3.60586 q^{82} +6.23489 q^{83} -1.30906 q^{84} +0.959044 q^{85} +10.3853 q^{86} -1.62932 q^{87} +1.00000 q^{88} -4.85596 q^{89} +2.88711 q^{90} -6.80132 q^{91} +6.94577 q^{92} +1.85602 q^{93} +0.509239 q^{94} -0.980111 q^{95} -0.335989 q^{96} -11.4470 q^{97} -8.17988 q^{98} +2.88711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 2 q^{3} + 7 q^{4} + 7 q^{5} + 2 q^{6} - 3 q^{7} - 7 q^{8} + 5 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 2 * q^3 + 7 * q^4 + 7 * q^5 + 2 * q^6 - 3 * q^7 - 7 * q^8 + 5 * q^9	\( 7 q - 7 q^{2} - 2 q^{3} + 7 q^{4} + 7 q^{5} + 2 q^{6} - 3 q^{7} - 7 q^{8} + 5 q^{9} - 7 q^{10} - 7 q^{11} - 2 q^{12} - 3 q^{13} + 3 q^{14} - 2 q^{15} + 7 q^{16} - 11 q^{17} - 5 q^{18} - 8 q^{19} + 7 q^{20} - 3 q^{21} + 7 q^{22} + 8 q^{23} + 2 q^{24} + 7 q^{25} + 3 q^{26} - 11 q^{27} - 3 q^{28} - 9 q^{29} + 2 q^{30} - 9 q^{31} - 7 q^{32} + 2 q^{33} + 11 q^{34} - 3 q^{35} + 5 q^{36} + 21 q^{37} + 8 q^{38} + 39 q^{39} - 7 q^{40} - 10 q^{41} + 3 q^{42} - 5 q^{43} - 7 q^{44} + 5 q^{45} - 8 q^{46} + 19 q^{47} - 2 q^{48} - 14 q^{49} - 7 q^{50} + 37 q^{51} - 3 q^{52} - 13 q^{53} + 11 q^{54} - 7 q^{55} + 3 q^{56} - 13 q^{57} + 9 q^{58} + 5 q^{59} - 2 q^{60} - 12 q^{61} + 9 q^{62} - 12 q^{63} + 7 q^{64} - 3 q^{65} - 2 q^{66} - 23 q^{67} - 11 q^{68} - 24 q^{69} + 3 q^{70} + 22 q^{71} - 5 q^{72} + 7 q^{73} - 21 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} - 39 q^{78} - 32 q^{79} + 7 q^{80} + 27 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - 11 q^{85} + 5 q^{86} - 13 q^{87} + 7 q^{88} + 20 q^{89} - 5 q^{90} - 2 q^{91} + 8 q^{92} - 25 q^{93} - 19 q^{94} - 8 q^{95} + 2 q^{96} - 2 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 2 * q^3 + 7 * q^4 + 7 * q^5 + 2 * q^6 - 3 * q^7 - 7 * q^8 + 5 * q^9 - 7 * q^10 - 7 * q^11 - 2 * q^12 - 3 * q^13 + 3 * q^14 - 2 * q^15 + 7 * q^16 - 11 * q^17 - 5 * q^18 - 8 * q^19 + 7 * q^20 - 3 * q^21 + 7 * q^22 + 8 * q^23 + 2 * q^24 + 7 * q^25 + 3 * q^26 - 11 * q^27 - 3 * q^28 - 9 * q^29 + 2 * q^30 - 9 * q^31 - 7 * q^32 + 2 * q^33 + 11 * q^34 - 3 * q^35 + 5 * q^36 + 21 * q^37 + 8 * q^38 + 39 * q^39 - 7 * q^40 - 10 * q^41 + 3 * q^42 - 5 * q^43 - 7 * q^44 + 5 * q^45 - 8 * q^46 + 19 * q^47 - 2 * q^48 - 14 * q^49 - 7 * q^50 + 37 * q^51 - 3 * q^52 - 13 * q^53 + 11 * q^54 - 7 * q^55 + 3 * q^56 - 13 * q^57 + 9 * q^58 + 5 * q^59 - 2 * q^60 - 12 * q^61 + 9 * q^62 - 12 * q^63 + 7 * q^64 - 3 * q^65 - 2 * q^66 - 23 * q^67 - 11 * q^68 - 24 * q^69 + 3 * q^70 + 22 * q^71 - 5 * q^72 + 7 * q^73 - 21 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 - 39 * q^78 - 32 * q^79 + 7 * q^80 + 27 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - 11 * q^85 + 5 * q^86 - 13 * q^87 + 7 * q^88 + 20 * q^89 - 5 * q^90 - 2 * q^91 + 8 * q^92 - 25 * q^93 - 19 * q^94 - 8 * q^95 + 2 * q^96 - 2 * q^97 + 14 * q^98 - 5 * 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
$3$	0.335989	0.193983	0.0969917	−	0.995285i	$-0.469078\pi$
$3$	0.335989	0.193983	0.0969917	+	0.995285i	$0.469078\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.335989	−0.137167
$7$	−3.89614	−1.47260	−0.736301	−	0.676655i	$-0.763429\pi$
$7$	−3.89614	−1.47260	−0.736301	+	0.676655i	$0.763429\pi$
$8$	−1.00000	−0.353553
$9$	−2.88711	−0.962370
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.335989	0.0969917
$13$	1.74566	0.484158	0.242079	−	0.970256i	$-0.422171\pi$
$13$	1.74566	0.484158	0.242079	+	0.970256i	$0.422171\pi$
$14$	3.89614	1.04129
$15$	0.335989	0.0867520
$16$	1.00000	0.250000
$17$	0.959044	0.232602	0.116301	−	0.993214i	$-0.462896\pi$
$17$	0.959044	0.232602	0.116301	+	0.993214i	$0.462896\pi$
$18$	2.88711	0.680499
$19$	−0.980111	−0.224853	−0.112426	−	0.993660i	$-0.535862\pi$
$19$	−0.980111	−0.224853	−0.112426	+	0.993660i	$0.535862\pi$
$20$	1.00000	0.223607
$21$	−1.30906	−0.285660
$22$	1.00000	0.213201
$23$	6.94577	1.44829	0.724146	−	0.689646i	$-0.242234\pi$
$23$	6.94577	1.44829	0.724146	+	0.689646i	$0.242234\pi$
$24$	−0.335989	−0.0685835
$25$	1.00000	0.200000
$26$	−1.74566	−0.342352
$27$	−1.97801	−0.380667
$28$	−3.89614	−0.736301
$29$	−4.84932	−0.900496	−0.450248	−	0.892904i	$-0.648664\pi$
$29$	−4.84932	−0.900496	−0.450248	+	0.892904i	$0.648664\pi$
$30$	−0.335989	−0.0613429
$31$	5.52406	0.992150	0.496075	−	0.868280i	$-0.334774\pi$
$31$	5.52406	0.992150	0.496075	+	0.868280i	$0.334774\pi$
$32$	−1.00000	−0.176777
$33$	−0.335989	−0.0584882
$34$	−0.959044	−0.164475
$35$	−3.89614	−0.658567
$36$	−2.88711	−0.481185
$37$	11.5299	1.89550	0.947752	−	0.319010i	$-0.103350\pi$
$37$	11.5299	1.89550	0.947752	+	0.319010i	$0.103350\pi$
$38$	0.980111	0.158995
$39$	0.586522	0.0939187
$40$	−1.00000	−0.158114
$41$	3.60586	0.563141	0.281570	−	0.959541i	$-0.409145\pi$
$41$	3.60586	0.563141	0.281570	+	0.959541i	$0.409145\pi$
$42$	1.30906	0.201992
$43$	−10.3853	−1.58374	−0.791870	−	0.610690i	$-0.790892\pi$
$43$	−10.3853	−1.58374	−0.791870	+	0.610690i	$0.790892\pi$
$44$	−1.00000	−0.150756
$45$	−2.88711	−0.430385
$46$	−6.94577	−1.02410
$47$	−0.509239	−0.0742802	−0.0371401	−	0.999310i	$-0.511825\pi$
$47$	−0.509239	−0.0742802	−0.0371401	+	0.999310i	$0.511825\pi$
$48$	0.335989	0.0484959
$49$	8.17988	1.16855
$50$	−1.00000	−0.141421
$51$	0.322228	0.0451210
$52$	1.74566	0.242079
$53$	−13.9395	−1.91474	−0.957370	−	0.288864i	$-0.906722\pi$
$53$	−13.9395	−1.91474	−0.957370	+	0.288864i	$0.906722\pi$
$54$	1.97801	0.269172
$55$	−1.00000	−0.134840
$56$	3.89614	0.520643
$57$	−0.329307	−0.0436178
$58$	4.84932	0.636747
$59$	8.18800	1.06599	0.532993	−	0.846119i	$-0.321067\pi$
$59$	8.18800	1.06599	0.532993	+	0.846119i	$0.321067\pi$
$60$	0.335989	0.0433760
$61$	−1.07784	−0.138003	−0.0690015	−	0.997617i	$-0.521981\pi$
$61$	−1.07784	−0.138003	−0.0690015	+	0.997617i	$0.521981\pi$
$62$	−5.52406	−0.701556
$63$	11.2486	1.41719
$64$	1.00000	0.125000
$65$	1.74566	0.216522
$66$	0.335989	0.0413574
$67$	−5.45954	−0.666989	−0.333494	−	0.942752i	$-0.608228\pi$
$67$	−5.45954	−0.666989	−0.333494	+	0.942752i	$0.608228\pi$
$68$	0.959044	0.116301
$69$	2.33370	0.280945
$70$	3.89614	0.465677
$71$	−1.51738	−0.180079	−0.0900397	−	0.995938i	$-0.528699\pi$
$71$	−1.51738	−0.180079	−0.0900397	+	0.995938i	$0.528699\pi$
$72$	2.88711	0.340249
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−11.5299	−1.34032
$75$	0.335989	0.0387967
$76$	−0.980111	−0.112426
$77$	3.89614	0.444006
$78$	−0.586522	−0.0664106
$79$	1.12029	0.126043	0.0630215	−	0.998012i	$-0.479926\pi$
$79$	1.12029	0.126043	0.0630215	+	0.998012i	$0.479926\pi$
$80$	1.00000	0.111803
$81$	7.99675	0.888527
$82$	−3.60586	−0.398200
$83$	6.23489	0.684368	0.342184	−	0.939633i	$-0.388833\pi$
$83$	6.23489	0.684368	0.342184	+	0.939633i	$0.388833\pi$
$84$	−1.30906	−0.142830
$85$	0.959044	0.104023
$86$	10.3853	1.11987
$87$	−1.62932	−0.174681
$88$	1.00000	0.106600
$89$	−4.85596	−0.514730	−0.257365	−	0.966314i	$-0.582854\pi$
$89$	−4.85596	−0.514730	−0.257365	+	0.966314i	$0.582854\pi$
$90$	2.88711	0.304328
$91$	−6.80132	−0.712972
$92$	6.94577	0.724146
$93$	1.85602	0.192461
$94$	0.509239	0.0525240
$95$	−0.980111	−0.100557
$96$	−0.335989	−0.0342918
$97$	−11.4470	−1.16226	−0.581131	−	0.813810i	$-0.697390\pi$
$97$	−11.4470	−1.16226	−0.581131	+	0.813810i	$0.697390\pi$
$98$	−8.17988	−0.826293
$99$	2.88711	0.290166
$100$	1.00000	0.100000
$101$	10.2835	1.02325	0.511624	−	0.859209i	$-0.329044\pi$
$101$	10.2835	1.02325	0.511624	+	0.859209i	$0.329044\pi$
$102$	−0.322228	−0.0319053
$103$	10.0223	0.987527	0.493763	−	0.869596i	$-0.335621\pi$
$103$	10.0223	0.987527	0.493763	+	0.869596i	$0.335621\pi$
$104$	−1.74566	−0.171176
$105$	−1.30906	−0.127751
$106$	13.9395	1.35393
$107$	13.3186	1.28756	0.643781	−	0.765210i	$-0.277365\pi$
$107$	13.3186	1.28756	0.643781	+	0.765210i	$0.277365\pi$
$108$	−1.97801	−0.190334
$109$	−19.9949	−1.91517	−0.957584	−	0.288155i	$-0.906958\pi$
$109$	−19.9949	−1.91517	−0.957584	+	0.288155i	$0.906958\pi$
$110$	1.00000	0.0953463
$111$	3.87392	0.367696
$112$	−3.89614	−0.368150
$113$	0.671551	0.0631742	0.0315871	−	0.999501i	$-0.489944\pi$
$113$	0.671551	0.0631742	0.0315871	+	0.999501i	$0.489944\pi$
$114$	0.329307	0.0308424
$115$	6.94577	0.647696
$116$	−4.84932	−0.450248
$117$	−5.03991	−0.465940
$118$	−8.18800	−0.753767
$119$	−3.73656	−0.342530
$120$	−0.335989	−0.0306715
$121$	1.00000	0.0909091
$122$	1.07784	0.0975828
$123$	1.21153	0.109240
$124$	5.52406	0.496075
$125$	1.00000	0.0894427
$126$	−11.2486	−1.00210
$127$	−1.38315	−0.122735	−0.0613674	−	0.998115i	$-0.519546\pi$
$127$	−1.38315	−0.122735	−0.0613674	+	0.998115i	$0.519546\pi$
$128$	−1.00000	−0.0883883
$129$	−3.48934	−0.307219
$130$	−1.74566	−0.153104
$131$	9.38664	0.820115	0.410057	−	0.912060i	$-0.365509\pi$
$131$	9.38664	0.820115	0.410057	+	0.912060i	$0.365509\pi$
$132$	−0.335989	−0.0292441
$133$	3.81865	0.331119
$134$	5.45954	0.471632
$135$	−1.97801	−0.170240
$136$	−0.959044	−0.0822373
$137$	2.65020	0.226422	0.113211	−	0.993571i	$-0.463886\pi$
$137$	2.65020	0.226422	0.113211	+	0.993571i	$0.463886\pi$
$138$	−2.33370	−0.198658
$139$	−0.560214	−0.0475167	−0.0237584	−	0.999718i	$-0.507563\pi$
$139$	−0.560214	−0.0475167	−0.0237584	+	0.999718i	$0.507563\pi$
$140$	−3.89614	−0.329284
$141$	−0.171099	−0.0144091
$142$	1.51738	0.127335
$143$	−1.74566	−0.145979
$144$	−2.88711	−0.240593
$145$	−4.84932	−0.402714
$146$	−1.00000	−0.0827606
$147$	2.74835	0.226680
$148$	11.5299	0.947752
$149$	−17.5080	−1.43431	−0.717156	−	0.696913i	$-0.754556\pi$
$149$	−17.5080	−1.43431	−0.717156	+	0.696913i	$0.754556\pi$
$150$	−0.335989	−0.0274334
$151$	10.8173	0.880297	0.440148	−	0.897925i	$-0.354926\pi$
$151$	10.8173	0.880297	0.440148	+	0.897925i	$0.354926\pi$
$152$	0.980111	0.0794975
$153$	−2.76887	−0.223850
$154$	−3.89614	−0.313960
$155$	5.52406	0.443703
$156$	0.586522	0.0469594
$157$	4.23203	0.337753	0.168876	−	0.985637i	$-0.445986\pi$
$157$	4.23203	0.337753	0.168876	+	0.985637i	$0.445986\pi$
$158$	−1.12029	−0.0891258
$159$	−4.68353	−0.371428
$160$	−1.00000	−0.0790569
$161$	−27.0617	−2.13276
$162$	−7.99675	−0.628284
$163$	7.63996	0.598408	0.299204	−	0.954189i	$-0.403279\pi$
$163$	7.63996	0.598408	0.299204	+	0.954189i	$0.403279\pi$
$164$	3.60586	0.281570
$165$	−0.335989	−0.0261567
$166$	−6.23489	−0.483921
$167$	−20.2510	−1.56707	−0.783535	−	0.621348i	$-0.786585\pi$
$167$	−20.2510	−1.56707	−0.783535	+	0.621348i	$0.786585\pi$
$168$	1.30906	0.100996
$169$	−9.95268	−0.765591
$170$	−0.959044	−0.0735553
$171$	2.82969	0.216392
$172$	−10.3853	−0.791870
$173$	−8.08350	−0.614577	−0.307288	−	0.951616i	$-0.599422\pi$
$173$	−8.08350	−0.614577	−0.307288	+	0.951616i	$0.599422\pi$
$174$	1.62932	0.123518
$175$	−3.89614	−0.294520
$176$	−1.00000	−0.0753778
$177$	2.75108	0.206784
$178$	4.85596	0.363969
$179$	−2.80638	−0.209759	−0.104879	−	0.994485i	$-0.533446\pi$
$179$	−2.80638	−0.209759	−0.104879	+	0.994485i	$0.533446\pi$
$180$	−2.88711	−0.215193
$181$	−3.68996	−0.274273	−0.137136	−	0.990552i	$-0.543790\pi$
$181$	−3.68996	−0.274273	−0.137136	+	0.990552i	$0.543790\pi$
$182$	6.80132	0.504147
$183$	−0.362142	−0.0267703
$184$	−6.94577	−0.512049
$185$	11.5299	0.847695
$186$	−1.85602	−0.136090
$187$	−0.959044	−0.0701322
$188$	−0.509239	−0.0371401
$189$	7.70658	0.560571
$190$	0.980111	0.0711048
$191$	−5.55551	−0.401983	−0.200991	−	0.979593i	$-0.564416\pi$
$191$	−5.55551	−0.401983	−0.200991	+	0.979593i	$0.564416\pi$
$192$	0.335989	0.0242479
$193$	−12.2871	−0.884442	−0.442221	−	0.896906i	$-0.645809\pi$
$193$	−12.2871	−0.884442	−0.442221	+	0.896906i	$0.645809\pi$
$194$	11.4470	0.821844
$195$	0.586522	0.0420017
$196$	8.17988	0.584277
$197$	−12.7441	−0.907980	−0.453990	−	0.891007i	$-0.650000\pi$
$197$	−12.7441	−0.907980	−0.453990	+	0.891007i	$0.650000\pi$
$198$	−2.88711	−0.205178
$199$	−15.2138	−1.07848	−0.539240	−	0.842152i	$-0.681288\pi$
$199$	−15.2138	−1.07848	−0.539240	+	0.842152i	$0.681288\pi$
$200$	−1.00000	−0.0707107
$201$	−1.83435	−0.129385
$202$	−10.2835	−0.723546
$203$	18.8936	1.32607
$204$	0.322228	0.0225605
$205$	3.60586	0.251844
$206$	−10.0223	−0.698287
$207$	−20.0532	−1.39379
$208$	1.74566	0.121040
$209$	0.980111	0.0677957
$210$	1.30906	0.0903337
$211$	−1.58414	−0.109056	−0.0545282	−	0.998512i	$-0.517365\pi$
$211$	−1.58414	−0.109056	−0.0545282	+	0.998512i	$0.517365\pi$
$212$	−13.9395	−0.957370
$213$	−0.509822	−0.0349324
$214$	−13.3186	−0.910444
$215$	−10.3853	−0.708270
$216$	1.97801	0.134586
$217$	−21.5225	−1.46104
$218$	19.9949	1.35423
$219$	0.335989	0.0227040
$220$	−1.00000	−0.0674200
$221$	1.67416	0.112616
$222$	−3.87392	−0.260000
$223$	−14.0404	−0.940216	−0.470108	−	0.882609i	$-0.655785\pi$
$223$	−14.0404	−0.940216	−0.470108	+	0.882609i	$0.655785\pi$
$224$	3.89614	0.260322
$225$	−2.88711	−0.192474
$226$	−0.671551	−0.0446709
$227$	−21.1343	−1.40273	−0.701366	−	0.712802i	$-0.747426\pi$
$227$	−21.1343	−1.40273	−0.701366	+	0.712802i	$0.747426\pi$
$228$	−0.329307	−0.0218089
$229$	25.1319	1.66076	0.830381	−	0.557195i	$-0.188123\pi$
$229$	25.1319	1.66076	0.830381	+	0.557195i	$0.188123\pi$
$230$	−6.94577	−0.457990
$231$	1.30906	0.0861298
$232$	4.84932	0.318373
$233$	−17.9567	−1.17639	−0.588193	−	0.808721i	$-0.700160\pi$
$233$	−17.9567	−1.17639	−0.588193	+	0.808721i	$0.700160\pi$
$234$	5.03991	0.329469
$235$	−0.509239	−0.0332191
$236$	8.18800	0.532993
$237$	0.376407	0.0244502
$238$	3.73656	0.242205
$239$	−20.8922	−1.35141	−0.675703	−	0.737174i	$-0.736160\pi$
$239$	−20.8922	−1.35141	−0.675703	+	0.737174i	$0.736160\pi$
$240$	0.335989	0.0216880
$241$	19.2749	1.24160	0.620802	−	0.783968i	$-0.286807\pi$
$241$	19.2749	1.24160	0.620802	+	0.783968i	$0.286807\pi$
$242$	−1.00000	−0.0642824
$243$	8.62084	0.553027
$244$	−1.07784	−0.0690015
$245$	8.17988	0.522593
$246$	−1.21153	−0.0772443
$247$	−1.71094	−0.108864
$248$	−5.52406	−0.350778
$249$	2.09485	0.132756
$250$	−1.00000	−0.0632456
$251$	24.6268	1.55443	0.777215	−	0.629235i	$-0.216632\pi$
$251$	24.6268	1.55443	0.777215	+	0.629235i	$0.216632\pi$
$252$	11.2486	0.708594
$253$	−6.94577	−0.436677
$254$	1.38315	0.0867866
$255$	0.322228	0.0201787
$256$	1.00000	0.0625000
$257$	−21.4789	−1.33982	−0.669909	−	0.742444i	$-0.733667\pi$
$257$	−21.4789	−1.33982	−0.669909	+	0.742444i	$0.733667\pi$
$258$	3.48934	0.217237
$259$	−44.9220	−2.79132
$260$	1.74566	0.108261
$261$	14.0005	0.866611
$262$	−9.38664	−0.579909
$263$	−24.9244	−1.53690	−0.768451	−	0.639908i	$-0.778972\pi$
$263$	−24.9244	−1.53690	−0.768451	+	0.639908i	$0.778972\pi$
$264$	0.335989	0.0206787
$265$	−13.9395	−0.856298
$266$	−3.81865	−0.234136
$267$	−1.63155	−0.0998492
$268$	−5.45954	−0.333494
$269$	8.53693	0.520506	0.260253	−	0.965541i	$-0.416194\pi$
$269$	8.53693	0.520506	0.260253	+	0.965541i	$0.416194\pi$
$270$	1.97801	0.120378
$271$	−5.28281	−0.320908	−0.160454	−	0.987043i	$-0.551296\pi$
$271$	−5.28281	−0.320908	−0.160454	+	0.987043i	$0.551296\pi$
$272$	0.959044	0.0581506
$273$	−2.28517	−0.138305
$274$	−2.65020	−0.160105
$275$	−1.00000	−0.0603023
$276$	2.33370	0.140472
$277$	18.9964	1.14138	0.570691	−	0.821165i	$-0.306676\pi$
$277$	18.9964	1.14138	0.570691	+	0.821165i	$0.306676\pi$
$278$	0.560214	0.0335994
$279$	−15.9486	−0.954816
$280$	3.89614	0.232839
$281$	3.56290	0.212545	0.106273	−	0.994337i	$-0.466108\pi$
$281$	3.56290	0.212545	0.106273	+	0.994337i	$0.466108\pi$
$282$	0.171099	0.0101888
$283$	−8.21577	−0.488377	−0.244188	−	0.969728i	$-0.578521\pi$
$283$	−8.21577	−0.488377	−0.244188	+	0.969728i	$0.578521\pi$
$284$	−1.51738	−0.0900397
$285$	−0.329307	−0.0195065
$286$	1.74566	0.103223
$287$	−14.0489	−0.829281
$288$	2.88711	0.170125
$289$	−16.0802	−0.945896
$290$	4.84932	0.284762
$291$	−3.84605	−0.225460
$292$	1.00000	0.0585206
$293$	−7.91890	−0.462627	−0.231313	−	0.972879i	$-0.574302\pi$
$293$	−7.91890	−0.462627	−0.231313	+	0.972879i	$0.574302\pi$
$294$	−2.74835	−0.160287
$295$	8.18800	0.476724
$296$	−11.5299	−0.670162
$297$	1.97801	0.114776
$298$	17.5080	1.01421
$299$	12.1249	0.701203
$300$	0.335989	0.0193983
$301$	40.4625	2.33222
$302$	−10.8173	−0.622464
$303$	3.45515	0.198493
$304$	−0.980111	−0.0562132
$305$	−1.07784	−0.0617168
$306$	2.76887	0.158286
$307$	−13.9135	−0.794083	−0.397042	−	0.917801i	$-0.629963\pi$
$307$	−13.9135	−0.794083	−0.397042	+	0.917801i	$0.629963\pi$
$308$	3.89614	0.222003
$309$	3.36738	0.191564
$310$	−5.52406	−0.313745
$311$	−10.2283	−0.579994	−0.289997	−	0.957028i	$-0.593654\pi$
$311$	−10.2283	−0.579994	−0.289997	+	0.957028i	$0.593654\pi$
$312$	−0.586522	−0.0332053
$313$	−25.5366	−1.44342	−0.721708	−	0.692198i	$-0.756643\pi$
$313$	−25.5366	−1.44342	−0.721708	+	0.692198i	$0.756643\pi$
$314$	−4.23203	−0.238827
$315$	11.2486	0.633786
$316$	1.12029	0.0630215
$317$	−23.7939	−1.33640	−0.668199	−	0.743983i	$-0.732935\pi$
$317$	−23.7939	−1.33640	−0.668199	+	0.743983i	$0.732935\pi$
$318$	4.68353	0.262639
$319$	4.84932	0.271510
$320$	1.00000	0.0559017
$321$	4.47492	0.249766
$322$	27.0617	1.50809
$323$	−0.939969	−0.0523013
$324$	7.99675	0.444264
$325$	1.74566	0.0968317
$326$	−7.63996	−0.423138
$327$	−6.71808	−0.371511
$328$	−3.60586	−0.199100
$329$	1.98407	0.109385
$330$	0.335989	0.0184956
$331$	16.7293	0.919524	0.459762	−	0.888042i	$-0.347935\pi$
$331$	16.7293	0.919524	0.459762	+	0.888042i	$0.347935\pi$
$332$	6.23489	0.342184
$333$	−33.2881	−1.82418
$334$	20.2510	1.10809
$335$	−5.45954	−0.298286
$336$	−1.30906	−0.0714151
$337$	2.49915	0.136138	0.0680688	−	0.997681i	$-0.478316\pi$
$337$	2.49915	0.136138	0.0680688	+	0.997681i	$0.478316\pi$
$338$	9.95268	0.541354
$339$	0.225634	0.0122548
$340$	0.959044	0.0520114
$341$	−5.52406	−0.299144
$342$	−2.82969	−0.153012
$343$	−4.59697	−0.248213
$344$	10.3853	0.559937
$345$	2.33370	0.125642
$346$	8.08350	0.434571
$347$	−6.24909	−0.335469	−0.167734	−	0.985832i	$-0.553645\pi$
$347$	−6.24909	−0.335469	−0.167734	+	0.985832i	$0.553645\pi$
$348$	−1.62932	−0.0873406
$349$	−16.5092	−0.883719	−0.441860	−	0.897084i	$-0.645681\pi$
$349$	−16.5092	−0.883719	−0.441860	+	0.897084i	$0.645681\pi$
$350$	3.89614	0.208257
$351$	−3.45292	−0.184303
$352$	1.00000	0.0533002
$353$	−17.3092	−0.921278	−0.460639	−	0.887588i	$-0.652380\pi$
$353$	−17.3092	−0.921278	−0.460639	+	0.887588i	$0.652380\pi$
$354$	−2.75108	−0.146218
$355$	−1.51738	−0.0805339
$356$	−4.85596	−0.257365
$357$	−1.25545	−0.0664452
$358$	2.80638	0.148322
$359$	0.413339	0.0218152	0.0109076	−	0.999941i	$-0.496528\pi$
$359$	0.413339	0.0218152	0.0109076	+	0.999941i	$0.496528\pi$
$360$	2.88711	0.152164
$361$	−18.0394	−0.949441
$362$	3.68996	0.193940
$363$	0.335989	0.0176349
$364$	−6.80132	−0.356486
$365$	1.00000	0.0523424
$366$	0.362142	0.0189295
$367$	5.33049	0.278249	0.139125	−	0.990275i	$-0.455571\pi$
$367$	5.33049	0.278249	0.139125	+	0.990275i	$0.455571\pi$
$368$	6.94577	0.362073
$369$	−10.4105	−0.541950
$370$	−11.5299	−0.599411
$371$	54.3103	2.81965
$372$	1.85602	0.0962303
$373$	−11.5391	−0.597474	−0.298737	−	0.954335i	$-0.596565\pi$
$373$	−11.5391	−0.597474	−0.298737	+	0.954335i	$0.596565\pi$
$374$	0.959044	0.0495910
$375$	0.335989	0.0173504
$376$	0.509239	0.0262620
$377$	−8.46525	−0.435983
$378$	−7.70658	−0.396384
$379$	−4.75712	−0.244357	−0.122179	−	0.992508i	$-0.538988\pi$
$379$	−4.75712	−0.244357	−0.122179	+	0.992508i	$0.538988\pi$
$380$	−0.980111	−0.0502787
$381$	−0.464724	−0.0238085
$382$	5.55551	0.284245
$383$	19.7687	1.01014	0.505068	−	0.863080i	$-0.331468\pi$
$383$	19.7687	1.01014	0.505068	+	0.863080i	$0.331468\pi$
$384$	−0.335989	−0.0171459
$385$	3.89614	0.198565
$386$	12.2871	0.625395
$387$	29.9835	1.52414
$388$	−11.4470	−0.581131
$389$	−37.5199	−1.90233	−0.951167	−	0.308678i	$-0.900113\pi$
$389$	−37.5199	−1.90233	−0.951167	+	0.308678i	$0.900113\pi$
$390$	−0.586522	−0.0296997
$391$	6.66129	0.336876
$392$	−8.17988	−0.413146
$393$	3.15381	0.159089
$394$	12.7441	0.642039
$395$	1.12029	0.0563681
$396$	2.88711	0.145083
$397$	0.136112	0.00683128	0.00341564	−	0.999994i	$-0.498913\pi$
$397$	0.136112	0.00683128	0.00341564	+	0.999994i	$0.498913\pi$
$398$	15.2138	0.762600
$399$	1.28302	0.0642316
$400$	1.00000	0.0500000
$401$	33.8959	1.69268	0.846339	−	0.532644i	$-0.178802\pi$
$401$	33.8959	1.69268	0.846339	+	0.532644i	$0.178802\pi$
$402$	1.83435	0.0914888
$403$	9.64311	0.480358
$404$	10.2835	0.511624
$405$	7.99675	0.397361
$406$	−18.8936	−0.937674
$407$	−11.5299	−0.571516
$408$	−0.322228	−0.0159527
$409$	9.94131	0.491566	0.245783	−	0.969325i	$-0.420955\pi$
$409$	9.94131	0.491566	0.245783	+	0.969325i	$0.420955\pi$
$410$	−3.60586	−0.178081
$411$	0.890439	0.0439221
$412$	10.0223	0.493763
$413$	−31.9016	−1.56977
$414$	20.0532	0.985561
$415$	6.23489	0.306059
$416$	−1.74566	−0.0855879
$417$	−0.188226	−0.00921746
$418$	−0.980111	−0.0479388
$419$	7.90368	0.386120	0.193060	−	0.981187i	$-0.438159\pi$
$419$	7.90368	0.386120	0.193060	+	0.981187i	$0.438159\pi$
$420$	−1.30906	−0.0638756
$421$	−4.51286	−0.219943	−0.109972	−	0.993935i	$-0.535076\pi$
$421$	−4.51286	−0.219943	−0.109972	+	0.993935i	$0.535076\pi$
$422$	1.58414	0.0771145
$423$	1.47023	0.0714850
$424$	13.9395	0.676963
$425$	0.959044	0.0465204
$426$	0.509822	0.0247009
$427$	4.19940	0.203223
$428$	13.3186	0.643781
$429$	−0.586522	−0.0283176
$430$	10.3853	0.500823
$431$	−29.7472	−1.43287	−0.716436	−	0.697653i	$-0.754228\pi$
$431$	−29.7472	−1.43287	−0.716436	+	0.697653i	$0.754228\pi$
$432$	−1.97801	−0.0951668
$433$	−2.96742	−0.142605	−0.0713026	−	0.997455i	$-0.522716\pi$
$433$	−2.96742	−0.142605	−0.0713026	+	0.997455i	$0.522716\pi$
$434$	21.5225	1.03311
$435$	−1.62932	−0.0781198
$436$	−19.9949	−0.957584
$437$	−6.80763	−0.325653
$438$	−0.335989	−0.0160542
$439$	39.1993	1.87088	0.935441	−	0.353484i	$-0.115003\pi$
$439$	39.1993	1.87088	0.935441	+	0.353484i	$0.115003\pi$
$440$	1.00000	0.0476731
$441$	−23.6162	−1.12458
$442$	−1.67416	−0.0796318
$443$	−39.3331	−1.86877	−0.934386	−	0.356262i	$-0.884051\pi$
$443$	−39.3331	−1.86877	−0.934386	+	0.356262i	$0.884051\pi$
$444$	3.87392	0.183848
$445$	−4.85596	−0.230194
$446$	14.0404	0.664833
$447$	−5.88250	−0.278233
$448$	−3.89614	−0.184075
$449$	−12.6810	−0.598453	−0.299226	−	0.954182i	$-0.596729\pi$
$449$	−12.6810	−0.598453	−0.299226	+	0.954182i	$0.596729\pi$
$450$	2.88711	0.136100
$451$	−3.60586	−0.169793
$452$	0.671551	0.0315871
$453$	3.63448	0.170763
$454$	21.1343	0.991881
$455$	−6.80132	−0.318851
$456$	0.329307	0.0154212
$457$	20.8924	0.977304	0.488652	−	0.872479i	$-0.337489\pi$
$457$	20.8924	0.977304	0.488652	+	0.872479i	$0.337489\pi$
$458$	−25.1319	−1.17434
$459$	−1.89699	−0.0885441
$460$	6.94577	0.323848
$461$	−22.0708	−1.02794	−0.513969	−	0.857809i	$-0.671825\pi$
$461$	−22.0708	−1.02794	−0.513969	+	0.857809i	$0.671825\pi$
$462$	−1.30906	−0.0609030
$463$	6.80122	0.316079	0.158040	−	0.987433i	$-0.449483\pi$
$463$	6.80122	0.316079	0.158040	+	0.987433i	$0.449483\pi$
$464$	−4.84932	−0.225124
$465$	1.85602	0.0860710
$466$	17.9567	0.831830
$467$	12.2490	0.566815	0.283407	−	0.959000i	$-0.408535\pi$
$467$	12.2490	0.566815	0.283407	+	0.959000i	$0.408535\pi$
$468$	−5.03991	−0.232970
$469$	21.2711	0.982208
$470$	0.509239	0.0234894
$471$	1.42192	0.0655185
$472$	−8.18800	−0.376883
$473$	10.3853	0.477516
$474$	−0.376407	−0.0172889
$475$	−0.980111	−0.0449706
$476$	−3.73656	−0.171265
$477$	40.2449	1.84269
$478$	20.8922	0.955588
$479$	36.9045	1.68621	0.843105	−	0.537749i	$-0.180725\pi$
$479$	36.9045	1.68621	0.843105	+	0.537749i	$0.180725\pi$
$480$	−0.335989	−0.0153357
$481$	20.1273	0.917724
$482$	−19.2749	−0.877946
$483$	−9.09243	−0.413720
$484$	1.00000	0.0454545
$485$	−11.4470	−0.519780
$486$	−8.62084	−0.391049
$487$	−12.0601	−0.546496	−0.273248	−	0.961944i	$-0.588098\pi$
$487$	−12.0601	−0.546496	−0.273248	+	0.961944i	$0.588098\pi$
$488$	1.07784	0.0487914
$489$	2.56694	0.116081
$490$	−8.17988	−0.369529
$491$	36.0095	1.62509	0.812544	−	0.582900i	$-0.198082\pi$
$491$	36.0095	1.62509	0.812544	+	0.582900i	$0.198082\pi$
$492$	1.21153	0.0546200
$493$	−4.65071	−0.209457
$494$	1.71094	0.0769788
$495$	2.88711	0.129766
$496$	5.52406	0.248038
$497$	5.91190	0.265185
$498$	−2.09485	−0.0938727
$499$	16.2652	0.728129	0.364064	−	0.931374i	$-0.381389\pi$
$499$	16.2652	0.728129	0.364064	+	0.931374i	$0.381389\pi$
$500$	1.00000	0.0447214
$501$	−6.80412	−0.303985
$502$	−24.6268	−1.09915
$503$	12.5998	0.561795	0.280898	−	0.959738i	$-0.409368\pi$
$503$	12.5998	0.561795	0.280898	+	0.959738i	$0.409368\pi$
$504$	−11.2486	−0.501052
$505$	10.2835	0.457611
$506$	6.94577	0.308777
$507$	−3.34399	−0.148512
$508$	−1.38315	−0.0613674
$509$	22.1999	0.983994	0.491997	−	0.870597i	$-0.336267\pi$
$509$	22.1999	0.983994	0.491997	+	0.870597i	$0.336267\pi$
$510$	−0.322228	−0.0142685
$511$	−3.89614	−0.172355
$512$	−1.00000	−0.0441942
$513$	1.93867	0.0855942
$514$	21.4789	0.947394
$515$	10.0223	0.441635
$516$	−3.48934	−0.153610
$517$	0.509239	0.0223963
$518$	44.9220	1.97376
$519$	−2.71597	−0.119218
$520$	−1.74566	−0.0765522
$521$	32.6464	1.43027	0.715133	−	0.698989i	$-0.246366\pi$
$521$	32.6464	1.43027	0.715133	+	0.698989i	$0.246366\pi$
$522$	−14.0005	−0.612786
$523$	−6.44934	−0.282010	−0.141005	−	0.990009i	$-0.545033\pi$
$523$	−6.44934	−0.282010	−0.141005	+	0.990009i	$0.545033\pi$
$524$	9.38664	0.410057
$525$	−1.30906	−0.0571320
$526$	24.9244	1.08675
$527$	5.29781	0.230776
$528$	−0.335989	−0.0146221
$529$	25.2437	1.09755
$530$	13.9395	0.605494
$531$	−23.6397	−1.02587
$532$	3.81865	0.165559
$533$	6.29460	0.272649
$534$	1.63155	0.0706040
$535$	13.3186	0.575815
$536$	5.45954	0.235816
$537$	−0.942912	−0.0406897
$538$	−8.53693	−0.368053
$539$	−8.17988	−0.352332
$540$	−1.97801	−0.0851198
$541$	−15.9433	−0.685457	−0.342728	−	0.939435i	$-0.611351\pi$
$541$	−15.9433	−0.685457	−0.342728	+	0.939435i	$0.611351\pi$
$542$	5.28281	0.226916
$543$	−1.23979	−0.0532043
$544$	−0.959044	−0.0411187
$545$	−19.9949	−0.856489
$546$	2.28517	0.0977963
$547$	−8.13824	−0.347966	−0.173983	−	0.984749i	$-0.555664\pi$
$547$	−8.13824	−0.347966	−0.173983	+	0.984749i	$0.555664\pi$
$548$	2.65020	0.113211
$549$	3.11184	0.132810
$550$	1.00000	0.0426401
$551$	4.75287	0.202479
$552$	−2.33370	−0.0993290
$553$	−4.36482	−0.185611
$554$	−18.9964	−0.807078
$555$	3.87392	0.164439
$556$	−0.560214	−0.0237584
$557$	−12.9861	−0.550238	−0.275119	−	0.961410i	$-0.588717\pi$
$557$	−12.9861	−0.550238	−0.275119	+	0.961410i	$0.588717\pi$
$558$	15.9486	0.675157
$559$	−18.1291	−0.766781
$560$	−3.89614	−0.164642
$561$	−0.322228	−0.0136045
$562$	−3.56290	−0.150292
$563$	10.6101	0.447163	0.223582	−	0.974685i	$-0.428225\pi$
$563$	10.6101	0.447163	0.223582	+	0.974685i	$0.428225\pi$
$564$	−0.171099	−0.00720456
$565$	0.671551	0.0282524
$566$	8.21577	0.345334
$567$	−31.1564	−1.30845
$568$	1.51738	0.0636677
$569$	10.5979	0.444287	0.222144	−	0.975014i	$-0.428695\pi$
$569$	10.5979	0.444287	0.222144	+	0.975014i	$0.428695\pi$
$570$	0.329307	0.0137931
$571$	−8.35238	−0.349536	−0.174768	−	0.984610i	$-0.555918\pi$
$571$	−8.35238	−0.349536	−0.174768	+	0.984610i	$0.555918\pi$
$572$	−1.74566	−0.0729896
$573$	−1.86659	−0.0779780
$574$	14.0489	0.586390
$575$	6.94577	0.289659
$576$	−2.88711	−0.120296
$577$	−43.2318	−1.79976	−0.899881	−	0.436135i	$-0.856347\pi$
$577$	−43.2318	−1.79976	−0.899881	+	0.436135i	$0.856347\pi$
$578$	16.0802	0.668850
$579$	−4.12832	−0.171567
$580$	−4.84932	−0.201357
$581$	−24.2920	−1.00780
$582$	3.84605	0.159424
$583$	13.9395	0.577316
$584$	−1.00000	−0.0413803
$585$	−5.03991	−0.208375
$586$	7.91890	0.327127
$587$	31.6612	1.30680	0.653399	−	0.757014i	$-0.273342\pi$
$587$	31.6612	1.30680	0.653399	+	0.757014i	$0.273342\pi$
$588$	2.74835	0.113340
$589$	−5.41419	−0.223088
$590$	−8.18800	−0.337095
$591$	−4.28188	−0.176133
$592$	11.5299	0.473876
$593$	−32.2462	−1.32419	−0.662097	−	0.749418i	$-0.730333\pi$
$593$	−32.2462	−1.32419	−0.662097	+	0.749418i	$0.730333\pi$
$594$	−1.97801	−0.0811586
$595$	−3.73656	−0.153184
$596$	−17.5080	−0.717156
$597$	−5.11168	−0.209207
$598$	−12.1249	−0.495825
$599$	−27.8704	−1.13875	−0.569377	−	0.822076i	$-0.692816\pi$
$599$	−27.8704	−1.13875	−0.569377	+	0.822076i	$0.692816\pi$
$600$	−0.335989	−0.0137167
$601$	20.9338	0.853907	0.426953	−	0.904274i	$-0.359587\pi$
$601$	20.9338	0.853907	0.426953	+	0.904274i	$0.359587\pi$
$602$	−40.4625	−1.64913
$603$	15.7623	0.641890
$604$	10.8173	0.440148
$605$	1.00000	0.0406558
$606$	−3.45515	−0.140356
$607$	−14.7593	−0.599062	−0.299531	−	0.954087i	$-0.596830\pi$
$607$	−14.7593	−0.599062	−0.299531	+	0.954087i	$0.596830\pi$
$608$	0.980111	0.0397488
$609$	6.34805	0.257236
$610$	1.07784	0.0436404
$611$	−0.888957	−0.0359634
$612$	−2.76887	−0.111925
$613$	−38.8212	−1.56797	−0.783987	−	0.620777i	$-0.786817\pi$
$613$	−38.8212	−1.56797	−0.783987	+	0.620777i	$0.786817\pi$
$614$	13.9135	0.561502
$615$	1.21153	0.0488536
$616$	−3.89614	−0.156980
$617$	−24.0293	−0.967383	−0.483692	−	0.875239i	$-0.660704\pi$
$617$	−24.0293	−0.967383	−0.483692	+	0.875239i	$0.660704\pi$
$618$	−3.36738	−0.135456
$619$	−15.4934	−0.622732	−0.311366	−	0.950290i	$-0.600786\pi$
$619$	−15.4934	−0.622732	−0.311366	+	0.950290i	$0.600786\pi$
$620$	5.52406	0.221851
$621$	−13.7388	−0.551318
$622$	10.2283	0.410118
$623$	18.9195	0.757993
$624$	0.586522	0.0234797
$625$	1.00000	0.0400000
$626$	25.5366	1.02065
$627$	0.329307	0.0131512
$628$	4.23203	0.168876
$629$	11.0577	0.440898
$630$	−11.2486	−0.448154
$631$	−36.8713	−1.46782	−0.733912	−	0.679245i	$-0.762307\pi$
$631$	−36.8713	−1.46782	−0.733912	+	0.679245i	$0.762307\pi$
$632$	−1.12029	−0.0445629
$633$	−0.532252	−0.0211551
$634$	23.7939	0.944976
$635$	−1.38315	−0.0548887
$636$	−4.68353	−0.185714
$637$	14.2793	0.565765
$638$	−4.84932	−0.191986
$639$	4.38083	0.173303
$640$	−1.00000	−0.0395285
$641$	24.5577	0.969972	0.484986	−	0.874522i	$-0.338825\pi$
$641$	24.5577	0.969972	0.484986	+	0.874522i	$0.338825\pi$
$642$	−4.47492	−0.176611
$643$	−23.8649	−0.941139	−0.470570	−	0.882363i	$-0.655952\pi$
$643$	−23.8649	−0.941139	−0.470570	+	0.882363i	$0.655952\pi$
$644$	−27.0617	−1.06638
$645$	−3.48934	−0.137393
$646$	0.939969	0.0369826
$647$	41.6014	1.63552	0.817759	−	0.575561i	$-0.195216\pi$
$647$	41.6014	1.63552	0.817759	+	0.575561i	$0.195216\pi$
$648$	−7.99675	−0.314142
$649$	−8.18800	−0.321407
$650$	−1.74566	−0.0684703
$651$	−7.23132	−0.283418
$652$	7.63996	0.299204
$653$	−26.4275	−1.03419	−0.517094	−	0.855928i	$-0.672986\pi$
$653$	−26.4275	−1.03419	−0.517094	+	0.855928i	$0.672986\pi$
$654$	6.71808	0.262698
$655$	9.38664	0.366766
$656$	3.60586	0.140785
$657$	−2.88711	−0.112637
$658$	−1.98407	−0.0773469
$659$	4.57532	0.178229	0.0891145	−	0.996021i	$-0.471596\pi$
$659$	4.57532	0.178229	0.0891145	+	0.996021i	$0.471596\pi$
$660$	−0.335989	−0.0130784
$661$	−22.0588	−0.857988	−0.428994	−	0.903307i	$-0.641132\pi$
$661$	−22.0588	−0.857988	−0.428994	+	0.903307i	$0.641132\pi$
$662$	−16.7293	−0.650202
$663$	0.562500	0.0218457
$664$	−6.23489	−0.241961
$665$	3.81865	0.148081
$666$	33.2881	1.28989
$667$	−33.6822	−1.30418
$668$	−20.2510	−0.783535
$669$	−4.71743	−0.182386
$670$	5.45954	0.210920
$671$	1.07784	0.0416095
$672$	1.30906	0.0504981
$673$	8.74607	0.337136	0.168568	−	0.985690i	$-0.446086\pi$
$673$	8.74607	0.337136	0.168568	+	0.985690i	$0.446086\pi$
$674$	−2.49915	−0.0962638
$675$	−1.97801	−0.0761335
$676$	−9.95268	−0.382795
$677$	11.5994	0.445803	0.222901	−	0.974841i	$-0.428447\pi$
$677$	11.5994	0.445803	0.222901	+	0.974841i	$0.428447\pi$
$678$	−0.225634	−0.00866542
$679$	44.5989	1.71155
$680$	−0.959044	−0.0367776
$681$	−7.10089	−0.272107
$682$	5.52406	0.211527
$683$	46.2393	1.76930	0.884648	−	0.466259i	$-0.154399\pi$
$683$	46.2393	1.76930	0.884648	+	0.466259i	$0.154399\pi$
$684$	2.82969	0.108196
$685$	2.65020	0.101259
$686$	4.59697	0.175513
$687$	8.44405	0.322160
$688$	−10.3853	−0.395935
$689$	−24.3336	−0.927038
$690$	−2.33370	−0.0888426
$691$	−14.2148	−0.540757	−0.270378	−	0.962754i	$-0.587149\pi$
$691$	−14.2148	−0.540757	−0.270378	+	0.962754i	$0.587149\pi$
$692$	−8.08350	−0.307288
$693$	−11.2486	−0.427298
$694$	6.24909	0.237212
$695$	−0.560214	−0.0212501
$696$	1.62932	0.0617592
$697$	3.45818	0.130988
$698$	16.5092	0.624884
$699$	−6.03327	−0.228199
$700$	−3.89614	−0.147260
$701$	−14.2807	−0.539375	−0.269688	−	0.962948i	$-0.586920\pi$
$701$	−14.2807	−0.539375	−0.269688	+	0.962948i	$0.586920\pi$
$702$	3.45292	0.130322
$703$	−11.3006	−0.426209
$704$	−1.00000	−0.0376889
$705$	−0.171099	−0.00644395
$706$	17.3092	0.651442
$707$	−40.0660	−1.50684
$708$	2.75108	0.103392
$709$	−50.9992	−1.91531	−0.957657	−	0.287912i	$-0.907039\pi$
$709$	−50.9992	−1.91531	−0.957657	+	0.287912i	$0.907039\pi$
$710$	1.51738	0.0569461
$711$	−3.23441	−0.121300
$712$	4.85596	0.181985
$713$	38.3688	1.43692
$714$	1.25545	0.0469839
$715$	−1.74566	−0.0652839
$716$	−2.80638	−0.104879
$717$	−7.01956	−0.262150
$718$	−0.413339	−0.0154257
$719$	32.3171	1.20523	0.602613	−	0.798034i	$-0.294126\pi$
$719$	32.3171	1.20523	0.602613	+	0.798034i	$0.294126\pi$
$720$	−2.88711	−0.107596
$721$	−39.0483	−1.45423
$722$	18.0394	0.671356
$723$	6.47615	0.240850
$724$	−3.68996	−0.137136
$725$	−4.84932	−0.180099
$726$	−0.335989	−0.0124697
$727$	−3.72434	−0.138128	−0.0690640	−	0.997612i	$-0.522001\pi$
$727$	−3.72434	−0.138128	−0.0690640	+	0.997612i	$0.522001\pi$
$728$	6.80132	0.252074
$729$	−21.0937	−0.781249
$730$	−1.00000	−0.0370117
$731$	−9.95993	−0.368381
$732$	−0.362142	−0.0133851
$733$	20.6576	0.763006	0.381503	−	0.924368i	$-0.375407\pi$
$733$	20.6576	0.763006	0.381503	+	0.924368i	$0.375407\pi$
$734$	−5.33049	−0.196752
$735$	2.74835	0.101374
$736$	−6.94577	−0.256024
$737$	5.45954	0.201105
$738$	10.4105	0.383216
$739$	−5.69672	−0.209557	−0.104779	−	0.994496i	$-0.533413\pi$
$739$	−5.69672	−0.209557	−0.104779	+	0.994496i	$0.533413\pi$
$740$	11.5299	0.423847
$741$	−0.574857	−0.0211179
$742$	−54.3103	−1.99379
$743$	−16.2116	−0.594745	−0.297373	−	0.954762i	$-0.596110\pi$
$743$	−16.2116	−0.594745	−0.297373	+	0.954762i	$0.596110\pi$
$744$	−1.85602	−0.0680451
$745$	−17.5080	−0.641444
$746$	11.5391	0.422478
$747$	−18.0008	−0.658615
$748$	−0.959044	−0.0350661
$749$	−51.8913	−1.89607
$750$	−0.335989	−0.0122686
$751$	−49.5907	−1.80959	−0.904795	−	0.425847i	$-0.859976\pi$
$751$	−49.5907	−1.80959	−0.904795	+	0.425847i	$0.859976\pi$
$752$	−0.509239	−0.0185700
$753$	8.27434	0.301534
$754$	8.46525	0.308286
$755$	10.8173	0.393681
$756$	7.70658	0.280286
$757$	−38.7790	−1.40945	−0.704723	−	0.709483i	$-0.748929\pi$
$757$	−38.7790	−1.40945	−0.704723	+	0.709483i	$0.748929\pi$
$758$	4.75712	0.172787
$759$	−2.33370	−0.0847081
$760$	0.980111	0.0355524
$761$	12.9517	0.469500	0.234750	−	0.972056i	$-0.424573\pi$
$761$	12.9517	0.469500	0.234750	+	0.972056i	$0.424573\pi$
$762$	0.464724	0.0168352
$763$	77.9030	2.82028
$764$	−5.55551	−0.200991
$765$	−2.76887	−0.100109
$766$	−19.7687	−0.714274
$767$	14.2934	0.516106
$768$	0.335989	0.0121240
$769$	−39.3012	−1.41724	−0.708619	−	0.705591i	$-0.750681\pi$
$769$	−39.3012	−1.41724	−0.708619	+	0.705591i	$0.750681\pi$
$770$	−3.89614	−0.140407
$771$	−7.21668	−0.259902
$772$	−12.2871	−0.442221
$773$	18.9570	0.681836	0.340918	−	0.940093i	$-0.389262\pi$
$773$	18.9570	0.681836	0.340918	+	0.940093i	$0.389262\pi$
$774$	−29.9835	−1.07773
$775$	5.52406	0.198430
$776$	11.4470	0.410922
$777$	−15.0933	−0.541470
$778$	37.5199	1.34515
$779$	−3.53414	−0.126624
$780$	0.586522	0.0210009
$781$	1.51738	0.0542960
$782$	−6.66129	−0.238207
$783$	9.59198	0.342789
$784$	8.17988	0.292139
$785$	4.23203	0.151048
$786$	−3.15381	−0.112493
$787$	−44.6479	−1.59153	−0.795763	−	0.605608i	$-0.792930\pi$
$787$	−44.6479	−1.59153	−0.795763	+	0.605608i	$0.792930\pi$
$788$	−12.7441	−0.453990
$789$	−8.37432	−0.298134
$790$	−1.12029	−0.0398583
$791$	−2.61646	−0.0930305
$792$	−2.88711	−0.102589
$793$	−1.88154	−0.0668153
$794$	−0.136112	−0.00483044
$795$	−4.68353	−0.166108
$796$	−15.2138	−0.539240
$797$	28.5006	1.00954	0.504771	−	0.863253i	$-0.331577\pi$
$797$	28.5006	1.00954	0.504771	+	0.863253i	$0.331577\pi$
$798$	−1.28302	−0.0454186
$799$	−0.488382	−0.0172777
$800$	−1.00000	−0.0353553
$801$	14.0197	0.495361
$802$	−33.8959	−1.19690
$803$	−1.00000	−0.0352892
$804$	−1.83435	−0.0646924
$805$	−27.0617	−0.953798
$806$	−9.64311	−0.339664
$807$	2.86831	0.100969
$808$	−10.2835	−0.361773
$809$	29.8587	1.04978	0.524888	−	0.851171i	$-0.324107\pi$
$809$	29.8587	1.04978	0.524888	+	0.851171i	$0.324107\pi$
$810$	−7.99675	−0.280977
$811$	−42.0638	−1.47706	−0.738531	−	0.674220i	$-0.764480\pi$
$811$	−42.0638	−1.47706	−0.738531	+	0.674220i	$0.764480\pi$
$812$	18.8936	0.663036
$813$	−1.77497	−0.0622508
$814$	11.5299	0.404123
$815$	7.63996	0.267616
$816$	0.322228	0.0112802
$817$	10.1787	0.356109
$818$	−9.94131	−0.347590
$819$	19.6362	0.686143
$820$	3.60586	0.125922
$821$	46.0941	1.60870	0.804348	−	0.594159i	$-0.202515\pi$
$821$	46.0941	1.60870	0.804348	+	0.594159i	$0.202515\pi$
$822$	−0.890439	−0.0310576
$823$	5.14944	0.179498	0.0897490	−	0.995964i	$-0.471393\pi$
$823$	5.14944	0.179498	0.0897490	+	0.995964i	$0.471393\pi$
$824$	−10.0223	−0.349143
$825$	−0.335989	−0.0116976
$826$	31.9016	1.11000
$827$	22.8896	0.795950	0.397975	−	0.917396i	$-0.369713\pi$
$827$	22.8896	0.795950	0.397975	+	0.917396i	$0.369713\pi$
$828$	−20.0532	−0.696897
$829$	31.2814	1.08645	0.543224	−	0.839588i	$-0.317203\pi$
$829$	31.2814	1.08645	0.543224	+	0.839588i	$0.317203\pi$
$830$	−6.23489	−0.216416
$831$	6.38257	0.221409
$832$	1.74566	0.0605198
$833$	7.84486	0.271808
$834$	0.188226	0.00651773
$835$	−20.2510	−0.700815
$836$	0.980111	0.0338979
$837$	−10.9266	−0.377679
$838$	−7.90368	−0.273028
$839$	50.5127	1.74389	0.871947	−	0.489601i	$-0.162858\pi$
$839$	50.5127	1.74389	0.871947	+	0.489601i	$0.162858\pi$
$840$	1.30906	0.0451668
$841$	−5.48411	−0.189107
$842$	4.51286	0.155523
$843$	1.19710	0.0412302
$844$	−1.58414	−0.0545282
$845$	−9.95268	−0.342383
$846$	−1.47023	−0.0505475
$847$	−3.89614	−0.133873
$848$	−13.9395	−0.478685
$849$	−2.76041	−0.0947370
$850$	−0.959044	−0.0328949
$851$	80.0840	2.74524
$852$	−0.509822	−0.0174662
$853$	45.8129	1.56860	0.784302	−	0.620380i	$-0.213022\pi$
$853$	45.8129	1.56860	0.784302	+	0.620380i	$0.213022\pi$
$854$	−4.19940	−0.143701
$855$	2.82969	0.0967734
$856$	−13.3186	−0.455222
$857$	−42.1839	−1.44098	−0.720488	−	0.693467i	$-0.756082\pi$
$857$	−42.1839	−1.44098	−0.720488	+	0.693467i	$0.756082\pi$
$858$	0.586522	0.0200235
$859$	−20.1299	−0.686823	−0.343411	−	0.939185i	$-0.611583\pi$
$859$	−20.1299	−0.686823	−0.343411	+	0.939185i	$0.611583\pi$
$860$	−10.3853	−0.354135
$861$	−4.72028	−0.160867
$862$	29.7472	1.01319
$863$	7.46431	0.254088	0.127044	−	0.991897i	$-0.459451\pi$
$863$	7.46431	0.254088	0.127044	+	0.991897i	$0.459451\pi$
$864$	1.97801	0.0672931
$865$	−8.08350	−0.274847
$866$	2.96742	0.100837
$867$	−5.40278	−0.183488
$868$	−21.5225	−0.730521
$869$	−1.12029	−0.0380034
$870$	1.62932	0.0552391
$871$	−9.53049	−0.322928
$872$	19.9949	0.677114
$873$	33.0486	1.11853
$874$	6.80763	0.230271
$875$	−3.89614	−0.131713
$876$	0.335989	0.0113520
$877$	−21.1766	−0.715083	−0.357541	−	0.933897i	$-0.616385\pi$
$877$	−21.1766	−0.715083	−0.357541	+	0.933897i	$0.616385\pi$
$878$	−39.1993	−1.32291
$879$	−2.66066	−0.0897419
$880$	−1.00000	−0.0337100
$881$	−4.45792	−0.150191	−0.0750956	−	0.997176i	$-0.523926\pi$
$881$	−4.45792	−0.150191	−0.0750956	+	0.997176i	$0.523926\pi$
$882$	23.6162	0.795199
$883$	−41.2163	−1.38704	−0.693519	−	0.720439i	$-0.743940\pi$
$883$	−41.2163	−1.38704	−0.693519	+	0.720439i	$0.743940\pi$
$884$	1.67416	0.0563082
$885$	2.75108	0.0924765
$886$	39.3331	1.32142
$887$	−17.2112	−0.577895	−0.288948	−	0.957345i	$-0.593305\pi$
$887$	−17.2112	−0.577895	−0.288948	+	0.957345i	$0.593305\pi$
$888$	−3.87392	−0.130000
$889$	5.38895	0.180739
$890$	4.85596	0.162772
$891$	−7.99675	−0.267901
$892$	−14.0404	−0.470108
$893$	0.499111	0.0167021
$894$	5.88250	0.196740
$895$	−2.80638	−0.0938069
$896$	3.89614	0.130161
$897$	4.07385	0.136022
$898$	12.6810	0.423170
$899$	−26.7879	−0.893427
$900$	−2.88711	−0.0962370
$901$	−13.3686	−0.445373
$902$	3.60586	0.120062
$903$	13.5949	0.452412
$904$	−0.671551	−0.0223355
$905$	−3.68996	−0.122658
$906$	−3.63448	−0.120748
$907$	−12.6840	−0.421166	−0.210583	−	0.977576i	$-0.567536\pi$
$907$	−12.6840	−0.421166	−0.210583	+	0.977576i	$0.567536\pi$
$908$	−21.1343	−0.701366
$909$	−29.6897	−0.984744
$910$	6.80132	0.225462
$911$	32.7914	1.08643	0.543213	−	0.839595i	$-0.317207\pi$
$911$	32.7914	1.08643	0.543213	+	0.839595i	$0.317207\pi$
$912$	−0.329307	−0.0109044
$913$	−6.23489	−0.206345
$914$	−20.8924	−0.691058
$915$	−0.362142	−0.0119720
$916$	25.1319	0.830381
$917$	−36.5716	−1.20770
$918$	1.89699	0.0626101
$919$	−33.9905	−1.12124	−0.560622	−	0.828072i	$-0.689438\pi$
$919$	−33.9905	−1.12124	−0.560622	+	0.828072i	$0.689438\pi$
$920$	−6.94577	−0.228995
$921$	−4.67477	−0.154039
$922$	22.0708	0.726862
$923$	−2.64882	−0.0871869
$924$	1.30906	0.0430649
$925$	11.5299	0.379101
$926$	−6.80122	−0.223502
$927$	−28.9355	−0.950367
$928$	4.84932	0.159187
$929$	−29.3188	−0.961920	−0.480960	−	0.876743i	$-0.659712\pi$
$929$	−29.3188	−0.961920	−0.480960	+	0.876743i	$0.659712\pi$
$930$	−1.85602	−0.0608614
$931$	−8.01719	−0.262753
$932$	−17.9567	−0.588193
$933$	−3.43660	−0.112509
$934$	−12.2490	−0.400799
$935$	−0.959044	−0.0313641
$936$	5.03991	0.164735
$937$	15.8650	0.518286	0.259143	−	0.965839i	$-0.416560\pi$
$937$	15.8650	0.518286	0.259143	+	0.965839i	$0.416560\pi$
$938$	−21.2711	−0.694526
$939$	−8.58003	−0.279999
$940$	−0.509239	−0.0166095
$941$	10.0241	0.326776	0.163388	−	0.986562i	$-0.447758\pi$
$941$	10.0241	0.326776	0.163388	+	0.986562i	$0.447758\pi$
$942$	−1.42192	−0.0463286
$943$	25.0455	0.815592
$944$	8.18800	0.266497
$945$	7.70658	0.250695
$946$	−10.3853	−0.337655
$947$	47.0859	1.53009	0.765043	−	0.643980i	$-0.222718\pi$
$947$	47.0859	1.53009	0.765043	+	0.643980i	$0.222718\pi$
$948$	0.376407	0.0122251
$949$	1.74566	0.0566664
$950$	0.980111	0.0317990
$951$	−7.99449	−0.259239
$952$	3.73656	0.121103
$953$	−14.0595	−0.455431	−0.227715	−	0.973728i	$-0.573126\pi$
$953$	−14.0595	−0.455431	−0.227715	+	0.973728i	$0.573126\pi$
$954$	−40.2449	−1.30298
$955$	−5.55551	−0.179772
$956$	−20.8922	−0.675703
$957$	1.62932	0.0526684
$958$	−36.9045	−1.19233
$959$	−10.3255	−0.333429
$960$	0.335989	0.0108440
$961$	−0.484787	−0.0156383
$962$	−20.1273	−0.648929
$963$	−38.4524	−1.23911
$964$	19.2749	0.620802
$965$	−12.2871	−0.395535
$966$	9.09243	0.292544
$967$	10.8076	0.347550	0.173775	−	0.984785i	$-0.444404\pi$
$967$	10.8076	0.347550	0.173775	+	0.984785i	$0.444404\pi$
$968$	−1.00000	−0.0321412
$969$	−0.315820	−0.0101456
$970$	11.4470	0.367540
$971$	14.5698	0.467568	0.233784	−	0.972289i	$-0.424889\pi$
$971$	14.5698	0.467568	0.233784	+	0.972289i	$0.424889\pi$
$972$	8.62084	0.276513
$973$	2.18267	0.0699732
$974$	12.0601	0.386431
$975$	0.586522	0.0187837
$976$	−1.07784	−0.0345007
$977$	−47.0432	−1.50505	−0.752523	−	0.658566i	$-0.771163\pi$
$977$	−47.0432	−1.50505	−0.752523	+	0.658566i	$0.771163\pi$
$978$	−2.56694	−0.0820818
$979$	4.85596	0.155197
$980$	8.17988	0.261297
$981$	57.7276	1.84310
$982$	−36.0095	−1.14911
$983$	1.20702	0.0384979	0.0192489	−	0.999815i	$-0.493872\pi$
$983$	1.20702	0.0384979	0.0192489	+	0.999815i	$0.493872\pi$
$984$	−1.21153	−0.0386221
$985$	−12.7441	−0.406061
$986$	4.65071	0.148109
$987$	0.666624	0.0212189
$988$	−1.71094	−0.0544322
$989$	−72.1337	−2.29372
$990$	−2.88711	−0.0917584
$991$	30.5202	0.969505	0.484753	−	0.874651i	$-0.338910\pi$
$991$	30.5202	0.969505	0.484753	+	0.874651i	$0.338910\pi$
$992$	−5.52406	−0.175389
$993$	5.62086	0.178372
$994$	−5.91190	−0.187514
$995$	−15.2138	−0.482310
$996$	2.09485	0.0663780
$997$	33.1228	1.04901	0.524505	−	0.851407i	$-0.324250\pi$
$997$	33.1228	1.04901	0.524505	+	0.851407i	$0.324250\pi$
$998$	−16.2652	−0.514865
$999$	−22.8062	−0.721556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.z.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.z.1.4	✓	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.335989 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.335989 q^{6} -3.89614 q^{7} -1.00000 q^{8} -2.88711 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.335989 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.335989 q^{6} -3.89614 q^{7} -1.00000 q^{8} -2.88711 q^{9} -1.00000 q^{10} -1.00000 q^{11} +0.335989 q^{12} +1.74566 q^{13} +3.89614 q^{14} +0.335989 q^{15} +1.00000 q^{16} +0.959044 q^{17} +2.88711 q^{18} -0.980111 q^{19} +1.00000 q^{20} -1.30906 q^{21} +1.00000 q^{22} +6.94577 q^{23} -0.335989 q^{24} +1.00000 q^{25} -1.74566 q^{26} -1.97801 q^{27} -3.89614 q^{28} -4.84932 q^{29} -0.335989 q^{30} +5.52406 q^{31} -1.00000 q^{32} -0.335989 q^{33} -0.959044 q^{34} -3.89614 q^{35} -2.88711 q^{36} +11.5299 q^{37} +0.980111 q^{38} +0.586522 q^{39} -1.00000 q^{40} +3.60586 q^{41} +1.30906 q^{42} -10.3853 q^{43} -1.00000 q^{44} -2.88711 q^{45} -6.94577 q^{46} -0.509239 q^{47} +0.335989 q^{48} +8.17988 q^{49} -1.00000 q^{50} +0.322228 q^{51} +1.74566 q^{52} -13.9395 q^{53} +1.97801 q^{54} -1.00000 q^{55} +3.89614 q^{56} -0.329307 q^{57} +4.84932 q^{58} +8.18800 q^{59} +0.335989 q^{60} -1.07784 q^{61} -5.52406 q^{62} +11.2486 q^{63} +1.00000 q^{64} +1.74566 q^{65} +0.335989 q^{66} -5.45954 q^{67} +0.959044 q^{68} +2.33370 q^{69} +3.89614 q^{70} -1.51738 q^{71} +2.88711 q^{72} +1.00000 q^{73} -11.5299 q^{74} +0.335989 q^{75} -0.980111 q^{76} +3.89614 q^{77} -0.586522 q^{78} +1.12029 q^{79} +1.00000 q^{80} +7.99675 q^{81} -3.60586 q^{82} +6.23489 q^{83} -1.30906 q^{84} +0.959044 q^{85} +10.3853 q^{86} -1.62932 q^{87} +1.00000 q^{88} -4.85596 q^{89} +2.88711 q^{90} -6.80132 q^{91} +6.94577 q^{92} +1.85602 q^{93} +0.509239 q^{94} -0.980111 q^{95} -0.335989 q^{96} -11.4470 q^{97} -8.17988 q^{98} +2.88711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 2 q^{3} + 7 q^{4} + 7 q^{5} + 2 q^{6} - 3 q^{7} - 7 q^{8} + 5 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 2 * q^3 + 7 * q^4 + 7 * q^5 + 2 * q^6 - 3 * q^7 - 7 * q^8 + 5 * q^9	\( 7 q - 7 q^{2} - 2 q^{3} + 7 q^{4} + 7 q^{5} + 2 q^{6} - 3 q^{7} - 7 q^{8} + 5 q^{9} - 7 q^{10} - 7 q^{11} - 2 q^{12} - 3 q^{13} + 3 q^{14} - 2 q^{15} + 7 q^{16} - 11 q^{17} - 5 q^{18} - 8 q^{19} + 7 q^{20} - 3 q^{21} + 7 q^{22} + 8 q^{23} + 2 q^{24} + 7 q^{25} + 3 q^{26} - 11 q^{27} - 3 q^{28} - 9 q^{29} + 2 q^{30} - 9 q^{31} - 7 q^{32} + 2 q^{33} + 11 q^{34} - 3 q^{35} + 5 q^{36} + 21 q^{37} + 8 q^{38} + 39 q^{39} - 7 q^{40} - 10 q^{41} + 3 q^{42} - 5 q^{43} - 7 q^{44} + 5 q^{45} - 8 q^{46} + 19 q^{47} - 2 q^{48} - 14 q^{49} - 7 q^{50} + 37 q^{51} - 3 q^{52} - 13 q^{53} + 11 q^{54} - 7 q^{55} + 3 q^{56} - 13 q^{57} + 9 q^{58} + 5 q^{59} - 2 q^{60} - 12 q^{61} + 9 q^{62} - 12 q^{63} + 7 q^{64} - 3 q^{65} - 2 q^{66} - 23 q^{67} - 11 q^{68} - 24 q^{69} + 3 q^{70} + 22 q^{71} - 5 q^{72} + 7 q^{73} - 21 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} - 39 q^{78} - 32 q^{79} + 7 q^{80} + 27 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - 11 q^{85} + 5 q^{86} - 13 q^{87} + 7 q^{88} + 20 q^{89} - 5 q^{90} - 2 q^{91} + 8 q^{92} - 25 q^{93} - 19 q^{94} - 8 q^{95} + 2 q^{96} - 2 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 2 * q^3 + 7 * q^4 + 7 * q^5 + 2 * q^6 - 3 * q^7 - 7 * q^8 + 5 * q^9 - 7 * q^10 - 7 * q^11 - 2 * q^12 - 3 * q^13 + 3 * q^14 - 2 * q^15 + 7 * q^16 - 11 * q^17 - 5 * q^18 - 8 * q^19 + 7 * q^20 - 3 * q^21 + 7 * q^22 + 8 * q^23 + 2 * q^24 + 7 * q^25 + 3 * q^26 - 11 * q^27 - 3 * q^28 - 9 * q^29 + 2 * q^30 - 9 * q^31 - 7 * q^32 + 2 * q^33 + 11 * q^34 - 3 * q^35 + 5 * q^36 + 21 * q^37 + 8 * q^38 + 39 * q^39 - 7 * q^40 - 10 * q^41 + 3 * q^42 - 5 * q^43 - 7 * q^44 + 5 * q^45 - 8 * q^46 + 19 * q^47 - 2 * q^48 - 14 * q^49 - 7 * q^50 + 37 * q^51 - 3 * q^52 - 13 * q^53 + 11 * q^54 - 7 * q^55 + 3 * q^56 - 13 * q^57 + 9 * q^58 + 5 * q^59 - 2 * q^60 - 12 * q^61 + 9 * q^62 - 12 * q^63 + 7 * q^64 - 3 * q^65 - 2 * q^66 - 23 * q^67 - 11 * q^68 - 24 * q^69 + 3 * q^70 + 22 * q^71 - 5 * q^72 + 7 * q^73 - 21 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 - 39 * q^78 - 32 * q^79 + 7 * q^80 + 27 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - 11 * q^85 + 5 * q^86 - 13 * q^87 + 7 * q^88 + 20 * q^89 - 5 * q^90 - 2 * q^91 + 8 * q^92 - 25 * q^93 - 19 * q^94 - 8 * q^95 + 2 * q^96 - 2 * q^97 + 14 * q^98 - 5 * q^99

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