LMFDB - Embedded newform 7007.2.a.bi.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7007,2,Mod(1,7007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7007, 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("7007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7007 = 7^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7007.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:	$55.9511766963$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1001)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	7007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27102 q^{2} -0.785231 q^{3} +3.15753 q^{4} -4.14311 q^{5} +1.78328 q^{6} -2.62878 q^{8} -2.38341 q^{9} +O(q^{10})$	\(q-2.27102 q^{2} -0.785231 q^{3} +3.15753 q^{4} -4.14311 q^{5} +1.78328 q^{6} -2.62878 q^{8} -2.38341 q^{9} +9.40907 q^{10} +1.00000 q^{11} -2.47939 q^{12} +1.00000 q^{13} +3.25329 q^{15} -0.345059 q^{16} -6.36889 q^{17} +5.41278 q^{18} +3.29075 q^{19} -13.0820 q^{20} -2.27102 q^{22} -3.01769 q^{23} +2.06420 q^{24} +12.1653 q^{25} -2.27102 q^{26} +4.22722 q^{27} +8.47095 q^{29} -7.38830 q^{30} -1.95231 q^{31} +6.04119 q^{32} -0.785231 q^{33} +14.4639 q^{34} -7.52570 q^{36} +0.328351 q^{37} -7.47336 q^{38} -0.785231 q^{39} +10.8913 q^{40} -11.0106 q^{41} +1.32838 q^{43} +3.15753 q^{44} +9.87473 q^{45} +6.85323 q^{46} -6.69805 q^{47} +0.270951 q^{48} -27.6277 q^{50} +5.00105 q^{51} +3.15753 q^{52} -2.78282 q^{53} -9.60011 q^{54} -4.14311 q^{55} -2.58400 q^{57} -19.2377 q^{58} +5.58820 q^{59} +10.2724 q^{60} -3.90227 q^{61} +4.43374 q^{62} -13.0295 q^{64} -4.14311 q^{65} +1.78328 q^{66} +5.13761 q^{67} -20.1100 q^{68} +2.36958 q^{69} -10.0945 q^{71} +6.26546 q^{72} +2.40184 q^{73} -0.745692 q^{74} -9.55259 q^{75} +10.3906 q^{76} +1.78328 q^{78} -15.2363 q^{79} +1.42961 q^{80} +3.83089 q^{81} +25.0053 q^{82} +1.36569 q^{83} +26.3870 q^{85} -3.01677 q^{86} -6.65165 q^{87} -2.62878 q^{88} -9.64884 q^{89} -22.4257 q^{90} -9.52845 q^{92} +1.53302 q^{93} +15.2114 q^{94} -13.6339 q^{95} -4.74373 q^{96} +5.16276 q^{97} -2.38341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9	$ 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9} + 3 q^{10} + 25 q^{11} - 9 q^{12} + 25 q^{13} + 32 q^{16} + q^{17} + 44 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{22} + 15 q^{23} + 4 q^{24} + 50 q^{25} + 6 q^{26} + 17 q^{27} + 24 q^{29} + q^{30} + 12 q^{31} + 48 q^{32} + 2 q^{33} + 8 q^{34} + 30 q^{36} + 33 q^{37} - 16 q^{38} + 2 q^{39} + 21 q^{40} - 12 q^{41} + 38 q^{43} + 30 q^{44} + 22 q^{45} + 39 q^{46} - 4 q^{47} - 82 q^{48} + 16 q^{50} + 51 q^{51} + 30 q^{52} + 2 q^{53} - 10 q^{54} + q^{55} + 38 q^{57} + 17 q^{58} + 4 q^{59} - 33 q^{60} + 22 q^{61} - 42 q^{62} + 41 q^{64} + q^{65} - 2 q^{66} + 24 q^{67} - 14 q^{68} + 30 q^{69} + 9 q^{71} + 102 q^{72} - 11 q^{73} + 39 q^{74} + 16 q^{75} - 58 q^{76} - 2 q^{78} + 19 q^{79} + 33 q^{80} + 73 q^{81} + 32 q^{82} - 16 q^{83} + 14 q^{85} + 27 q^{86} + 11 q^{87} + 21 q^{88} - 13 q^{89} - 40 q^{90} + 17 q^{93} + 56 q^{94} + 15 q^{95} - 55 q^{96} - 34 q^{97} + 37 q^{99}+O(q^{100}) $ 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9 + 3 * q^10 + 25 * q^11 - 9 * q^12 + 25 * q^13 + 32 * q^16 + q^17 + 44 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^22 + 15 * q^23 + 4 * q^24 + 50 * q^25 + 6 * q^26 + 17 * q^27 + 24 * q^29 + q^30 + 12 * q^31 + 48 * q^32 + 2 * q^33 + 8 * q^34 + 30 * q^36 + 33 * q^37 - 16 * q^38 + 2 * q^39 + 21 * q^40 - 12 * q^41 + 38 * q^43 + 30 * q^44 + 22 * q^45 + 39 * q^46 - 4 * q^47 - 82 * q^48 + 16 * q^50 + 51 * q^51 + 30 * q^52 + 2 * q^53 - 10 * q^54 + q^55 + 38 * q^57 + 17 * q^58 + 4 * q^59 - 33 * q^60 + 22 * q^61 - 42 * q^62 + 41 * q^64 + q^65 - 2 * q^66 + 24 * q^67 - 14 * q^68 + 30 * q^69 + 9 * q^71 + 102 * q^72 - 11 * q^73 + 39 * q^74 + 16 * q^75 - 58 * q^76 - 2 * q^78 + 19 * q^79 + 33 * q^80 + 73 * q^81 + 32 * q^82 - 16 * q^83 + 14 * q^85 + 27 * q^86 + 11 * q^87 + 21 * q^88 - 13 * q^89 - 40 * q^90 + 17 * q^93 + 56 * q^94 + 15 * q^95 - 55 * q^96 - 34 * q^97 + 37 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.27102	−1.60585	−0.802927	−	0.596078i	$-0.796725\pi$
$2$	−2.27102	−1.60585	−0.802927	+	0.596078i	$0.796725\pi$
$3$	−0.785231	−0.453353	−0.226677	−	0.973970i	$-0.572786\pi$
$3$	−0.785231	−0.453353	−0.226677	+	0.973970i	$0.572786\pi$
$4$	3.15753	1.57877
$5$	−4.14311	−1.85285	−0.926427	−	0.376476i	$-0.877136\pi$
$5$	−4.14311	−1.85285	−0.926427	+	0.376476i	$0.877136\pi$
$6$	1.78328	0.728019
$7$	0	0
$7$	0	0
$8$	−2.62878	−0.929413
$9$	−2.38341	−0.794471
$10$	9.40907	2.97541
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.47939	−0.715739
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	3.25329	0.839997
$16$	−0.345059	−0.0862647
$17$	−6.36889	−1.54468	−0.772342	−	0.635207i	$-0.780915\pi$
$17$	−6.36889	−1.54468	−0.772342	+	0.635207i	$0.780915\pi$
$18$	5.41278	1.27580
$19$	3.29075	0.754950	0.377475	−	0.926020i	$-0.376792\pi$
$19$	3.29075	0.754950	0.377475	+	0.926020i	$0.376792\pi$
$20$	−13.0820	−2.92522
$21$	0	0
$22$	−2.27102	−0.484183
$23$	−3.01769	−0.629232	−0.314616	−	0.949219i	$-0.601876\pi$
$23$	−3.01769	−0.629232	−0.314616	+	0.949219i	$0.601876\pi$
$24$	2.06420	0.421352
$25$	12.1653	2.43306
$26$	−2.27102	−0.445384
$27$	4.22722	0.813529
$28$	0	0
$29$	8.47095	1.57302	0.786508	−	0.617580i	$-0.211887\pi$
$29$	8.47095	1.57302	0.786508	+	0.617580i	$0.211887\pi$
$30$	−7.38830	−1.34891
$31$	−1.95231	−0.350646	−0.175323	−	0.984511i	$-0.556097\pi$
$31$	−1.95231	−0.350646	−0.175323	+	0.984511i	$0.556097\pi$
$32$	6.04119	1.06794
$33$	−0.785231	−0.136691
$34$	14.4639	2.48054
$35$	0	0
$36$	−7.52570	−1.25428
$37$	0.328351	0.0539806	0.0269903	−	0.999636i	$-0.491408\pi$
$37$	0.328351	0.0539806	0.0269903	+	0.999636i	$0.491408\pi$
$38$	−7.47336	−1.21234
$39$	−0.785231	−0.125738
$40$	10.8913	1.72207
$41$	−11.0106	−1.71957	−0.859783	−	0.510660i	$-0.829401\pi$
$41$	−11.0106	−1.71957	−0.859783	+	0.510660i	$0.829401\pi$
$42$	0	0
$43$	1.32838	0.202576	0.101288	−	0.994857i	$-0.467704\pi$
$43$	1.32838	0.202576	0.101288	+	0.994857i	$0.467704\pi$
$44$	3.15753	0.476016
$45$	9.87473	1.47204
$46$	6.85323	1.01045
$47$	−6.69805	−0.977011	−0.488505	−	0.872561i	$-0.662458\pi$
$47$	−6.69805	−0.977011	−0.488505	+	0.872561i	$0.662458\pi$
$48$	0.270951	0.0391084
$49$	0	0
$50$	−27.6277	−3.90715
$51$	5.00105	0.700288
$52$	3.15753	0.437871
$53$	−2.78282	−0.382250	−0.191125	−	0.981566i	$-0.561214\pi$
$53$	−2.78282	−0.382250	−0.191125	+	0.981566i	$0.561214\pi$
$54$	−9.60011	−1.30641
$55$	−4.14311	−0.558656
$56$	0	0
$57$	−2.58400	−0.342259
$58$	−19.2377	−2.52603
$59$	5.58820	0.727522	0.363761	−	0.931492i	$-0.381493\pi$
$59$	5.58820	0.727522	0.363761	+	0.931492i	$0.381493\pi$
$60$	10.2724	1.32616
$61$	−3.90227	−0.499635	−0.249817	−	0.968293i	$-0.580371\pi$
$61$	−3.90227	−0.499635	−0.249817	+	0.968293i	$0.580371\pi$
$62$	4.43374	0.563086
$63$	0	0
$64$	−13.0295	−1.62869
$65$	−4.14311	−0.513889
$66$	1.78328	0.219506
$67$	5.13761	0.627659	0.313829	−	0.949479i	$-0.398388\pi$
$67$	5.13761	0.627659	0.313829	+	0.949479i	$0.398388\pi$
$68$	−20.1100	−2.43869
$69$	2.36958	0.285264
$70$	0	0
$71$	−10.0945	−1.19800	−0.599000	−	0.800749i	$-0.704435\pi$
$71$	−10.0945	−1.19800	−0.599000	+	0.800749i	$0.704435\pi$
$72$	6.26546	0.738391
$73$	2.40184	0.281115	0.140557	−	0.990073i	$-0.455111\pi$
$73$	2.40184	0.281115	0.140557	+	0.990073i	$0.455111\pi$
$74$	−0.745692	−0.0866850
$75$	−9.55259	−1.10304
$76$	10.3906	1.19189
$77$	0	0
$78$	1.78328	0.201916
$79$	−15.2363	−1.71422	−0.857110	−	0.515133i	$-0.827743\pi$
$79$	−15.2363	−1.71422	−0.857110	+	0.515133i	$0.827743\pi$
$80$	1.42961	0.159836
$81$	3.83089	0.425655
$82$	25.0053	2.76137
$83$	1.36569	0.149904	0.0749522	−	0.997187i	$-0.476120\pi$
$83$	1.36569	0.149904	0.0749522	+	0.997187i	$0.476120\pi$
$84$	0	0
$85$	26.3870	2.86207
$86$	−3.01677	−0.325307
$87$	−6.65165	−0.713132
$88$	−2.62878	−0.280229
$89$	−9.64884	−1.02277	−0.511387	−	0.859350i	$-0.670868\pi$
$89$	−9.64884	−1.02277	−0.511387	+	0.859350i	$0.670868\pi$
$90$	−22.4257	−2.36388
$91$	0	0
$92$	−9.52845	−0.993410
$93$	1.53302	0.158966
$94$	15.2114	1.56894
$95$	−13.6339	−1.39881
$96$	−4.74373	−0.484155
$97$	5.16276	0.524199	0.262100	−	0.965041i	$-0.415585\pi$
$97$	5.16276	0.524199	0.262100	+	0.965041i	$0.415585\pi$
$98$	0	0
$99$	−2.38341	−0.239542
$100$	38.4124	3.84124
$101$	−9.96653	−0.991707	−0.495853	−	0.868406i	$-0.665145\pi$
$101$	−9.96653	−0.991707	−0.495853	+	0.868406i	$0.665145\pi$
$102$	−11.3575	−1.12456
$103$	19.2903	1.90073	0.950365	−	0.311137i	$-0.100710\pi$
$103$	19.2903	1.90073	0.950365	+	0.311137i	$0.100710\pi$
$104$	−2.62878	−0.257773
$105$	0	0
$106$	6.31985	0.613838
$107$	19.9923	1.93273	0.966363	−	0.257181i	$-0.0827938\pi$
$107$	19.9923	1.93273	0.966363	+	0.257181i	$0.0827938\pi$
$108$	13.3476	1.28437
$109$	−16.6573	−1.59548	−0.797741	−	0.603000i	$-0.793972\pi$
$109$	−16.6573	−1.59548	−0.797741	+	0.603000i	$0.793972\pi$
$110$	9.40907	0.897120
$111$	−0.257832	−0.0244723
$112$	0	0
$113$	3.05610	0.287494	0.143747	−	0.989614i	$-0.454085\pi$
$113$	3.05610	0.287494	0.143747	+	0.989614i	$0.454085\pi$
$114$	5.86831	0.549618
$115$	12.5026	1.16587
$116$	26.7473	2.48342
$117$	−2.38341	−0.220347
$118$	−12.6909	−1.16829
$119$	0	0
$120$	−8.55218	−0.780704
$121$	1.00000	0.0909091
$122$	8.86213	0.802340
$123$	8.64586	0.779571
$124$	−6.16449	−0.553588
$125$	−29.6867	−2.65526
$126$	0	0
$127$	−16.3053	−1.44686	−0.723430	−	0.690398i	$-0.757435\pi$
$127$	−16.3053	−1.44686	−0.723430	+	0.690398i	$0.757435\pi$
$128$	17.5080	1.54750
$129$	−1.04308	−0.0918384
$130$	9.40907	0.825230
$131$	−12.5622	−1.09757	−0.548784	−	0.835964i	$-0.684909\pi$
$131$	−12.5622	−1.09757	−0.548784	+	0.835964i	$0.684909\pi$
$132$	−2.47939	−0.215803
$133$	0	0
$134$	−11.6676	−1.00793
$135$	−17.5138	−1.50735
$136$	16.7424	1.43565
$137$	−21.5293	−1.83938	−0.919688	−	0.392650i	$-0.871558\pi$
$137$	−21.5293	−1.83938	−0.919688	+	0.392650i	$0.871558\pi$
$138$	−5.38137	−0.458093
$139$	−6.38590	−0.541645	−0.270822	−	0.962629i	$-0.587296\pi$
$139$	−6.38590	−0.541645	−0.270822	+	0.962629i	$0.587296\pi$
$140$	0	0
$141$	5.25951	0.442931
$142$	22.9249	1.92381
$143$	1.00000	0.0836242
$144$	0.822417	0.0685348
$145$	−35.0960	−2.91457
$146$	−5.45463	−0.451429
$147$	0	0
$148$	1.03678	0.0852227
$149$	15.9538	1.30699	0.653494	−	0.756931i	$-0.273302\pi$
$149$	15.9538	1.30699	0.653494	+	0.756931i	$0.273302\pi$
$150$	21.6941	1.77132
$151$	−11.7052	−0.952556	−0.476278	−	0.879295i	$-0.658014\pi$
$151$	−11.7052	−0.952556	−0.476278	+	0.879295i	$0.658014\pi$
$152$	−8.65064	−0.701660
$153$	15.1797	1.22721
$154$	0	0
$155$	8.08864	0.649695
$156$	−2.47939	−0.198510
$157$	−22.0791	−1.76210	−0.881050	−	0.473023i	$-0.843163\pi$
$157$	−22.0791	−1.76210	−0.881050	+	0.473023i	$0.843163\pi$
$158$	34.6020	2.75279
$159$	2.18516	0.173294
$160$	−25.0293	−1.97874
$161$	0	0
$162$	−8.70003	−0.683539
$163$	6.72039	0.526382	0.263191	−	0.964744i	$-0.415225\pi$
$163$	6.72039	0.526382	0.263191	+	0.964744i	$0.415225\pi$
$164$	−34.7663	−2.71479
$165$	3.25329	0.253269
$166$	−3.10152	−0.240725
$167$	−22.4309	−1.73575	−0.867877	−	0.496779i	$-0.834516\pi$
$167$	−22.4309	−1.73575	−0.867877	+	0.496779i	$0.834516\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−59.9254	−4.59607
$171$	−7.84321	−0.599785
$172$	4.19439	0.319820
$173$	2.06502	0.157000	0.0785002	−	0.996914i	$-0.474987\pi$
$173$	2.06502	0.157000	0.0785002	+	0.996914i	$0.474987\pi$
$174$	15.1060	1.14519
$175$	0	0
$176$	−0.345059	−0.0260098
$177$	−4.38803	−0.329824
$178$	21.9127	1.64243
$179$	13.0264	0.973640	0.486820	−	0.873502i	$-0.338157\pi$
$179$	13.0264	0.973640	0.486820	+	0.873502i	$0.338157\pi$
$180$	31.1798	2.32400
$181$	−3.22566	−0.239761	−0.119881	−	0.992788i	$-0.538251\pi$
$181$	−3.22566	−0.239761	−0.119881	+	0.992788i	$0.538251\pi$
$182$	0	0
$183$	3.06418	0.226511
$184$	7.93283	0.584816
$185$	−1.36039	−0.100018
$186$	−3.48151	−0.255277
$187$	−6.36889	−0.465740
$188$	−21.1493	−1.54247
$189$	0	0
$190$	30.9629	2.24629
$191$	−12.5460	−0.907798	−0.453899	−	0.891053i	$-0.649967\pi$
$191$	−12.5460	−0.907798	−0.453899	+	0.891053i	$0.649967\pi$
$192$	10.2312	0.738373
$193$	−8.50030	−0.611865	−0.305933	−	0.952053i	$-0.598968\pi$
$193$	−8.50030	−0.611865	−0.305933	+	0.952053i	$0.598968\pi$
$194$	−11.7247	−0.841787
$195$	3.25329	0.232973
$196$	0	0
$197$	2.65637	0.189258	0.0946292	−	0.995513i	$-0.469833\pi$
$197$	2.65637	0.189258	0.0946292	+	0.995513i	$0.469833\pi$
$198$	5.41278	0.384669
$199$	−2.74763	−0.194774	−0.0973871	−	0.995247i	$-0.531048\pi$
$199$	−2.74763	−0.194774	−0.0973871	+	0.995247i	$0.531048\pi$
$200$	−31.9799	−2.26132
$201$	−4.03421	−0.284551
$202$	22.6342	1.59254
$203$	0	0
$204$	15.7910	1.10559
$205$	45.6180	3.18610
$206$	−43.8087	−3.05229
$207$	7.19240	0.499906
$208$	−0.345059	−0.0239255
$209$	3.29075	0.227626
$210$	0	0
$211$	18.2572	1.25687	0.628437	−	0.777860i	$-0.283695\pi$
$211$	18.2572	1.25687	0.628437	+	0.777860i	$0.283695\pi$
$212$	−8.78686	−0.603484
$213$	7.92654	0.543117
$214$	−45.4029	−3.10368
$215$	−5.50361	−0.375343
$216$	−11.1124	−0.756105
$217$	0	0
$218$	37.8291	2.56211
$219$	−1.88600	−0.127444
$220$	−13.0820	−0.881987
$221$	−6.36889	−0.428418
$222$	0.585541	0.0392989
$223$	0.927758	0.0621273	0.0310636	−	0.999517i	$-0.490111\pi$
$223$	0.927758	0.0621273	0.0310636	+	0.999517i	$0.490111\pi$
$224$	0	0
$225$	−28.9950	−1.93300
$226$	−6.94047	−0.461673
$227$	1.03342	0.0685902	0.0342951	−	0.999412i	$-0.489081\pi$
$227$	1.03342	0.0685902	0.0342951	+	0.999412i	$0.489081\pi$
$228$	−8.15906	−0.540347
$229$	11.3832	0.752220	0.376110	−	0.926575i	$-0.377261\pi$
$229$	11.3832	0.752220	0.376110	+	0.926575i	$0.377261\pi$
$230$	−28.3937	−1.87222
$231$	0	0
$232$	−22.2682	−1.46198
$233$	8.72299	0.571462	0.285731	−	0.958310i	$-0.407764\pi$
$233$	8.72299	0.571462	0.285731	+	0.958310i	$0.407764\pi$
$234$	5.41278	0.353844
$235$	27.7507	1.81026
$236$	17.6449	1.14859
$237$	11.9640	0.777148
$238$	0	0
$239$	−4.80249	−0.310647	−0.155324	−	0.987864i	$-0.549642\pi$
$239$	−4.80249	−0.310647	−0.155324	+	0.987864i	$0.549642\pi$
$240$	−1.12258	−0.0724621
$241$	−27.1135	−1.74654	−0.873268	−	0.487241i	$-0.838003\pi$
$241$	−27.1135	−1.74654	−0.873268	+	0.487241i	$0.838003\pi$
$242$	−2.27102	−0.145987
$243$	−15.6898	−1.00650
$244$	−12.3215	−0.788806
$245$	0	0
$246$	−19.6349	−1.25188
$247$	3.29075	0.209385
$248$	5.13220	0.325895
$249$	−1.07239	−0.0679597
$250$	67.4191	4.26396
$251$	−1.50176	−0.0947903	−0.0473952	−	0.998876i	$-0.515092\pi$
$251$	−1.50176	−0.0947903	−0.0473952	+	0.998876i	$0.515092\pi$
$252$	0	0
$253$	−3.01769	−0.189721
$254$	37.0296	2.32344
$255$	−20.7199	−1.29753
$256$	−13.7019	−0.856367
$257$	−23.2981	−1.45330	−0.726649	−	0.687009i	$-0.758923\pi$
$257$	−23.2981	−1.45330	−0.726649	+	0.687009i	$0.758923\pi$
$258$	2.36886	0.147479
$259$	0	0
$260$	−13.0820	−0.811310
$261$	−20.1898	−1.24972
$262$	28.5291	1.76253
$263$	−15.2366	−0.939529	−0.469765	−	0.882792i	$-0.655661\pi$
$263$	−15.2366	−0.939529	−0.469765	+	0.882792i	$0.655661\pi$
$264$	2.06420	0.127043
$265$	11.5295	0.708254
$266$	0	0
$267$	7.57657	0.463678
$268$	16.2222	0.990926
$269$	18.1824	1.10860	0.554300	−	0.832317i	$-0.312986\pi$
$269$	18.1824	1.10860	0.554300	+	0.832317i	$0.312986\pi$
$270$	39.7742	2.42058
$271$	−6.90045	−0.419173	−0.209586	−	0.977790i	$-0.567212\pi$
$271$	−6.90045	−0.419173	−0.209586	+	0.977790i	$0.567212\pi$
$272$	2.19764	0.133252
$273$	0	0
$274$	48.8936	2.95377
$275$	12.1653	0.733597
$276$	7.48204	0.450366
$277$	1.05126	0.0631642	0.0315821	−	0.999501i	$-0.489945\pi$
$277$	1.05126	0.0631642	0.0315821	+	0.999501i	$0.489945\pi$
$278$	14.5025	0.869802
$279$	4.65317	0.278578
$280$	0	0
$281$	−5.74650	−0.342807	−0.171404	−	0.985201i	$-0.554830\pi$
$281$	−5.74650	−0.342807	−0.171404	+	0.985201i	$0.554830\pi$
$282$	−11.9445	−0.711282
$283$	2.10650	0.125218	0.0626091	−	0.998038i	$-0.480058\pi$
$283$	2.10650	0.125218	0.0626091	+	0.998038i	$0.480058\pi$
$284$	−31.8738	−1.89136
$285$	10.7058	0.634156
$286$	−2.27102	−0.134288
$287$	0	0
$288$	−14.3986	−0.848448
$289$	23.5628	1.38605
$290$	79.7038	4.68037
$291$	−4.05396	−0.237648
$292$	7.58390	0.443814
$293$	−9.10953	−0.532184	−0.266092	−	0.963948i	$-0.585733\pi$
$293$	−9.10953	−0.532184	−0.266092	+	0.963948i	$0.585733\pi$
$294$	0	0
$295$	−23.1525	−1.34799
$296$	−0.863162	−0.0501703
$297$	4.22722	0.245288
$298$	−36.2315	−2.09883
$299$	−3.01769	−0.174518
$300$	−30.1626	−1.74144
$301$	0	0
$302$	26.5827	1.52967
$303$	7.82603	0.449593
$304$	−1.13550	−0.0651255
$305$	16.1675	0.925749
$306$	−34.4734	−1.97071
$307$	12.1378	0.692743	0.346371	−	0.938097i	$-0.387414\pi$
$307$	12.1378	0.692743	0.346371	+	0.938097i	$0.387414\pi$
$308$	0	0
$309$	−15.1473	−0.861702
$310$	−18.3695	−1.04332
$311$	13.8753	0.786798	0.393399	−	0.919368i	$-0.371299\pi$
$311$	13.8753	0.786798	0.393399	+	0.919368i	$0.371299\pi$
$312$	2.06420	0.116862
$313$	−9.56489	−0.540639	−0.270320	−	0.962771i	$-0.587129\pi$
$313$	−9.56489	−0.540639	−0.270320	+	0.962771i	$0.587129\pi$
$314$	50.1420	2.82967
$315$	0	0
$316$	−48.1092	−2.70635
$317$	−4.36060	−0.244916	−0.122458	−	0.992474i	$-0.539078\pi$
$317$	−4.36060	−0.244916	−0.122458	+	0.992474i	$0.539078\pi$
$318$	−4.96254	−0.278286
$319$	8.47095	0.474282
$320$	53.9828	3.01773
$321$	−15.6986	−0.876208
$322$	0	0
$323$	−20.9584	−1.16616
$324$	12.0962	0.672009
$325$	12.1653	0.674811
$326$	−15.2621	−0.845292
$327$	13.0798	0.723317
$328$	28.9444	1.59819
$329$	0	0
$330$	−7.38830	−0.406712
$331$	−7.52977	−0.413874	−0.206937	−	0.978354i	$-0.566349\pi$
$331$	−7.52977	−0.413874	−0.206937	+	0.978354i	$0.566349\pi$
$332$	4.31222	0.236664
$333$	−0.782596	−0.0428860
$334$	50.9410	2.78737
$335$	−21.2857	−1.16296
$336$	0	0
$337$	29.7772	1.62207	0.811035	−	0.584998i	$-0.198905\pi$
$337$	29.7772	1.62207	0.811035	+	0.584998i	$0.198905\pi$
$338$	−2.27102	−0.123527
$339$	−2.39975	−0.130336
$340$	83.3178	4.51854
$341$	−1.95231	−0.105724
$342$	17.8121	0.963168
$343$	0	0
$344$	−3.49201	−0.188276
$345$	−9.81744	−0.528553
$346$	−4.68970	−0.252120
$347$	−12.7628	−0.685143	−0.342571	−	0.939492i	$-0.611298\pi$
$347$	−12.7628	−0.685143	−0.342571	+	0.939492i	$0.611298\pi$
$348$	−21.0028	−1.12587
$349$	−31.2207	−1.67121	−0.835603	−	0.549334i	$-0.814881\pi$
$349$	−31.2207	−1.67121	−0.835603	+	0.549334i	$0.814881\pi$
$350$	0	0
$351$	4.22722	0.225632
$352$	6.04119	0.321996
$353$	0.434758	0.0231399	0.0115699	−	0.999933i	$-0.496317\pi$
$353$	0.434758	0.0231399	0.0115699	+	0.999933i	$0.496317\pi$
$354$	9.96530	0.529650
$355$	41.8227	2.21972
$356$	−30.4665	−1.61472
$357$	0	0
$358$	−29.5833	−1.56352
$359$	−0.396911	−0.0209481	−0.0104741	−	0.999945i	$-0.503334\pi$
$359$	−0.396911	−0.0209481	−0.0104741	+	0.999945i	$0.503334\pi$
$360$	−25.9585	−1.36813
$361$	−8.17097	−0.430051
$362$	7.32553	0.385021
$363$	−0.785231	−0.0412139
$364$	0	0
$365$	−9.95109	−0.520864
$366$	−6.95882	−0.363743
$367$	19.5273	1.01932	0.509659	−	0.860376i	$-0.329771\pi$
$367$	19.5273	1.01932	0.509659	+	0.860376i	$0.329771\pi$
$368$	1.04128	0.0542805
$369$	26.2428	1.36614
$370$	3.08948	0.160615
$371$	0	0
$372$	4.84055	0.250971
$373$	−9.80962	−0.507923	−0.253962	−	0.967214i	$-0.581734\pi$
$373$	−9.80962	−0.507923	−0.253962	+	0.967214i	$0.581734\pi$
$374$	14.4639	0.747910
$375$	23.3109	1.20377
$376$	17.6077	0.908046
$377$	8.47095	0.436276
$378$	0	0
$379$	−0.468658	−0.0240733	−0.0120367	−	0.999928i	$-0.503831\pi$
$379$	−0.468658	−0.0240733	−0.0120367	+	0.999928i	$0.503831\pi$
$380$	−43.0495	−2.20839
$381$	12.8034	0.655938
$382$	28.4923	1.45779
$383$	9.21230	0.470726	0.235363	−	0.971907i	$-0.424372\pi$
$383$	9.21230	0.470726	0.235363	+	0.971907i	$0.424372\pi$
$384$	−13.7478	−0.701565
$385$	0	0
$386$	19.3044	0.982566
$387$	−3.16607	−0.160940
$388$	16.3016	0.827588
$389$	−16.8146	−0.852534	−0.426267	−	0.904597i	$-0.640172\pi$
$389$	−16.8146	−0.852534	−0.426267	+	0.904597i	$0.640172\pi$
$390$	−7.38830	−0.374121
$391$	19.2194	0.971964
$392$	0	0
$393$	9.86426	0.497586
$394$	−6.03267	−0.303921
$395$	63.1257	3.17620
$396$	−7.52570	−0.378181
$397$	−13.6024	−0.682684	−0.341342	−	0.939939i	$-0.610881\pi$
$397$	−13.6024	−0.682684	−0.341342	+	0.939939i	$0.610881\pi$
$398$	6.23992	0.312779
$399$	0	0
$400$	−4.19775	−0.209888
$401$	−32.2334	−1.60966	−0.804829	−	0.593506i	$-0.797743\pi$
$401$	−32.2334	−1.60966	−0.804829	+	0.593506i	$0.797743\pi$
$402$	9.16177	0.456948
$403$	−1.95231	−0.0972517
$404$	−31.4696	−1.56567
$405$	−15.8718	−0.788675
$406$	0	0
$407$	0.328351	0.0162758
$408$	−13.1467	−0.650856
$409$	−17.4929	−0.864968	−0.432484	−	0.901642i	$-0.642363\pi$
$409$	−17.4929	−0.864968	−0.432484	+	0.901642i	$0.642363\pi$
$410$	−103.599	−5.11641
$411$	16.9055	0.833887
$412$	60.9097	3.00081
$413$	0	0
$414$	−16.3341	−0.802776
$415$	−5.65822	−0.277751
$416$	6.04119	0.296194
$417$	5.01440	0.245556
$418$	−7.47336	−0.365534
$419$	−9.24569	−0.451682	−0.225841	−	0.974164i	$-0.572513\pi$
$419$	−9.24569	−0.451682	−0.225841	+	0.974164i	$0.572513\pi$
$420$	0	0
$421$	10.1709	0.495702	0.247851	−	0.968798i	$-0.420276\pi$
$421$	10.1709	0.495702	0.247851	+	0.968798i	$0.420276\pi$
$422$	−41.4624	−2.01836
$423$	15.9642	0.776206
$424$	7.31542	0.355268
$425$	−77.4797	−3.75832
$426$	−18.0013	−0.872167
$427$	0	0
$428$	63.1262	3.05132
$429$	−0.785231	−0.0379113
$430$	12.4988	0.602746
$431$	29.9704	1.44362	0.721812	−	0.692089i	$-0.243309\pi$
$431$	29.9704	1.44362	0.721812	+	0.692089i	$0.243309\pi$
$432$	−1.45864	−0.0701788
$433$	15.7476	0.756781	0.378391	−	0.925646i	$-0.376478\pi$
$433$	15.7476	0.756781	0.378391	+	0.925646i	$0.376478\pi$
$434$	0	0
$435$	27.5585	1.32133
$436$	−52.5960	−2.51889
$437$	−9.93046	−0.475038
$438$	4.28315	0.204657
$439$	7.20298	0.343779	0.171890	−	0.985116i	$-0.445013\pi$
$439$	7.20298	0.343779	0.171890	+	0.985116i	$0.445013\pi$
$440$	10.8913	0.519222
$441$	0	0
$442$	14.4639	0.687977
$443$	27.2182	1.29317	0.646587	−	0.762840i	$-0.276196\pi$
$443$	27.2182	1.29317	0.646587	+	0.762840i	$0.276196\pi$
$444$	−0.814111	−0.0386360
$445$	39.9761	1.89505
$446$	−2.10696	−0.0997673
$447$	−12.5274	−0.592528
$448$	0	0
$449$	−7.02644	−0.331598	−0.165799	−	0.986160i	$-0.553020\pi$
$449$	−7.02644	−0.331598	−0.165799	+	0.986160i	$0.553020\pi$
$450$	65.8482	3.10411
$451$	−11.0106	−0.518469
$452$	9.64974	0.453886
$453$	9.19129	0.431844
$454$	−2.34691	−0.110146
$455$	0	0
$456$	6.79275	0.318100
$457$	18.1827	0.850552	0.425276	−	0.905064i	$-0.360177\pi$
$457$	18.1827	0.850552	0.425276	+	0.905064i	$0.360177\pi$
$458$	−25.8514	−1.20796
$459$	−26.9227	−1.25665
$460$	39.4774	1.84064
$461$	−1.31125	−0.0610710	−0.0305355	−	0.999534i	$-0.509721\pi$
$461$	−1.31125	−0.0610710	−0.0305355	+	0.999534i	$0.509721\pi$
$462$	0	0
$463$	−0.677978	−0.0315083	−0.0157542	−	0.999876i	$-0.505015\pi$
$463$	−0.677978	−0.0315083	−0.0157542	+	0.999876i	$0.505015\pi$
$464$	−2.92298	−0.135696
$465$	−6.35145	−0.294542
$466$	−19.8101	−0.917684
$467$	14.5521	0.673391	0.336695	−	0.941614i	$-0.390691\pi$
$467$	14.5521	0.673391	0.336695	+	0.941614i	$0.390691\pi$
$468$	−7.52570	−0.347876
$469$	0	0
$470$	−63.0224	−2.90701
$471$	17.3372	0.798854
$472$	−14.6901	−0.676168
$473$	1.32838	0.0610789
$474$	−27.1706	−1.24799
$475$	40.0330	1.83684
$476$	0	0
$477$	6.63262	0.303687
$478$	10.9066	0.498854
$479$	−15.1697	−0.693120	−0.346560	−	0.938028i	$-0.612650\pi$
$479$	−15.1697	−0.693120	−0.346560	+	0.938028i	$0.612650\pi$
$480$	19.6538	0.897068
$481$	0.328351	0.0149715
$482$	61.5753	2.80468
$483$	0	0
$484$	3.15753	0.143524
$485$	−21.3899	−0.971264
$486$	35.6318	1.61629
$487$	25.8358	1.17073	0.585366	−	0.810769i	$-0.300951\pi$
$487$	25.8358	1.17073	0.585366	+	0.810769i	$0.300951\pi$
$488$	10.2582	0.464367
$489$	−5.27706	−0.238637
$490$	0	0
$491$	−9.45648	−0.426765	−0.213383	−	0.976969i	$-0.568448\pi$
$491$	−9.45648	−0.426765	−0.213383	+	0.976969i	$0.568448\pi$
$492$	27.2996	1.23076
$493$	−53.9506	−2.42981
$494$	−7.47336	−0.336242
$495$	9.87473	0.443836
$496$	0.673663	0.0302484
$497$	0	0
$498$	2.43541	0.109133
$499$	34.0681	1.52510	0.762549	−	0.646930i	$-0.223947\pi$
$499$	34.0681	1.52510	0.762549	+	0.646930i	$0.223947\pi$
$500$	−93.7366	−4.19203
$501$	17.6134	0.786910
$502$	3.41053	0.152219
$503$	38.5584	1.71923	0.859617	−	0.510938i	$-0.170702\pi$
$503$	38.5584	1.71923	0.859617	+	0.510938i	$0.170702\pi$
$504$	0	0
$505$	41.2924	1.83749
$506$	6.85323	0.304663
$507$	−0.785231	−0.0348733
$508$	−51.4844	−2.28425
$509$	−23.6778	−1.04950	−0.524749	−	0.851257i	$-0.675841\pi$
$509$	−23.6778	−1.04950	−0.524749	+	0.851257i	$0.675841\pi$
$510$	47.0553	2.08364
$511$	0	0
$512$	−3.89873	−0.172301
$513$	13.9107	0.614174
$514$	52.9106	2.33378
$515$	−79.9218	−3.52177
$516$	−3.29357	−0.144991
$517$	−6.69805	−0.294580
$518$	0	0
$519$	−1.62152	−0.0711767
$520$	10.8913	0.477615
$521$	7.16583	0.313941	0.156970	−	0.987603i	$-0.449827\pi$
$521$	7.16583	0.313941	0.156970	+	0.987603i	$0.449827\pi$
$522$	45.8514	2.00686
$523$	3.30652	0.144584	0.0722919	−	0.997384i	$-0.476969\pi$
$523$	3.30652	0.144584	0.0722919	+	0.997384i	$0.476969\pi$
$524$	−39.6657	−1.73280
$525$	0	0
$526$	34.6026	1.50875
$527$	12.4341	0.541637
$528$	0.270951	0.0117916
$529$	−13.8935	−0.604067
$530$	−26.1838	−1.13735
$531$	−13.3190	−0.577995
$532$	0	0
$533$	−11.0106	−0.476922
$534$	−17.2065	−0.744599
$535$	−82.8301	−3.58106
$536$	−13.5056	−0.583354
$537$	−10.2287	−0.441403
$538$	−41.2926	−1.78025
$539$	0	0
$540$	−55.3005	−2.37975
$541$	2.57121	0.110545	0.0552726	−	0.998471i	$-0.482397\pi$
$541$	2.57121	0.110545	0.0552726	+	0.998471i	$0.482397\pi$
$542$	15.6711	0.673130
$543$	2.53289	0.108697
$544$	−38.4757	−1.64963
$545$	69.0131	2.95619
$546$	0	0
$547$	11.5061	0.491964	0.245982	−	0.969274i	$-0.420890\pi$
$547$	11.5061	0.491964	0.245982	+	0.969274i	$0.420890\pi$
$548$	−67.9796	−2.90394
$549$	9.30072	0.396945
$550$	−27.6277	−1.17805
$551$	27.8758	1.18755
$552$	−6.22911	−0.265128
$553$	0	0
$554$	−2.38744	−0.101432
$555$	1.06822	0.0453436
$556$	−20.1637	−0.855130
$557$	8.83171	0.374212	0.187106	−	0.982340i	$-0.440089\pi$
$557$	8.83171	0.374212	0.187106	+	0.982340i	$0.440089\pi$
$558$	−10.5674	−0.447355
$559$	1.32838	0.0561844
$560$	0	0
$561$	5.00105	0.211145
$562$	13.0504	0.550498
$563$	7.56693	0.318908	0.159454	−	0.987205i	$-0.449027\pi$
$563$	7.56693	0.318908	0.159454	+	0.987205i	$0.449027\pi$
$564$	16.6071	0.699284
$565$	−12.6618	−0.532684
$566$	−4.78390	−0.201082
$567$	0	0
$568$	26.5363	1.11344
$569$	16.4980	0.691632	0.345816	−	0.938302i	$-0.387602\pi$
$569$	16.4980	0.691632	0.345816	+	0.938302i	$0.387602\pi$
$570$	−24.3130	−1.01836
$571$	16.2789	0.681251	0.340625	−	0.940199i	$-0.389361\pi$
$571$	16.2789	0.681251	0.340625	+	0.940199i	$0.389361\pi$
$572$	3.15753	0.132023
$573$	9.85153	0.411553
$574$	0	0
$575$	−36.7112	−1.53096
$576$	31.0548	1.29395
$577$	−28.5007	−1.18650	−0.593250	−	0.805019i	$-0.702155\pi$
$577$	−28.5007	−1.18650	−0.593250	+	0.805019i	$0.702155\pi$
$578$	−53.5116	−2.22579
$579$	6.67470	0.277391
$580$	−110.817	−4.60142
$581$	0	0
$582$	9.20663	0.381627
$583$	−2.78282	−0.115253
$584$	−6.31391	−0.261271
$585$	9.87473	0.408270
$586$	20.6879	0.854610
$587$	−24.0629	−0.993182	−0.496591	−	0.867985i	$-0.665415\pi$
$587$	−24.0629	−0.993182	−0.496591	+	0.867985i	$0.665415\pi$
$588$	0	0
$589$	−6.42458	−0.264720
$590$	52.5798	2.16468
$591$	−2.08586	−0.0858009
$592$	−0.113300	−0.00465662
$593$	−17.2471	−0.708255	−0.354128	−	0.935197i	$-0.615222\pi$
$593$	−17.2471	−0.708255	−0.354128	+	0.935197i	$0.615222\pi$
$594$	−9.60011	−0.393897
$595$	0	0
$596$	50.3747	2.06343
$597$	2.15752	0.0883015
$598$	6.85323	0.280250
$599$	23.8411	0.974122	0.487061	−	0.873368i	$-0.338069\pi$
$599$	23.8411	0.974122	0.487061	+	0.873368i	$0.338069\pi$
$600$	25.1116	1.02518
$601$	32.5888	1.32932	0.664662	−	0.747145i	$-0.268576\pi$
$601$	32.5888	1.32932	0.664662	+	0.747145i	$0.268576\pi$
$602$	0	0
$603$	−12.2450	−0.498657
$604$	−36.9595	−1.50386
$605$	−4.14311	−0.168441
$606$	−17.7731	−0.721981
$607$	−10.3806	−0.421336	−0.210668	−	0.977558i	$-0.567564\pi$
$607$	−10.3806	−0.421336	−0.210668	+	0.977558i	$0.567564\pi$
$608$	19.8800	0.806242
$609$	0	0
$610$	−36.7168	−1.48662
$611$	−6.69805	−0.270974
$612$	47.9304	1.93747
$613$	−11.1406	−0.449965	−0.224982	−	0.974363i	$-0.572232\pi$
$613$	−11.1406	−0.449965	−0.224982	+	0.974363i	$0.572232\pi$
$614$	−27.5653	−1.11244
$615$	−35.8207	−1.44443
$616$	0	0
$617$	−13.4213	−0.540322	−0.270161	−	0.962815i	$-0.587077\pi$
$617$	−13.4213	−0.540322	−0.270161	+	0.962815i	$0.587077\pi$
$618$	34.3999	1.38377
$619$	−5.84025	−0.234740	−0.117370	−	0.993088i	$-0.537446\pi$
$619$	−5.84025	−0.234740	−0.117370	+	0.993088i	$0.537446\pi$
$620$	25.5401	1.02572
$621$	−12.7564	−0.511899
$622$	−31.5111	−1.26348
$623$	0	0
$624$	0.270951	0.0108467
$625$	62.1685	2.48674
$626$	21.7221	0.868188
$627$	−2.58400	−0.103195
$628$	−69.7153	−2.78194
$629$	−2.09123	−0.0833830
$630$	0	0
$631$	16.6168	0.661505	0.330753	−	0.943717i	$-0.392697\pi$
$631$	16.6168	0.661505	0.330753	+	0.943717i	$0.392697\pi$
$632$	40.0529	1.59322
$633$	−14.3361	−0.569808
$634$	9.90301	0.393299
$635$	67.5545	2.68082
$636$	6.89971	0.273591
$637$	0	0
$638$	−19.2377	−0.761628
$639$	24.0594	0.951776
$640$	−72.5374	−2.86729
$641$	−15.2008	−0.600397	−0.300199	−	0.953877i	$-0.597053\pi$
$641$	−15.2008	−0.600397	−0.300199	+	0.953877i	$0.597053\pi$
$642$	35.6517	1.40706
$643$	−35.7016	−1.40794	−0.703968	−	0.710232i	$-0.748590\pi$
$643$	−35.7016	−1.40794	−0.703968	+	0.710232i	$0.748590\pi$
$644$	0	0
$645$	4.32160	0.170163
$646$	47.5970	1.87268
$647$	27.9914	1.10046	0.550229	−	0.835014i	$-0.314541\pi$
$647$	27.9914	1.10046	0.550229	+	0.835014i	$0.314541\pi$
$648$	−10.0706	−0.395609
$649$	5.58820	0.219356
$650$	−27.6277	−1.08365
$651$	0	0
$652$	21.2199	0.831034
$653$	23.5595	0.921955	0.460978	−	0.887412i	$-0.347499\pi$
$653$	23.5595	0.921955	0.460978	+	0.887412i	$0.347499\pi$
$654$	−29.7046	−1.16154
$655$	52.0467	2.03363
$656$	3.79930	0.148338
$657$	−5.72458	−0.223337
$658$	0	0
$659$	39.9052	1.55449	0.777243	−	0.629201i	$-0.216618\pi$
$659$	39.9052	1.55449	0.777243	+	0.629201i	$0.216618\pi$
$660$	10.2724	0.399852
$661$	46.6727	1.81536	0.907679	−	0.419666i	$-0.137853\pi$
$661$	46.6727	1.81536	0.907679	+	0.419666i	$0.137853\pi$
$662$	17.1003	0.664621
$663$	5.00105	0.194225
$664$	−3.59011	−0.139323
$665$	0	0
$666$	1.77729	0.0688687
$667$	−25.5627	−0.989792
$668$	−70.8262	−2.74035
$669$	−0.728504	−0.0281656
$670$	48.3402	1.86754
$671$	−3.90227	−0.150645
$672$	0	0
$673$	−31.3871	−1.20988	−0.604942	−	0.796269i	$-0.706804\pi$
$673$	−31.3871	−1.20988	−0.604942	+	0.796269i	$0.706804\pi$
$674$	−67.6247	−2.60481
$675$	51.4255	1.97937
$676$	3.15753	0.121444
$677$	41.2230	1.58433	0.792164	−	0.610309i	$-0.208955\pi$
$677$	41.2230	1.58433	0.792164	+	0.610309i	$0.208955\pi$
$678$	5.44987	0.209301
$679$	0	0
$680$	−69.3655	−2.66005
$681$	−0.811470	−0.0310956
$682$	4.43374	0.169777
$683$	34.2894	1.31205	0.656024	−	0.754740i	$-0.272237\pi$
$683$	34.2894	1.31205	0.656024	+	0.754740i	$0.272237\pi$
$684$	−24.7652	−0.946921
$685$	89.1983	3.40809
$686$	0	0
$687$	−8.93841	−0.341022
$688$	−0.458368	−0.0174751
$689$	−2.78282	−0.106017
$690$	22.2956	0.848779
$691$	5.88929	0.224039	0.112020	−	0.993706i	$-0.464268\pi$
$691$	5.88929	0.224039	0.112020	+	0.993706i	$0.464268\pi$
$692$	6.52036	0.247867
$693$	0	0
$694$	28.9846	1.10024
$695$	26.4574	1.00359
$696$	17.4857	0.662794
$697$	70.1253	2.65619
$698$	70.9028	2.68371
$699$	−6.84956	−0.259074
$700$	0	0
$701$	−18.0148	−0.680408	−0.340204	−	0.940352i	$-0.610496\pi$
$701$	−18.0148	−0.680408	−0.340204	+	0.940352i	$0.610496\pi$
$702$	−9.60011	−0.362333
$703$	1.08052	0.0407527
$704$	−13.0295	−0.491069
$705$	−21.7907	−0.820686
$706$	−0.987345	−0.0371592
$707$	0	0
$708$	−13.8553	−0.520715
$709$	−25.2594	−0.948636	−0.474318	−	0.880354i	$-0.657305\pi$
$709$	−25.2594	−0.948636	−0.474318	+	0.880354i	$0.657305\pi$
$710$	−94.9802	−3.56454
$711$	36.3144	1.36190
$712$	25.3646	0.950580
$713$	5.89148	0.220638
$714$	0	0
$715$	−4.14311	−0.154943
$716$	41.1313	1.53715
$717$	3.77106	0.140833
$718$	0.901392	0.0336397
$719$	13.6261	0.508169	0.254084	−	0.967182i	$-0.418226\pi$
$719$	13.6261	0.508169	0.254084	+	0.967182i	$0.418226\pi$
$720$	−3.40736	−0.126985
$721$	0	0
$722$	18.5564	0.690599
$723$	21.2904	0.791797
$724$	−10.1851	−0.378527
$725$	103.052	3.82725
$726$	1.78328	0.0661835
$727$	−19.5005	−0.723233	−0.361617	−	0.932327i	$-0.617775\pi$
$727$	−19.5005	−0.723233	−0.361617	+	0.932327i	$0.617775\pi$
$728$	0	0
$729$	0.827444	0.0306461
$730$	22.5991	0.836431
$731$	−8.46030	−0.312915
$732$	9.67526	0.357608
$733$	34.8795	1.28830	0.644152	−	0.764897i	$-0.277210\pi$
$733$	34.8795	1.28830	0.644152	+	0.764897i	$0.277210\pi$
$734$	−44.3470	−1.63688
$735$	0	0
$736$	−18.2304	−0.671983
$737$	5.13761	0.189246
$738$	−59.5979	−2.19383
$739$	−18.2008	−0.669527	−0.334764	−	0.942302i	$-0.608656\pi$
$739$	−18.2008	−0.669527	−0.334764	+	0.942302i	$0.608656\pi$
$740$	−4.29549	−0.157905
$741$	−2.58400	−0.0949256
$742$	0	0
$743$	40.1960	1.47465	0.737325	−	0.675538i	$-0.236089\pi$
$743$	40.1960	1.47465	0.737325	+	0.675538i	$0.236089\pi$
$744$	−4.02996	−0.147745
$745$	−66.0984	−2.42166
$746$	22.2779	0.815650
$747$	−3.25501	−0.119095
$748$	−20.1100	−0.735294
$749$	0	0
$750$	−52.9395	−1.93308
$751$	1.88782	0.0688875	0.0344438	−	0.999407i	$-0.489034\pi$
$751$	1.88782	0.0688875	0.0344438	+	0.999407i	$0.489034\pi$
$752$	2.31122	0.0842815
$753$	1.17923	0.0429735
$754$	−19.2377	−0.700596
$755$	48.4959	1.76495
$756$	0	0
$757$	−6.01988	−0.218796	−0.109398	−	0.993998i	$-0.534892\pi$
$757$	−6.01988	−0.218796	−0.109398	+	0.993998i	$0.534892\pi$
$758$	1.06433	0.0386583
$759$	2.36958	0.0860104
$760$	35.8405	1.30007
$761$	−40.6555	−1.47376	−0.736880	−	0.676024i	$-0.763702\pi$
$761$	−40.6555	−1.47376	−0.736880	+	0.676024i	$0.763702\pi$
$762$	−29.0768	−1.05334
$763$	0	0
$764$	−39.6145	−1.43320
$765$	−62.8911	−2.27383
$766$	−20.9213	−0.755918
$767$	5.58820	0.201778
$768$	10.7591	0.388237
$769$	−6.78124	−0.244538	−0.122269	−	0.992497i	$-0.539017\pi$
$769$	−6.78124	−0.244538	−0.122269	+	0.992497i	$0.539017\pi$
$770$	0	0
$771$	18.2944	0.658858
$772$	−26.8400	−0.965992
$773$	−8.27605	−0.297669	−0.148834	−	0.988862i	$-0.547552\pi$
$773$	−8.27605	−0.297669	−0.148834	+	0.988862i	$0.547552\pi$
$774$	7.19021	0.258447
$775$	−23.7505	−0.853144
$776$	−13.5718	−0.487198
$777$	0	0
$778$	38.1863	1.36905
$779$	−36.2331	−1.29819
$780$	10.2724	0.367810
$781$	−10.0945	−0.361211
$782$	−43.6475	−1.56083
$783$	35.8086	1.27969
$784$	0	0
$785$	91.4758	3.26491
$786$	−22.4019	−0.799050
$787$	−22.9253	−0.817198	−0.408599	−	0.912714i	$-0.633983\pi$
$787$	−22.9253	−0.817198	−0.408599	+	0.912714i	$0.633983\pi$
$788$	8.38757	0.298795
$789$	11.9643	0.425939
$790$	−143.360	−5.10051
$791$	0	0
$792$	6.26546	0.222633
$793$	−3.90227	−0.138574
$794$	30.8913	1.09629
$795$	−9.05335	−0.321089
$796$	−8.67572	−0.307503
$797$	14.7394	0.522095	0.261047	−	0.965326i	$-0.415932\pi$
$797$	14.7394	0.522095	0.261047	+	0.965326i	$0.415932\pi$
$798$	0	0
$799$	42.6592	1.50917
$800$	73.4930	2.59837
$801$	22.9972	0.812565
$802$	73.2027	2.58488
$803$	2.40184	0.0847592
$804$	−12.7381	−0.449240
$805$	0	0
$806$	4.43374	0.156172
$807$	−14.2774	−0.502587
$808$	26.1998	0.921705
$809$	−3.29817	−0.115958	−0.0579788	−	0.998318i	$-0.518466\pi$
$809$	−3.29817	−0.115958	−0.0579788	+	0.998318i	$0.518466\pi$
$810$	36.0451	1.26650
$811$	30.5929	1.07426	0.537131	−	0.843499i	$-0.319508\pi$
$811$	30.5929	1.07426	0.537131	+	0.843499i	$0.319508\pi$
$812$	0	0
$813$	5.41845	0.190033
$814$	−0.745692	−0.0261365
$815$	−27.8433	−0.975308
$816$	−1.72566	−0.0604101
$817$	4.37136	0.152934
$818$	39.7267	1.38901
$819$	0	0
$820$	144.040	5.03011
$821$	−41.1615	−1.43655	−0.718273	−	0.695762i	$-0.755067\pi$
$821$	−41.1615	−1.43655	−0.718273	+	0.695762i	$0.755067\pi$
$822$	−38.3927	−1.33910
$823$	22.0044	0.767026	0.383513	−	0.923536i	$-0.374714\pi$
$823$	22.0044	0.767026	0.383513	+	0.923536i	$0.374714\pi$
$824$	−50.7099	−1.76656
$825$	−9.55259	−0.332578
$826$	0	0
$827$	27.9838	0.973094	0.486547	−	0.873654i	$-0.338256\pi$
$827$	27.9838	0.973094	0.486547	+	0.873654i	$0.338256\pi$
$828$	22.7102	0.789235
$829$	36.2369	1.25856	0.629280	−	0.777179i	$-0.283350\pi$
$829$	36.2369	1.25856	0.629280	+	0.777179i	$0.283350\pi$
$830$	12.8499	0.446027
$831$	−0.825484	−0.0286357
$832$	−13.0295	−0.451718
$833$	0	0
$834$	−11.3878	−0.394328
$835$	92.9335	3.21610
$836$	10.3906	0.359368
$837$	−8.25286	−0.285261
$838$	20.9972	0.725335
$839$	20.6379	0.712499	0.356249	−	0.934391i	$-0.384055\pi$
$839$	20.6379	0.712499	0.356249	+	0.934391i	$0.384055\pi$
$840$	0	0
$841$	42.7570	1.47438
$842$	−23.0984	−0.796024
$843$	4.51233	0.155413
$844$	57.6476	1.98431
$845$	−4.14311	−0.142527
$846$	−36.2550	−1.24647
$847$	0	0
$848$	0.960238	0.0329747
$849$	−1.65409	−0.0567681
$850$	175.958	6.03530
$851$	−0.990862	−0.0339663
$852$	25.0283	0.857455
$853$	11.0598	0.378681	0.189341	−	0.981911i	$-0.439365\pi$
$853$	11.0598	0.378681	0.189341	+	0.981911i	$0.439365\pi$
$854$	0	0
$855$	32.4953	1.11131
$856$	−52.5552	−1.79630
$857$	31.7650	1.08507	0.542535	−	0.840033i	$-0.317464\pi$
$857$	31.7650	1.08507	0.542535	+	0.840033i	$0.317464\pi$
$858$	1.78328	0.0608800
$859$	−33.3096	−1.13651	−0.568254	−	0.822853i	$-0.692381\pi$
$859$	−33.3096	−1.13651	−0.568254	+	0.822853i	$0.692381\pi$
$860$	−17.3778	−0.592579
$861$	0	0
$862$	−68.0634	−2.31825
$863$	−11.4232	−0.388852	−0.194426	−	0.980917i	$-0.562284\pi$
$863$	−11.4232	−0.388852	−0.194426	+	0.980917i	$0.562284\pi$
$864$	25.5374	0.868802
$865$	−8.55559	−0.290899
$866$	−35.7631	−1.21528
$867$	−18.5023	−0.628370
$868$	0	0
$869$	−15.2363	−0.516857
$870$	−62.5859	−2.12186
$871$	5.13761	0.174081
$872$	43.7884	1.48286
$873$	−12.3050	−0.416461
$874$	22.5523	0.762842
$875$	0	0
$876$	−5.95511	−0.201205
$877$	52.5822	1.77557	0.887787	−	0.460255i	$-0.152242\pi$
$877$	52.5822	1.77557	0.887787	+	0.460255i	$0.152242\pi$
$878$	−16.3581	−0.552059
$879$	7.15308	0.241268
$880$	1.42961	0.0481923
$881$	8.38259	0.282417	0.141208	−	0.989980i	$-0.454901\pi$
$881$	8.38259	0.282417	0.141208	+	0.989980i	$0.454901\pi$
$882$	0	0
$883$	41.4771	1.39582	0.697908	−	0.716187i	$-0.254114\pi$
$883$	41.4771	1.39582	0.697908	+	0.716187i	$0.254114\pi$
$884$	−20.1100	−0.676372
$885$	18.1801	0.611116
$886$	−61.8130	−2.07665
$887$	51.5029	1.72930	0.864649	−	0.502377i	$-0.167541\pi$
$887$	51.5029	1.72930	0.864649	+	0.502377i	$0.167541\pi$
$888$	0.677782	0.0227449
$889$	0	0
$890$	−90.7866	−3.04317
$891$	3.83089	0.128340
$892$	2.92942	0.0980844
$893$	−22.0416	−0.737594
$894$	28.4501	0.951513
$895$	−53.9698	−1.80401
$896$	0	0
$897$	2.36958	0.0791181
$898$	15.9572	0.532498
$899$	−16.5380	−0.551572
$900$	−91.5526	−3.05175
$901$	17.7235	0.590456
$902$	25.0053	0.832585
$903$	0	0
$904$	−8.03381	−0.267201
$905$	13.3642	0.444242
$906$	−20.8736	−0.693479
$907$	−34.0327	−1.13004	−0.565018	−	0.825078i	$-0.691131\pi$
$907$	−34.0327	−1.13004	−0.565018	+	0.825078i	$0.691131\pi$
$908$	3.26304	0.108288
$909$	23.7543	0.787882
$910$	0	0
$911$	46.5665	1.54282	0.771408	−	0.636340i	$-0.219553\pi$
$911$	46.5665	1.54282	0.771408	+	0.636340i	$0.219553\pi$
$912$	0.891631	0.0295249
$913$	1.36569	0.0451979
$914$	−41.2933	−1.36586
$915$	−12.6952	−0.419692
$916$	35.9427	1.18758
$917$	0	0
$918$	61.1421	2.01799
$919$	4.42153	0.145853	0.0729265	−	0.997337i	$-0.476766\pi$
$919$	4.42153	0.145853	0.0729265	+	0.997337i	$0.476766\pi$
$920$	−32.8666	−1.08358
$921$	−9.53100	−0.314057
$922$	2.97788	0.0980712
$923$	−10.0945	−0.332265
$924$	0	0
$925$	3.99450	0.131338
$926$	1.53970	0.0505977
$927$	−45.9768	−1.51007
$928$	51.1746	1.67989
$929$	−5.48564	−0.179978	−0.0899890	−	0.995943i	$-0.528683\pi$
$929$	−5.48564	−0.179978	−0.0899890	+	0.995943i	$0.528683\pi$
$930$	14.4243	0.472991
$931$	0	0
$932$	27.5431	0.902204
$933$	−10.8953	−0.356697
$934$	−33.0481	−1.08137
$935$	26.3870	0.862947
$936$	6.26546	0.204793
$937$	40.2838	1.31601	0.658007	−	0.753011i	$-0.271400\pi$
$937$	40.2838	1.31601	0.658007	+	0.753011i	$0.271400\pi$
$938$	0	0
$939$	7.51065	0.245101
$940$	87.6238	2.85797
$941$	2.09074	0.0681561	0.0340781	−	0.999419i	$-0.489151\pi$
$941$	2.09074	0.0681561	0.0340781	+	0.999419i	$0.489151\pi$
$942$	−39.3730	−1.28284
$943$	33.2266	1.08201
$944$	−1.92826	−0.0627594
$945$	0	0
$946$	−3.01677	−0.0980837
$947$	−21.6344	−0.703022	−0.351511	−	0.936184i	$-0.614332\pi$
$947$	−21.6344	−0.703022	−0.351511	+	0.936184i	$0.614332\pi$
$948$	37.7768	1.22693
$949$	2.40184	0.0779671
$950$	−90.9158	−2.94970
$951$	3.42408	0.111033
$952$	0	0
$953$	7.63969	0.247474	0.123737	−	0.992315i	$-0.460512\pi$
$953$	7.63969	0.247474	0.123737	+	0.992315i	$0.460512\pi$
$954$	−15.0628	−0.487676
$955$	51.9795	1.68202
$956$	−15.1640	−0.490439
$957$	−6.65165	−0.215017
$958$	34.4506	1.11305
$959$	0	0
$960$	−42.3889	−1.36810
$961$	−27.1885	−0.877047
$962$	−0.745692	−0.0240421
$963$	−47.6498	−1.53549
$964$	−85.6118	−2.75737
$965$	35.2176	1.13370
$966$	0	0
$967$	−1.54205	−0.0495891	−0.0247945	−	0.999693i	$-0.507893\pi$
$967$	−1.54205	−0.0495891	−0.0247945	+	0.999693i	$0.507893\pi$
$968$	−2.62878	−0.0844921
$969$	16.4572	0.528682
$970$	48.5768	1.55971
$971$	39.8392	1.27850	0.639251	−	0.768998i	$-0.279244\pi$
$971$	39.8392	1.27850	0.639251	+	0.768998i	$0.279244\pi$
$972$	−49.5410	−1.58903
$973$	0	0
$974$	−58.6736	−1.88002
$975$	−9.55259	−0.305928
$976$	1.34651	0.0431008
$977$	2.40462	0.0769306	0.0384653	−	0.999260i	$-0.487753\pi$
$977$	2.40462	0.0769306	0.0384653	+	0.999260i	$0.487753\pi$
$978$	11.9843	0.383216
$979$	−9.64884	−0.308378
$980$	0	0
$981$	39.7013	1.26756
$982$	21.4759	0.685322
$983$	−42.5104	−1.35587	−0.677935	−	0.735122i	$-0.737125\pi$
$983$	−42.5104	−1.35587	−0.677935	+	0.735122i	$0.737125\pi$
$984$	−22.7280	−0.724543
$985$	−11.0056	−0.350668
$986$	122.523	3.90192
$987$	0	0
$988$	10.3906	0.330570
$989$	−4.00863	−0.127467
$990$	−22.4257	−0.712736
$991$	−40.1276	−1.27470	−0.637348	−	0.770576i	$-0.719968\pi$
$991$	−40.1276	−1.27470	−0.637348	+	0.770576i	$0.719968\pi$
$992$	−11.7943	−0.374469
$993$	5.91261	0.187631
$994$	0	0
$995$	11.3837	0.360888
$996$	−3.38609	−0.107292
$997$	48.6376	1.54037	0.770184	−	0.637821i	$-0.220164\pi$
$997$	48.6376	1.54037	0.770184	+	0.637821i	$0.220164\pi$
$998$	−77.3694	−2.44909
$999$	1.38801	0.0439148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7007.2.a.bi.1.2		25
7.3	odd	6		1001.2.i.d.716.24	yes	50
7.5	odd	6		1001.2.i.d.144.24	✓	50
7.6	odd	2		7007.2.a.bh.1.2		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.24	✓	50	7.5	odd	6
1001.2.i.d.716.24	yes	50	7.3	odd	6
7007.2.a.bh.1.2		25	7.6	odd	2
7007.2.a.bi.1.2		25	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:	\( N \)	\(=\)	\( 7007 = 7^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27102 q^{2} -0.785231 q^{3} +3.15753 q^{4} -4.14311 q^{5} +1.78328 q^{6} -2.62878 q^{8} -2.38341 q^{9} +O(q^{10})\)	\(q-2.27102 q^{2} -0.785231 q^{3} +3.15753 q^{4} -4.14311 q^{5} +1.78328 q^{6} -2.62878 q^{8} -2.38341 q^{9} +9.40907 q^{10} +1.00000 q^{11} -2.47939 q^{12} +1.00000 q^{13} +3.25329 q^{15} -0.345059 q^{16} -6.36889 q^{17} +5.41278 q^{18} +3.29075 q^{19} -13.0820 q^{20} -2.27102 q^{22} -3.01769 q^{23} +2.06420 q^{24} +12.1653 q^{25} -2.27102 q^{26} +4.22722 q^{27} +8.47095 q^{29} -7.38830 q^{30} -1.95231 q^{31} +6.04119 q^{32} -0.785231 q^{33} +14.4639 q^{34} -7.52570 q^{36} +0.328351 q^{37} -7.47336 q^{38} -0.785231 q^{39} +10.8913 q^{40} -11.0106 q^{41} +1.32838 q^{43} +3.15753 q^{44} +9.87473 q^{45} +6.85323 q^{46} -6.69805 q^{47} +0.270951 q^{48} -27.6277 q^{50} +5.00105 q^{51} +3.15753 q^{52} -2.78282 q^{53} -9.60011 q^{54} -4.14311 q^{55} -2.58400 q^{57} -19.2377 q^{58} +5.58820 q^{59} +10.2724 q^{60} -3.90227 q^{61} +4.43374 q^{62} -13.0295 q^{64} -4.14311 q^{65} +1.78328 q^{66} +5.13761 q^{67} -20.1100 q^{68} +2.36958 q^{69} -10.0945 q^{71} +6.26546 q^{72} +2.40184 q^{73} -0.745692 q^{74} -9.55259 q^{75} +10.3906 q^{76} +1.78328 q^{78} -15.2363 q^{79} +1.42961 q^{80} +3.83089 q^{81} +25.0053 q^{82} +1.36569 q^{83} +26.3870 q^{85} -3.01677 q^{86} -6.65165 q^{87} -2.62878 q^{88} -9.64884 q^{89} -22.4257 q^{90} -9.52845 q^{92} +1.53302 q^{93} +15.2114 q^{94} -13.6339 q^{95} -4.74373 q^{96} +5.16276 q^{97} -2.38341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9	\( 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9} + 3 q^{10} + 25 q^{11} - 9 q^{12} + 25 q^{13} + 32 q^{16} + q^{17} + 44 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{22} + 15 q^{23} + 4 q^{24} + 50 q^{25} + 6 q^{26} + 17 q^{27} + 24 q^{29} + q^{30} + 12 q^{31} + 48 q^{32} + 2 q^{33} + 8 q^{34} + 30 q^{36} + 33 q^{37} - 16 q^{38} + 2 q^{39} + 21 q^{40} - 12 q^{41} + 38 q^{43} + 30 q^{44} + 22 q^{45} + 39 q^{46} - 4 q^{47} - 82 q^{48} + 16 q^{50} + 51 q^{51} + 30 q^{52} + 2 q^{53} - 10 q^{54} + q^{55} + 38 q^{57} + 17 q^{58} + 4 q^{59} - 33 q^{60} + 22 q^{61} - 42 q^{62} + 41 q^{64} + q^{65} - 2 q^{66} + 24 q^{67} - 14 q^{68} + 30 q^{69} + 9 q^{71} + 102 q^{72} - 11 q^{73} + 39 q^{74} + 16 q^{75} - 58 q^{76} - 2 q^{78} + 19 q^{79} + 33 q^{80} + 73 q^{81} + 32 q^{82} - 16 q^{83} + 14 q^{85} + 27 q^{86} + 11 q^{87} + 21 q^{88} - 13 q^{89} - 40 q^{90} + 17 q^{93} + 56 q^{94} + 15 q^{95} - 55 q^{96} - 34 q^{97} + 37 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9 + 3 * q^10 + 25 * q^11 - 9 * q^12 + 25 * q^13 + 32 * q^16 + q^17 + 44 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^22 + 15 * q^23 + 4 * q^24 + 50 * q^25 + 6 * q^26 + 17 * q^27 + 24 * q^29 + q^30 + 12 * q^31 + 48 * q^32 + 2 * q^33 + 8 * q^34 + 30 * q^36 + 33 * q^37 - 16 * q^38 + 2 * q^39 + 21 * q^40 - 12 * q^41 + 38 * q^43 + 30 * q^44 + 22 * q^45 + 39 * q^46 - 4 * q^47 - 82 * q^48 + 16 * q^50 + 51 * q^51 + 30 * q^52 + 2 * q^53 - 10 * q^54 + q^55 + 38 * q^57 + 17 * q^58 + 4 * q^59 - 33 * q^60 + 22 * q^61 - 42 * q^62 + 41 * q^64 + q^65 - 2 * q^66 + 24 * q^67 - 14 * q^68 + 30 * q^69 + 9 * q^71 + 102 * q^72 - 11 * q^73 + 39 * q^74 + 16 * q^75 - 58 * q^76 - 2 * q^78 + 19 * q^79 + 33 * q^80 + 73 * q^81 + 32 * q^82 - 16 * q^83 + 14 * q^85 + 27 * q^86 + 11 * q^87 + 21 * q^88 - 13 * q^89 - 40 * q^90 + 17 * q^93 + 56 * q^94 + 15 * q^95 - 55 * q^96 - 34 * q^97 + 37 * q^99

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