LMFDB - Embedded newform 6050.2.a.dd.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6050,2,Mod(1,6050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6050.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6050 = 2 \cdot 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6050.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:	$48.3094932229$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.28400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 17x^{2} + 71 $ x^4 - 17*x^2 + 71
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.71698$ of defining polynomial
Character	$\chi$	$=$	6050.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -5.01420 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -5.01420 q^{7} -1.00000 q^{8} -0.381966 q^{9} +1.61803 q^{12} +2.33501 q^{13} +5.01420 q^{14} +1.00000 q^{16} +0.0611504 q^{17} +0.381966 q^{18} -2.06115 q^{19} -8.11314 q^{21} +3.91525 q^{23} -1.61803 q^{24} -2.33501 q^{26} -5.47214 q^{27} -5.01420 q^{28} -4.13712 q^{29} -8.87707 q^{31} -1.00000 q^{32} -0.0611504 q^{34} -0.381966 q^{36} +4.55688 q^{37} +2.06115 q^{38} +3.77813 q^{39} -4.57985 q^{41} +8.11314 q^{42} +3.61803 q^{43} -3.91525 q^{46} +8.87707 q^{47} +1.61803 q^{48} +18.1422 q^{49} +0.0989434 q^{51} +2.33501 q^{52} +2.22187 q^{53} +5.47214 q^{54} +5.01420 q^{56} -3.33501 q^{57} +4.13712 q^{58} +1.93885 q^{59} -9.69338 q^{61} +8.87707 q^{62} +1.91525 q^{63} +1.00000 q^{64} +2.49573 q^{67} +0.0611504 q^{68} +6.33501 q^{69} +8.81631 q^{71} +0.381966 q^{72} +5.39616 q^{73} -4.55688 q^{74} -2.06115 q^{76} -3.77813 q^{78} -6.65520 q^{79} -7.70820 q^{81} +4.57985 q^{82} +11.0520 q^{83} -8.11314 q^{84} -3.61803 q^{86} -6.69401 q^{87} +6.09017 q^{89} -11.7082 q^{91} +3.91525 q^{92} -14.3634 q^{93} -8.87707 q^{94} -1.61803 q^{96} -7.30225 q^{97} -18.1422 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{6} + 2 q^{7} - 4 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^6 + 2 * q^7 - 4 * q^8 - 6 * q^9	$ 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{6} + 2 q^{7} - 4 q^{8} - 6 q^{9} + 2 q^{12} - 6 q^{13} - 2 q^{14} + 4 q^{16} - 2 q^{17} + 6 q^{18} - 6 q^{19} - 4 q^{21} - 2 q^{24} + 6 q^{26} - 4 q^{27} + 2 q^{28} - 14 q^{29} - 16 q^{31} - 4 q^{32} + 2 q^{34} - 6 q^{36} + 16 q^{37} + 6 q^{38} + 2 q^{39} - 10 q^{41} + 4 q^{42} + 10 q^{43} + 16 q^{47} + 2 q^{48} + 24 q^{49} - 6 q^{51} - 6 q^{52} + 22 q^{53} + 4 q^{54} - 2 q^{56} + 2 q^{57} + 14 q^{58} + 10 q^{59} - 10 q^{61} + 16 q^{62} - 8 q^{63} + 4 q^{64} + 10 q^{67} - 2 q^{68} + 10 q^{69} + 26 q^{71} + 6 q^{72} + 4 q^{73} - 16 q^{74} - 6 q^{76} - 2 q^{78} + 6 q^{79} - 4 q^{81} + 10 q^{82} + 18 q^{83} - 4 q^{84} - 10 q^{86} - 22 q^{87} + 2 q^{89} - 20 q^{91} + 2 q^{93} - 16 q^{94} - 2 q^{96} + 28 q^{97} - 24 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^6 + 2 * q^7 - 4 * q^8 - 6 * q^9 + 2 * q^12 - 6 * q^13 - 2 * q^14 + 4 * q^16 - 2 * q^17 + 6 * q^18 - 6 * q^19 - 4 * q^21 - 2 * q^24 + 6 * q^26 - 4 * q^27 + 2 * q^28 - 14 * q^29 - 16 * q^31 - 4 * q^32 + 2 * q^34 - 6 * q^36 + 16 * q^37 + 6 * q^38 + 2 * q^39 - 10 * q^41 + 4 * q^42 + 10 * q^43 + 16 * q^47 + 2 * q^48 + 24 * q^49 - 6 * q^51 - 6 * q^52 + 22 * q^53 + 4 * q^54 - 2 * q^56 + 2 * q^57 + 14 * q^58 + 10 * q^59 - 10 * q^61 + 16 * q^62 - 8 * q^63 + 4 * q^64 + 10 * q^67 - 2 * q^68 + 10 * q^69 + 26 * q^71 + 6 * q^72 + 4 * q^73 - 16 * q^74 - 6 * q^76 - 2 * q^78 + 6 * q^79 - 4 * q^81 + 10 * q^82 + 18 * q^83 - 4 * q^84 - 10 * q^86 - 22 * q^87 + 2 * q^89 - 20 * q^91 + 2 * q^93 - 16 * q^94 - 2 * q^96 + 28 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.61803	−0.660560
$7$	−5.01420	−1.89519	−0.947594	−	0.319477i	$-0.896493\pi$
$7$	−5.01420	−1.89519	−0.947594	+	0.319477i	$0.896493\pi$
$8$	−1.00000	−0.353553
$9$	−0.381966	−0.127322
$10$	0	0
$11$	0	0
$11$	0	0
$12$	1.61803	0.467086
$13$	2.33501	0.647616	0.323808	−	0.946123i	$-0.395037\pi$
$13$	2.33501	0.647616	0.323808	+	0.946123i	$0.395037\pi$
$14$	5.01420	1.34010
$15$	0	0
$16$	1.00000	0.250000
$17$	0.0611504	0.0148311	0.00741557	−	0.999973i	$-0.497640\pi$
$17$	0.0611504	0.0148311	0.00741557	+	0.999973i	$0.497640\pi$
$18$	0.381966	0.0900303
$19$	−2.06115	−0.472860	−0.236430	−	0.971648i	$-0.575977\pi$
$19$	−2.06115	−0.472860	−0.236430	+	0.971648i	$0.575977\pi$
$20$	0	0
$21$	−8.11314	−1.77043
$22$	0	0
$23$	3.91525	0.816387	0.408193	−	0.912896i	$-0.366159\pi$
$23$	3.91525	0.816387	0.408193	+	0.912896i	$0.366159\pi$
$24$	−1.61803	−0.330280
$25$	0	0
$26$	−2.33501	−0.457933
$27$	−5.47214	−1.05311
$28$	−5.01420	−0.947594
$29$	−4.13712	−0.768245	−0.384122	−	0.923282i	$-0.625496\pi$
$29$	−4.13712	−0.768245	−0.384122	+	0.923282i	$0.625496\pi$
$30$	0	0
$31$	−8.87707	−1.59437	−0.797185	−	0.603736i	$-0.793678\pi$
$31$	−8.87707	−1.59437	−0.797185	+	0.603736i	$0.793678\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−0.0611504	−0.0104872
$35$	0	0
$36$	−0.381966	−0.0636610
$37$	4.55688	0.749147	0.374574	−	0.927197i	$-0.377789\pi$
$37$	4.55688	0.749147	0.374574	+	0.927197i	$0.377789\pi$
$38$	2.06115	0.334363
$39$	3.77813	0.604985
$40$	0	0
$41$	−4.57985	−0.715253	−0.357626	−	0.933865i	$-0.616414\pi$
$41$	−4.57985	−0.715253	−0.357626	+	0.933865i	$0.616414\pi$
$42$	8.11314	1.25188
$43$	3.61803	0.551745	0.275873	−	0.961194i	$-0.411033\pi$
$43$	3.61803	0.551745	0.275873	+	0.961194i	$0.411033\pi$
$44$	0	0
$45$	0	0
$46$	−3.91525	−0.577272
$47$	8.87707	1.29485	0.647427	−	0.762128i	$-0.275845\pi$
$47$	8.87707	1.29485	0.647427	+	0.762128i	$0.275845\pi$
$48$	1.61803	0.233543
$49$	18.1422	2.59174
$50$	0	0
$51$	0.0989434	0.0138548
$52$	2.33501	0.323808
$53$	2.22187	0.305198	0.152599	−	0.988288i	$-0.451236\pi$
$53$	2.22187	0.305198	0.152599	+	0.988288i	$0.451236\pi$
$54$	5.47214	0.744663
$55$	0	0
$56$	5.01420	0.670050
$57$	−3.33501	−0.441733
$58$	4.13712	0.543231
$59$	1.93885	0.252417	0.126208	−	0.992004i	$-0.459719\pi$
$59$	1.93885	0.252417	0.126208	+	0.992004i	$0.459719\pi$
$60$	0	0
$61$	−9.69338	−1.24111	−0.620555	−	0.784163i	$-0.713093\pi$
$61$	−9.69338	−1.24111	−0.620555	+	0.784163i	$0.713093\pi$
$62$	8.87707	1.12739
$63$	1.91525	0.241299
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	2.49573	0.304902	0.152451	−	0.988311i	$-0.451283\pi$
$67$	2.49573	0.304902	0.152451	+	0.988311i	$0.451283\pi$
$68$	0.0611504	0.00741557
$69$	6.33501	0.762646
$70$	0	0
$71$	8.81631	1.04630	0.523152	−	0.852240i	$-0.324756\pi$
$71$	8.81631	1.04630	0.523152	+	0.852240i	$0.324756\pi$
$72$	0.381966	0.0450151
$73$	5.39616	0.631573	0.315786	−	0.948830i	$-0.397732\pi$
$73$	5.39616	0.631573	0.315786	+	0.948830i	$0.397732\pi$
$74$	−4.55688	−0.529727
$75$	0	0
$76$	−2.06115	−0.236430
$77$	0	0
$78$	−3.77813	−0.427789
$79$	−6.65520	−0.748768	−0.374384	−	0.927274i	$-0.622146\pi$
$79$	−6.65520	−0.748768	−0.374384	+	0.927274i	$0.622146\pi$
$80$	0	0
$81$	−7.70820	−0.856467
$82$	4.57985	0.505760
$83$	11.0520	1.21311	0.606557	−	0.795040i	$-0.292550\pi$
$83$	11.0520	1.21311	0.606557	+	0.795040i	$0.292550\pi$
$84$	−8.11314	−0.885216
$85$	0	0
$86$	−3.61803	−0.390143
$87$	−6.69401	−0.717673
$88$	0	0
$89$	6.09017	0.645557	0.322778	−	0.946475i	$-0.395383\pi$
$89$	6.09017	0.645557	0.322778	+	0.946475i	$0.395383\pi$
$90$	0	0
$91$	−11.7082	−1.22735
$92$	3.91525	0.408193
$93$	−14.3634	−1.48942
$94$	−8.87707	−0.915600
$95$	0	0
$96$	−1.61803	−0.165140
$97$	−7.30225	−0.741431	−0.370716	−	0.928746i	$-0.620888\pi$
$97$	−7.30225	−0.741431	−0.370716	+	0.928746i	$0.620888\pi$
$98$	−18.1422	−1.83263
$99$	0	0
$100$	0	0
$101$	−0.221872	−0.0220771	−0.0110386	−	0.999939i	$-0.503514\pi$
$101$	−0.221872	−0.0220771	−0.0110386	+	0.999939i	$0.503514\pi$
$102$	−0.0989434	−0.00979685
$103$	0.566045	0.0557741	0.0278870	−	0.999611i	$-0.491122\pi$
$103$	0.566045	0.0557741	0.0278870	+	0.999611i	$0.491122\pi$
$104$	−2.33501	−0.228967
$105$	0	0
$106$	−2.22187	−0.215807
$107$	−2.23002	−0.215584	−0.107792	−	0.994173i	$-0.534378\pi$
$107$	−2.23002	−0.215584	−0.107792	+	0.994173i	$0.534378\pi$
$108$	−5.47214	−0.526557
$109$	7.86288	0.753127	0.376563	−	0.926391i	$-0.377106\pi$
$109$	7.86288	0.753127	0.376563	+	0.926391i	$0.377106\pi$
$110$	0	0
$111$	7.37319	0.699832
$112$	−5.01420	−0.473797
$113$	−12.5617	−1.18170	−0.590852	−	0.806780i	$-0.701208\pi$
$113$	−12.5617	−1.18170	−0.590852	+	0.806780i	$0.701208\pi$
$114$	3.33501	0.312352
$115$	0	0
$116$	−4.13712	−0.384122
$117$	−0.891895	−0.0824557
$118$	−1.93885	−0.178486
$119$	−0.306620	−0.0281078
$120$	0	0
$121$	0	0
$122$	9.69338	0.877597
$123$	−7.41036	−0.668169
$124$	−8.87707	−0.797185
$125$	0	0
$126$	−1.91525	−0.170624
$127$	14.4630	1.28338	0.641691	−	0.766964i	$-0.278233\pi$
$127$	14.4630	1.28338	0.641691	+	0.766964i	$0.278233\pi$
$128$	−1.00000	−0.0883883
$129$	5.85410	0.515425
$130$	0	0
$131$	15.3256	1.33900	0.669502	−	0.742810i	$-0.266507\pi$
$131$	15.3256	1.33900	0.669502	+	0.742810i	$0.266507\pi$
$132$	0	0
$133$	10.3350	0.896159
$134$	−2.49573	−0.215599
$135$	0	0
$136$	−0.0611504	−0.00524360
$137$	−1.10437	−0.0943523	−0.0471762	−	0.998887i	$-0.515022\pi$
$137$	−1.10437	−0.0943523	−0.0471762	+	0.998887i	$0.515022\pi$
$138$	−6.33501	−0.539272
$139$	−9.90609	−0.840224	−0.420112	−	0.907472i	$-0.638009\pi$
$139$	−9.90609	−0.840224	−0.420112	+	0.907472i	$0.638009\pi$
$140$	0	0
$141$	14.3634	1.20962
$142$	−8.81631	−0.739848
$143$	0	0
$144$	−0.381966	−0.0318305
$145$	0	0
$146$	−5.39616	−0.446590
$147$	29.3546	2.42113
$148$	4.55688	0.374574
$149$	8.79232	0.720295	0.360148	−	0.932895i	$-0.382726\pi$
$149$	8.79232	0.720295	0.360148	+	0.932895i	$0.382726\pi$
$150$	0	0
$151$	21.5903	1.75699	0.878497	−	0.477747i	$-0.158547\pi$
$151$	21.5903	1.75699	0.878497	+	0.477747i	$0.158547\pi$
$152$	2.06115	0.167181
$153$	−0.0233574	−0.00188833
$154$	0	0
$155$	0	0
$156$	3.77813	0.302492
$157$	3.41472	0.272525	0.136262	−	0.990673i	$-0.456491\pi$
$157$	3.41472	0.272525	0.136262	+	0.990673i	$0.456491\pi$
$158$	6.65520	0.529459
$159$	3.59506	0.285107
$160$	0	0
$161$	−19.6318	−1.54721
$162$	7.70820	0.605614
$163$	17.4104	1.36368	0.681842	−	0.731499i	$-0.261179\pi$
$163$	17.4104	1.36368	0.681842	+	0.731499i	$0.261179\pi$
$164$	−4.57985	−0.357626
$165$	0	0
$166$	−11.0520	−0.857801
$167$	3.30599	0.255825	0.127913	−	0.991785i	$-0.459172\pi$
$167$	3.30599	0.255825	0.127913	+	0.991785i	$0.459172\pi$
$168$	8.11314	0.625942
$169$	−7.54772	−0.580594
$170$	0	0
$171$	0.787289	0.0602055
$172$	3.61803	0.275873
$173$	5.12859	0.389920	0.194960	−	0.980811i	$-0.437542\pi$
$173$	5.12859	0.389920	0.194960	+	0.980811i	$0.437542\pi$
$174$	6.69401	0.507471
$175$	0	0
$176$	0	0
$177$	3.13712	0.235801
$178$	−6.09017	−0.456478
$179$	−14.4394	−1.07925	−0.539625	−	0.841906i	$-0.681434\pi$
$179$	−14.4394	−1.07925	−0.539625	+	0.841906i	$0.681434\pi$
$180$	0	0
$181$	11.9061	0.884973	0.442486	−	0.896775i	$-0.354097\pi$
$181$	11.9061	0.884973	0.442486	+	0.896775i	$0.354097\pi$
$182$	11.7082	0.867870
$183$	−15.6842	−1.15941
$184$	−3.91525	−0.288636
$185$	0	0
$186$	14.3634	1.05318
$187$	0	0
$188$	8.87707	0.647427
$189$	27.4384	1.99585
$190$	0	0
$191$	10.5181	0.761061	0.380531	−	0.924768i	$-0.375741\pi$
$191$	10.5181	0.761061	0.380531	+	0.924768i	$0.375741\pi$
$192$	1.61803	0.116772
$193$	4.86869	0.350456	0.175228	−	0.984528i	$-0.443934\pi$
$193$	4.86869	0.350456	0.175228	+	0.984528i	$0.443934\pi$
$194$	7.30225	0.524271
$195$	0	0
$196$	18.1422	1.29587
$197$	−15.9760	−1.13824	−0.569122	−	0.822253i	$-0.692717\pi$
$197$	−15.9760	−1.13824	−0.569122	+	0.822253i	$0.692717\pi$
$198$	0	0
$199$	16.7076	1.18437	0.592184	−	0.805803i	$-0.298266\pi$
$199$	16.7076	1.18437	0.592184	+	0.805803i	$0.298266\pi$
$200$	0	0
$201$	4.03818	0.284831
$202$	0.221872	0.0156109
$203$	20.7444	1.45597
$204$	0.0989434	0.00692742
$205$	0	0
$206$	−0.566045	−0.0394382
$207$	−1.49549	−0.103944
$208$	2.33501	0.161904
$209$	0	0
$210$	0	0
$211$	−15.7460	−1.08400	−0.542000	−	0.840379i	$-0.682333\pi$
$211$	−15.7460	−1.08400	−0.542000	+	0.840379i	$0.682333\pi$
$212$	2.22187	0.152599
$213$	14.2651	0.977428
$214$	2.23002	0.152441
$215$	0	0
$216$	5.47214	0.372332
$217$	44.5114	3.02163
$218$	−7.86288	−0.532541
$219$	8.73117	0.589998
$220$	0	0
$221$	0.142787	0.00960488
$222$	−7.37319	−0.494856
$223$	14.5556	0.974717	0.487358	−	0.873202i	$-0.337961\pi$
$223$	14.5556	0.974717	0.487358	+	0.873202i	$0.337961\pi$
$224$	5.01420	0.335025
$225$	0	0
$226$	12.5617	0.835590
$227$	−9.83656	−0.652875	−0.326438	−	0.945219i	$-0.605848\pi$
$227$	−9.83656	−0.652875	−0.326438	+	0.945219i	$0.605848\pi$
$228$	−3.33501	−0.220867
$229$	−15.5479	−1.02743	−0.513716	−	0.857960i	$-0.671732\pi$
$229$	−15.5479	−1.02743	−0.513716	+	0.857960i	$0.671732\pi$
$230$	0	0
$231$	0	0
$232$	4.13712	0.271616
$233$	25.8967	1.69655	0.848274	−	0.529557i	$-0.177642\pi$
$233$	25.8967	1.69655	0.848274	+	0.529557i	$0.177642\pi$
$234$	0.891895	0.0583050
$235$	0	0
$236$	1.93885	0.126208
$237$	−10.7683	−0.699479
$238$	0.306620	0.0198752
$239$	19.9960	1.29344	0.646718	−	0.762730i	$-0.276141\pi$
$239$	19.9960	1.29344	0.646718	+	0.762730i	$0.276141\pi$
$240$	0	0
$241$	9.01381	0.580630	0.290315	−	0.956931i	$-0.406240\pi$
$241$	9.01381	0.580630	0.290315	+	0.956931i	$0.406240\pi$
$242$	0	0
$243$	3.94427	0.253025
$244$	−9.69338	−0.620555
$245$	0	0
$246$	7.41036	0.472467
$247$	−4.81281	−0.306232
$248$	8.87707	0.563695
$249$	17.8825	1.13326
$250$	0	0
$251$	1.31165	0.0827909	0.0413954	−	0.999143i	$-0.486820\pi$
$251$	1.31165	0.0827909	0.0413954	+	0.999143i	$0.486820\pi$
$252$	1.91525	0.120650
$253$	0	0
$254$	−14.4630	−0.907488
$255$	0	0
$256$	1.00000	0.0625000
$257$	4.46399	0.278456	0.139228	−	0.990260i	$-0.455538\pi$
$257$	4.46399	0.278456	0.139228	+	0.990260i	$0.455538\pi$
$258$	−5.85410	−0.364460
$259$	−22.8491	−1.41977
$260$	0	0
$261$	1.58024	0.0978145
$262$	−15.3256	−0.946819
$263$	14.1791	0.874320	0.437160	−	0.899384i	$-0.355984\pi$
$263$	14.1791	0.874320	0.437160	+	0.899384i	$0.355984\pi$
$264$	0	0
$265$	0	0
$266$	−10.3350	−0.633680
$267$	9.85410	0.603061
$268$	2.49573	0.152451
$269$	−31.9952	−1.95078	−0.975392	−	0.220477i	$-0.929239\pi$
$269$	−31.9952	−1.95078	−0.975392	+	0.220477i	$0.929239\pi$
$270$	0	0
$271$	1.06139	0.0644749	0.0322374	−	0.999480i	$-0.489737\pi$
$271$	1.06139	0.0644749	0.0322374	+	0.999480i	$0.489737\pi$
$272$	0.0611504	0.00370779
$273$	−18.9443	−1.14656
$274$	1.10437	0.0667172
$275$	0	0
$276$	6.33501	0.381323
$277$	−6.63325	−0.398553	−0.199277	−	0.979943i	$-0.563859\pi$
$277$	−6.63325	−0.398553	−0.199277	+	0.979943i	$0.563859\pi$
$278$	9.90609	0.594128
$279$	3.39074	0.202998
$280$	0	0
$281$	15.6464	0.933387	0.466694	−	0.884419i	$-0.345445\pi$
$281$	15.6464	0.933387	0.466694	+	0.884419i	$0.345445\pi$
$282$	−14.3634	−0.855328
$283$	22.5005	1.33752	0.668759	−	0.743479i	$-0.266826\pi$
$283$	22.5005	1.33752	0.668759	+	0.743479i	$0.266826\pi$
$284$	8.81631	0.523152
$285$	0	0
$286$	0	0
$287$	22.9643	1.35554
$288$	0.381966	0.0225076
$289$	−16.9963	−0.999780
$290$	0	0
$291$	−11.8153	−0.692625
$292$	5.39616	0.315786
$293$	18.1887	1.06260	0.531298	−	0.847185i	$-0.321704\pi$
$293$	18.1887	1.06260	0.531298	+	0.847185i	$0.321704\pi$
$294$	−29.3546	−1.71200
$295$	0	0
$296$	−4.55688	−0.264863
$297$	0	0
$298$	−8.79232	−0.509326
$299$	9.14216	0.528705
$300$	0	0
$301$	−18.1415	−1.04566
$302$	−21.5903	−1.24238
$303$	−0.358997	−0.0206238
$304$	−2.06115	−0.118215
$305$	0	0
$306$	0.0233574	0.00133525
$307$	−12.3820	−0.706676	−0.353338	−	0.935496i	$-0.614953\pi$
$307$	−12.3820	−0.706676	−0.353338	+	0.935496i	$0.614953\pi$
$308$	0	0
$309$	0.915880	0.0521026
$310$	0	0
$311$	9.40997	0.533590	0.266795	−	0.963753i	$-0.414035\pi$
$311$	9.40997	0.533590	0.266795	+	0.963753i	$0.414035\pi$
$312$	−3.77813	−0.213894
$313$	−15.2317	−0.860947	−0.430473	−	0.902603i	$-0.641653\pi$
$313$	−15.2317	−0.860947	−0.430473	+	0.902603i	$0.641653\pi$
$314$	−3.41472	−0.192704
$315$	0	0
$316$	−6.65520	−0.374384
$317$	13.4567	0.755803	0.377901	−	0.925846i	$-0.376646\pi$
$317$	13.4567	0.755803	0.377901	+	0.925846i	$0.376646\pi$
$318$	−3.59506	−0.201601
$319$	0	0
$320$	0	0
$321$	−3.60824	−0.201393
$322$	19.6318	1.09404
$323$	−0.126040	−0.00701306
$324$	−7.70820	−0.428234
$325$	0	0
$326$	−17.4104	−0.964271
$327$	12.7224	0.703550
$328$	4.57985	0.252880
$329$	−44.5114	−2.45399
$330$	0	0
$331$	−3.82236	−0.210096	−0.105048	−	0.994467i	$-0.533500\pi$
$331$	−3.82236	−0.210096	−0.105048	+	0.994467i	$0.533500\pi$
$332$	11.0520	0.606557
$333$	−1.74057	−0.0953829
$334$	−3.30599	−0.180896
$335$	0	0
$336$	−8.11314	−0.442608
$337$	9.46671	0.515685	0.257842	−	0.966187i	$-0.416988\pi$
$337$	9.46671	0.515685	0.257842	+	0.966187i	$0.416988\pi$
$338$	7.54772	0.410542
$339$	−20.3252	−1.10391
$340$	0	0
$341$	0	0
$342$	−0.787289	−0.0425717
$343$	−55.8690	−3.01664
$344$	−3.61803	−0.195071
$345$	0	0
$346$	−5.12859	−0.275715
$347$	16.5424	0.888045	0.444023	−	0.896016i	$-0.353551\pi$
$347$	16.5424	0.888045	0.444023	+	0.896016i	$0.353551\pi$
$348$	−6.69401	−0.358837
$349$	29.2269	1.56448	0.782240	−	0.622977i	$-0.214077\pi$
$349$	29.2269	1.56448	0.782240	+	0.622977i	$0.214077\pi$
$350$	0	0
$351$	−12.7775	−0.682012
$352$	0	0
$353$	−27.9200	−1.48603	−0.743017	−	0.669272i	$-0.766606\pi$
$353$	−27.9200	−1.48603	−0.743017	+	0.669272i	$0.766606\pi$
$354$	−3.13712	−0.166736
$355$	0	0
$356$	6.09017	0.322778
$357$	−0.496121	−0.0262575
$358$	14.4394	0.763145
$359$	17.0142	0.897975	0.448987	−	0.893538i	$-0.351785\pi$
$359$	17.0142	0.897975	0.448987	+	0.893538i	$0.351785\pi$
$360$	0	0
$361$	−14.7517	−0.776403
$362$	−11.9061	−0.625770
$363$	0	0
$364$	−11.7082	−0.613677
$365$	0	0
$366$	15.6842	0.819827
$367$	29.4391	1.53671	0.768355	−	0.640024i	$-0.221075\pi$
$367$	29.4391	1.53671	0.768355	+	0.640024i	$0.221075\pi$
$368$	3.91525	0.204097
$369$	1.74935	0.0910674
$370$	0	0
$371$	−11.1409	−0.578407
$372$	−14.3634	−0.744708
$373$	−16.0743	−0.832297	−0.416149	−	0.909297i	$-0.636620\pi$
$373$	−16.0743	−0.832297	−0.416149	+	0.909297i	$0.636620\pi$
$374$	0	0
$375$	0	0
$376$	−8.87707	−0.457800
$377$	−9.66023	−0.497527
$378$	−27.4384	−1.41128
$379$	18.1230	0.930914	0.465457	−	0.885070i	$-0.345890\pi$
$379$	18.1230	0.930914	0.465457	+	0.885070i	$0.345890\pi$
$380$	0	0
$381$	23.4016	1.19890
$382$	−10.5181	−0.538151
$383$	13.2121	0.675106	0.337553	−	0.941307i	$-0.390401\pi$
$383$	13.2121	0.675106	0.337553	+	0.941307i	$0.390401\pi$
$384$	−1.61803	−0.0825700
$385$	0	0
$386$	−4.86869	−0.247810
$387$	−1.38197	−0.0702493
$388$	−7.30225	−0.370716
$389$	−26.5245	−1.34485	−0.672423	−	0.740167i	$-0.734746\pi$
$389$	−26.5245	−1.34485	−0.672423	+	0.740167i	$0.734746\pi$
$390$	0	0
$391$	0.239419	0.0121079
$392$	−18.1422	−0.916317
$393$	24.7974	1.25086
$394$	15.9760	0.804860
$395$	0	0
$396$	0	0
$397$	30.3246	1.52195	0.760974	−	0.648783i	$-0.224722\pi$
$397$	30.3246	1.52195	0.760974	+	0.648783i	$0.224722\pi$
$398$	−16.7076	−0.837475
$399$	16.7224	0.837167
$400$	0	0
$401$	19.4762	0.972593	0.486296	−	0.873794i	$-0.338348\pi$
$401$	19.4762	0.972593	0.486296	+	0.873794i	$0.338348\pi$
$402$	−4.03818	−0.201406
$403$	−20.7281	−1.03254
$404$	−0.221872	−0.0110386
$405$	0	0
$406$	−20.7444	−1.02952
$407$	0	0
$408$	−0.0989434	−0.00489843
$409$	−28.3303	−1.40084	−0.700420	−	0.713730i	$-0.747004\pi$
$409$	−28.3303	−1.40084	−0.700420	+	0.713730i	$0.747004\pi$
$410$	0	0
$411$	−1.78690	−0.0881413
$412$	0.566045	0.0278870
$413$	−9.72177	−0.478377
$414$	1.49549	0.0734995
$415$	0	0
$416$	−2.33501	−0.114483
$417$	−16.0284	−0.784914
$418$	0	0
$419$	−15.4826	−0.756374	−0.378187	−	0.925729i	$-0.623452\pi$
$419$	−15.4826	−0.756374	−0.378187	+	0.925729i	$0.623452\pi$
$420$	0	0
$421$	21.4863	1.04718	0.523590	−	0.851970i	$-0.324592\pi$
$421$	21.4863	1.04718	0.523590	+	0.851970i	$0.324592\pi$
$422$	15.7460	0.766503
$423$	−3.39074	−0.164863
$424$	−2.22187	−0.107904
$425$	0	0
$426$	−14.2651	−0.691146
$427$	48.6045	2.35214
$428$	−2.23002	−0.107792
$429$	0	0
$430$	0	0
$431$	26.4390	1.27352	0.636761	−	0.771062i	$-0.280274\pi$
$431$	26.4390	1.27352	0.636761	+	0.771062i	$0.280274\pi$
$432$	−5.47214	−0.263278
$433$	32.8819	1.58020	0.790101	−	0.612977i	$-0.210028\pi$
$433$	32.8819	1.58020	0.790101	+	0.612977i	$0.210028\pi$
$434$	−44.5114	−2.13661
$435$	0	0
$436$	7.86288	0.376563
$437$	−8.06992	−0.386037
$438$	−8.73117	−0.417192
$439$	−12.1796	−0.581299	−0.290649	−	0.956830i	$-0.593871\pi$
$439$	−12.1796	−0.581299	−0.290649	+	0.956830i	$0.593871\pi$
$440$	0	0
$441$	−6.92969	−0.329985
$442$	−0.142787	−0.00679168
$443$	−16.6090	−0.789118	−0.394559	−	0.918871i	$-0.629103\pi$
$443$	−16.6090	−0.789118	−0.394559	+	0.918871i	$0.629103\pi$
$444$	7.37319	0.349916
$445$	0	0
$446$	−14.5556	−0.689229
$447$	14.2263	0.672880
$448$	−5.01420	−0.236898
$449$	−5.36364	−0.253126	−0.126563	−	0.991959i	$-0.540395\pi$
$449$	−5.36364	−0.253126	−0.126563	+	0.991959i	$0.540395\pi$
$450$	0	0
$451$	0	0
$452$	−12.5617	−0.590852
$453$	34.9339	1.64134
$454$	9.83656	0.461652
$455$	0	0
$456$	3.33501	0.156176
$457$	−3.61237	−0.168980	−0.0844898	−	0.996424i	$-0.526926\pi$
$457$	−3.61237	−0.168980	−0.0844898	+	0.996424i	$0.526926\pi$
$458$	15.5479	0.726504
$459$	−0.334623	−0.0156189
$460$	0	0
$461$	−40.6625	−1.89384	−0.946922	−	0.321464i	$-0.895825\pi$
$461$	−40.6625	−1.89384	−0.946922	+	0.321464i	$0.895825\pi$
$462$	0	0
$463$	−2.11880	−0.0984690	−0.0492345	−	0.998787i	$-0.515678\pi$
$463$	−2.11880	−0.0984690	−0.0492345	+	0.998787i	$0.515678\pi$
$464$	−4.13712	−0.192061
$465$	0	0
$466$	−25.8967	−1.19964
$467$	−13.7549	−0.636502	−0.318251	−	0.948007i	$-0.603095\pi$
$467$	−13.7549	−0.636502	−0.318251	+	0.948007i	$0.603095\pi$
$468$	−0.891895	−0.0412279
$469$	−12.5141	−0.577847
$470$	0	0
$471$	5.52514	0.254585
$472$	−1.93885	−0.0892428
$473$	0	0
$474$	10.7683	0.494606
$475$	0	0
$476$	−0.306620	−0.0140539
$477$	−0.848680	−0.0388584
$478$	−19.9960	−0.914597
$479$	31.4107	1.43519	0.717597	−	0.696459i	$-0.245242\pi$
$479$	31.4107	1.43519	0.717597	+	0.696459i	$0.245242\pi$
$480$	0	0
$481$	10.6404	0.485159
$482$	−9.01381	−0.410568
$483$	−31.7650	−1.44536
$484$	0	0
$485$	0	0
$486$	−3.94427	−0.178916
$487$	−7.51032	−0.340325	−0.170162	−	0.985416i	$-0.554429\pi$
$487$	−7.51032	−0.340325	−0.170162	+	0.985416i	$0.554429\pi$
$488$	9.69338	0.438799
$489$	28.1706	1.27392
$490$	0	0
$491$	11.2618	0.508236	0.254118	−	0.967173i	$-0.418215\pi$
$491$	11.2618	0.508236	0.254118	+	0.967173i	$0.418215\pi$
$492$	−7.41036	−0.334085
$493$	−0.252987	−0.0113939
$494$	4.81281	0.216539
$495$	0	0
$496$	−8.87707	−0.398592
$497$	−44.2067	−1.98294
$498$	−17.8825	−0.801334
$499$	−26.9808	−1.20783	−0.603913	−	0.797050i	$-0.706393\pi$
$499$	−26.9808	−1.20783	−0.603913	+	0.797050i	$0.706393\pi$
$500$	0	0
$501$	5.34921	0.238985
$502$	−1.31165	−0.0585420
$503$	−32.1556	−1.43375	−0.716873	−	0.697204i	$-0.754427\pi$
$503$	−32.1556	−1.43375	−0.716873	+	0.697204i	$0.754427\pi$
$504$	−1.91525	−0.0853121
$505$	0	0
$506$	0	0
$507$	−12.2125	−0.542375
$508$	14.4630	0.641691
$509$	11.7809	0.522177	0.261089	−	0.965315i	$-0.415919\pi$
$509$	11.7809	0.522177	0.261089	+	0.965315i	$0.415919\pi$
$510$	0	0
$511$	−27.0574	−1.19695
$512$	−1.00000	−0.0441942
$513$	11.2789	0.497975
$514$	−4.46399	−0.196898
$515$	0	0
$516$	5.85410	0.257712
$517$	0	0
$518$	22.8491	1.00393
$519$	8.29823	0.364252
$520$	0	0
$521$	2.32624	0.101914	0.0509572	−	0.998701i	$-0.483773\pi$
$521$	2.32624	0.101914	0.0509572	+	0.998701i	$0.483773\pi$
$522$	−1.58024	−0.0691653
$523$	1.53391	0.0670734	0.0335367	−	0.999437i	$-0.489323\pi$
$523$	1.53391	0.0670734	0.0335367	+	0.999437i	$0.489323\pi$
$524$	15.3256	0.669502
$525$	0	0
$526$	−14.1791	−0.618237
$527$	−0.542836	−0.0236463
$528$	0	0
$529$	−7.67080	−0.333513
$530$	0	0
$531$	−0.740575	−0.0321382
$532$	10.3350	0.448080
$533$	−10.6940	−0.463209
$534$	−9.85410	−0.426429
$535$	0	0
$536$	−2.49573	−0.107799
$537$	−23.3634	−1.00821
$538$	31.9952	1.37941
$539$	0	0
$540$	0	0
$541$	−15.4419	−0.663897	−0.331949	−	0.943297i	$-0.607706\pi$
$541$	−15.4419	−0.663897	−0.331949	+	0.943297i	$0.607706\pi$
$542$	−1.06139	−0.0455906
$543$	19.2645	0.826717
$544$	−0.0611504	−0.00262180
$545$	0	0
$546$	18.9443	0.810740
$547$	−10.6472	−0.455241	−0.227621	−	0.973750i	$-0.573095\pi$
$547$	−10.6472	−0.455241	−0.227621	+	0.973750i	$0.573095\pi$
$548$	−1.10437	−0.0471762
$549$	3.70254	0.158021
$550$	0	0
$551$	8.52724	0.363272
$552$	−6.33501	−0.269636
$553$	33.3705	1.41906
$554$	6.63325	0.281820
$555$	0	0
$556$	−9.90609	−0.420112
$557$	33.9197	1.43722	0.718611	−	0.695412i	$-0.244778\pi$
$557$	33.9197	1.43722	0.718611	+	0.695412i	$0.244778\pi$
$558$	−3.39074	−0.143541
$559$	8.44815	0.357319
$560$	0	0
$561$	0	0
$562$	−15.6464	−0.660005
$563$	1.34378	0.0566338	0.0283169	−	0.999599i	$-0.490985\pi$
$563$	1.34378	0.0566338	0.0283169	+	0.999599i	$0.490985\pi$
$564$	14.3634	0.604808
$565$	0	0
$566$	−22.5005	−0.945768
$567$	38.6504	1.62317
$568$	−8.81631	−0.369924
$569$	−31.4091	−1.31674	−0.658369	−	0.752695i	$-0.728753\pi$
$569$	−31.4091	−1.31674	−0.658369	+	0.752695i	$0.728753\pi$
$570$	0	0
$571$	9.25361	0.387252	0.193626	−	0.981075i	$-0.437975\pi$
$571$	9.25361	0.387252	0.193626	+	0.981075i	$0.437975\pi$
$572$	0	0
$573$	17.0186	0.710962
$574$	−22.9643	−0.958510
$575$	0	0
$576$	−0.381966	−0.0159153
$577$	43.3829	1.80605	0.903026	−	0.429585i	$-0.141340\pi$
$577$	43.3829	1.80605	0.903026	+	0.429585i	$0.141340\pi$
$578$	16.9963	0.706951
$579$	7.87770	0.327386
$580$	0	0
$581$	−55.4168	−2.29908
$582$	11.8153	0.489760
$583$	0	0
$584$	−5.39616	−0.223295
$585$	0	0
$586$	−18.1887	−0.751369
$587$	−3.21247	−0.132593	−0.0662964	−	0.997800i	$-0.521118\pi$
$587$	−3.21247	−0.132593	−0.0662964	+	0.997800i	$0.521118\pi$
$588$	29.3546	1.21056
$589$	18.2970	0.753914
$590$	0	0
$591$	−25.8497	−1.06332
$592$	4.55688	0.187287
$593$	0.0315027	0.00129366	0.000646829	−	1.00000i	$-0.499794\pi$
$593$	0.0315027	0.00129366	0.000646829		1.00000i	$0.499794\pi$
$594$	0	0
$595$	0	0
$596$	8.79232	0.360148
$597$	27.0334	1.10640
$598$	−9.14216	−0.373851
$599$	−10.5189	−0.429789	−0.214894	−	0.976637i	$-0.568941\pi$
$599$	−10.5189	−0.429789	−0.214894	+	0.976637i	$0.568941\pi$
$600$	0	0
$601$	24.1186	0.983817	0.491908	−	0.870647i	$-0.336300\pi$
$601$	24.1186	0.983817	0.491908	+	0.870647i	$0.336300\pi$
$602$	18.1415	0.739394
$603$	−0.953285	−0.0388208
$604$	21.5903	0.878497
$605$	0	0
$606$	0.358997	0.0145833
$607$	2.48968	0.101053	0.0505266	−	0.998723i	$-0.483910\pi$
$607$	2.48968	0.101053	0.0505266	+	0.998723i	$0.483910\pi$
$608$	2.06115	0.0835907
$609$	33.5651	1.36013
$610$	0	0
$611$	20.7281	0.838568
$612$	−0.0233574	−0.000944165 0
$613$	−37.5728	−1.51755	−0.758775	−	0.651353i	$-0.774202\pi$
$613$	−37.5728	−1.51755	−0.758775	+	0.651353i	$0.774202\pi$
$614$	12.3820	0.499695
$615$	0	0
$616$	0	0
$617$	−45.5803	−1.83499	−0.917496	−	0.397744i	$-0.869793\pi$
$617$	−45.5803	−1.83499	−0.917496	+	0.397744i	$0.869793\pi$
$618$	−0.915880	−0.0368421
$619$	5.74019	0.230718	0.115359	−	0.993324i	$-0.463198\pi$
$619$	5.74019	0.230718	0.115359	+	0.993324i	$0.463198\pi$
$620$	0	0
$621$	−21.4248	−0.859747
$622$	−9.40997	−0.377305
$623$	−30.5373	−1.22345
$624$	3.77813	0.151246
$625$	0	0
$626$	15.2317	0.608781
$627$	0	0
$628$	3.41472	0.136262
$629$	0.278655	0.0111107
$630$	0	0
$631$	11.9768	0.476789	0.238394	−	0.971168i	$-0.423379\pi$
$631$	11.9768	0.476789	0.238394	+	0.971168i	$0.423379\pi$
$632$	6.65520	0.264730
$633$	−25.4776	−1.01264
$634$	−13.4567	−0.534433
$635$	0	0
$636$	3.59506	0.142554
$637$	42.3621	1.67845
$638$	0	0
$639$	−3.36753	−0.133217
$640$	0	0
$641$	−35.1196	−1.38714	−0.693571	−	0.720389i	$-0.743964\pi$
$641$	−35.1196	−1.38714	−0.693571	+	0.720389i	$0.743964\pi$
$642$	3.60824	0.142406
$643$	35.6472	1.40579	0.702894	−	0.711294i	$-0.251891\pi$
$643$	35.6472	1.40579	0.702894	+	0.711294i	$0.251891\pi$
$644$	−19.6318	−0.773603
$645$	0	0
$646$	0.126040	0.00495898
$647$	−20.1564	−0.792428	−0.396214	−	0.918158i	$-0.629676\pi$
$647$	−20.1564	−0.792428	−0.396214	+	0.918158i	$0.629676\pi$
$648$	7.70820	0.302807
$649$	0	0
$650$	0	0
$651$	72.0209	2.82272
$652$	17.4104	0.681842
$653$	−24.3839	−0.954215	−0.477108	−	0.878845i	$-0.658315\pi$
$653$	−24.3839	−0.954215	−0.477108	+	0.878845i	$0.658315\pi$
$654$	−12.7224	−0.497485
$655$	0	0
$656$	−4.57985	−0.178813
$657$	−2.06115	−0.0804131
$658$	44.5114	1.73523
$659$	−6.98788	−0.272209	−0.136104	−	0.990694i	$-0.543458\pi$
$659$	−6.98788	−0.272209	−0.136104	+	0.990694i	$0.543458\pi$
$660$	0	0
$661$	−3.61827	−0.140735	−0.0703673	−	0.997521i	$-0.522417\pi$
$661$	−3.61827	−0.140735	−0.0703673	+	0.997521i	$0.522417\pi$
$662$	3.82236	0.148560
$663$	0.231034	0.00897261
$664$	−11.0520	−0.428900
$665$	0	0
$666$	1.74057	0.0674459
$667$	−16.1979	−0.627185
$668$	3.30599	0.127913
$669$	23.5515	0.910554
$670$	0	0
$671$	0	0
$672$	8.11314	0.312971
$673$	−7.96850	−0.307163	−0.153581	−	0.988136i	$-0.549081\pi$
$673$	−7.96850	−0.307163	−0.153581	+	0.988136i	$0.549081\pi$
$674$	−9.46671	−0.364644
$675$	0	0
$676$	−7.54772	−0.290297
$677$	−14.4346	−0.554766	−0.277383	−	0.960759i	$-0.589467\pi$
$677$	−14.4346	−0.554766	−0.277383	+	0.960759i	$0.589467\pi$
$678$	20.3252	0.780585
$679$	36.6149	1.40515
$680$	0	0
$681$	−15.9159	−0.609898
$682$	0	0
$683$	29.6723	1.13538	0.567690	−	0.823242i	$-0.307837\pi$
$683$	29.6723	1.13538	0.567690	+	0.823242i	$0.307837\pi$
$684$	0.787289	0.0301028
$685$	0	0
$686$	55.8690	2.13309
$687$	−25.1570	−0.959799
$688$	3.61803	0.137936
$689$	5.18810	0.197651
$690$	0	0
$691$	32.3618	1.23110	0.615550	−	0.788098i	$-0.288934\pi$
$691$	32.3618	1.23110	0.615550	+	0.788098i	$0.288934\pi$
$692$	5.12859	0.194960
$693$	0	0
$694$	−16.5424	−0.627943
$695$	0	0
$696$	6.69401	0.253736
$697$	−0.280060	−0.0106080
$698$	−29.2269	−1.10625
$699$	41.9017	1.58487
$700$	0	0
$701$	18.9662	0.716344	0.358172	−	0.933656i	$-0.383400\pi$
$701$	18.9662	0.716344	0.358172	+	0.933656i	$0.383400\pi$
$702$	12.7775	0.482256
$703$	−9.39242	−0.354242
$704$	0	0
$705$	0	0
$706$	27.9200	1.05078
$707$	1.11251	0.0418403
$708$	3.13712	0.117900
$709$	8.38816	0.315024	0.157512	−	0.987517i	$-0.449653\pi$
$709$	8.38816	0.315024	0.157512	+	0.987517i	$0.449653\pi$
$710$	0	0
$711$	2.54206	0.0953347
$712$	−6.09017	−0.228239
$713$	−34.7560	−1.30162
$714$	0.496121	0.0185669
$715$	0	0
$716$	−14.4394	−0.539625
$717$	32.3542	1.20829
$718$	−17.0142	−0.634964
$719$	7.54709	0.281459	0.140730	−	0.990048i	$-0.455055\pi$
$719$	7.54709	0.281459	0.140730	+	0.990048i	$0.455055\pi$
$720$	0	0
$721$	−2.83826	−0.105702
$722$	14.7517	0.549000
$723$	14.5846	0.542409
$724$	11.9061	0.442486
$725$	0	0
$726$	0	0
$727$	24.2826	0.900593	0.450297	−	0.892879i	$-0.351318\pi$
$727$	24.2826	0.900593	0.450297	+	0.892879i	$0.351318\pi$
$728$	11.7082	0.433935
$729$	29.5066	1.09284
$730$	0	0
$731$	0.221244	0.00818301
$732$	−15.6842	−0.579705
$733$	21.4016	0.790486	0.395243	−	0.918577i	$-0.370660\pi$
$733$	21.4016	0.790486	0.395243	+	0.918577i	$0.370660\pi$
$734$	−29.4391	−1.08662
$735$	0	0
$736$	−3.91525	−0.144318
$737$	0	0
$738$	−1.74935	−0.0643944
$739$	35.1561	1.29324	0.646619	−	0.762813i	$-0.276182\pi$
$739$	35.1561	1.29324	0.646619	+	0.762813i	$0.276182\pi$
$740$	0	0
$741$	−7.78729	−0.286073
$742$	11.1409	0.408995
$743$	−34.1000	−1.25101	−0.625504	−	0.780221i	$-0.715107\pi$
$743$	−34.1000	−1.25101	−0.625504	+	0.780221i	$0.715107\pi$
$744$	14.3634	0.526588
$745$	0	0
$746$	16.0743	0.588523
$747$	−4.22148	−0.154456
$748$	0	0
$749$	11.1817	0.408572
$750$	0	0
$751$	−35.8201	−1.30709	−0.653547	−	0.756886i	$-0.726720\pi$
$751$	−35.8201	−1.30709	−0.653547	+	0.756886i	$0.726720\pi$
$752$	8.87707	0.323713
$753$	2.12230	0.0773409
$754$	9.66023	0.351805
$755$	0	0
$756$	27.4384	0.997924
$757$	24.2280	0.880580	0.440290	−	0.897856i	$-0.354876\pi$
$757$	24.2280	0.880580	0.440290	+	0.897856i	$0.354876\pi$
$758$	−18.1230	−0.658256
$759$	0	0
$760$	0	0
$761$	10.6573	0.386326	0.193163	−	0.981167i	$-0.438125\pi$
$761$	10.6573	0.386326	0.193163	+	0.981167i	$0.438125\pi$
$762$	−23.4016	−0.847750
$763$	−39.4260	−1.42732
$764$	10.5181	0.380531
$765$	0	0
$766$	−13.2121	−0.477372
$767$	4.52724	0.163469
$768$	1.61803	0.0583858
$769$	25.8297	0.931444	0.465722	−	0.884931i	$-0.345795\pi$
$769$	25.8297	0.931444	0.465722	+	0.884931i	$0.345795\pi$
$770$	0	0
$771$	7.22289	0.260126
$772$	4.86869	0.175228
$773$	−12.0580	−0.433698	−0.216849	−	0.976205i	$-0.569578\pi$
$773$	−12.0580	−0.433698	−0.216849	+	0.976205i	$0.569578\pi$
$774$	1.38197	0.0496737
$775$	0	0
$776$	7.30225	0.262136
$777$	−36.9706	−1.32631
$778$	26.5245	0.950950
$779$	9.43977	0.338215
$780$	0	0
$781$	0	0
$782$	−0.239419	−0.00856161
$783$	22.6389	0.809049
$784$	18.1422	0.647934
$785$	0	0
$786$	−24.7974	−0.884492
$787$	−18.1572	−0.647235	−0.323618	−	0.946188i	$-0.604899\pi$
$787$	−18.1572	−0.647235	−0.323618	+	0.946188i	$0.604899\pi$
$788$	−15.9760	−0.569122
$789$	22.9422	0.816765
$790$	0	0
$791$	62.9867	2.23955
$792$	0	0
$793$	−22.6342	−0.803762
$794$	−30.3246	−1.07618
$795$	0	0
$796$	16.7076	0.592184
$797$	1.61067	0.0570527	0.0285263	−	0.999593i	$-0.490919\pi$
$797$	1.61067	0.0570527	0.0285263	+	0.999593i	$0.490919\pi$
$798$	−16.7224	−0.591967
$799$	0.542836	0.0192042
$800$	0	0
$801$	−2.32624	−0.0821936
$802$	−19.4762	−0.687727
$803$	0	0
$804$	4.03818	0.142416
$805$	0	0
$806$	20.7281	0.730115
$807$	−51.7694	−1.82237
$808$	0.221872	0.00780544
$809$	25.6203	0.900763	0.450382	−	0.892836i	$-0.351288\pi$
$809$	25.6203	0.900763	0.450382	+	0.892836i	$0.351288\pi$
$810$	0	0
$811$	43.8508	1.53981	0.769904	−	0.638160i	$-0.220304\pi$
$811$	43.8508	1.53981	0.769904	+	0.638160i	$0.220304\pi$
$812$	20.7444	0.727984
$813$	1.71737	0.0602306
$814$	0	0
$815$	0	0
$816$	0.0989434	0.00346371
$817$	−7.45731	−0.260898
$818$	28.3303	0.990544
$819$	4.47214	0.156269
$820$	0	0
$821$	−17.6022	−0.614321	−0.307160	−	0.951658i	$-0.599379\pi$
$821$	−17.6022	−0.614321	−0.307160	+	0.951658i	$0.599379\pi$
$822$	1.78690	0.0623253
$823$	−12.6552	−0.441133	−0.220566	−	0.975372i	$-0.570791\pi$
$823$	−12.6552	−0.441133	−0.220566	+	0.975372i	$0.570791\pi$
$824$	−0.566045	−0.0197191
$825$	0	0
$826$	9.72177	0.338264
$827$	8.84431	0.307547	0.153773	−	0.988106i	$-0.450857\pi$
$827$	8.84431	0.307547	0.153773	+	0.988106i	$0.450857\pi$
$828$	−1.49549	−0.0519720
$829$	37.7230	1.31017	0.655087	−	0.755553i	$-0.272632\pi$
$829$	37.7230	1.31017	0.655087	+	0.755553i	$0.272632\pi$
$830$	0	0
$831$	−10.7328	−0.372317
$832$	2.33501	0.0809520
$833$	1.10940	0.0384384
$834$	16.0284	0.555018
$835$	0	0
$836$	0	0
$837$	48.5765	1.67905
$838$	15.4826	0.534837
$839$	−38.4879	−1.32875	−0.664374	−	0.747400i	$-0.731302\pi$
$839$	−38.4879	−1.32875	−0.664374	+	0.747400i	$0.731302\pi$
$840$	0	0
$841$	−11.8842	−0.409800
$842$	−21.4863	−0.740468
$843$	25.3164	0.871945
$844$	−15.7460	−0.542000
$845$	0	0
$846$	3.39074	0.116576
$847$	0	0
$848$	2.22187	0.0762994
$849$	36.4066	1.24947
$850$	0	0
$851$	17.8413	0.611594
$852$	14.2651	0.488714
$853$	50.8896	1.74243	0.871213	−	0.490905i	$-0.163334\pi$
$853$	50.8896	1.74243	0.871213	+	0.490905i	$0.163334\pi$
$854$	−48.6045	−1.66321
$855$	0	0
$856$	2.23002	0.0762204
$857$	11.5197	0.393506	0.196753	−	0.980453i	$-0.436960\pi$
$857$	11.5197	0.393506	0.196753	+	0.980453i	$0.436960\pi$
$858$	0	0
$859$	23.9497	0.817153	0.408577	−	0.912724i	$-0.366025\pi$
$859$	23.9497	0.817153	0.408577	+	0.912724i	$0.366025\pi$
$860$	0	0
$861$	37.1570	1.26631
$862$	−26.4390	−0.900516
$863$	−40.0096	−1.36194	−0.680971	−	0.732310i	$-0.738442\pi$
$863$	−40.0096	−1.36194	−0.680971	+	0.732310i	$0.738442\pi$
$864$	5.47214	0.186166
$865$	0	0
$866$	−32.8819	−1.11737
$867$	−27.5005	−0.933967
$868$	44.5114	1.51081
$869$	0	0
$870$	0	0
$871$	5.82757	0.197460
$872$	−7.86288	−0.266271
$873$	2.78921	0.0944005
$874$	8.06992	0.272969
$875$	0	0
$876$	8.73117	0.294999
$877$	−25.9821	−0.877353	−0.438677	−	0.898645i	$-0.644553\pi$
$877$	−25.9821	−0.877353	−0.438677	+	0.898645i	$0.644553\pi$
$878$	12.1796	0.411040
$879$	29.4300	0.992648
$880$	0	0
$881$	25.1372	0.846893	0.423446	−	0.905921i	$-0.360820\pi$
$881$	25.1372	0.846893	0.423446	+	0.905921i	$0.360820\pi$
$882$	6.92969	0.233335
$883$	43.4707	1.46291	0.731453	−	0.681892i	$-0.238843\pi$
$883$	43.4707	1.46291	0.731453	+	0.681892i	$0.238843\pi$
$884$	0.142787	0.00480244
$885$	0	0
$886$	16.6090	0.557991
$887$	−28.6080	−0.960563	−0.480281	−	0.877114i	$-0.659465\pi$
$887$	−28.6080	−0.960563	−0.480281	+	0.877114i	$0.659465\pi$
$888$	−7.37319	−0.247428
$889$	−72.5202	−2.43225
$890$	0	0
$891$	0	0
$892$	14.5556	0.487358
$893$	−18.2970	−0.612285
$894$	−14.2263	−0.475798
$895$	0	0
$896$	5.01420	0.167513
$897$	14.7923	0.493901
$898$	5.36364	0.178987
$899$	36.7255	1.22487
$900$	0	0
$901$	0.135868	0.00452643
$902$	0	0
$903$	−29.3536	−0.976827
$904$	12.5617	0.417795
$905$	0	0
$906$	−34.9339	−1.16060
$907$	−47.7110	−1.58422	−0.792108	−	0.610381i	$-0.791017\pi$
$907$	−47.7110	−1.58422	−0.792108	+	0.610381i	$0.791017\pi$
$908$	−9.83656	−0.326438
$909$	0.0847477	0.00281090
$910$	0	0
$911$	49.8139	1.65041	0.825203	−	0.564836i	$-0.191060\pi$
$911$	49.8139	1.65041	0.825203	+	0.564836i	$0.191060\pi$
$912$	−3.33501	−0.110433
$913$	0	0
$914$	3.61237	0.119487
$915$	0	0
$916$	−15.5479	−0.513716
$917$	−76.8456	−2.53767
$918$	0.334623	0.0110442
$919$	−42.8988	−1.41510	−0.707550	−	0.706664i	$-0.750199\pi$
$919$	−42.8988	−1.41510	−0.707550	+	0.706664i	$0.750199\pi$
$920$	0	0
$921$	−20.0344	−0.660157
$922$	40.6625	1.33915
$923$	20.5862	0.677602
$924$	0	0
$925$	0	0
$926$	2.11880	0.0696281
$927$	−0.216210	−0.00710127
$928$	4.13712	0.135808
$929$	−3.96430	−0.130065	−0.0650323	−	0.997883i	$-0.520715\pi$
$929$	−3.96430	−0.130065	−0.0650323	+	0.997883i	$0.520715\pi$
$930$	0	0
$931$	−37.3937	−1.22553
$932$	25.8967	0.848274
$933$	15.2257	0.498465
$934$	13.7549	0.450075
$935$	0	0
$936$	0.891895	0.0291525
$937$	2.11919	0.0692309	0.0346155	−	0.999401i	$-0.488979\pi$
$937$	2.11919	0.0692309	0.0346155	+	0.999401i	$0.488979\pi$
$938$	12.5141	0.408600
$939$	−24.6454	−0.804273
$940$	0	0
$941$	5.04462	0.164450	0.0822250	−	0.996614i	$-0.473797\pi$
$941$	5.04462	0.164450	0.0822250	+	0.996614i	$0.473797\pi$
$942$	−5.52514	−0.180019
$943$	−17.9313	−0.583923
$944$	1.93885	0.0631042
$945$	0	0
$946$	0	0
$947$	0.986192	0.0320470	0.0160235	−	0.999872i	$-0.494899\pi$
$947$	0.986192	0.0320470	0.0160235	+	0.999872i	$0.494899\pi$
$948$	−10.7683	−0.349739
$949$	12.6001	0.409017
$950$	0	0
$951$	21.7734	0.706050
$952$	0.306620	0.00993761
$953$	−22.9625	−0.743828	−0.371914	−	0.928267i	$-0.621298\pi$
$953$	−22.9625	−0.743828	−0.371914	+	0.928267i	$0.621298\pi$
$954$	0.848680	0.0274770
$955$	0	0
$956$	19.9960	0.646718
$957$	0	0
$958$	−31.4107	−1.01484
$959$	5.53751	0.178815
$960$	0	0
$961$	47.8024	1.54201
$962$	−10.6404	−0.343059
$963$	0.851791	0.0274486
$964$	9.01381	0.290315
$965$	0	0
$966$	31.7650	1.02202
$967$	−20.1267	−0.647231	−0.323616	−	0.946189i	$-0.604898\pi$
$967$	−20.1267	−0.647231	−0.323616	+	0.946189i	$0.604898\pi$
$968$	0	0
$969$	−0.203937	−0.00655141
$970$	0	0
$971$	−21.9357	−0.703951	−0.351976	−	0.936009i	$-0.614490\pi$
$971$	−21.9357	−0.703951	−0.351976	+	0.936009i	$0.614490\pi$
$972$	3.94427	0.126513
$973$	49.6711	1.59238
$974$	7.51032	0.240646
$975$	0	0
$976$	−9.69338	−0.310278
$977$	−59.0578	−1.88943	−0.944714	−	0.327896i	$-0.893660\pi$
$977$	−59.0578	−1.88943	−0.944714	+	0.327896i	$0.893660\pi$
$978$	−28.1706	−0.900795
$979$	0	0
$980$	0	0
$981$	−3.00335	−0.0958896
$982$	−11.2618	−0.359377
$983$	−48.3411	−1.54184	−0.770921	−	0.636931i	$-0.780204\pi$
$983$	−48.3411	−1.54184	−0.770921	+	0.636931i	$0.780204\pi$
$984$	7.41036	0.236234
$985$	0	0
$986$	0.252987	0.00805674
$987$	−72.0209	−2.29245
$988$	−4.81281	−0.153116
$989$	14.1655	0.450437
$990$	0	0
$991$	−55.0154	−1.74762	−0.873811	−	0.486266i	$-0.838359\pi$
$991$	−55.0154	−1.74762	−0.873811	+	0.486266i	$0.838359\pi$
$992$	8.87707	0.281847
$993$	−6.18471	−0.196266
$994$	44.2067	1.40215
$995$	0	0
$996$	17.8825	0.566628
$997$	22.9699	0.727465	0.363733	−	0.931503i	$-0.381502\pi$
$997$	22.9699	0.727465	0.363733	+	0.931503i	$0.381502\pi$
$998$	26.9808	0.854063
$999$	−24.9359	−0.788937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6050.2.a.dd.1.3		4
5.2	odd	4		1210.2.b.k.969.1		8
5.3	odd	4		1210.2.b.k.969.7		8
5.4	even	2		6050.2.a.di.1.2		4
11.5	even	5		550.2.h.n.201.1		8
11.9	even	5		550.2.h.n.301.1		8
11.10	odd	2		6050.2.a.dl.1.4		4
55.9	even	10		550.2.h.j.301.2		8
55.27	odd	20		110.2.j.b.69.4	yes	16
55.32	even	4		1210.2.b.l.969.5		8
55.38	odd	20		110.2.j.b.69.2	yes	16
55.42	odd	20		110.2.j.b.59.2	✓	16
55.43	even	4		1210.2.b.l.969.3		8
55.49	even	10		550.2.h.j.201.2		8
55.53	odd	20		110.2.j.b.59.4	yes	16
55.54	odd	2		6050.2.a.da.1.1		4
165.38	even	20		990.2.ba.h.289.3		16
165.53	even	20		990.2.ba.h.829.1		16
165.137	even	20		990.2.ba.h.289.1		16
165.152	even	20		990.2.ba.h.829.3		16
220.27	even	20		880.2.cd.b.289.2		16
220.163	even	20		880.2.cd.b.609.2		16
220.203	even	20		880.2.cd.b.289.4		16
220.207	even	20		880.2.cd.b.609.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.2	✓	16	55.42	odd	20
110.2.j.b.59.4	yes	16	55.53	odd	20
110.2.j.b.69.2	yes	16	55.38	odd	20
110.2.j.b.69.4	yes	16	55.27	odd	20
550.2.h.j.201.2		8	55.49	even	10
550.2.h.j.301.2		8	55.9	even	10
550.2.h.n.201.1		8	11.5	even	5
550.2.h.n.301.1		8	11.9	even	5
880.2.cd.b.289.2		16	220.27	even	20
880.2.cd.b.289.4		16	220.203	even	20
880.2.cd.b.609.2		16	220.163	even	20
880.2.cd.b.609.4		16	220.207	even	20
990.2.ba.h.289.1		16	165.137	even	20
990.2.ba.h.289.3		16	165.38	even	20
990.2.ba.h.829.1		16	165.53	even	20
990.2.ba.h.829.3		16	165.152	even	20
1210.2.b.k.969.1		8	5.2	odd	4
1210.2.b.k.969.7		8	5.3	odd	4
1210.2.b.l.969.3		8	55.43	even	4
1210.2.b.l.969.5		8	55.32	even	4
6050.2.a.da.1.1		4	55.54	odd	2
6050.2.a.dd.1.3		4	1.1	even	1	trivial
6050.2.a.di.1.2		4	5.4	even	2
6050.2.a.dl.1.4		4	11.10	odd	2

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:	\( N \)	\(=\)	\( 6050 = 2 \cdot 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6050.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -5.01420 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -5.01420 q^{7} -1.00000 q^{8} -0.381966 q^{9} +1.61803 q^{12} +2.33501 q^{13} +5.01420 q^{14} +1.00000 q^{16} +0.0611504 q^{17} +0.381966 q^{18} -2.06115 q^{19} -8.11314 q^{21} +3.91525 q^{23} -1.61803 q^{24} -2.33501 q^{26} -5.47214 q^{27} -5.01420 q^{28} -4.13712 q^{29} -8.87707 q^{31} -1.00000 q^{32} -0.0611504 q^{34} -0.381966 q^{36} +4.55688 q^{37} +2.06115 q^{38} +3.77813 q^{39} -4.57985 q^{41} +8.11314 q^{42} +3.61803 q^{43} -3.91525 q^{46} +8.87707 q^{47} +1.61803 q^{48} +18.1422 q^{49} +0.0989434 q^{51} +2.33501 q^{52} +2.22187 q^{53} +5.47214 q^{54} +5.01420 q^{56} -3.33501 q^{57} +4.13712 q^{58} +1.93885 q^{59} -9.69338 q^{61} +8.87707 q^{62} +1.91525 q^{63} +1.00000 q^{64} +2.49573 q^{67} +0.0611504 q^{68} +6.33501 q^{69} +8.81631 q^{71} +0.381966 q^{72} +5.39616 q^{73} -4.55688 q^{74} -2.06115 q^{76} -3.77813 q^{78} -6.65520 q^{79} -7.70820 q^{81} +4.57985 q^{82} +11.0520 q^{83} -8.11314 q^{84} -3.61803 q^{86} -6.69401 q^{87} +6.09017 q^{89} -11.7082 q^{91} +3.91525 q^{92} -14.3634 q^{93} -8.87707 q^{94} -1.61803 q^{96} -7.30225 q^{97} -18.1422 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{6} + 2 q^{7} - 4 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^6 + 2 * q^7 - 4 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{6} + 2 q^{7} - 4 q^{8} - 6 q^{9} + 2 q^{12} - 6 q^{13} - 2 q^{14} + 4 q^{16} - 2 q^{17} + 6 q^{18} - 6 q^{19} - 4 q^{21} - 2 q^{24} + 6 q^{26} - 4 q^{27} + 2 q^{28} - 14 q^{29} - 16 q^{31} - 4 q^{32} + 2 q^{34} - 6 q^{36} + 16 q^{37} + 6 q^{38} + 2 q^{39} - 10 q^{41} + 4 q^{42} + 10 q^{43} + 16 q^{47} + 2 q^{48} + 24 q^{49} - 6 q^{51} - 6 q^{52} + 22 q^{53} + 4 q^{54} - 2 q^{56} + 2 q^{57} + 14 q^{58} + 10 q^{59} - 10 q^{61} + 16 q^{62} - 8 q^{63} + 4 q^{64} + 10 q^{67} - 2 q^{68} + 10 q^{69} + 26 q^{71} + 6 q^{72} + 4 q^{73} - 16 q^{74} - 6 q^{76} - 2 q^{78} + 6 q^{79} - 4 q^{81} + 10 q^{82} + 18 q^{83} - 4 q^{84} - 10 q^{86} - 22 q^{87} + 2 q^{89} - 20 q^{91} + 2 q^{93} - 16 q^{94} - 2 q^{96} + 28 q^{97} - 24 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^6 + 2 * q^7 - 4 * q^8 - 6 * q^9 + 2 * q^12 - 6 * q^13 - 2 * q^14 + 4 * q^16 - 2 * q^17 + 6 * q^18 - 6 * q^19 - 4 * q^21 - 2 * q^24 + 6 * q^26 - 4 * q^27 + 2 * q^28 - 14 * q^29 - 16 * q^31 - 4 * q^32 + 2 * q^34 - 6 * q^36 + 16 * q^37 + 6 * q^38 + 2 * q^39 - 10 * q^41 + 4 * q^42 + 10 * q^43 + 16 * q^47 + 2 * q^48 + 24 * q^49 - 6 * q^51 - 6 * q^52 + 22 * q^53 + 4 * q^54 - 2 * q^56 + 2 * q^57 + 14 * q^58 + 10 * q^59 - 10 * q^61 + 16 * q^62 - 8 * q^63 + 4 * q^64 + 10 * q^67 - 2 * q^68 + 10 * q^69 + 26 * q^71 + 6 * q^72 + 4 * q^73 - 16 * q^74 - 6 * q^76 - 2 * q^78 + 6 * q^79 - 4 * q^81 + 10 * q^82 + 18 * q^83 - 4 * q^84 - 10 * q^86 - 22 * q^87 + 2 * q^89 - 20 * q^91 + 2 * q^93 - 16 * q^94 - 2 * q^96 + 28 * q^97 - 24 * q^98

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