LMFDB - Embedded newform 4025.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.122821.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 4x^{3} + 4x^{2} + 3x - 1 $ x^5 - 2x^4 - 4x^3 + 4x^2 + 3x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.266708$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.733292 q^{2} +2.28713 q^{3} -1.46228 q^{4} +1.67714 q^{6} +1.00000 q^{7} -2.53886 q^{8} +2.23098 q^{9} +O(q^{10})$	\(q+0.733292 q^{2} +2.28713 q^{3} -1.46228 q^{4} +1.67714 q^{6} +1.00000 q^{7} -2.53886 q^{8} +2.23098 q^{9} -1.13397 q^{11} -3.34444 q^{12} -2.86841 q^{13} +0.733292 q^{14} +1.06284 q^{16} +3.10402 q^{17} +1.63596 q^{18} +3.94929 q^{19} +2.28713 q^{21} -0.831532 q^{22} -1.00000 q^{23} -5.80672 q^{24} -2.10338 q^{26} -1.75886 q^{27} -1.46228 q^{28} +9.89909 q^{29} -4.11469 q^{31} +5.85710 q^{32} -2.59354 q^{33} +2.27615 q^{34} -3.26232 q^{36} +11.6257 q^{37} +2.89598 q^{38} -6.56044 q^{39} -5.43200 q^{41} +1.67714 q^{42} +9.33312 q^{43} +1.65819 q^{44} -0.733292 q^{46} +10.1555 q^{47} +2.43085 q^{48} +1.00000 q^{49} +7.09930 q^{51} +4.19443 q^{52} -1.15554 q^{53} -1.28976 q^{54} -2.53886 q^{56} +9.03255 q^{57} +7.25892 q^{58} -0.424170 q^{59} +4.49645 q^{61} -3.01727 q^{62} +2.23098 q^{63} +2.16929 q^{64} -1.90182 q^{66} +6.95759 q^{67} -4.53895 q^{68} -2.28713 q^{69} -7.94018 q^{71} -5.66415 q^{72} +4.12844 q^{73} +8.52503 q^{74} -5.77498 q^{76} -1.13397 q^{77} -4.81071 q^{78} -3.37584 q^{79} -10.7157 q^{81} -3.98324 q^{82} +6.96848 q^{83} -3.34444 q^{84} +6.84390 q^{86} +22.6405 q^{87} +2.87900 q^{88} +9.78134 q^{89} -2.86841 q^{91} +1.46228 q^{92} -9.41085 q^{93} +7.44698 q^{94} +13.3960 q^{96} -14.7782 q^{97} +0.733292 q^{98} -2.52986 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 7 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 7 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	$ 5 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 7 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - 11 q^{11} + 14 q^{12} + 7 q^{13} + 3 q^{14} - q^{16} - q^{17} + 17 q^{18} + 2 q^{19} + 6 q^{21} - 2 q^{22} - 5 q^{23} + 12 q^{24} + 8 q^{26} + 15 q^{27} + 3 q^{28} - 14 q^{29} - 6 q^{31} + 4 q^{32} - 22 q^{33} + 4 q^{34} + 28 q^{36} + q^{37} + 31 q^{38} + 15 q^{39} + 7 q^{41} + 7 q^{42} + 12 q^{43} - 11 q^{44} - 3 q^{46} + 24 q^{47} + 4 q^{48} + 5 q^{49} - 28 q^{51} + 36 q^{52} + 21 q^{53} + 49 q^{54} + 3 q^{56} + 15 q^{57} - 9 q^{58} - q^{59} + 7 q^{61} + 26 q^{62} + 5 q^{63} - 15 q^{64} - 45 q^{66} + 35 q^{67} - 43 q^{68} - 6 q^{69} - 32 q^{71} + 36 q^{72} + 7 q^{73} - 10 q^{74} + 10 q^{76} - 11 q^{77} + 8 q^{78} + 18 q^{79} + 21 q^{81} - 33 q^{82} + q^{83} + 14 q^{84} - 26 q^{86} + 18 q^{87} - 41 q^{88} + q^{89} + 7 q^{91} - 3 q^{92} + 19 q^{93} + 14 q^{94} + 26 q^{96} + 9 q^{97} + 3 q^{98} - 54 q^{99}+O(q^{100}) $ 5 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 7 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - 11 * q^11 + 14 * q^12 + 7 * q^13 + 3 * q^14 - q^16 - q^17 + 17 * q^18 + 2 * q^19 + 6 * q^21 - 2 * q^22 - 5 * q^23 + 12 * q^24 + 8 * q^26 + 15 * q^27 + 3 * q^28 - 14 * q^29 - 6 * q^31 + 4 * q^32 - 22 * q^33 + 4 * q^34 + 28 * q^36 + q^37 + 31 * q^38 + 15 * q^39 + 7 * q^41 + 7 * q^42 + 12 * q^43 - 11 * q^44 - 3 * q^46 + 24 * q^47 + 4 * q^48 + 5 * q^49 - 28 * q^51 + 36 * q^52 + 21 * q^53 + 49 * q^54 + 3 * q^56 + 15 * q^57 - 9 * q^58 - q^59 + 7 * q^61 + 26 * q^62 + 5 * q^63 - 15 * q^64 - 45 * q^66 + 35 * q^67 - 43 * q^68 - 6 * q^69 - 32 * q^71 + 36 * q^72 + 7 * q^73 - 10 * q^74 + 10 * q^76 - 11 * q^77 + 8 * q^78 + 18 * q^79 + 21 * q^81 - 33 * q^82 + q^83 + 14 * q^84 - 26 * q^86 + 18 * q^87 - 41 * q^88 + q^89 + 7 * q^91 - 3 * q^92 + 19 * q^93 + 14 * q^94 + 26 * q^96 + 9 * q^97 + 3 * q^98 - 54 * 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 $

$2$	0.733292	0.518516	0.259258	−	0.965808i	$-0.416522\pi$
$2$	0.733292	0.518516	0.259258	+	0.965808i	$0.416522\pi$
$3$	2.28713	1.32048	0.660238	−	0.751056i	$-0.270455\pi$
$3$	2.28713	1.32048	0.660238	+	0.751056i	$0.270455\pi$
$4$	−1.46228	−0.731142
$5$	0	0
$5$	0	0
$6$	1.67714	0.684688
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.53886	−0.897624
$9$	2.23098	0.743659
$10$	0	0
$11$	−1.13397	−0.341905	−0.170953	−	0.985279i	$-0.554685\pi$
$11$	−1.13397	−0.341905	−0.170953	+	0.985279i	$0.554685\pi$
$12$	−3.34444	−0.965455
$13$	−2.86841	−0.795554	−0.397777	−	0.917482i	$-0.630218\pi$
$13$	−2.86841	−0.795554	−0.397777	+	0.917482i	$0.630218\pi$
$14$	0.733292	0.195980
$15$	0	0
$16$	1.06284	0.265710
$17$	3.10402	0.752835	0.376417	−	0.926450i	$-0.377156\pi$
$17$	3.10402	0.752835	0.376417	+	0.926450i	$0.377156\pi$
$18$	1.63596	0.385599
$19$	3.94929	0.906030	0.453015	−	0.891503i	$-0.350348\pi$
$19$	3.94929	0.906030	0.453015	+	0.891503i	$0.350348\pi$
$20$	0	0
$21$	2.28713	0.499093
$22$	−0.831532	−0.177283
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−5.80672	−1.18529
$25$	0	0
$26$	−2.10338	−0.412507
$27$	−1.75886	−0.338492
$28$	−1.46228	−0.276346
$29$	9.89909	1.83822	0.919108	−	0.394006i	$-0.128911\pi$
$29$	9.89909	1.83822	0.919108	+	0.394006i	$0.128911\pi$
$30$	0	0
$31$	−4.11469	−0.739021	−0.369510	−	0.929227i	$-0.620475\pi$
$31$	−4.11469	−0.739021	−0.369510	+	0.929227i	$0.620475\pi$
$32$	5.85710	1.03540
$33$	−2.59354	−0.451478
$34$	2.27615	0.390357
$35$	0	0
$36$	−3.26232	−0.543720
$37$	11.6257	1.91125	0.955627	−	0.294579i	$-0.0951796\pi$
$37$	11.6257	1.91125	0.955627	+	0.294579i	$0.0951796\pi$
$38$	2.89598	0.469790
$39$	−6.56044	−1.05051
$40$	0	0
$41$	−5.43200	−0.848336	−0.424168	−	0.905584i	$-0.639433\pi$
$41$	−5.43200	−0.848336	−0.424168	+	0.905584i	$0.639433\pi$
$42$	1.67714	0.258788
$43$	9.33312	1.42329	0.711644	−	0.702540i	$-0.247951\pi$
$43$	9.33312	1.42329	0.711644	+	0.702540i	$0.247951\pi$
$44$	1.65819	0.249981
$45$	0	0
$46$	−0.733292	−0.108118
$47$	10.1555	1.48134	0.740669	−	0.671870i	$-0.234509\pi$
$47$	10.1555	1.48134	0.740669	+	0.671870i	$0.234509\pi$
$48$	2.43085	0.350863
$49$	1.00000	0.142857
$50$	0	0
$51$	7.09930	0.994101
$52$	4.19443	0.581663
$53$	−1.15554	−0.158726	−0.0793630	−	0.996846i	$-0.525289\pi$
$53$	−1.15554	−0.158726	−0.0793630	+	0.996846i	$0.525289\pi$
$54$	−1.28976	−0.175514
$55$	0	0
$56$	−2.53886	−0.339270
$57$	9.03255	1.19639
$58$	7.25892	0.953144
$59$	−0.424170	−0.0552222	−0.0276111	−	0.999619i	$-0.508790\pi$
$59$	−0.424170	−0.0552222	−0.0276111	+	0.999619i	$0.508790\pi$
$60$	0	0
$61$	4.49645	0.575711	0.287856	−	0.957674i	$-0.407058\pi$
$61$	4.49645	0.575711	0.287856	+	0.957674i	$0.407058\pi$
$62$	−3.01727	−0.383194
$63$	2.23098	0.281077
$64$	2.16929	0.271161
$65$	0	0
$66$	−1.90182	−0.234098
$67$	6.95759	0.850004	0.425002	−	0.905192i	$-0.360273\pi$
$67$	6.95759	0.850004	0.425002	+	0.905192i	$0.360273\pi$
$68$	−4.53895	−0.550429
$69$	−2.28713	−0.275338
$70$	0	0
$71$	−7.94018	−0.942326	−0.471163	−	0.882046i	$-0.656166\pi$
$71$	−7.94018	−0.942326	−0.471163	+	0.882046i	$0.656166\pi$
$72$	−5.66415	−0.667526
$73$	4.12844	0.483197	0.241598	−	0.970376i	$-0.422328\pi$
$73$	4.12844	0.483197	0.241598	+	0.970376i	$0.422328\pi$
$74$	8.52503	0.991015
$75$	0	0
$76$	−5.77498	−0.662436
$77$	−1.13397	−0.129228
$78$	−4.81071	−0.544706
$79$	−3.37584	−0.379812	−0.189906	−	0.981802i	$-0.560818\pi$
$79$	−3.37584	−0.379812	−0.189906	+	0.981802i	$0.560818\pi$
$80$	0	0
$81$	−10.7157	−1.19063
$82$	−3.98324	−0.439875
$83$	6.96848	0.764890	0.382445	−	0.923978i	$-0.375082\pi$
$83$	6.96848	0.764890	0.382445	+	0.923978i	$0.375082\pi$
$84$	−3.34444	−0.364908
$85$	0	0
$86$	6.84390	0.737997
$87$	22.6405	2.42732
$88$	2.87900	0.306902
$89$	9.78134	1.03682	0.518410	−	0.855132i	$-0.326524\pi$
$89$	9.78134	1.03682	0.518410	+	0.855132i	$0.326524\pi$
$90$	0	0
$91$	−2.86841	−0.300691
$92$	1.46228	0.152454
$93$	−9.41085	−0.975860
$94$	7.44698	0.768097
$95$	0	0
$96$	13.3960	1.36722
$97$	−14.7782	−1.50050	−0.750249	−	0.661156i	$-0.770066\pi$
$97$	−14.7782	−1.50050	−0.750249	+	0.661156i	$0.770066\pi$
$98$	0.733292	0.0740737
$99$	−2.52986	−0.254261
$100$	0	0
$101$	−6.16466	−0.613406	−0.306703	−	0.951805i	$-0.599226\pi$
$101$	−6.16466	−0.613406	−0.306703	+	0.951805i	$0.599226\pi$
$102$	5.20586	0.515457
$103$	−7.93368	−0.781729	−0.390864	−	0.920448i	$-0.627824\pi$
$103$	−7.93368	−0.781729	−0.390864	+	0.920448i	$0.627824\pi$
$104$	7.28250	0.714108
$105$	0	0
$106$	−0.847350	−0.0823019
$107$	9.70742	0.938452	0.469226	−	0.883078i	$-0.344533\pi$
$107$	9.70742	0.938452	0.469226	+	0.883078i	$0.344533\pi$
$108$	2.57195	0.247486
$109$	15.1030	1.44660	0.723301	−	0.690533i	$-0.242624\pi$
$109$	15.1030	1.44660	0.723301	+	0.690533i	$0.242624\pi$
$110$	0	0
$111$	26.5895	2.52377
$112$	1.06284	0.100429
$113$	8.99925	0.846579	0.423289	−	0.905995i	$-0.360875\pi$
$113$	8.99925	0.846579	0.423289	+	0.905995i	$0.360875\pi$
$114$	6.62350	0.620347
$115$	0	0
$116$	−14.4753	−1.34400
$117$	−6.39936	−0.591621
$118$	−0.311040	−0.0286336
$119$	3.10402	0.284545
$120$	0	0
$121$	−9.71411	−0.883101
$122$	3.29721	0.298515
$123$	−12.4237	−1.12021
$124$	6.01685	0.540329
$125$	0	0
$126$	1.63596	0.145743
$127$	16.9953	1.50809	0.754044	−	0.656824i	$-0.228101\pi$
$127$	16.9953	1.50809	0.754044	+	0.656824i	$0.228101\pi$
$128$	−10.1235	−0.894797
$129$	21.3461	1.87942
$130$	0	0
$131$	6.99715	0.611344	0.305672	−	0.952137i	$-0.401119\pi$
$131$	6.99715	0.611344	0.305672	+	0.952137i	$0.401119\pi$
$132$	3.79249	0.330094
$133$	3.94929	0.342447
$134$	5.10194	0.440741
$135$	0	0
$136$	−7.88068	−0.675762
$137$	−5.70971	−0.487814	−0.243907	−	0.969799i	$-0.578429\pi$
$137$	−5.70971	−0.487814	−0.243907	+	0.969799i	$0.578429\pi$
$138$	−1.67714	−0.142767
$139$	−8.27361	−0.701758	−0.350879	−	0.936421i	$-0.614117\pi$
$139$	−8.27361	−0.701758	−0.350879	+	0.936421i	$0.614117\pi$
$140$	0	0
$141$	23.2271	1.95607
$142$	−5.82247	−0.488611
$143$	3.25270	0.272004
$144$	2.37117	0.197597
$145$	0	0
$146$	3.02735	0.250545
$147$	2.28713	0.188640
$148$	−17.0001	−1.39740
$149$	−16.5496	−1.35580	−0.677899	−	0.735155i	$-0.737109\pi$
$149$	−16.5496	−1.35580	−0.677899	+	0.735155i	$0.737109\pi$
$150$	0	0
$151$	3.08236	0.250839	0.125419	−	0.992104i	$-0.459972\pi$
$151$	3.08236	0.250839	0.125419	+	0.992104i	$0.459972\pi$
$152$	−10.0267	−0.813274
$153$	6.92499	0.559852
$154$	−0.831532	−0.0670068
$155$	0	0
$156$	9.59321	0.768072
$157$	−16.1448	−1.28849	−0.644247	−	0.764818i	$-0.722829\pi$
$157$	−16.1448	−1.28849	−0.644247	+	0.764818i	$0.722829\pi$
$158$	−2.47548	−0.196938
$159$	−2.64288	−0.209594
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−7.85771	−0.617360
$163$	1.49705	0.117258	0.0586290	−	0.998280i	$-0.481327\pi$
$163$	1.49705	0.117258	0.0586290	+	0.998280i	$0.481327\pi$
$164$	7.94312	0.620254
$165$	0	0
$166$	5.10993	0.396608
$167$	3.08534	0.238751	0.119375	−	0.992849i	$-0.461911\pi$
$167$	3.08534	0.238751	0.119375	+	0.992849i	$0.461911\pi$
$168$	−5.80672	−0.447998
$169$	−4.77222	−0.367094
$170$	0	0
$171$	8.81078	0.673777
$172$	−13.6477	−1.04063
$173$	14.4702	1.10015	0.550075	−	0.835115i	$-0.314599\pi$
$173$	14.4702	1.10015	0.550075	+	0.835115i	$0.314599\pi$
$174$	16.6021	1.25860
$175$	0	0
$176$	−1.20523	−0.0908475
$177$	−0.970133	−0.0729197
$178$	7.17257	0.537607
$179$	−16.5522	−1.23717	−0.618586	−	0.785717i	$-0.712294\pi$
$179$	−16.5522	−1.23717	−0.618586	+	0.785717i	$0.712294\pi$
$180$	0	0
$181$	4.58801	0.341024	0.170512	−	0.985356i	$-0.445458\pi$
$181$	4.58801	0.341024	0.170512	+	0.985356i	$0.445458\pi$
$182$	−2.10338	−0.155913
$183$	10.2840	0.760214
$184$	2.53886	0.187168
$185$	0	0
$186$	−6.90090	−0.505999
$187$	−3.51987	−0.257398
$188$	−14.8503	−1.08307
$189$	−1.75886	−0.127938
$190$	0	0
$191$	−13.6251	−0.985878	−0.492939	−	0.870064i	$-0.664077\pi$
$191$	−13.6251	−0.985878	−0.492939	+	0.870064i	$0.664077\pi$
$192$	4.96144	0.358061
$193$	−21.1953	−1.52567	−0.762834	−	0.646595i	$-0.776193\pi$
$193$	−21.1953	−1.52567	−0.762834	+	0.646595i	$0.776193\pi$
$194$	−10.8367	−0.778031
$195$	0	0
$196$	−1.46228	−0.104449
$197$	14.6377	1.04289	0.521445	−	0.853285i	$-0.325393\pi$
$197$	14.6377	1.04289	0.521445	+	0.853285i	$0.325393\pi$
$198$	−1.85513	−0.131838
$199$	−2.80337	−0.198726	−0.0993629	−	0.995051i	$-0.531680\pi$
$199$	−2.80337	−0.198726	−0.0993629	+	0.995051i	$0.531680\pi$
$200$	0	0
$201$	15.9129	1.12241
$202$	−4.52049	−0.318061
$203$	9.89909	0.694780
$204$	−10.3812	−0.726828
$205$	0	0
$206$	−5.81770	−0.405338
$207$	−2.23098	−0.155064
$208$	−3.04866	−0.211386
$209$	−4.47838	−0.309776
$210$	0	0
$211$	23.3558	1.60788	0.803940	−	0.594711i	$-0.202734\pi$
$211$	23.3558	1.60788	0.803940	+	0.594711i	$0.202734\pi$
$212$	1.68973	0.116051
$213$	−18.1602	−1.24432
$214$	7.11837	0.486602
$215$	0	0
$216$	4.46550	0.303839
$217$	−4.11469	−0.279324
$218$	11.0749	0.750086
$219$	9.44228	0.638050
$220$	0	0
$221$	−8.90359	−0.598921
$222$	19.4979	1.30861
$223$	1.62654	0.108921	0.0544605	−	0.998516i	$-0.482656\pi$
$223$	1.62654	0.108921	0.0544605	+	0.998516i	$0.482656\pi$
$224$	5.85710	0.391344
$225$	0	0
$226$	6.59908	0.438964
$227$	22.5035	1.49361	0.746805	−	0.665043i	$-0.231587\pi$
$227$	22.5035	1.49361	0.746805	+	0.665043i	$0.231587\pi$
$228$	−13.2082	−0.874731
$229$	−5.88789	−0.389083	−0.194541	−	0.980894i	$-0.562322\pi$
$229$	−5.88789	−0.389083	−0.194541	+	0.980894i	$0.562322\pi$
$230$	0	0
$231$	−2.59354	−0.170643
$232$	−25.1325	−1.65003
$233$	2.82115	0.184820	0.0924098	−	0.995721i	$-0.470543\pi$
$233$	2.82115	0.184820	0.0924098	+	0.995721i	$0.470543\pi$
$234$	−4.69260	−0.306765
$235$	0	0
$236$	0.620257	0.0403753
$237$	−7.72100	−0.501533
$238$	2.27615	0.147541
$239$	−17.6587	−1.14225	−0.571123	−	0.820864i	$-0.693492\pi$
$239$	−17.6587	−1.14225	−0.571123	+	0.820864i	$0.693492\pi$
$240$	0	0
$241$	21.4815	1.38374	0.691872	−	0.722021i	$-0.256786\pi$
$241$	21.4815	1.38374	0.691872	+	0.722021i	$0.256786\pi$
$242$	−7.12328	−0.457902
$243$	−19.2316	−1.23371
$244$	−6.57508	−0.420927
$245$	0	0
$246$	−9.11020	−0.580845
$247$	−11.3282	−0.720795
$248$	10.4466	0.663363
$249$	15.9378	1.01002
$250$	0	0
$251$	−9.78261	−0.617473	−0.308736	−	0.951148i	$-0.599906\pi$
$251$	−9.78261	−0.617473	−0.308736	+	0.951148i	$0.599906\pi$
$252$	−3.26232	−0.205507
$253$	1.13397	0.0712922
$254$	12.4625	0.781967
$255$	0	0
$256$	−11.7620	−0.735127
$257$	−10.9555	−0.683383	−0.341692	−	0.939812i	$-0.611000\pi$
$257$	−10.9555	−0.683383	−0.341692	+	0.939812i	$0.611000\pi$
$258$	15.6529	0.974508
$259$	11.6257	0.722386
$260$	0	0
$261$	22.0847	1.36701
$262$	5.13095	0.316991
$263$	−16.8184	−1.03707	−0.518534	−	0.855057i	$-0.673522\pi$
$263$	−16.8184	−1.03707	−0.518534	+	0.855057i	$0.673522\pi$
$264$	6.58465	0.405257
$265$	0	0
$266$	2.89598	0.177564
$267$	22.3712	1.36910
$268$	−10.1740	−0.621474
$269$	−22.5826	−1.37689	−0.688443	−	0.725291i	$-0.741705\pi$
$269$	−22.5826	−1.37689	−0.688443	+	0.725291i	$0.741705\pi$
$270$	0	0
$271$	−0.368904	−0.0224093	−0.0112047	−	0.999937i	$-0.503567\pi$
$271$	−0.368904	−0.0224093	−0.0112047	+	0.999937i	$0.503567\pi$
$272$	3.29907	0.200035
$273$	−6.56044	−0.397056
$274$	−4.18689	−0.252939
$275$	0	0
$276$	3.34444	0.201311
$277$	32.4204	1.94795	0.973977	−	0.226648i	$-0.0727768\pi$
$277$	32.4204	1.94795	0.973977	+	0.226648i	$0.0727768\pi$
$278$	−6.06697	−0.363873
$279$	−9.17979	−0.549579
$280$	0	0
$281$	−21.6461	−1.29130	−0.645648	−	0.763635i	$-0.723413\pi$
$281$	−21.6461	−1.29130	−0.645648	+	0.763635i	$0.723413\pi$
$282$	17.0322	1.01425
$283$	24.8260	1.47576	0.737878	−	0.674935i	$-0.235828\pi$
$283$	24.8260	1.47576	0.737878	+	0.674935i	$0.235828\pi$
$284$	11.6108	0.688974
$285$	0	0
$286$	2.38517	0.141038
$287$	−5.43200	−0.320641
$288$	13.0671	0.769983
$289$	−7.36508	−0.433240
$290$	0	0
$291$	−33.7997	−1.98137
$292$	−6.03694	−0.353285
$293$	−18.2507	−1.06622	−0.533108	−	0.846047i	$-0.678976\pi$
$293$	−18.2507	−1.06622	−0.533108	+	0.846047i	$0.678976\pi$
$294$	1.67714	0.0978125
$295$	0	0
$296$	−29.5161	−1.71559
$297$	1.99449	0.115732
$298$	−12.1357	−0.703002
$299$	2.86841	0.165884
$300$	0	0
$301$	9.33312	0.537952
$302$	2.26027	0.130064
$303$	−14.0994	−0.809989
$304$	4.19746	0.240741
$305$	0	0
$306$	5.07804	0.290292
$307$	−27.2652	−1.55611	−0.778054	−	0.628197i	$-0.783793\pi$
$307$	−27.2652	−1.55611	−0.778054	+	0.628197i	$0.783793\pi$
$308$	1.65819	0.0944840
$309$	−18.1454	−1.03225
$310$	0	0
$311$	31.5142	1.78700	0.893502	−	0.449059i	$-0.148241\pi$
$311$	31.5142	1.78700	0.893502	+	0.449059i	$0.148241\pi$
$312$	16.6561	0.942963
$313$	−7.36248	−0.416152	−0.208076	−	0.978113i	$-0.566720\pi$
$313$	−7.36248	−0.416152	−0.208076	+	0.978113i	$0.566720\pi$
$314$	−11.8388	−0.668104
$315$	0	0
$316$	4.93644	0.277696
$317$	27.6125	1.55087	0.775435	−	0.631427i	$-0.217531\pi$
$317$	27.6125	1.55087	0.775435	+	0.631427i	$0.217531\pi$
$318$	−1.93800	−0.108678
$319$	−11.2253	−0.628496
$320$	0	0
$321$	22.2022	1.23920
$322$	−0.733292	−0.0408648
$323$	12.2587	0.682091
$324$	15.6693	0.870519
$325$	0	0
$326$	1.09777	0.0608001
$327$	34.5425	1.91020
$328$	13.7911	0.761486
$329$	10.1555	0.559893
$330$	0	0
$331$	24.4188	1.34218	0.671088	−	0.741377i	$-0.265827\pi$
$331$	24.4188	1.34218	0.671088	+	0.741377i	$0.265827\pi$
$332$	−10.1899	−0.559243
$333$	25.9367	1.42132
$334$	2.26245	0.123796
$335$	0	0
$336$	2.43085	0.132614
$337$	22.9377	1.24950	0.624748	−	0.780826i	$-0.285202\pi$
$337$	22.9377	1.24950	0.624748	+	0.780826i	$0.285202\pi$
$338$	−3.49943	−0.190344
$339$	20.5825	1.11789
$340$	0	0
$341$	4.66595	0.252675
$342$	6.46087	0.349364
$343$	1.00000	0.0539949
$344$	−23.6955	−1.27758
$345$	0	0
$346$	10.6109	0.570445
$347$	−10.2217	−0.548731	−0.274365	−	0.961626i	$-0.588468\pi$
$347$	−10.2217	−0.548731	−0.274365	+	0.961626i	$0.588468\pi$
$348$	−33.1069	−1.77472
$349$	17.4562	0.934411	0.467206	−	0.884149i	$-0.345261\pi$
$349$	17.4562	0.934411	0.467206	+	0.884149i	$0.345261\pi$
$350$	0	0
$351$	5.04513	0.269289
$352$	−6.64178	−0.354008
$353$	2.73759	0.145707	0.0728537	−	0.997343i	$-0.476789\pi$
$353$	2.73759	0.145707	0.0728537	+	0.997343i	$0.476789\pi$
$354$	−0.711391	−0.0378100
$355$	0	0
$356$	−14.3031	−0.758062
$357$	7.09930	0.375735
$358$	−12.1376	−0.641493
$359$	−2.51474	−0.132723	−0.0663614	−	0.997796i	$-0.521139\pi$
$359$	−2.51474	−0.132723	−0.0663614	+	0.997796i	$0.521139\pi$
$360$	0	0
$361$	−3.40310	−0.179110
$362$	3.36435	0.176826
$363$	−22.2175	−1.16611
$364$	4.19443	0.219848
$365$	0	0
$366$	7.54116	0.394183
$367$	−24.9785	−1.30387	−0.651934	−	0.758275i	$-0.726042\pi$
$367$	−24.9785	−1.30387	−0.651934	+	0.758275i	$0.726042\pi$
$368$	−1.06284	−0.0554043
$369$	−12.1187	−0.630872
$370$	0	0
$371$	−1.15554	−0.0599928
$372$	13.7613	0.713492
$373$	7.08551	0.366874	0.183437	−	0.983031i	$-0.441278\pi$
$373$	7.08551	0.366874	0.183437	+	0.983031i	$0.441278\pi$
$374$	−2.58109	−0.133465
$375$	0	0
$376$	−25.7835	−1.32968
$377$	−28.3947	−1.46240
$378$	−1.28976	−0.0663379
$379$	−4.99296	−0.256471	−0.128236	−	0.991744i	$-0.540931\pi$
$379$	−4.99296	−0.256471	−0.128236	+	0.991744i	$0.540931\pi$
$380$	0	0
$381$	38.8705	1.99139
$382$	−9.99118	−0.511193
$383$	−13.1941	−0.674189	−0.337095	−	0.941471i	$-0.609444\pi$
$383$	−13.1941	−0.674189	−0.337095	+	0.941471i	$0.609444\pi$
$384$	−23.1537	−1.18156
$385$	0	0
$386$	−15.5423	−0.791082
$387$	20.8220	1.05844
$388$	21.6099	1.09708
$389$	16.2945	0.826164	0.413082	−	0.910694i	$-0.364452\pi$
$389$	16.2945	0.826164	0.413082	+	0.910694i	$0.364452\pi$
$390$	0	0
$391$	−3.10402	−0.156977
$392$	−2.53886	−0.128232
$393$	16.0034	0.807266
$394$	10.7337	0.540754
$395$	0	0
$396$	3.69938	0.185901
$397$	17.2702	0.866765	0.433383	−	0.901210i	$-0.357320\pi$
$397$	17.2702	0.866765	0.433383	+	0.901210i	$0.357320\pi$
$398$	−2.05569	−0.103042
$399$	9.03255	0.452193
$400$	0	0
$401$	5.11468	0.255415	0.127707	−	0.991812i	$-0.459238\pi$
$401$	5.11468	0.255415	0.127707	+	0.991812i	$0.459238\pi$
$402$	11.6688	0.581988
$403$	11.8026	0.587931
$404$	9.01447	0.448487
$405$	0	0
$406$	7.25892	0.360254
$407$	−13.1832	−0.653468
$408$	−18.0242	−0.892329
$409$	−15.6146	−0.772093	−0.386047	−	0.922479i	$-0.626160\pi$
$409$	−15.6146	−0.772093	−0.386047	+	0.922479i	$0.626160\pi$
$410$	0	0
$411$	−13.0589	−0.644147
$412$	11.6013	0.571554
$413$	−0.424170	−0.0208720
$414$	−1.63596	−0.0804029
$415$	0	0
$416$	−16.8006	−0.823715
$417$	−18.9228	−0.926656
$418$	−3.28396	−0.160624
$419$	−8.17923	−0.399582	−0.199791	−	0.979839i	$-0.564026\pi$
$419$	−8.17923	−0.399582	−0.199791	+	0.979839i	$0.564026\pi$
$420$	0	0
$421$	−6.08280	−0.296457	−0.148229	−	0.988953i	$-0.547357\pi$
$421$	−6.08280	−0.296457	−0.148229	+	0.988953i	$0.547357\pi$
$422$	17.1266	0.833710
$423$	22.6568	1.10161
$424$	2.93377	0.142476
$425$	0	0
$426$	−13.3168	−0.645199
$427$	4.49645	0.217598
$428$	−14.1950	−0.686141
$429$	7.43935	0.359175
$430$	0	0
$431$	−27.0010	−1.30059	−0.650296	−	0.759681i	$-0.725355\pi$
$431$	−27.0010	−1.30059	−0.650296	+	0.759681i	$0.725355\pi$
$432$	−1.86938	−0.0899407
$433$	24.2386	1.16483	0.582417	−	0.812890i	$-0.302107\pi$
$433$	24.2386	1.16483	0.582417	+	0.812890i	$0.302107\pi$
$434$	−3.01727	−0.144834
$435$	0	0
$436$	−22.0848	−1.05767
$437$	−3.94929	−0.188920
$438$	6.92395	0.330839
$439$	−22.6760	−1.08227	−0.541134	−	0.840936i	$-0.682005\pi$
$439$	−22.6760	−1.08227	−0.541134	+	0.840936i	$0.682005\pi$
$440$	0	0
$441$	2.23098	0.106237
$442$	−6.52893	−0.310550
$443$	−8.00374	−0.380269	−0.190134	−	0.981758i	$-0.560892\pi$
$443$	−8.00374	−0.380269	−0.190134	+	0.981758i	$0.560892\pi$
$444$	−38.8814	−1.84523
$445$	0	0
$446$	1.19273	0.0564773
$447$	−37.8512	−1.79030
$448$	2.16929	0.102489
$449$	0.121558	0.00573670	0.00286835	−	0.999996i	$-0.499087\pi$
$449$	0.121558	0.00573670	0.00286835	+	0.999996i	$0.499087\pi$
$450$	0	0
$451$	6.15973	0.290050
$452$	−13.1595	−0.618969
$453$	7.04976	0.331227
$454$	16.5016	0.774460
$455$	0	0
$456$	−22.9324	−1.07391
$457$	−25.1666	−1.17724	−0.588622	−	0.808409i	$-0.700329\pi$
$457$	−25.1666	−1.17724	−0.588622	+	0.808409i	$0.700329\pi$
$458$	−4.31754	−0.201746
$459$	−5.45953	−0.254829
$460$	0	0
$461$	−6.94397	−0.323413	−0.161707	−	0.986839i	$-0.551700\pi$
$461$	−6.94397	−0.323413	−0.161707	+	0.986839i	$0.551700\pi$
$462$	−1.90182	−0.0884809
$463$	−39.3157	−1.82716	−0.913578	−	0.406664i	$-0.866692\pi$
$463$	−39.3157	−1.82716	−0.913578	+	0.406664i	$0.866692\pi$
$464$	10.5211	0.488431
$465$	0	0
$466$	2.06873	0.0958319
$467$	30.7539	1.42312	0.711561	−	0.702625i	$-0.247989\pi$
$467$	30.7539	1.42312	0.711561	+	0.702625i	$0.247989\pi$
$468$	9.35767	0.432559
$469$	6.95759	0.321271
$470$	0	0
$471$	−36.9253	−1.70143
$472$	1.07691	0.0495688
$473$	−10.5835	−0.486630
$474$	−5.66175	−0.260053
$475$	0	0
$476$	−4.53895	−0.208043
$477$	−2.57799	−0.118038
$478$	−12.9490	−0.592273
$479$	12.5788	0.574740	0.287370	−	0.957820i	$-0.407219\pi$
$479$	12.5788	0.574740	0.287370	+	0.957820i	$0.407219\pi$
$480$	0	0
$481$	−33.3473	−1.52051
$482$	15.7522	0.717492
$483$	−2.28713	−0.104068
$484$	14.2048	0.645672
$485$	0	0
$486$	−14.1024	−0.639696
$487$	22.6937	1.02835	0.514175	−	0.857685i	$-0.328098\pi$
$487$	22.6937	1.02835	0.514175	+	0.857685i	$0.328098\pi$
$488$	−11.4159	−0.516772
$489$	3.42395	0.154836
$490$	0	0
$491$	−27.9622	−1.26192	−0.630959	−	0.775816i	$-0.717338\pi$
$491$	−27.9622	−1.26192	−0.630959	+	0.775816i	$0.717338\pi$
$492$	18.1670	0.819030
$493$	30.7270	1.38387
$494$	−8.30687	−0.373744
$495$	0	0
$496$	−4.37325	−0.196365
$497$	−7.94018	−0.356166
$498$	11.6871	0.523711
$499$	−19.7137	−0.882508	−0.441254	−	0.897382i	$-0.645466\pi$
$499$	−19.7137	−0.882508	−0.441254	+	0.897382i	$0.645466\pi$
$500$	0	0
$501$	7.05658	0.315265
$502$	−7.17350	−0.320169
$503$	32.8177	1.46327	0.731634	−	0.681698i	$-0.238758\pi$
$503$	32.8177	1.46327	0.731634	+	0.681698i	$0.238758\pi$
$504$	−5.66415	−0.252301
$505$	0	0
$506$	0.831532	0.0369661
$507$	−10.9147	−0.484739
$508$	−24.8519	−1.10263
$509$	1.36384	0.0604510	0.0302255	−	0.999543i	$-0.490377\pi$
$509$	1.36384	0.0604510	0.0302255	+	0.999543i	$0.490377\pi$
$510$	0	0
$511$	4.12844	0.182631
$512$	11.6220	0.513623
$513$	−6.94624	−0.306684
$514$	−8.03356	−0.354345
$515$	0	0
$516$	−31.2140	−1.37412
$517$	−11.5161	−0.506477
$518$	8.52503	0.374568
$519$	33.0953	1.45272
$520$	0	0
$521$	−29.6415	−1.29862	−0.649309	−	0.760524i	$-0.724942\pi$
$521$	−29.6415	−1.29862	−0.649309	+	0.760524i	$0.724942\pi$
$522$	16.1945	0.708814
$523$	−14.7647	−0.645616	−0.322808	−	0.946464i	$-0.604627\pi$
$523$	−14.7647	−0.645616	−0.322808	+	0.946464i	$0.604627\pi$
$524$	−10.2318	−0.446979
$525$	0	0
$526$	−12.3328	−0.537736
$527$	−12.7721	−0.556361
$528$	−2.75652	−0.119962
$529$	1.00000	0.0434783
$530$	0	0
$531$	−0.946314	−0.0410665
$532$	−5.77498	−0.250377
$533$	15.5812	0.674897
$534$	16.4046	0.709898
$535$	0	0
$536$	−17.6644	−0.762984
$537$	−37.8571	−1.63366
$538$	−16.5596	−0.713937
$539$	−1.13397	−0.0488436
$540$	0	0
$541$	−7.27643	−0.312838	−0.156419	−	0.987691i	$-0.549995\pi$
$541$	−7.27643	−0.312838	−0.156419	+	0.987691i	$0.549995\pi$
$542$	−0.270514	−0.0116196
$543$	10.4934	0.450314
$544$	18.1805	0.779484
$545$	0	0
$546$	−4.81071	−0.205880
$547$	−25.9534	−1.10969	−0.554844	−	0.831954i	$-0.687222\pi$
$547$	−25.9534	−1.10969	−0.554844	+	0.831954i	$0.687222\pi$
$548$	8.34922	0.356661
$549$	10.0315	0.428133
$550$	0	0
$551$	39.0944	1.66548
$552$	5.80672	0.247150
$553$	−3.37584	−0.143555
$554$	23.7736	1.01004
$555$	0	0
$556$	12.0984	0.513085
$557$	14.9284	0.632536	0.316268	−	0.948670i	$-0.397570\pi$
$557$	14.9284	0.632536	0.316268	+	0.948670i	$0.397570\pi$
$558$	−6.73146	−0.284966
$559$	−26.7712	−1.13230
$560$	0	0
$561$	−8.05040	−0.339888
$562$	−15.8729	−0.669558
$563$	−44.3837	−1.87055	−0.935274	−	0.353924i	$-0.884847\pi$
$563$	−44.3837	−1.87055	−0.935274	+	0.353924i	$0.884847\pi$
$564$	−33.9646	−1.43017
$565$	0	0
$566$	18.2047	0.765202
$567$	−10.7157	−0.450016
$568$	20.1590	0.845854
$569$	29.5342	1.23814	0.619069	−	0.785337i	$-0.287510\pi$
$569$	29.5342	1.23814	0.619069	+	0.785337i	$0.287510\pi$
$570$	0	0
$571$	−2.00602	−0.0839494	−0.0419747	−	0.999119i	$-0.513365\pi$
$571$	−2.00602	−0.0839494	−0.0419747	+	0.999119i	$0.513365\pi$
$572$	−4.75636	−0.198873
$573$	−31.1624	−1.30183
$574$	−3.98324	−0.166257
$575$	0	0
$576$	4.83963	0.201651
$577$	−34.7457	−1.44648	−0.723242	−	0.690595i	$-0.757349\pi$
$577$	−34.7457	−1.44648	−0.723242	+	0.690595i	$0.757349\pi$
$578$	−5.40075	−0.224642
$579$	−48.4764	−2.01461
$580$	0	0
$581$	6.96848	0.289101
$582$	−24.7850	−1.02737
$583$	1.31035	0.0542693
$584$	−10.4815	−0.433729
$585$	0	0
$586$	−13.3831	−0.552850
$587$	8.43350	0.348088	0.174044	−	0.984738i	$-0.444317\pi$
$587$	8.43350	0.348088	0.174044	+	0.984738i	$0.444317\pi$
$588$	−3.34444	−0.137922
$589$	−16.2501	−0.669575
$590$	0	0
$591$	33.4783	1.37711
$592$	12.3562	0.507838
$593$	−3.62184	−0.148731	−0.0743655	−	0.997231i	$-0.523693\pi$
$593$	−3.62184	−0.148731	−0.0743655	+	0.997231i	$0.523693\pi$
$594$	1.46255	0.0600090
$595$	0	0
$596$	24.2002	0.991280
$597$	−6.41169	−0.262413
$598$	2.10338	0.0860137
$599$	44.3439	1.81184	0.905922	−	0.423445i	$-0.139179\pi$
$599$	44.3439	1.81184	0.905922	+	0.423445i	$0.139179\pi$
$600$	0	0
$601$	19.8470	0.809575	0.404787	−	0.914411i	$-0.367346\pi$
$601$	19.8470	0.809575	0.404787	+	0.914411i	$0.367346\pi$
$602$	6.84390	0.278937
$603$	15.5222	0.632113
$604$	−4.50728	−0.183399
$605$	0	0
$606$	−10.3390	−0.419992
$607$	−11.9616	−0.485506	−0.242753	−	0.970088i	$-0.578051\pi$
$607$	−11.9616	−0.485506	−0.242753	+	0.970088i	$0.578051\pi$
$608$	23.1314	0.938102
$609$	22.6405	0.917441
$610$	0	0
$611$	−29.1303	−1.17848
$612$	−10.1263	−0.409331
$613$	33.2113	1.34139	0.670695	−	0.741733i	$-0.265996\pi$
$613$	33.2113	1.34139	0.670695	+	0.741733i	$0.265996\pi$
$614$	−19.9934	−0.806867
$615$	0	0
$616$	2.87900	0.115998
$617$	−38.5844	−1.55335	−0.776675	−	0.629902i	$-0.783095\pi$
$617$	−38.5844	−1.55335	−0.776675	+	0.629902i	$0.783095\pi$
$618$	−13.3059	−0.535240
$619$	24.0092	0.965010	0.482505	−	0.875893i	$-0.339727\pi$
$619$	24.0092	0.965010	0.482505	+	0.875893i	$0.339727\pi$
$620$	0	0
$621$	1.75886	0.0705805
$622$	23.1091	0.926590
$623$	9.78134	0.391881
$624$	−6.97268	−0.279131
$625$	0	0
$626$	−5.39885	−0.215781
$627$	−10.2427	−0.409052
$628$	23.6082	0.942071
$629$	36.0864	1.43886
$630$	0	0
$631$	19.6058	0.780496	0.390248	−	0.920710i	$-0.372389\pi$
$631$	19.6058	0.780496	0.390248	+	0.920710i	$0.372389\pi$
$632$	8.57081	0.340928
$633$	53.4178	2.12317
$634$	20.2480	0.804150
$635$	0	0
$636$	3.86464	0.153243
$637$	−2.86841	−0.113651
$638$	−8.23141	−0.325885
$639$	−17.7144	−0.700769
$640$	0	0
$641$	25.4461	1.00506	0.502531	−	0.864559i	$-0.332402\pi$
$641$	25.4461	1.00506	0.502531	+	0.864559i	$0.332402\pi$
$642$	16.2807	0.642546
$643$	14.6172	0.576445	0.288223	−	0.957563i	$-0.406936\pi$
$643$	14.6172	0.576445	0.288223	+	0.957563i	$0.406936\pi$
$644$	1.46228	0.0576220
$645$	0	0
$646$	8.98918	0.353675
$647$	13.0383	0.512587	0.256293	−	0.966599i	$-0.417499\pi$
$647$	13.0383	0.512587	0.256293	+	0.966599i	$0.417499\pi$
$648$	27.2056	1.06874
$649$	0.480997	0.0188808
$650$	0	0
$651$	−9.41085	−0.368840
$652$	−2.18911	−0.0857322
$653$	38.8239	1.51930	0.759649	−	0.650334i	$-0.225371\pi$
$653$	38.8239	1.51930	0.759649	+	0.650334i	$0.225371\pi$
$654$	25.3297	0.990471
$655$	0	0
$656$	−5.77334	−0.225411
$657$	9.21045	0.359334
$658$	7.44698	0.290313
$659$	−11.0095	−0.428869	−0.214434	−	0.976738i	$-0.568791\pi$
$659$	−11.0095	−0.428869	−0.214434	+	0.976738i	$0.568791\pi$
$660$	0	0
$661$	−9.93207	−0.386313	−0.193156	−	0.981168i	$-0.561872\pi$
$661$	−9.93207	−0.386313	−0.193156	+	0.981168i	$0.561872\pi$
$662$	17.9061	0.695940
$663$	−20.3637	−0.790861
$664$	−17.6920	−0.686584
$665$	0	0
$666$	19.0192	0.736977
$667$	−9.89909	−0.383294
$668$	−4.51164	−0.174561
$669$	3.72011	0.143828
$670$	0	0
$671$	−5.09885	−0.196839
$672$	13.3960	0.516760
$673$	−36.1421	−1.39317	−0.696587	−	0.717472i	$-0.745299\pi$
$673$	−36.1421	−1.39317	−0.696587	+	0.717472i	$0.745299\pi$
$674$	16.8200	0.647883
$675$	0	0
$676$	6.97834	0.268398
$677$	−14.2271	−0.546792	−0.273396	−	0.961902i	$-0.588147\pi$
$677$	−14.2271	−0.546792	−0.273396	+	0.961902i	$0.588147\pi$
$678$	15.0930	0.579642
$679$	−14.7782	−0.567135
$680$	0	0
$681$	51.4685	1.97228
$682$	3.42150	0.131016
$683$	22.1724	0.848401	0.424201	−	0.905568i	$-0.360555\pi$
$683$	22.1724	0.848401	0.424201	+	0.905568i	$0.360555\pi$
$684$	−12.8839	−0.492626
$685$	0	0
$686$	0.733292	0.0279972
$687$	−13.4664	−0.513775
$688$	9.91960	0.378181
$689$	3.31457	0.126275
$690$	0	0
$691$	23.3417	0.887960	0.443980	−	0.896037i	$-0.353566\pi$
$691$	23.3417	0.887960	0.443980	+	0.896037i	$0.353566\pi$
$692$	−21.1595	−0.804365
$693$	−2.52986	−0.0961016
$694$	−7.49550	−0.284525
$695$	0	0
$696$	−57.4813	−2.17882
$697$	−16.8610	−0.638657
$698$	12.8005	0.484507
$699$	6.45234	0.244050
$700$	0	0
$701$	18.2656	0.689881	0.344940	−	0.938625i	$-0.387899\pi$
$701$	18.2656	0.689881	0.344940	+	0.938625i	$0.387899\pi$
$702$	3.69955	0.139631
$703$	45.9133	1.73165
$704$	−2.45991	−0.0927113
$705$	0	0
$706$	2.00745	0.0755515
$707$	−6.16466	−0.231846
$708$	1.41861	0.0533146
$709$	−2.72101	−0.102190	−0.0510949	−	0.998694i	$-0.516271\pi$
$709$	−2.72101	−0.102190	−0.0510949	+	0.998694i	$0.516271\pi$
$710$	0	0
$711$	−7.53143	−0.282451
$712$	−24.8335	−0.930674
$713$	4.11469	0.154096
$714$	5.20586	0.194824
$715$	0	0
$716$	24.2040	0.904548
$717$	−40.3878	−1.50831
$718$	−1.84404	−0.0688188
$719$	−8.32409	−0.310436	−0.155218	−	0.987880i	$-0.549608\pi$
$719$	−8.32409	−0.310436	−0.155218	+	0.987880i	$0.549608\pi$
$720$	0	0
$721$	−7.93368	−0.295466
$722$	−2.49546	−0.0928715
$723$	49.1310	1.82720
$724$	−6.70897	−0.249337
$725$	0	0
$726$	−16.2919	−0.604648
$727$	−39.8613	−1.47837	−0.739187	−	0.673500i	$-0.764790\pi$
$727$	−39.8613	−1.47837	−0.739187	+	0.673500i	$0.764790\pi$
$728$	7.28250	0.269908
$729$	−11.8382	−0.438452
$730$	0	0
$731$	28.9702	1.07150
$732$	−15.0381	−0.555824
$733$	−23.5226	−0.868828	−0.434414	−	0.900713i	$-0.643044\pi$
$733$	−23.5226	−0.868828	−0.434414	+	0.900713i	$0.643044\pi$
$734$	−18.3166	−0.676076
$735$	0	0
$736$	−5.85710	−0.215896
$737$	−7.88970	−0.290621
$738$	−8.88652	−0.327117
$739$	21.3054	0.783731	0.391866	−	0.920023i	$-0.371830\pi$
$739$	21.3054	0.783731	0.391866	+	0.920023i	$0.371830\pi$
$740$	0	0
$741$	−25.9091	−0.951794
$742$	−0.847350	−0.0311072
$743$	−45.0052	−1.65108	−0.825541	−	0.564342i	$-0.809130\pi$
$743$	−45.0052	−1.65108	−0.825541	+	0.564342i	$0.809130\pi$
$744$	23.8929	0.875955
$745$	0	0
$746$	5.19575	0.190230
$747$	15.5465	0.568817
$748$	5.14704	0.188194
$749$	9.70742	0.354701
$750$	0	0
$751$	−24.3734	−0.889400	−0.444700	−	0.895680i	$-0.646690\pi$
$751$	−24.3734	−0.889400	−0.444700	+	0.895680i	$0.646690\pi$
$752$	10.7937	0.393606
$753$	−22.3741	−0.815358
$754$	−20.8216	−0.758277
$755$	0	0
$756$	2.57195	0.0935409
$757$	−34.7459	−1.26286	−0.631430	−	0.775433i	$-0.717532\pi$
$757$	−34.7459	−1.26286	−0.631430	+	0.775433i	$0.717532\pi$
$758$	−3.66130	−0.132984
$759$	2.59354	0.0941397
$760$	0	0
$761$	−30.1865	−1.09426	−0.547130	−	0.837048i	$-0.684280\pi$
$761$	−30.1865	−1.09426	−0.547130	+	0.837048i	$0.684280\pi$
$762$	28.5034	1.03257
$763$	15.1030	0.546764
$764$	19.9238	0.720816
$765$	0	0
$766$	−9.67516	−0.349578
$767$	1.21669	0.0439323
$768$	−26.9013	−0.970718
$769$	−0.280206	−0.0101045	−0.00505224	−	0.999987i	$-0.501608\pi$
$769$	−0.280206	−0.0101045	−0.00505224	+	0.999987i	$0.501608\pi$
$770$	0	0
$771$	−25.0566	−0.902392
$772$	30.9935	1.11548
$773$	−2.26476	−0.0814579	−0.0407290	−	0.999170i	$-0.512968\pi$
$773$	−2.26476	−0.0814579	−0.0407290	+	0.999170i	$0.512968\pi$
$774$	15.2686	0.548818
$775$	0	0
$776$	37.5198	1.34688
$777$	26.5895	0.953894
$778$	11.9486	0.428379
$779$	−21.4525	−0.768617
$780$	0	0
$781$	9.00394	0.322186
$782$	−2.27615	−0.0813950
$783$	−17.4111	−0.622222
$784$	1.06284	0.0379585
$785$	0	0
$786$	11.7352	0.418580
$787$	12.2514	0.436714	0.218357	−	0.975869i	$-0.429930\pi$
$787$	12.2514	0.436714	0.218357	+	0.975869i	$0.429930\pi$
$788$	−21.4044	−0.762500
$789$	−38.4660	−1.36943
$790$	0	0
$791$	8.99925	0.319977
$792$	6.42298	0.228231
$793$	−12.8977	−0.458009
$794$	12.6641	0.449431
$795$	0	0
$796$	4.09932	0.145297
$797$	−6.57854	−0.233024	−0.116512	−	0.993189i	$-0.537171\pi$
$797$	−6.57854	−0.233024	−0.116512	+	0.993189i	$0.537171\pi$
$798$	6.62350	0.234469
$799$	31.5230	1.11520
$800$	0	0
$801$	21.8219	0.771040
$802$	3.75055	0.132437
$803$	−4.68153	−0.165208
$804$	−23.2692	−0.820641
$805$	0	0
$806$	8.65477	0.304851
$807$	−51.6494	−1.81815
$808$	15.6512	0.550608
$809$	−36.2737	−1.27531	−0.637657	−	0.770320i	$-0.720096\pi$
$809$	−36.2737	−1.27531	−0.637657	+	0.770320i	$0.720096\pi$
$810$	0	0
$811$	30.2323	1.06160	0.530799	−	0.847497i	$-0.321892\pi$
$811$	30.2323	1.06160	0.530799	+	0.847497i	$0.321892\pi$
$812$	−14.4753	−0.507983
$813$	−0.843732	−0.0295910
$814$	−9.66715	−0.338833
$815$	0	0
$816$	7.54541	0.264142
$817$	36.8592	1.28954
$818$	−11.4501	−0.400343
$819$	−6.39936	−0.223612
$820$	0	0
$821$	−41.1529	−1.43625	−0.718123	−	0.695916i	$-0.754999\pi$
$821$	−41.1529	−1.43625	−0.718123	+	0.695916i	$0.754999\pi$
$822$	−9.57597	−0.334000
$823$	13.7373	0.478854	0.239427	−	0.970914i	$-0.423040\pi$
$823$	13.7373	0.478854	0.239427	+	0.970914i	$0.423040\pi$
$824$	20.1425	0.701698
$825$	0	0
$826$	−0.311040	−0.0108225
$827$	−1.00276	−0.0348695	−0.0174347	−	0.999848i	$-0.505550\pi$
$827$	−1.00276	−0.0348695	−0.0174347	+	0.999848i	$0.505550\pi$
$828$	3.26232	0.113373
$829$	7.43293	0.258156	0.129078	−	0.991634i	$-0.458798\pi$
$829$	7.43293	0.258156	0.129078	+	0.991634i	$0.458798\pi$
$830$	0	0
$831$	74.1498	2.57223
$832$	−6.22240	−0.215723
$833$	3.10402	0.107548
$834$	−13.8760	−0.480485
$835$	0	0
$836$	6.54867	0.226490
$837$	7.23716	0.250153
$838$	−5.99776	−0.207189
$839$	42.2017	1.45697	0.728483	−	0.685064i	$-0.240226\pi$
$839$	42.2017	1.45697	0.728483	+	0.685064i	$0.240226\pi$
$840$	0	0
$841$	68.9921	2.37904
$842$	−4.46047	−0.153718
$843$	−49.5075	−1.70513
$844$	−34.1528	−1.17559
$845$	0	0
$846$	16.6140	0.571202
$847$	−9.71411	−0.333781
$848$	−1.22816	−0.0421750
$849$	56.7805	1.94870
$850$	0	0
$851$	−11.6257	−0.398524
$852$	26.5554	0.909774
$853$	−16.8248	−0.576072	−0.288036	−	0.957620i	$-0.593002\pi$
$853$	−16.8248	−0.576072	−0.288036	+	0.957620i	$0.593002\pi$
$854$	3.29721	0.112828
$855$	0	0
$856$	−24.6458	−0.842377
$857$	34.9858	1.19509	0.597547	−	0.801834i	$-0.296142\pi$
$857$	34.9858	1.19509	0.597547	+	0.801834i	$0.296142\pi$
$858$	5.45521	0.186238
$859$	−22.2186	−0.758090	−0.379045	−	0.925378i	$-0.623747\pi$
$859$	−22.2186	−0.758090	−0.379045	+	0.925378i	$0.623747\pi$
$860$	0	0
$861$	−12.4237	−0.423399
$862$	−19.7996	−0.674377
$863$	7.00003	0.238284	0.119142	−	0.992877i	$-0.461986\pi$
$863$	7.00003	0.238284	0.119142	+	0.992877i	$0.461986\pi$
$864$	−10.3018	−0.350474
$865$	0	0
$866$	17.7740	0.603985
$867$	−16.8449	−0.572083
$868$	6.01685	0.204225
$869$	3.82811	0.129860
$870$	0	0
$871$	−19.9572	−0.676224
$872$	−38.3444	−1.29850
$873$	−32.9698	−1.11586
$874$	−2.89598	−0.0979581
$875$	0	0
$876$	−13.8073	−0.466505
$877$	46.0015	1.55336	0.776681	−	0.629895i	$-0.216902\pi$
$877$	46.0015	1.55336	0.776681	+	0.629895i	$0.216902\pi$
$878$	−16.6282	−0.561173
$879$	−41.7417	−1.40791
$880$	0	0
$881$	−8.33958	−0.280968	−0.140484	−	0.990083i	$-0.544866\pi$
$881$	−8.33958	−0.280968	−0.140484	+	0.990083i	$0.544866\pi$
$882$	1.63596	0.0550855
$883$	−5.28794	−0.177953	−0.0889766	−	0.996034i	$-0.528360\pi$
$883$	−5.28794	−0.177953	−0.0889766	+	0.996034i	$0.528360\pi$
$884$	13.0196	0.437896
$885$	0	0
$886$	−5.86907	−0.197175
$887$	23.9425	0.803911	0.401955	−	0.915659i	$-0.368331\pi$
$887$	23.9425	0.803911	0.401955	+	0.915659i	$0.368331\pi$
$888$	−67.5072	−2.26539
$889$	16.9953	0.570003
$890$	0	0
$891$	12.1513	0.407083
$892$	−2.37846	−0.0796367
$893$	40.1072	1.34214
$894$	−27.7559	−0.928298
$895$	0	0
$896$	−10.1235	−0.338202
$897$	6.56044	0.219047
$898$	0.0891378	0.00297457
$899$	−40.7317	−1.35848
$900$	0	0
$901$	−3.58683	−0.119494
$902$	4.51688	0.150396
$903$	21.3461	0.710354
$904$	−22.8479	−0.759909
$905$	0	0
$906$	5.16953	0.171746
$907$	−40.6837	−1.35088	−0.675441	−	0.737414i	$-0.736047\pi$
$907$	−40.6837	−1.35088	−0.675441	+	0.737414i	$0.736047\pi$
$908$	−32.9065	−1.09204
$909$	−13.7532	−0.456165
$910$	0	0
$911$	−34.5428	−1.14445	−0.572227	−	0.820095i	$-0.693920\pi$
$911$	−34.5428	−1.14445	−0.572227	+	0.820095i	$0.693920\pi$
$912$	9.60014	0.317893
$913$	−7.90206	−0.261520
$914$	−18.4545	−0.610419
$915$	0	0
$916$	8.60977	0.284475
$917$	6.99715	0.231066
$918$	−4.00343	−0.132133
$919$	32.3585	1.06741	0.533704	−	0.845671i	$-0.320800\pi$
$919$	32.3585	1.06741	0.533704	+	0.845671i	$0.320800\pi$
$920$	0	0
$921$	−62.3592	−2.05481
$922$	−5.09196	−0.167695
$923$	22.7757	0.749671
$924$	3.79249	0.124764
$925$	0	0
$926$	−28.8299	−0.947409
$927$	−17.6999	−0.581339
$928$	57.9800	1.90329
$929$	11.7640	0.385964	0.192982	−	0.981202i	$-0.438184\pi$
$929$	11.7640	0.385964	0.192982	+	0.981202i	$0.438184\pi$
$930$	0	0
$931$	3.94929	0.129433
$932$	−4.12532	−0.135129
$933$	72.0771	2.35970
$934$	22.5516	0.737911
$935$	0	0
$936$	16.2471	0.531053
$937$	−1.12479	−0.0367452	−0.0183726	−	0.999831i	$-0.505849\pi$
$937$	−1.12479	−0.0367452	−0.0183726	+	0.999831i	$0.505849\pi$
$938$	5.10194	0.166584
$939$	−16.8390	−0.549519
$940$	0	0
$941$	−25.8186	−0.841661	−0.420831	−	0.907139i	$-0.638261\pi$
$941$	−25.8186	−0.841661	−0.420831	+	0.907139i	$0.638261\pi$
$942$	−27.0770	−0.882216
$943$	5.43200	0.176890
$944$	−0.450824	−0.0146731
$945$	0	0
$946$	−7.76079	−0.252325
$947$	−19.0148	−0.617897	−0.308949	−	0.951079i	$-0.599977\pi$
$947$	−19.0148	−0.617897	−0.308949	+	0.951079i	$0.599977\pi$
$948$	11.2903	0.366692
$949$	−11.8420	−0.384409
$950$	0	0
$951$	63.1534	2.04789
$952$	−7.88068	−0.255414
$953$	−32.3679	−1.04850	−0.524250	−	0.851565i	$-0.675654\pi$
$953$	−32.3679	−1.04850	−0.524250	+	0.851565i	$0.675654\pi$
$954$	−1.89042	−0.0612046
$955$	0	0
$956$	25.8220	0.835144
$957$	−25.6737	−0.829914
$958$	9.22394	0.298012
$959$	−5.70971	−0.184376
$960$	0	0
$961$	−14.0693	−0.453848
$962$	−24.4533	−0.788406
$963$	21.6570	0.697888
$964$	−31.4120	−1.01171
$965$	0	0
$966$	−1.67714	−0.0539610
$967$	21.9795	0.706814	0.353407	−	0.935470i	$-0.385023\pi$
$967$	21.9795	0.706814	0.353407	+	0.935470i	$0.385023\pi$
$968$	24.6628	0.792692
$969$	28.0372	0.900685
$970$	0	0
$971$	−32.2572	−1.03518	−0.517591	−	0.855628i	$-0.673171\pi$
$971$	−32.2572	−1.03518	−0.517591	+	0.855628i	$0.673171\pi$
$972$	28.1220	0.902015
$973$	−8.27361	−0.265240
$974$	16.6411	0.533216
$975$	0	0
$976$	4.77900	0.152972
$977$	−39.2501	−1.25572	−0.627861	−	0.778325i	$-0.716069\pi$
$977$	−39.2501	−1.25572	−0.627861	+	0.778325i	$0.716069\pi$
$978$	2.51076	0.0802851
$979$	−11.0918	−0.354494
$980$	0	0
$981$	33.6944	1.07578
$982$	−20.5045	−0.654324
$983$	−3.65649	−0.116624	−0.0583120	−	0.998298i	$-0.518572\pi$
$983$	−3.65649	−0.116624	−0.0583120	+	0.998298i	$0.518572\pi$
$984$	31.5421	1.00553
$985$	0	0
$986$	22.5318	0.717560
$987$	23.2271	0.739326
$988$	16.5650	0.527003
$989$	−9.33312	−0.296776
$990$	0	0
$991$	−16.1466	−0.512913	−0.256457	−	0.966556i	$-0.582555\pi$
$991$	−16.1466	−0.512913	−0.256457	+	0.966556i	$0.582555\pi$
$992$	−24.1002	−0.765181
$993$	55.8490	1.77231
$994$	−5.82247	−0.184677
$995$	0	0
$996$	−23.3056	−0.738467
$997$	40.3553	1.27807	0.639033	−	0.769180i	$-0.279335\pi$
$997$	40.3553	1.27807	0.639033	+	0.769180i	$0.279335\pi$
$998$	−14.4559	−0.457594
$999$	−20.4480	−0.646945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.r.1.3		5
5.4	even	2		805.2.a.k.1.3	✓	5
15.14	odd	2		7245.2.a.bi.1.3		5
35.34	odd	2		5635.2.a.x.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.k.1.3	✓	5	5.4	even	2
4025.2.a.r.1.3		5	1.1	even	1	trivial
5635.2.a.x.1.3		5	35.34	odd	2
7245.2.a.bi.1.3		5	15.14	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.733292 q^{2} +2.28713 q^{3} -1.46228 q^{4} +1.67714 q^{6} +1.00000 q^{7} -2.53886 q^{8} +2.23098 q^{9} +O(q^{10})\)	\(q+0.733292 q^{2} +2.28713 q^{3} -1.46228 q^{4} +1.67714 q^{6} +1.00000 q^{7} -2.53886 q^{8} +2.23098 q^{9} -1.13397 q^{11} -3.34444 q^{12} -2.86841 q^{13} +0.733292 q^{14} +1.06284 q^{16} +3.10402 q^{17} +1.63596 q^{18} +3.94929 q^{19} +2.28713 q^{21} -0.831532 q^{22} -1.00000 q^{23} -5.80672 q^{24} -2.10338 q^{26} -1.75886 q^{27} -1.46228 q^{28} +9.89909 q^{29} -4.11469 q^{31} +5.85710 q^{32} -2.59354 q^{33} +2.27615 q^{34} -3.26232 q^{36} +11.6257 q^{37} +2.89598 q^{38} -6.56044 q^{39} -5.43200 q^{41} +1.67714 q^{42} +9.33312 q^{43} +1.65819 q^{44} -0.733292 q^{46} +10.1555 q^{47} +2.43085 q^{48} +1.00000 q^{49} +7.09930 q^{51} +4.19443 q^{52} -1.15554 q^{53} -1.28976 q^{54} -2.53886 q^{56} +9.03255 q^{57} +7.25892 q^{58} -0.424170 q^{59} +4.49645 q^{61} -3.01727 q^{62} +2.23098 q^{63} +2.16929 q^{64} -1.90182 q^{66} +6.95759 q^{67} -4.53895 q^{68} -2.28713 q^{69} -7.94018 q^{71} -5.66415 q^{72} +4.12844 q^{73} +8.52503 q^{74} -5.77498 q^{76} -1.13397 q^{77} -4.81071 q^{78} -3.37584 q^{79} -10.7157 q^{81} -3.98324 q^{82} +6.96848 q^{83} -3.34444 q^{84} +6.84390 q^{86} +22.6405 q^{87} +2.87900 q^{88} +9.78134 q^{89} -2.86841 q^{91} +1.46228 q^{92} -9.41085 q^{93} +7.44698 q^{94} +13.3960 q^{96} -14.7782 q^{97} +0.733292 q^{98} -2.52986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 7 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 7 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 7 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - 11 q^{11} + 14 q^{12} + 7 q^{13} + 3 q^{14} - q^{16} - q^{17} + 17 q^{18} + 2 q^{19} + 6 q^{21} - 2 q^{22} - 5 q^{23} + 12 q^{24} + 8 q^{26} + 15 q^{27} + 3 q^{28} - 14 q^{29} - 6 q^{31} + 4 q^{32} - 22 q^{33} + 4 q^{34} + 28 q^{36} + q^{37} + 31 q^{38} + 15 q^{39} + 7 q^{41} + 7 q^{42} + 12 q^{43} - 11 q^{44} - 3 q^{46} + 24 q^{47} + 4 q^{48} + 5 q^{49} - 28 q^{51} + 36 q^{52} + 21 q^{53} + 49 q^{54} + 3 q^{56} + 15 q^{57} - 9 q^{58} - q^{59} + 7 q^{61} + 26 q^{62} + 5 q^{63} - 15 q^{64} - 45 q^{66} + 35 q^{67} - 43 q^{68} - 6 q^{69} - 32 q^{71} + 36 q^{72} + 7 q^{73} - 10 q^{74} + 10 q^{76} - 11 q^{77} + 8 q^{78} + 18 q^{79} + 21 q^{81} - 33 q^{82} + q^{83} + 14 q^{84} - 26 q^{86} + 18 q^{87} - 41 q^{88} + q^{89} + 7 q^{91} - 3 q^{92} + 19 q^{93} + 14 q^{94} + 26 q^{96} + 9 q^{97} + 3 q^{98} - 54 q^{99}+O(q^{100}) \) 5 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 7 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - 11 * q^11 + 14 * q^12 + 7 * q^13 + 3 * q^14 - q^16 - q^17 + 17 * q^18 + 2 * q^19 + 6 * q^21 - 2 * q^22 - 5 * q^23 + 12 * q^24 + 8 * q^26 + 15 * q^27 + 3 * q^28 - 14 * q^29 - 6 * q^31 + 4 * q^32 - 22 * q^33 + 4 * q^34 + 28 * q^36 + q^37 + 31 * q^38 + 15 * q^39 + 7 * q^41 + 7 * q^42 + 12 * q^43 - 11 * q^44 - 3 * q^46 + 24 * q^47 + 4 * q^48 + 5 * q^49 - 28 * q^51 + 36 * q^52 + 21 * q^53 + 49 * q^54 + 3 * q^56 + 15 * q^57 - 9 * q^58 - q^59 + 7 * q^61 + 26 * q^62 + 5 * q^63 - 15 * q^64 - 45 * q^66 + 35 * q^67 - 43 * q^68 - 6 * q^69 - 32 * q^71 + 36 * q^72 + 7 * q^73 - 10 * q^74 + 10 * q^76 - 11 * q^77 + 8 * q^78 + 18 * q^79 + 21 * q^81 - 33 * q^82 + q^83 + 14 * q^84 - 26 * q^86 + 18 * q^87 - 41 * q^88 + q^89 + 7 * q^91 - 3 * q^92 + 19 * q^93 + 14 * q^94 + 26 * q^96 + 9 * q^97 + 3 * q^98 - 54 * q^99

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