LMFDB - Embedded newform 1875.2.a.k.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.44400625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 $ x^6 - 11x^4 - x^3 + 29x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.68704$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68704 q^{2} +1.00000 q^{3} +5.22020 q^{4} +2.68704 q^{6} -1.68704 q^{7} +8.65280 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.68704 q^{2} +1.00000 q^{3} +5.22020 q^{4} +2.68704 q^{6} -1.68704 q^{7} +8.65280 q^{8} +1.00000 q^{9} +1.07882 q^{11} +5.22020 q^{12} -2.67723 q^{13} -4.53315 q^{14} +12.8101 q^{16} +3.93167 q^{17} +2.68704 q^{18} -1.17755 q^{19} -1.68704 q^{21} +2.89883 q^{22} +4.06295 q^{23} +8.65280 q^{24} -7.19384 q^{26} +1.00000 q^{27} -8.80669 q^{28} +5.95595 q^{29} -7.10310 q^{31} +17.1155 q^{32} +1.07882 q^{33} +10.5646 q^{34} +5.22020 q^{36} +4.58187 q^{37} -3.16412 q^{38} -2.67723 q^{39} -11.2614 q^{41} -4.53315 q^{42} -2.58587 q^{43} +5.63164 q^{44} +10.9173 q^{46} +1.91782 q^{47} +12.8101 q^{48} -4.15389 q^{49} +3.93167 q^{51} -13.9757 q^{52} +2.54861 q^{53} +2.68704 q^{54} -14.5976 q^{56} -1.17755 q^{57} +16.0039 q^{58} +1.33599 q^{59} -7.28106 q^{61} -19.0863 q^{62} -1.68704 q^{63} +20.3701 q^{64} +2.89883 q^{66} -12.4451 q^{67} +20.5241 q^{68} +4.06295 q^{69} -5.98480 q^{71} +8.65280 q^{72} +3.30065 q^{73} +12.3117 q^{74} -6.14702 q^{76} -1.82001 q^{77} -7.19384 q^{78} -4.00404 q^{79} +1.00000 q^{81} -30.2600 q^{82} -8.87482 q^{83} -8.80669 q^{84} -6.94834 q^{86} +5.95595 q^{87} +9.33480 q^{88} +15.4436 q^{89} +4.51660 q^{91} +21.2094 q^{92} -7.10310 q^{93} +5.15327 q^{94} +17.1155 q^{96} -10.7682 q^{97} -11.1617 q^{98} +1.07882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9	$ 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{11} + 10 q^{12} + 6 q^{13} - 22 q^{14} + 18 q^{16} + 13 q^{17} + 11 q^{19} + 6 q^{21} + 16 q^{22} + 13 q^{23} + 3 q^{24} - 28 q^{26} + 6 q^{27} + 7 q^{28} - 3 q^{29} - 11 q^{31} + 16 q^{32} + 3 q^{33} + 15 q^{34} + 10 q^{36} + 21 q^{37} - 9 q^{38} + 6 q^{39} - q^{41} - 22 q^{42} + 2 q^{43} + 9 q^{44} + 19 q^{46} + 14 q^{47} + 18 q^{48} - 14 q^{49} + 13 q^{51} + 13 q^{52} + 23 q^{53} - 35 q^{56} + 11 q^{57} + 22 q^{58} + 9 q^{59} + 11 q^{61} - 23 q^{62} + 6 q^{63} - 23 q^{64} + 16 q^{66} + 8 q^{67} + 50 q^{68} + 13 q^{69} - 8 q^{71} + 3 q^{72} + 13 q^{73} - 22 q^{74} - 26 q^{76} - 13 q^{77} - 28 q^{78} - 5 q^{79} + 6 q^{81} - 13 q^{82} - 20 q^{83} + 7 q^{84} - 37 q^{86} - 3 q^{87} + 28 q^{88} - 4 q^{89} + 34 q^{91} + 61 q^{92} - 11 q^{93} + 41 q^{94} + 16 q^{96} - 7 q^{97} - 41 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^11 + 10 * q^12 + 6 * q^13 - 22 * q^14 + 18 * q^16 + 13 * q^17 + 11 * q^19 + 6 * q^21 + 16 * q^22 + 13 * q^23 + 3 * q^24 - 28 * q^26 + 6 * q^27 + 7 * q^28 - 3 * q^29 - 11 * q^31 + 16 * q^32 + 3 * q^33 + 15 * q^34 + 10 * q^36 + 21 * q^37 - 9 * q^38 + 6 * q^39 - q^41 - 22 * q^42 + 2 * q^43 + 9 * q^44 + 19 * q^46 + 14 * q^47 + 18 * q^48 - 14 * q^49 + 13 * q^51 + 13 * q^52 + 23 * q^53 - 35 * q^56 + 11 * q^57 + 22 * q^58 + 9 * q^59 + 11 * q^61 - 23 * q^62 + 6 * q^63 - 23 * q^64 + 16 * q^66 + 8 * q^67 + 50 * q^68 + 13 * q^69 - 8 * q^71 + 3 * q^72 + 13 * q^73 - 22 * q^74 - 26 * q^76 - 13 * q^77 - 28 * q^78 - 5 * q^79 + 6 * q^81 - 13 * q^82 - 20 * q^83 + 7 * q^84 - 37 * q^86 - 3 * q^87 + 28 * q^88 - 4 * q^89 + 34 * q^91 + 61 * q^92 - 11 * q^93 + 41 * q^94 + 16 * q^96 - 7 * q^97 - 41 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.68704	1.90003	0.950013	−	0.312211i	$-0.101069\pi$
$2$	2.68704	1.90003	0.950013	+	0.312211i	$0.101069\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.22020	2.61010
$5$	0	0
$5$	0	0
$6$	2.68704	1.09698
$7$	−1.68704	−0.637642	−0.318821	−	0.947815i	$-0.603287\pi$
$7$	−1.68704	−0.637642	−0.318821	+	0.947815i	$0.603287\pi$
$8$	8.65280	3.05923
$9$	1.00000	0.333333
$10$	0	0
$11$	1.07882	0.325276	0.162638	−	0.986686i	$-0.448000\pi$
$11$	1.07882	0.325276	0.162638	+	0.986686i	$0.448000\pi$
$12$	5.22020	1.50694
$13$	−2.67723	−0.742531	−0.371265	−	0.928527i	$-0.621076\pi$
$13$	−2.67723	−0.742531	−0.371265	+	0.928527i	$0.621076\pi$
$14$	−4.53315	−1.21154
$15$	0	0
$16$	12.8101	3.20251
$17$	3.93167	0.953570	0.476785	−	0.879020i	$-0.341802\pi$
$17$	3.93167	0.953570	0.476785	+	0.879020i	$0.341802\pi$
$18$	2.68704	0.633342
$19$	−1.17755	−0.270148	−0.135074	−	0.990836i	$-0.543127\pi$
$19$	−1.17755	−0.270148	−0.135074	+	0.990836i	$0.543127\pi$
$20$	0	0
$21$	−1.68704	−0.368143
$22$	2.89883	0.618032
$23$	4.06295	0.847183	0.423591	−	0.905853i	$-0.360769\pi$
$23$	4.06295	0.847183	0.423591	+	0.905853i	$0.360769\pi$
$24$	8.65280	1.76625
$25$	0	0
$26$	−7.19384	−1.41083
$27$	1.00000	0.192450
$28$	−8.80669	−1.66431
$29$	5.95595	1.10599	0.552996	−	0.833184i	$-0.313484\pi$
$29$	5.95595	1.10599	0.552996	+	0.833184i	$0.313484\pi$
$30$	0	0
$31$	−7.10310	−1.27575	−0.637877	−	0.770138i	$-0.720187\pi$
$31$	−7.10310	−1.27575	−0.637877	+	0.770138i	$0.720187\pi$
$32$	17.1155	3.02563
$33$	1.07882	0.187798
$34$	10.5646	1.81181
$35$	0	0
$36$	5.22020	0.870033
$37$	4.58187	0.753254	0.376627	−	0.926365i	$-0.377084\pi$
$37$	4.58187	0.753254	0.376627	+	0.926365i	$0.377084\pi$
$38$	−3.16412	−0.513287
$39$	−2.67723	−0.428700
$40$	0	0
$41$	−11.2614	−1.75874	−0.879371	−	0.476137i	$-0.842037\pi$
$41$	−11.2614	−1.75874	−0.879371	+	0.476137i	$0.842037\pi$
$42$	−4.53315	−0.699481
$43$	−2.58587	−0.394342	−0.197171	−	0.980369i	$-0.563175\pi$
$43$	−2.58587	−0.394342	−0.197171	+	0.980369i	$0.563175\pi$
$44$	5.63164	0.849002
$45$	0	0
$46$	10.9173	1.60967
$47$	1.91782	0.279743	0.139871	−	0.990170i	$-0.455331\pi$
$47$	1.91782	0.279743	0.139871	+	0.990170i	$0.455331\pi$
$48$	12.8101	1.84897
$49$	−4.15389	−0.593413
$50$	0	0
$51$	3.93167	0.550544
$52$	−13.9757	−1.93808
$53$	2.54861	0.350078	0.175039	−	0.984561i	$-0.443995\pi$
$53$	2.54861	0.350078	0.175039	+	0.984561i	$0.443995\pi$
$54$	2.68704	0.365660
$55$	0	0
$56$	−14.5976	−1.95069
$57$	−1.17755	−0.155970
$58$	16.0039	2.10141
$59$	1.33599	0.173931	0.0869654	−	0.996211i	$-0.472283\pi$
$59$	1.33599	0.173931	0.0869654	+	0.996211i	$0.472283\pi$
$60$	0	0
$61$	−7.28106	−0.932245	−0.466122	−	0.884720i	$-0.654349\pi$
$61$	−7.28106	−0.932245	−0.466122	+	0.884720i	$0.654349\pi$
$62$	−19.0863	−2.42397
$63$	−1.68704	−0.212547
$64$	20.3701	2.54626
$65$	0	0
$66$	2.89883	0.356821
$67$	−12.4451	−1.52041	−0.760203	−	0.649686i	$-0.774900\pi$
$67$	−12.4451	−1.52041	−0.760203	+	0.649686i	$0.774900\pi$
$68$	20.5241	2.48891
$69$	4.06295	0.489121
$70$	0	0
$71$	−5.98480	−0.710266	−0.355133	−	0.934816i	$-0.615564\pi$
$71$	−5.98480	−0.710266	−0.355133	+	0.934816i	$0.615564\pi$
$72$	8.65280	1.01974
$73$	3.30065	0.386312	0.193156	−	0.981168i	$-0.438128\pi$
$73$	3.30065	0.386312	0.193156	+	0.981168i	$0.438128\pi$
$74$	12.3117	1.43120
$75$	0	0
$76$	−6.14702	−0.705112
$77$	−1.82001	−0.207410
$78$	−7.19384	−0.814542
$79$	−4.00404	−0.450490	−0.225245	−	0.974302i	$-0.572318\pi$
$79$	−4.00404	−0.450490	−0.225245	+	0.974302i	$0.572318\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−30.2600	−3.34166
$83$	−8.87482	−0.974138	−0.487069	−	0.873364i	$-0.661934\pi$
$83$	−8.87482	−0.974138	−0.487069	+	0.873364i	$0.661934\pi$
$84$	−8.80669	−0.960889
$85$	0	0
$86$	−6.94834	−0.749259
$87$	5.95595	0.638545
$88$	9.33480	0.995093
$89$	15.4436	1.63702	0.818509	−	0.574493i	$-0.194801\pi$
$89$	15.4436	1.63702	0.818509	+	0.574493i	$0.194801\pi$
$90$	0	0
$91$	4.51660	0.473469
$92$	21.2094	2.21123
$93$	−7.10310	−0.736557
$94$	5.15327	0.531519
$95$	0	0
$96$	17.1155	1.74685
$97$	−10.7682	−1.09335	−0.546673	−	0.837346i	$-0.684106\pi$
$97$	−10.7682	−1.09335	−0.546673	+	0.837346i	$0.684106\pi$
$98$	−11.1617	−1.12750
$99$	1.07882	0.108425
$100$	0	0
$101$	−13.5654	−1.34981	−0.674905	−	0.737905i	$-0.735815\pi$
$101$	−13.5654	−1.34981	−0.674905	+	0.737905i	$0.735815\pi$
$102$	10.5646	1.04605
$103$	−1.36904	−0.134895	−0.0674476	−	0.997723i	$-0.521486\pi$
$103$	−1.36904	−0.134895	−0.0674476	+	0.997723i	$0.521486\pi$
$104$	−23.1656	−2.27157
$105$	0	0
$106$	6.84822	0.665158
$107$	−11.0115	−1.06452	−0.532262	−	0.846579i	$-0.678658\pi$
$107$	−11.0115	−1.06452	−0.532262	+	0.846579i	$0.678658\pi$
$108$	5.22020	0.502314
$109$	3.44890	0.330344	0.165172	−	0.986265i	$-0.447182\pi$
$109$	3.44890	0.330344	0.165172	+	0.986265i	$0.447182\pi$
$110$	0	0
$111$	4.58187	0.434891
$112$	−21.6111	−2.04206
$113$	−6.05194	−0.569319	−0.284660	−	0.958629i	$-0.591881\pi$
$113$	−6.05194	−0.569319	−0.284660	+	0.958629i	$0.591881\pi$
$114$	−3.16412	−0.296347
$115$	0	0
$116$	31.0912	2.88675
$117$	−2.67723	−0.247510
$118$	3.58986	0.330473
$119$	−6.63289	−0.608036
$120$	0	0
$121$	−9.83615	−0.894196
$122$	−19.5645	−1.77129
$123$	−11.2614	−1.01541
$124$	−37.0796	−3.32984
$125$	0	0
$126$	−4.53315	−0.403845
$127$	20.2362	1.79567	0.897835	−	0.440332i	$-0.145139\pi$
$127$	20.2362	1.79567	0.897835	+	0.440332i	$0.145139\pi$
$128$	20.5042	1.81233
$129$	−2.58587	−0.227673
$130$	0	0
$131$	−3.05011	−0.266490	−0.133245	−	0.991083i	$-0.542540\pi$
$131$	−3.05011	−0.266490	−0.133245	+	0.991083i	$0.542540\pi$
$132$	5.63164	0.490171
$133$	1.98657	0.172257
$134$	−33.4404	−2.88881
$135$	0	0
$136$	34.0200	2.91719
$137$	20.5100	1.75229	0.876145	−	0.482048i	$-0.160107\pi$
$137$	20.5100	1.75229	0.876145	+	0.482048i	$0.160107\pi$
$138$	10.9173	0.929343
$139$	18.3184	1.55374	0.776871	−	0.629659i	$-0.216806\pi$
$139$	18.3184	1.55374	0.776871	+	0.629659i	$0.216806\pi$
$140$	0	0
$141$	1.91782	0.161510
$142$	−16.0814	−1.34952
$143$	−2.88825	−0.241527
$144$	12.8101	1.06750
$145$	0	0
$146$	8.86899	0.734003
$147$	−4.15389	−0.342607
$148$	23.9182	1.96607
$149$	0.705938	0.0578327	0.0289163	−	0.999582i	$-0.490794\pi$
$149$	0.705938	0.0578327	0.0289163	+	0.999582i	$0.490794\pi$
$150$	0	0
$151$	7.04538	0.573345	0.286673	−	0.958029i	$-0.407451\pi$
$151$	7.04538	0.573345	0.286673	+	0.958029i	$0.407451\pi$
$152$	−10.1891	−0.826443
$153$	3.93167	0.317857
$154$	−4.89045	−0.394083
$155$	0	0
$156$	−13.9757	−1.11895
$157$	5.12880	0.409323	0.204662	−	0.978833i	$-0.434391\pi$
$157$	5.12880	0.409323	0.204662	+	0.978833i	$0.434391\pi$
$158$	−10.7590	−0.855942
$159$	2.54861	0.202118
$160$	0	0
$161$	−6.85436	−0.540199
$162$	2.68704	0.211114
$163$	24.2613	1.90029	0.950146	−	0.311806i	$-0.100934\pi$
$163$	24.2613	1.90029	0.950146	+	0.311806i	$0.100934\pi$
$164$	−58.7869	−4.59049
$165$	0	0
$166$	−23.8470	−1.85089
$167$	−4.54890	−0.352004	−0.176002	−	0.984390i	$-0.556317\pi$
$167$	−4.54890	−0.352004	−0.176002	+	0.984390i	$0.556317\pi$
$168$	−14.5976	−1.12623
$169$	−5.83243	−0.448648
$170$	0	0
$171$	−1.17755	−0.0900492
$172$	−13.4988	−1.02927
$173$	2.67729	0.203550	0.101775	−	0.994807i	$-0.467548\pi$
$173$	2.67729	0.203550	0.101775	+	0.994807i	$0.467548\pi$
$174$	16.0039	1.21325
$175$	0	0
$176$	13.8197	1.04170
$177$	1.33599	0.100419
$178$	41.4976	3.11038
$179$	−15.6266	−1.16799	−0.583995	−	0.811757i	$-0.698511\pi$
$179$	−15.6266	−1.16799	−0.583995	+	0.811757i	$0.698511\pi$
$180$	0	0
$181$	0.202843	0.0150772	0.00753859	−	0.999972i	$-0.497600\pi$
$181$	0.202843	0.0150772	0.00753859	+	0.999972i	$0.497600\pi$
$182$	12.1363	0.899603
$183$	−7.28106	−0.538232
$184$	35.1559	2.59172
$185$	0	0
$186$	−19.0863	−1.39948
$187$	4.24155	0.310173
$188$	10.0114	0.730156
$189$	−1.68704	−0.122714
$190$	0	0
$191$	−7.91975	−0.573053	−0.286526	−	0.958072i	$-0.592501\pi$
$191$	−7.91975	−0.573053	−0.286526	+	0.958072i	$0.592501\pi$
$192$	20.3701	1.47008
$193$	16.4269	1.18243	0.591216	−	0.806513i	$-0.298648\pi$
$193$	16.4269	1.18243	0.591216	+	0.806513i	$0.298648\pi$
$194$	−28.9346	−2.07738
$195$	0	0
$196$	−21.6841	−1.54887
$197$	17.1369	1.22095	0.610475	−	0.792035i	$-0.290978\pi$
$197$	17.1369	1.22095	0.610475	+	0.792035i	$0.290978\pi$
$198$	2.89883	0.206011
$199$	−2.01848	−0.143086	−0.0715430	−	0.997438i	$-0.522792\pi$
$199$	−2.01848	−0.143086	−0.0715430	+	0.997438i	$0.522792\pi$
$200$	0	0
$201$	−12.4451	−0.877806
$202$	−36.4509	−2.56467
$203$	−10.0479	−0.705227
$204$	20.5241	1.43697
$205$	0	0
$206$	−3.67866	−0.256304
$207$	4.06295	0.282394
$208$	−34.2955	−2.37796
$209$	−1.27036	−0.0878725
$210$	0	0
$211$	−23.8213	−1.63993	−0.819963	−	0.572416i	$-0.806006\pi$
$211$	−23.8213	−1.63993	−0.819963	+	0.572416i	$0.806006\pi$
$212$	13.3042	0.913738
$213$	−5.98480	−0.410072
$214$	−29.5884	−2.02262
$215$	0	0
$216$	8.65280	0.588749
$217$	11.9832	0.813475
$218$	9.26733	0.627663
$219$	3.30065	0.223037
$220$	0	0
$221$	−10.5260	−0.708055
$222$	12.3117	0.826305
$223$	−13.1112	−0.877989	−0.438995	−	0.898490i	$-0.644665\pi$
$223$	−13.1112	−0.877989	−0.438995	+	0.898490i	$0.644665\pi$
$224$	−28.8746	−1.92927
$225$	0	0
$226$	−16.2618	−1.08172
$227$	26.2807	1.74431	0.872155	−	0.489229i	$-0.162722\pi$
$227$	26.2807	1.74431	0.872155	+	0.489229i	$0.162722\pi$
$228$	−6.14702	−0.407096
$229$	1.99605	0.131903	0.0659513	−	0.997823i	$-0.478992\pi$
$229$	1.99605	0.131903	0.0659513	+	0.997823i	$0.478992\pi$
$230$	0	0
$231$	−1.82001	−0.119748
$232$	51.5357	3.38348
$233$	0.525548	0.0344298	0.0172149	−	0.999852i	$-0.494520\pi$
$233$	0.525548	0.0344298	0.0172149	+	0.999852i	$0.494520\pi$
$234$	−7.19384	−0.470276
$235$	0	0
$236$	6.97412	0.453976
$237$	−4.00404	−0.260090
$238$	−17.8229	−1.15528
$239$	−7.00971	−0.453421	−0.226710	−	0.973962i	$-0.572797\pi$
$239$	−7.00971	−0.453421	−0.226710	+	0.973962i	$0.572797\pi$
$240$	0	0
$241$	2.31554	0.149157	0.0745786	−	0.997215i	$-0.476239\pi$
$241$	2.31554	0.149157	0.0745786	+	0.997215i	$0.476239\pi$
$242$	−26.4302	−1.69899
$243$	1.00000	0.0641500
$244$	−38.0086	−2.43325
$245$	0	0
$246$	−30.2600	−1.92931
$247$	3.15257	0.200593
$248$	−61.4617	−3.90282
$249$	−8.87482	−0.562419
$250$	0	0
$251$	−6.17885	−0.390005	−0.195003	−	0.980803i	$-0.562472\pi$
$251$	−6.17885	−0.390005	−0.195003	+	0.980803i	$0.562472\pi$
$252$	−8.80669	−0.554769
$253$	4.38318	0.275568
$254$	54.3755	3.41182
$255$	0	0
$256$	14.3555	0.897217
$257$	−13.2239	−0.824882	−0.412441	−	0.910984i	$-0.635324\pi$
$257$	−13.2239	−0.824882	−0.412441	+	0.910984i	$0.635324\pi$
$258$	−6.94834	−0.432585
$259$	−7.72980	−0.480306
$260$	0	0
$261$	5.95595	0.368664
$262$	−8.19578	−0.506337
$263$	6.97643	0.430185	0.215092	−	0.976594i	$-0.430995\pi$
$263$	6.97643	0.430185	0.215092	+	0.976594i	$0.430995\pi$
$264$	9.33480	0.574517
$265$	0	0
$266$	5.33800	0.327294
$267$	15.4436	0.945133
$268$	−64.9656	−3.96841
$269$	23.7199	1.44623	0.723113	−	0.690730i	$-0.242711\pi$
$269$	23.7199	1.44623	0.723113	+	0.690730i	$0.242711\pi$
$270$	0	0
$271$	28.9910	1.76108	0.880539	−	0.473975i	$-0.157181\pi$
$271$	28.9910	1.76108	0.880539	+	0.473975i	$0.157181\pi$
$272$	50.3649	3.05382
$273$	4.51660	0.273357
$274$	55.1113	3.32940
$275$	0	0
$276$	21.2094	1.27665
$277$	8.58667	0.515923	0.257962	−	0.966155i	$-0.416949\pi$
$277$	8.58667	0.515923	0.257962	+	0.966155i	$0.416949\pi$
$278$	49.2222	2.95215
$279$	−7.10310	−0.425251
$280$	0	0
$281$	17.1661	1.02405	0.512023	−	0.858972i	$-0.328896\pi$
$281$	17.1661	1.02405	0.512023	+	0.858972i	$0.328896\pi$
$282$	5.15327	0.306872
$283$	9.62005	0.571853	0.285926	−	0.958252i	$-0.407699\pi$
$283$	9.62005	0.571853	0.285926	+	0.958252i	$0.407699\pi$
$284$	−31.2419	−1.85386
$285$	0	0
$286$	−7.76084	−0.458908
$287$	18.9985	1.12145
$288$	17.1155	1.00854
$289$	−1.54198	−0.0907048
$290$	0	0
$291$	−10.7682	−0.631243
$292$	17.2301	1.00831
$293$	−16.8202	−0.982649	−0.491324	−	0.870977i	$-0.663487\pi$
$293$	−16.8202	−0.982649	−0.491324	+	0.870977i	$0.663487\pi$
$294$	−11.1617	−0.650962
$295$	0	0
$296$	39.6460	2.30438
$297$	1.07882	0.0625994
$298$	1.89688	0.109884
$299$	−10.8775	−0.629059
$300$	0	0
$301$	4.36247	0.251449
$302$	18.9312	1.08937
$303$	−13.5654	−0.779313
$304$	−15.0844	−0.865151
$305$	0	0
$306$	10.5646	0.603936
$307$	−11.3212	−0.646134	−0.323067	−	0.946376i	$-0.604714\pi$
$307$	−11.3212	−0.646134	−0.323067	+	0.946376i	$0.604714\pi$
$308$	−9.50081	−0.541359
$309$	−1.36904	−0.0778818
$310$	0	0
$311$	18.5635	1.05264	0.526318	−	0.850288i	$-0.323572\pi$
$311$	18.5635	1.05264	0.526318	+	0.850288i	$0.323572\pi$
$312$	−23.1656	−1.31149
$313$	9.69951	0.548249	0.274124	−	0.961694i	$-0.411612\pi$
$313$	9.69951	0.548249	0.274124	+	0.961694i	$0.411612\pi$
$314$	13.7813	0.777724
$315$	0	0
$316$	−20.9019	−1.17582
$317$	−7.47647	−0.419920	−0.209960	−	0.977710i	$-0.567333\pi$
$317$	−7.47647	−0.419920	−0.209960	+	0.977710i	$0.567333\pi$
$318$	6.84822	0.384029
$319$	6.42538	0.359752
$320$	0	0
$321$	−11.0115	−0.614604
$322$	−18.4180	−1.02639
$323$	−4.62972	−0.257605
$324$	5.22020	0.290011
$325$	0	0
$326$	65.1911	3.61060
$327$	3.44890	0.190724
$328$	−97.4430	−5.38039
$329$	−3.23544	−0.178376
$330$	0	0
$331$	−25.2570	−1.38825	−0.694125	−	0.719854i	$-0.744209\pi$
$331$	−25.2570	−1.38825	−0.694125	+	0.719854i	$0.744209\pi$
$332$	−46.3283	−2.54259
$333$	4.58187	0.251085
$334$	−12.2231	−0.668817
$335$	0	0
$336$	−21.6111	−1.17898
$337$	13.0240	0.709463	0.354731	−	0.934968i	$-0.384572\pi$
$337$	13.0240	0.709463	0.354731	+	0.934968i	$0.384572\pi$
$338$	−15.6720	−0.852443
$339$	−6.05194	−0.328697
$340$	0	0
$341$	−7.66295	−0.414972
$342$	−3.16412	−0.171096
$343$	18.8171	1.01603
$344$	−22.3750	−1.20638
$345$	0	0
$346$	7.19398	0.386751
$347$	6.00149	0.322177	0.161089	−	0.986940i	$-0.448500\pi$
$347$	6.00149	0.322177	0.161089	+	0.986940i	$0.448500\pi$
$348$	31.0912	1.66666
$349$	−22.7183	−1.21608	−0.608042	−	0.793905i	$-0.708045\pi$
$349$	−22.7183	−1.21608	−0.608042	+	0.793905i	$0.708045\pi$
$350$	0	0
$351$	−2.67723	−0.142900
$352$	18.4646	0.984164
$353$	4.85493	0.258402	0.129201	−	0.991618i	$-0.458759\pi$
$353$	4.85493	0.258402	0.129201	+	0.991618i	$0.458759\pi$
$354$	3.58986	0.190799
$355$	0	0
$356$	80.6186	4.27278
$357$	−6.63289	−0.351050
$358$	−41.9895	−2.21921
$359$	28.8910	1.52481	0.762403	−	0.647102i	$-0.224019\pi$
$359$	28.8910	1.52481	0.762403	+	0.647102i	$0.224019\pi$
$360$	0	0
$361$	−17.6134	−0.927020
$362$	0.545047	0.0286470
$363$	−9.83615	−0.516264
$364$	23.5776	1.23580
$365$	0	0
$366$	−19.5645	−1.02265
$367$	14.7089	0.767800	0.383900	−	0.923375i	$-0.374581\pi$
$367$	14.7089	0.767800	0.383900	+	0.923375i	$0.374581\pi$
$368$	52.0465	2.71311
$369$	−11.2614	−0.586247
$370$	0	0
$371$	−4.29961	−0.223225
$372$	−37.0796	−1.92249
$373$	33.0391	1.71070	0.855350	−	0.518051i	$-0.173342\pi$
$373$	33.0391	1.71070	0.855350	+	0.518051i	$0.173342\pi$
$374$	11.3972	0.589337
$375$	0	0
$376$	16.5945	0.855797
$377$	−15.9455	−0.821233
$378$	−4.53315	−0.233160
$379$	−15.1556	−0.778493	−0.389247	−	0.921134i	$-0.627265\pi$
$379$	−15.1556	−0.778493	−0.389247	+	0.921134i	$0.627265\pi$
$380$	0	0
$381$	20.2362	1.03673
$382$	−21.2807	−1.08882
$383$	8.00811	0.409195	0.204598	−	0.978846i	$-0.434411\pi$
$383$	8.00811	0.409195	0.204598	+	0.978846i	$0.434411\pi$
$384$	20.5042	1.04635
$385$	0	0
$386$	44.1397	2.24665
$387$	−2.58587	−0.131447
$388$	−56.2121	−2.85374
$389$	1.07463	0.0544858	0.0272429	−	0.999629i	$-0.491327\pi$
$389$	1.07463	0.0544858	0.0272429	+	0.999629i	$0.491327\pi$
$390$	0	0
$391$	15.9742	0.807848
$392$	−35.9428	−1.81538
$393$	−3.05011	−0.153858
$394$	46.0475	2.31984
$395$	0	0
$396$	5.63164	0.283001
$397$	24.2139	1.21526	0.607630	−	0.794220i	$-0.292120\pi$
$397$	24.2139	1.21526	0.607630	+	0.794220i	$0.292120\pi$
$398$	−5.42373	−0.271867
$399$	1.98657	0.0994529
$400$	0	0
$401$	−1.99317	−0.0995340	−0.0497670	−	0.998761i	$-0.515848\pi$
$401$	−1.99317	−0.0995340	−0.0497670	+	0.998761i	$0.515848\pi$
$402$	−33.4404	−1.66785
$403$	19.0166	0.947287
$404$	−70.8142	−3.52314
$405$	0	0
$406$	−26.9992	−1.33995
$407$	4.94300	0.245015
$408$	34.0200	1.68424
$409$	6.66478	0.329552	0.164776	−	0.986331i	$-0.447310\pi$
$409$	6.66478	0.329552	0.164776	+	0.986331i	$0.447310\pi$
$410$	0	0
$411$	20.5100	1.01168
$412$	−7.14664	−0.352090
$413$	−2.25387	−0.110906
$414$	10.9173	0.536556
$415$	0	0
$416$	−45.8223	−2.24662
$417$	18.3184	0.897054
$418$	−3.41351	−0.166960
$419$	21.3540	1.04321	0.521606	−	0.853186i	$-0.325333\pi$
$419$	21.3540	1.04321	0.521606	+	0.853186i	$0.325333\pi$
$420$	0	0
$421$	22.3367	1.08863	0.544313	−	0.838882i	$-0.316790\pi$
$421$	22.3367	1.08863	0.544313	+	0.838882i	$0.316790\pi$
$422$	−64.0088	−3.11590
$423$	1.91782	0.0932476
$424$	22.0526	1.07097
$425$	0	0
$426$	−16.0814	−0.779147
$427$	12.2835	0.594438
$428$	−57.4823	−2.77851
$429$	−2.88825	−0.139446
$430$	0	0
$431$	−30.4129	−1.46494	−0.732469	−	0.680800i	$-0.761632\pi$
$431$	−30.4129	−1.46494	−0.732469	+	0.680800i	$0.761632\pi$
$432$	12.8101	0.616324
$433$	−0.576639	−0.0277115	−0.0138558	−	0.999904i	$-0.504411\pi$
$433$	−0.576639	−0.0277115	−0.0138558	+	0.999904i	$0.504411\pi$
$434$	32.1994	1.54562
$435$	0	0
$436$	18.0039	0.862231
$437$	−4.78431	−0.228864
$438$	8.86899	0.423777
$439$	12.8045	0.611125	0.305563	−	0.952172i	$-0.401155\pi$
$439$	12.8045	0.611125	0.305563	+	0.952172i	$0.401155\pi$
$440$	0	0
$441$	−4.15389	−0.197804
$442$	−28.2838	−1.34532
$443$	−14.3147	−0.680110	−0.340055	−	0.940405i	$-0.610446\pi$
$443$	−14.3147	−0.680110	−0.340055	+	0.940405i	$0.610446\pi$
$444$	23.9182	1.13511
$445$	0	0
$446$	−35.2303	−1.66820
$447$	0.705938	0.0333897
$448$	−34.3652	−1.62360
$449$	−11.9663	−0.564724	−0.282362	−	0.959308i	$-0.591118\pi$
$449$	−11.9663	−0.564724	−0.282362	+	0.959308i	$0.591118\pi$
$450$	0	0
$451$	−12.1490	−0.572076
$452$	−31.5923	−1.48598
$453$	7.04538	0.331021
$454$	70.6173	3.31424
$455$	0	0
$456$	−10.1891	−0.477147
$457$	8.22154	0.384587	0.192294	−	0.981337i	$-0.438407\pi$
$457$	8.22154	0.384587	0.192294	+	0.981337i	$0.438407\pi$
$458$	5.36346	0.250618
$459$	3.93167	0.183515
$460$	0	0
$461$	1.27216	0.0592505	0.0296253	−	0.999561i	$-0.490569\pi$
$461$	1.27216	0.0592505	0.0296253	+	0.999561i	$0.490569\pi$
$462$	−4.89045	−0.227524
$463$	−32.6764	−1.51860	−0.759300	−	0.650740i	$-0.774459\pi$
$463$	−32.6764	−1.51860	−0.759300	+	0.650740i	$0.774459\pi$
$464$	76.2960	3.54195
$465$	0	0
$466$	1.41217	0.0654175
$467$	−14.4347	−0.667958	−0.333979	−	0.942581i	$-0.608391\pi$
$467$	−14.4347	−0.667958	−0.333979	+	0.942581i	$0.608391\pi$
$468$	−13.9757	−0.646026
$469$	20.9953	0.969474
$470$	0	0
$471$	5.12880	0.236323
$472$	11.5600	0.532094
$473$	−2.78968	−0.128270
$474$	−10.7590	−0.494178
$475$	0	0
$476$	−34.6250	−1.58703
$477$	2.54861	0.116693
$478$	−18.8354	−0.861511
$479$	−16.8618	−0.770436	−0.385218	−	0.922826i	$-0.625874\pi$
$479$	−16.8618	−0.770436	−0.385218	+	0.922826i	$0.625874\pi$
$480$	0	0
$481$	−12.2667	−0.559314
$482$	6.22196	0.283403
$483$	−6.85436	−0.311884
$484$	−51.3466	−2.33394
$485$	0	0
$486$	2.68704	0.121887
$487$	−39.8235	−1.80457	−0.902287	−	0.431135i	$-0.858113\pi$
$487$	−39.8235	−1.80457	−0.902287	+	0.431135i	$0.858113\pi$
$488$	−63.0016	−2.85195
$489$	24.2613	1.09713
$490$	0	0
$491$	14.0255	0.632961	0.316480	−	0.948599i	$-0.397499\pi$
$491$	14.0255	0.632961	0.316480	+	0.948599i	$0.397499\pi$
$492$	−58.7869	−2.65032
$493$	23.4168	1.05464
$494$	8.47108	0.381132
$495$	0	0
$496$	−90.9911	−4.08562
$497$	10.0966	0.452895
$498$	−23.8470	−1.06861
$499$	15.2315	0.681857	0.340929	−	0.940089i	$-0.389259\pi$
$499$	15.2315	0.681857	0.340929	+	0.940089i	$0.389259\pi$
$500$	0	0
$501$	−4.54890	−0.203230
$502$	−16.6028	−0.741020
$503$	−23.7330	−1.05820	−0.529101	−	0.848559i	$-0.677471\pi$
$503$	−23.7330	−1.05820	−0.529101	+	0.848559i	$0.677471\pi$
$504$	−14.5976	−0.650231
$505$	0	0
$506$	11.7778	0.523586
$507$	−5.83243	−0.259027
$508$	105.637	4.68688
$509$	−12.5097	−0.554482	−0.277241	−	0.960800i	$-0.589420\pi$
$509$	−12.5097	−0.554482	−0.277241	+	0.960800i	$0.589420\pi$
$510$	0	0
$511$	−5.56834	−0.246329
$512$	−2.43464	−0.107597
$513$	−1.17755	−0.0519899
$514$	−35.5331	−1.56730
$515$	0	0
$516$	−13.4988	−0.594249
$517$	2.06898	0.0909936
$518$	−20.7703	−0.912595
$519$	2.67729	0.117520
$520$	0	0
$521$	−27.9638	−1.22512	−0.612559	−	0.790425i	$-0.709860\pi$
$521$	−27.9638	−1.22512	−0.612559	+	0.790425i	$0.709860\pi$
$522$	16.0039	0.700471
$523$	−15.7013	−0.686569	−0.343285	−	0.939231i	$-0.611540\pi$
$523$	−15.7013	−0.686569	−0.343285	+	0.939231i	$0.611540\pi$
$524$	−15.9222	−0.695564
$525$	0	0
$526$	18.7460	0.817362
$527$	−27.9270	−1.21652
$528$	13.8197	0.601426
$529$	−6.49247	−0.282281
$530$	0	0
$531$	1.33599	0.0579769
$532$	10.3703	0.449609
$533$	30.1495	1.30592
$534$	41.4976	1.79578
$535$	0	0
$536$	−107.685	−4.65127
$537$	−15.6266	−0.674340
$538$	63.7363	2.74787
$539$	−4.48129	−0.193023
$540$	0	0
$541$	−23.9783	−1.03091	−0.515455	−	0.856917i	$-0.672377\pi$
$541$	−23.9783	−1.03091	−0.515455	+	0.856917i	$0.672377\pi$
$542$	77.9000	3.34609
$543$	0.202843	0.00870482
$544$	67.2927	2.88515
$545$	0	0
$546$	12.1363	0.519386
$547$	5.62681	0.240585	0.120293	−	0.992738i	$-0.461617\pi$
$547$	5.62681	0.240585	0.120293	+	0.992738i	$0.461617\pi$
$548$	107.066	4.57365
$549$	−7.28106	−0.310748
$550$	0	0
$551$	−7.01341	−0.298781
$552$	35.1559	1.49633
$553$	6.75498	0.287251
$554$	23.0728	0.980268
$555$	0	0
$556$	95.6254	4.05542
$557$	42.4247	1.79759	0.898796	−	0.438366i	$-0.144443\pi$
$557$	42.4247	1.79759	0.898796	+	0.438366i	$0.144443\pi$
$558$	−19.0863	−0.807989
$559$	6.92298	0.292811
$560$	0	0
$561$	4.24155	0.179079
$562$	46.1261	1.94571
$563$	−5.78597	−0.243850	−0.121925	−	0.992539i	$-0.538907\pi$
$563$	−5.78597	−0.243850	−0.121925	+	0.992539i	$0.538907\pi$
$564$	10.0114	0.421556
$565$	0	0
$566$	25.8495	1.08653
$567$	−1.68704	−0.0708491
$568$	−51.7853	−2.17286
$569$	−22.0056	−0.922522	−0.461261	−	0.887265i	$-0.652603\pi$
$569$	−22.0056	−0.922522	−0.461261	+	0.887265i	$0.652603\pi$
$570$	0	0
$571$	33.6143	1.40672	0.703358	−	0.710835i	$-0.251683\pi$
$571$	33.6143	1.40672	0.703358	+	0.710835i	$0.251683\pi$
$572$	−15.0772	−0.630410
$573$	−7.91975	−0.330852
$574$	51.0499	2.13078
$575$	0	0
$576$	20.3701	0.848754
$577$	−40.2350	−1.67501	−0.837503	−	0.546433i	$-0.815985\pi$
$577$	−40.2350	−1.67501	−0.837503	+	0.546433i	$0.815985\pi$
$578$	−4.14337	−0.172341
$579$	16.4269	0.682677
$580$	0	0
$581$	14.9722	0.621151
$582$	−28.9346	−1.19938
$583$	2.74948	0.113872
$584$	28.5599	1.18182
$585$	0	0
$586$	−45.1967	−1.86706
$587$	2.82299	0.116517	0.0582587	−	0.998302i	$-0.481445\pi$
$587$	2.82299	0.116517	0.0582587	+	0.998302i	$0.481445\pi$
$588$	−21.6841	−0.894238
$589$	8.36423	0.344642
$590$	0	0
$591$	17.1369	0.704916
$592$	58.6939	2.41231
$593$	24.6805	1.01351	0.506754	−	0.862091i	$-0.330845\pi$
$593$	24.6805	1.01351	0.506754	+	0.862091i	$0.330845\pi$
$594$	2.89883	0.118940
$595$	0	0
$596$	3.68513	0.150949
$597$	−2.01848	−0.0826108
$598$	−29.2282	−1.19523
$599$	−7.71547	−0.315245	−0.157623	−	0.987499i	$-0.550383\pi$
$599$	−7.71547	−0.315245	−0.157623	+	0.987499i	$0.550383\pi$
$600$	0	0
$601$	22.6506	0.923938	0.461969	−	0.886896i	$-0.347143\pi$
$601$	22.6506	0.923938	0.461969	+	0.886896i	$0.347143\pi$
$602$	11.7222	0.477759
$603$	−12.4451	−0.506802
$604$	36.7783	1.49649
$605$	0	0
$606$	−36.4509	−1.48072
$607$	24.6423	1.00020	0.500099	−	0.865968i	$-0.333297\pi$
$607$	24.6423	1.00020	0.500099	+	0.865968i	$0.333297\pi$
$608$	−20.1543	−0.817367
$609$	−10.0479	−0.407163
$610$	0	0
$611$	−5.13445	−0.207718
$612$	20.5241	0.829637
$613$	41.8034	1.68842	0.844211	−	0.536011i	$-0.180069\pi$
$613$	41.8034	1.68842	0.844211	+	0.536011i	$0.180069\pi$
$614$	−30.4205	−1.22767
$615$	0	0
$616$	−15.7482	−0.634513
$617$	−15.9390	−0.641680	−0.320840	−	0.947133i	$-0.603965\pi$
$617$	−15.9390	−0.641680	−0.320840	+	0.947133i	$0.603965\pi$
$618$	−3.67866	−0.147977
$619$	−47.1700	−1.89592	−0.947961	−	0.318385i	$-0.896859\pi$
$619$	−47.1700	−1.89592	−0.947961	+	0.318385i	$0.896859\pi$
$620$	0	0
$621$	4.06295	0.163040
$622$	49.8808	2.00004
$623$	−26.0540	−1.04383
$624$	−34.2955	−1.37292
$625$	0	0
$626$	26.0630	1.04169
$627$	−1.27036	−0.0507332
$628$	26.7734	1.06837
$629$	18.0144	0.718280
$630$	0	0
$631$	32.3634	1.28836	0.644182	−	0.764872i	$-0.277198\pi$
$631$	32.3634	1.28836	0.644182	+	0.764872i	$0.277198\pi$
$632$	−34.6462	−1.37815
$633$	−23.8213	−0.946812
$634$	−20.0896	−0.797859
$635$	0	0
$636$	13.3042	0.527547
$637$	11.1209	0.440627
$638$	17.2653	0.683539
$639$	−5.98480	−0.236755
$640$	0	0
$641$	18.0042	0.711122	0.355561	−	0.934653i	$-0.384290\pi$
$641$	18.0042	0.711122	0.355561	+	0.934653i	$0.384290\pi$
$642$	−29.5884	−1.16776
$643$	−21.8891	−0.863224	−0.431612	−	0.902059i	$-0.642055\pi$
$643$	−21.8891	−0.863224	−0.431612	+	0.902059i	$0.642055\pi$
$644$	−35.7811	−1.40997
$645$	0	0
$646$	−12.4403	−0.489455
$647$	−19.0263	−0.748003	−0.374001	−	0.927428i	$-0.622015\pi$
$647$	−19.0263	−0.748003	−0.374001	+	0.927428i	$0.622015\pi$
$648$	8.65280	0.339914
$649$	1.44129	0.0565755
$650$	0	0
$651$	11.9832	0.469660
$652$	126.649	4.95995
$653$	2.31971	0.0907774	0.0453887	−	0.998969i	$-0.485547\pi$
$653$	2.31971	0.0907774	0.0453887	+	0.998969i	$0.485547\pi$
$654$	9.26733	0.362381
$655$	0	0
$656$	−144.260	−5.63239
$657$	3.30065	0.128771
$658$	−8.69378	−0.338919
$659$	7.19180	0.280153	0.140076	−	0.990141i	$-0.455265\pi$
$659$	7.19180	0.280153	0.140076	+	0.990141i	$0.455265\pi$
$660$	0	0
$661$	43.0214	1.67334	0.836669	−	0.547709i	$-0.184500\pi$
$661$	43.0214	1.67334	0.836669	+	0.547709i	$0.184500\pi$
$662$	−67.8666	−2.63771
$663$	−10.5260	−0.408796
$664$	−76.7920	−2.98011
$665$	0	0
$666$	12.3117	0.477067
$667$	24.1987	0.936977
$668$	−23.7461	−0.918765
$669$	−13.1112	−0.506907
$670$	0	0
$671$	−7.85494	−0.303237
$672$	−28.8746	−1.11386
$673$	29.8031	1.14882	0.574412	−	0.818566i	$-0.305231\pi$
$673$	29.8031	1.14882	0.574412	+	0.818566i	$0.305231\pi$
$674$	34.9961	1.34800
$675$	0	0
$676$	−30.4464	−1.17102
$677$	26.7346	1.02749	0.513746	−	0.857942i	$-0.328257\pi$
$677$	26.7346	1.02749	0.513746	+	0.857942i	$0.328257\pi$
$678$	−16.2618	−0.624532
$679$	18.1664	0.697163
$680$	0	0
$681$	26.2807	1.00708
$682$	−20.5907	−0.788457
$683$	−28.4950	−1.09033	−0.545165	−	0.838329i	$-0.683533\pi$
$683$	−28.4950	−1.09033	−0.545165	+	0.838329i	$0.683533\pi$
$684$	−6.14702	−0.235037
$685$	0	0
$686$	50.5623	1.93048
$687$	1.99605	0.0761540
$688$	−33.1251	−1.26288
$689$	−6.82321	−0.259944
$690$	0	0
$691$	34.6469	1.31803	0.659015	−	0.752130i	$-0.270973\pi$
$691$	34.6469	1.31803	0.659015	+	0.752130i	$0.270973\pi$
$692$	13.9760	0.531286
$693$	−1.82001	−0.0691365
$694$	16.1263	0.612145
$695$	0	0
$696$	51.5357	1.95345
$697$	−44.2763	−1.67708
$698$	−61.0451	−2.31059
$699$	0.525548	0.0198781
$700$	0	0
$701$	0.973305	0.0367612	0.0183806	−	0.999831i	$-0.494149\pi$
$701$	0.973305	0.0367612	0.0183806	+	0.999831i	$0.494149\pi$
$702$	−7.19384	−0.271514
$703$	−5.39536	−0.203490
$704$	21.9756	0.828237
$705$	0	0
$706$	13.0454	0.490971
$707$	22.8854	0.860696
$708$	6.97412	0.262103
$709$	−11.3242	−0.425291	−0.212645	−	0.977129i	$-0.568208\pi$
$709$	−11.3242	−0.425291	−0.212645	+	0.977129i	$0.568208\pi$
$710$	0	0
$711$	−4.00404	−0.150163
$712$	133.630	5.00801
$713$	−28.8595	−1.08080
$714$	−17.8229	−0.667004
$715$	0	0
$716$	−81.5742	−3.04857
$717$	−7.00971	−0.261783
$718$	77.6312	2.89717
$719$	−30.7320	−1.14611	−0.573056	−	0.819516i	$-0.694242\pi$
$719$	−30.7320	−1.14611	−0.573056	+	0.819516i	$0.694242\pi$
$720$	0	0
$721$	2.30962	0.0860149
$722$	−47.3279	−1.76136
$723$	2.31554	0.0861159
$724$	1.05888	0.0393529
$725$	0	0
$726$	−26.4302	−0.980915
$727$	6.56836	0.243607	0.121803	−	0.992554i	$-0.461132\pi$
$727$	6.56836	0.243607	0.121803	+	0.992554i	$0.461132\pi$
$728$	39.0813	1.44845
$729$	1.00000	0.0370370
$730$	0	0
$731$	−10.1668	−0.376032
$732$	−38.0086	−1.40484
$733$	31.9276	1.17927	0.589636	−	0.807669i	$-0.299271\pi$
$733$	31.9276	1.17927	0.589636	+	0.807669i	$0.299271\pi$
$734$	39.5235	1.45884
$735$	0	0
$736$	69.5395	2.56326
$737$	−13.4259	−0.494551
$738$	−30.2600	−1.11389
$739$	−15.3072	−0.563083	−0.281542	−	0.959549i	$-0.590846\pi$
$739$	−15.3072	−0.563083	−0.281542	+	0.959549i	$0.590846\pi$
$740$	0	0
$741$	3.15257	0.115812
$742$	−11.5532	−0.424132
$743$	−16.5455	−0.606995	−0.303498	−	0.952832i	$-0.598154\pi$
$743$	−16.5455	−0.606995	−0.303498	+	0.952832i	$0.598154\pi$
$744$	−61.4617	−2.25330
$745$	0	0
$746$	88.7774	3.25037
$747$	−8.87482	−0.324713
$748$	22.1417	0.809582
$749$	18.5769	0.678786
$750$	0	0
$751$	46.0279	1.67958	0.839791	−	0.542911i	$-0.182678\pi$
$751$	46.0279	1.67958	0.839791	+	0.542911i	$0.182678\pi$
$752$	24.5674	0.895880
$753$	−6.17885	−0.225170
$754$	−42.8461	−1.56036
$755$	0	0
$756$	−8.80669	−0.320296
$757$	26.5282	0.964184	0.482092	−	0.876121i	$-0.339877\pi$
$757$	26.5282	0.964184	0.482092	+	0.876121i	$0.339877\pi$
$758$	−40.7239	−1.47916
$759$	4.38318	0.159099
$760$	0	0
$761$	−28.4241	−1.03037	−0.515187	−	0.857078i	$-0.672277\pi$
$761$	−28.4241	−1.03037	−0.515187	+	0.857078i	$0.672277\pi$
$762$	54.3755	1.96982
$763$	−5.81843	−0.210641
$764$	−41.3426	−1.49572
$765$	0	0
$766$	21.5181	0.777481
$767$	−3.57675	−0.129149
$768$	14.3555	0.518009
$769$	−8.95952	−0.323089	−0.161544	−	0.986865i	$-0.551647\pi$
$769$	−8.95952	−0.323089	−0.161544	+	0.986865i	$0.551647\pi$
$770$	0	0
$771$	−13.2239	−0.476246
$772$	85.7515	3.08626
$773$	−23.1042	−0.831001	−0.415500	−	0.909593i	$-0.636393\pi$
$773$	−23.1042	−0.831001	−0.415500	+	0.909593i	$0.636393\pi$
$774$	−6.94834	−0.249753
$775$	0	0
$776$	−93.1752	−3.34479
$777$	−7.72980	−0.277305
$778$	2.88757	0.103524
$779$	13.2609	0.475120
$780$	0	0
$781$	−6.45651	−0.231032
$782$	42.9232	1.53493
$783$	5.95595	0.212848
$784$	−53.2115	−1.90041
$785$	0	0
$786$	−8.19578	−0.292334
$787$	2.03390	0.0725009	0.0362504	−	0.999343i	$-0.488459\pi$
$787$	2.03390	0.0725009	0.0362504	+	0.999343i	$0.488459\pi$
$788$	89.4578	3.18680
$789$	6.97643	0.248367
$790$	0	0
$791$	10.2099	0.363022
$792$	9.33480	0.331698
$793$	19.4931	0.692220
$794$	65.0637	2.30902
$795$	0	0
$796$	−10.5368	−0.373469
$797$	12.1923	0.431874	0.215937	−	0.976407i	$-0.430719\pi$
$797$	12.1923	0.431874	0.215937	+	0.976407i	$0.430719\pi$
$798$	5.33800	0.188963
$799$	7.54024	0.266754
$800$	0	0
$801$	15.4436	0.545673
$802$	−5.35572	−0.189117
$803$	3.56080	0.125658
$804$	−64.9656	−2.29116
$805$	0	0
$806$	51.0985	1.79987
$807$	23.7199	0.834979
$808$	−117.379	−4.12938
$809$	8.83355	0.310571	0.155286	−	0.987870i	$-0.450370\pi$
$809$	8.83355	0.310571	0.155286	+	0.987870i	$0.450370\pi$
$810$	0	0
$811$	−13.9184	−0.488741	−0.244370	−	0.969682i	$-0.578581\pi$
$811$	−13.9184	−0.488741	−0.244370	+	0.969682i	$0.578581\pi$
$812$	−52.4522	−1.84071
$813$	28.9910	1.01676
$814$	13.2820	0.465535
$815$	0	0
$816$	50.3649	1.76312
$817$	3.04498	0.106530
$818$	17.9085	0.626158
$819$	4.51660	0.157823
$820$	0	0
$821$	−29.4930	−1.02931	−0.514656	−	0.857397i	$-0.672080\pi$
$821$	−29.4930	−1.02931	−0.514656	+	0.857397i	$0.672080\pi$
$822$	55.1113	1.92223
$823$	41.9661	1.46285	0.731423	−	0.681924i	$-0.238857\pi$
$823$	41.9661	1.46285	0.731423	+	0.681924i	$0.238857\pi$
$824$	−11.8460	−0.412675
$825$	0	0
$826$	−6.05624	−0.210724
$827$	−37.4674	−1.30287	−0.651435	−	0.758704i	$-0.725833\pi$
$827$	−37.4674	−1.30287	−0.651435	+	0.758704i	$0.725833\pi$
$828$	21.2094	0.737077
$829$	−9.55614	−0.331899	−0.165949	−	0.986134i	$-0.553069\pi$
$829$	−9.55614	−0.331899	−0.165949	+	0.986134i	$0.553069\pi$
$830$	0	0
$831$	8.58667	0.297868
$832$	−54.5355	−1.89068
$833$	−16.3317	−0.565860
$834$	49.2222	1.70443
$835$	0	0
$836$	−6.63152	−0.229356
$837$	−7.10310	−0.245519
$838$	57.3792	1.98213
$839$	54.7310	1.88952	0.944761	−	0.327759i	$-0.106293\pi$
$839$	54.7310	1.88952	0.944761	+	0.327759i	$0.106293\pi$
$840$	0	0
$841$	6.47334	0.223219
$842$	60.0197	2.06842
$843$	17.1661	0.591233
$844$	−124.352	−4.28037
$845$	0	0
$846$	5.15327	0.177173
$847$	16.5940	0.570177
$848$	32.6478	1.12113
$849$	9.62005	0.330159
$850$	0	0
$851$	18.6159	0.638144
$852$	−31.2419	−1.07033
$853$	15.3067	0.524092	0.262046	−	0.965055i	$-0.415603\pi$
$853$	15.3067	0.524092	0.262046	+	0.965055i	$0.415603\pi$
$854$	33.0062	1.12945
$855$	0	0
$856$	−95.2806	−3.25662
$857$	8.66910	0.296131	0.148065	−	0.988978i	$-0.452695\pi$
$857$	8.66910	0.296131	0.148065	+	0.988978i	$0.452695\pi$
$858$	−7.76084	−0.264951
$859$	−30.4078	−1.03750	−0.518750	−	0.854926i	$-0.673603\pi$
$859$	−30.4078	−1.03750	−0.518750	+	0.854926i	$0.673603\pi$
$860$	0	0
$861$	18.9985	0.647468
$862$	−81.7208	−2.78342
$863$	18.0425	0.614175	0.307088	−	0.951681i	$-0.400646\pi$
$863$	18.0425	0.614175	0.307088	+	0.951681i	$0.400646\pi$
$864$	17.1155	0.582283
$865$	0	0
$866$	−1.54945	−0.0526526
$867$	−1.54198	−0.0523684
$868$	62.5548	2.12325
$869$	−4.31963	−0.146533
$870$	0	0
$871$	33.3183	1.12895
$872$	29.8426	1.01060
$873$	−10.7682	−0.364449
$874$	−12.8556	−0.434848
$875$	0	0
$876$	17.2301	0.582149
$877$	−22.3057	−0.753211	−0.376605	−	0.926374i	$-0.622909\pi$
$877$	−22.3057	−0.753211	−0.376605	+	0.926374i	$0.622909\pi$
$878$	34.4062	1.16115
$879$	−16.8202	−0.567332
$880$	0	0
$881$	7.75956	0.261426	0.130713	−	0.991420i	$-0.458273\pi$
$881$	7.75956	0.261426	0.130713	+	0.991420i	$0.458273\pi$
$882$	−11.1617	−0.375833
$883$	19.9527	0.671462	0.335731	−	0.941958i	$-0.391017\pi$
$883$	19.9527	0.671462	0.335731	+	0.941958i	$0.391017\pi$
$884$	−54.9477	−1.84809
$885$	0	0
$886$	−38.4641	−1.29223
$887$	−8.60289	−0.288857	−0.144428	−	0.989515i	$-0.546134\pi$
$887$	−8.60289	−0.288857	−0.144428	+	0.989515i	$0.546134\pi$
$888$	39.6460	1.33043
$889$	−34.1393	−1.14499
$890$	0	0
$891$	1.07882	0.0361418
$892$	−68.4429	−2.29164
$893$	−2.25832	−0.0755719
$894$	1.89688	0.0634413
$895$	0	0
$896$	−34.5915	−1.15562
$897$	−10.8775	−0.363187
$898$	−32.1539	−1.07299
$899$	−42.3057	−1.41097
$900$	0	0
$901$	10.0203	0.333824
$902$	−32.6450	−1.08696
$903$	4.36247	0.145174
$904$	−52.3663	−1.74168
$905$	0	0
$906$	18.9312	0.628948
$907$	−6.26125	−0.207902	−0.103951	−	0.994582i	$-0.533148\pi$
$907$	−6.26125	−0.207902	−0.103951	+	0.994582i	$0.533148\pi$
$908$	137.190	4.55282
$909$	−13.5654	−0.449937
$910$	0	0
$911$	0.905575	0.0300030	0.0150015	−	0.999887i	$-0.495225\pi$
$911$	0.905575	0.0300030	0.0150015	+	0.999887i	$0.495225\pi$
$912$	−15.0844	−0.499495
$913$	−9.57431	−0.316863
$914$	22.0916	0.730726
$915$	0	0
$916$	10.4198	0.344279
$917$	5.14567	0.169925
$918$	10.5646	0.348682
$919$	43.9933	1.45120	0.725602	−	0.688114i	$-0.241561\pi$
$919$	43.9933	1.45120	0.725602	+	0.688114i	$0.241561\pi$
$920$	0	0
$921$	−11.3212	−0.373046
$922$	3.41836	0.112578
$923$	16.0227	0.527394
$924$	−9.50081	−0.312554
$925$	0	0
$926$	−87.8029	−2.88538
$927$	−1.36904	−0.0449651
$928$	101.939	3.34632
$929$	−36.7447	−1.20555	−0.602777	−	0.797910i	$-0.705939\pi$
$929$	−36.7447	−1.20555	−0.602777	+	0.797910i	$0.705939\pi$
$930$	0	0
$931$	4.89140	0.160309
$932$	2.74347	0.0898652
$933$	18.5635	0.607740
$934$	−38.7866	−1.26914
$935$	0	0
$936$	−23.1656	−0.757190
$937$	−24.6490	−0.805248	−0.402624	−	0.915366i	$-0.631902\pi$
$937$	−24.6490	−0.805248	−0.402624	+	0.915366i	$0.631902\pi$
$938$	56.4153	1.84203
$939$	9.69951	0.316532
$940$	0	0
$941$	−59.1479	−1.92817	−0.964083	−	0.265602i	$-0.914429\pi$
$941$	−59.1479	−1.92817	−0.964083	+	0.265602i	$0.914429\pi$
$942$	13.7813	0.449019
$943$	−45.7546	−1.48998
$944$	17.1141	0.557016
$945$	0	0
$946$	−7.49600	−0.243716
$947$	30.0960	0.977989	0.488995	−	0.872287i	$-0.337364\pi$
$947$	30.0960	0.977989	0.488995	+	0.872287i	$0.337364\pi$
$948$	−20.9019	−0.678861
$949$	−8.83661	−0.286849
$950$	0	0
$951$	−7.47647	−0.242441
$952$	−57.3931	−1.86012
$953$	20.6393	0.668572	0.334286	−	0.942472i	$-0.391505\pi$
$953$	20.6393	0.668572	0.334286	+	0.942472i	$0.391505\pi$
$954$	6.84822	0.221719
$955$	0	0
$956$	−36.5921	−1.18347
$957$	6.42538	0.207703
$958$	−45.3084	−1.46385
$959$	−34.6013	−1.11733
$960$	0	0
$961$	19.4540	0.627549
$962$	−32.9612	−1.06271
$963$	−11.0115	−0.354842
$964$	12.0876	0.389315
$965$	0	0
$966$	−18.4180	−0.592588
$967$	22.6016	0.726817	0.363408	−	0.931630i	$-0.381613\pi$
$967$	22.6016	0.726817	0.363408	+	0.931630i	$0.381613\pi$
$968$	−85.1103	−2.73555
$969$	−4.62972	−0.148728
$970$	0	0
$971$	24.1381	0.774628	0.387314	−	0.921948i	$-0.373403\pi$
$971$	24.1381	0.774628	0.387314	+	0.921948i	$0.373403\pi$
$972$	5.22020	0.167438
$973$	−30.9038	−0.990732
$974$	−107.007	−3.42874
$975$	0	0
$976$	−93.2708	−2.98553
$977$	−23.0506	−0.737454	−0.368727	−	0.929538i	$-0.620206\pi$
$977$	−23.0506	−0.737454	−0.368727	+	0.929538i	$0.620206\pi$
$978$	65.1911	2.08458
$979$	16.6608	0.532483
$980$	0	0
$981$	3.44890	0.110115
$982$	37.6870	1.20264
$983$	−29.8713	−0.952745	−0.476373	−	0.879243i	$-0.658049\pi$
$983$	−29.8713	−0.952745	−0.476373	+	0.879243i	$0.658049\pi$
$984$	−97.4430	−3.10637
$985$	0	0
$986$	62.9220	2.00384
$987$	−3.23544	−0.102985
$988$	16.4570	0.523567
$989$	−10.5063	−0.334079
$990$	0	0
$991$	16.6560	0.529096	0.264548	−	0.964372i	$-0.414777\pi$
$991$	16.6560	0.529096	0.264548	+	0.964372i	$0.414777\pi$
$992$	−121.573	−3.85996
$993$	−25.2570	−0.801507
$994$	27.1300	0.860513
$995$	0	0
$996$	−46.3283	−1.46797
$997$	−12.4934	−0.395669	−0.197835	−	0.980235i	$-0.563391\pi$
$997$	−12.4934	−0.395669	−0.197835	+	0.980235i	$0.563391\pi$
$998$	40.9278	1.29555
$999$	4.58187	0.144964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.k.1.6		6
3.2	odd	2		5625.2.a.q.1.1		6
5.2	odd	4		1875.2.b.f.1249.12		12
5.3	odd	4		1875.2.b.f.1249.1		12
5.4	even	2		1875.2.a.j.1.1		6
15.14	odd	2		5625.2.a.p.1.6		6
25.2	odd	20		375.2.i.d.274.6		24
25.9	even	10		75.2.g.c.31.1	✓	12
25.11	even	5		375.2.g.c.226.3		12
25.12	odd	20		375.2.i.d.349.1		24
25.13	odd	20		375.2.i.d.349.6		24
25.14	even	10		75.2.g.c.46.1	yes	12
25.16	even	5		375.2.g.c.151.3		12
25.23	odd	20		375.2.i.d.274.1		24
75.14	odd	10		225.2.h.d.46.3		12
75.59	odd	10		225.2.h.d.181.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.1	✓	12	25.9	even	10
75.2.g.c.46.1	yes	12	25.14	even	10
225.2.h.d.46.3		12	75.14	odd	10
225.2.h.d.181.3		12	75.59	odd	10
375.2.g.c.151.3		12	25.16	even	5
375.2.g.c.226.3		12	25.11	even	5
375.2.i.d.274.1		24	25.23	odd	20
375.2.i.d.274.6		24	25.2	odd	20
375.2.i.d.349.1		24	25.12	odd	20
375.2.i.d.349.6		24	25.13	odd	20
1875.2.a.j.1.1		6	5.4	even	2
1875.2.a.k.1.6		6	1.1	even	1	trivial
1875.2.b.f.1249.1		12	5.3	odd	4
1875.2.b.f.1249.12		12	5.2	odd	4
5625.2.a.p.1.6		6	15.14	odd	2
5625.2.a.q.1.1		6	3.2	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+2.68704 q^{2} +1.00000 q^{3} +5.22020 q^{4} +2.68704 q^{6} -1.68704 q^{7} +8.65280 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.68704 q^{2} +1.00000 q^{3} +5.22020 q^{4} +2.68704 q^{6} -1.68704 q^{7} +8.65280 q^{8} +1.00000 q^{9} +1.07882 q^{11} +5.22020 q^{12} -2.67723 q^{13} -4.53315 q^{14} +12.8101 q^{16} +3.93167 q^{17} +2.68704 q^{18} -1.17755 q^{19} -1.68704 q^{21} +2.89883 q^{22} +4.06295 q^{23} +8.65280 q^{24} -7.19384 q^{26} +1.00000 q^{27} -8.80669 q^{28} +5.95595 q^{29} -7.10310 q^{31} +17.1155 q^{32} +1.07882 q^{33} +10.5646 q^{34} +5.22020 q^{36} +4.58187 q^{37} -3.16412 q^{38} -2.67723 q^{39} -11.2614 q^{41} -4.53315 q^{42} -2.58587 q^{43} +5.63164 q^{44} +10.9173 q^{46} +1.91782 q^{47} +12.8101 q^{48} -4.15389 q^{49} +3.93167 q^{51} -13.9757 q^{52} +2.54861 q^{53} +2.68704 q^{54} -14.5976 q^{56} -1.17755 q^{57} +16.0039 q^{58} +1.33599 q^{59} -7.28106 q^{61} -19.0863 q^{62} -1.68704 q^{63} +20.3701 q^{64} +2.89883 q^{66} -12.4451 q^{67} +20.5241 q^{68} +4.06295 q^{69} -5.98480 q^{71} +8.65280 q^{72} +3.30065 q^{73} +12.3117 q^{74} -6.14702 q^{76} -1.82001 q^{77} -7.19384 q^{78} -4.00404 q^{79} +1.00000 q^{81} -30.2600 q^{82} -8.87482 q^{83} -8.80669 q^{84} -6.94834 q^{86} +5.95595 q^{87} +9.33480 q^{88} +15.4436 q^{89} +4.51660 q^{91} +21.2094 q^{92} -7.10310 q^{93} +5.15327 q^{94} +17.1155 q^{96} -10.7682 q^{97} -11.1617 q^{98} +1.07882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9	\( 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{11} + 10 q^{12} + 6 q^{13} - 22 q^{14} + 18 q^{16} + 13 q^{17} + 11 q^{19} + 6 q^{21} + 16 q^{22} + 13 q^{23} + 3 q^{24} - 28 q^{26} + 6 q^{27} + 7 q^{28} - 3 q^{29} - 11 q^{31} + 16 q^{32} + 3 q^{33} + 15 q^{34} + 10 q^{36} + 21 q^{37} - 9 q^{38} + 6 q^{39} - q^{41} - 22 q^{42} + 2 q^{43} + 9 q^{44} + 19 q^{46} + 14 q^{47} + 18 q^{48} - 14 q^{49} + 13 q^{51} + 13 q^{52} + 23 q^{53} - 35 q^{56} + 11 q^{57} + 22 q^{58} + 9 q^{59} + 11 q^{61} - 23 q^{62} + 6 q^{63} - 23 q^{64} + 16 q^{66} + 8 q^{67} + 50 q^{68} + 13 q^{69} - 8 q^{71} + 3 q^{72} + 13 q^{73} - 22 q^{74} - 26 q^{76} - 13 q^{77} - 28 q^{78} - 5 q^{79} + 6 q^{81} - 13 q^{82} - 20 q^{83} + 7 q^{84} - 37 q^{86} - 3 q^{87} + 28 q^{88} - 4 q^{89} + 34 q^{91} + 61 q^{92} - 11 q^{93} + 41 q^{94} + 16 q^{96} - 7 q^{97} - 41 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^11 + 10 * q^12 + 6 * q^13 - 22 * q^14 + 18 * q^16 + 13 * q^17 + 11 * q^19 + 6 * q^21 + 16 * q^22 + 13 * q^23 + 3 * q^24 - 28 * q^26 + 6 * q^27 + 7 * q^28 - 3 * q^29 - 11 * q^31 + 16 * q^32 + 3 * q^33 + 15 * q^34 + 10 * q^36 + 21 * q^37 - 9 * q^38 + 6 * q^39 - q^41 - 22 * q^42 + 2 * q^43 + 9 * q^44 + 19 * q^46 + 14 * q^47 + 18 * q^48 - 14 * q^49 + 13 * q^51 + 13 * q^52 + 23 * q^53 - 35 * q^56 + 11 * q^57 + 22 * q^58 + 9 * q^59 + 11 * q^61 - 23 * q^62 + 6 * q^63 - 23 * q^64 + 16 * q^66 + 8 * q^67 + 50 * q^68 + 13 * q^69 - 8 * q^71 + 3 * q^72 + 13 * q^73 - 22 * q^74 - 26 * q^76 - 13 * q^77 - 28 * q^78 - 5 * q^79 + 6 * q^81 - 13 * q^82 - 20 * q^83 + 7 * q^84 - 37 * q^86 - 3 * q^87 + 28 * q^88 - 4 * q^89 + 34 * q^91 + 61 * q^92 - 11 * q^93 + 41 * q^94 + 16 * q^96 - 7 * q^97 - 41 * q^98 + 3 * q^99

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