LMFDB - Embedded newform 1875.2.a.j.1.1

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:	$1$
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			1.1
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	$-0.898931\pi$
$2$	−2.68704	−1.90003	−0.950013	+	0.312211i	$0.898931\pi$
$3$	−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	$-0.396713\pi$
$7$	1.68704	0.637642	0.318821	+	0.947815i	$0.396713\pi$
$8$	−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	$-0.378924\pi$
$13$	2.67723	0.742531	0.371265	+	0.928527i	$0.378924\pi$
$14$	−4.53315	−1.21154
$15$	0	0
$16$	12.8101	3.20251
$17$	−3.93167	−0.953570	−0.476785	−	0.879020i	$-0.658198\pi$
$17$	−3.93167	−0.953570	−0.476785	+	0.879020i	$0.658198\pi$
$18$	−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	$-0.639231\pi$
$23$	−4.06295	−0.847183	−0.423591	+	0.905853i	$0.639231\pi$
$24$	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	$-0.622916\pi$
$37$	−4.58187	−0.753254	−0.376627	+	0.926365i	$0.622916\pi$
$38$	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	$-0.436825\pi$
$43$	2.58587	0.394342	0.197171	+	0.980369i	$0.436825\pi$
$44$	5.63164	0.849002
$45$	0	0
$46$	10.9173	1.60967
$47$	−1.91782	−0.279743	−0.139871	−	0.990170i	$-0.544669\pi$
$47$	−1.91782	−0.279743	−0.139871	+	0.990170i	$0.544669\pi$
$48$	−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	$-0.556005\pi$
$53$	−2.54861	−0.350078	−0.175039	+	0.984561i	$0.556005\pi$
$54$	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	$-0.225100\pi$
$67$	12.4451	1.52041	0.760203	+	0.649686i	$0.225100\pi$
$68$	−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	$-0.561872\pi$
$73$	−3.30065	−0.386312	−0.193156	+	0.981168i	$0.561872\pi$
$74$	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	$-0.338066\pi$
$83$	8.87482	0.974138	0.487069	+	0.873364i	$0.338066\pi$
$84$	−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	$-0.315894\pi$
$97$	10.7682	1.09335	0.546673	+	0.837346i	$0.315894\pi$
$98$	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	$-0.478514\pi$
$103$	1.36904	0.134895	0.0674476	+	0.997723i	$0.478514\pi$
$104$	−23.1656	−2.27157
$105$	0	0
$106$	6.84822	0.665158
$107$	11.0115	1.06452	0.532262	−	0.846579i	$-0.321342\pi$
$107$	11.0115	1.06452	0.532262	+	0.846579i	$0.321342\pi$
$108$	−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	$-0.408119\pi$
$113$	6.05194	0.569319	0.284660	+	0.958629i	$0.408119\pi$
$114$	−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	$-0.854861\pi$
$127$	−20.2362	−1.79567	−0.897835	+	0.440332i	$0.854861\pi$
$128$	−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	$-0.839893\pi$
$137$	−20.5100	−1.75229	−0.876145	+	0.482048i	$0.839893\pi$
$138$	−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	$-0.565609\pi$
$157$	−5.12880	−0.409323	−0.204662	+	0.978833i	$0.565609\pi$
$158$	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	$-0.899066\pi$
$163$	−24.2613	−1.90029	−0.950146	+	0.311806i	$0.899066\pi$
$164$	−58.7869	−4.59049
$165$	0	0
$166$	−23.8470	−1.85089
$167$	4.54890	0.352004	0.176002	−	0.984390i	$-0.443683\pi$
$167$	4.54890	0.352004	0.176002	+	0.984390i	$0.443683\pi$
$168$	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	$-0.532452\pi$
$173$	−2.67729	−0.203550	−0.101775	+	0.994807i	$0.532452\pi$
$174$	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	$-0.701352\pi$
$193$	−16.4269	−1.18243	−0.591216	+	0.806513i	$0.701352\pi$
$194$	−28.9346	−2.07738
$195$	0	0
$196$	−21.6841	−1.54887
$197$	−17.1369	−1.22095	−0.610475	−	0.792035i	$-0.709022\pi$
$197$	−17.1369	−1.22095	−0.610475	+	0.792035i	$0.709022\pi$
$198$	−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	$-0.355335\pi$
$223$	13.1112	0.877989	0.438995	+	0.898490i	$0.355335\pi$
$224$	−28.8746	−1.92927
$225$	0	0
$226$	−16.2618	−1.08172
$227$	−26.2807	−1.74431	−0.872155	−	0.489229i	$-0.837278\pi$
$227$	−26.2807	−1.74431	−0.872155	+	0.489229i	$0.837278\pi$
$228$	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	$-0.505480\pi$
$233$	−0.525548	−0.0344298	−0.0172149	+	0.999852i	$0.505480\pi$
$234$	−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	$-0.364676\pi$
$257$	13.2239	0.824882	0.412441	+	0.910984i	$0.364676\pi$
$258$	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	$-0.569005\pi$
$263$	−6.97643	−0.430185	−0.215092	+	0.976594i	$0.569005\pi$
$264$	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	$-0.583051\pi$
$277$	−8.58667	−0.515923	−0.257962	+	0.966155i	$0.583051\pi$
$278$	−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	$-0.592301\pi$
$283$	−9.62005	−0.571853	−0.285926	+	0.958252i	$0.592301\pi$
$284$	−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	$-0.336513\pi$
$293$	16.8202	0.982649	0.491324	+	0.870977i	$0.336513\pi$
$294$	−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	$-0.395286\pi$
$307$	11.3212	0.646134	0.323067	+	0.946376i	$0.395286\pi$
$308$	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	$-0.588388\pi$
$313$	−9.69951	−0.548249	−0.274124	+	0.961694i	$0.588388\pi$
$314$	13.7813	0.777724
$315$	0	0
$316$	−20.9019	−1.17582
$317$	7.47647	0.419920	0.209960	−	0.977710i	$-0.432667\pi$
$317$	7.47647	0.419920	0.209960	+	0.977710i	$0.432667\pi$
$318$	−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	$-0.615428\pi$
$337$	−13.0240	−0.709463	−0.354731	+	0.934968i	$0.615428\pi$
$338$	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	$-0.551500\pi$
$347$	−6.00149	−0.322177	−0.161089	+	0.986940i	$0.551500\pi$
$348$	−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	$-0.541241\pi$
$353$	−4.85493	−0.258402	−0.129201	+	0.991618i	$0.541241\pi$
$354$	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	$-0.625419\pi$
$367$	−14.7089	−0.767800	−0.383900	+	0.923375i	$0.625419\pi$
$368$	−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	$-0.826658\pi$
$373$	−33.0391	−1.71070	−0.855350	+	0.518051i	$0.826658\pi$
$374$	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	$-0.565589\pi$
$383$	−8.00811	−0.409195	−0.204598	+	0.978846i	$0.565589\pi$
$384$	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	$-0.707880\pi$
$397$	−24.2139	−1.21526	−0.607630	+	0.794220i	$0.707880\pi$
$398$	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	$-0.495589\pi$
$433$	0.576639	0.0277115	0.0138558	+	0.999904i	$0.495589\pi$
$434$	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	$-0.389554\pi$
$443$	14.3147	0.680110	0.340055	+	0.940405i	$0.389554\pi$
$444$	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	$-0.561593\pi$
$457$	−8.22154	−0.384587	−0.192294	+	0.981337i	$0.561593\pi$
$458$	−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	$-0.225541\pi$
$463$	32.6764	1.51860	0.759300	+	0.650740i	$0.225541\pi$
$464$	76.2960	3.54195
$465$	0	0
$466$	1.41217	0.0654175
$467$	14.4347	0.667958	0.333979	−	0.942581i	$-0.391609\pi$
$467$	14.4347	0.667958	0.333979	+	0.942581i	$0.391609\pi$
$468$	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	$-0.141887\pi$
$487$	39.8235	1.80457	0.902287	+	0.431135i	$0.141887\pi$
$488$	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	$-0.322529\pi$
$503$	23.7330	1.05820	0.529101	+	0.848559i	$0.322529\pi$
$504$	−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	$-0.388460\pi$
$523$	15.7013	0.686569	0.343285	+	0.939231i	$0.388460\pi$
$524$	−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	$-0.538383\pi$
$547$	−5.62681	−0.240585	−0.120293	+	0.992738i	$0.538383\pi$
$548$	−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	$-0.855557\pi$
$557$	−42.4247	−1.79759	−0.898796	+	0.438366i	$0.855557\pi$
$558$	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	$-0.461093\pi$
$563$	5.78597	0.243850	0.121925	+	0.992539i	$0.461093\pi$
$564$	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	$-0.184015\pi$
$577$	40.2350	1.67501	0.837503	+	0.546433i	$0.184015\pi$
$578$	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	$-0.518555\pi$
$587$	−2.82299	−0.116517	−0.0582587	+	0.998302i	$0.518555\pi$
$588$	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	$-0.669155\pi$
$593$	−24.6805	−1.01351	−0.506754	+	0.862091i	$0.669155\pi$
$594$	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	$-0.666703\pi$
$607$	−24.6423	−1.00020	−0.500099	+	0.865968i	$0.666703\pi$
$608$	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	$-0.819931\pi$
$613$	−41.8034	−1.68842	−0.844211	+	0.536011i	$0.819931\pi$
$614$	−30.4205	−1.22767
$615$	0	0
$616$	−15.7482	−0.634513
$617$	15.9390	0.641680	0.320840	−	0.947133i	$-0.396035\pi$
$617$	15.9390	0.641680	0.320840	+	0.947133i	$0.396035\pi$
$618$	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	$-0.357945\pi$
$643$	21.8891	0.863224	0.431612	+	0.902059i	$0.357945\pi$
$644$	−35.7811	−1.40997
$645$	0	0
$646$	−12.4403	−0.489455
$647$	19.0263	0.748003	0.374001	−	0.927428i	$-0.377985\pi$
$647$	19.0263	0.748003	0.374001	+	0.927428i	$0.377985\pi$
$648$	−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	$-0.514453\pi$
$653$	−2.31971	−0.0907774	−0.0453887	+	0.998969i	$0.514453\pi$
$654$	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	$-0.694769\pi$
$673$	−29.8031	−1.14882	−0.574412	+	0.818566i	$0.694769\pi$
$674$	34.9961	1.34800
$675$	0	0
$676$	−30.4464	−1.17102
$677$	−26.7346	−1.02749	−0.513746	−	0.857942i	$-0.671743\pi$
$677$	−26.7346	−1.02749	−0.513746	+	0.857942i	$0.671743\pi$
$678$	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	$-0.316467\pi$
$683$	28.4950	1.09033	0.545165	+	0.838329i	$0.316467\pi$
$684$	−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	$-0.538868\pi$
$727$	−6.56836	−0.243607	−0.121803	+	0.992554i	$0.538868\pi$
$728$	−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	$-0.700729\pi$
$733$	−31.9276	−1.17927	−0.589636	+	0.807669i	$0.700729\pi$
$734$	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	$-0.401846\pi$
$743$	16.5455	0.606995	0.303498	+	0.952832i	$0.401846\pi$
$744$	−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	$-0.660123\pi$
$757$	−26.5282	−0.964184	−0.482092	+	0.876121i	$0.660123\pi$
$758$	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	$-0.363607\pi$
$773$	23.1042	0.831001	0.415500	+	0.909593i	$0.363607\pi$
$774$	−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	$-0.511541\pi$
$787$	−2.03390	−0.0725009	−0.0362504	+	0.999343i	$0.511541\pi$
$788$	−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	$-0.569281\pi$
$797$	−12.1923	−0.431874	−0.215937	+	0.976407i	$0.569281\pi$
$798$	−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	$-0.761143\pi$
$823$	−41.9661	−1.46285	−0.731423	+	0.681924i	$0.761143\pi$
$824$	−11.8460	−0.412675
$825$	0	0
$826$	−6.05624	−0.210724
$827$	37.4674	1.30287	0.651435	−	0.758704i	$-0.274167\pi$
$827$	37.4674	1.30287	0.651435	+	0.758704i	$0.274167\pi$
$828$	−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	$-0.584397\pi$
$853$	−15.3067	−0.524092	−0.262046	+	0.965055i	$0.584397\pi$
$854$	33.0062	1.12945
$855$	0	0
$856$	−95.2806	−3.25662
$857$	−8.66910	−0.296131	−0.148065	−	0.988978i	$-0.547305\pi$
$857$	−8.66910	−0.296131	−0.148065	+	0.988978i	$0.547305\pi$
$858$	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	$-0.599354\pi$
$863$	−18.0425	−0.614175	−0.307088	+	0.951681i	$0.599354\pi$
$864$	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	$-0.377091\pi$
$877$	22.3057	0.753211	0.376605	+	0.926374i	$0.377091\pi$
$878$	−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	$-0.608983\pi$
$883$	−19.9527	−0.671462	−0.335731	+	0.941958i	$0.608983\pi$
$884$	−54.9477	−1.84809
$885$	0	0
$886$	−38.4641	−1.29223
$887$	8.60289	0.288857	0.144428	−	0.989515i	$-0.453866\pi$
$887$	8.60289	0.288857	0.144428	+	0.989515i	$0.453866\pi$
$888$	−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	$-0.466852\pi$
$907$	6.26125	0.207902	0.103951	+	0.994582i	$0.466852\pi$
$908$	−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	$-0.368098\pi$
$937$	24.6490	0.805248	0.402624	+	0.915366i	$0.368098\pi$
$938$	−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	$-0.662636\pi$
$947$	−30.0960	−0.977989	−0.488995	+	0.872287i	$0.662636\pi$
$948$	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	$-0.608495\pi$
$953$	−20.6393	−0.668572	−0.334286	+	0.942472i	$0.608495\pi$
$954$	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	$-0.618387\pi$
$967$	−22.6016	−0.726817	−0.363408	+	0.931630i	$0.618387\pi$
$968$	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	$-0.379794\pi$
$977$	23.0506	0.737454	0.368727	+	0.929538i	$0.379794\pi$
$978$	−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	$-0.341951\pi$
$983$	29.8713	0.952745	0.476373	+	0.879243i	$0.341951\pi$
$984$	−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	$-0.436609\pi$
$997$	12.4934	0.395669	0.197835	+	0.980235i	$0.436609\pi$
$998$	−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.j.1.1		6
3.2	odd	2		5625.2.a.p.1.6		6
5.2	odd	4		1875.2.b.f.1249.1		12
5.3	odd	4		1875.2.b.f.1249.12		12
5.4	even	2		1875.2.a.k.1.6		6
15.14	odd	2		5625.2.a.q.1.1		6
25.2	odd	20		375.2.i.d.274.1		24
25.9	even	10		375.2.g.c.151.3		12
25.11	even	5		75.2.g.c.46.1	yes	12
25.12	odd	20		375.2.i.d.349.6		24
25.13	odd	20		375.2.i.d.349.1		24
25.14	even	10		375.2.g.c.226.3		12
25.16	even	5		75.2.g.c.31.1	✓	12
25.23	odd	20		375.2.i.d.274.6		24
75.11	odd	10		225.2.h.d.46.3		12
75.41	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	25.16	even	5
75.2.g.c.46.1	yes	12	25.11	even	5
225.2.h.d.46.3		12	75.11	odd	10
225.2.h.d.181.3		12	75.41	odd	10
375.2.g.c.151.3		12	25.9	even	10
375.2.g.c.226.3		12	25.14	even	10
375.2.i.d.274.1		24	25.2	odd	20
375.2.i.d.274.6		24	25.23	odd	20
375.2.i.d.349.1		24	25.13	odd	20
375.2.i.d.349.6		24	25.12	odd	20
1875.2.a.j.1.1		6	1.1	even	1	trivial
1875.2.a.k.1.6		6	5.4	even	2
1875.2.b.f.1249.1		12	5.2	odd	4
1875.2.b.f.1249.12		12	5.3	odd	4
5625.2.a.p.1.6		6	3.2	odd	2
5625.2.a.q.1.1		6	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
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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