LMFDB - Embedded newform 1075.2.a.p.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,2,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.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:	$8.58391821729$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.32503921.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 5x^{4} + 13x^{3} + 9x^{2} - 11x - 7 $ x^6 - 3x^5 - 5x^4 + 13x^3 + 9x^2 - 11*x - 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.96109$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.961086 q^{2} -3.34672 q^{3} -1.07631 q^{4} -3.21649 q^{6} +1.04792 q^{7} -2.95660 q^{8} +8.20055 q^{9} +O(q^{10})$	\(q+0.961086 q^{2} -3.34672 q^{3} -1.07631 q^{4} -3.21649 q^{6} +1.04792 q^{7} -2.95660 q^{8} +8.20055 q^{9} +3.80960 q^{11} +3.60212 q^{12} -3.92217 q^{13} +1.00714 q^{14} -0.688920 q^{16} +3.10840 q^{17} +7.88143 q^{18} -2.51080 q^{19} -3.50711 q^{21} +3.66136 q^{22} +6.92390 q^{23} +9.89493 q^{24} -3.76954 q^{26} -17.4048 q^{27} -1.12789 q^{28} -6.74126 q^{29} -5.01791 q^{31} +5.25109 q^{32} -12.7497 q^{33} +2.98744 q^{34} -8.82637 q^{36} -9.44246 q^{37} -2.41310 q^{38} +13.1264 q^{39} -6.22467 q^{41} -3.37063 q^{42} -1.00000 q^{43} -4.10033 q^{44} +6.65446 q^{46} +3.32457 q^{47} +2.30562 q^{48} -5.90186 q^{49} -10.4030 q^{51} +4.22149 q^{52} +3.86539 q^{53} -16.7275 q^{54} -3.09829 q^{56} +8.40296 q^{57} -6.47893 q^{58} +0.532954 q^{59} -0.858069 q^{61} -4.82264 q^{62} +8.59354 q^{63} +6.42459 q^{64} -12.2535 q^{66} -13.9880 q^{67} -3.34562 q^{68} -23.1724 q^{69} +3.96999 q^{71} -24.2458 q^{72} +1.49935 q^{73} -9.07501 q^{74} +2.70241 q^{76} +3.99217 q^{77} +12.6156 q^{78} -3.34869 q^{79} +33.6474 q^{81} -5.98244 q^{82} -11.3091 q^{83} +3.77475 q^{84} -0.961086 q^{86} +22.5611 q^{87} -11.2635 q^{88} -14.5431 q^{89} -4.11013 q^{91} -7.45229 q^{92} +16.7935 q^{93} +3.19520 q^{94} -17.5739 q^{96} -5.95219 q^{97} -5.67219 q^{98} +31.2408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9	$ 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 5 q^{16} - 6 q^{17} + 11 q^{18} + 6 q^{19} - 12 q^{21} + q^{22} - 32 q^{26} - 10 q^{27} + 10 q^{28} - 10 q^{29} - 11 q^{32} - 6 q^{33} + 14 q^{34} - 41 q^{36} - 28 q^{37} + 6 q^{38} + 8 q^{39} - 6 q^{41} - 5 q^{42} - 6 q^{43} + 4 q^{44} - 8 q^{46} + 6 q^{47} + 32 q^{48} + 20 q^{49} - 8 q^{51} + 16 q^{52} + 4 q^{53} - 5 q^{54} - 35 q^{56} - 4 q^{57} + 26 q^{58} - 20 q^{59} - 8 q^{61} - 2 q^{62} + 2 q^{63} + 17 q^{64} - 35 q^{66} - 22 q^{67} - 22 q^{68} - 42 q^{69} + 8 q^{71} + 2 q^{72} - 34 q^{73} + 45 q^{74} - 16 q^{76} - 8 q^{77} + 26 q^{78} - 16 q^{79} + 46 q^{81} - 22 q^{82} + 14 q^{83} + 37 q^{84} + 3 q^{86} + 2 q^{87} - 20 q^{88} + 24 q^{91} - 46 q^{92} - 30 q^{93} + 12 q^{94} - 23 q^{96} - 34 q^{97} - 32 q^{98} - 16 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 5 * q^16 - 6 * q^17 + 11 * q^18 + 6 * q^19 - 12 * q^21 + q^22 - 32 * q^26 - 10 * q^27 + 10 * q^28 - 10 * q^29 - 11 * q^32 - 6 * q^33 + 14 * q^34 - 41 * q^36 - 28 * q^37 + 6 * q^38 + 8 * q^39 - 6 * q^41 - 5 * q^42 - 6 * q^43 + 4 * q^44 - 8 * q^46 + 6 * q^47 + 32 * q^48 + 20 * q^49 - 8 * q^51 + 16 * q^52 + 4 * q^53 - 5 * q^54 - 35 * q^56 - 4 * q^57 + 26 * q^58 - 20 * q^59 - 8 * q^61 - 2 * q^62 + 2 * q^63 + 17 * q^64 - 35 * q^66 - 22 * q^67 - 22 * q^68 - 42 * q^69 + 8 * q^71 + 2 * q^72 - 34 * q^73 + 45 * q^74 - 16 * q^76 - 8 * q^77 + 26 * q^78 - 16 * q^79 + 46 * q^81 - 22 * q^82 + 14 * q^83 + 37 * q^84 + 3 * q^86 + 2 * q^87 - 20 * q^88 + 24 * q^91 - 46 * q^92 - 30 * q^93 + 12 * q^94 - 23 * q^96 - 34 * q^97 - 32 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.961086	0.679590	0.339795	−	0.940499i	$-0.389642\pi$
$2$	0.961086	0.679590	0.339795	+	0.940499i	$0.389642\pi$
$3$	−3.34672	−1.93223	−0.966116	−	0.258110i	$-0.916900\pi$
$3$	−3.34672	−1.93223	−0.966116	+	0.258110i	$0.916900\pi$
$4$	−1.07631	−0.538157
$5$	0	0
$5$	0	0
$6$	−3.21649	−1.31313
$7$	1.04792	0.396077	0.198039	−	0.980194i	$-0.436543\pi$
$7$	1.04792	0.396077	0.198039	+	0.980194i	$0.436543\pi$
$8$	−2.95660	−1.04532
$9$	8.20055	2.73352
$10$	0	0
$11$	3.80960	1.14864	0.574319	−	0.818631i	$-0.305267\pi$
$11$	3.80960	1.14864	0.574319	+	0.818631i	$0.305267\pi$
$12$	3.60212	1.03984
$13$	−3.92217	−1.08781	−0.543907	−	0.839145i	$-0.683056\pi$
$13$	−3.92217	−1.08781	−0.543907	+	0.839145i	$0.683056\pi$
$14$	1.00714	0.269170
$15$	0	0
$16$	−0.688920	−0.172230
$17$	3.10840	0.753898	0.376949	−	0.926234i	$-0.376973\pi$
$17$	3.10840	0.753898	0.376949	+	0.926234i	$0.376973\pi$
$18$	7.88143	1.85767
$19$	−2.51080	−0.576018	−0.288009	−	0.957628i	$-0.592993\pi$
$19$	−2.51080	−0.576018	−0.288009	+	0.957628i	$0.592993\pi$
$20$	0	0
$21$	−3.50711	−0.765313
$22$	3.66136	0.780604
$23$	6.92390	1.44373	0.721867	−	0.692032i	$-0.243284\pi$
$23$	6.92390	1.44373	0.721867	+	0.692032i	$0.243284\pi$
$24$	9.89493	2.01979
$25$	0	0
$26$	−3.76954	−0.739268
$27$	−17.4048	−3.34956
$28$	−1.12789	−0.213152
$29$	−6.74126	−1.25182	−0.625910	−	0.779895i	$-0.715272\pi$
$29$	−6.74126	−1.25182	−0.625910	+	0.779895i	$0.715272\pi$
$30$	0	0
$31$	−5.01791	−0.901243	−0.450622	−	0.892715i	$-0.648798\pi$
$31$	−5.01791	−0.901243	−0.450622	+	0.892715i	$0.648798\pi$
$32$	5.25109	0.928271
$33$	−12.7497	−2.21944
$34$	2.98744	0.512342
$35$	0	0
$36$	−8.82637	−1.47106
$37$	−9.44246	−1.55233	−0.776165	−	0.630529i	$-0.782838\pi$
$37$	−9.44246	−1.55233	−0.776165	+	0.630529i	$0.782838\pi$
$38$	−2.41310	−0.391456
$39$	13.1264	2.10191
$40$	0	0
$41$	−6.22467	−0.972130	−0.486065	−	0.873923i	$-0.661568\pi$
$41$	−6.22467	−0.972130	−0.486065	+	0.873923i	$0.661568\pi$
$42$	−3.37063	−0.520099
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−4.10033	−0.618148
$45$	0	0
$46$	6.65446	0.981147
$47$	3.32457	0.484939	0.242469	−	0.970159i	$-0.422043\pi$
$47$	3.32457	0.484939	0.242469	+	0.970159i	$0.422043\pi$
$48$	2.30562	0.332788
$49$	−5.90186	−0.843123
$50$	0	0
$51$	−10.4030	−1.45671
$52$	4.22149	0.585415
$53$	3.86539	0.530952	0.265476	−	0.964117i	$-0.414471\pi$
$53$	3.86539	0.530952	0.265476	+	0.964117i	$0.414471\pi$
$54$	−16.7275	−2.27633
$55$	0	0
$56$	−3.09829	−0.414026
$57$	8.40296	1.11300
$58$	−6.47893	−0.850725
$59$	0.532954	0.0693846	0.0346923	−	0.999398i	$-0.488955\pi$
$59$	0.532954	0.0693846	0.0346923	+	0.999398i	$0.488955\pi$
$60$	0	0
$61$	−0.858069	−0.109865	−0.0549323	−	0.998490i	$-0.517494\pi$
$61$	−0.858069	−0.109865	−0.0549323	+	0.998490i	$0.517494\pi$
$62$	−4.82264	−0.612476
$63$	8.59354	1.08268
$64$	6.42459	0.803074
$65$	0	0
$66$	−12.2535	−1.50831
$67$	−13.9880	−1.70891	−0.854453	−	0.519528i	$-0.826108\pi$
$67$	−13.9880	−1.70891	−0.854453	+	0.519528i	$0.826108\pi$
$68$	−3.34562	−0.405716
$69$	−23.1724	−2.78963
$70$	0	0
$71$	3.96999	0.471151	0.235575	−	0.971856i	$-0.424303\pi$
$71$	3.96999	0.471151	0.235575	+	0.971856i	$0.424303\pi$
$72$	−24.2458	−2.85739
$73$	1.49935	0.175486	0.0877428	−	0.996143i	$-0.472035\pi$
$73$	1.49935	0.175486	0.0877428	+	0.996143i	$0.472035\pi$
$74$	−9.07501	−1.05495
$75$	0	0
$76$	2.70241	0.309988
$77$	3.99217	0.454950
$78$	12.6156	1.42844
$79$	−3.34869	−0.376757	−0.188379	−	0.982096i	$-0.560323\pi$
$79$	−3.34869	−0.376757	−0.188379	+	0.982096i	$0.560323\pi$
$80$	0	0
$81$	33.6474	3.73860
$82$	−5.98244	−0.660650
$83$	−11.3091	−1.24133	−0.620665	−	0.784076i	$-0.713137\pi$
$83$	−11.3091	−1.24133	−0.620665	+	0.784076i	$0.713137\pi$
$84$	3.77475	0.411859
$85$	0	0
$86$	−0.961086	−0.103637
$87$	22.5611	2.41881
$88$	−11.2635	−1.20069
$89$	−14.5431	−1.54157	−0.770783	−	0.637098i	$-0.780135\pi$
$89$	−14.5431	−1.54157	−0.770783	+	0.637098i	$0.780135\pi$
$90$	0	0
$91$	−4.11013	−0.430859
$92$	−7.45229	−0.776955
$93$	16.7935	1.74141
$94$	3.19520	0.329560
$95$	0	0
$96$	−17.5739	−1.79363
$97$	−5.95219	−0.604353	−0.302176	−	0.953252i	$-0.597713\pi$
$97$	−5.95219	−0.604353	−0.302176	+	0.953252i	$0.597713\pi$
$98$	−5.67219	−0.572978
$99$	31.2408	3.13982
$100$	0	0
$101$	−3.26036	−0.324418	−0.162209	−	0.986756i	$-0.551862\pi$
$101$	−3.26036	−0.324418	−0.162209	+	0.986756i	$0.551862\pi$
$102$	−9.99814	−0.989963
$103$	10.2910	1.01400	0.507000	−	0.861946i	$-0.330755\pi$
$103$	10.2910	1.01400	0.507000	+	0.861946i	$0.330755\pi$
$104$	11.5963	1.13711
$105$	0	0
$106$	3.71497	0.360830
$107$	13.9970	1.35314	0.676569	−	0.736379i	$-0.263466\pi$
$107$	13.9970	1.35314	0.676569	+	0.736379i	$0.263466\pi$
$108$	18.7330	1.80259
$109$	9.20055	0.881253	0.440626	−	0.897691i	$-0.354756\pi$
$109$	9.20055	0.881253	0.440626	+	0.897691i	$0.354756\pi$
$110$	0	0
$111$	31.6013	2.99946
$112$	−0.721935	−0.0682165
$113$	−12.1563	−1.14357	−0.571785	−	0.820403i	$-0.693749\pi$
$113$	−12.1563	−1.14357	−0.571785	+	0.820403i	$0.693749\pi$
$114$	8.07597	0.756384
$115$	0	0
$116$	7.25571	0.673676
$117$	−32.1640	−2.97356
$118$	0.512214	0.0471531
$119$	3.25737	0.298602
$120$	0	0
$121$	3.51308	0.319371
$122$	−0.824678	−0.0746629
$123$	20.8322	1.87838
$124$	5.40085	0.485010
$125$	0	0
$126$	8.25913	0.735782
$127$	5.81757	0.516226	0.258113	−	0.966115i	$-0.416899\pi$
$127$	5.81757	0.516226	0.258113	+	0.966115i	$0.416899\pi$
$128$	−4.32760	−0.382509
$129$	3.34672	0.294662
$130$	0	0
$131$	−8.68448	−0.758766	−0.379383	−	0.925240i	$-0.623864\pi$
$131$	−8.68448	−0.758766	−0.379383	+	0.925240i	$0.623864\pi$
$132$	13.7227	1.19440
$133$	−2.63113	−0.228148
$134$	−13.4437	−1.16136
$135$	0	0
$136$	−9.19031	−0.788063
$137$	−11.8875	−1.01562	−0.507811	−	0.861469i	$-0.669545\pi$
$137$	−11.8875	−1.01562	−0.507811	+	0.861469i	$0.669545\pi$
$138$	−22.2706	−1.89580
$139$	−7.31139	−0.620144	−0.310072	−	0.950713i	$-0.600353\pi$
$139$	−7.31139	−0.620144	−0.310072	+	0.950713i	$0.600353\pi$
$140$	0	0
$141$	−11.1264	−0.937014
$142$	3.81550	0.320189
$143$	−14.9419	−1.24951
$144$	−5.64953	−0.470794
$145$	0	0
$146$	1.44100	0.119258
$147$	19.7519	1.62911
$148$	10.1631	0.835398
$149$	−1.48920	−0.122000	−0.0609999	−	0.998138i	$-0.519429\pi$
$149$	−1.48920	−0.122000	−0.0609999	+	0.998138i	$0.519429\pi$
$150$	0	0
$151$	7.37239	0.599956	0.299978	−	0.953946i	$-0.403021\pi$
$151$	7.37239	0.599956	0.299978	+	0.953946i	$0.403021\pi$
$152$	7.42345	0.602121
$153$	25.4906	2.06079
$154$	3.83682	0.309180
$155$	0	0
$156$	−14.1281	−1.13116
$157$	−13.8203	−1.10298	−0.551491	−	0.834181i	$-0.685941\pi$
$157$	−13.8203	−1.10298	−0.551491	+	0.834181i	$0.685941\pi$
$158$	−3.21838	−0.256041
$159$	−12.9364	−1.02592
$160$	0	0
$161$	7.25571	0.571830
$162$	32.3380	2.54071
$163$	5.34566	0.418705	0.209352	−	0.977840i	$-0.432864\pi$
$163$	5.34566	0.418705	0.209352	+	0.977840i	$0.432864\pi$
$164$	6.69970	0.523159
$165$	0	0
$166$	−10.8690	−0.843596
$167$	16.9897	1.31470	0.657352	−	0.753583i	$-0.271676\pi$
$167$	16.9897	1.31470	0.657352	+	0.753583i	$0.271676\pi$
$168$	10.3691	0.799995
$169$	2.38343	0.183341
$170$	0	0
$171$	−20.5900	−1.57455
$172$	1.07631	0.0820682
$173$	−15.3994	−1.17079	−0.585396	−	0.810747i	$-0.699061\pi$
$173$	−15.3994	−1.17079	−0.585396	+	0.810747i	$0.699061\pi$
$174$	21.6832	1.64380
$175$	0	0
$176$	−2.62451	−0.197830
$177$	−1.78365	−0.134067
$178$	−13.9772	−1.04763
$179$	8.78812	0.656855	0.328428	−	0.944529i	$-0.393481\pi$
$179$	8.78812	0.656855	0.328428	+	0.944529i	$0.393481\pi$
$180$	0	0
$181$	6.01132	0.446818	0.223409	−	0.974725i	$-0.428281\pi$
$181$	6.01132	0.446818	0.223409	+	0.974725i	$0.428281\pi$
$182$	−3.95019	−0.292808
$183$	2.87172	0.212284
$184$	−20.4712	−1.50916
$185$	0	0
$186$	16.1400	1.18345
$187$	11.8418	0.865957
$188$	−3.57828	−0.260973
$189$	−18.2389	−1.32668
$190$	0	0
$191$	−4.03167	−0.291721	−0.145861	−	0.989305i	$-0.546595\pi$
$191$	−4.03167	−0.291721	−0.145861	+	0.989305i	$0.546595\pi$
$192$	−21.5013	−1.55172
$193$	−9.36887	−0.674386	−0.337193	−	0.941436i	$-0.609478\pi$
$193$	−9.36887	−0.674386	−0.337193	+	0.941436i	$0.609478\pi$
$194$	−5.72056	−0.410712
$195$	0	0
$196$	6.35225	0.453732
$197$	1.54441	0.110034	0.0550172	−	0.998485i	$-0.482479\pi$
$197$	1.54441	0.110034	0.0550172	+	0.998485i	$0.482479\pi$
$198$	30.0251	2.13379
$199$	7.05873	0.500380	0.250190	−	0.968197i	$-0.419507\pi$
$199$	7.05873	0.500380	0.250190	+	0.968197i	$0.419507\pi$
$200$	0	0
$201$	46.8140	3.30200
$202$	−3.13349	−0.220471
$203$	−7.06432	−0.495818
$204$	11.1969	0.783937
$205$	0	0
$206$	9.89050	0.689104
$207$	56.7798	3.94647
$208$	2.70206	0.187354
$209$	−9.56516	−0.661636
$210$	0	0
$211$	−6.13118	−0.422088	−0.211044	−	0.977477i	$-0.567686\pi$
$211$	−6.13118	−0.422088	−0.211044	+	0.977477i	$0.567686\pi$
$212$	−4.16037	−0.285736
$213$	−13.2864	−0.910372
$214$	13.4523	0.919580
$215$	0	0
$216$	51.4591	3.50135
$217$	−5.25838	−0.356962
$218$	8.84252	0.598891
$219$	−5.01791	−0.339079
$220$	0	0
$221$	−12.1917	−0.820102
$222$	30.3716	2.03841
$223$	−27.2744	−1.82643	−0.913216	−	0.407476i	$-0.866409\pi$
$223$	−27.2744	−1.82643	−0.913216	+	0.407476i	$0.866409\pi$
$224$	5.50274	0.367667
$225$	0	0
$226$	−11.6833	−0.777160
$227$	−16.4632	−1.09270	−0.546352	−	0.837556i	$-0.683984\pi$
$227$	−16.4632	−1.09270	−0.546352	+	0.837556i	$0.683984\pi$
$228$	−9.04422	−0.598968
$229$	19.7868	1.30755	0.653774	−	0.756690i	$-0.273185\pi$
$229$	19.7868	1.30755	0.653774	+	0.756690i	$0.273185\pi$
$230$	0	0
$231$	−13.3607	−0.879068
$232$	19.9312	1.30855
$233$	−17.6310	−1.15505	−0.577523	−	0.816374i	$-0.695981\pi$
$233$	−17.6310	−1.15505	−0.577523	+	0.816374i	$0.695981\pi$
$234$	−30.9123	−2.02080
$235$	0	0
$236$	−0.573625	−0.0373398
$237$	11.2071	0.727982
$238$	3.13061	0.202927
$239$	−26.8657	−1.73780	−0.868899	−	0.494989i	$-0.835172\pi$
$239$	−26.8657	−1.73780	−0.868899	+	0.494989i	$0.835172\pi$
$240$	0	0
$241$	−14.6191	−0.941697	−0.470849	−	0.882214i	$-0.656052\pi$
$241$	−14.6191	−0.941697	−0.470849	+	0.882214i	$0.656052\pi$
$242$	3.37637	0.217041
$243$	−60.3940	−3.87428
$244$	0.923552	0.0591244
$245$	0	0
$246$	20.0216	1.27653
$247$	9.84780	0.626601
$248$	14.8360	0.942084
$249$	37.8483	2.39854
$250$	0	0
$251$	26.3485	1.66310	0.831550	−	0.555449i	$-0.187454\pi$
$251$	26.3485	1.66310	0.831550	+	0.555449i	$0.187454\pi$
$252$	−9.24935	−0.582654
$253$	26.3773	1.65833
$254$	5.59119	0.350822
$255$	0	0
$256$	−17.0084	−1.06302
$257$	18.5180	1.15512	0.577562	−	0.816347i	$-0.304004\pi$
$257$	18.5180	1.15512	0.577562	+	0.816347i	$0.304004\pi$
$258$	3.21649	0.200250
$259$	−9.89497	−0.614843
$260$	0	0
$261$	−55.2820	−3.42187
$262$	−8.34653	−0.515650
$263$	21.0989	1.30101	0.650506	−	0.759501i	$-0.274557\pi$
$263$	21.0989	1.30101	0.650506	+	0.759501i	$0.274557\pi$
$264$	37.6957	2.32001
$265$	0	0
$266$	−2.52874	−0.155047
$267$	48.6717	2.97866
$268$	15.0555	0.919660
$269$	8.98198	0.547641	0.273820	−	0.961781i	$-0.411713\pi$
$269$	8.98198	0.547641	0.273820	+	0.961781i	$0.411713\pi$
$270$	0	0
$271$	−25.0299	−1.52046	−0.760229	−	0.649655i	$-0.774913\pi$
$271$	−25.0299	−1.52046	−0.760229	+	0.649655i	$0.774913\pi$
$272$	−2.14144	−0.129844
$273$	13.7555	0.832519
$274$	−11.4249	−0.690206
$275$	0	0
$276$	24.9407	1.50126
$277$	−22.8701	−1.37413	−0.687065	−	0.726596i	$-0.741101\pi$
$277$	−22.8701	−1.37413	−0.687065	+	0.726596i	$0.741101\pi$
$278$	−7.02687	−0.421444
$279$	−41.1496	−2.46356
$280$	0	0
$281$	20.0119	1.19381	0.596905	−	0.802312i	$-0.296397\pi$
$281$	20.0119	1.19381	0.596905	+	0.802312i	$0.296397\pi$
$282$	−10.6934	−0.636785
$283$	3.86725	0.229884	0.114942	−	0.993372i	$-0.463332\pi$
$283$	3.86725	0.229884	0.114942	+	0.993372i	$0.463332\pi$
$284$	−4.27295	−0.253553
$285$	0	0
$286$	−14.3605	−0.849152
$287$	−6.52297	−0.385039
$288$	43.0618	2.53744
$289$	−7.33783	−0.431637
$290$	0	0
$291$	19.9203	1.16775
$292$	−1.61377	−0.0944388
$293$	−9.48279	−0.553991	−0.276995	−	0.960871i	$-0.589339\pi$
$293$	−9.48279	−0.553991	−0.276995	+	0.960871i	$0.589339\pi$
$294$	18.9833	1.10713
$295$	0	0
$296$	27.9176	1.62268
$297$	−66.3054	−3.84743
$298$	−1.43125	−0.0829098
$299$	−27.1567	−1.57051
$300$	0	0
$301$	−1.04792	−0.0604013
$302$	7.08550	0.407725
$303$	10.9115	0.626851
$304$	1.72974	0.0992076
$305$	0	0
$306$	24.4987	1.40050
$307$	24.1217	1.37670	0.688348	−	0.725381i	$-0.258336\pi$
$307$	24.1217	1.37670	0.688348	+	0.725381i	$0.258336\pi$
$308$	−4.29683	−0.244834
$309$	−34.4410	−1.95928
$310$	0	0
$311$	−15.7450	−0.892817	−0.446409	−	0.894829i	$-0.647297\pi$
$311$	−15.7450	−0.892817	−0.446409	+	0.894829i	$0.647297\pi$
$312$	−38.8096	−2.19716
$313$	12.4616	0.704370	0.352185	−	0.935930i	$-0.385439\pi$
$313$	12.4616	0.704370	0.352185	+	0.935930i	$0.385439\pi$
$314$	−13.2825	−0.749576
$315$	0	0
$316$	3.60424	0.202754
$317$	−23.0929	−1.29703	−0.648513	−	0.761204i	$-0.724609\pi$
$317$	−23.0929	−1.29703	−0.648513	+	0.761204i	$0.724609\pi$
$318$	−12.4330	−0.697207
$319$	−25.6815	−1.43789
$320$	0	0
$321$	−46.8440	−2.61458
$322$	6.97336	0.388610
$323$	−7.80459	−0.434259
$324$	−36.2151	−2.01195
$325$	0	0
$326$	5.13764	0.284548
$327$	−30.7917	−1.70278
$328$	18.4039	1.01618
$329$	3.48389	0.192073
$330$	0	0
$331$	15.4811	0.850917	0.425459	−	0.904978i	$-0.360113\pi$
$331$	15.4811	0.850917	0.425459	+	0.904978i	$0.360113\pi$
$332$	12.1721	0.668031
$333$	−77.4334	−4.24332
$334$	16.3286	0.893461
$335$	0	0
$336$	2.41612	0.131810
$337$	−1.53743	−0.0837494	−0.0418747	−	0.999123i	$-0.513333\pi$
$337$	−1.53743	−0.0837494	−0.0418747	+	0.999123i	$0.513333\pi$
$338$	2.29068	0.124597
$339$	40.6838	2.20964
$340$	0	0
$341$	−19.1162	−1.03520
$342$	−19.7887	−1.07005
$343$	−13.5201	−0.730019
$344$	2.95660	0.159409
$345$	0	0
$346$	−14.8001	−0.795659
$347$	−2.57880	−0.138437	−0.0692186	−	0.997602i	$-0.522051\pi$
$347$	−2.57880	−0.138437	−0.0692186	+	0.997602i	$0.522051\pi$
$348$	−24.2829	−1.30170
$349$	−8.24847	−0.441531	−0.220765	−	0.975327i	$-0.570855\pi$
$349$	−8.24847	−0.441531	−0.220765	+	0.975327i	$0.570855\pi$
$350$	0	0
$351$	68.2646	3.64370
$352$	20.0046	1.06625
$353$	−5.67923	−0.302275	−0.151138	−	0.988513i	$-0.548294\pi$
$353$	−5.67923	−0.302275	−0.151138	+	0.988513i	$0.548294\pi$
$354$	−1.71424	−0.0911108
$355$	0	0
$356$	15.6529	0.829605
$357$	−10.9015	−0.576968
$358$	8.44614	0.446392
$359$	16.2873	0.859612	0.429806	−	0.902921i	$-0.358582\pi$
$359$	16.2873	0.859612	0.429806	+	0.902921i	$0.358582\pi$
$360$	0	0
$361$	−12.6959	−0.668204
$362$	5.77740	0.303653
$363$	−11.7573	−0.617098
$364$	4.42379	0.231870
$365$	0	0
$366$	2.75997	0.144266
$367$	−28.5302	−1.48926	−0.744631	−	0.667476i	$-0.767375\pi$
$367$	−28.5302	−1.48926	−0.744631	+	0.667476i	$0.767375\pi$
$368$	−4.77002	−0.248654
$369$	−51.0457	−2.65733
$370$	0	0
$371$	4.05063	0.210298
$372$	−18.0751	−0.937152
$373$	18.9227	0.979781	0.489890	−	0.871784i	$-0.337037\pi$
$373$	18.9227	0.979781	0.489890	+	0.871784i	$0.337037\pi$
$374$	11.3810	0.588496
$375$	0	0
$376$	−9.82944	−0.506914
$377$	26.4404	1.36175
$378$	−17.5291	−0.901601
$379$	−27.2694	−1.40074	−0.700368	−	0.713782i	$-0.746981\pi$
$379$	−27.2694	−1.40074	−0.700368	+	0.713782i	$0.746981\pi$
$380$	0	0
$381$	−19.4698	−0.997468
$382$	−3.87478	−0.198251
$383$	13.5035	0.689997	0.344998	−	0.938603i	$-0.387879\pi$
$383$	13.5035	0.689997	0.344998	+	0.938603i	$0.387879\pi$
$384$	14.4833	0.739097
$385$	0	0
$386$	−9.00429	−0.458306
$387$	−8.20055	−0.416857
$388$	6.40642	0.325237
$389$	−1.95591	−0.0991684	−0.0495842	−	0.998770i	$-0.515790\pi$
$389$	−1.95591	−0.0991684	−0.0495842	+	0.998770i	$0.515790\pi$
$390$	0	0
$391$	21.5223	1.08843
$392$	17.4494	0.881330
$393$	29.0645	1.46611
$394$	1.48431	0.0747783
$395$	0	0
$396$	−33.6250	−1.68972
$397$	−4.31193	−0.216410	−0.108205	−	0.994129i	$-0.534510\pi$
$397$	−4.31193	−0.216410	−0.108205	+	0.994129i	$0.534510\pi$
$398$	6.78404	0.340053
$399$	8.80565	0.440834
$400$	0	0
$401$	−2.75013	−0.137335	−0.0686673	−	0.997640i	$-0.521875\pi$
$401$	−2.75013	−0.137335	−0.0686673	+	0.997640i	$0.521875\pi$
$402$	44.9922	2.24401
$403$	19.6811	0.980385
$404$	3.50917	0.174588
$405$	0	0
$406$	−6.78942	−0.336953
$407$	−35.9720	−1.78307
$408$	30.7574	1.52272
$409$	15.2874	0.755913	0.377957	−	0.925823i	$-0.376627\pi$
$409$	15.2874	0.755913	0.377957	+	0.925823i	$0.376627\pi$
$410$	0	0
$411$	39.7843	1.96241
$412$	−11.0763	−0.545691
$413$	0.558494	0.0274817
$414$	54.5703	2.68198
$415$	0	0
$416$	−20.5957	−1.00979
$417$	24.4692	1.19826
$418$	−9.19294	−0.449642
$419$	19.8287	0.968695	0.484348	−	0.874876i	$-0.339057\pi$
$419$	19.8287	0.968695	0.484348	+	0.874876i	$0.339057\pi$
$420$	0	0
$421$	25.9083	1.26269	0.631347	−	0.775500i	$-0.282502\pi$
$421$	25.9083	1.26269	0.631347	+	0.775500i	$0.282502\pi$
$422$	−5.89259	−0.286847
$423$	27.2633	1.32559
$424$	−11.4284	−0.555013
$425$	0	0
$426$	−12.7694	−0.618680
$427$	−0.899190	−0.0435149
$428$	−15.0651	−0.728201
$429$	50.0064	2.41433
$430$	0	0
$431$	−7.39129	−0.356026	−0.178013	−	0.984028i	$-0.556967\pi$
$431$	−7.39129	−0.356026	−0.178013	+	0.984028i	$0.556967\pi$
$432$	11.9905	0.576894
$433$	18.2307	0.876112	0.438056	−	0.898948i	$-0.355667\pi$
$433$	18.2307	0.876112	0.438056	+	0.898948i	$0.355667\pi$
$434$	−5.05375	−0.242588
$435$	0	0
$436$	−9.90268	−0.474252
$437$	−17.3846	−0.831616
$438$	−4.82264	−0.230435
$439$	18.1736	0.867378	0.433689	−	0.901063i	$-0.357212\pi$
$439$	18.1736	0.867378	0.433689	+	0.901063i	$0.357212\pi$
$440$	0	0
$441$	−48.3985	−2.30469
$442$	−11.7173	−0.557333
$443$	−16.3939	−0.778898	−0.389449	−	0.921048i	$-0.627335\pi$
$443$	−16.3939	−0.778898	−0.389449	+	0.921048i	$0.627335\pi$
$444$	−34.0129	−1.61418
$445$	0	0
$446$	−26.2131	−1.24123
$447$	4.98393	0.235732
$448$	6.73247	0.318079
$449$	38.0392	1.79518	0.897591	−	0.440829i	$-0.145315\pi$
$449$	38.0392	1.79518	0.897591	+	0.440829i	$0.145315\pi$
$450$	0	0
$451$	−23.7135	−1.11663
$452$	13.0840	0.615421
$453$	−24.6733	−1.15925
$454$	−15.8226	−0.742591
$455$	0	0
$456$	−24.8442	−1.16344
$457$	−2.75237	−0.128750	−0.0643751	−	0.997926i	$-0.520505\pi$
$457$	−2.75237	−0.128750	−0.0643751	+	0.997926i	$0.520505\pi$
$458$	19.0168	0.888596
$459$	−54.1011	−2.52522
$460$	0	0
$461$	3.54354	0.165039	0.0825196	−	0.996589i	$-0.473703\pi$
$461$	3.54354	0.165039	0.0825196	+	0.996589i	$0.473703\pi$
$462$	−12.8408	−0.597406
$463$	0.000675058 0	3.13726e−5 0	1.56863e−5	−	1.00000i	$-0.499995\pi$
$463$	0.000675058 0	3.13726e−5 0	1.56863e−5		1.00000i	$0.499995\pi$
$464$	4.64419	0.215601
$465$	0	0
$466$	−16.9449	−0.784958
$467$	22.6537	1.04829	0.524145	−	0.851629i	$-0.324385\pi$
$467$	22.6537	1.04829	0.524145	+	0.851629i	$0.324385\pi$
$468$	34.6185	1.60024
$469$	−14.6583	−0.676859
$470$	0	0
$471$	46.2528	2.13122
$472$	−1.57573	−0.0725289
$473$	−3.80960	−0.175166
$474$	10.7710	0.494729
$475$	0	0
$476$	−3.50595	−0.160695
$477$	31.6983	1.45137
$478$	−25.8203	−1.18099
$479$	7.60936	0.347681	0.173840	−	0.984774i	$-0.444382\pi$
$479$	7.60936	0.347681	0.173840	+	0.984774i	$0.444382\pi$
$480$	0	0
$481$	37.0349	1.68865
$482$	−14.0502	−0.639968
$483$	−24.2829	−1.10491
$484$	−3.78117	−0.171871
$485$	0	0
$486$	−58.0439	−2.63292
$487$	21.1107	0.956617	0.478308	−	0.878192i	$-0.341250\pi$
$487$	21.1107	0.956617	0.478308	+	0.878192i	$0.341250\pi$
$488$	2.53697	0.114843
$489$	−17.8904	−0.809034
$490$	0	0
$491$	−41.0223	−1.85131	−0.925654	−	0.378371i	$-0.876484\pi$
$491$	−41.0223	−1.85131	−0.925654	+	0.378371i	$0.876484\pi$
$492$	−22.4220	−1.01086
$493$	−20.9546	−0.943746
$494$	9.46458	0.425832
$495$	0	0
$496$	3.45694	0.155221
$497$	4.16024	0.186612
$498$	36.3755	1.63002
$499$	35.8979	1.60701	0.803506	−	0.595297i	$-0.202966\pi$
$499$	35.8979	1.60701	0.803506	+	0.595297i	$0.202966\pi$
$500$	0	0
$501$	−56.8599	−2.54031
$502$	25.3231	1.13023
$503$	−21.6405	−0.964902	−0.482451	−	0.875923i	$-0.660253\pi$
$503$	−21.6405	−0.964902	−0.482451	+	0.875923i	$0.660253\pi$
$504$	−25.4077	−1.13175
$505$	0	0
$506$	25.3509	1.12698
$507$	−7.97668	−0.354257
$508$	−6.26154	−0.277811
$509$	−26.4281	−1.17141	−0.585703	−	0.810526i	$-0.699181\pi$
$509$	−26.4281	−1.17141	−0.585703	+	0.810526i	$0.699181\pi$
$510$	0	0
$511$	1.57120	0.0695059
$512$	−7.69131	−0.339911
$513$	43.7000	1.92940
$514$	17.7974	0.785011
$515$	0	0
$516$	−3.60212	−0.158575
$517$	12.6653	0.557019
$518$	−9.50991	−0.417842
$519$	51.5374	2.26224
$520$	0	0
$521$	36.3043	1.59052	0.795261	−	0.606268i	$-0.207334\pi$
$521$	36.3043	1.59052	0.795261	+	0.606268i	$0.207334\pi$
$522$	−53.1308	−2.32547
$523$	16.3441	0.714680	0.357340	−	0.933974i	$-0.383684\pi$
$523$	16.3441	0.714680	0.357340	+	0.933974i	$0.383684\pi$
$524$	9.34722	0.408335
$525$	0	0
$526$	20.2778	0.884155
$527$	−15.5977	−0.679446
$528$	8.78352	0.382253
$529$	24.9404	1.08437
$530$	0	0
$531$	4.37051	0.189664
$532$	2.83192	0.122779
$533$	24.4142	1.05750
$534$	46.7777	2.02427
$535$	0	0
$536$	41.3570	1.78635
$537$	−29.4114	−1.26920
$538$	8.63245	0.372171
$539$	−22.4837	−0.968443
$540$	0	0
$541$	42.8254	1.84121	0.920605	−	0.390495i	$-0.127696\pi$
$541$	42.8254	1.84121	0.920605	+	0.390495i	$0.127696\pi$
$542$	−24.0559	−1.03329
$543$	−20.1182	−0.863356
$544$	16.3225	0.699822
$545$	0	0
$546$	13.2202	0.565772
$547$	31.3047	1.33849	0.669245	−	0.743041i	$-0.266617\pi$
$547$	31.3047	1.33849	0.669245	+	0.743041i	$0.266617\pi$
$548$	12.7947	0.546564
$549$	−7.03664	−0.300316
$550$	0	0
$551$	16.9260	0.721071
$552$	68.5115	2.91604
$553$	−3.50917	−0.149225
$554$	−21.9801	−0.933845
$555$	0	0
$556$	7.86935	0.333735
$557$	−29.4409	−1.24745	−0.623725	−	0.781644i	$-0.714381\pi$
$557$	−29.4409	−1.24745	−0.623725	+	0.781644i	$0.714381\pi$
$558$	−39.5483	−1.67421
$559$	3.92217	0.165890
$560$	0	0
$561$	−39.6312	−1.67323
$562$	19.2332	0.811302
$563$	19.3264	0.814512	0.407256	−	0.913314i	$-0.366486\pi$
$563$	19.3264	0.814512	0.407256	+	0.913314i	$0.366486\pi$
$564$	11.9755	0.504260
$565$	0	0
$566$	3.71676	0.156227
$567$	35.2598	1.48077
$568$	−11.7377	−0.492502
$569$	−38.1058	−1.59748	−0.798739	−	0.601678i	$-0.794499\pi$
$569$	−38.1058	−1.59748	−0.798739	+	0.601678i	$0.794499\pi$
$570$	0	0
$571$	19.7102	0.824844	0.412422	−	0.910993i	$-0.364683\pi$
$571$	19.7102	0.824844	0.412422	+	0.910993i	$0.364683\pi$
$572$	16.0822	0.672430
$573$	13.4929	0.563673
$574$	−6.26914	−0.261669
$575$	0	0
$576$	52.6852	2.19522
$577$	−17.6037	−0.732851	−0.366426	−	0.930447i	$-0.619419\pi$
$577$	−17.6037	−0.732851	−0.366426	+	0.930447i	$0.619419\pi$
$578$	−7.05229	−0.293336
$579$	31.3550	1.30307
$580$	0	0
$581$	−11.8510	−0.491663
$582$	19.1451	0.793591
$583$	14.7256	0.609872
$584$	−4.43298	−0.183438
$585$	0	0
$586$	−9.11378	−0.376487
$587$	6.67913	0.275677	0.137839	−	0.990455i	$-0.455984\pi$
$587$	6.67913	0.275677	0.137839	+	0.990455i	$0.455984\pi$
$588$	−21.2592	−0.876716
$589$	12.5990	0.519132
$590$	0	0
$591$	−5.16870	−0.212612
$592$	6.50510	0.267358
$593$	30.2525	1.24232	0.621161	−	0.783683i	$-0.286661\pi$
$593$	30.2525	1.24232	0.621161	+	0.783683i	$0.286661\pi$
$594$	−63.7252	−2.61467
$595$	0	0
$596$	1.60284	0.0656550
$597$	−23.6236	−0.966850
$598$	−26.0999	−1.06731
$599$	−31.7917	−1.29897	−0.649487	−	0.760373i	$-0.725016\pi$
$599$	−31.7917	−1.29897	−0.649487	+	0.760373i	$0.725016\pi$
$600$	0	0
$601$	28.1307	1.14748	0.573738	−	0.819039i	$-0.305493\pi$
$601$	28.1307	1.14748	0.573738	+	0.819039i	$0.305493\pi$
$602$	−1.00714	−0.0410481
$603$	−114.709	−4.67132
$604$	−7.93500	−0.322871
$605$	0	0
$606$	10.4869	0.426002
$607$	−19.7540	−0.801789	−0.400894	−	0.916124i	$-0.631301\pi$
$607$	−19.7540	−0.801789	−0.400894	+	0.916124i	$0.631301\pi$
$608$	−13.1845	−0.534700
$609$	23.6423	0.958035
$610$	0	0
$611$	−13.0395	−0.527523
$612$	−27.4359	−1.10903
$613$	40.4420	1.63344	0.816718	−	0.577037i	$-0.195791\pi$
$613$	40.4420	1.63344	0.816718	+	0.577037i	$0.195791\pi$
$614$	23.1830	0.935589
$615$	0	0
$616$	−11.8033	−0.475567
$617$	−11.2943	−0.454691	−0.227345	−	0.973814i	$-0.573005\pi$
$617$	−11.2943	−0.454691	−0.227345	+	0.973814i	$0.573005\pi$
$618$	−33.1008	−1.33151
$619$	−0.481208	−0.0193414	−0.00967069	−	0.999953i	$-0.503078\pi$
$619$	−0.481208	−0.0193414	−0.00967069	+	0.999953i	$0.503078\pi$
$620$	0	0
$621$	−120.509	−4.83586
$622$	−15.1323	−0.606750
$623$	−15.2400	−0.610580
$624$	−9.04306	−0.362012
$625$	0	0
$626$	11.9766	0.478683
$627$	32.0119	1.27843
$628$	14.8750	0.593578
$629$	−29.3510	−1.17030
$630$	0	0
$631$	1.70739	0.0679700	0.0339850	−	0.999422i	$-0.489180\pi$
$631$	1.70739	0.0679700	0.0339850	+	0.999422i	$0.489180\pi$
$632$	9.90075	0.393830
$633$	20.5193	0.815571
$634$	−22.1943	−0.881446
$635$	0	0
$636$	13.9236	0.552107
$637$	23.1481	0.917161
$638$	−24.6821	−0.977176
$639$	32.5561	1.28790
$640$	0	0
$641$	6.15055	0.242932	0.121466	−	0.992596i	$-0.461240\pi$
$641$	6.15055	0.242932	0.121466	+	0.992596i	$0.461240\pi$
$642$	−45.0211	−1.77684
$643$	12.2185	0.481849	0.240925	−	0.970544i	$-0.422549\pi$
$643$	12.2185	0.481849	0.240925	+	0.970544i	$0.422549\pi$
$644$	−7.80942	−0.307734
$645$	0	0
$646$	−7.50088	−0.295118
$647$	−10.5198	−0.413576	−0.206788	−	0.978386i	$-0.566301\pi$
$647$	−10.5198	−0.413576	−0.206788	+	0.978386i	$0.566301\pi$
$648$	−99.4819	−3.90802
$649$	2.03034	0.0796979
$650$	0	0
$651$	17.5983	0.689733
$652$	−5.75361	−0.225329
$653$	−11.9933	−0.469333	−0.234667	−	0.972076i	$-0.575400\pi$
$653$	−11.9933	−0.469333	−0.234667	+	0.972076i	$0.575400\pi$
$654$	−29.5935	−1.15720
$655$	0	0
$656$	4.28830	0.167430
$657$	12.2955	0.479693
$658$	3.34832	0.130531
$659$	−22.6279	−0.881459	−0.440729	−	0.897640i	$-0.645280\pi$
$659$	−22.6279	−0.881459	−0.440729	+	0.897640i	$0.645280\pi$
$660$	0	0
$661$	−12.1581	−0.472896	−0.236448	−	0.971644i	$-0.575983\pi$
$661$	−12.1581	−0.472896	−0.236448	+	0.971644i	$0.575983\pi$
$662$	14.8786	0.578275
$663$	40.8022	1.58463
$664$	33.4364	1.29758
$665$	0	0
$666$	−74.4201	−2.88372
$667$	−46.6758	−1.80729
$668$	−18.2863	−0.707518
$669$	91.2800	3.52909
$670$	0	0
$671$	−3.26890	−0.126195
$672$	−18.4161	−0.710418
$673$	42.4437	1.63608	0.818042	−	0.575159i	$-0.195060\pi$
$673$	42.4437	1.63608	0.818042	+	0.575159i	$0.195060\pi$
$674$	−1.47761	−0.0569153
$675$	0	0
$676$	−2.56532	−0.0986662
$677$	−40.8173	−1.56874	−0.784368	−	0.620296i	$-0.787013\pi$
$677$	−40.8173	−1.56874	−0.784368	+	0.620296i	$0.787013\pi$
$678$	39.1007	1.50165
$679$	−6.23743	−0.239371
$680$	0	0
$681$	55.0979	2.11136
$682$	−18.3724	−0.703514
$683$	7.60851	0.291132	0.145566	−	0.989349i	$-0.453500\pi$
$683$	7.60851	0.291132	0.145566	+	0.989349i	$0.453500\pi$
$684$	22.1613	0.847357
$685$	0	0
$686$	−12.9940	−0.496114
$687$	−66.2209	−2.52648
$688$	0.688920	0.0262648
$689$	−15.1607	−0.577577
$690$	0	0
$691$	9.74464	0.370704	0.185352	−	0.982672i	$-0.440658\pi$
$691$	9.74464	0.370704	0.185352	+	0.982672i	$0.440658\pi$
$692$	16.5746	0.630070
$693$	32.7380	1.24361
$694$	−2.47845	−0.0940806
$695$	0	0
$696$	−66.7043	−2.52842
$697$	−19.3488	−0.732887
$698$	−7.92749	−0.300060
$699$	59.0061	2.23182
$700$	0	0
$701$	15.7112	0.593405	0.296703	−	0.954970i	$-0.404113\pi$
$701$	15.7112	0.593405	0.296703	+	0.954970i	$0.404113\pi$
$702$	65.6081	2.47622
$703$	23.7082	0.894170
$704$	24.4751	0.922442
$705$	0	0
$706$	−5.45823	−0.205423
$707$	−3.41661	−0.128495
$708$	1.91976	0.0721492
$709$	−3.50957	−0.131805	−0.0659023	−	0.997826i	$-0.520993\pi$
$709$	−3.50957	−0.131805	−0.0659023	+	0.997826i	$0.520993\pi$
$710$	0	0
$711$	−27.4611	−1.02987
$712$	42.9982	1.61142
$713$	−34.7435	−1.30115
$714$	−10.4773	−0.392102
$715$	0	0
$716$	−9.45878	−0.353491
$717$	89.9121	3.35783
$718$	15.6535	0.584184
$719$	−17.4311	−0.650070	−0.325035	−	0.945702i	$-0.605376\pi$
$719$	−17.4311	−0.650070	−0.325035	+	0.945702i	$0.605376\pi$
$720$	0	0
$721$	10.7841	0.401622
$722$	−12.2018	−0.454105
$723$	48.9260	1.81958
$724$	−6.47007	−0.240458
$725$	0	0
$726$	−11.2998	−0.419374
$727$	−13.2692	−0.492126	−0.246063	−	0.969254i	$-0.579137\pi$
$727$	−13.2692	−0.492126	−0.246063	+	0.969254i	$0.579137\pi$
$728$	12.1520	0.450384
$729$	101.180	3.74740
$730$	0	0
$731$	−3.10840	−0.114968
$732$	−3.09087	−0.114242
$733$	−27.7882	−1.02638	−0.513190	−	0.858275i	$-0.671537\pi$
$733$	−27.7882	−1.02638	−0.513190	+	0.858275i	$0.671537\pi$
$734$	−27.4199	−1.01209
$735$	0	0
$736$	36.3580	1.34018
$737$	−53.2887	−1.96292
$738$	−49.0593	−1.80590
$739$	32.6256	1.20015	0.600076	−	0.799943i	$-0.295137\pi$
$739$	32.6256	1.20015	0.600076	+	0.799943i	$0.295137\pi$
$740$	0	0
$741$	−32.9579	−1.21074
$742$	3.89300	0.142917
$743$	−0.626913	−0.0229992	−0.0114996	−	0.999934i	$-0.503661\pi$
$743$	−0.626913	−0.0229992	−0.0114996	+	0.999934i	$0.503661\pi$
$744$	−49.6518	−1.82032
$745$	0	0
$746$	18.1863	0.665850
$747$	−92.7405	−3.39320
$748$	−12.7455	−0.466021
$749$	14.6677	0.535948
$750$	0	0
$751$	−24.5560	−0.896062	−0.448031	−	0.894018i	$-0.647875\pi$
$751$	−24.5560	−0.896062	−0.448031	+	0.894018i	$0.647875\pi$
$752$	−2.29037	−0.0835210
$753$	−88.1810	−3.21349
$754$	25.4115	0.925431
$755$	0	0
$756$	19.6308	0.713964
$757$	−21.2772	−0.773334	−0.386667	−	0.922219i	$-0.626374\pi$
$757$	−21.2772	−0.773334	−0.386667	+	0.922219i	$0.626374\pi$
$758$	−26.2083	−0.951927
$759$	−88.2775	−3.20427
$760$	0	0
$761$	8.46163	0.306734	0.153367	−	0.988169i	$-0.450988\pi$
$761$	8.46163	0.306734	0.153367	+	0.988169i	$0.450988\pi$
$762$	−18.7122	−0.677870
$763$	9.64146	0.349044
$764$	4.33934	0.156992
$765$	0	0
$766$	12.9780	0.468915
$767$	−2.09034	−0.0754776
$768$	56.9223	2.05401
$769$	3.07985	0.111062	0.0555312	−	0.998457i	$-0.482315\pi$
$769$	3.07985	0.111062	0.0555312	+	0.998457i	$0.482315\pi$
$770$	0	0
$771$	−61.9747	−2.23197
$772$	10.0838	0.362926
$773$	37.7252	1.35688	0.678440	−	0.734656i	$-0.262656\pi$
$773$	37.7252	1.35688	0.678440	+	0.734656i	$0.262656\pi$
$774$	−7.88143	−0.283292
$775$	0	0
$776$	17.5982	0.631740
$777$	33.1157	1.18802
$778$	−1.87979	−0.0673939
$779$	15.6289	0.559964
$780$	0	0
$781$	15.1241	0.541182
$782$	20.6848	0.739685
$783$	117.330	4.19304
$784$	4.06591	0.145211
$785$	0	0
$786$	27.9335	0.996355
$787$	26.7780	0.954532	0.477266	−	0.878759i	$-0.341628\pi$
$787$	26.7780	0.954532	0.477266	+	0.878759i	$0.341628\pi$
$788$	−1.66227	−0.0592158
$789$	−70.6121	−2.51386
$790$	0	0
$791$	−12.7389	−0.452943
$792$	−92.3667	−3.28211
$793$	3.36549	0.119512
$794$	−4.14414	−0.147070
$795$	0	0
$796$	−7.59741	−0.269283
$797$	−24.9616	−0.884185	−0.442092	−	0.896970i	$-0.645764\pi$
$797$	−24.9616	−0.884185	−0.442092	+	0.896970i	$0.645764\pi$
$798$	8.46299	0.299587
$799$	10.3341	0.365595
$800$	0	0
$801$	−119.261	−4.21390
$802$	−2.64311	−0.0933313
$803$	5.71193	0.201570
$804$	−50.3865	−1.77700
$805$	0	0
$806$	18.9152	0.666260
$807$	−30.0602	−1.05817
$808$	9.63959	0.339120
$809$	1.06313	0.0373777	0.0186889	−	0.999825i	$-0.494051\pi$
$809$	1.06313	0.0373777	0.0186889	+	0.999825i	$0.494051\pi$
$810$	0	0
$811$	−24.7285	−0.868336	−0.434168	−	0.900832i	$-0.642958\pi$
$811$	−24.7285	−0.868336	−0.434168	+	0.900832i	$0.642958\pi$
$812$	7.60342	0.266828
$813$	83.7681	2.93788
$814$	−34.5722	−1.21176
$815$	0	0
$816$	7.16681	0.250889
$817$	2.51080	0.0878419
$818$	14.6925	0.513711
$819$	−33.7053	−1.17776
$820$	0	0
$821$	−5.85939	−0.204494	−0.102247	−	0.994759i	$-0.532603\pi$
$821$	−5.85939	−0.204494	−0.102247	+	0.994759i	$0.532603\pi$
$822$	38.2361	1.33364
$823$	−32.0474	−1.11710	−0.558551	−	0.829470i	$-0.688642\pi$
$823$	−32.0474	−1.11710	−0.558551	+	0.829470i	$0.688642\pi$
$824$	−30.4263	−1.05995
$825$	0	0
$826$	0.536761	0.0186763
$827$	21.8116	0.758462	0.379231	−	0.925302i	$-0.376189\pi$
$827$	21.8116	0.758462	0.379231	+	0.925302i	$0.376189\pi$
$828$	−61.1129	−2.12382
$829$	−44.1903	−1.53479	−0.767397	−	0.641173i	$-0.778448\pi$
$829$	−44.1903	−1.53479	−0.767397	+	0.641173i	$0.778448\pi$
$830$	0	0
$831$	76.5398	2.65514
$832$	−25.1983	−0.873596
$833$	−18.3454	−0.635629
$834$	23.5170	0.814327
$835$	0	0
$836$	10.2951	0.356064
$837$	87.3357	3.01876
$838$	19.0571	0.658316
$839$	−4.69180	−0.161979	−0.0809895	−	0.996715i	$-0.525808\pi$
$839$	−4.69180	−0.161979	−0.0809895	+	0.996715i	$0.525808\pi$
$840$	0	0
$841$	16.4446	0.567054
$842$	24.9001	0.858115
$843$	−66.9743	−2.30672
$844$	6.59907	0.227149
$845$	0	0
$846$	26.2024	0.900857
$847$	3.68143	0.126495
$848$	−2.66294	−0.0914459
$849$	−12.9426	−0.444189
$850$	0	0
$851$	−65.3787	−2.24115
$852$	14.3004	0.489923
$853$	32.5983	1.11615	0.558073	−	0.829792i	$-0.311541\pi$
$853$	32.5983	1.11615	0.558073	+	0.829792i	$0.311541\pi$
$854$	−0.864199	−0.0295723
$855$	0	0
$856$	−41.3835	−1.41446
$857$	50.7839	1.73474	0.867372	−	0.497660i	$-0.165807\pi$
$857$	50.7839	1.73474	0.867372	+	0.497660i	$0.165807\pi$
$858$	48.0605	1.64076
$859$	−52.8932	−1.80469	−0.902346	−	0.431013i	$-0.858156\pi$
$859$	−52.8932	−1.80469	−0.902346	+	0.431013i	$0.858156\pi$
$860$	0	0
$861$	21.8306	0.743984
$862$	−7.10367	−0.241952
$863$	16.1016	0.548106	0.274053	−	0.961715i	$-0.411636\pi$
$863$	16.1016	0.548106	0.274053	+	0.961715i	$0.411636\pi$
$864$	−91.3942	−3.10929
$865$	0	0
$866$	17.5213	0.595397
$867$	24.5577	0.834023
$868$	5.65967	0.192102
$869$	−12.7572	−0.432758
$870$	0	0
$871$	54.8634	1.85897
$872$	−27.2024	−0.921188
$873$	−48.8112	−1.65201
$874$	−16.7080	−0.565158
$875$	0	0
$876$	5.40085	0.182478
$877$	−4.54878	−0.153601	−0.0768007	−	0.997046i	$-0.524471\pi$
$877$	−4.54878	−0.153601	−0.0768007	+	0.997046i	$0.524471\pi$
$878$	17.4664	0.589462
$879$	31.7363	1.07044
$880$	0	0
$881$	16.7936	0.565791	0.282896	−	0.959151i	$-0.408705\pi$
$881$	16.7936	0.565791	0.282896	+	0.959151i	$0.408705\pi$
$882$	−46.5151	−1.56624
$883$	17.1894	0.578469	0.289235	−	0.957258i	$-0.406599\pi$
$883$	17.1894	0.578469	0.289235	+	0.957258i	$0.406599\pi$
$884$	13.1221	0.441344
$885$	0	0
$886$	−15.7560	−0.529332
$887$	−44.9056	−1.50778	−0.753891	−	0.656999i	$-0.771825\pi$
$887$	−44.9056	−1.50778	−0.753891	+	0.656999i	$0.771825\pi$
$888$	−93.4324	−3.13539
$889$	6.09637	0.204466
$890$	0	0
$891$	128.183	4.29430
$892$	29.3559	0.982907
$893$	−8.34735	−0.279333
$894$	4.78998	0.160201
$895$	0	0
$896$	−4.53499	−0.151503
$897$	90.8860	3.03460
$898$	36.5590	1.21999
$899$	33.8270	1.12819
$900$	0	0
$901$	12.0152	0.400284
$902$	−22.7907	−0.758848
$903$	3.50711	0.116709
$904$	35.9414	1.19539
$905$	0	0
$906$	−23.7132	−0.787818
$907$	2.26848	0.0753235	0.0376618	−	0.999291i	$-0.488009\pi$
$907$	2.26848	0.0753235	0.0376618	+	0.999291i	$0.488009\pi$
$908$	17.7196	0.588046
$909$	−26.7368	−0.886802
$910$	0	0
$911$	2.14063	0.0709223	0.0354612	−	0.999371i	$-0.488710\pi$
$911$	2.14063	0.0709223	0.0354612	+	0.999371i	$0.488710\pi$
$912$	−5.78897	−0.191692
$913$	−43.0830	−1.42584
$914$	−2.64526	−0.0874974
$915$	0	0
$916$	−21.2968	−0.703666
$917$	−9.10066	−0.300530
$918$	−51.9958	−1.71612
$919$	56.9925	1.88001	0.940005	−	0.341161i	$-0.110820\pi$
$919$	56.9925	1.88001	0.940005	+	0.341161i	$0.110820\pi$
$920$	0	0
$921$	−80.7285	−2.66009
$922$	3.40565	0.112159
$923$	−15.5710	−0.512525
$924$	14.3803	0.473077
$925$	0	0
$926$	0.000648789 0	2.13205e−5 0
$927$	84.3916	2.77178
$928$	−35.3990	−1.16203
$929$	−35.6332	−1.16909	−0.584544	−	0.811362i	$-0.698727\pi$
$929$	−35.6332	−1.16909	−0.584544	+	0.811362i	$0.698727\pi$
$930$	0	0
$931$	14.8184	0.485654
$932$	18.9765	0.621596
$933$	52.6941	1.72513
$934$	21.7722	0.712407
$935$	0	0
$936$	95.0960	3.10831
$937$	−43.3277	−1.41546	−0.707728	−	0.706485i	$-0.750280\pi$
$937$	−43.3277	−1.41546	−0.707728	+	0.706485i	$0.750280\pi$
$938$	−14.0879	−0.459987
$939$	−41.7055	−1.36101
$940$	0	0
$941$	12.7557	0.415823	0.207912	−	0.978148i	$-0.433333\pi$
$941$	12.7557	0.415823	0.207912	+	0.978148i	$0.433333\pi$
$942$	44.4529	1.44835
$943$	−43.0990	−1.40350
$944$	−0.367163	−0.0119501
$945$	0	0
$946$	−3.66136	−0.119041
$947$	41.2156	1.33933	0.669663	−	0.742665i	$-0.266438\pi$
$947$	41.2156	1.33933	0.669663	+	0.742665i	$0.266438\pi$
$948$	−12.0624	−0.391769
$949$	−5.88071	−0.190896
$950$	0	0
$951$	77.2855	2.50615
$952$	−9.63073	−0.312134
$953$	−23.7817	−0.770364	−0.385182	−	0.922841i	$-0.625861\pi$
$953$	−23.7817	−0.770364	−0.385182	+	0.922841i	$0.625861\pi$
$954$	30.4648	0.986334
$955$	0	0
$956$	28.9159	0.935208
$957$	85.9489	2.77833
$958$	7.31325	0.236280
$959$	−12.4572	−0.402265
$960$	0	0
$961$	−5.82059	−0.187761
$962$	35.5938	1.14759
$963$	114.783	3.69883
$964$	15.7347	0.506781
$965$	0	0
$966$	−23.3379	−0.750885
$967$	15.0163	0.482892	0.241446	−	0.970414i	$-0.422378\pi$
$967$	15.0163	0.482892	0.241446	+	0.970414i	$0.422378\pi$
$968$	−10.3868	−0.333843
$969$	26.1198	0.839089
$970$	0	0
$971$	−0.584297	−0.0187510	−0.00937550	−	0.999956i	$-0.502984\pi$
$971$	−0.584297	−0.0187510	−0.00937550	+	0.999956i	$0.502984\pi$
$972$	65.0029	2.08497
$973$	−7.66177	−0.245625
$974$	20.2892	0.650108
$975$	0	0
$976$	0.591141	0.0189220
$977$	−11.2437	−0.359718	−0.179859	−	0.983692i	$-0.557564\pi$
$977$	−11.2437	−0.359718	−0.179859	+	0.983692i	$0.557564\pi$
$978$	−17.1943	−0.549812
$979$	−55.4035	−1.77070
$980$	0	0
$981$	75.4496	2.40892
$982$	−39.4259	−1.25813
$983$	3.80876	0.121481	0.0607403	−	0.998154i	$-0.480654\pi$
$983$	3.80876	0.121481	0.0607403	+	0.998154i	$0.480654\pi$
$984$	−61.5926	−1.96350
$985$	0	0
$986$	−20.1391	−0.641360
$987$	−11.6596	−0.371130
$988$	−10.5993	−0.337210
$989$	−6.92390	−0.220167
$990$	0	0
$991$	21.7364	0.690480	0.345240	−	0.938514i	$-0.387797\pi$
$991$	21.7364	0.690480	0.345240	+	0.938514i	$0.387797\pi$
$992$	−26.3495	−0.836598
$993$	−51.8109	−1.64417
$994$	3.99835	0.126820
$995$	0	0
$996$	−40.7366	−1.29079
$997$	11.3635	0.359885	0.179942	−	0.983677i	$-0.442409\pi$
$997$	11.3635	0.359885	0.179942	+	0.983677i	$0.442409\pi$
$998$	34.5010	1.09211
$999$	164.344	5.19962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.p.1.5		6
3.2	odd	2		9675.2.a.cl.1.2		6
5.2	odd	4		1075.2.b.k.474.8		12
5.3	odd	4		1075.2.b.k.474.5		12
5.4	even	2		215.2.a.d.1.2	✓	6
15.14	odd	2		1935.2.a.z.1.5		6
20.19	odd	2		3440.2.a.x.1.1		6
215.214	odd	2		9245.2.a.n.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.a.d.1.2	✓	6	5.4	even	2
1075.2.a.p.1.5		6	1.1	even	1	trivial
1075.2.b.k.474.5		12	5.3	odd	4
1075.2.b.k.474.8		12	5.2	odd	4
1935.2.a.z.1.5		6	15.14	odd	2
3440.2.a.x.1.1		6	20.19	odd	2
9245.2.a.n.1.5		6	215.214	odd	2
9675.2.a.cl.1.2		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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q+0.961086 q^{2} -3.34672 q^{3} -1.07631 q^{4} -3.21649 q^{6} +1.04792 q^{7} -2.95660 q^{8} +8.20055 q^{9} +O(q^{10})\)	\(q+0.961086 q^{2} -3.34672 q^{3} -1.07631 q^{4} -3.21649 q^{6} +1.04792 q^{7} -2.95660 q^{8} +8.20055 q^{9} +3.80960 q^{11} +3.60212 q^{12} -3.92217 q^{13} +1.00714 q^{14} -0.688920 q^{16} +3.10840 q^{17} +7.88143 q^{18} -2.51080 q^{19} -3.50711 q^{21} +3.66136 q^{22} +6.92390 q^{23} +9.89493 q^{24} -3.76954 q^{26} -17.4048 q^{27} -1.12789 q^{28} -6.74126 q^{29} -5.01791 q^{31} +5.25109 q^{32} -12.7497 q^{33} +2.98744 q^{34} -8.82637 q^{36} -9.44246 q^{37} -2.41310 q^{38} +13.1264 q^{39} -6.22467 q^{41} -3.37063 q^{42} -1.00000 q^{43} -4.10033 q^{44} +6.65446 q^{46} +3.32457 q^{47} +2.30562 q^{48} -5.90186 q^{49} -10.4030 q^{51} +4.22149 q^{52} +3.86539 q^{53} -16.7275 q^{54} -3.09829 q^{56} +8.40296 q^{57} -6.47893 q^{58} +0.532954 q^{59} -0.858069 q^{61} -4.82264 q^{62} +8.59354 q^{63} +6.42459 q^{64} -12.2535 q^{66} -13.9880 q^{67} -3.34562 q^{68} -23.1724 q^{69} +3.96999 q^{71} -24.2458 q^{72} +1.49935 q^{73} -9.07501 q^{74} +2.70241 q^{76} +3.99217 q^{77} +12.6156 q^{78} -3.34869 q^{79} +33.6474 q^{81} -5.98244 q^{82} -11.3091 q^{83} +3.77475 q^{84} -0.961086 q^{86} +22.5611 q^{87} -11.2635 q^{88} -14.5431 q^{89} -4.11013 q^{91} -7.45229 q^{92} +16.7935 q^{93} +3.19520 q^{94} -17.5739 q^{96} -5.95219 q^{97} -5.67219 q^{98} +31.2408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9	\( 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 5 q^{16} - 6 q^{17} + 11 q^{18} + 6 q^{19} - 12 q^{21} + q^{22} - 32 q^{26} - 10 q^{27} + 10 q^{28} - 10 q^{29} - 11 q^{32} - 6 q^{33} + 14 q^{34} - 41 q^{36} - 28 q^{37} + 6 q^{38} + 8 q^{39} - 6 q^{41} - 5 q^{42} - 6 q^{43} + 4 q^{44} - 8 q^{46} + 6 q^{47} + 32 q^{48} + 20 q^{49} - 8 q^{51} + 16 q^{52} + 4 q^{53} - 5 q^{54} - 35 q^{56} - 4 q^{57} + 26 q^{58} - 20 q^{59} - 8 q^{61} - 2 q^{62} + 2 q^{63} + 17 q^{64} - 35 q^{66} - 22 q^{67} - 22 q^{68} - 42 q^{69} + 8 q^{71} + 2 q^{72} - 34 q^{73} + 45 q^{74} - 16 q^{76} - 8 q^{77} + 26 q^{78} - 16 q^{79} + 46 q^{81} - 22 q^{82} + 14 q^{83} + 37 q^{84} + 3 q^{86} + 2 q^{87} - 20 q^{88} + 24 q^{91} - 46 q^{92} - 30 q^{93} + 12 q^{94} - 23 q^{96} - 34 q^{97} - 32 q^{98} - 16 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 5 * q^16 - 6 * q^17 + 11 * q^18 + 6 * q^19 - 12 * q^21 + q^22 - 32 * q^26 - 10 * q^27 + 10 * q^28 - 10 * q^29 - 11 * q^32 - 6 * q^33 + 14 * q^34 - 41 * q^36 - 28 * q^37 + 6 * q^38 + 8 * q^39 - 6 * q^41 - 5 * q^42 - 6 * q^43 + 4 * q^44 - 8 * q^46 + 6 * q^47 + 32 * q^48 + 20 * q^49 - 8 * q^51 + 16 * q^52 + 4 * q^53 - 5 * q^54 - 35 * q^56 - 4 * q^57 + 26 * q^58 - 20 * q^59 - 8 * q^61 - 2 * q^62 + 2 * q^63 + 17 * q^64 - 35 * q^66 - 22 * q^67 - 22 * q^68 - 42 * q^69 + 8 * q^71 + 2 * q^72 - 34 * q^73 + 45 * q^74 - 16 * q^76 - 8 * q^77 + 26 * q^78 - 16 * q^79 + 46 * q^81 - 22 * q^82 + 14 * q^83 + 37 * q^84 + 3 * q^86 + 2 * q^87 - 20 * q^88 + 24 * q^91 - 46 * q^92 - 30 * q^93 + 12 * q^94 - 23 * q^96 - 34 * q^97 - 32 * q^98 - 16 * q^99

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