LMFDB - Embedded newform 1475.2.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1475,2,Mod(1,1475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1475, 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("1475.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1475 = 5^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1475.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:	$11.7779342981$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.138136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 3x^{2} + 4x - 2 $ x^5 - x^4 - 6x^3 + 3x^2 + 4*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 59)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.514054$ of defining polynomial
Character	$\chi$	$=$	1475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.67791 q^{2} -2.37659 q^{3} +0.815372 q^{4} -3.98770 q^{6} -2.73575 q^{7} -1.98770 q^{8} +2.64817 q^{9} +O(q^{10})$	\(q+1.67791 q^{2} -2.37659 q^{3} +0.815372 q^{4} -3.98770 q^{6} -2.73575 q^{7} -1.98770 q^{8} +2.64817 q^{9} -4.63749 q^{11} -1.93780 q^{12} +2.63749 q^{13} -4.59033 q^{14} -4.96591 q^{16} +5.59666 q^{17} +4.44339 q^{18} +5.09371 q^{19} +6.50175 q^{21} -7.78129 q^{22} +0.971892 q^{23} +4.72393 q^{24} +4.42547 q^{26} +0.836147 q^{27} -2.23065 q^{28} +9.11967 q^{29} -3.10224 q^{31} -4.35695 q^{32} +11.0214 q^{33} +9.39067 q^{34} +2.15925 q^{36} -9.78129 q^{37} +8.54677 q^{38} -6.26824 q^{39} +8.36990 q^{41} +10.9093 q^{42} +5.66560 q^{43} -3.78129 q^{44} +1.63074 q^{46} +0.644186 q^{47} +11.8019 q^{48} +0.484320 q^{49} -13.3010 q^{51} +2.15054 q^{52} -1.65827 q^{53} +1.40298 q^{54} +5.43783 q^{56} -12.1056 q^{57} +15.3020 q^{58} +1.00000 q^{59} +1.92587 q^{61} -5.20527 q^{62} -7.24474 q^{63} +2.62127 q^{64} +18.4929 q^{66} +10.6724 q^{67} +4.56336 q^{68} -2.30979 q^{69} -3.73455 q^{71} -5.26376 q^{72} -2.57803 q^{73} -16.4121 q^{74} +4.15327 q^{76} +12.6870 q^{77} -10.5175 q^{78} +2.14522 q^{79} -9.93170 q^{81} +14.0439 q^{82} -13.5994 q^{83} +5.30135 q^{84} +9.50635 q^{86} -21.6737 q^{87} +9.21792 q^{88} +8.86886 q^{89} -7.21552 q^{91} +0.792454 q^{92} +7.37275 q^{93} +1.08088 q^{94} +10.3547 q^{96} +8.89107 q^{97} +0.812644 q^{98} -12.2809 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{3} + 8 q^{4} - 4 q^{6} - 2 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 2 * q^3 + 8 * q^4 - 4 * q^6 - 2 * q^7 + 6 * q^8 + 5 * q^9	$ 5 q + 2 q^{3} + 8 q^{4} - 4 q^{6} - 2 q^{7} + 6 q^{8} + 5 q^{9} - 2 q^{11} + 22 q^{12} - 8 q^{13} - 18 q^{14} + 10 q^{16} + q^{17} + 2 q^{18} + 6 q^{19} + 15 q^{21} - 8 q^{22} + 8 q^{23} + 6 q^{24} + 8 q^{26} + 11 q^{27} + 2 q^{28} + 14 q^{29} + 2 q^{32} + 14 q^{33} - 2 q^{34} + 42 q^{36} - 18 q^{37} - 18 q^{39} - 10 q^{41} - 34 q^{42} + 4 q^{43} + 12 q^{44} + 16 q^{46} + 20 q^{47} + 54 q^{48} + q^{49} - 12 q^{51} - 28 q^{52} + 10 q^{53} - 26 q^{54} - 38 q^{56} + 3 q^{57} + 38 q^{58} + 5 q^{59} + 22 q^{61} - 48 q^{62} + 12 q^{63} + 18 q^{64} + 28 q^{66} + 14 q^{68} - 4 q^{69} + 3 q^{71} - 28 q^{72} + 8 q^{73} + 8 q^{74} + 14 q^{76} - 2 q^{77} - 20 q^{78} + 10 q^{79} - 3 q^{81} + 48 q^{82} - 6 q^{83} + 28 q^{84} - 8 q^{86} - 11 q^{87} + 24 q^{88} + 10 q^{89} + 6 q^{91} - 4 q^{92} - 6 q^{93} - 36 q^{94} + 42 q^{96} + 22 q^{97} - 24 q^{98} - 4 q^{99}+O(q^{100}) $ 5 * q + 2 * q^3 + 8 * q^4 - 4 * q^6 - 2 * q^7 + 6 * q^8 + 5 * q^9 - 2 * q^11 + 22 * q^12 - 8 * q^13 - 18 * q^14 + 10 * q^16 + q^17 + 2 * q^18 + 6 * q^19 + 15 * q^21 - 8 * q^22 + 8 * q^23 + 6 * q^24 + 8 * q^26 + 11 * q^27 + 2 * q^28 + 14 * q^29 + 2 * q^32 + 14 * q^33 - 2 * q^34 + 42 * q^36 - 18 * q^37 - 18 * q^39 - 10 * q^41 - 34 * q^42 + 4 * q^43 + 12 * q^44 + 16 * q^46 + 20 * q^47 + 54 * q^48 + q^49 - 12 * q^51 - 28 * q^52 + 10 * q^53 - 26 * q^54 - 38 * q^56 + 3 * q^57 + 38 * q^58 + 5 * q^59 + 22 * q^61 - 48 * q^62 + 12 * q^63 + 18 * q^64 + 28 * q^66 + 14 * q^68 - 4 * q^69 + 3 * q^71 - 28 * q^72 + 8 * q^73 + 8 * q^74 + 14 * q^76 - 2 * q^77 - 20 * q^78 + 10 * q^79 - 3 * q^81 + 48 * q^82 - 6 * q^83 + 28 * q^84 - 8 * q^86 - 11 * q^87 + 24 * q^88 + 10 * q^89 + 6 * q^91 - 4 * q^92 - 6 * q^93 - 36 * q^94 + 42 * q^96 + 22 * q^97 - 24 * q^98 - 4 * 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 $

$2$	1.67791	1.18646	0.593230	−	0.805033i	$-0.297853\pi$
$2$	1.67791	1.18646	0.593230	+	0.805033i	$0.297853\pi$
$3$	−2.37659	−1.37212	−0.686062	−	0.727543i	$-0.740662\pi$
$3$	−2.37659	−1.37212	−0.686062	+	0.727543i	$0.740662\pi$
$4$	0.815372	0.407686
$5$	0	0
$5$	0	0
$6$	−3.98770	−1.62797
$7$	−2.73575	−1.03402	−0.517008	−	0.855981i	$-0.672954\pi$
$7$	−2.73575	−1.03402	−0.517008	+	0.855981i	$0.672954\pi$
$8$	−1.98770	−0.702756
$9$	2.64817	0.882725
$10$	0	0
$11$	−4.63749	−1.39826	−0.699129	−	0.714996i	$-0.746429\pi$
$11$	−4.63749	−1.39826	−0.699129	+	0.714996i	$0.746429\pi$
$12$	−1.93780	−0.559396
$13$	2.63749	0.731509	0.365755	−	0.930711i	$-0.380811\pi$
$13$	2.63749	0.731509	0.365755	+	0.930711i	$0.380811\pi$
$14$	−4.59033	−1.22682
$15$	0	0
$16$	−4.96591	−1.24148
$17$	5.59666	1.35739	0.678694	−	0.734421i	$-0.262546\pi$
$17$	5.59666	1.35739	0.678694	+	0.734421i	$0.262546\pi$
$18$	4.44339	1.04732
$19$	5.09371	1.16858	0.584288	−	0.811546i	$-0.301374\pi$
$19$	5.09371	1.16858	0.584288	+	0.811546i	$0.301374\pi$
$20$	0	0
$21$	6.50175	1.41880
$22$	−7.78129	−1.65898
$23$	0.971892	0.202654	0.101327	−	0.994853i	$-0.467691\pi$
$23$	0.971892	0.202654	0.101327	+	0.994853i	$0.467691\pi$
$24$	4.72393	0.964269
$25$	0	0
$26$	4.42547	0.867906
$27$	0.836147	0.160917
$28$	−2.23065	−0.421554
$29$	9.11967	1.69348	0.846740	−	0.532007i	$-0.178562\pi$
$29$	9.11967	1.69348	0.846740	+	0.532007i	$0.178562\pi$
$30$	0	0
$31$	−3.10224	−0.557179	−0.278590	−	0.960410i	$-0.589867\pi$
$31$	−3.10224	−0.557179	−0.278590	+	0.960410i	$0.589867\pi$
$32$	−4.35695	−0.770207
$33$	11.0214	1.91858
$34$	9.39067	1.61049
$35$	0	0
$36$	2.15925	0.359875
$37$	−9.78129	−1.60803	−0.804017	−	0.594607i	$-0.797308\pi$
$37$	−9.78129	−1.60803	−0.804017	+	0.594607i	$0.797308\pi$
$38$	8.54677	1.38647
$39$	−6.26824	−1.00372
$40$	0	0
$41$	8.36990	1.30716	0.653579	−	0.756858i	$-0.273267\pi$
$41$	8.36990	1.30716	0.653579	+	0.756858i	$0.273267\pi$
$42$	10.9093	1.68335
$43$	5.66560	0.863996	0.431998	−	0.901875i	$-0.357809\pi$
$43$	5.66560	0.863996	0.431998	+	0.901875i	$0.357809\pi$
$44$	−3.78129	−0.570050
$45$	0	0
$46$	1.63074	0.240440
$47$	0.644186	0.0939641	0.0469821	−	0.998896i	$-0.485040\pi$
$47$	0.644186	0.0939641	0.0469821	+	0.998896i	$0.485040\pi$
$48$	11.8019	1.70346
$49$	0.484320	0.0691886
$50$	0	0
$51$	−13.3010	−1.86251
$52$	2.15054	0.298226
$53$	−1.65827	−0.227781	−0.113890	−	0.993493i	$-0.536331\pi$
$53$	−1.65827	−0.227781	−0.113890	+	0.993493i	$0.536331\pi$
$54$	1.40298	0.190921
$55$	0	0
$56$	5.43783	0.726661
$57$	−12.1056	−1.60343
$58$	15.3020	2.00925
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0	0
$61$	1.92587	0.246582	0.123291	−	0.992371i	$-0.460655\pi$
$61$	1.92587	0.246582	0.123291	+	0.992371i	$0.460655\pi$
$62$	−5.20527	−0.661070
$63$	−7.24474	−0.912751
$64$	2.62127	0.327658
$65$	0	0
$66$	18.4929	2.27632
$67$	10.6724	1.30384	0.651918	−	0.758290i	$-0.273965\pi$
$67$	10.6724	1.30384	0.651918	+	0.758290i	$0.273965\pi$
$68$	4.56336	0.553389
$69$	−2.30979	−0.278066
$70$	0	0
$71$	−3.73455	−0.443209	−0.221605	−	0.975137i	$-0.571129\pi$
$71$	−3.73455	−0.443209	−0.221605	+	0.975137i	$0.571129\pi$
$72$	−5.26376	−0.620340
$73$	−2.57803	−0.301735	−0.150868	−	0.988554i	$-0.548207\pi$
$73$	−2.57803	−0.301735	−0.150868	+	0.988554i	$0.548207\pi$
$74$	−16.4121	−1.90787
$75$	0	0
$76$	4.15327	0.476413
$77$	12.6870	1.44582
$78$	−10.5175	−1.19088
$79$	2.14522	0.241356	0.120678	−	0.992692i	$-0.461493\pi$
$79$	2.14522	0.241356	0.120678	+	0.992692i	$0.461493\pi$
$80$	0	0
$81$	−9.93170	−1.10352
$82$	14.0439	1.55089
$83$	−13.5994	−1.49273	−0.746366	−	0.665535i	$-0.768203\pi$
$83$	−13.5994	−1.49273	−0.746366	+	0.665535i	$0.768203\pi$
$84$	5.30135	0.578424
$85$	0	0
$86$	9.50635	1.02510
$87$	−21.6737	−2.32367
$88$	9.21792	0.982634
$89$	8.86886	0.940097	0.470049	−	0.882641i	$-0.344236\pi$
$89$	8.86886	0.940097	0.470049	+	0.882641i	$0.344236\pi$
$90$	0	0
$91$	−7.21552	−0.756392
$92$	0.792454	0.0826191
$93$	7.37275	0.764519
$94$	1.08088	0.111485
$95$	0	0
$96$	10.3547	1.05682
$97$	8.89107	0.902751	0.451376	−	0.892334i	$-0.350933\pi$
$97$	8.89107	0.902751	0.451376	+	0.892334i	$0.350933\pi$
$98$	0.812644	0.0820895
$99$	−12.2809	−1.23428
$100$	0	0
$101$	8.26622	0.822520	0.411260	−	0.911518i	$-0.365089\pi$
$101$	8.26622	0.822520	0.411260	+	0.911518i	$0.365089\pi$
$102$	−22.3178	−2.20979
$103$	0.930344	0.0916695	0.0458347	−	0.998949i	$-0.485405\pi$
$103$	0.930344	0.0916695	0.0458347	+	0.998949i	$0.485405\pi$
$104$	−5.24253	−0.514073
$105$	0	0
$106$	−2.78242	−0.270253
$107$	−3.38129	−0.326881	−0.163441	−	0.986553i	$-0.552259\pi$
$107$	−3.38129	−0.326881	−0.163441	+	0.986553i	$0.552259\pi$
$108$	0.681771	0.0656034
$109$	19.9933	1.91501	0.957506	−	0.288414i	$-0.0931279\pi$
$109$	19.9933	1.91501	0.957506	+	0.288414i	$0.0931279\pi$
$110$	0	0
$111$	23.2461	2.20642
$112$	13.5855	1.28371
$113$	−0.968641	−0.0911220	−0.0455610	−	0.998962i	$-0.514508\pi$
$113$	−0.968641	−0.0911220	−0.0455610	+	0.998962i	$0.514508\pi$
$114$	−20.3121	−1.90241
$115$	0	0
$116$	7.43593	0.690409
$117$	6.98454	0.645721
$118$	1.67791	0.154464
$119$	−15.3110	−1.40356
$120$	0	0
$121$	10.5064	0.955123
$122$	3.23142	0.292559
$123$	−19.8918	−1.79358
$124$	−2.52948	−0.227154
$125$	0	0
$126$	−12.1560	−1.08294
$127$	12.5251	1.11142	0.555711	−	0.831376i	$-0.312446\pi$
$127$	12.5251	1.11142	0.555711	+	0.831376i	$0.312446\pi$
$128$	13.1121	1.15896
$129$	−13.4648	−1.18551
$130$	0	0
$131$	−11.3090	−0.988072	−0.494036	−	0.869442i	$-0.664479\pi$
$131$	−11.3090	−0.988072	−0.494036	+	0.869442i	$0.664479\pi$
$132$	8.98656	0.782180
$133$	−13.9351	−1.20833
$134$	17.9072	1.54695
$135$	0	0
$136$	−11.1244	−0.953914
$137$	11.4517	0.978382	0.489191	−	0.872177i	$-0.337292\pi$
$137$	11.4517	0.978382	0.489191	+	0.872177i	$0.337292\pi$
$138$	−3.87561	−0.329914
$139$	−8.13314	−0.689844	−0.344922	−	0.938631i	$-0.612095\pi$
$139$	−8.13314	−0.689844	−0.344922	+	0.938631i	$0.612095\pi$
$140$	0	0
$141$	−1.53096	−0.128930
$142$	−6.26622	−0.525850
$143$	−12.2314	−1.02284
$144$	−13.1506	−1.09588
$145$	0	0
$146$	−4.32569	−0.357997
$147$	−1.15103	−0.0949354
$148$	−7.97539	−0.655573
$149$	−12.6657	−1.03761	−0.518806	−	0.854892i	$-0.673623\pi$
$149$	−12.6657	−1.03761	−0.518806	+	0.854892i	$0.673623\pi$
$150$	0	0
$151$	12.8241	1.04361	0.521804	−	0.853066i	$-0.325259\pi$
$151$	12.8241	1.04361	0.521804	+	0.853066i	$0.325259\pi$
$152$	−10.1247	−0.821225
$153$	14.8209	1.19820
$154$	21.2876	1.71541
$155$	0	0
$156$	−5.11095	−0.409203
$157$	−2.29045	−0.182797	−0.0913987	−	0.995814i	$-0.529134\pi$
$157$	−2.29045	−0.182797	−0.0913987	+	0.995814i	$0.529134\pi$
$158$	3.59948	0.286360
$159$	3.94102	0.312543
$160$	0	0
$161$	−2.65885	−0.209547
$162$	−16.6645	−1.30928
$163$	−10.3337	−0.809401	−0.404701	−	0.914449i	$-0.632624\pi$
$163$	−10.3337	−0.809401	−0.404701	+	0.914449i	$0.632624\pi$
$164$	6.82458	0.532910
$165$	0	0
$166$	−22.8186	−1.77107
$167$	4.75711	0.368116	0.184058	−	0.982915i	$-0.441077\pi$
$167$	4.75711	0.368116	0.184058	+	0.982915i	$0.441077\pi$
$168$	−12.9235	−0.997069
$169$	−6.04362	−0.464894
$170$	0	0
$171$	13.4890	1.03153
$172$	4.61958	0.352239
$173$	11.3165	0.860380	0.430190	−	0.902738i	$-0.358446\pi$
$173$	11.3165	0.860380	0.430190	+	0.902738i	$0.358446\pi$
$174$	−36.3665	−2.75693
$175$	0	0
$176$	23.0294	1.73591
$177$	−2.37659	−0.178635
$178$	14.8811	1.11539
$179$	15.1224	1.13030	0.565152	−	0.824987i	$-0.308818\pi$
$179$	15.1224	1.13030	0.565152	+	0.824987i	$0.308818\pi$
$180$	0	0
$181$	14.5597	1.08222	0.541108	−	0.840953i	$-0.318005\pi$
$181$	14.5597	1.08222	0.541108	+	0.840953i	$0.318005\pi$
$182$	−12.1070	−0.897429
$183$	−4.57699	−0.338341
$184$	−1.93183	−0.142416
$185$	0	0
$186$	12.3708	0.907071
$187$	−25.9545	−1.89798
$188$	0.525251	0.0383079
$189$	−2.28749	−0.166390
$190$	0	0
$191$	−6.73851	−0.487581	−0.243791	−	0.969828i	$-0.578391\pi$
$191$	−6.73851	−0.487581	−0.243791	+	0.969828i	$0.578391\pi$
$192$	−6.22967	−0.449588
$193$	−14.9907	−1.07905	−0.539526	−	0.841969i	$-0.681397\pi$
$193$	−14.9907	−1.07905	−0.539526	+	0.841969i	$0.681397\pi$
$194$	14.9184	1.07108
$195$	0	0
$196$	0.394901	0.0282072
$197$	10.2521	0.730430	0.365215	−	0.930923i	$-0.380996\pi$
$197$	10.2521	0.730430	0.365215	+	0.930923i	$0.380996\pi$
$198$	−20.6062	−1.46442
$199$	2.89840	0.205462	0.102731	−	0.994709i	$-0.467242\pi$
$199$	2.89840	0.205462	0.102731	+	0.994709i	$0.467242\pi$
$200$	0	0
$201$	−25.3638	−1.78902
$202$	13.8700	0.975887
$203$	−24.9491	−1.75109
$204$	−10.8452	−0.759318
$205$	0	0
$206$	1.56103	0.108762
$207$	2.57374	0.178887
$208$	−13.0976	−0.908153
$209$	−23.6220	−1.63397
$210$	0	0
$211$	−1.16840	−0.0804360	−0.0402180	−	0.999191i	$-0.512805\pi$
$211$	−1.16840	−0.0804360	−0.0402180	+	0.999191i	$0.512805\pi$
$212$	−1.35211	−0.0928631
$213$	8.87548	0.608138
$214$	−5.67349	−0.387832
$215$	0	0
$216$	−1.66200	−0.113085
$217$	8.48695	0.576132
$218$	33.5469	2.27208
$219$	6.12691	0.414018
$220$	0	0
$221$	14.7612	0.992943
$222$	39.0048	2.61783
$223$	21.2702	1.42436	0.712180	−	0.701997i	$-0.247708\pi$
$223$	21.2702	1.42436	0.712180	+	0.701997i	$0.247708\pi$
$224$	11.9195	0.796406
$225$	0	0
$226$	−1.62529	−0.108113
$227$	13.0776	0.867993	0.433996	−	0.900915i	$-0.357103\pi$
$227$	13.0776	0.867993	0.433996	+	0.900915i	$0.357103\pi$
$228$	−9.87061	−0.653697
$229$	−3.02142	−0.199661	−0.0998304	−	0.995004i	$-0.531830\pi$
$229$	−3.02142	−0.199661	−0.0998304	+	0.995004i	$0.531830\pi$
$230$	0	0
$231$	−30.1518	−1.98384
$232$	−18.1271	−1.19010
$233$	2.84069	0.186100	0.0930500	−	0.995661i	$-0.470338\pi$
$233$	2.84069	0.186100	0.0930500	+	0.995661i	$0.470338\pi$
$234$	11.7194	0.766122
$235$	0	0
$236$	0.815372	0.0530762
$237$	−5.09831	−0.331171
$238$	−25.6905	−1.66527
$239$	18.8482	1.21919	0.609594	−	0.792714i	$-0.291333\pi$
$239$	18.8482	1.21919	0.609594	+	0.792714i	$0.291333\pi$
$240$	0	0
$241$	−22.5419	−1.45205	−0.726027	−	0.687666i	$-0.758635\pi$
$241$	−22.5419	−1.45205	−0.726027	+	0.687666i	$0.758635\pi$
$242$	17.6287	1.13321
$243$	21.0951	1.35325
$244$	1.57030	0.100528
$245$	0	0
$246$	−33.3766	−2.12801
$247$	13.4346	0.854825
$248$	6.16631	0.391561
$249$	32.3203	2.04821
$250$	0	0
$251$	−10.0028	−0.631369	−0.315684	−	0.948864i	$-0.602234\pi$
$251$	−10.0028	−0.631369	−0.315684	+	0.948864i	$0.602234\pi$
$252$	−5.90716	−0.372116
$253$	−4.50714	−0.283362
$254$	21.0159	1.31866
$255$	0	0
$256$	16.7584	1.04740
$257$	−0.971402	−0.0605944	−0.0302972	−	0.999541i	$-0.509645\pi$
$257$	−0.971402	−0.0605944	−0.0302972	+	0.999541i	$0.509645\pi$
$258$	−22.5927	−1.40656
$259$	26.7591	1.66273
$260$	0	0
$261$	24.1505	1.49488
$262$	−18.9754	−1.17231
$263$	12.6563	0.780419	0.390210	−	0.920726i	$-0.372402\pi$
$263$	12.6563	0.780419	0.390210	+	0.920726i	$0.372402\pi$
$264$	−21.9072	−1.34830
$265$	0	0
$266$	−23.3818	−1.43363
$267$	−21.0776	−1.28993
$268$	8.70194	0.531556
$269$	−17.5277	−1.06868	−0.534342	−	0.845269i	$-0.679440\pi$
$269$	−17.5277	−1.06868	−0.534342	+	0.845269i	$0.679440\pi$
$270$	0	0
$271$	−13.4119	−0.814712	−0.407356	−	0.913269i	$-0.633549\pi$
$271$	−13.4119	−0.814712	−0.407356	+	0.913269i	$0.633549\pi$
$272$	−27.7925	−1.68517
$273$	17.1483	1.03786
$274$	19.2148	1.16081
$275$	0	0
$276$	−1.88334	−0.113364
$277$	−16.7324	−1.00535	−0.502677	−	0.864474i	$-0.667652\pi$
$277$	−16.7324	−1.00535	−0.502677	+	0.864474i	$0.667652\pi$
$278$	−13.6466	−0.818472
$279$	−8.21528	−0.491836
$280$	0	0
$281$	9.38249	0.559712	0.279856	−	0.960042i	$-0.409713\pi$
$281$	9.38249	0.559712	0.279856	+	0.960042i	$0.409713\pi$
$282$	−2.56882	−0.152971
$283$	5.41405	0.321832	0.160916	−	0.986968i	$-0.448555\pi$
$283$	5.41405	0.321832	0.160916	+	0.986968i	$0.448555\pi$
$284$	−3.04505	−0.180690
$285$	0	0
$286$	−20.5231	−1.21356
$287$	−22.8979	−1.35162
$288$	−11.5380	−0.679881
$289$	14.3226	0.842504
$290$	0	0
$291$	−21.1304	−1.23869
$292$	−2.10205	−0.123013
$293$	−5.82885	−0.340525	−0.170262	−	0.985399i	$-0.554462\pi$
$293$	−5.82885	−0.340525	−0.170262	+	0.985399i	$0.554462\pi$
$294$	−1.93132	−0.112637
$295$	0	0
$296$	19.4422	1.13006
$297$	−3.87763	−0.225003
$298$	−21.2518	−1.23108
$299$	2.56336	0.148243
$300$	0	0
$301$	−15.4997	−0.893386
$302$	21.5176	1.23820
$303$	−19.6454	−1.12860
$304$	−25.2949	−1.45076
$305$	0	0
$306$	24.8681	1.42162
$307$	33.2375	1.89696	0.948482	−	0.316832i	$-0.102619\pi$
$307$	33.2375	1.89696	0.948482	+	0.316832i	$0.102619\pi$
$308$	10.3446	0.589441
$309$	−2.21104	−0.125782
$310$	0	0
$311$	−28.3671	−1.60855	−0.804276	−	0.594256i	$-0.797447\pi$
$311$	−28.3671	−1.60855	−0.804276	+	0.594256i	$0.797447\pi$
$312$	12.4593	0.705372
$313$	−13.4267	−0.758922	−0.379461	−	0.925208i	$-0.623891\pi$
$313$	−13.4267	−0.758922	−0.379461	+	0.925208i	$0.623891\pi$
$314$	−3.84316	−0.216882
$315$	0	0
$316$	1.74916	0.0983977
$317$	11.7821	0.661751	0.330875	−	0.943674i	$-0.392656\pi$
$317$	11.7821	0.661751	0.330875	+	0.943674i	$0.392656\pi$
$318$	6.61267	0.370820
$319$	−42.2924	−2.36792
$320$	0	0
$321$	8.03593	0.448522
$322$	−4.46131	−0.248619
$323$	28.5077	1.58621
$324$	−8.09803	−0.449891
$325$	0	0
$326$	−17.3391	−0.960322
$327$	−47.5159	−2.62763
$328$	−16.6368	−0.918614
$329$	−1.76233	−0.0971604
$330$	0	0
$331$	8.07562	0.443876	0.221938	−	0.975061i	$-0.428762\pi$
$331$	8.07562	0.443876	0.221938	+	0.975061i	$0.428762\pi$
$332$	−11.0886	−0.608567
$333$	−25.9025	−1.41945
$334$	7.98198	0.436755
$335$	0	0
$336$	−32.2871	−1.76141
$337$	−28.9410	−1.57652	−0.788259	−	0.615343i	$-0.789017\pi$
$337$	−28.9410	−1.57652	−0.788259	+	0.615343i	$0.789017\pi$
$338$	−10.1406	−0.551578
$339$	2.30206	0.125031
$340$	0	0
$341$	14.3866	0.779080
$342$	22.6333	1.22387
$343$	17.8253	0.962474
$344$	−11.2615	−0.607179
$345$	0	0
$346$	18.9881	1.02081
$347$	−14.9237	−0.801144	−0.400572	−	0.916265i	$-0.631189\pi$
$347$	−14.9237	−0.801144	−0.400572	+	0.916265i	$0.631189\pi$
$348$	−17.6721	−0.947326
$349$	28.4736	1.52416	0.762078	−	0.647486i	$-0.224179\pi$
$349$	28.4736	1.52416	0.762078	+	0.647486i	$0.224179\pi$
$350$	0	0
$351$	2.20533	0.117712
$352$	20.2053	1.07695
$353$	−5.45885	−0.290545	−0.145273	−	0.989392i	$-0.546406\pi$
$353$	−5.45885	−0.290545	−0.145273	+	0.989392i	$0.546406\pi$
$354$	−3.98770	−0.211944
$355$	0	0
$356$	7.23142	0.383265
$357$	36.3881	1.92586
$358$	25.3740	1.34106
$359$	−22.3420	−1.17917	−0.589584	−	0.807707i	$-0.700708\pi$
$359$	−22.3420	−1.17917	−0.589584	+	0.807707i	$0.700708\pi$
$360$	0	0
$361$	6.94585	0.365571
$362$	24.4298	1.28400
$363$	−24.9693	−1.31055
$364$	−5.88334	−0.308371
$365$	0	0
$366$	−7.67977	−0.401428
$367$	−15.7826	−0.823843	−0.411922	−	0.911219i	$-0.635142\pi$
$367$	−15.7826	−0.823843	−0.411922	+	0.911219i	$0.635142\pi$
$368$	−4.82633	−0.251590
$369$	22.1649	1.15386
$370$	0	0
$371$	4.53661	0.235529
$372$	6.01154	0.311684
$373$	16.1570	0.836578	0.418289	−	0.908314i	$-0.362630\pi$
$373$	16.1570	0.836578	0.418289	+	0.908314i	$0.362630\pi$
$374$	−43.5492	−2.25187
$375$	0	0
$376$	−1.28044	−0.0660339
$377$	24.0531	1.23880
$378$	−3.83819	−0.197415
$379$	35.2096	1.80860	0.904298	−	0.426901i	$-0.140395\pi$
$379$	35.2096	1.80860	0.904298	+	0.426901i	$0.140395\pi$
$380$	0	0
$381$	−29.7670	−1.52501
$382$	−11.3066	−0.578496
$383$	−19.3312	−0.987778	−0.493889	−	0.869525i	$-0.664425\pi$
$383$	−19.3312	−0.987778	−0.493889	+	0.869525i	$0.664425\pi$
$384$	−31.1622	−1.59024
$385$	0	0
$386$	−25.1530	−1.28025
$387$	15.0035	0.762671
$388$	7.24953	0.368039
$389$	15.1861	0.769966	0.384983	−	0.922924i	$-0.374207\pi$
$389$	15.1861	0.769966	0.384983	+	0.922924i	$0.374207\pi$
$390$	0	0
$391$	5.43935	0.275080
$392$	−0.962681	−0.0486227
$393$	26.8768	1.35576
$394$	17.2020	0.866625
$395$	0	0
$396$	−10.0135	−0.503197
$397$	27.1015	1.36019	0.680093	−	0.733126i	$-0.261939\pi$
$397$	27.1015	1.36019	0.680093	+	0.733126i	$0.261939\pi$
$398$	4.86325	0.243773
$399$	33.1180	1.65797
$400$	0	0
$401$	3.93624	0.196567	0.0982833	−	0.995158i	$-0.468665\pi$
$401$	3.93624	0.196567	0.0982833	+	0.995158i	$0.468665\pi$
$402$	−42.5581	−2.12260
$403$	−8.18215	−0.407582
$404$	6.74005	0.335330
$405$	0	0
$406$	−41.8623	−2.07759
$407$	45.3607	2.24844
$408$	26.4382	1.30889
$409$	−16.6724	−0.824395	−0.412197	−	0.911095i	$-0.635239\pi$
$409$	−16.6724	−0.824395	−0.412197	+	0.911095i	$0.635239\pi$
$410$	0	0
$411$	−27.2159	−1.34246
$412$	0.758576	0.0373724
$413$	−2.73575	−0.134617
$414$	4.31850	0.212242
$415$	0	0
$416$	−11.4914	−0.563414
$417$	19.3291	0.946551
$418$	−39.6356	−1.93864
$419$	28.6751	1.40087	0.700434	−	0.713717i	$-0.252990\pi$
$419$	28.6751	1.40087	0.700434	+	0.713717i	$0.252990\pi$
$420$	0	0
$421$	35.9208	1.75067	0.875337	−	0.483512i	$-0.160639\pi$
$421$	35.9208	1.75067	0.875337	+	0.483512i	$0.160639\pi$
$422$	−1.96047	−0.0954341
$423$	1.70592	0.0829444
$424$	3.29613	0.160074
$425$	0	0
$426$	14.8922	0.721531
$427$	−5.26868	−0.254970
$428$	−2.75701	−0.133265
$429$	29.0689	1.40346
$430$	0	0
$431$	16.5377	0.796594	0.398297	−	0.917257i	$-0.369601\pi$
$431$	16.5377	0.796594	0.398297	+	0.917257i	$0.369601\pi$
$432$	−4.15223	−0.199774
$433$	−2.60455	−0.125167	−0.0625834	−	0.998040i	$-0.519934\pi$
$433$	−2.60455	−0.125167	−0.0625834	+	0.998040i	$0.519934\pi$
$434$	14.2403	0.683557
$435$	0	0
$436$	16.3020	0.780724
$437$	4.95053	0.236816
$438$	10.2804	0.491216
$439$	−8.93982	−0.426674	−0.213337	−	0.976979i	$-0.568433\pi$
$439$	−8.93982	−0.426674	−0.213337	+	0.976979i	$0.568433\pi$
$440$	0	0
$441$	1.28256	0.0610745
$442$	24.7678	1.17809
$443$	5.11288	0.242920	0.121460	−	0.992596i	$-0.461242\pi$
$443$	5.11288	0.242920	0.121460	+	0.992596i	$0.461242\pi$
$444$	18.9542	0.899528
$445$	0	0
$446$	35.6895	1.68995
$447$	30.1011	1.42373
$448$	−7.17113	−0.338804
$449$	−1.49082	−0.0703563	−0.0351782	−	0.999381i	$-0.511200\pi$
$449$	−1.49082	−0.0703563	−0.0351782	+	0.999381i	$0.511200\pi$
$450$	0	0
$451$	−38.8154	−1.82774
$452$	−0.789803	−0.0371492
$453$	−30.4775	−1.43196
$454$	21.9431	1.02984
$455$	0	0
$456$	24.0623	1.12682
$457$	26.1838	1.22483	0.612414	−	0.790537i	$-0.290199\pi$
$457$	26.1838	1.22483	0.612414	+	0.790537i	$0.290199\pi$
$458$	−5.06966	−0.236889
$459$	4.67963	0.218426
$460$	0	0
$461$	33.3178	1.55177	0.775883	−	0.630877i	$-0.217305\pi$
$461$	33.3178	1.55177	0.775883	+	0.630877i	$0.217305\pi$
$462$	−50.5920	−2.35375
$463$	4.55992	0.211917	0.105959	−	0.994371i	$-0.466209\pi$
$463$	4.55992	0.211917	0.105959	+	0.994371i	$0.466209\pi$
$464$	−45.2875	−2.10242
$465$	0	0
$466$	4.76642	0.220800
$467$	9.97741	0.461699	0.230850	−	0.972989i	$-0.425849\pi$
$467$	9.97741	0.461699	0.230850	+	0.972989i	$0.425849\pi$
$468$	5.69500	0.263252
$469$	−29.1969	−1.34819
$470$	0	0
$471$	5.44345	0.250821
$472$	−1.98770	−0.0914911
$473$	−26.2742	−1.20809
$474$	−8.55449	−0.392921
$475$	0	0
$476$	−12.4842	−0.572213
$477$	−4.39138	−0.201068
$478$	31.6255	1.44652
$479$	2.02213	0.0923934	0.0461967	−	0.998932i	$-0.485290\pi$
$479$	2.02213	0.0923934	0.0461967	+	0.998932i	$0.485290\pi$
$480$	0	0
$481$	−25.7981	−1.17629
$482$	−37.8233	−1.72280
$483$	6.31900	0.287524
$484$	8.56659	0.389391
$485$	0	0
$486$	35.3957	1.60558
$487$	29.7909	1.34995	0.674977	−	0.737839i	$-0.264154\pi$
$487$	29.7909	1.34995	0.674977	+	0.737839i	$0.264154\pi$
$488$	−3.82803	−0.173287
$489$	24.5591	1.11060
$490$	0	0
$491$	−17.2544	−0.778681	−0.389340	−	0.921094i	$-0.627297\pi$
$491$	−17.2544	−0.778681	−0.389340	+	0.921094i	$0.627297\pi$
$492$	−16.2192	−0.731219
$493$	51.0397	2.29871
$494$	22.5421	1.01421
$495$	0	0
$496$	15.4055	0.691726
$497$	10.2168	0.458285
$498$	54.2304	2.43012
$499$	39.9386	1.78790	0.893948	−	0.448170i	$-0.147924\pi$
$499$	39.9386	1.78790	0.893948	+	0.448170i	$0.147924\pi$
$500$	0	0
$501$	−11.3057	−0.505101
$502$	−16.7837	−0.749093
$503$	−1.00590	−0.0448509	−0.0224255	−	0.999749i	$-0.507139\pi$
$503$	−1.00590	−0.0448509	−0.0224255	+	0.999749i	$0.507139\pi$
$504$	14.4003	0.641442
$505$	0	0
$506$	−7.56257	−0.336197
$507$	14.3632	0.637892
$508$	10.2126	0.453111
$509$	−25.5615	−1.13299	−0.566496	−	0.824065i	$-0.691701\pi$
$509$	−25.5615	−1.13299	−0.566496	+	0.824065i	$0.691701\pi$
$510$	0	0
$511$	7.05283	0.311999
$512$	1.89479	0.0837389
$513$	4.25909	0.188043
$514$	−1.62992	−0.0718928
$515$	0	0
$516$	−10.9788	−0.483316
$517$	−2.98741	−0.131386
$518$	44.8993	1.97276
$519$	−26.8948	−1.18055
$520$	0	0
$521$	−15.6291	−0.684724	−0.342362	−	0.939568i	$-0.611227\pi$
$521$	−15.6291	−0.684724	−0.342362	+	0.939568i	$0.611227\pi$
$522$	40.5222	1.77361
$523$	32.1747	1.40690	0.703450	−	0.710745i	$-0.251642\pi$
$523$	32.1747	1.40690	0.703450	+	0.710745i	$0.251642\pi$
$524$	−9.22105	−0.402823
$525$	0	0
$526$	21.2361	0.925936
$527$	−17.3622	−0.756309
$528$	−54.7314	−2.38188
$529$	−22.0554	−0.958932
$530$	0	0
$531$	2.64817	0.114921
$532$	−11.3623	−0.492618
$533$	22.0756	0.956199
$534$	−35.3663	−1.53045
$535$	0	0
$536$	−21.2134	−0.916279
$537$	−35.9398	−1.55092
$538$	−29.4099	−1.26795
$539$	−2.24603	−0.0967435
$540$	0	0
$541$	13.2460	0.569489	0.284744	−	0.958603i	$-0.408091\pi$
$541$	13.2460	0.569489	0.284744	+	0.958603i	$0.408091\pi$
$542$	−22.5039	−0.966623
$543$	−34.6025	−1.48493
$544$	−24.3844	−1.04547
$545$	0	0
$546$	28.7733	1.23138
$547$	16.9699	0.725580	0.362790	−	0.931871i	$-0.381824\pi$
$547$	16.9699	0.725580	0.362790	+	0.931871i	$0.381824\pi$
$548$	9.33737	0.398873
$549$	5.10003	0.217664
$550$	0	0
$551$	46.4529	1.97896
$552$	4.59115	0.195412
$553$	−5.86879	−0.249566
$554$	−28.0755	−1.19281
$555$	0	0
$556$	−6.63153	−0.281240
$557$	−37.6742	−1.59631	−0.798154	−	0.602454i	$-0.794190\pi$
$557$	−37.6742	−1.59631	−0.798154	+	0.602454i	$0.794190\pi$
$558$	−13.7845	−0.583543
$559$	14.9430	0.632021
$560$	0	0
$561$	61.6831	2.60426
$562$	15.7429	0.664076
$563$	8.06376	0.339847	0.169923	−	0.985457i	$-0.445648\pi$
$563$	8.06376	0.339847	0.169923	+	0.985457i	$0.445648\pi$
$564$	−1.24831	−0.0525632
$565$	0	0
$566$	9.08427	0.381840
$567$	27.1706	1.14106
$568$	7.42314	0.311468
$569$	11.4030	0.478039	0.239020	−	0.971015i	$-0.423174\pi$
$569$	11.4030	0.478039	0.239020	+	0.971015i	$0.423174\pi$
$570$	0	0
$571$	20.3683	0.852386	0.426193	−	0.904632i	$-0.359854\pi$
$571$	20.3683	0.852386	0.426193	+	0.904632i	$0.359854\pi$
$572$	−9.97312	−0.416997
$573$	16.0147	0.669022
$574$	−38.4206	−1.60365
$575$	0	0
$576$	6.94157	0.289232
$577$	10.7377	0.447018	0.223509	−	0.974702i	$-0.428249\pi$
$577$	10.7377	0.447018	0.223509	+	0.974702i	$0.428249\pi$
$578$	24.0320	0.999597
$579$	35.6267	1.48059
$580$	0	0
$581$	37.2047	1.54351
$582$	−35.4549	−1.46965
$583$	7.69021	0.318496
$584$	5.12433	0.212046
$585$	0	0
$586$	−9.78026	−0.404019
$587$	−9.24052	−0.381397	−0.190699	−	0.981649i	$-0.561075\pi$
$587$	−9.24052	−0.381397	−0.190699	+	0.981649i	$0.561075\pi$
$588$	−0.938518	−0.0387038
$589$	−15.8019	−0.651106
$590$	0	0
$591$	−24.3650	−1.00224
$592$	48.5730	1.99634
$593$	11.7426	0.482209	0.241105	−	0.970499i	$-0.422490\pi$
$593$	11.7426	0.482209	0.241105	+	0.970499i	$0.422490\pi$
$594$	−6.50630	−0.266957
$595$	0	0
$596$	−10.3272	−0.423020
$597$	−6.88831	−0.281920
$598$	4.30108	0.175884
$599$	3.12494	0.127682	0.0638408	−	0.997960i	$-0.479665\pi$
$599$	3.12494	0.127682	0.0638408	+	0.997960i	$0.479665\pi$
$600$	0	0
$601$	37.4918	1.52932	0.764661	−	0.644432i	$-0.222906\pi$
$601$	37.4918	1.52932	0.764661	+	0.644432i	$0.222906\pi$
$602$	−26.0070	−1.05997
$603$	28.2622	1.15093
$604$	10.4564	0.425464
$605$	0	0
$606$	−32.9632	−1.33904
$607$	−0.298520	−0.0121165	−0.00605827	−	0.999982i	$-0.501928\pi$
$607$	−0.298520	−0.0121165	−0.00605827	+	0.999982i	$0.501928\pi$
$608$	−22.1930	−0.900046
$609$	59.2938	2.40271
$610$	0	0
$611$	1.69904	0.0687356
$612$	12.0846	0.488490
$613$	−19.2758	−0.778544	−0.389272	−	0.921123i	$-0.627273\pi$
$613$	−19.2758	−0.778544	−0.389272	+	0.921123i	$0.627273\pi$
$614$	55.7694	2.25067
$615$	0	0
$616$	−25.2179	−1.01606
$617$	−3.25419	−0.131009	−0.0655044	−	0.997852i	$-0.520866\pi$
$617$	−3.25419	−0.131009	−0.0655044	+	0.997852i	$0.520866\pi$
$618$	−3.70993	−0.149235
$619$	−10.2635	−0.412523	−0.206262	−	0.978497i	$-0.566130\pi$
$619$	−10.2635	−0.412523	−0.206262	+	0.978497i	$0.566130\pi$
$620$	0	0
$621$	0.812644	0.0326103
$622$	−47.5974	−1.90848
$623$	−24.2630	−0.972075
$624$	31.1275	1.24610
$625$	0	0
$626$	−22.5288	−0.900430
$627$	56.1399	2.24201
$628$	−1.86757	−0.0745240
$629$	−54.7425	−2.18273
$630$	0	0
$631$	20.7678	0.826755	0.413377	−	0.910560i	$-0.364349\pi$
$631$	20.7678	0.826755	0.413377	+	0.910560i	$0.364349\pi$
$632$	−4.26405	−0.169615
$633$	2.77681	0.110368
$634$	19.7693	0.785140
$635$	0	0
$636$	3.21340	0.127420
$637$	1.27739	0.0506121
$638$	−70.9628	−2.80944
$639$	−9.88973	−0.391232
$640$	0	0
$641$	0.740143	0.0292339	0.0146170	−	0.999893i	$-0.495347\pi$
$641$	0.740143	0.0292339	0.0146170	+	0.999893i	$0.495347\pi$
$642$	13.4835	0.532153
$643$	−9.79184	−0.386152	−0.193076	−	0.981184i	$-0.561846\pi$
$643$	−9.79184	−0.386152	−0.193076	+	0.981184i	$0.561846\pi$
$644$	−2.16796	−0.0854294
$645$	0	0
$646$	47.8333	1.88198
$647$	−29.7122	−1.16811	−0.584053	−	0.811716i	$-0.698534\pi$
$647$	−29.7122	−1.16811	−0.584053	+	0.811716i	$0.698534\pi$
$648$	19.7412	0.775507
$649$	−4.63749	−0.182038
$650$	0	0
$651$	−20.1700	−0.790525
$652$	−8.42585	−0.329982
$653$	−3.44040	−0.134633	−0.0673167	−	0.997732i	$-0.521444\pi$
$653$	−3.44040	−0.134633	−0.0673167	+	0.997732i	$0.521444\pi$
$654$	−79.7272	−3.11758
$655$	0	0
$656$	−41.5642	−1.62281
$657$	−6.82706	−0.266349
$658$	−2.95703	−0.115277
$659$	−24.4162	−0.951120	−0.475560	−	0.879683i	$-0.657754\pi$
$659$	−24.4162	−0.951120	−0.475560	+	0.879683i	$0.657754\pi$
$660$	0	0
$661$	−0.839085	−0.0326366	−0.0163183	−	0.999867i	$-0.505195\pi$
$661$	−0.839085	−0.0326366	−0.0163183	+	0.999867i	$0.505195\pi$
$662$	13.5501	0.526641
$663$	−35.0812	−1.36244
$664$	27.0315	1.04903
$665$	0	0
$666$	−43.4621	−1.68412
$667$	8.86334	0.343190
$668$	3.87881	0.150076
$669$	−50.5506	−1.95440
$670$	0	0
$671$	−8.93119	−0.344785
$672$	−28.3278	−1.09277
$673$	−22.6306	−0.872347	−0.436174	−	0.899863i	$-0.643667\pi$
$673$	−22.6306	−0.872347	−0.436174	+	0.899863i	$0.643667\pi$
$674$	−48.5604	−1.87048
$675$	0	0
$676$	−4.92780	−0.189531
$677$	−44.5659	−1.71281	−0.856404	−	0.516306i	$-0.827307\pi$
$677$	−44.5659	−1.71281	−0.856404	+	0.516306i	$0.827307\pi$
$678$	3.86264	0.148344
$679$	−24.3237	−0.933459
$680$	0	0
$681$	−31.0802	−1.19099
$682$	24.1394	0.924347
$683$	−16.3169	−0.624349	−0.312175	−	0.950025i	$-0.601057\pi$
$683$	−16.3169	−0.624349	−0.312175	+	0.950025i	$0.601057\pi$
$684$	10.9986	0.420541
$685$	0	0
$686$	29.9091	1.14194
$687$	7.18066	0.273959
$688$	−28.1349	−1.07263
$689$	−4.37367	−0.166624
$690$	0	0
$691$	−48.7032	−1.85276	−0.926379	−	0.376593i	$-0.877096\pi$
$691$	−48.7032	−1.85276	−0.926379	+	0.376593i	$0.877096\pi$
$692$	9.22719	0.350765
$693$	33.5974	1.27626
$694$	−25.0405	−0.950524
$695$	0	0
$696$	43.0807	1.63297
$697$	46.8434	1.77432
$698$	47.7760	1.80835
$699$	−6.75116	−0.255352
$700$	0	0
$701$	−14.1855	−0.535780	−0.267890	−	0.963449i	$-0.586326\pi$
$701$	−14.1855	−0.535780	−0.267890	+	0.963449i	$0.586326\pi$
$702$	3.70034	0.139660
$703$	−49.8230	−1.87911
$704$	−12.1561	−0.458151
$705$	0	0
$706$	−9.15944	−0.344720
$707$	−22.6143	−0.850499
$708$	−1.93780	−0.0728272
$709$	44.2873	1.66324	0.831622	−	0.555342i	$-0.187413\pi$
$709$	44.2873	1.66324	0.831622	+	0.555342i	$0.187413\pi$
$710$	0	0
$711$	5.68092	0.213051
$712$	−17.6286	−0.660659
$713$	−3.01504	−0.112914
$714$	61.0558	2.28496
$715$	0	0
$716$	12.3304	0.460809
$717$	−44.7944	−1.67288
$718$	−37.4879	−1.39903
$719$	−32.6473	−1.21754	−0.608770	−	0.793347i	$-0.708337\pi$
$719$	−32.6473	−1.21754	−0.608770	+	0.793347i	$0.708337\pi$
$720$	0	0
$721$	−2.54519	−0.0947877
$722$	11.6545	0.433735
$723$	53.5729	1.99240
$724$	11.8716	0.441204
$725$	0	0
$726$	−41.8961	−1.55491
$727$	28.0563	1.04055	0.520276	−	0.853998i	$-0.325829\pi$
$727$	28.0563	1.04055	0.520276	+	0.853998i	$0.325829\pi$
$728$	14.3423	0.531559
$729$	−20.3393	−0.753308
$730$	0	0
$731$	31.7084	1.17278
$732$	−3.73195	−0.137937
$733$	−20.1894	−0.745711	−0.372855	−	0.927889i	$-0.621621\pi$
$733$	−20.1894	−0.745711	−0.372855	+	0.927889i	$0.621621\pi$
$734$	−26.4817	−0.977457
$735$	0	0
$736$	−4.23449	−0.156085
$737$	−49.4930	−1.82310
$738$	37.1907	1.36901
$739$	−12.3300	−0.453567	−0.226784	−	0.973945i	$-0.572821\pi$
$739$	−12.3300	−0.453567	−0.226784	+	0.973945i	$0.572821\pi$
$740$	0	0
$741$	−31.9286	−1.17293
$742$	7.61200	0.279445
$743$	−26.4462	−0.970216	−0.485108	−	0.874454i	$-0.661220\pi$
$743$	−26.4462	−0.970216	−0.485108	+	0.874454i	$0.661220\pi$
$744$	−14.6548	−0.537270
$745$	0	0
$746$	27.1100	0.992567
$747$	−36.0137	−1.31767
$748$	−21.1626	−0.773780
$749$	9.25035	0.338001
$750$	0	0
$751$	−3.38998	−0.123702	−0.0618511	−	0.998085i	$-0.519700\pi$
$751$	−3.38998	−0.123702	−0.0618511	+	0.998085i	$0.519700\pi$
$752$	−3.19897	−0.116654
$753$	23.7724	0.866316
$754$	40.3588	1.46978
$755$	0	0
$756$	−1.86515	−0.0678350
$757$	9.70230	0.352636	0.176318	−	0.984333i	$-0.443581\pi$
$757$	9.70230	0.352636	0.176318	+	0.984333i	$0.443581\pi$
$758$	59.0785	2.14583
$759$	10.7116	0.388807
$760$	0	0
$761$	29.0592	1.05339	0.526697	−	0.850053i	$-0.323430\pi$
$761$	29.0592	1.05339	0.526697	+	0.850053i	$0.323430\pi$
$762$	−49.9462	−1.80936
$763$	−54.6967	−1.98015
$764$	−5.49440	−0.198780
$765$	0	0
$766$	−32.4360	−1.17196
$767$	2.63749	0.0952344
$768$	−39.8279	−1.43716
$769$	−2.83160	−0.102110	−0.0510550	−	0.998696i	$-0.516258\pi$
$769$	−2.83160	−0.102110	−0.0510550	+	0.998696i	$0.516258\pi$
$770$	0	0
$771$	2.30862	0.0831431
$772$	−12.2230	−0.439915
$773$	44.8970	1.61483	0.807417	−	0.589981i	$-0.200865\pi$
$773$	44.8970	1.61483	0.807417	+	0.589981i	$0.200865\pi$
$774$	25.1745	0.904878
$775$	0	0
$776$	−17.6727	−0.634414
$777$	−63.5955	−2.28147
$778$	25.4809	0.913534
$779$	42.6338	1.52751
$780$	0	0
$781$	17.3189	0.619720
$782$	9.12672	0.326371
$783$	7.62538	0.272509
$784$	−2.40509	−0.0858962
$785$	0	0
$786$	45.0968	1.60855
$787$	−37.2282	−1.32704	−0.663522	−	0.748157i	$-0.730939\pi$
$787$	−37.2282	−1.32704	−0.663522	+	0.748157i	$0.730939\pi$
$788$	8.35926	0.297786
$789$	−30.0788	−1.07083
$790$	0	0
$791$	2.64996	0.0942216
$792$	24.4107	0.867395
$793$	5.07946	0.180377
$794$	45.4738	1.61381
$795$	0	0
$796$	2.36328	0.0837641
$797$	52.7211	1.86748	0.933739	−	0.357954i	$-0.116525\pi$
$797$	52.7211	1.86748	0.933739	+	0.357954i	$0.116525\pi$
$798$	55.5689	1.96712
$799$	3.60529	0.127546
$800$	0	0
$801$	23.4863	0.829847
$802$	6.60465	0.233218
$803$	11.9556	0.421903
$804$	−20.6809	−0.729360
$805$	0	0
$806$	−13.7289	−0.483579
$807$	41.6562	1.46637
$808$	−16.4307	−0.578031
$809$	−48.9659	−1.72155	−0.860775	−	0.508985i	$-0.830021\pi$
$809$	−48.9659	−1.72155	−0.860775	+	0.508985i	$0.830021\pi$
$810$	0	0
$811$	−37.5215	−1.31756	−0.658778	−	0.752337i	$-0.728926\pi$
$811$	−37.5215	−1.31756	−0.658778	+	0.752337i	$0.728926\pi$
$812$	−20.3428	−0.713893
$813$	31.8745	1.11789
$814$	76.1110	2.66769
$815$	0	0
$816$	66.0514	2.31226
$817$	28.8589	1.00965
$818$	−27.9747	−0.978111
$819$	−19.1080	−0.667686
$820$	0	0
$821$	−52.8967	−1.84611	−0.923054	−	0.384670i	$-0.874315\pi$
$821$	−52.8967	−1.84611	−0.923054	+	0.384670i	$0.874315\pi$
$822$	−45.6657	−1.59278
$823$	−0.816933	−0.0284765	−0.0142382	−	0.999899i	$-0.504532\pi$
$823$	−0.816933	−0.0284765	−0.0142382	+	0.999899i	$0.504532\pi$
$824$	−1.84924	−0.0644213
$825$	0	0
$826$	−4.59033	−0.159718
$827$	48.7014	1.69351	0.846757	−	0.531980i	$-0.178552\pi$
$827$	48.7014	1.69351	0.846757	+	0.531980i	$0.178552\pi$
$828$	2.09856	0.0729299
$829$	26.4106	0.917278	0.458639	−	0.888623i	$-0.348337\pi$
$829$	26.4106	0.917278	0.458639	+	0.888623i	$0.348337\pi$
$830$	0	0
$831$	39.7661	1.37947
$832$	6.91358	0.239685
$833$	2.71057	0.0939159
$834$	32.4325	1.12304
$835$	0	0
$836$	−19.2608	−0.666147
$837$	−2.59393	−0.0896593
$838$	48.1141	1.66207
$839$	−27.1270	−0.936527	−0.468263	−	0.883589i	$-0.655120\pi$
$839$	−27.1270	−0.936527	−0.468263	+	0.883589i	$0.655120\pi$
$840$	0	0
$841$	54.1684	1.86788
$842$	60.2718	2.07710
$843$	−22.2983	−0.767995
$844$	−0.952682	−0.0327927
$845$	0	0
$846$	2.86237	0.0984102
$847$	−28.7427	−0.987612
$848$	8.23482	0.282785
$849$	−12.8670	−0.441593
$850$	0	0
$851$	−9.50635	−0.325874
$852$	7.23682	0.247929
$853$	−9.27134	−0.317445	−0.158722	−	0.987323i	$-0.550737\pi$
$853$	−9.27134	−0.317445	−0.158722	+	0.987323i	$0.550737\pi$
$854$	−8.84036	−0.302511
$855$	0	0
$856$	6.72097	0.229718
$857$	−8.37114	−0.285953	−0.142976	−	0.989726i	$-0.545667\pi$
$857$	−8.37114	−0.285953	−0.142976	+	0.989726i	$0.545667\pi$
$858$	48.7750	1.66515
$859$	−12.2897	−0.419320	−0.209660	−	0.977774i	$-0.567236\pi$
$859$	−12.2897	−0.419320	−0.209660	+	0.977774i	$0.567236\pi$
$860$	0	0
$861$	54.4190	1.85459
$862$	27.7487	0.945126
$863$	−18.3251	−0.623795	−0.311898	−	0.950116i	$-0.600965\pi$
$863$	−18.3251	−0.623795	−0.311898	+	0.950116i	$0.600965\pi$
$864$	−3.64305	−0.123939
$865$	0	0
$866$	−4.37019	−0.148505
$867$	−34.0389	−1.15602
$868$	6.92003	0.234881
$869$	−9.94846	−0.337478
$870$	0	0
$871$	28.1483	0.953768
$872$	−39.7406	−1.34579
$873$	23.5451	0.796880
$874$	8.30654	0.280973
$875$	0	0
$876$	4.99571	0.168790
$877$	−43.6238	−1.47307	−0.736536	−	0.676398i	$-0.763540\pi$
$877$	−43.6238	−1.47307	−0.736536	+	0.676398i	$0.763540\pi$
$878$	−15.0002	−0.506232
$879$	13.8528	0.467242
$880$	0	0
$881$	47.1731	1.58930	0.794651	−	0.607066i	$-0.207654\pi$
$881$	47.1731	1.58930	0.794651	+	0.607066i	$0.207654\pi$
$882$	2.15202	0.0724624
$883$	−35.5777	−1.19728	−0.598642	−	0.801017i	$-0.704293\pi$
$883$	−35.5777	−1.19728	−0.598642	+	0.801017i	$0.704293\pi$
$884$	12.0358	0.404809
$885$	0	0
$886$	8.57893	0.288215
$887$	−32.7437	−1.09942	−0.549712	−	0.835354i	$-0.685263\pi$
$887$	−32.7437	−1.09942	−0.549712	+	0.835354i	$0.685263\pi$
$888$	−46.2061	−1.55058
$889$	−34.2655	−1.14923
$890$	0	0
$891$	46.0582	1.54301
$892$	17.3432	0.580692
$893$	3.28129	0.109804
$894$	50.5068	1.68920
$895$	0	0
$896$	−35.8715	−1.19838
$897$	−6.09205	−0.203408
$898$	−2.50146	−0.0834749
$899$	−28.2914	−0.943572
$900$	0	0
$901$	−9.28076	−0.309187
$902$	−65.1286	−2.16854
$903$	36.8363	1.22584
$904$	1.92536	0.0640366
$905$	0	0
$906$	−51.1384	−1.69896
$907$	−31.7177	−1.05317	−0.526585	−	0.850122i	$-0.676528\pi$
$907$	−31.7177	−1.05317	−0.526585	+	0.850122i	$0.676528\pi$
$908$	10.6631	0.353869
$909$	21.8904	0.726059
$910$	0	0
$911$	−16.4378	−0.544610	−0.272305	−	0.962211i	$-0.587786\pi$
$911$	−16.4378	−0.544610	−0.272305	+	0.962211i	$0.587786\pi$
$912$	60.1156	1.99063
$913$	63.0673	2.08722
$914$	43.9340	1.45321
$915$	0	0
$916$	−2.46358	−0.0813990
$917$	30.9386	1.02168
$918$	7.85198	0.259154
$919$	12.1542	0.400931	0.200465	−	0.979701i	$-0.435755\pi$
$919$	12.1542	0.400931	0.200465	+	0.979701i	$0.435755\pi$
$920$	0	0
$921$	−78.9918	−2.60287
$922$	55.9042	1.84111
$923$	−9.84985	−0.324212
$924$	−24.5850	−0.808786
$925$	0	0
$926$	7.65112	0.251432
$927$	2.46371	0.0809189
$928$	−39.7340	−1.30433
$929$	−7.94177	−0.260561	−0.130280	−	0.991477i	$-0.541588\pi$
$929$	−7.94177	−0.260561	−0.130280	+	0.991477i	$0.541588\pi$
$930$	0	0
$931$	2.46699	0.0808522
$932$	2.31622	0.0758704
$933$	67.4170	2.20713
$934$	16.7412	0.547788
$935$	0	0
$936$	−13.8831	−0.453785
$937$	−38.0835	−1.24413	−0.622067	−	0.782964i	$-0.713707\pi$
$937$	−38.0835	−1.24413	−0.622067	+	0.782964i	$0.713707\pi$
$938$	−48.9896	−1.59957
$939$	31.9097	1.04133
$940$	0	0
$941$	−17.0666	−0.556355	−0.278178	−	0.960530i	$-0.589730\pi$
$941$	−17.0666	−0.556355	−0.278178	+	0.960530i	$0.589730\pi$
$942$	9.13360	0.297589
$943$	8.13464	0.264900
$944$	−4.96591	−0.161627
$945$	0	0
$946$	−44.0857	−1.43335
$947$	14.0376	0.456161	0.228081	−	0.973642i	$-0.426755\pi$
$947$	14.0376	0.456161	0.228081	+	0.973642i	$0.426755\pi$
$948$	−4.15702	−0.135014
$949$	−6.79953	−0.220722
$950$	0	0
$951$	−28.0013	−0.908004
$952$	30.4337	0.986362
$953$	−7.22577	−0.234066	−0.117033	−	0.993128i	$-0.537338\pi$
$953$	−7.22577	−0.234066	−0.117033	+	0.993128i	$0.537338\pi$
$954$	−7.36833	−0.238559
$955$	0	0
$956$	15.3683	0.497046
$957$	100.512	3.24908
$958$	3.39294	0.109621
$959$	−31.3289	−1.01166
$960$	0	0
$961$	−21.3761	−0.689551
$962$	−43.2868	−1.39562
$963$	−8.95424	−0.288546
$964$	−18.3801	−0.591983
$965$	0	0
$966$	10.6027	0.341136
$967$	−33.7845	−1.08644	−0.543219	−	0.839591i	$-0.682795\pi$
$967$	−33.7845	−1.08644	−0.543219	+	0.839591i	$0.682795\pi$
$968$	−20.8834	−0.671219
$969$	−67.7512	−2.17648
$970$	0	0
$971$	−7.22399	−0.231829	−0.115914	−	0.993259i	$-0.536980\pi$
$971$	−7.22399	−0.231829	−0.115914	+	0.993259i	$0.536980\pi$
$972$	17.2004	0.551702
$973$	22.2502	0.713309
$974$	49.9863	1.60167
$975$	0	0
$976$	−9.56368	−0.306126
$977$	−4.15890	−0.133055	−0.0665275	−	0.997785i	$-0.521192\pi$
$977$	−4.15890	−0.133055	−0.0665275	+	0.997785i	$0.521192\pi$
$978$	41.2078	1.31768
$979$	−41.1293	−1.31450
$980$	0	0
$981$	52.9458	1.69043
$982$	−28.9513	−0.923873
$983$	42.6101	1.35905	0.679525	−	0.733652i	$-0.262186\pi$
$983$	42.6101	1.35905	0.679525	+	0.733652i	$0.262186\pi$
$984$	39.5388	1.26045
$985$	0	0
$986$	85.6398	2.72733
$987$	4.18833	0.133316
$988$	10.9542	0.348500
$989$	5.50635	0.175092
$990$	0	0
$991$	20.9162	0.664424	0.332212	−	0.943205i	$-0.392205\pi$
$991$	20.9162	0.664424	0.332212	+	0.943205i	$0.392205\pi$
$992$	13.5163	0.429143
$993$	−19.1924	−0.609054
$994$	17.1428	0.543737
$995$	0	0
$996$	26.3531	0.835029
$997$	−19.5524	−0.619231	−0.309616	−	0.950862i	$-0.600200\pi$
$997$	−19.5524	−0.619231	−0.309616	+	0.950862i	$0.600200\pi$
$998$	67.0132	2.12127
$999$	−8.17859	−0.258759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1475.2.a.i.1.4		5
5.2	odd	4		1475.2.b.e.1299.8		10
5.3	odd	4		1475.2.b.e.1299.3		10
5.4	even	2		59.2.a.a.1.2	✓	5
15.14	odd	2		531.2.a.f.1.4		5
20.19	odd	2		944.2.a.n.1.1		5
35.34	odd	2		2891.2.a.f.1.2		5
40.19	odd	2		3776.2.a.bl.1.5		5
40.29	even	2		3776.2.a.bn.1.1		5
55.54	odd	2		7139.2.a.k.1.4		5
60.59	even	2		8496.2.a.bv.1.4		5
65.64	even	2		9971.2.a.d.1.4		5
295.294	odd	2		3481.2.a.d.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.2.a.a.1.2	✓	5	5.4	even	2
531.2.a.f.1.4		5	15.14	odd	2
944.2.a.n.1.1		5	20.19	odd	2
1475.2.a.i.1.4		5	1.1	even	1	trivial
1475.2.b.e.1299.3		10	5.3	odd	4
1475.2.b.e.1299.8		10	5.2	odd	4
2891.2.a.f.1.2		5	35.34	odd	2
3481.2.a.d.1.4		5	295.294	odd	2
3776.2.a.bl.1.5		5	40.19	odd	2
3776.2.a.bn.1.1		5	40.29	even	2
7139.2.a.k.1.4		5	55.54	odd	2
8496.2.a.bv.1.4		5	60.59	even	2
9971.2.a.d.1.4		5	65.64	even	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:	\( N \)	\(=\)	\( 1475 = 5^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1475.a (trivial)

\(f(q)\)	\(=\)	\(q+1.67791 q^{2} -2.37659 q^{3} +0.815372 q^{4} -3.98770 q^{6} -2.73575 q^{7} -1.98770 q^{8} +2.64817 q^{9} +O(q^{10})\)	\(q+1.67791 q^{2} -2.37659 q^{3} +0.815372 q^{4} -3.98770 q^{6} -2.73575 q^{7} -1.98770 q^{8} +2.64817 q^{9} -4.63749 q^{11} -1.93780 q^{12} +2.63749 q^{13} -4.59033 q^{14} -4.96591 q^{16} +5.59666 q^{17} +4.44339 q^{18} +5.09371 q^{19} +6.50175 q^{21} -7.78129 q^{22} +0.971892 q^{23} +4.72393 q^{24} +4.42547 q^{26} +0.836147 q^{27} -2.23065 q^{28} +9.11967 q^{29} -3.10224 q^{31} -4.35695 q^{32} +11.0214 q^{33} +9.39067 q^{34} +2.15925 q^{36} -9.78129 q^{37} +8.54677 q^{38} -6.26824 q^{39} +8.36990 q^{41} +10.9093 q^{42} +5.66560 q^{43} -3.78129 q^{44} +1.63074 q^{46} +0.644186 q^{47} +11.8019 q^{48} +0.484320 q^{49} -13.3010 q^{51} +2.15054 q^{52} -1.65827 q^{53} +1.40298 q^{54} +5.43783 q^{56} -12.1056 q^{57} +15.3020 q^{58} +1.00000 q^{59} +1.92587 q^{61} -5.20527 q^{62} -7.24474 q^{63} +2.62127 q^{64} +18.4929 q^{66} +10.6724 q^{67} +4.56336 q^{68} -2.30979 q^{69} -3.73455 q^{71} -5.26376 q^{72} -2.57803 q^{73} -16.4121 q^{74} +4.15327 q^{76} +12.6870 q^{77} -10.5175 q^{78} +2.14522 q^{79} -9.93170 q^{81} +14.0439 q^{82} -13.5994 q^{83} +5.30135 q^{84} +9.50635 q^{86} -21.6737 q^{87} +9.21792 q^{88} +8.86886 q^{89} -7.21552 q^{91} +0.792454 q^{92} +7.37275 q^{93} +1.08088 q^{94} +10.3547 q^{96} +8.89107 q^{97} +0.812644 q^{98} -12.2809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{3} + 8 q^{4} - 4 q^{6} - 2 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 2 * q^3 + 8 * q^4 - 4 * q^6 - 2 * q^7 + 6 * q^8 + 5 * q^9	\( 5 q + 2 q^{3} + 8 q^{4} - 4 q^{6} - 2 q^{7} + 6 q^{8} + 5 q^{9} - 2 q^{11} + 22 q^{12} - 8 q^{13} - 18 q^{14} + 10 q^{16} + q^{17} + 2 q^{18} + 6 q^{19} + 15 q^{21} - 8 q^{22} + 8 q^{23} + 6 q^{24} + 8 q^{26} + 11 q^{27} + 2 q^{28} + 14 q^{29} + 2 q^{32} + 14 q^{33} - 2 q^{34} + 42 q^{36} - 18 q^{37} - 18 q^{39} - 10 q^{41} - 34 q^{42} + 4 q^{43} + 12 q^{44} + 16 q^{46} + 20 q^{47} + 54 q^{48} + q^{49} - 12 q^{51} - 28 q^{52} + 10 q^{53} - 26 q^{54} - 38 q^{56} + 3 q^{57} + 38 q^{58} + 5 q^{59} + 22 q^{61} - 48 q^{62} + 12 q^{63} + 18 q^{64} + 28 q^{66} + 14 q^{68} - 4 q^{69} + 3 q^{71} - 28 q^{72} + 8 q^{73} + 8 q^{74} + 14 q^{76} - 2 q^{77} - 20 q^{78} + 10 q^{79} - 3 q^{81} + 48 q^{82} - 6 q^{83} + 28 q^{84} - 8 q^{86} - 11 q^{87} + 24 q^{88} + 10 q^{89} + 6 q^{91} - 4 q^{92} - 6 q^{93} - 36 q^{94} + 42 q^{96} + 22 q^{97} - 24 q^{98} - 4 q^{99}+O(q^{100}) \) 5 * q + 2 * q^3 + 8 * q^4 - 4 * q^6 - 2 * q^7 + 6 * q^8 + 5 * q^9 - 2 * q^11 + 22 * q^12 - 8 * q^13 - 18 * q^14 + 10 * q^16 + q^17 + 2 * q^18 + 6 * q^19 + 15 * q^21 - 8 * q^22 + 8 * q^23 + 6 * q^24 + 8 * q^26 + 11 * q^27 + 2 * q^28 + 14 * q^29 + 2 * q^32 + 14 * q^33 - 2 * q^34 + 42 * q^36 - 18 * q^37 - 18 * q^39 - 10 * q^41 - 34 * q^42 + 4 * q^43 + 12 * q^44 + 16 * q^46 + 20 * q^47 + 54 * q^48 + q^49 - 12 * q^51 - 28 * q^52 + 10 * q^53 - 26 * q^54 - 38 * q^56 + 3 * q^57 + 38 * q^58 + 5 * q^59 + 22 * q^61 - 48 * q^62 + 12 * q^63 + 18 * q^64 + 28 * q^66 + 14 * q^68 - 4 * q^69 + 3 * q^71 - 28 * q^72 + 8 * q^73 + 8 * q^74 + 14 * q^76 - 2 * q^77 - 20 * q^78 + 10 * q^79 - 3 * q^81 + 48 * q^82 - 6 * q^83 + 28 * q^84 - 8 * q^86 - 11 * q^87 + 24 * q^88 + 10 * q^89 + 6 * q^91 - 4 * q^92 - 6 * q^93 - 36 * q^94 + 42 * q^96 + 22 * q^97 - 24 * q^98 - 4 * q^99

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