LMFDB - Embedded newform 1875.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.46840000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 8x^{3} + 31x^{2} - 15x - 9 $ x^6 - x^5 - 11x^4 + 8x^3 + 31x^2 - 15x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.02791$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02791 q^{2} -1.00000 q^{3} +2.11242 q^{4} +2.02791 q^{6} +0.505614 q^{7} -0.227977 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.02791 q^{2} -1.00000 q^{3} +2.11242 q^{4} +2.02791 q^{6} +0.505614 q^{7} -0.227977 q^{8} +1.00000 q^{9} +0.687513 q^{11} -2.11242 q^{12} -5.78627 q^{13} -1.02534 q^{14} -3.76252 q^{16} -4.74333 q^{17} -2.02791 q^{18} +4.23709 q^{19} -0.505614 q^{21} -1.39422 q^{22} +8.36239 q^{23} +0.227977 q^{24} +11.7340 q^{26} -1.00000 q^{27} +1.06807 q^{28} +4.88758 q^{29} +2.68853 q^{31} +8.08601 q^{32} -0.687513 q^{33} +9.61905 q^{34} +2.11242 q^{36} -11.3806 q^{37} -8.59244 q^{38} +5.78627 q^{39} +0.144247 q^{41} +1.02534 q^{42} +5.94442 q^{43} +1.45232 q^{44} -16.9582 q^{46} -6.10650 q^{47} +3.76252 q^{48} -6.74435 q^{49} +4.74333 q^{51} -12.2230 q^{52} +10.8398 q^{53} +2.02791 q^{54} -0.115269 q^{56} -4.23709 q^{57} -9.91157 q^{58} -6.96817 q^{59} -3.98042 q^{61} -5.45211 q^{62} +0.505614 q^{63} -8.87266 q^{64} +1.39422 q^{66} -1.31351 q^{67} -10.0199 q^{68} -8.36239 q^{69} -3.79321 q^{71} -0.227977 q^{72} -10.9252 q^{73} +23.0787 q^{74} +8.95051 q^{76} +0.347616 q^{77} -11.7340 q^{78} -1.89869 q^{79} +1.00000 q^{81} -0.292519 q^{82} +2.51849 q^{83} -1.06807 q^{84} -12.0548 q^{86} -4.88758 q^{87} -0.156737 q^{88} +15.0809 q^{89} -2.92562 q^{91} +17.6649 q^{92} -2.68853 q^{93} +12.3834 q^{94} -8.08601 q^{96} +1.17394 q^{97} +13.6769 q^{98} +0.687513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9} - 11 q^{12} - 4 q^{14} + 17 q^{16} + 2 q^{17} + q^{18} - 2 q^{19} + 2 q^{21} + 9 q^{22} - q^{23} - 6 q^{24} + 37 q^{26} - 6 q^{27} - 44 q^{28} + 31 q^{29} - 2 q^{31} + 33 q^{32} + 37 q^{34} + 11 q^{36} - 22 q^{37} + 27 q^{38} + 33 q^{41} + 4 q^{42} - 3 q^{43} - 11 q^{44} - 12 q^{46} - 6 q^{47} - 17 q^{48} + 4 q^{49} - 2 q^{51} - 33 q^{52} + 14 q^{53} - q^{54} - 30 q^{56} + 2 q^{57} - q^{58} - 8 q^{59} + 34 q^{61} + 31 q^{62} - 2 q^{63} + 12 q^{64} - 9 q^{66} + 2 q^{67} + 27 q^{68} + q^{69} - 3 q^{71} + 6 q^{72} - 36 q^{73} + 36 q^{74} + 27 q^{76} + 16 q^{77} - 37 q^{78} + 25 q^{79} + 6 q^{81} + 36 q^{82} - 12 q^{83} + 44 q^{84} - 30 q^{86} - 31 q^{87} + 56 q^{88} + 18 q^{89} + 28 q^{91} + 3 q^{92} + 2 q^{93} - 50 q^{94} - 33 q^{96} + 7 q^{97} + 15 q^{98}+O(q^{100}) $ 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9 - 11 * q^12 - 4 * q^14 + 17 * q^16 + 2 * q^17 + q^18 - 2 * q^19 + 2 * q^21 + 9 * q^22 - q^23 - 6 * q^24 + 37 * q^26 - 6 * q^27 - 44 * q^28 + 31 * q^29 - 2 * q^31 + 33 * q^32 + 37 * q^34 + 11 * q^36 - 22 * q^37 + 27 * q^38 + 33 * q^41 + 4 * q^42 - 3 * q^43 - 11 * q^44 - 12 * q^46 - 6 * q^47 - 17 * q^48 + 4 * q^49 - 2 * q^51 - 33 * q^52 + 14 * q^53 - q^54 - 30 * q^56 + 2 * q^57 - q^58 - 8 * q^59 + 34 * q^61 + 31 * q^62 - 2 * q^63 + 12 * q^64 - 9 * q^66 + 2 * q^67 + 27 * q^68 + q^69 - 3 * q^71 + 6 * q^72 - 36 * q^73 + 36 * q^74 + 27 * q^76 + 16 * q^77 - 37 * q^78 + 25 * q^79 + 6 * q^81 + 36 * q^82 - 12 * q^83 + 44 * q^84 - 30 * q^86 - 31 * q^87 + 56 * q^88 + 18 * q^89 + 28 * q^91 + 3 * q^92 + 2 * q^93 - 50 * q^94 - 33 * q^96 + 7 * q^97 + 15 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.02791	−1.43395	−0.716975	−	0.697099i	$-0.754474\pi$
$2$	−2.02791	−1.43395	−0.716975	+	0.697099i	$0.754474\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.11242	1.05621
$5$	0	0
$5$	0	0
$6$	2.02791	0.827891
$7$	0.505614	0.191104	0.0955521	−	0.995424i	$-0.469538\pi$
$7$	0.505614	0.191104	0.0955521	+	0.995424i	$0.469538\pi$
$8$	−0.227977	−0.0806021
$9$	1.00000	0.333333
$10$	0	0
$11$	0.687513	0.207293	0.103647	−	0.994614i	$-0.466949\pi$
$11$	0.687513	0.207293	0.103647	+	0.994614i	$0.466949\pi$
$12$	−2.11242	−0.609803
$13$	−5.78627	−1.60482	−0.802412	−	0.596771i	$-0.796450\pi$
$13$	−5.78627	−1.60482	−0.802412	+	0.596771i	$0.796450\pi$
$14$	−1.02534	−0.274034
$15$	0	0
$16$	−3.76252	−0.940631
$17$	−4.74333	−1.15043	−0.575214	−	0.818003i	$-0.695081\pi$
$17$	−4.74333	−1.15043	−0.575214	+	0.818003i	$0.695081\pi$
$18$	−2.02791	−0.477983
$19$	4.23709	0.972055	0.486027	−	0.873944i	$-0.338446\pi$
$19$	4.23709	0.972055	0.486027	+	0.873944i	$0.338446\pi$
$20$	0	0
$21$	−0.505614	−0.110334
$22$	−1.39422	−0.297248
$23$	8.36239	1.74368	0.871839	−	0.489792i	$-0.162927\pi$
$23$	8.36239	1.74368	0.871839	+	0.489792i	$0.162927\pi$
$24$	0.227977	0.0465357
$25$	0	0
$26$	11.7340	2.30124
$27$	−1.00000	−0.192450
$28$	1.06807	0.201846
$29$	4.88758	0.907601	0.453800	−	0.891103i	$-0.350068\pi$
$29$	4.88758	0.907601	0.453800	+	0.891103i	$0.350068\pi$
$30$	0	0
$31$	2.68853	0.482875	0.241437	−	0.970416i	$-0.422381\pi$
$31$	2.68853	0.482875	0.241437	+	0.970416i	$0.422381\pi$
$32$	8.08601	1.42942
$33$	−0.687513	−0.119681
$34$	9.61905	1.64965
$35$	0	0
$36$	2.11242	0.352070
$37$	−11.3806	−1.87095	−0.935476	−	0.353390i	$-0.885029\pi$
$37$	−11.3806	−1.87095	−0.935476	+	0.353390i	$0.885029\pi$
$38$	−8.59244	−1.39388
$39$	5.78627	0.926545
$40$	0	0
$41$	0.144247	0.0225275	0.0112638	−	0.999937i	$-0.496415\pi$
$41$	0.144247	0.0225275	0.0112638	+	0.999937i	$0.496415\pi$
$42$	1.02534	0.158213
$43$	5.94442	0.906516	0.453258	−	0.891379i	$-0.350262\pi$
$43$	5.94442	0.906516	0.453258	+	0.891379i	$0.350262\pi$
$44$	1.45232	0.218945
$45$	0	0
$46$	−16.9582	−2.50035
$47$	−6.10650	−0.890725	−0.445362	−	0.895350i	$-0.646925\pi$
$47$	−6.10650	−0.890725	−0.445362	+	0.895350i	$0.646925\pi$
$48$	3.76252	0.543073
$49$	−6.74435	−0.963479
$50$	0	0
$51$	4.74333	0.664200
$52$	−12.2230	−1.69503
$53$	10.8398	1.48896	0.744481	−	0.667643i	$-0.232697\pi$
$53$	10.8398	1.48896	0.744481	+	0.667643i	$0.232697\pi$
$54$	2.02791	0.275964
$55$	0	0
$56$	−0.115269	−0.0154034
$57$	−4.23709	−0.561216
$58$	−9.91157	−1.30145
$59$	−6.96817	−0.907179	−0.453589	−	0.891211i	$-0.649857\pi$
$59$	−6.96817	−0.907179	−0.453589	+	0.891211i	$0.649857\pi$
$60$	0	0
$61$	−3.98042	−0.509641	−0.254820	−	0.966988i	$-0.582016\pi$
$61$	−3.98042	−0.509641	−0.254820	+	0.966988i	$0.582016\pi$
$62$	−5.45211	−0.692418
$63$	0.505614	0.0637014
$64$	−8.87266	−1.10908
$65$	0	0
$66$	1.39422	0.171616
$67$	−1.31351	−0.160470	−0.0802352	−	0.996776i	$-0.525567\pi$
$67$	−1.31351	−0.160470	−0.0802352	+	0.996776i	$0.525567\pi$
$68$	−10.0199	−1.21509
$69$	−8.36239	−1.00671
$70$	0	0
$71$	−3.79321	−0.450172	−0.225086	−	0.974339i	$-0.572266\pi$
$71$	−3.79321	−0.450172	−0.225086	+	0.974339i	$0.572266\pi$
$72$	−0.227977	−0.0268674
$73$	−10.9252	−1.27870	−0.639351	−	0.768915i	$-0.720797\pi$
$73$	−10.9252	−1.27870	−0.639351	+	0.768915i	$0.720797\pi$
$74$	23.0787	2.68285
$75$	0	0
$76$	8.95051	1.02669
$77$	0.347616	0.0396146
$78$	−11.7340	−1.32862
$79$	−1.89869	−0.213620	−0.106810	−	0.994279i	$-0.534064\pi$
$79$	−1.89869	−0.213620	−0.106810	+	0.994279i	$0.534064\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.292519	−0.0323033
$83$	2.51849	0.276441	0.138220	−	0.990402i	$-0.455862\pi$
$83$	2.51849	0.276441	0.138220	+	0.990402i	$0.455862\pi$
$84$	−1.06807	−0.116536
$85$	0	0
$86$	−12.0548	−1.29990
$87$	−4.88758	−0.524004
$88$	−0.156737	−0.0167083
$89$	15.0809	1.59858	0.799289	−	0.600947i	$-0.205210\pi$
$89$	15.0809	1.59858	0.799289	+	0.600947i	$0.205210\pi$
$90$	0	0
$91$	−2.92562	−0.306689
$92$	17.6649	1.84169
$93$	−2.68853	−0.278788
$94$	12.3834	1.27725
$95$	0	0
$96$	−8.08601	−0.825275
$97$	1.17394	0.119195	0.0595977	−	0.998222i	$-0.481018\pi$
$97$	1.17394	0.119195	0.0595977	+	0.998222i	$0.481018\pi$
$98$	13.6769	1.38158
$99$	0.687513	0.0690977
$100$	0	0
$101$	7.23262	0.719672	0.359836	−	0.933016i	$-0.382833\pi$
$101$	7.23262	0.719672	0.359836	+	0.933016i	$0.382833\pi$
$102$	−9.61905	−0.952428
$103$	18.4207	1.81505	0.907524	−	0.420000i	$-0.137970\pi$
$103$	18.4207	1.81505	0.907524	+	0.420000i	$0.137970\pi$
$104$	1.31914	0.129352
$105$	0	0
$106$	−21.9822	−2.13510
$107$	17.5572	1.69732	0.848661	−	0.528937i	$-0.177409\pi$
$107$	17.5572	1.69732	0.848661	+	0.528937i	$0.177409\pi$
$108$	−2.11242	−0.203268
$109$	11.4098	1.09286	0.546429	−	0.837506i	$-0.315987\pi$
$109$	11.4098	1.09286	0.546429	+	0.837506i	$0.315987\pi$
$110$	0	0
$111$	11.3806	1.08019
$112$	−1.90238	−0.179758
$113$	9.64827	0.907632	0.453816	−	0.891095i	$-0.350062\pi$
$113$	9.64827	0.907632	0.453816	+	0.891095i	$0.350062\pi$
$114$	8.59244	0.804755
$115$	0	0
$116$	10.3246	0.958617
$117$	−5.78627	−0.534941
$118$	14.1308	1.30085
$119$	−2.39830	−0.219852
$120$	0	0
$121$	−10.5273	−0.957030
$122$	8.07194	0.730799
$123$	−0.144247	−0.0130063
$124$	5.67931	0.510017
$125$	0	0
$126$	−1.02534	−0.0913446
$127$	4.32804	0.384051	0.192026	−	0.981390i	$-0.438494\pi$
$127$	4.32804	0.384051	0.192026	+	0.981390i	$0.438494\pi$
$128$	1.82094	0.160950
$129$	−5.94442	−0.523377
$130$	0	0
$131$	−10.1642	−0.888047	−0.444023	−	0.896015i	$-0.646449\pi$
$131$	−10.1642	−0.888047	−0.444023	+	0.896015i	$0.646449\pi$
$132$	−1.45232	−0.126408
$133$	2.14233	0.185764
$134$	2.66368	0.230106
$135$	0	0
$136$	1.08137	0.0927269
$137$	5.57509	0.476312	0.238156	−	0.971227i	$-0.423457\pi$
$137$	5.57509	0.476312	0.238156	+	0.971227i	$0.423457\pi$
$138$	16.9582	1.44358
$139$	9.24097	0.783809	0.391904	−	0.920006i	$-0.371816\pi$
$139$	9.24097	0.783809	0.391904	+	0.920006i	$0.371816\pi$
$140$	0	0
$141$	6.10650	0.514260
$142$	7.69230	0.645523
$143$	−3.97814	−0.332669
$144$	−3.76252	−0.313544
$145$	0	0
$146$	22.1554	1.83359
$147$	6.74435	0.556265
$148$	−24.0405	−1.97612
$149$	−9.91157	−0.811988	−0.405994	−	0.913876i	$-0.633075\pi$
$149$	−9.91157	−0.811988	−0.405994	+	0.913876i	$0.633075\pi$
$150$	0	0
$151$	−21.8846	−1.78094	−0.890471	−	0.455041i	$-0.849625\pi$
$151$	−21.8846	−1.78094	−0.890471	+	0.455041i	$0.849625\pi$
$152$	−0.965960	−0.0783497
$153$	−4.74333	−0.383476
$154$	−0.704935	−0.0568053
$155$	0	0
$156$	12.2230	0.978626
$157$	4.47331	0.357009	0.178504	−	0.983939i	$-0.442874\pi$
$157$	4.47331	0.357009	0.178504	+	0.983939i	$0.442874\pi$
$158$	3.85038	0.306320
$159$	−10.8398	−0.859653
$160$	0	0
$161$	4.22814	0.333224
$162$	−2.02791	−0.159328
$163$	14.2898	1.11927	0.559634	−	0.828740i	$-0.310942\pi$
$163$	14.2898	1.11927	0.559634	+	0.828740i	$0.310942\pi$
$164$	0.304709	0.0237938
$165$	0	0
$166$	−5.10728	−0.396402
$167$	−0.473306	−0.0366255	−0.0183128	−	0.999832i	$-0.505829\pi$
$167$	−0.473306	−0.0366255	−0.0183128	+	0.999832i	$0.505829\pi$
$168$	0.115269	0.00889316
$169$	20.4810	1.57546
$170$	0	0
$171$	4.23709	0.324018
$172$	12.5571	0.957471
$173$	2.14939	0.163415	0.0817074	−	0.996656i	$-0.473963\pi$
$173$	2.14939	0.163415	0.0817074	+	0.996656i	$0.473963\pi$
$174$	9.91157	0.751394
$175$	0	0
$176$	−2.58678	−0.194986
$177$	6.96817	0.523760
$178$	−30.5828	−2.29228
$179$	−1.35831	−0.101525	−0.0507623	−	0.998711i	$-0.516165\pi$
$179$	−1.35831	−0.101525	−0.0507623	+	0.998711i	$0.516165\pi$
$180$	0	0
$181$	3.37725	0.251029	0.125515	−	0.992092i	$-0.459942\pi$
$181$	3.37725	0.251029	0.125515	+	0.992092i	$0.459942\pi$
$182$	5.93290	0.439776
$183$	3.98042	0.294241
$184$	−1.90643	−0.140544
$185$	0	0
$186$	5.45211	0.399768
$187$	−3.26110	−0.238476
$188$	−12.8995	−0.940792
$189$	−0.505614	−0.0367780
$190$	0	0
$191$	21.8942	1.58421	0.792103	−	0.610388i	$-0.208986\pi$
$191$	21.8942	1.58421	0.792103	+	0.610388i	$0.208986\pi$
$192$	8.87266	0.640329
$193$	20.3890	1.46763	0.733817	−	0.679347i	$-0.237737\pi$
$193$	20.3890	1.46763	0.733817	+	0.679347i	$0.237737\pi$
$194$	−2.38064	−0.170920
$195$	0	0
$196$	−14.2469	−1.01764
$197$	24.9688	1.77895	0.889477	−	0.456980i	$-0.151069\pi$
$197$	24.9688	1.77895	0.889477	+	0.456980i	$0.151069\pi$
$198$	−1.39422	−0.0990826
$199$	−10.2138	−0.724038	−0.362019	−	0.932171i	$-0.617913\pi$
$199$	−10.2138	−0.724038	−0.362019	+	0.932171i	$0.617913\pi$
$200$	0	0
$201$	1.31351	0.0926477
$202$	−14.6671	−1.03197
$203$	2.47123	0.173446
$204$	10.0199	0.701534
$205$	0	0
$206$	−37.3556	−2.60269
$207$	8.36239	0.581226
$208$	21.7710	1.50955
$209$	2.91305	0.201500
$210$	0	0
$211$	5.46907	0.376507	0.188253	−	0.982121i	$-0.439717\pi$
$211$	5.46907	0.376507	0.188253	+	0.982121i	$0.439717\pi$
$212$	22.8982	1.57266
$213$	3.79321	0.259907
$214$	−35.6045	−2.43387
$215$	0	0
$216$	0.227977	0.0155119
$217$	1.35936	0.0922794
$218$	−23.1380	−1.56710
$219$	10.9252	0.738259
$220$	0	0
$221$	27.4462	1.84623
$222$	−23.0787	−1.54894
$223$	−22.8887	−1.53274	−0.766370	−	0.642399i	$-0.777939\pi$
$223$	−22.8887	−1.53274	−0.766370	+	0.642399i	$0.777939\pi$
$224$	4.08840	0.273168
$225$	0	0
$226$	−19.5658	−1.30150
$227$	12.9219	0.857659	0.428829	−	0.903386i	$-0.358926\pi$
$227$	12.9219	0.857659	0.428829	+	0.903386i	$0.358926\pi$
$228$	−8.95051	−0.592762
$229$	14.5252	0.959850	0.479925	−	0.877309i	$-0.340664\pi$
$229$	14.5252	0.959850	0.479925	+	0.877309i	$0.340664\pi$
$230$	0	0
$231$	−0.347616	−0.0228715
$232$	−1.11426	−0.0731545
$233$	9.94748	0.651681	0.325841	−	0.945425i	$-0.394353\pi$
$233$	9.94748	0.651681	0.325841	+	0.945425i	$0.394353\pi$
$234$	11.7340	0.767078
$235$	0	0
$236$	−14.7197	−0.958171
$237$	1.89869	0.123333
$238$	4.86353	0.315256
$239$	1.58509	0.102531	0.0512656	−	0.998685i	$-0.483674\pi$
$239$	1.58509	0.102531	0.0512656	+	0.998685i	$0.483674\pi$
$240$	0	0
$241$	23.7485	1.52978	0.764889	−	0.644163i	$-0.222794\pi$
$241$	23.7485	1.52978	0.764889	+	0.644163i	$0.222794\pi$
$242$	21.3485	1.37233
$243$	−1.00000	−0.0641500
$244$	−8.40832	−0.538288
$245$	0	0
$246$	0.292519	0.0186503
$247$	−24.5170	−1.55998
$248$	−0.612924	−0.0389207
$249$	−2.51849	−0.159603
$250$	0	0
$251$	20.2887	1.28061	0.640307	−	0.768119i	$-0.278807\pi$
$251$	20.2887	1.28061	0.640307	+	0.768119i	$0.278807\pi$
$252$	1.06807	0.0672821
$253$	5.74925	0.361452
$254$	−8.77687	−0.550710
$255$	0	0
$256$	14.0526	0.878289
$257$	−21.8997	−1.36607	−0.683033	−	0.730387i	$-0.739340\pi$
$257$	−21.8997	−1.36607	−0.683033	+	0.730387i	$0.739340\pi$
$258$	12.0548	0.750496
$259$	−5.75417	−0.357547
$260$	0	0
$261$	4.88758	0.302534
$262$	20.6120	1.27341
$263$	−4.76922	−0.294083	−0.147041	−	0.989130i	$-0.546975\pi$
$263$	−4.76922	−0.294083	−0.147041	+	0.989130i	$0.546975\pi$
$264$	0.156737	0.00964652
$265$	0	0
$266$	−4.34446	−0.266376
$267$	−15.0809	−0.922939
$268$	−2.77468	−0.169490
$269$	−12.0532	−0.734899	−0.367450	−	0.930043i	$-0.619769\pi$
$269$	−12.0532	−0.734899	−0.367450	+	0.930043i	$0.619769\pi$
$270$	0	0
$271$	27.5843	1.67562	0.837812	−	0.545959i	$-0.183834\pi$
$271$	27.5843	1.67562	0.837812	+	0.545959i	$0.183834\pi$
$272$	17.8469	1.08213
$273$	2.92562	0.177067
$274$	−11.3058	−0.683008
$275$	0	0
$276$	−17.6649	−1.06330
$277$	28.9858	1.74159	0.870795	−	0.491646i	$-0.163605\pi$
$277$	28.9858	1.74159	0.870795	+	0.491646i	$0.163605\pi$
$278$	−18.7399	−1.12394
$279$	2.68853	0.160958
$280$	0	0
$281$	5.93418	0.354003	0.177002	−	0.984211i	$-0.443360\pi$
$281$	5.93418	0.354003	0.177002	+	0.984211i	$0.443360\pi$
$282$	−12.3834	−0.737423
$283$	−15.2381	−0.905812	−0.452906	−	0.891558i	$-0.649613\pi$
$283$	−15.2381	−0.905812	−0.452906	+	0.891558i	$0.649613\pi$
$284$	−8.01286	−0.475476
$285$	0	0
$286$	8.06731	0.477030
$287$	0.0729331	0.00430511
$288$	8.08601	0.476473
$289$	5.49921	0.323483
$290$	0	0
$291$	−1.17394	−0.0688175
$292$	−23.0787	−1.35058
$293$	1.73298	0.101242	0.0506208	−	0.998718i	$-0.483880\pi$
$293$	1.73298	0.101242	0.0506208	+	0.998718i	$0.483880\pi$
$294$	−13.6769	−0.797656
$295$	0	0
$296$	2.59451	0.150803
$297$	−0.687513	−0.0398936
$298$	20.0998	1.16435
$299$	−48.3871	−2.79830
$300$	0	0
$301$	3.00558	0.173239
$302$	44.3800	2.55378
$303$	−7.23262	−0.415503
$304$	−15.9421	−0.914344
$305$	0	0
$306$	9.61905	0.549885
$307$	11.6087	0.662541	0.331271	−	0.943536i	$-0.392523\pi$
$307$	11.6087	0.662541	0.331271	+	0.943536i	$0.392523\pi$
$308$	0.734312	0.0418413
$309$	−18.4207	−1.04792
$310$	0	0
$311$	6.60870	0.374745	0.187372	−	0.982289i	$-0.440003\pi$
$311$	6.60870	0.374745	0.187372	+	0.982289i	$0.440003\pi$
$312$	−1.31914	−0.0746815
$313$	12.5410	0.708860	0.354430	−	0.935082i	$-0.384675\pi$
$313$	12.5410	0.708860	0.354430	+	0.935082i	$0.384675\pi$
$314$	−9.07146	−0.511932
$315$	0	0
$316$	−4.01084	−0.225627
$317$	−11.7318	−0.658925	−0.329463	−	0.944169i	$-0.606868\pi$
$317$	−11.7318	−0.658925	−0.329463	+	0.944169i	$0.606868\pi$
$318$	21.9822	1.23270
$319$	3.36028	0.188139
$320$	0	0
$321$	−17.5572	−0.979949
$322$	−8.57429	−0.477827
$323$	−20.0979	−1.11828
$324$	2.11242	0.117357
$325$	0	0
$326$	−28.9785	−1.60497
$327$	−11.4098	−0.630962
$328$	−0.0328849	−0.00181577
$329$	−3.08753	−0.170221
$330$	0	0
$331$	8.16236	0.448644	0.224322	−	0.974515i	$-0.427983\pi$
$331$	8.16236	0.448644	0.224322	+	0.974515i	$0.427983\pi$
$332$	5.32012	0.291979
$333$	−11.3806	−0.623651
$334$	0.959822	0.0525191
$335$	0	0
$336$	1.90238	0.103784
$337$	−11.1478	−0.607259	−0.303629	−	0.952790i	$-0.598198\pi$
$337$	−11.1478	−0.607259	−0.303629	+	0.952790i	$0.598198\pi$
$338$	−41.5336	−2.25913
$339$	−9.64827	−0.524022
$340$	0	0
$341$	1.84840	0.100097
$342$	−8.59244	−0.464626
$343$	−6.94934	−0.375229
$344$	−1.35519	−0.0730671
$345$	0	0
$346$	−4.35876	−0.234329
$347$	−10.2954	−0.552687	−0.276343	−	0.961059i	$-0.589123\pi$
$347$	−10.2954	−0.552687	−0.276343	+	0.961059i	$0.589123\pi$
$348$	−10.3246	−0.553458
$349$	20.8288	1.11494	0.557471	−	0.830196i	$-0.311772\pi$
$349$	20.8288	1.11494	0.557471	+	0.830196i	$0.311772\pi$
$350$	0	0
$351$	5.78627	0.308848
$352$	5.55924	0.296308
$353$	27.6165	1.46988	0.734939	−	0.678133i	$-0.237211\pi$
$353$	27.6165	1.46988	0.734939	+	0.678133i	$0.237211\pi$
$354$	−14.1308	−0.751045
$355$	0	0
$356$	31.8573	1.68843
$357$	2.39830	0.126931
$358$	2.75452	0.145581
$359$	19.2421	1.01556	0.507781	−	0.861486i	$-0.330466\pi$
$359$	19.2421	1.01556	0.507781	+	0.861486i	$0.330466\pi$
$360$	0	0
$361$	−1.04708	−0.0551095
$362$	−6.84877	−0.359963
$363$	10.5273	0.552541
$364$	−6.18014	−0.323927
$365$	0	0
$366$	−8.07194	−0.421927
$367$	8.23097	0.429653	0.214826	−	0.976652i	$-0.431081\pi$
$367$	8.23097	0.429653	0.214826	+	0.976652i	$0.431081\pi$
$368$	−31.4637	−1.64016
$369$	0.144247	0.00750918
$370$	0	0
$371$	5.48076	0.284547
$372$	−5.67931	−0.294459
$373$	29.1863	1.51121	0.755606	−	0.655027i	$-0.227343\pi$
$373$	29.1863	1.51121	0.755606	+	0.655027i	$0.227343\pi$
$374$	6.61323	0.341962
$375$	0	0
$376$	1.39214	0.0717943
$377$	−28.2809	−1.45654
$378$	1.02534	0.0527378
$379$	−4.34734	−0.223308	−0.111654	−	0.993747i	$-0.535615\pi$
$379$	−4.34734	−0.223308	−0.111654	+	0.993747i	$0.535615\pi$
$380$	0	0
$381$	−4.32804	−0.221732
$382$	−44.3994	−2.27167
$383$	−22.6224	−1.15595	−0.577976	−	0.816054i	$-0.696157\pi$
$383$	−22.6224	−1.15595	−0.577976	+	0.816054i	$0.696157\pi$
$384$	−1.82094	−0.0929243
$385$	0	0
$386$	−41.3471	−2.10451
$387$	5.94442	0.302172
$388$	2.47985	0.125895
$389$	11.2860	0.572221	0.286111	−	0.958197i	$-0.407638\pi$
$389$	11.2860	0.572221	0.286111	+	0.958197i	$0.407638\pi$
$390$	0	0
$391$	−39.6656	−2.00598
$392$	1.53756	0.0776585
$393$	10.1642	0.512714
$394$	−50.6345	−2.55093
$395$	0	0
$396$	1.45232	0.0729817
$397$	−9.06606	−0.455013	−0.227506	−	0.973777i	$-0.573057\pi$
$397$	−9.06606	−0.455013	−0.227506	+	0.973777i	$0.573057\pi$
$398$	20.7127	1.03823
$399$	−2.14233	−0.107251
$400$	0	0
$401$	−11.9700	−0.597752	−0.298876	−	0.954292i	$-0.596612\pi$
$401$	−11.9700	−0.597752	−0.298876	+	0.954292i	$0.596612\pi$
$402$	−2.66368	−0.132852
$403$	−15.5566	−0.774929
$404$	15.2783	0.760125
$405$	0	0
$406$	−5.01143	−0.248713
$407$	−7.82428	−0.387835
$408$	−1.08137	−0.0535359
$409$	−23.1228	−1.14335	−0.571673	−	0.820481i	$-0.693706\pi$
$409$	−23.1228	−1.14335	−0.571673	+	0.820481i	$0.693706\pi$
$410$	0	0
$411$	−5.57509	−0.274999
$412$	38.9123	1.91707
$413$	−3.52321	−0.173366
$414$	−16.9582	−0.833449
$415$	0	0
$416$	−46.7879	−2.29396
$417$	−9.24097	−0.452532
$418$	−5.90741	−0.288941
$419$	−32.8579	−1.60521	−0.802606	−	0.596509i	$-0.796554\pi$
$419$	−32.8579	−1.60521	−0.802606	+	0.596509i	$0.796554\pi$
$420$	0	0
$421$	8.70039	0.424031	0.212016	−	0.977266i	$-0.431997\pi$
$421$	8.70039	0.424031	0.212016	+	0.977266i	$0.431997\pi$
$422$	−11.0908	−0.539891
$423$	−6.10650	−0.296908
$424$	−2.47123	−0.120014
$425$	0	0
$426$	−7.69230	−0.372693
$427$	−2.01256	−0.0973945
$428$	37.0883	1.79273
$429$	3.97814	0.192066
$430$	0	0
$431$	5.70635	0.274865	0.137432	−	0.990511i	$-0.456115\pi$
$431$	5.70635	0.274865	0.137432	+	0.990511i	$0.456115\pi$
$432$	3.76252	0.181024
$433$	−18.2221	−0.875700	−0.437850	−	0.899048i	$-0.644260\pi$
$433$	−18.2221	−0.875700	−0.437850	+	0.899048i	$0.644260\pi$
$434$	−2.75666	−0.132324
$435$	0	0
$436$	24.1022	1.15429
$437$	35.4322	1.69495
$438$	−22.1554	−1.05863
$439$	13.2419	0.632002	0.316001	−	0.948759i	$-0.397660\pi$
$439$	13.2419	0.632002	0.316001	+	0.948759i	$0.397660\pi$
$440$	0	0
$441$	−6.74435	−0.321160
$442$	−55.6585	−2.64740
$443$	26.3276	1.25086	0.625431	−	0.780279i	$-0.284923\pi$
$443$	26.3276	1.25086	0.625431	+	0.780279i	$0.284923\pi$
$444$	24.0405	1.14091
$445$	0	0
$446$	46.4162	2.19787
$447$	9.91157	0.468801
$448$	−4.48614	−0.211950
$449$	22.2932	1.05208	0.526040	−	0.850460i	$-0.323676\pi$
$449$	22.2932	1.05208	0.526040	+	0.850460i	$0.323676\pi$
$450$	0	0
$451$	0.0991714	0.00466980
$452$	20.3812	0.958650
$453$	21.8846	1.02823
$454$	−26.2045	−1.22984
$455$	0	0
$456$	0.965960	0.0452352
$457$	−17.3159	−0.810002	−0.405001	−	0.914316i	$-0.632729\pi$
$457$	−17.3159	−0.810002	−0.405001	+	0.914316i	$0.632729\pi$
$458$	−29.4557	−1.37638
$459$	4.74333	0.221400
$460$	0	0
$461$	−16.2204	−0.755460	−0.377730	−	0.925916i	$-0.623295\pi$
$461$	−16.2204	−0.755460	−0.377730	+	0.925916i	$0.623295\pi$
$462$	0.704935	0.0327965
$463$	−20.1061	−0.934412	−0.467206	−	0.884149i	$-0.654739\pi$
$463$	−20.1061	−0.934412	−0.467206	+	0.884149i	$0.654739\pi$
$464$	−18.3896	−0.853717
$465$	0	0
$466$	−20.1726	−0.934478
$467$	32.4922	1.50356	0.751780	−	0.659414i	$-0.229195\pi$
$467$	32.4922	1.50356	0.751780	+	0.659414i	$0.229195\pi$
$468$	−12.2230	−0.565010
$469$	−0.664128	−0.0306666
$470$	0	0
$471$	−4.47331	−0.206119
$472$	1.58858	0.0731205
$473$	4.08687	0.187914
$474$	−3.85038	−0.176854
$475$	0	0
$476$	−5.06621	−0.232209
$477$	10.8398	0.496321
$478$	−3.21443	−0.147025
$479$	−8.99966	−0.411205	−0.205603	−	0.978636i	$-0.565915\pi$
$479$	−8.99966	−0.411205	−0.205603	+	0.978636i	$0.565915\pi$
$480$	0	0
$481$	65.8510	3.00255
$482$	−48.1599	−2.19362
$483$	−4.22814	−0.192387
$484$	−22.2381	−1.01082
$485$	0	0
$486$	2.02791	0.0919879
$487$	−40.1153	−1.81780	−0.908898	−	0.417018i	$-0.863075\pi$
$487$	−40.1153	−1.81780	−0.908898	+	0.417018i	$0.863075\pi$
$488$	0.907446	0.0410781
$489$	−14.2898	−0.646209
$490$	0	0
$491$	−35.7772	−1.61460	−0.807302	−	0.590138i	$-0.799073\pi$
$491$	−35.7772	−1.61460	−0.807302	+	0.590138i	$0.799073\pi$
$492$	−0.304709	−0.0137374
$493$	−23.1834	−1.04413
$494$	49.7182	2.23693
$495$	0	0
$496$	−10.1157	−0.454207
$497$	−1.91790	−0.0860297
$498$	5.10728	0.228863
$499$	14.9592	0.669665	0.334832	−	0.942278i	$-0.391320\pi$
$499$	14.9592	0.669665	0.334832	+	0.942278i	$0.391320\pi$
$500$	0	0
$501$	0.473306	0.0211458
$502$	−41.1437	−1.83633
$503$	33.8165	1.50780	0.753901	−	0.656988i	$-0.228170\pi$
$503$	33.8165	1.50780	0.753901	+	0.656988i	$0.228170\pi$
$504$	−0.115269	−0.00513447
$505$	0	0
$506$	−11.6590	−0.518304
$507$	−20.4810	−0.909592
$508$	9.14263	0.405639
$509$	4.54546	0.201474	0.100737	−	0.994913i	$-0.467880\pi$
$509$	4.54546	0.201474	0.100737	+	0.994913i	$0.467880\pi$
$510$	0	0
$511$	−5.52395	−0.244365
$512$	−32.1393	−1.42037
$513$	−4.23709	−0.187072
$514$	44.4107	1.95887
$515$	0	0
$516$	−12.5571	−0.552796
$517$	−4.19830	−0.184641
$518$	11.6689	0.512704
$519$	−2.14939	−0.0943476
$520$	0	0
$521$	−27.5808	−1.20834	−0.604169	−	0.796857i	$-0.706495\pi$
$521$	−27.5808	−1.20834	−0.604169	+	0.796857i	$0.706495\pi$
$522$	−9.91157	−0.433818
$523$	8.22959	0.359855	0.179927	−	0.983680i	$-0.442414\pi$
$523$	8.22959	0.359855	0.179927	+	0.983680i	$0.442414\pi$
$524$	−21.4710	−0.937964
$525$	0	0
$526$	9.67155	0.421700
$527$	−12.7526	−0.555513
$528$	2.58678	0.112575
$529$	46.9295	2.04041
$530$	0	0
$531$	−6.96817	−0.302393
$532$	4.52550	0.196206
$533$	−0.834650	−0.0361527
$534$	30.5828	1.32345
$535$	0	0
$536$	0.299450	0.0129343
$537$	1.35831	0.0586152
$538$	24.4429	1.05381
$539$	−4.63683	−0.199723
$540$	0	0
$541$	17.8165	0.765993	0.382996	−	0.923750i	$-0.374892\pi$
$541$	17.8165	0.765993	0.382996	+	0.923750i	$0.374892\pi$
$542$	−55.9384	−2.40276
$543$	−3.37725	−0.144932
$544$	−38.3547	−1.64444
$545$	0	0
$546$	−5.93290	−0.253905
$547$	9.56762	0.409082	0.204541	−	0.978858i	$-0.434430\pi$
$547$	9.56762	0.409082	0.204541	+	0.978858i	$0.434430\pi$
$548$	11.7769	0.503086
$549$	−3.98042	−0.169880
$550$	0	0
$551$	20.7091	0.882238
$552$	1.90643	0.0811432
$553$	−0.960007	−0.0408236
$554$	−58.7807	−2.49735
$555$	0	0
$556$	19.5208	0.827866
$557$	20.5472	0.870613	0.435306	−	0.900282i	$-0.356640\pi$
$557$	20.5472	0.870613	0.435306	+	0.900282i	$0.356640\pi$
$558$	−5.45211	−0.230806
$559$	−34.3961	−1.45480
$560$	0	0
$561$	3.26110	0.137684
$562$	−12.0340	−0.507623
$563$	−18.7411	−0.789842	−0.394921	−	0.918715i	$-0.629228\pi$
$563$	−18.7411	−0.789842	−0.394921	+	0.918715i	$0.629228\pi$
$564$	12.8995	0.543167
$565$	0	0
$566$	30.9015	1.29889
$567$	0.505614	0.0212338
$568$	0.864766	0.0362848
$569$	4.66977	0.195767	0.0978834	−	0.995198i	$-0.468793\pi$
$569$	4.66977	0.195767	0.0978834	+	0.995198i	$0.468793\pi$
$570$	0	0
$571$	14.9699	0.626471	0.313235	−	0.949676i	$-0.398587\pi$
$571$	14.9699	0.626471	0.313235	+	0.949676i	$0.398587\pi$
$572$	−8.40350	−0.351368
$573$	−21.8942	−0.914641
$574$	−0.147902	−0.00617330
$575$	0	0
$576$	−8.87266	−0.369694
$577$	15.6712	0.652400	0.326200	−	0.945301i	$-0.394232\pi$
$577$	15.6712	0.652400	0.326200	+	0.945301i	$0.394232\pi$
$578$	−11.1519	−0.463858
$579$	−20.3890	−0.847339
$580$	0	0
$581$	1.27339	0.0528290
$582$	2.38064	0.0986808
$583$	7.45251	0.308652
$584$	2.49070	0.103066
$585$	0	0
$586$	−3.51432	−0.145175
$587$	30.0310	1.23951	0.619756	−	0.784794i	$-0.287231\pi$
$587$	30.0310	1.23951	0.619756	+	0.784794i	$0.287231\pi$
$588$	14.2469	0.587533
$589$	11.3916	0.469381
$590$	0	0
$591$	−24.9688	−1.02708
$592$	42.8196	1.75987
$593$	26.2392	1.07751	0.538757	−	0.842461i	$-0.318894\pi$
$593$	26.2392	1.07751	0.538757	+	0.842461i	$0.318894\pi$
$594$	1.39422	0.0572053
$595$	0	0
$596$	−20.9374	−0.857630
$597$	10.2138	0.418024
$598$	98.1246	4.01261
$599$	−15.5681	−0.636095	−0.318048	−	0.948075i	$-0.603027\pi$
$599$	−15.5681	−0.636095	−0.318048	+	0.948075i	$0.603027\pi$
$600$	0	0
$601$	−6.27437	−0.255937	−0.127969	−	0.991778i	$-0.540846\pi$
$601$	−6.27437	−0.255937	−0.127969	+	0.991778i	$0.540846\pi$
$602$	−6.09505	−0.248416
$603$	−1.31351	−0.0534902
$604$	−46.2294	−1.88105
$605$	0	0
$606$	14.6671	0.595810
$607$	−8.47616	−0.344037	−0.172018	−	0.985094i	$-0.555029\pi$
$607$	−8.47616	−0.344037	−0.172018	+	0.985094i	$0.555029\pi$
$608$	34.2611	1.38947
$609$	−2.47123	−0.100139
$610$	0	0
$611$	35.3339	1.42946
$612$	−10.0199	−0.405031
$613$	−6.60744	−0.266872	−0.133436	−	0.991057i	$-0.542601\pi$
$613$	−6.60744	−0.266872	−0.133436	+	0.991057i	$0.542601\pi$
$614$	−23.5413	−0.950051
$615$	0	0
$616$	−0.0792486	−0.00319302
$617$	−25.1919	−1.01419	−0.507094	−	0.861891i	$-0.669280\pi$
$617$	−25.1919	−1.01419	−0.507094	+	0.861891i	$0.669280\pi$
$618$	37.3556	1.50266
$619$	1.45782	0.0585949	0.0292975	−	0.999571i	$-0.490673\pi$
$619$	1.45782	0.0585949	0.0292975	+	0.999571i	$0.490673\pi$
$620$	0	0
$621$	−8.36239	−0.335571
$622$	−13.4018	−0.537365
$623$	7.62514	0.305495
$624$	−21.7710	−0.871537
$625$	0	0
$626$	−25.4321	−1.01647
$627$	−2.91305	−0.116336
$628$	9.44950	0.377076
$629$	53.9818	2.15239
$630$	0	0
$631$	15.0828	0.600435	0.300218	−	0.953871i	$-0.402941\pi$
$631$	15.0828	0.600435	0.300218	+	0.953871i	$0.402941\pi$
$632$	0.432859	0.0172182
$633$	−5.46907	−0.217376
$634$	23.7911	0.944865
$635$	0	0
$636$	−22.8982	−0.907974
$637$	39.0247	1.54621
$638$	−6.81434	−0.269782
$639$	−3.79321	−0.150057
$640$	0	0
$641$	−5.23264	−0.206677	−0.103338	−	0.994646i	$-0.532952\pi$
$641$	−5.23264	−0.206677	−0.103338	+	0.994646i	$0.532952\pi$
$642$	35.6045	1.40520
$643$	−36.4602	−1.43785	−0.718925	−	0.695088i	$-0.755366\pi$
$643$	−36.4602	−1.43785	−0.718925	+	0.695088i	$0.755366\pi$
$644$	8.93161	0.351955
$645$	0	0
$646$	40.7568	1.60355
$647$	−5.06588	−0.199160	−0.0995801	−	0.995030i	$-0.531750\pi$
$647$	−5.06588	−0.199160	−0.0995801	+	0.995030i	$0.531750\pi$
$648$	−0.227977	−0.00895579
$649$	−4.79071	−0.188052
$650$	0	0
$651$	−1.35936	−0.0532776
$652$	30.1862	1.18218
$653$	−21.3639	−0.836033	−0.418017	−	0.908439i	$-0.637275\pi$
$653$	−21.3639	−0.836033	−0.418017	+	0.908439i	$0.637275\pi$
$654$	23.1380	0.904767
$655$	0	0
$656$	−0.542731	−0.0211901
$657$	−10.9252	−0.426234
$658$	6.26124	0.244089
$659$	−47.2176	−1.83934	−0.919668	−	0.392696i	$-0.871542\pi$
$659$	−47.2176	−1.83934	−0.919668	+	0.392696i	$0.871542\pi$
$660$	0	0
$661$	−23.7835	−0.925072	−0.462536	−	0.886601i	$-0.653060\pi$
$661$	−23.7835	−0.925072	−0.462536	+	0.886601i	$0.653060\pi$
$662$	−16.5525	−0.643332
$663$	−27.4462	−1.06592
$664$	−0.574159	−0.0222817
$665$	0	0
$666$	23.0787	0.894283
$667$	40.8718	1.58256
$668$	−0.999821	−0.0386842
$669$	22.8887	0.884928
$670$	0	0
$671$	−2.73659	−0.105645
$672$	−4.08840	−0.157714
$673$	−26.1124	−1.00656	−0.503279	−	0.864124i	$-0.667873\pi$
$673$	−26.1124	−1.00656	−0.503279	+	0.864124i	$0.667873\pi$
$674$	22.6067	0.870778
$675$	0	0
$676$	43.2644	1.66402
$677$	−11.8091	−0.453861	−0.226931	−	0.973911i	$-0.572869\pi$
$677$	−11.8091	−0.453861	−0.226931	+	0.973911i	$0.572869\pi$
$678$	19.5658	0.751421
$679$	0.593560	0.0227787
$680$	0	0
$681$	−12.9219	−0.495169
$682$	−3.74839	−0.143533
$683$	5.41899	0.207352	0.103676	−	0.994611i	$-0.466940\pi$
$683$	5.41899	0.207352	0.103676	+	0.994611i	$0.466940\pi$
$684$	8.95051	0.342231
$685$	0	0
$686$	14.0926	0.538059
$687$	−14.5252	−0.554170
$688$	−22.3660	−0.852696
$689$	−62.7221	−2.38952
$690$	0	0
$691$	48.1513	1.83176	0.915880	−	0.401451i	$-0.131494\pi$
$691$	48.1513	1.83176	0.915880	+	0.401451i	$0.131494\pi$
$692$	4.54041	0.172600
$693$	0.347616	0.0132049
$694$	20.8782	0.792524
$695$	0	0
$696$	1.11426	0.0422358
$697$	−0.684210	−0.0259163
$698$	−42.2390	−1.59877
$699$	−9.94748	−0.376248
$700$	0	0
$701$	46.4747	1.75532	0.877662	−	0.479280i	$-0.159102\pi$
$701$	46.4747	1.75532	0.877662	+	0.479280i	$0.159102\pi$
$702$	−11.7340	−0.442873
$703$	−48.2204	−1.81867
$704$	−6.10007	−0.229905
$705$	0	0
$706$	−56.0038	−2.10773
$707$	3.65691	0.137532
$708$	14.7197	0.553200
$709$	2.73598	0.102752	0.0513760	−	0.998679i	$-0.483639\pi$
$709$	2.73598	0.102752	0.0513760	+	0.998679i	$0.483639\pi$
$710$	0	0
$711$	−1.89869	−0.0712066
$712$	−3.43811	−0.128849
$713$	22.4826	0.841979
$714$	−4.86353	−0.182013
$715$	0	0
$716$	−2.86931	−0.107231
$717$	−1.58509	−0.0591964
$718$	−39.0213	−1.45626
$719$	21.7083	0.809584	0.404792	−	0.914409i	$-0.367344\pi$
$719$	21.7083	0.809584	0.404792	+	0.914409i	$0.367344\pi$
$720$	0	0
$721$	9.31378	0.346863
$722$	2.12338	0.0790242
$723$	−23.7485	−0.883217
$724$	7.13418	0.265140
$725$	0	0
$726$	−21.3485	−0.792316
$727$	−25.8542	−0.958879	−0.479439	−	0.877575i	$-0.659160\pi$
$727$	−25.8542	−0.958879	−0.479439	+	0.877575i	$0.659160\pi$
$728$	0.666975	0.0247197
$729$	1.00000	0.0370370
$730$	0	0
$731$	−28.1964	−1.04288
$732$	8.40832	0.310781
$733$	6.28263	0.232054	0.116027	−	0.993246i	$-0.462984\pi$
$733$	6.28263	0.232054	0.116027	+	0.993246i	$0.462984\pi$
$734$	−16.6917	−0.616100
$735$	0	0
$736$	67.6184	2.49245
$737$	−0.903054	−0.0332644
$738$	−0.292519	−0.0107678
$739$	23.7681	0.874325	0.437162	−	0.899383i	$-0.355983\pi$
$739$	23.7681	0.874325	0.437162	+	0.899383i	$0.355983\pi$
$740$	0	0
$741$	24.5170	0.900653
$742$	−11.1145	−0.408026
$743$	14.8532	0.544912	0.272456	−	0.962168i	$-0.412164\pi$
$743$	14.8532	0.544912	0.272456	+	0.962168i	$0.412164\pi$
$744$	0.612924	0.0224709
$745$	0	0
$746$	−59.1873	−2.16700
$747$	2.51849	0.0921469
$748$	−6.88882	−0.251880
$749$	8.87719	0.324365
$750$	0	0
$751$	26.1668	0.954841	0.477421	−	0.878675i	$-0.341572\pi$
$751$	26.1668	0.954841	0.477421	+	0.878675i	$0.341572\pi$
$752$	22.9758	0.837843
$753$	−20.2887	−0.739363
$754$	57.3511	2.08860
$755$	0	0
$756$	−1.06807	−0.0388453
$757$	−13.1012	−0.476170	−0.238085	−	0.971244i	$-0.576520\pi$
$757$	−13.1012	−0.476170	−0.238085	+	0.971244i	$0.576520\pi$
$758$	8.81602	0.320212
$759$	−5.74925	−0.208685
$760$	0	0
$761$	−36.3328	−1.31706	−0.658531	−	0.752554i	$-0.728822\pi$
$761$	−36.3328	−1.31706	−0.658531	+	0.752554i	$0.728822\pi$
$762$	8.77687	0.317953
$763$	5.76894	0.208850
$764$	46.2496	1.67325
$765$	0	0
$766$	45.8762	1.65758
$767$	40.3198	1.45586
$768$	−14.0526	−0.507080
$769$	−18.6504	−0.672550	−0.336275	−	0.941764i	$-0.609167\pi$
$769$	−18.6504	−0.672550	−0.336275	+	0.941764i	$0.609167\pi$
$770$	0	0
$771$	21.8997	0.788699
$772$	43.0702	1.55013
$773$	−9.15449	−0.329264	−0.164632	−	0.986355i	$-0.552644\pi$
$773$	−9.15449	−0.329264	−0.164632	+	0.986355i	$0.552644\pi$
$774$	−12.0548	−0.433299
$775$	0	0
$776$	−0.267631	−0.00960740
$777$	5.75417	0.206430
$778$	−22.8869	−0.820536
$779$	0.611186	0.0218980
$780$	0	0
$781$	−2.60788	−0.0933174
$782$	80.4383	2.87647
$783$	−4.88758	−0.174668
$784$	25.3758	0.906278
$785$	0	0
$786$	−20.6120	−0.735206
$787$	−36.1383	−1.28819	−0.644095	−	0.764945i	$-0.722766\pi$
$787$	−36.1383	−1.28819	−0.644095	+	0.764945i	$0.722766\pi$
$788$	52.7446	1.87895
$789$	4.76922	0.169789
$790$	0	0
$791$	4.87830	0.173452
$792$	−0.156737	−0.00556942
$793$	23.0318	0.817884
$794$	18.3852	0.652465
$795$	0	0
$796$	−21.5759	−0.764736
$797$	−15.1491	−0.536608	−0.268304	−	0.963334i	$-0.586463\pi$
$797$	−15.1491	−0.536608	−0.268304	+	0.963334i	$0.586463\pi$
$798$	4.34446	0.153792
$799$	28.9652	1.02471
$800$	0	0
$801$	15.0809	0.532859
$802$	24.2740	0.857146
$803$	−7.51124	−0.265066
$804$	2.77468	0.0978554
$805$	0	0
$806$	31.5474	1.11121
$807$	12.0532	0.424294
$808$	−1.64887	−0.0580071
$809$	33.2017	1.16731	0.583654	−	0.812002i	$-0.301622\pi$
$809$	33.2017	1.16731	0.583654	+	0.812002i	$0.301622\pi$
$810$	0	0
$811$	26.6013	0.934098	0.467049	−	0.884231i	$-0.345317\pi$
$811$	26.6013	0.934098	0.467049	+	0.884231i	$0.345317\pi$
$812$	5.22028	0.183196
$813$	−27.5843	−0.967422
$814$	15.8669	0.556136
$815$	0	0
$816$	−17.8469	−0.624766
$817$	25.1870	0.881183
$818$	46.8909	1.63950
$819$	−2.92562	−0.102230
$820$	0	0
$821$	2.75480	0.0961432	0.0480716	−	0.998844i	$-0.484692\pi$
$821$	2.75480	0.0961432	0.0480716	+	0.998844i	$0.484692\pi$
$822$	11.3058	0.394335
$823$	−4.73309	−0.164985	−0.0824926	−	0.996592i	$-0.526288\pi$
$823$	−4.73309	−0.164985	−0.0824926	+	0.996592i	$0.526288\pi$
$824$	−4.19951	−0.146297
$825$	0	0
$826$	7.14475	0.248598
$827$	−39.6187	−1.37768	−0.688838	−	0.724916i	$-0.741879\pi$
$827$	−39.6187	−1.37768	−0.688838	+	0.724916i	$0.741879\pi$
$828$	17.6649	0.613897
$829$	−16.0834	−0.558600	−0.279300	−	0.960204i	$-0.590102\pi$
$829$	−16.0834	−0.558600	−0.279300	+	0.960204i	$0.590102\pi$
$830$	0	0
$831$	−28.9858	−1.00551
$832$	51.3396	1.77988
$833$	31.9907	1.10841
$834$	18.7399	0.648908
$835$	0	0
$836$	6.15359	0.212826
$837$	−2.68853	−0.0929293
$838$	66.6328	2.30179
$839$	−36.4617	−1.25880	−0.629400	−	0.777082i	$-0.716699\pi$
$839$	−36.4617	−1.25880	−0.629400	+	0.777082i	$0.716699\pi$
$840$	0	0
$841$	−5.11156	−0.176261
$842$	−17.6436	−0.608039
$843$	−5.93418	−0.204384
$844$	11.5530	0.397670
$845$	0	0
$846$	12.3834	0.425751
$847$	−5.32277	−0.182892
$848$	−40.7850	−1.40056
$849$	15.2381	0.522971
$850$	0	0
$851$	−95.1686	−3.26234
$852$	8.01286	0.274516
$853$	−25.0460	−0.857560	−0.428780	−	0.903409i	$-0.641056\pi$
$853$	−25.0460	−0.857560	−0.428780	+	0.903409i	$0.641056\pi$
$854$	4.08129	0.139659
$855$	0	0
$856$	−4.00265	−0.136808
$857$	−15.1391	−0.517140	−0.258570	−	0.965993i	$-0.583251\pi$
$857$	−15.1391	−0.517140	−0.258570	+	0.965993i	$0.583251\pi$
$858$	−8.06731	−0.275413
$859$	24.3545	0.830966	0.415483	−	0.909601i	$-0.363613\pi$
$859$	24.3545	0.830966	0.415483	+	0.909601i	$0.363613\pi$
$860$	0	0
$861$	−0.0729331	−0.00248555
$862$	−11.5720	−0.394142
$863$	29.0380	0.988466	0.494233	−	0.869329i	$-0.335449\pi$
$863$	29.0380	0.988466	0.494233	+	0.869329i	$0.335449\pi$
$864$	−8.08601	−0.275092
$865$	0	0
$866$	36.9529	1.25571
$867$	−5.49921	−0.186763
$868$	2.87154	0.0974665
$869$	−1.30538	−0.0442819
$870$	0	0
$871$	7.60031	0.257527
$872$	−2.60117	−0.0880866
$873$	1.17394	0.0397318
$874$	−71.8533	−2.43047
$875$	0	0
$876$	23.0787	0.779756
$877$	−16.8629	−0.569420	−0.284710	−	0.958614i	$-0.591897\pi$
$877$	−16.8629	−0.569420	−0.284710	+	0.958614i	$0.591897\pi$
$878$	−26.8534	−0.906259
$879$	−1.73298	−0.0584518
$880$	0	0
$881$	−50.2279	−1.69222	−0.846110	−	0.533008i	$-0.821062\pi$
$881$	−50.2279	−1.69222	−0.846110	+	0.533008i	$0.821062\pi$
$882$	13.6769	0.460527
$883$	−7.42047	−0.249719	−0.124859	−	0.992174i	$-0.539848\pi$
$883$	−7.42047	−0.249719	−0.124859	+	0.992174i	$0.539848\pi$
$884$	57.9780	1.95001
$885$	0	0
$886$	−53.3900	−1.79367
$887$	39.7855	1.33587	0.667933	−	0.744221i	$-0.267179\pi$
$887$	39.7855	1.33587	0.667933	+	0.744221i	$0.267179\pi$
$888$	−2.59451	−0.0870660
$889$	2.18832	0.0733938
$890$	0	0
$891$	0.687513	0.0230326
$892$	−48.3505	−1.61890
$893$	−25.8738	−0.865833
$894$	−20.0998	−0.672237
$895$	0	0
$896$	0.920691	0.0307581
$897$	48.3871	1.61560
$898$	−45.2086	−1.50863
$899$	13.1404	0.438258
$900$	0	0
$901$	−51.4168	−1.71294
$902$	−0.201111	−0.00669626
$903$	−3.00558	−0.100020
$904$	−2.19958	−0.0731571
$905$	0	0
$906$	−44.3800	−1.47443
$907$	46.5970	1.54723	0.773614	−	0.633657i	$-0.218447\pi$
$907$	46.5970	1.54723	0.773614	+	0.633657i	$0.218447\pi$
$908$	27.2965	0.905868
$909$	7.23262	0.239891
$910$	0	0
$911$	47.5250	1.57457	0.787287	−	0.616586i	$-0.211485\pi$
$911$	47.5250	1.57457	0.787287	+	0.616586i	$0.211485\pi$
$912$	15.9421	0.527897
$913$	1.73150	0.0573042
$914$	35.1150	1.16150
$915$	0	0
$916$	30.6833	1.01380
$917$	−5.13914	−0.169709
$918$	−9.61905	−0.317476
$919$	−29.4578	−0.971723	−0.485862	−	0.874036i	$-0.661494\pi$
$919$	−29.4578	−0.971723	−0.485862	+	0.874036i	$0.661494\pi$
$920$	0	0
$921$	−11.6087	−0.382518
$922$	32.8936	1.08329
$923$	21.9486	0.722446
$924$	−0.734312	−0.0241571
$925$	0	0
$926$	40.7735	1.33990
$927$	18.4207	0.605016
$928$	39.5210	1.29734
$929$	33.9108	1.11258	0.556288	−	0.830989i	$-0.312225\pi$
$929$	33.9108	1.11258	0.556288	+	0.830989i	$0.312225\pi$
$930$	0	0
$931$	−28.5764	−0.936555
$932$	21.0133	0.688312
$933$	−6.60870	−0.216359
$934$	−65.8913	−2.15603
$935$	0	0
$936$	1.31914	0.0431174
$937$	16.1534	0.527708	0.263854	−	0.964563i	$-0.415006\pi$
$937$	16.1534	0.527708	0.263854	+	0.964563i	$0.415006\pi$
$938$	1.34679	0.0439743
$939$	−12.5410	−0.409261
$940$	0	0
$941$	32.2573	1.05156	0.525778	−	0.850622i	$-0.323774\pi$
$941$	32.2573	1.05156	0.525778	+	0.850622i	$0.323774\pi$
$942$	9.07146	0.295564
$943$	1.20625	0.0392808
$944$	26.2179	0.853320
$945$	0	0
$946$	−8.28780	−0.269460
$947$	−20.9811	−0.681796	−0.340898	−	0.940100i	$-0.610731\pi$
$947$	−20.9811	−0.681796	−0.340898	+	0.940100i	$0.610731\pi$
$948$	4.01084	0.130266
$949$	63.2164	2.05209
$950$	0	0
$951$	11.7318	0.380431
$952$	0.546757	0.0177205
$953$	−19.0273	−0.616354	−0.308177	−	0.951329i	$-0.599719\pi$
$953$	−19.0273	−0.616354	−0.308177	+	0.951329i	$0.599719\pi$
$954$	−21.9822	−0.711699
$955$	0	0
$956$	3.34838	0.108294
$957$	−3.36028	−0.108622
$958$	18.2505	0.589647
$959$	2.81885	0.0910253
$960$	0	0
$961$	−23.7718	−0.766832
$962$	−133.540	−4.30550
$963$	17.5572	0.565774
$964$	50.1669	1.61577
$965$	0	0
$966$	8.57429	0.275873
$967$	17.7570	0.571027	0.285513	−	0.958375i	$-0.407836\pi$
$967$	17.7570	0.571027	0.285513	+	0.958375i	$0.407836\pi$
$968$	2.39999	0.0771386
$969$	20.0979	0.645638
$970$	0	0
$971$	−19.0906	−0.612648	−0.306324	−	0.951927i	$-0.599099\pi$
$971$	−19.0906	−0.612648	−0.306324	+	0.951927i	$0.599099\pi$
$972$	−2.11242	−0.0677559
$973$	4.67236	0.149789
$974$	81.3502	2.60663
$975$	0	0
$976$	14.9764	0.479384
$977$	3.22285	0.103108	0.0515541	−	0.998670i	$-0.483583\pi$
$977$	3.22285	0.103108	0.0515541	+	0.998670i	$0.483583\pi$
$978$	28.9785	0.926631
$979$	10.3684	0.331374
$980$	0	0
$981$	11.4098	0.364286
$982$	72.5530	2.31526
$983$	−35.6008	−1.13549	−0.567744	−	0.823205i	$-0.692184\pi$
$983$	−35.6008	−1.13549	−0.567744	+	0.823205i	$0.692184\pi$
$984$	0.0328849	0.00104833
$985$	0	0
$986$	47.0139	1.49723
$987$	3.08753	0.0982773
$988$	−51.7901	−1.64766
$989$	49.7096	1.58067
$990$	0	0
$991$	−17.0654	−0.542100	−0.271050	−	0.962565i	$-0.587371\pi$
$991$	−17.0654	−0.542100	−0.271050	+	0.962565i	$0.587371\pi$
$992$	21.7395	0.690230
$993$	−8.16236	−0.259025
$994$	3.88933	0.123362
$995$	0	0
$996$	−5.32012	−0.168574
$997$	36.5010	1.15600	0.577998	−	0.816038i	$-0.303834\pi$
$997$	36.5010	1.15600	0.577998	+	0.816038i	$0.303834\pi$
$998$	−30.3359	−0.960265
$999$	11.3806	0.360065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.l.1.2	yes	6
3.2	odd	2		5625.2.a.o.1.5		6
5.2	odd	4		1875.2.b.e.1249.4		12
5.3	odd	4		1875.2.b.e.1249.9		12
5.4	even	2		1875.2.a.i.1.5	✓	6
15.14	odd	2		5625.2.a.r.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.i.1.5	✓	6	5.4	even	2
1875.2.a.l.1.2	yes	6	1.1	even	1	trivial
1875.2.b.e.1249.4		12	5.2	odd	4
1875.2.b.e.1249.9		12	5.3	odd	4
5625.2.a.o.1.5		6	3.2	odd	2
5625.2.a.r.1.2		6	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q-2.02791 q^{2} -1.00000 q^{3} +2.11242 q^{4} +2.02791 q^{6} +0.505614 q^{7} -0.227977 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.02791 q^{2} -1.00000 q^{3} +2.11242 q^{4} +2.02791 q^{6} +0.505614 q^{7} -0.227977 q^{8} +1.00000 q^{9} +0.687513 q^{11} -2.11242 q^{12} -5.78627 q^{13} -1.02534 q^{14} -3.76252 q^{16} -4.74333 q^{17} -2.02791 q^{18} +4.23709 q^{19} -0.505614 q^{21} -1.39422 q^{22} +8.36239 q^{23} +0.227977 q^{24} +11.7340 q^{26} -1.00000 q^{27} +1.06807 q^{28} +4.88758 q^{29} +2.68853 q^{31} +8.08601 q^{32} -0.687513 q^{33} +9.61905 q^{34} +2.11242 q^{36} -11.3806 q^{37} -8.59244 q^{38} +5.78627 q^{39} +0.144247 q^{41} +1.02534 q^{42} +5.94442 q^{43} +1.45232 q^{44} -16.9582 q^{46} -6.10650 q^{47} +3.76252 q^{48} -6.74435 q^{49} +4.74333 q^{51} -12.2230 q^{52} +10.8398 q^{53} +2.02791 q^{54} -0.115269 q^{56} -4.23709 q^{57} -9.91157 q^{58} -6.96817 q^{59} -3.98042 q^{61} -5.45211 q^{62} +0.505614 q^{63} -8.87266 q^{64} +1.39422 q^{66} -1.31351 q^{67} -10.0199 q^{68} -8.36239 q^{69} -3.79321 q^{71} -0.227977 q^{72} -10.9252 q^{73} +23.0787 q^{74} +8.95051 q^{76} +0.347616 q^{77} -11.7340 q^{78} -1.89869 q^{79} +1.00000 q^{81} -0.292519 q^{82} +2.51849 q^{83} -1.06807 q^{84} -12.0548 q^{86} -4.88758 q^{87} -0.156737 q^{88} +15.0809 q^{89} -2.92562 q^{91} +17.6649 q^{92} -2.68853 q^{93} +12.3834 q^{94} -8.08601 q^{96} +1.17394 q^{97} +13.6769 q^{98} +0.687513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9} - 11 q^{12} - 4 q^{14} + 17 q^{16} + 2 q^{17} + q^{18} - 2 q^{19} + 2 q^{21} + 9 q^{22} - q^{23} - 6 q^{24} + 37 q^{26} - 6 q^{27} - 44 q^{28} + 31 q^{29} - 2 q^{31} + 33 q^{32} + 37 q^{34} + 11 q^{36} - 22 q^{37} + 27 q^{38} + 33 q^{41} + 4 q^{42} - 3 q^{43} - 11 q^{44} - 12 q^{46} - 6 q^{47} - 17 q^{48} + 4 q^{49} - 2 q^{51} - 33 q^{52} + 14 q^{53} - q^{54} - 30 q^{56} + 2 q^{57} - q^{58} - 8 q^{59} + 34 q^{61} + 31 q^{62} - 2 q^{63} + 12 q^{64} - 9 q^{66} + 2 q^{67} + 27 q^{68} + q^{69} - 3 q^{71} + 6 q^{72} - 36 q^{73} + 36 q^{74} + 27 q^{76} + 16 q^{77} - 37 q^{78} + 25 q^{79} + 6 q^{81} + 36 q^{82} - 12 q^{83} + 44 q^{84} - 30 q^{86} - 31 q^{87} + 56 q^{88} + 18 q^{89} + 28 q^{91} + 3 q^{92} + 2 q^{93} - 50 q^{94} - 33 q^{96} + 7 q^{97} + 15 q^{98}+O(q^{100}) \) 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9 - 11 * q^12 - 4 * q^14 + 17 * q^16 + 2 * q^17 + q^18 - 2 * q^19 + 2 * q^21 + 9 * q^22 - q^23 - 6 * q^24 + 37 * q^26 - 6 * q^27 - 44 * q^28 + 31 * q^29 - 2 * q^31 + 33 * q^32 + 37 * q^34 + 11 * q^36 - 22 * q^37 + 27 * q^38 + 33 * q^41 + 4 * q^42 - 3 * q^43 - 11 * q^44 - 12 * q^46 - 6 * q^47 - 17 * q^48 + 4 * q^49 - 2 * q^51 - 33 * q^52 + 14 * q^53 - q^54 - 30 * q^56 + 2 * q^57 - q^58 - 8 * q^59 + 34 * q^61 + 31 * q^62 - 2 * q^63 + 12 * q^64 - 9 * q^66 + 2 * q^67 + 27 * q^68 + q^69 - 3 * q^71 + 6 * q^72 - 36 * q^73 + 36 * q^74 + 27 * q^76 + 16 * q^77 - 37 * q^78 + 25 * q^79 + 6 * q^81 + 36 * q^82 - 12 * q^83 + 44 * q^84 - 30 * q^86 - 31 * q^87 + 56 * q^88 + 18 * q^89 + 28 * q^91 + 3 * q^92 + 2 * q^93 - 50 * q^94 - 33 * q^96 + 7 * q^97 + 15 * q^98

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