LMFDB - Embedded newform 3850.2.a.bk.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.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:	$30.7424047782$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	3850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} +0.732051 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} +0.732051 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.46410 q^{9} +1.00000 q^{11} -0.732051 q^{12} +0.267949 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.73205 q^{17} +2.46410 q^{18} -4.46410 q^{19} -0.732051 q^{21} -1.00000 q^{22} +1.73205 q^{23} +0.732051 q^{24} -0.267949 q^{26} +4.00000 q^{27} +1.00000 q^{28} -0.464102 q^{29} +2.46410 q^{31} -1.00000 q^{32} -0.732051 q^{33} -4.73205 q^{34} -2.46410 q^{36} -1.46410 q^{37} +4.46410 q^{38} -0.196152 q^{39} -9.46410 q^{41} +0.732051 q^{42} -2.26795 q^{43} +1.00000 q^{44} -1.73205 q^{46} +6.00000 q^{47} -0.732051 q^{48} +1.00000 q^{49} -3.46410 q^{51} +0.267949 q^{52} +4.73205 q^{53} -4.00000 q^{54} -1.00000 q^{56} +3.26795 q^{57} +0.464102 q^{58} -6.92820 q^{59} +6.39230 q^{61} -2.46410 q^{62} -2.46410 q^{63} +1.00000 q^{64} +0.732051 q^{66} +6.73205 q^{67} +4.73205 q^{68} -1.26795 q^{69} -8.66025 q^{71} +2.46410 q^{72} +2.92820 q^{73} +1.46410 q^{74} -4.46410 q^{76} +1.00000 q^{77} +0.196152 q^{78} +7.66025 q^{79} +4.46410 q^{81} +9.46410 q^{82} +3.00000 q^{83} -0.732051 q^{84} +2.26795 q^{86} +0.339746 q^{87} -1.00000 q^{88} -1.73205 q^{89} +0.267949 q^{91} +1.73205 q^{92} -1.80385 q^{93} -6.00000 q^{94} +0.732051 q^{96} +7.19615 q^{97} -1.00000 q^{98} -2.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{16} + 6 q^{17} - 2 q^{18} - 2 q^{19} + 2 q^{21} - 2 q^{22} - 2 q^{24} - 4 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} - 2 q^{31} - 2 q^{32} + 2 q^{33} - 6 q^{34} + 2 q^{36} + 4 q^{37} + 2 q^{38} + 10 q^{39} - 12 q^{41} - 2 q^{42} - 8 q^{43} + 2 q^{44} + 12 q^{47} + 2 q^{48} + 2 q^{49} + 4 q^{52} + 6 q^{53} - 8 q^{54} - 2 q^{56} + 10 q^{57} - 6 q^{58} - 8 q^{61} + 2 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{66} + 10 q^{67} + 6 q^{68} - 6 q^{69} - 2 q^{72} - 8 q^{73} - 4 q^{74} - 2 q^{76} + 2 q^{77} - 10 q^{78} - 2 q^{79} + 2 q^{81} + 12 q^{82} + 6 q^{83} + 2 q^{84} + 8 q^{86} + 18 q^{87} - 2 q^{88} + 4 q^{91} - 14 q^{93} - 12 q^{94} - 2 q^{96} + 4 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 + 2 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^16 + 6 * q^17 - 2 * q^18 - 2 * q^19 + 2 * q^21 - 2 * q^22 - 2 * q^24 - 4 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 - 2 * q^31 - 2 * q^32 + 2 * q^33 - 6 * q^34 + 2 * q^36 + 4 * q^37 + 2 * q^38 + 10 * q^39 - 12 * q^41 - 2 * q^42 - 8 * q^43 + 2 * q^44 + 12 * q^47 + 2 * q^48 + 2 * q^49 + 4 * q^52 + 6 * q^53 - 8 * q^54 - 2 * q^56 + 10 * q^57 - 6 * q^58 - 8 * q^61 + 2 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^66 + 10 * q^67 + 6 * q^68 - 6 * q^69 - 2 * q^72 - 8 * q^73 - 4 * q^74 - 2 * q^76 + 2 * q^77 - 10 * q^78 - 2 * q^79 + 2 * q^81 + 12 * q^82 + 6 * q^83 + 2 * q^84 + 8 * q^86 + 18 * q^87 - 2 * q^88 + 4 * q^91 - 14 * q^93 - 12 * q^94 - 2 * q^96 + 4 * q^97 - 2 * q^98 + 2 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.732051	−0.422650	−0.211325	−	0.977416i	$-0.567778\pi$
$3$	−0.732051	−0.422650	−0.211325	+	0.977416i	$0.567778\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0.732051	0.298858
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.46410	−0.821367
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.732051	−0.211325
$13$	0.267949	0.0743157	0.0371579	−	0.999309i	$-0.488170\pi$
$13$	0.267949	0.0743157	0.0371579	+	0.999309i	$0.488170\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	4.73205	1.14769	0.573845	−	0.818964i	$-0.305451\pi$
$17$	4.73205	1.14769	0.573845	+	0.818964i	$0.305451\pi$
$18$	2.46410	0.580794
$19$	−4.46410	−1.02414	−0.512068	−	0.858945i	$-0.671120\pi$
$19$	−4.46410	−1.02414	−0.512068	+	0.858945i	$0.671120\pi$
$20$	0	0
$21$	−0.732051	−0.159747
$22$	−1.00000	−0.213201
$23$	1.73205	0.361158	0.180579	−	0.983561i	$-0.442203\pi$
$23$	1.73205	0.361158	0.180579	+	0.983561i	$0.442203\pi$
$24$	0.732051	0.149429
$25$	0	0
$26$	−0.267949	−0.0525492
$27$	4.00000	0.769800
$28$	1.00000	0.188982
$29$	−0.464102	−0.0861815	−0.0430908	−	0.999071i	$-0.513720\pi$
$29$	−0.464102	−0.0861815	−0.0430908	+	0.999071i	$0.513720\pi$
$30$	0	0
$31$	2.46410	0.442566	0.221283	−	0.975210i	$-0.428976\pi$
$31$	2.46410	0.442566	0.221283	+	0.975210i	$0.428976\pi$
$32$	−1.00000	−0.176777
$33$	−0.732051	−0.127434
$34$	−4.73205	−0.811540
$35$	0	0
$36$	−2.46410	−0.410684
$37$	−1.46410	−0.240697	−0.120348	−	0.992732i	$-0.538401\pi$
$37$	−1.46410	−0.240697	−0.120348	+	0.992732i	$0.538401\pi$
$38$	4.46410	0.724173
$39$	−0.196152	−0.0314095
$40$	0	0
$41$	−9.46410	−1.47804	−0.739022	−	0.673681i	$-0.764712\pi$
$41$	−9.46410	−1.47804	−0.739022	+	0.673681i	$0.764712\pi$
$42$	0.732051	0.112958
$43$	−2.26795	−0.345859	−0.172930	−	0.984934i	$-0.555323\pi$
$43$	−2.26795	−0.345859	−0.172930	+	0.984934i	$0.555323\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	−1.73205	−0.255377
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	−0.732051	−0.105662
$49$	1.00000	0.142857
$50$	0	0
$51$	−3.46410	−0.485071
$52$	0.267949	0.0371579
$53$	4.73205	0.649997	0.324999	−	0.945715i	$-0.394636\pi$
$53$	4.73205	0.649997	0.324999	+	0.945715i	$0.394636\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	−1.00000	−0.133631
$57$	3.26795	0.432850
$58$	0.464102	0.0609395
$59$	−6.92820	−0.901975	−0.450988	−	0.892530i	$-0.648928\pi$
$59$	−6.92820	−0.901975	−0.450988	+	0.892530i	$0.648928\pi$
$60$	0	0
$61$	6.39230	0.818451	0.409225	−	0.912433i	$-0.365799\pi$
$61$	6.39230	0.818451	0.409225	+	0.912433i	$0.365799\pi$
$62$	−2.46410	−0.312941
$63$	−2.46410	−0.310448
$64$	1.00000	0.125000
$65$	0	0
$66$	0.732051	0.0901092
$67$	6.73205	0.822451	0.411225	−	0.911534i	$-0.365101\pi$
$67$	6.73205	0.822451	0.411225	+	0.911534i	$0.365101\pi$
$68$	4.73205	0.573845
$69$	−1.26795	−0.152643
$70$	0	0
$71$	−8.66025	−1.02778	−0.513892	−	0.857855i	$-0.671797\pi$
$71$	−8.66025	−1.02778	−0.513892	+	0.857855i	$0.671797\pi$
$72$	2.46410	0.290397
$73$	2.92820	0.342720	0.171360	−	0.985208i	$-0.445184\pi$
$73$	2.92820	0.342720	0.171360	+	0.985208i	$0.445184\pi$
$74$	1.46410	0.170198
$75$	0	0
$76$	−4.46410	−0.512068
$77$	1.00000	0.113961
$78$	0.196152	0.0222099
$79$	7.66025	0.861846	0.430923	−	0.902389i	$-0.358188\pi$
$79$	7.66025	0.861846	0.430923	+	0.902389i	$0.358188\pi$
$80$	0	0
$81$	4.46410	0.496011
$82$	9.46410	1.04514
$83$	3.00000	0.329293	0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000	0.329293	0.164646	+	0.986353i	$0.447352\pi$
$84$	−0.732051	−0.0798733
$85$	0	0
$86$	2.26795	0.244559
$87$	0.339746	0.0364246
$88$	−1.00000	−0.106600
$89$	−1.73205	−0.183597	−0.0917985	−	0.995778i	$-0.529262\pi$
$89$	−1.73205	−0.183597	−0.0917985	+	0.995778i	$0.529262\pi$
$90$	0	0
$91$	0.267949	0.0280887
$92$	1.73205	0.180579
$93$	−1.80385	−0.187050
$94$	−6.00000	−0.618853
$95$	0	0
$96$	0.732051	0.0747146
$97$	7.19615	0.730659	0.365329	−	0.930878i	$-0.380956\pi$
$97$	7.19615	0.730659	0.365329	+	0.930878i	$0.380956\pi$
$98$	−1.00000	−0.101015
$99$	−2.46410	−0.247652
$100$	0	0
$101$	11.1962	1.11406	0.557029	−	0.830493i	$-0.311941\pi$
$101$	11.1962	1.11406	0.557029	+	0.830493i	$0.311941\pi$
$102$	3.46410	0.342997
$103$	−7.92820	−0.781189	−0.390595	−	0.920563i	$-0.627731\pi$
$103$	−7.92820	−0.781189	−0.390595	+	0.920563i	$0.627731\pi$
$104$	−0.267949	−0.0262746
$105$	0	0
$106$	−4.73205	−0.459617
$107$	4.26795	0.412598	0.206299	−	0.978489i	$-0.433858\pi$
$107$	4.26795	0.412598	0.206299	+	0.978489i	$0.433858\pi$
$108$	4.00000	0.384900
$109$	−7.00000	−0.670478	−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000	−0.670478	−0.335239	+	0.942133i	$0.608817\pi$
$110$	0	0
$111$	1.07180	0.101730
$112$	1.00000	0.0944911
$113$	−6.92820	−0.651751	−0.325875	−	0.945413i	$-0.605659\pi$
$113$	−6.92820	−0.651751	−0.325875	+	0.945413i	$0.605659\pi$
$114$	−3.26795	−0.306071
$115$	0	0
$116$	−0.464102	−0.0430908
$117$	−0.660254	−0.0610405
$118$	6.92820	0.637793
$119$	4.73205	0.433786
$120$	0	0
$121$	1.00000	0.0909091
$122$	−6.39230	−0.578732
$123$	6.92820	0.624695
$124$	2.46410	0.221283
$125$	0	0
$126$	2.46410	0.219520
$127$	−1.46410	−0.129918	−0.0649590	−	0.997888i	$-0.520692\pi$
$127$	−1.46410	−0.129918	−0.0649590	+	0.997888i	$0.520692\pi$
$128$	−1.00000	−0.0883883
$129$	1.66025	0.146177
$130$	0	0
$131$	6.46410	0.564771	0.282386	−	0.959301i	$-0.408874\pi$
$131$	6.46410	0.564771	0.282386	+	0.959301i	$0.408874\pi$
$132$	−0.732051	−0.0637168
$133$	−4.46410	−0.387087
$134$	−6.73205	−0.581561
$135$	0	0
$136$	−4.73205	−0.405770
$137$	5.53590	0.472964	0.236482	−	0.971636i	$-0.424006\pi$
$137$	5.53590	0.472964	0.236482	+	0.971636i	$0.424006\pi$
$138$	1.26795	0.107935
$139$	−1.00000	−0.0848189	−0.0424094	−	0.999100i	$-0.513503\pi$
$139$	−1.00000	−0.0848189	−0.0424094	+	0.999100i	$0.513503\pi$
$140$	0	0
$141$	−4.39230	−0.369899
$142$	8.66025	0.726752
$143$	0.267949	0.0224070
$144$	−2.46410	−0.205342
$145$	0	0
$146$	−2.92820	−0.242340
$147$	−0.732051	−0.0603785
$148$	−1.46410	−0.120348
$149$	13.8564	1.13516	0.567581	−	0.823318i	$-0.307880\pi$
$149$	13.8564	1.13516	0.567581	+	0.823318i	$0.307880\pi$
$150$	0	0
$151$	−1.80385	−0.146795	−0.0733975	−	0.997303i	$-0.523384\pi$
$151$	−1.80385	−0.146795	−0.0733975	+	0.997303i	$0.523384\pi$
$152$	4.46410	0.362086
$153$	−11.6603	−0.942676
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	−0.196152	−0.0157048
$157$	11.8038	0.942050	0.471025	−	0.882120i	$-0.343884\pi$
$157$	11.8038	0.942050	0.471025	+	0.882120i	$0.343884\pi$
$158$	−7.66025	−0.609417
$159$	−3.46410	−0.274721
$160$	0	0
$161$	1.73205	0.136505
$162$	−4.46410	−0.350733
$163$	12.3923	0.970640	0.485320	−	0.874337i	$-0.338703\pi$
$163$	12.3923	0.970640	0.485320	+	0.874337i	$0.338703\pi$
$164$	−9.46410	−0.739022
$165$	0	0
$166$	−3.00000	−0.232845
$167$	5.66025	0.438004	0.219002	−	0.975724i	$-0.429720\pi$
$167$	5.66025	0.438004	0.219002	+	0.975724i	$0.429720\pi$
$168$	0.732051	0.0564789
$169$	−12.9282	−0.994477
$170$	0	0
$171$	11.0000	0.841191
$172$	−2.26795	−0.172930
$173$	−6.12436	−0.465626	−0.232813	−	0.972522i	$-0.574793\pi$
$173$	−6.12436	−0.465626	−0.232813	+	0.972522i	$0.574793\pi$
$174$	−0.339746	−0.0257561
$175$	0	0
$176$	1.00000	0.0753778
$177$	5.07180	0.381220
$178$	1.73205	0.129823
$179$	−9.12436	−0.681986	−0.340993	−	0.940066i	$-0.610763\pi$
$179$	−9.12436	−0.681986	−0.340993	+	0.940066i	$0.610763\pi$
$180$	0	0
$181$	−6.53590	−0.485810	−0.242905	−	0.970050i	$-0.578100\pi$
$181$	−6.53590	−0.485810	−0.242905	+	0.970050i	$0.578100\pi$
$182$	−0.267949	−0.0198617
$183$	−4.67949	−0.345918
$184$	−1.73205	−0.127688
$185$	0	0
$186$	1.80385	0.132265
$187$	4.73205	0.346042
$188$	6.00000	0.437595
$189$	4.00000	0.290957
$190$	0	0
$191$	25.0526	1.81274	0.906370	−	0.422485i	$-0.138842\pi$
$191$	25.0526	1.81274	0.906370	+	0.422485i	$0.138842\pi$
$192$	−0.732051	−0.0528312
$193$	−15.3205	−1.10279	−0.551397	−	0.834243i	$-0.685905\pi$
$193$	−15.3205	−1.10279	−0.551397	+	0.834243i	$0.685905\pi$
$194$	−7.19615	−0.516654
$195$	0	0
$196$	1.00000	0.0714286
$197$	25.3923	1.80913	0.904563	−	0.426339i	$-0.140197\pi$
$197$	25.3923	1.80913	0.904563	+	0.426339i	$0.140197\pi$
$198$	2.46410	0.175116
$199$	−15.7846	−1.11894	−0.559471	−	0.828850i	$-0.688996\pi$
$199$	−15.7846	−1.11894	−0.559471	+	0.828850i	$0.688996\pi$
$200$	0	0
$201$	−4.92820	−0.347609
$202$	−11.1962	−0.787759
$203$	−0.464102	−0.0325735
$204$	−3.46410	−0.242536
$205$	0	0
$206$	7.92820	0.552384
$207$	−4.26795	−0.296643
$208$	0.267949	0.0185789
$209$	−4.46410	−0.308788
$210$	0	0
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	4.73205	0.324999
$213$	6.33975	0.434392
$214$	−4.26795	−0.291751
$215$	0	0
$216$	−4.00000	−0.272166
$217$	2.46410	0.167274
$218$	7.00000	0.474100
$219$	−2.14359	−0.144851
$220$	0	0
$221$	1.26795	0.0852915
$222$	−1.07180	−0.0719343
$223$	14.0000	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	6.92820	0.460857
$227$	15.9282	1.05719	0.528596	−	0.848874i	$-0.322719\pi$
$227$	15.9282	1.05719	0.528596	+	0.848874i	$0.322719\pi$
$228$	3.26795	0.216425
$229$	3.85641	0.254839	0.127419	−	0.991849i	$-0.459331\pi$
$229$	3.85641	0.254839	0.127419	+	0.991849i	$0.459331\pi$
$230$	0	0
$231$	−0.732051	−0.0481654
$232$	0.464102	0.0304698
$233$	−7.26795	−0.476139	−0.238070	−	0.971248i	$-0.576515\pi$
$233$	−7.26795	−0.476139	−0.238070	+	0.971248i	$0.576515\pi$
$234$	0.660254	0.0431622
$235$	0	0
$236$	−6.92820	−0.450988
$237$	−5.60770	−0.364259
$238$	−4.73205	−0.306733
$239$	22.3923	1.44844	0.724219	−	0.689570i	$-0.242201\pi$
$239$	22.3923	1.44844	0.724219	+	0.689570i	$0.242201\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	−1.00000	−0.0642824
$243$	−15.2679	−0.979439
$244$	6.39230	0.409225
$245$	0	0
$246$	−6.92820	−0.441726
$247$	−1.19615	−0.0761094
$248$	−2.46410	−0.156471
$249$	−2.19615	−0.139176
$250$	0	0
$251$	12.5885	0.794576	0.397288	−	0.917694i	$-0.369951\pi$
$251$	12.5885	0.794576	0.397288	+	0.917694i	$0.369951\pi$
$252$	−2.46410	−0.155224
$253$	1.73205	0.108893
$254$	1.46410	0.0918659
$255$	0	0
$256$	1.00000	0.0625000
$257$	−3.58846	−0.223842	−0.111921	−	0.993717i	$-0.535700\pi$
$257$	−3.58846	−0.223842	−0.111921	+	0.993717i	$0.535700\pi$
$258$	−1.66025	−0.103363
$259$	−1.46410	−0.0909748
$260$	0	0
$261$	1.14359	0.0707867
$262$	−6.46410	−0.399354
$263$	19.2679	1.18811	0.594056	−	0.804423i	$-0.297526\pi$
$263$	19.2679	1.18811	0.594056	+	0.804423i	$0.297526\pi$
$264$	0.732051	0.0450546
$265$	0	0
$266$	4.46410	0.273712
$267$	1.26795	0.0775972
$268$	6.73205	0.411225
$269$	12.5885	0.767532	0.383766	−	0.923430i	$-0.374627\pi$
$269$	12.5885	0.767532	0.383766	+	0.923430i	$0.374627\pi$
$270$	0	0
$271$	2.58846	0.157238	0.0786188	−	0.996905i	$-0.474949\pi$
$271$	2.58846	0.157238	0.0786188	+	0.996905i	$0.474949\pi$
$272$	4.73205	0.286923
$273$	−0.196152	−0.0118717
$274$	−5.53590	−0.334436
$275$	0	0
$276$	−1.26795	−0.0763216
$277$	−25.4641	−1.52999	−0.764995	−	0.644036i	$-0.777258\pi$
$277$	−25.4641	−1.52999	−0.764995	+	0.644036i	$0.777258\pi$
$278$	1.00000	0.0599760
$279$	−6.07180	−0.363509
$280$	0	0
$281$	12.5885	0.750964	0.375482	−	0.926830i	$-0.377477\pi$
$281$	12.5885	0.750964	0.375482	+	0.926830i	$0.377477\pi$
$282$	4.39230	0.261558
$283$	0.143594	0.00853575	0.00426787	−	0.999991i	$-0.498641\pi$
$283$	0.143594	0.00853575	0.00426787	+	0.999991i	$0.498641\pi$
$284$	−8.66025	−0.513892
$285$	0	0
$286$	−0.267949	−0.0158442
$287$	−9.46410	−0.558648
$288$	2.46410	0.145199
$289$	5.39230	0.317194
$290$	0	0
$291$	−5.26795	−0.308813
$292$	2.92820	0.171360
$293$	5.32051	0.310827	0.155414	−	0.987849i	$-0.450329\pi$
$293$	5.32051	0.310827	0.155414	+	0.987849i	$0.450329\pi$
$294$	0.732051	0.0426941
$295$	0	0
$296$	1.46410	0.0850992
$297$	4.00000	0.232104
$298$	−13.8564	−0.802680
$299$	0.464102	0.0268397
$300$	0	0
$301$	−2.26795	−0.130722
$302$	1.80385	0.103800
$303$	−8.19615	−0.470857
$304$	−4.46410	−0.256034
$305$	0	0
$306$	11.6603	0.666572
$307$	−2.14359	−0.122341	−0.0611707	−	0.998127i	$-0.519483\pi$
$307$	−2.14359	−0.122341	−0.0611707	+	0.998127i	$0.519483\pi$
$308$	1.00000	0.0569803
$309$	5.80385	0.330169
$310$	0	0
$311$	32.3205	1.83273	0.916364	−	0.400346i	$-0.131110\pi$
$311$	32.3205	1.83273	0.916364	+	0.400346i	$0.131110\pi$
$312$	0.196152	0.0111049
$313$	−17.8564	−1.00930	−0.504652	−	0.863323i	$-0.668379\pi$
$313$	−17.8564	−1.00930	−0.504652	+	0.863323i	$0.668379\pi$
$314$	−11.8038	−0.666130
$315$	0	0
$316$	7.66025	0.430923
$317$	34.0526	1.91258	0.956291	−	0.292416i	$-0.0944593\pi$
$317$	34.0526	1.91258	0.956291	+	0.292416i	$0.0944593\pi$
$318$	3.46410	0.194257
$319$	−0.464102	−0.0259847
$320$	0	0
$321$	−3.12436	−0.174385
$322$	−1.73205	−0.0965234
$323$	−21.1244	−1.17539
$324$	4.46410	0.248006
$325$	0	0
$326$	−12.3923	−0.686346
$327$	5.12436	0.283378
$328$	9.46410	0.522568
$329$	6.00000	0.330791
$330$	0	0
$331$	22.5359	1.23869	0.619343	−	0.785121i	$-0.287399\pi$
$331$	22.5359	1.23869	0.619343	+	0.785121i	$0.287399\pi$
$332$	3.00000	0.164646
$333$	3.60770	0.197700
$334$	−5.66025	−0.309715
$335$	0	0
$336$	−0.732051	−0.0399366
$337$	−6.19615	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$337$	−6.19615	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$338$	12.9282	0.703202
$339$	5.07180	0.275462
$340$	0	0
$341$	2.46410	0.133439
$342$	−11.0000	−0.594812
$343$	1.00000	0.0539949
$344$	2.26795	0.122280
$345$	0	0
$346$	6.12436	0.329247
$347$	11.3205	0.607717	0.303858	−	0.952717i	$-0.401725\pi$
$347$	11.3205	0.607717	0.303858	+	0.952717i	$0.401725\pi$
$348$	0.339746	0.0182123
$349$	−10.8038	−0.578317	−0.289158	−	0.957281i	$-0.593375\pi$
$349$	−10.8038	−0.578317	−0.289158	+	0.957281i	$0.593375\pi$
$350$	0	0
$351$	1.07180	0.0572083
$352$	−1.00000	−0.0533002
$353$	20.6603	1.09963	0.549817	−	0.835285i	$-0.314697\pi$
$353$	20.6603	1.09963	0.549817	+	0.835285i	$0.314697\pi$
$354$	−5.07180	−0.269563
$355$	0	0
$356$	−1.73205	−0.0917985
$357$	−3.46410	−0.183340
$358$	9.12436	0.482237
$359$	5.07180	0.267679	0.133840	−	0.991003i	$-0.457269\pi$
$359$	5.07180	0.267679	0.133840	+	0.991003i	$0.457269\pi$
$360$	0	0
$361$	0.928203	0.0488528
$362$	6.53590	0.343519
$363$	−0.732051	−0.0384227
$364$	0.267949	0.0140444
$365$	0	0
$366$	4.67949	0.244601
$367$	−10.4641	−0.546222	−0.273111	−	0.961983i	$-0.588053\pi$
$367$	−10.4641	−0.546222	−0.273111	+	0.961983i	$0.588053\pi$
$368$	1.73205	0.0902894
$369$	23.3205	1.21402
$370$	0	0
$371$	4.73205	0.245676
$372$	−1.80385	−0.0935251
$373$	4.78461	0.247738	0.123869	−	0.992299i	$-0.460470\pi$
$373$	4.78461	0.247738	0.123869	+	0.992299i	$0.460470\pi$
$374$	−4.73205	−0.244689
$375$	0	0
$376$	−6.00000	−0.309426
$377$	−0.124356	−0.00640464
$378$	−4.00000	−0.205738
$379$	13.6603	0.701680	0.350840	−	0.936435i	$-0.385896\pi$
$379$	13.6603	0.701680	0.350840	+	0.936435i	$0.385896\pi$
$380$	0	0
$381$	1.07180	0.0549098
$382$	−25.0526	−1.28180
$383$	23.7846	1.21534	0.607668	−	0.794191i	$-0.292105\pi$
$383$	23.7846	1.21534	0.607668	+	0.794191i	$0.292105\pi$
$384$	0.732051	0.0373573
$385$	0	0
$386$	15.3205	0.779793
$387$	5.58846	0.284077
$388$	7.19615	0.365329
$389$	34.0526	1.72653	0.863267	−	0.504748i	$-0.168415\pi$
$389$	34.0526	1.72653	0.863267	+	0.504748i	$0.168415\pi$
$390$	0	0
$391$	8.19615	0.414497
$392$	−1.00000	−0.0505076
$393$	−4.73205	−0.238700
$394$	−25.3923	−1.27925
$395$	0	0
$396$	−2.46410	−0.123826
$397$	18.3923	0.923083	0.461542	−	0.887119i	$-0.347296\pi$
$397$	18.3923	0.923083	0.461542	+	0.887119i	$0.347296\pi$
$398$	15.7846	0.791211
$399$	3.26795	0.163602
$400$	0	0
$401$	−3.00000	−0.149813	−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000	−0.149813	−0.0749064	+	0.997191i	$0.523866\pi$
$402$	4.92820	0.245796
$403$	0.660254	0.0328896
$404$	11.1962	0.557029
$405$	0	0
$406$	0.464102	0.0230330
$407$	−1.46410	−0.0725728
$408$	3.46410	0.171499
$409$	1.41154	0.0697963	0.0348981	−	0.999391i	$-0.488889\pi$
$409$	1.41154	0.0697963	0.0348981	+	0.999391i	$0.488889\pi$
$410$	0	0
$411$	−4.05256	−0.199898
$412$	−7.92820	−0.390595
$413$	−6.92820	−0.340915
$414$	4.26795	0.209758
$415$	0	0
$416$	−0.267949	−0.0131373
$417$	0.732051	0.0358487
$418$	4.46410	0.218346
$419$	−10.3923	−0.507697	−0.253849	−	0.967244i	$-0.581697\pi$
$419$	−10.3923	−0.507697	−0.253849	+	0.967244i	$0.581697\pi$
$420$	0	0
$421$	1.41154	0.0687944	0.0343972	−	0.999408i	$-0.489049\pi$
$421$	1.41154	0.0687944	0.0343972	+	0.999408i	$0.489049\pi$
$422$	−8.00000	−0.389434
$423$	−14.7846	−0.718852
$424$	−4.73205	−0.229809
$425$	0	0
$426$	−6.33975	−0.307162
$427$	6.39230	0.309345
$428$	4.26795	0.206299
$429$	−0.196152	−0.00947033
$430$	0	0
$431$	−2.53590	−0.122150	−0.0610750	−	0.998133i	$-0.519453\pi$
$431$	−2.53590	−0.122150	−0.0610750	+	0.998133i	$0.519453\pi$
$432$	4.00000	0.192450
$433$	33.0526	1.58840	0.794202	−	0.607653i	$-0.207889\pi$
$433$	33.0526	1.58840	0.794202	+	0.607653i	$0.207889\pi$
$434$	−2.46410	−0.118281
$435$	0	0
$436$	−7.00000	−0.335239
$437$	−7.73205	−0.369874
$438$	2.14359	0.102425
$439$	0.392305	0.0187237	0.00936184	−	0.999956i	$-0.497020\pi$
$439$	0.392305	0.0187237	0.00936184	+	0.999956i	$0.497020\pi$
$440$	0	0
$441$	−2.46410	−0.117338
$442$	−1.26795	−0.0603102
$443$	20.7846	0.987507	0.493753	−	0.869602i	$-0.335625\pi$
$443$	20.7846	0.987507	0.493753	+	0.869602i	$0.335625\pi$
$444$	1.07180	0.0508652
$445$	0	0
$446$	−14.0000	−0.662919
$447$	−10.1436	−0.479776
$448$	1.00000	0.0472456
$449$	39.9282	1.88433	0.942164	−	0.335152i	$-0.108788\pi$
$449$	39.9282	1.88433	0.942164	+	0.335152i	$0.108788\pi$
$450$	0	0
$451$	−9.46410	−0.445647
$452$	−6.92820	−0.325875
$453$	1.32051	0.0620429
$454$	−15.9282	−0.747548
$455$	0	0
$456$	−3.26795	−0.153036
$457$	16.1962	0.757624	0.378812	−	0.925474i	$-0.376333\pi$
$457$	16.1962	0.757624	0.378812	+	0.925474i	$0.376333\pi$
$458$	−3.85641	−0.180198
$459$	18.9282	0.883493
$460$	0	0
$461$	−18.9282	−0.881574	−0.440787	−	0.897612i	$-0.645301\pi$
$461$	−18.9282	−0.881574	−0.440787	+	0.897612i	$0.645301\pi$
$462$	0.732051	0.0340581
$463$	11.5885	0.538561	0.269281	−	0.963062i	$-0.413214\pi$
$463$	11.5885	0.538561	0.269281	+	0.963062i	$0.413214\pi$
$464$	−0.464102	−0.0215454
$465$	0	0
$466$	7.26795	0.336681
$467$	24.9282	1.15354	0.576770	−	0.816907i	$-0.304313\pi$
$467$	24.9282	1.15354	0.576770	+	0.816907i	$0.304313\pi$
$468$	−0.660254	−0.0305203
$469$	6.73205	0.310857
$470$	0	0
$471$	−8.64102	−0.398157
$472$	6.92820	0.318896
$473$	−2.26795	−0.104280
$474$	5.60770	0.257570
$475$	0	0
$476$	4.73205	0.216893
$477$	−11.6603	−0.533886
$478$	−22.3923	−1.02420
$479$	−24.2487	−1.10795	−0.553976	−	0.832533i	$-0.686890\pi$
$479$	−24.2487	−1.10795	−0.553976	+	0.832533i	$0.686890\pi$
$480$	0	0
$481$	−0.392305	−0.0178876
$482$	−2.00000	−0.0910975
$483$	−1.26795	−0.0576937
$484$	1.00000	0.0454545
$485$	0	0
$486$	15.2679	0.692568
$487$	−27.4449	−1.24365	−0.621823	−	0.783158i	$-0.713608\pi$
$487$	−27.4449	−1.24365	−0.621823	+	0.783158i	$0.713608\pi$
$488$	−6.39230	−0.289366
$489$	−9.07180	−0.410241
$490$	0	0
$491$	−30.1244	−1.35949	−0.679747	−	0.733447i	$-0.737910\pi$
$491$	−30.1244	−1.35949	−0.679747	+	0.733447i	$0.737910\pi$
$492$	6.92820	0.312348
$493$	−2.19615	−0.0989097
$494$	1.19615	0.0538174
$495$	0	0
$496$	2.46410	0.110641
$497$	−8.66025	−0.388465
$498$	2.19615	0.0984119
$499$	30.3923	1.36055	0.680273	−	0.732959i	$-0.261861\pi$
$499$	30.3923	1.36055	0.680273	+	0.732959i	$0.261861\pi$
$500$	0	0
$501$	−4.14359	−0.185122
$502$	−12.5885	−0.561850
$503$	0.928203	0.0413865	0.0206933	−	0.999786i	$-0.493413\pi$
$503$	0.928203	0.0413865	0.0206933	+	0.999786i	$0.493413\pi$
$504$	2.46410	0.109760
$505$	0	0
$506$	−1.73205	−0.0769991
$507$	9.46410	0.420316
$508$	−1.46410	−0.0649590
$509$	−12.5885	−0.557974	−0.278987	−	0.960295i	$-0.589999\pi$
$509$	−12.5885	−0.557974	−0.278987	+	0.960295i	$0.589999\pi$
$510$	0	0
$511$	2.92820	0.129536
$512$	−1.00000	−0.0441942
$513$	−17.8564	−0.788380
$514$	3.58846	0.158280
$515$	0	0
$516$	1.66025	0.0730886
$517$	6.00000	0.263880
$518$	1.46410	0.0643289
$519$	4.48334	0.196797
$520$	0	0
$521$	−21.5885	−0.945807	−0.472904	−	0.881114i	$-0.656794\pi$
$521$	−21.5885	−0.945807	−0.472904	+	0.881114i	$0.656794\pi$
$522$	−1.14359	−0.0500537
$523$	−25.9282	−1.13376	−0.566881	−	0.823800i	$-0.691850\pi$
$523$	−25.9282	−1.13376	−0.566881	+	0.823800i	$0.691850\pi$
$524$	6.46410	0.282386
$525$	0	0
$526$	−19.2679	−0.840123
$527$	11.6603	0.507929
$528$	−0.732051	−0.0318584
$529$	−20.0000	−0.869565
$530$	0	0
$531$	17.0718	0.740853
$532$	−4.46410	−0.193543
$533$	−2.53590	−0.109842
$534$	−1.26795	−0.0548695
$535$	0	0
$536$	−6.73205	−0.290780
$537$	6.67949	0.288241
$538$	−12.5885	−0.542727
$539$	1.00000	0.0430730
$540$	0	0
$541$	−12.3205	−0.529700	−0.264850	−	0.964290i	$-0.585322\pi$
$541$	−12.3205	−0.529700	−0.264850	+	0.964290i	$0.585322\pi$
$542$	−2.58846	−0.111184
$543$	4.78461	0.205327
$544$	−4.73205	−0.202885
$545$	0	0
$546$	0.196152	0.00839455
$547$	−28.8038	−1.23156	−0.615782	−	0.787917i	$-0.711160\pi$
$547$	−28.8038	−1.23156	−0.615782	+	0.787917i	$0.711160\pi$
$548$	5.53590	0.236482
$549$	−15.7513	−0.672249
$550$	0	0
$551$	2.07180	0.0882615
$552$	1.26795	0.0539675
$553$	7.66025	0.325747
$554$	25.4641	1.08187
$555$	0	0
$556$	−1.00000	−0.0424094
$557$	−18.7128	−0.792887	−0.396444	−	0.918059i	$-0.629756\pi$
$557$	−18.7128	−0.792887	−0.396444	+	0.918059i	$0.629756\pi$
$558$	6.07180	0.257040
$559$	−0.607695	−0.0257028
$560$	0	0
$561$	−3.46410	−0.146254
$562$	−12.5885	−0.531012
$563$	−2.78461	−0.117357	−0.0586787	−	0.998277i	$-0.518689\pi$
$563$	−2.78461	−0.117357	−0.0586787	+	0.998277i	$0.518689\pi$
$564$	−4.39230	−0.184949
$565$	0	0
$566$	−0.143594	−0.00603569
$567$	4.46410	0.187475
$568$	8.66025	0.363376
$569$	15.8038	0.662532	0.331266	−	0.943537i	$-0.392524\pi$
$569$	15.8038	0.662532	0.331266	+	0.943537i	$0.392524\pi$
$570$	0	0
$571$	23.5885	0.987146	0.493573	−	0.869704i	$-0.335691\pi$
$571$	23.5885	0.987146	0.493573	+	0.869704i	$0.335691\pi$
$572$	0.267949	0.0112035
$573$	−18.3397	−0.766154
$574$	9.46410	0.395024
$575$	0	0
$576$	−2.46410	−0.102671
$577$	20.2487	0.842965	0.421482	−	0.906837i	$-0.361510\pi$
$577$	20.2487	0.842965	0.421482	+	0.906837i	$0.361510\pi$
$578$	−5.39230	−0.224290
$579$	11.2154	0.466096
$580$	0	0
$581$	3.00000	0.124461
$582$	5.26795	0.218364
$583$	4.73205	0.195982
$584$	−2.92820	−0.121170
$585$	0	0
$586$	−5.32051	−0.219788
$587$	−19.6077	−0.809296	−0.404648	−	0.914472i	$-0.632606\pi$
$587$	−19.6077	−0.809296	−0.404648	+	0.914472i	$0.632606\pi$
$588$	−0.732051	−0.0301893
$589$	−11.0000	−0.453247
$590$	0	0
$591$	−18.5885	−0.764627
$592$	−1.46410	−0.0601742
$593$	−31.5167	−1.29423	−0.647117	−	0.762391i	$-0.724026\pi$
$593$	−31.5167	−1.29423	−0.647117	+	0.762391i	$0.724026\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	13.8564	0.567581
$597$	11.5551	0.472920
$598$	−0.464102	−0.0189785
$599$	−0.679492	−0.0277633	−0.0138816	−	0.999904i	$-0.504419\pi$
$599$	−0.679492	−0.0277633	−0.0138816	+	0.999904i	$0.504419\pi$
$600$	0	0
$601$	−41.8564	−1.70736	−0.853679	−	0.520799i	$-0.825634\pi$
$601$	−41.8564	−1.70736	−0.853679	+	0.520799i	$0.825634\pi$
$602$	2.26795	0.0924347
$603$	−16.5885	−0.675534
$604$	−1.80385	−0.0733975
$605$	0	0
$606$	8.19615	0.332946
$607$	−42.7846	−1.73657	−0.868287	−	0.496062i	$-0.834779\pi$
$607$	−42.7846	−1.73657	−0.868287	+	0.496062i	$0.834779\pi$
$608$	4.46410	0.181043
$609$	0.339746	0.0137672
$610$	0	0
$611$	1.60770	0.0650404
$612$	−11.6603	−0.471338
$613$	24.3923	0.985196	0.492598	−	0.870257i	$-0.336047\pi$
$613$	24.3923	0.985196	0.492598	+	0.870257i	$0.336047\pi$
$614$	2.14359	0.0865084
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	−8.32051	−0.334971	−0.167486	−	0.985875i	$-0.553565\pi$
$617$	−8.32051	−0.334971	−0.167486	+	0.985875i	$0.553565\pi$
$618$	−5.80385	−0.233465
$619$	−30.4449	−1.22368	−0.611841	−	0.790981i	$-0.709571\pi$
$619$	−30.4449	−1.22368	−0.611841	+	0.790981i	$0.709571\pi$
$620$	0	0
$621$	6.92820	0.278019
$622$	−32.3205	−1.29593
$623$	−1.73205	−0.0693932
$624$	−0.196152	−0.00785238
$625$	0	0
$626$	17.8564	0.713686
$627$	3.26795	0.130509
$628$	11.8038	0.471025
$629$	−6.92820	−0.276246
$630$	0	0
$631$	27.1769	1.08190	0.540948	−	0.841056i	$-0.318066\pi$
$631$	27.1769	1.08190	0.540948	+	0.841056i	$0.318066\pi$
$632$	−7.66025	−0.304709
$633$	−5.85641	−0.232771
$634$	−34.0526	−1.35240
$635$	0	0
$636$	−3.46410	−0.137361
$637$	0.267949	0.0106165
$638$	0.464102	0.0183740
$639$	21.3397	0.844187
$640$	0	0
$641$	12.7128	0.502126	0.251063	−	0.967971i	$-0.419220\pi$
$641$	12.7128	0.502126	0.251063	+	0.967971i	$0.419220\pi$
$642$	3.12436	0.123308
$643$	23.1244	0.911936	0.455968	−	0.889996i	$-0.349293\pi$
$643$	23.1244	0.911936	0.455968	+	0.889996i	$0.349293\pi$
$644$	1.73205	0.0682524
$645$	0	0
$646$	21.1244	0.831127
$647$	−6.00000	−0.235884	−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000	−0.235884	−0.117942	+	0.993020i	$0.537630\pi$
$648$	−4.46410	−0.175366
$649$	−6.92820	−0.271956
$650$	0	0
$651$	−1.80385	−0.0706984
$652$	12.3923	0.485320
$653$	27.3731	1.07119	0.535595	−	0.844475i	$-0.320087\pi$
$653$	27.3731	1.07119	0.535595	+	0.844475i	$0.320087\pi$
$654$	−5.12436	−0.200378
$655$	0	0
$656$	−9.46410	−0.369511
$657$	−7.21539	−0.281499
$658$	−6.00000	−0.233904
$659$	24.1244	0.939751	0.469876	−	0.882733i	$-0.344299\pi$
$659$	24.1244	0.939751	0.469876	+	0.882733i	$0.344299\pi$
$660$	0	0
$661$	−3.66025	−0.142367	−0.0711837	−	0.997463i	$-0.522678\pi$
$661$	−3.66025	−0.142367	−0.0711837	+	0.997463i	$0.522678\pi$
$662$	−22.5359	−0.875883
$663$	−0.928203	−0.0360484
$664$	−3.00000	−0.116423
$665$	0	0
$666$	−3.60770	−0.139795
$667$	−0.803848	−0.0311251
$668$	5.66025	0.219002
$669$	−10.2487	−0.396238
$670$	0	0
$671$	6.39230	0.246772
$672$	0.732051	0.0282395
$673$	−26.6410	−1.02694	−0.513468	−	0.858109i	$-0.671639\pi$
$673$	−26.6410	−1.02694	−0.513468	+	0.858109i	$0.671639\pi$
$674$	6.19615	0.238667
$675$	0	0
$676$	−12.9282	−0.497239
$677$	9.33975	0.358956	0.179478	−	0.983762i	$-0.442559\pi$
$677$	9.33975	0.358956	0.179478	+	0.983762i	$0.442559\pi$
$678$	−5.07180	−0.194781
$679$	7.19615	0.276163
$680$	0	0
$681$	−11.6603	−0.446822
$682$	−2.46410	−0.0943553
$683$	21.1244	0.808301	0.404151	−	0.914693i	$-0.367567\pi$
$683$	21.1244	0.808301	0.404151	+	0.914693i	$0.367567\pi$
$684$	11.0000	0.420596
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	−2.82309	−0.107707
$688$	−2.26795	−0.0864648
$689$	1.26795	0.0483050
$690$	0	0
$691$	50.2487	1.91155	0.955776	−	0.294097i	$-0.0950189\pi$
$691$	50.2487	1.91155	0.955776	+	0.294097i	$0.0950189\pi$
$692$	−6.12436	−0.232813
$693$	−2.46410	−0.0936035
$694$	−11.3205	−0.429721
$695$	0	0
$696$	−0.339746	−0.0128780
$697$	−44.7846	−1.69634
$698$	10.8038	0.408932
$699$	5.32051	0.201240
$700$	0	0
$701$	−39.0000	−1.47301	−0.736505	−	0.676432i	$-0.763525\pi$
$701$	−39.0000	−1.47301	−0.736505	+	0.676432i	$0.763525\pi$
$702$	−1.07180	−0.0404524
$703$	6.53590	0.246506
$704$	1.00000	0.0376889
$705$	0	0
$706$	−20.6603	−0.777559
$707$	11.1962	0.421075
$708$	5.07180	0.190610
$709$	12.9808	0.487503	0.243751	−	0.969838i	$-0.421622\pi$
$709$	12.9808	0.487503	0.243751	+	0.969838i	$0.421622\pi$
$710$	0	0
$711$	−18.8756	−0.707892
$712$	1.73205	0.0649113
$713$	4.26795	0.159836
$714$	3.46410	0.129641
$715$	0	0
$716$	−9.12436	−0.340993
$717$	−16.3923	−0.612182
$718$	−5.07180	−0.189278
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	0	0
$721$	−7.92820	−0.295262
$722$	−0.928203	−0.0345441
$723$	−1.46410	−0.0544505
$724$	−6.53590	−0.242905
$725$	0	0
$726$	0.732051	0.0271690
$727$	−40.7128	−1.50995	−0.754977	−	0.655751i	$-0.772352\pi$
$727$	−40.7128	−1.50995	−0.754977	+	0.655751i	$0.772352\pi$
$728$	−0.267949	−0.00993086
$729$	−2.21539	−0.0820515
$730$	0	0
$731$	−10.7321	−0.396939
$732$	−4.67949	−0.172959
$733$	−39.1962	−1.44774	−0.723871	−	0.689935i	$-0.757639\pi$
$733$	−39.1962	−1.44774	−0.723871	+	0.689935i	$0.757639\pi$
$734$	10.4641	0.386237
$735$	0	0
$736$	−1.73205	−0.0638442
$737$	6.73205	0.247978
$738$	−23.3205	−0.858440
$739$	29.4641	1.08385	0.541927	−	0.840425i	$-0.317695\pi$
$739$	29.4641	1.08385	0.541927	+	0.840425i	$0.317695\pi$
$740$	0	0
$741$	0.875644	0.0321676
$742$	−4.73205	−0.173719
$743$	−1.94744	−0.0714447	−0.0357223	−	0.999362i	$-0.511373\pi$
$743$	−1.94744	−0.0714447	−0.0357223	+	0.999362i	$0.511373\pi$
$744$	1.80385	0.0661323
$745$	0	0
$746$	−4.78461	−0.175177
$747$	−7.39230	−0.270470
$748$	4.73205	0.173021
$749$	4.26795	0.155947
$750$	0	0
$751$	16.9090	0.617017	0.308508	−	0.951222i	$-0.400170\pi$
$751$	16.9090	0.617017	0.308508	+	0.951222i	$0.400170\pi$
$752$	6.00000	0.218797
$753$	−9.21539	−0.335827
$754$	0.124356	0.00452877
$755$	0	0
$756$	4.00000	0.145479
$757$	−24.7846	−0.900812	−0.450406	−	0.892824i	$-0.648721\pi$
$757$	−24.7846	−0.900812	−0.450406	+	0.892824i	$0.648721\pi$
$758$	−13.6603	−0.496163
$759$	−1.26795	−0.0460236
$760$	0	0
$761$	25.5167	0.924978	0.462489	−	0.886625i	$-0.346956\pi$
$761$	25.5167	0.924978	0.462489	+	0.886625i	$0.346956\pi$
$762$	−1.07180	−0.0388271
$763$	−7.00000	−0.253417
$764$	25.0526	0.906370
$765$	0	0
$766$	−23.7846	−0.859373
$767$	−1.85641	−0.0670310
$768$	−0.732051	−0.0264156
$769$	−39.9090	−1.43915	−0.719577	−	0.694413i	$-0.755664\pi$
$769$	−39.9090	−1.43915	−0.719577	+	0.694413i	$0.755664\pi$
$770$	0	0
$771$	2.62693	0.0946067
$772$	−15.3205	−0.551397
$773$	12.0000	0.431610	0.215805	−	0.976436i	$-0.430762\pi$
$773$	12.0000	0.431610	0.215805	+	0.976436i	$0.430762\pi$
$774$	−5.58846	−0.200873
$775$	0	0
$776$	−7.19615	−0.258327
$777$	1.07180	0.0384505
$778$	−34.0526	−1.22084
$779$	42.2487	1.51372
$780$	0	0
$781$	−8.66025	−0.309888
$782$	−8.19615	−0.293094
$783$	−1.85641	−0.0663426
$784$	1.00000	0.0357143
$785$	0	0
$786$	4.73205	0.168787
$787$	34.7846	1.23994	0.619969	−	0.784627i	$-0.287145\pi$
$787$	34.7846	1.23994	0.619969	+	0.784627i	$0.287145\pi$
$788$	25.3923	0.904563
$789$	−14.1051	−0.502155
$790$	0	0
$791$	−6.92820	−0.246339
$792$	2.46410	0.0875580
$793$	1.71281	0.0608238
$794$	−18.3923	−0.652718
$795$	0	0
$796$	−15.7846	−0.559471
$797$	−35.6603	−1.26315	−0.631576	−	0.775314i	$-0.717591\pi$
$797$	−35.6603	−1.26315	−0.631576	+	0.775314i	$0.717591\pi$
$798$	−3.26795	−0.115684
$799$	28.3923	1.00445
$800$	0	0
$801$	4.26795	0.150801
$802$	3.00000	0.105934
$803$	2.92820	0.103334
$804$	−4.92820	−0.173804
$805$	0	0
$806$	−0.660254	−0.0232565
$807$	−9.21539	−0.324397
$808$	−11.1962	−0.393879
$809$	−0.339746	−0.0119448	−0.00597242	−	0.999982i	$-0.501901\pi$
$809$	−0.339746	−0.0119448	−0.00597242	+	0.999982i	$0.501901\pi$
$810$	0	0
$811$	−18.7846	−0.659617	−0.329808	−	0.944048i	$-0.606984\pi$
$811$	−18.7846	−0.659617	−0.329808	+	0.944048i	$0.606984\pi$
$812$	−0.464102	−0.0162868
$813$	−1.89488	−0.0664564
$814$	1.46410	0.0513167
$815$	0	0
$816$	−3.46410	−0.121268
$817$	10.1244	0.354206
$818$	−1.41154	−0.0493534
$819$	−0.660254	−0.0230711
$820$	0	0
$821$	−51.2487	−1.78859	−0.894296	−	0.447476i	$-0.852323\pi$
$821$	−51.2487	−1.78859	−0.894296	+	0.447476i	$0.852323\pi$
$822$	4.05256	0.141349
$823$	28.7846	1.00337	0.501684	−	0.865051i	$-0.332714\pi$
$823$	28.7846	1.00337	0.501684	+	0.865051i	$0.332714\pi$
$824$	7.92820	0.276192
$825$	0	0
$826$	6.92820	0.241063
$827$	12.8038	0.445233	0.222617	−	0.974906i	$-0.428540\pi$
$827$	12.8038	0.445233	0.222617	+	0.974906i	$0.428540\pi$
$828$	−4.26795	−0.148321
$829$	−28.9282	−1.00472	−0.502359	−	0.864659i	$-0.667534\pi$
$829$	−28.9282	−1.00472	−0.502359	+	0.864659i	$0.667534\pi$
$830$	0	0
$831$	18.6410	0.646650
$832$	0.267949	0.00928947
$833$	4.73205	0.163956
$834$	−0.732051	−0.0253488
$835$	0	0
$836$	−4.46410	−0.154394
$837$	9.85641	0.340687
$838$	10.3923	0.358996
$839$	−50.7846	−1.75328	−0.876640	−	0.481147i	$-0.840220\pi$
$839$	−50.7846	−1.75328	−0.876640	+	0.481147i	$0.840220\pi$
$840$	0	0
$841$	−28.7846	−0.992573
$842$	−1.41154	−0.0486450
$843$	−9.21539	−0.317395
$844$	8.00000	0.275371
$845$	0	0
$846$	14.7846	0.508305
$847$	1.00000	0.0343604
$848$	4.73205	0.162499
$849$	−0.105118	−0.00360763
$850$	0	0
$851$	−2.53590	−0.0869295
$852$	6.33975	0.217196
$853$	8.24871	0.282430	0.141215	−	0.989979i	$-0.454899\pi$
$853$	8.24871	0.282430	0.141215	+	0.989979i	$0.454899\pi$
$854$	−6.39230	−0.218740
$855$	0	0
$856$	−4.26795	−0.145876
$857$	26.1962	0.894844	0.447422	−	0.894323i	$-0.352342\pi$
$857$	26.1962	0.894844	0.447422	+	0.894323i	$0.352342\pi$
$858$	0.196152	0.00669653
$859$	5.80385	0.198025	0.0990124	−	0.995086i	$-0.468432\pi$
$859$	5.80385	0.198025	0.0990124	+	0.995086i	$0.468432\pi$
$860$	0	0
$861$	6.92820	0.236113
$862$	2.53590	0.0863730
$863$	12.8038	0.435848	0.217924	−	0.975966i	$-0.430072\pi$
$863$	12.8038	0.435848	0.217924	+	0.975966i	$0.430072\pi$
$864$	−4.00000	−0.136083
$865$	0	0
$866$	−33.0526	−1.12317
$867$	−3.94744	−0.134062
$868$	2.46410	0.0836371
$869$	7.66025	0.259856
$870$	0	0
$871$	1.80385	0.0611210
$872$	7.00000	0.237050
$873$	−17.7321	−0.600139
$874$	7.73205	0.261541
$875$	0	0
$876$	−2.14359	−0.0724253
$877$	−7.00000	−0.236373	−0.118187	−	0.992991i	$-0.537708\pi$
$877$	−7.00000	−0.236373	−0.118187	+	0.992991i	$0.537708\pi$
$878$	−0.392305	−0.0132396
$879$	−3.89488	−0.131371
$880$	0	0
$881$	−46.5167	−1.56719	−0.783593	−	0.621274i	$-0.786615\pi$
$881$	−46.5167	−1.56719	−0.783593	+	0.621274i	$0.786615\pi$
$882$	2.46410	0.0829706
$883$	0.392305	0.0132021	0.00660105	−	0.999978i	$-0.497899\pi$
$883$	0.392305	0.0132021	0.00660105	+	0.999978i	$0.497899\pi$
$884$	1.26795	0.0426457
$885$	0	0
$886$	−20.7846	−0.698273
$887$	−18.0000	−0.604381	−0.302190	−	0.953248i	$-0.597718\pi$
$887$	−18.0000	−0.604381	−0.302190	+	0.953248i	$0.597718\pi$
$888$	−1.07180	−0.0359671
$889$	−1.46410	−0.0491044
$890$	0	0
$891$	4.46410	0.149553
$892$	14.0000	0.468755
$893$	−26.7846	−0.896313
$894$	10.1436	0.339253
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	−0.339746	−0.0113438
$898$	−39.9282	−1.33242
$899$	−1.14359	−0.0381410
$900$	0	0
$901$	22.3923	0.745996
$902$	9.46410	0.315120
$903$	1.66025	0.0552498
$904$	6.92820	0.230429
$905$	0	0
$906$	−1.32051	−0.0438709
$907$	−45.6603	−1.51612	−0.758062	−	0.652183i	$-0.773854\pi$
$907$	−45.6603	−1.51612	−0.758062	+	0.652183i	$0.773854\pi$
$908$	15.9282	0.528596
$909$	−27.5885	−0.915051
$910$	0	0
$911$	33.0333	1.09444	0.547221	−	0.836988i	$-0.315686\pi$
$911$	33.0333	1.09444	0.547221	+	0.836988i	$0.315686\pi$
$912$	3.26795	0.108213
$913$	3.00000	0.0992855
$914$	−16.1962	−0.535721
$915$	0	0
$916$	3.85641	0.127419
$917$	6.46410	0.213463
$918$	−18.9282	−0.624724
$919$	28.7846	0.949517	0.474758	−	0.880116i	$-0.342535\pi$
$919$	28.7846	0.949517	0.474758	+	0.880116i	$0.342535\pi$
$920$	0	0
$921$	1.56922	0.0517075
$922$	18.9282	0.623367
$923$	−2.32051	−0.0763805
$924$	−0.732051	−0.0240827
$925$	0	0
$926$	−11.5885	−0.380820
$927$	19.5359	0.641643
$928$	0.464102	0.0152349
$929$	−19.7321	−0.647388	−0.323694	−	0.946162i	$-0.604925\pi$
$929$	−19.7321	−0.647388	−0.323694	+	0.946162i	$0.604925\pi$
$930$	0	0
$931$	−4.46410	−0.146305
$932$	−7.26795	−0.238070
$933$	−23.6603	−0.774602
$934$	−24.9282	−0.815676
$935$	0	0
$936$	0.660254	0.0215811
$937$	−52.5885	−1.71799	−0.858995	−	0.511984i	$-0.828911\pi$
$937$	−52.5885	−1.71799	−0.858995	+	0.511984i	$0.828911\pi$
$938$	−6.73205	−0.219809
$939$	13.0718	0.426582
$940$	0	0
$941$	−43.1769	−1.40753	−0.703764	−	0.710434i	$-0.748499\pi$
$941$	−43.1769	−1.40753	−0.703764	+	0.710434i	$0.748499\pi$
$942$	8.64102	0.281540
$943$	−16.3923	−0.533807
$944$	−6.92820	−0.225494
$945$	0	0
$946$	2.26795	0.0737374
$947$	−20.1962	−0.656287	−0.328143	−	0.944628i	$-0.606423\pi$
$947$	−20.1962	−0.656287	−0.328143	+	0.944628i	$0.606423\pi$
$948$	−5.60770	−0.182129
$949$	0.784610	0.0254695
$950$	0	0
$951$	−24.9282	−0.808352
$952$	−4.73205	−0.153367
$953$	−43.2679	−1.40159	−0.700793	−	0.713365i	$-0.747170\pi$
$953$	−43.2679	−1.40159	−0.700793	+	0.713365i	$0.747170\pi$
$954$	11.6603	0.377515
$955$	0	0
$956$	22.3923	0.724219
$957$	0.339746	0.0109824
$958$	24.2487	0.783440
$959$	5.53590	0.178763
$960$	0	0
$961$	−24.9282	−0.804136
$962$	0.392305	0.0126484
$963$	−10.5167	−0.338895
$964$	2.00000	0.0644157
$965$	0	0
$966$	1.26795	0.0407956
$967$	43.9090	1.41202	0.706009	−	0.708203i	$-0.250494\pi$
$967$	43.9090	1.41202	0.706009	+	0.708203i	$0.250494\pi$
$968$	−1.00000	−0.0321412
$969$	15.4641	0.496779
$970$	0	0
$971$	−52.6410	−1.68933	−0.844665	−	0.535295i	$-0.820201\pi$
$971$	−52.6410	−1.68933	−0.844665	+	0.535295i	$0.820201\pi$
$972$	−15.2679	−0.489720
$973$	−1.00000	−0.0320585
$974$	27.4449	0.879390
$975$	0	0
$976$	6.39230	0.204613
$977$	−30.2487	−0.967742	−0.483871	−	0.875139i	$-0.660770\pi$
$977$	−30.2487	−0.967742	−0.483871	+	0.875139i	$0.660770\pi$
$978$	9.07180	0.290084
$979$	−1.73205	−0.0553566
$980$	0	0
$981$	17.2487	0.550709
$982$	30.1244	0.961307
$983$	27.0000	0.861166	0.430583	−	0.902551i	$-0.358308\pi$
$983$	27.0000	0.861166	0.430583	+	0.902551i	$0.358308\pi$
$984$	−6.92820	−0.220863
$985$	0	0
$986$	2.19615	0.0699397
$987$	−4.39230	−0.139809
$988$	−1.19615	−0.0380547
$989$	−3.92820	−0.124910
$990$	0	0
$991$	−17.8564	−0.567227	−0.283614	−	0.958939i	$-0.591533\pi$
$991$	−17.8564	−0.567227	−0.283614	+	0.958939i	$0.591533\pi$
$992$	−2.46410	−0.0782353
$993$	−16.4974	−0.523530
$994$	8.66025	0.274687
$995$	0	0
$996$	−2.19615	−0.0695878
$997$	−20.1436	−0.637954	−0.318977	−	0.947762i	$-0.603339\pi$
$997$	−20.1436	−0.637954	−0.318977	+	0.947762i	$0.603339\pi$
$998$	−30.3923	−0.962052
$999$	−5.85641	−0.185289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.bk.1.1	✓	2
5.2	odd	4		3850.2.c.r.1849.2		4
5.3	odd	4		3850.2.c.r.1849.3		4
5.4	even	2		3850.2.a.bl.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3850.2.a.bk.1.1	✓	2	1.1	even	1	trivial
3850.2.a.bl.1.2	yes	2	5.4	even	2
3850.2.c.r.1849.2		4	5.2	odd	4
3850.2.c.r.1849.3		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} +0.732051 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} +0.732051 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.46410 q^{9} +1.00000 q^{11} -0.732051 q^{12} +0.267949 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.73205 q^{17} +2.46410 q^{18} -4.46410 q^{19} -0.732051 q^{21} -1.00000 q^{22} +1.73205 q^{23} +0.732051 q^{24} -0.267949 q^{26} +4.00000 q^{27} +1.00000 q^{28} -0.464102 q^{29} +2.46410 q^{31} -1.00000 q^{32} -0.732051 q^{33} -4.73205 q^{34} -2.46410 q^{36} -1.46410 q^{37} +4.46410 q^{38} -0.196152 q^{39} -9.46410 q^{41} +0.732051 q^{42} -2.26795 q^{43} +1.00000 q^{44} -1.73205 q^{46} +6.00000 q^{47} -0.732051 q^{48} +1.00000 q^{49} -3.46410 q^{51} +0.267949 q^{52} +4.73205 q^{53} -4.00000 q^{54} -1.00000 q^{56} +3.26795 q^{57} +0.464102 q^{58} -6.92820 q^{59} +6.39230 q^{61} -2.46410 q^{62} -2.46410 q^{63} +1.00000 q^{64} +0.732051 q^{66} +6.73205 q^{67} +4.73205 q^{68} -1.26795 q^{69} -8.66025 q^{71} +2.46410 q^{72} +2.92820 q^{73} +1.46410 q^{74} -4.46410 q^{76} +1.00000 q^{77} +0.196152 q^{78} +7.66025 q^{79} +4.46410 q^{81} +9.46410 q^{82} +3.00000 q^{83} -0.732051 q^{84} +2.26795 q^{86} +0.339746 q^{87} -1.00000 q^{88} -1.73205 q^{89} +0.267949 q^{91} +1.73205 q^{92} -1.80385 q^{93} -6.00000 q^{94} +0.732051 q^{96} +7.19615 q^{97} -1.00000 q^{98} -2.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{16} + 6 q^{17} - 2 q^{18} - 2 q^{19} + 2 q^{21} - 2 q^{22} - 2 q^{24} - 4 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} - 2 q^{31} - 2 q^{32} + 2 q^{33} - 6 q^{34} + 2 q^{36} + 4 q^{37} + 2 q^{38} + 10 q^{39} - 12 q^{41} - 2 q^{42} - 8 q^{43} + 2 q^{44} + 12 q^{47} + 2 q^{48} + 2 q^{49} + 4 q^{52} + 6 q^{53} - 8 q^{54} - 2 q^{56} + 10 q^{57} - 6 q^{58} - 8 q^{61} + 2 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{66} + 10 q^{67} + 6 q^{68} - 6 q^{69} - 2 q^{72} - 8 q^{73} - 4 q^{74} - 2 q^{76} + 2 q^{77} - 10 q^{78} - 2 q^{79} + 2 q^{81} + 12 q^{82} + 6 q^{83} + 2 q^{84} + 8 q^{86} + 18 q^{87} - 2 q^{88} + 4 q^{91} - 14 q^{93} - 12 q^{94} - 2 q^{96} + 4 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 + 2 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^16 + 6 * q^17 - 2 * q^18 - 2 * q^19 + 2 * q^21 - 2 * q^22 - 2 * q^24 - 4 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 - 2 * q^31 - 2 * q^32 + 2 * q^33 - 6 * q^34 + 2 * q^36 + 4 * q^37 + 2 * q^38 + 10 * q^39 - 12 * q^41 - 2 * q^42 - 8 * q^43 + 2 * q^44 + 12 * q^47 + 2 * q^48 + 2 * q^49 + 4 * q^52 + 6 * q^53 - 8 * q^54 - 2 * q^56 + 10 * q^57 - 6 * q^58 - 8 * q^61 + 2 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^66 + 10 * q^67 + 6 * q^68 - 6 * q^69 - 2 * q^72 - 8 * q^73 - 4 * q^74 - 2 * q^76 + 2 * q^77 - 10 * q^78 - 2 * q^79 + 2 * q^81 + 12 * q^82 + 6 * q^83 + 2 * q^84 + 8 * q^86 + 18 * q^87 - 2 * q^88 + 4 * q^91 - 14 * q^93 - 12 * q^94 - 2 * q^96 + 4 * q^97 - 2 * q^98 + 2 * q^99

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