LMFDB - Embedded newform 1175.2.a.i.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, 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("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.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:	$9.38242223750$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 8x^{9} + 44x^{8} + 8x^{7} - 156x^{6} + 48x^{5} + 208x^{4} - 96x^{3} - 86x^{2} + 41x + 4 $ x^11 - 4x^10 - 8x^9 + 44x^8 + 8x^7 - 156x^6 + 48x^5 + 208x^4 - 96x^3 - 86x^2 + 41x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 235)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.29770$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.29770 q^{2} -2.93223 q^{3} -0.315973 q^{4} -3.80515 q^{6} +1.39355 q^{7} -3.00544 q^{8} +5.59794 q^{9} +O(q^{10})$	\(q+1.29770 q^{2} -2.93223 q^{3} -0.315973 q^{4} -3.80515 q^{6} +1.39355 q^{7} -3.00544 q^{8} +5.59794 q^{9} +1.89487 q^{11} +0.926505 q^{12} +3.25256 q^{13} +1.80841 q^{14} -3.26821 q^{16} -6.69374 q^{17} +7.26445 q^{18} +2.33193 q^{19} -4.08620 q^{21} +2.45897 q^{22} -1.59282 q^{23} +8.81263 q^{24} +4.22084 q^{26} -7.61776 q^{27} -0.440325 q^{28} -3.02593 q^{29} -5.17742 q^{31} +1.76972 q^{32} -5.55618 q^{33} -8.68647 q^{34} -1.76880 q^{36} -6.68877 q^{37} +3.02614 q^{38} -9.53723 q^{39} +7.85273 q^{41} -5.30267 q^{42} -7.73676 q^{43} -0.598728 q^{44} -2.06701 q^{46} +1.00000 q^{47} +9.58314 q^{48} -5.05802 q^{49} +19.6275 q^{51} -1.02772 q^{52} -12.7095 q^{53} -9.88557 q^{54} -4.18823 q^{56} -6.83773 q^{57} -3.92675 q^{58} +1.58640 q^{59} -13.4926 q^{61} -6.71874 q^{62} +7.80102 q^{63} +8.83299 q^{64} -7.21026 q^{66} -10.9563 q^{67} +2.11504 q^{68} +4.67052 q^{69} +3.67827 q^{71} -16.8243 q^{72} -15.0486 q^{73} -8.68002 q^{74} -0.736826 q^{76} +2.64059 q^{77} -12.3765 q^{78} +3.62442 q^{79} +5.54314 q^{81} +10.1905 q^{82} +11.7569 q^{83} +1.29113 q^{84} -10.0400 q^{86} +8.87270 q^{87} -5.69491 q^{88} -10.8341 q^{89} +4.53260 q^{91} +0.503290 q^{92} +15.1814 q^{93} +1.29770 q^{94} -5.18921 q^{96} +2.02835 q^{97} -6.56379 q^{98} +10.6074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 4 q^{2} - 4 q^{3} + 10 q^{4} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q - 4 * q^2 - 4 * q^3 + 10 * q^4 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 9 * q^9	$ 11 q - 4 q^{2} - 4 q^{3} + 10 q^{4} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 9 q^{9} - 12 q^{12} - 19 q^{13} + 12 q^{16} - 16 q^{17} + 10 q^{18} - 6 q^{21} - 22 q^{22} - 3 q^{23} - 12 q^{24} + 6 q^{26} - 16 q^{27} - 18 q^{28} + 4 q^{29} + 2 q^{31} - 28 q^{32} - 18 q^{33} - 16 q^{34} - 8 q^{36} - 40 q^{37} + 14 q^{38} - 10 q^{39} + 4 q^{41} - 16 q^{42} - 23 q^{43} + 24 q^{44} - 16 q^{46} + 11 q^{47} + 18 q^{48} + 5 q^{49} + 12 q^{51} - 46 q^{52} - 16 q^{53} + 26 q^{56} - 42 q^{57} - 16 q^{58} + 7 q^{59} - 7 q^{61} - 14 q^{63} + 24 q^{64} + 12 q^{66} - 32 q^{67} + 58 q^{68} - 2 q^{69} - 17 q^{71} - 57 q^{73} - 16 q^{74} - 10 q^{76} - 8 q^{77} + 22 q^{78} - 13 q^{79} - 25 q^{81} - 12 q^{82} - 8 q^{83} - 4 q^{84} - 6 q^{86} + 10 q^{87} - 26 q^{88} - 37 q^{89} + 32 q^{91} - 4 q^{92} + 10 q^{93} - 4 q^{94} - 6 q^{96} - 32 q^{97} + 20 q^{98} - 8 q^{99}+O(q^{100}) $ 11 * q - 4 * q^2 - 4 * q^3 + 10 * q^4 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 9 * q^9 - 12 * q^12 - 19 * q^13 + 12 * q^16 - 16 * q^17 + 10 * q^18 - 6 * q^21 - 22 * q^22 - 3 * q^23 - 12 * q^24 + 6 * q^26 - 16 * q^27 - 18 * q^28 + 4 * q^29 + 2 * q^31 - 28 * q^32 - 18 * q^33 - 16 * q^34 - 8 * q^36 - 40 * q^37 + 14 * q^38 - 10 * q^39 + 4 * q^41 - 16 * q^42 - 23 * q^43 + 24 * q^44 - 16 * q^46 + 11 * q^47 + 18 * q^48 + 5 * q^49 + 12 * q^51 - 46 * q^52 - 16 * q^53 + 26 * q^56 - 42 * q^57 - 16 * q^58 + 7 * q^59 - 7 * q^61 - 14 * q^63 + 24 * q^64 + 12 * q^66 - 32 * q^67 + 58 * q^68 - 2 * q^69 - 17 * q^71 - 57 * q^73 - 16 * q^74 - 10 * q^76 - 8 * q^77 + 22 * q^78 - 13 * q^79 - 25 * q^81 - 12 * q^82 - 8 * q^83 - 4 * q^84 - 6 * q^86 + 10 * q^87 - 26 * q^88 - 37 * q^89 + 32 * q^91 - 4 * q^92 + 10 * q^93 - 4 * q^94 - 6 * q^96 - 32 * q^97 + 20 * q^98 - 8 * 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 $

$2$	1.29770	0.917613	0.458806	−	0.888536i	$-0.348277\pi$
$2$	1.29770	0.917613	0.458806	+	0.888536i	$0.348277\pi$
$3$	−2.93223	−1.69292	−0.846460	−	0.532452i	$-0.821271\pi$
$3$	−2.93223	−1.69292	−0.846460	+	0.532452i	$0.821271\pi$
$4$	−0.315973	−0.157987
$5$	0	0
$5$	0	0
$6$	−3.80515	−1.55345
$7$	1.39355	0.526713	0.263356	−	0.964699i	$-0.415170\pi$
$7$	1.39355	0.526713	0.263356	+	0.964699i	$0.415170\pi$
$8$	−3.00544	−1.06258
$9$	5.59794	1.86598
$10$	0	0
$11$	1.89487	0.571324	0.285662	−	0.958330i	$-0.407787\pi$
$11$	1.89487	0.571324	0.285662	+	0.958330i	$0.407787\pi$
$12$	0.926505	0.267459
$13$	3.25256	0.902097	0.451048	−	0.892499i	$-0.351050\pi$
$13$	3.25256	0.902097	0.451048	+	0.892499i	$0.351050\pi$
$14$	1.80841	0.483318
$15$	0	0
$16$	−3.26821	−0.817054
$17$	−6.69374	−1.62347	−0.811735	−	0.584026i	$-0.801476\pi$
$17$	−6.69374	−1.62347	−0.811735	+	0.584026i	$0.801476\pi$
$18$	7.26445	1.71225
$19$	2.33193	0.534981	0.267490	−	0.963561i	$-0.413806\pi$
$19$	2.33193	0.534981	0.267490	+	0.963561i	$0.413806\pi$
$20$	0	0
$21$	−4.08620	−0.891683
$22$	2.45897	0.524254
$23$	−1.59282	−0.332127	−0.166063	−	0.986115i	$-0.553106\pi$
$23$	−1.59282	−0.332127	−0.166063	+	0.986115i	$0.553106\pi$
$24$	8.81263	1.79887
$25$	0	0
$26$	4.22084	0.827776
$27$	−7.61776	−1.46604
$28$	−0.440325	−0.0832136
$29$	−3.02593	−0.561901	−0.280950	−	0.959722i	$-0.590650\pi$
$29$	−3.02593	−0.561901	−0.280950	+	0.959722i	$0.590650\pi$
$30$	0	0
$31$	−5.17742	−0.929892	−0.464946	−	0.885339i	$-0.653926\pi$
$31$	−5.17742	−0.929892	−0.464946	+	0.885339i	$0.653926\pi$
$32$	1.76972	0.312845
$33$	−5.55618	−0.967207
$34$	−8.68647	−1.48972
$35$	0	0
$36$	−1.76880	−0.294800
$37$	−6.68877	−1.09963	−0.549813	−	0.835288i	$-0.685301\pi$
$37$	−6.68877	−1.09963	−0.549813	+	0.835288i	$0.685301\pi$
$38$	3.02614	0.490905
$39$	−9.53723	−1.52718
$40$	0	0
$41$	7.85273	1.22639	0.613195	−	0.789931i	$-0.289884\pi$
$41$	7.85273	1.22639	0.613195	+	0.789931i	$0.289884\pi$
$42$	−5.30267	−0.818220
$43$	−7.73676	−1.17985	−0.589923	−	0.807460i	$-0.700842\pi$
$43$	−7.73676	−1.17985	−0.589923	+	0.807460i	$0.700842\pi$
$44$	−0.598728	−0.0902616
$45$	0	0
$46$	−2.06701	−0.304764
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	9.58314	1.38321
$49$	−5.05802	−0.722574
$50$	0	0
$51$	19.6275	2.74841
$52$	−1.02772	−0.142519
$53$	−12.7095	−1.74578	−0.872890	−	0.487918i	$-0.837757\pi$
$53$	−12.7095	−1.74578	−0.872890	+	0.487918i	$0.837757\pi$
$54$	−9.88557	−1.34526
$55$	0	0
$56$	−4.18823	−0.559676
$57$	−6.83773	−0.905680
$58$	−3.92675	−0.515607
$59$	1.58640	0.206532	0.103266	−	0.994654i	$-0.467071\pi$
$59$	1.58640	0.206532	0.103266	+	0.994654i	$0.467071\pi$
$60$	0	0
$61$	−13.4926	−1.72754	−0.863772	−	0.503882i	$-0.831905\pi$
$61$	−13.4926	−1.72754	−0.863772	+	0.503882i	$0.831905\pi$
$62$	−6.71874	−0.853280
$63$	7.80102	0.982836
$64$	8.83299	1.10412
$65$	0	0
$66$	−7.21026	−0.887521
$67$	−10.9563	−1.33852	−0.669261	−	0.743027i	$-0.733389\pi$
$67$	−10.9563	−1.33852	−0.669261	+	0.743027i	$0.733389\pi$
$68$	2.11504	0.256487
$69$	4.67052	0.562264
$70$	0	0
$71$	3.67827	0.436530	0.218265	−	0.975890i	$-0.429960\pi$
$71$	3.67827	0.436530	0.218265	+	0.975890i	$0.429960\pi$
$72$	−16.8243	−1.98276
$73$	−15.0486	−1.76130	−0.880652	−	0.473764i	$-0.842895\pi$
$73$	−15.0486	−1.76130	−0.880652	+	0.473764i	$0.842895\pi$
$74$	−8.68002	−1.00903
$75$	0	0
$76$	−0.736826	−0.0845198
$77$	2.64059	0.300924
$78$	−12.3765	−1.40136
$79$	3.62442	0.407779	0.203889	−	0.978994i	$-0.434642\pi$
$79$	3.62442	0.407779	0.203889	+	0.978994i	$0.434642\pi$
$80$	0	0
$81$	5.54314	0.615905
$82$	10.1905	1.12535
$83$	11.7569	1.29049	0.645245	−	0.763976i	$-0.276755\pi$
$83$	11.7569	1.29049	0.645245	+	0.763976i	$0.276755\pi$
$84$	1.29113	0.140874
$85$	0	0
$86$	−10.0400	−1.08264
$87$	8.87270	0.951253
$88$	−5.69491	−0.607080
$89$	−10.8341	−1.14841	−0.574207	−	0.818710i	$-0.694690\pi$
$89$	−10.8341	−1.14841	−0.574207	+	0.818710i	$0.694690\pi$
$90$	0	0
$91$	4.53260	0.475146
$92$	0.503290	0.0524716
$93$	15.1814	1.57423
$94$	1.29770	0.133848
$95$	0	0
$96$	−5.18921	−0.529621
$97$	2.02835	0.205948	0.102974	−	0.994684i	$-0.467164\pi$
$97$	2.02835	0.205948	0.102974	+	0.994684i	$0.467164\pi$
$98$	−6.56379	−0.663043
$99$	10.6074	1.06608
$100$	0	0
$101$	10.6122	1.05595	0.527974	−	0.849260i	$-0.322952\pi$
$101$	10.6122	1.05595	0.527974	+	0.849260i	$0.322952\pi$
$102$	25.4707	2.52197
$103$	13.4740	1.32763	0.663816	−	0.747896i	$-0.268936\pi$
$103$	13.4740	1.32763	0.663816	+	0.747896i	$0.268936\pi$
$104$	−9.77536	−0.958553
$105$	0	0
$106$	−16.4931	−1.60195
$107$	9.69212	0.936973	0.468486	−	0.883471i	$-0.344800\pi$
$107$	9.69212	0.936973	0.468486	+	0.883471i	$0.344800\pi$
$108$	2.40701	0.231614
$109$	4.71780	0.451884	0.225942	−	0.974141i	$-0.427454\pi$
$109$	4.71780	0.451884	0.225942	+	0.974141i	$0.427454\pi$
$110$	0	0
$111$	19.6130	1.86158
$112$	−4.55442	−0.430353
$113$	9.69806	0.912317	0.456158	−	0.889899i	$-0.349225\pi$
$113$	9.69806	0.912317	0.456158	+	0.889899i	$0.349225\pi$
$114$	−8.87333	−0.831063
$115$	0	0
$116$	0.956112	0.0887728
$117$	18.2076	1.68330
$118$	2.05868	0.189517
$119$	−9.32806	−0.855102
$120$	0	0
$121$	−7.40948	−0.673589
$122$	−17.5093	−1.58522
$123$	−23.0260	−2.07618
$124$	1.63593	0.146910
$125$	0	0
$126$	10.1234	0.901863
$127$	−6.34822	−0.563313	−0.281657	−	0.959515i	$-0.590884\pi$
$127$	−6.34822	−0.563313	−0.281657	+	0.959515i	$0.590884\pi$
$128$	7.92314	0.700314
$129$	22.6859	1.99738
$130$	0	0
$131$	−5.52549	−0.482764	−0.241382	−	0.970430i	$-0.577601\pi$
$131$	−5.52549	−0.482764	−0.241382	+	0.970430i	$0.577601\pi$
$132$	1.75560	0.152806
$133$	3.24966	0.281781
$134$	−14.2180	−1.22825
$135$	0	0
$136$	20.1176	1.72507
$137$	−9.99304	−0.853763	−0.426881	−	0.904308i	$-0.640388\pi$
$137$	−9.99304	−0.853763	−0.426881	+	0.904308i	$0.640388\pi$
$138$	6.06093	0.515941
$139$	12.9575	1.09904	0.549520	−	0.835480i	$-0.314810\pi$
$139$	12.9575	1.09904	0.549520	+	0.835480i	$0.314810\pi$
$140$	0	0
$141$	−2.93223	−0.246938
$142$	4.77329	0.400566
$143$	6.16316	0.515390
$144$	−18.2953	−1.52461
$145$	0	0
$146$	−19.5286	−1.61620
$147$	14.8312	1.22326
$148$	2.11347	0.173726
$149$	12.5053	1.02447	0.512235	−	0.858845i	$-0.328818\pi$
$149$	12.5053	1.02447	0.512235	+	0.858845i	$0.328818\pi$
$150$	0	0
$151$	−15.3584	−1.24985	−0.624925	−	0.780685i	$-0.714871\pi$
$151$	−15.3584	−1.24985	−0.624925	+	0.780685i	$0.714871\pi$
$152$	−7.00846	−0.568461
$153$	−37.4712	−3.02936
$154$	3.42670	0.276131
$155$	0	0
$156$	3.01351	0.241274
$157$	−0.665889	−0.0531437	−0.0265719	−	0.999647i	$-0.508459\pi$
$157$	−0.665889	−0.0531437	−0.0265719	+	0.999647i	$0.508459\pi$
$158$	4.70341	0.374183
$159$	37.2670	2.95547
$160$	0	0
$161$	−2.21968	−0.174935
$162$	7.19334	0.565162
$163$	−12.5178	−0.980469	−0.490235	−	0.871590i	$-0.663089\pi$
$163$	−12.5178	−0.980469	−0.490235	+	0.871590i	$0.663089\pi$
$164$	−2.48125	−0.193753
$165$	0	0
$166$	15.2570	1.18417
$167$	−8.29432	−0.641833	−0.320917	−	0.947107i	$-0.603991\pi$
$167$	−8.29432	−0.641833	−0.320917	+	0.947107i	$0.603991\pi$
$168$	12.2808	0.947488
$169$	−2.42087	−0.186221
$170$	0	0
$171$	13.0540	0.998264
$172$	2.44461	0.186400
$173$	7.03257	0.534677	0.267338	−	0.963603i	$-0.413856\pi$
$173$	7.03257	0.534677	0.267338	+	0.963603i	$0.413856\pi$
$174$	11.5141	0.872882
$175$	0	0
$176$	−6.19283	−0.466802
$177$	−4.65169	−0.349643
$178$	−14.0594	−1.05380
$179$	−20.5145	−1.53333	−0.766664	−	0.642048i	$-0.778085\pi$
$179$	−20.5145	−1.53333	−0.766664	+	0.642048i	$0.778085\pi$
$180$	0	0
$181$	7.06632	0.525236	0.262618	−	0.964900i	$-0.415414\pi$
$181$	7.06632	0.525236	0.262618	+	0.964900i	$0.415414\pi$
$182$	5.88196	0.436000
$183$	39.5632	2.92460
$184$	4.78714	0.352912
$185$	0	0
$186$	19.7008	1.44454
$187$	−12.6837	−0.927527
$188$	−0.315973	−0.0230447
$189$	−10.6157	−0.772181
$190$	0	0
$191$	−26.3516	−1.90673	−0.953366	−	0.301816i	$-0.902407\pi$
$191$	−26.3516	−1.90673	−0.953366	+	0.301816i	$0.902407\pi$
$192$	−25.9003	−1.86919
$193$	−17.1011	−1.23097	−0.615483	−	0.788150i	$-0.711039\pi$
$193$	−17.1011	−1.23097	−0.615483	+	0.788150i	$0.711039\pi$
$194$	2.63219	0.188980
$195$	0	0
$196$	1.59820	0.114157
$197$	16.2855	1.16029	0.580147	−	0.814512i	$-0.302995\pi$
$197$	16.2855	1.16029	0.580147	+	0.814512i	$0.302995\pi$
$198$	13.7652	0.978249
$199$	−3.59169	−0.254608	−0.127304	−	0.991864i	$-0.540632\pi$
$199$	−3.59169	−0.254608	−0.127304	+	0.991864i	$0.540632\pi$
$200$	0	0
$201$	32.1263	2.26601
$202$	13.7714	0.968952
$203$	−4.21678	−0.295960
$204$	−6.20178	−0.434211
$205$	0	0
$206$	17.4852	1.21825
$207$	−8.91654	−0.619742
$208$	−10.6301	−0.737062
$209$	4.41869	0.305647
$210$	0	0
$211$	19.8861	1.36901	0.684507	−	0.729006i	$-0.260017\pi$
$211$	19.8861	1.36901	0.684507	+	0.729006i	$0.260017\pi$
$212$	4.01585	0.275810
$213$	−10.7855	−0.739011
$214$	12.5775	0.859778
$215$	0	0
$216$	22.8947	1.55779
$217$	−7.21499	−0.489786
$218$	6.12230	0.414654
$219$	44.1258	2.98175
$220$	0	0
$221$	−21.7718	−1.46453
$222$	25.4518	1.70821
$223$	−0.488216	−0.0326934	−0.0163467	−	0.999866i	$-0.505204\pi$
$223$	−0.488216	−0.0326934	−0.0163467	+	0.999866i	$0.505204\pi$
$224$	2.46619	0.164779
$225$	0	0
$226$	12.5852	0.837153
$227$	5.47647	0.363486	0.181743	−	0.983346i	$-0.441826\pi$
$227$	5.47647	0.363486	0.181743	+	0.983346i	$0.441826\pi$
$228$	2.16054	0.143085
$229$	−27.9525	−1.84715	−0.923577	−	0.383413i	$-0.874748\pi$
$229$	−27.9525	−1.84715	−0.923577	+	0.383413i	$0.874748\pi$
$230$	0	0
$231$	−7.74282	−0.509440
$232$	9.09424	0.597066
$233$	−7.33594	−0.480593	−0.240297	−	0.970699i	$-0.577245\pi$
$233$	−7.33594	−0.480593	−0.240297	+	0.970699i	$0.577245\pi$
$234$	23.6281	1.54461
$235$	0	0
$236$	−0.501261	−0.0326293
$237$	−10.6276	−0.690337
$238$	−12.1050	−0.784653
$239$	16.6997	1.08022	0.540108	−	0.841596i	$-0.318383\pi$
$239$	16.6997	1.08022	0.540108	+	0.841596i	$0.318383\pi$
$240$	0	0
$241$	−14.4137	−0.928469	−0.464235	−	0.885712i	$-0.653671\pi$
$241$	−14.4137	−0.928469	−0.464235	+	0.885712i	$0.653671\pi$
$242$	−9.61528	−0.618094
$243$	6.59952	0.423360
$244$	4.26329	0.272929
$245$	0	0
$246$	−29.8808	−1.90513
$247$	7.58472	0.482604
$248$	15.5604	0.988087
$249$	−34.4739	−2.18470
$250$	0	0
$251$	−5.87354	−0.370734	−0.185367	−	0.982669i	$-0.559347\pi$
$251$	−5.87354	−0.370734	−0.185367	+	0.982669i	$0.559347\pi$
$252$	−2.46491	−0.155275
$253$	−3.01819	−0.189752
$254$	−8.23809	−0.516904
$255$	0	0
$256$	−7.38411	−0.461507
$257$	25.4666	1.58856	0.794281	−	0.607550i	$-0.207848\pi$
$257$	25.4666	1.58856	0.794281	+	0.607550i	$0.207848\pi$
$258$	29.4395	1.83283
$259$	−9.32114	−0.579187
$260$	0	0
$261$	−16.9390	−1.04850
$262$	−7.17043	−0.442991
$263$	5.72971	0.353309	0.176654	−	0.984273i	$-0.443472\pi$
$263$	5.72971	0.353309	0.176654	+	0.984273i	$0.443472\pi$
$264$	16.6988	1.02774
$265$	0	0
$266$	4.21708	0.258566
$267$	31.7681	1.94417
$268$	3.46189	0.211469
$269$	−13.4490	−0.820002	−0.410001	−	0.912085i	$-0.634472\pi$
$269$	−13.4490	−0.820002	−0.410001	+	0.912085i	$0.634472\pi$
$270$	0	0
$271$	−11.6192	−0.705819	−0.352909	−	0.935657i	$-0.614808\pi$
$271$	−11.6192	−0.705819	−0.352909	+	0.935657i	$0.614808\pi$
$272$	21.8766	1.32646
$273$	−13.2906	−0.804384
$274$	−12.9680	−0.783424
$275$	0	0
$276$	−1.47576	−0.0888303
$277$	−4.74524	−0.285114	−0.142557	−	0.989787i	$-0.545532\pi$
$277$	−4.74524	−0.285114	−0.142557	+	0.989787i	$0.545532\pi$
$278$	16.8150	1.00849
$279$	−28.9829	−1.73516
$280$	0	0
$281$	−11.6347	−0.694066	−0.347033	−	0.937853i	$-0.612811\pi$
$281$	−11.6347	−0.694066	−0.347033	+	0.937853i	$0.612811\pi$
$282$	−3.80515	−0.226593
$283$	29.1989	1.73569	0.867847	−	0.496831i	$-0.165503\pi$
$283$	29.1989	1.73569	0.867847	+	0.496831i	$0.165503\pi$
$284$	−1.16223	−0.0689659
$285$	0	0
$286$	7.99794	0.472928
$287$	10.9432	0.645956
$288$	9.90677	0.583762
$289$	27.8061	1.63565
$290$	0	0
$291$	−5.94758	−0.348653
$292$	4.75495	0.278263
$293$	20.8312	1.21697	0.608485	−	0.793565i	$-0.291778\pi$
$293$	20.8312	1.21697	0.608485	+	0.793565i	$0.291778\pi$
$294$	19.2465	1.12248
$295$	0	0
$296$	20.1027	1.16844
$297$	−14.4346	−0.837583
$298$	16.2281	0.940068
$299$	−5.18075	−0.299611
$300$	0	0
$301$	−10.7816	−0.621439
$302$	−19.9306	−1.14688
$303$	−31.1172	−1.78764
$304$	−7.62123	−0.437108
$305$	0	0
$306$	−48.6263	−2.77978
$307$	26.9005	1.53529	0.767647	−	0.640873i	$-0.221427\pi$
$307$	26.9005	1.53529	0.767647	+	0.640873i	$0.221427\pi$
$308$	−0.834357	−0.0475419
$309$	−39.5088	−2.24758
$310$	0	0
$311$	17.3804	0.985552	0.492776	−	0.870156i	$-0.335982\pi$
$311$	17.3804	0.985552	0.492776	+	0.870156i	$0.335982\pi$
$312$	28.6636	1.62275
$313$	−3.45677	−0.195388	−0.0976942	−	0.995216i	$-0.531147\pi$
$313$	−3.45677	−0.195388	−0.0976942	+	0.995216i	$0.531147\pi$
$314$	−0.864125	−0.0487654
$315$	0	0
$316$	−1.14522	−0.0644236
$317$	−8.80669	−0.494633	−0.247317	−	0.968935i	$-0.579549\pi$
$317$	−8.80669	−0.494633	−0.247317	+	0.968935i	$0.579549\pi$
$318$	48.3614	2.71197
$319$	−5.73373	−0.321027
$320$	0	0
$321$	−28.4195	−1.58622
$322$	−2.88048	−0.160523
$323$	−15.6093	−0.868525
$324$	−1.75149	−0.0973048
$325$	0	0
$326$	−16.2443	−0.899691
$327$	−13.8337	−0.765003
$328$	−23.6009	−1.30314
$329$	1.39355	0.0768289
$330$	0	0
$331$	17.0896	0.939329	0.469664	−	0.882845i	$-0.344375\pi$
$331$	17.0896	0.939329	0.469664	+	0.882845i	$0.344375\pi$
$332$	−3.71487	−0.203880
$333$	−37.4433	−2.05188
$334$	−10.7635	−0.588955
$335$	0	0
$336$	13.3546	0.728553
$337$	−10.1947	−0.555342	−0.277671	−	0.960676i	$-0.589563\pi$
$337$	−10.1947	−0.555342	−0.277671	+	0.960676i	$0.589563\pi$
$338$	−3.14157	−0.170879
$339$	−28.4369	−1.54448
$340$	0	0
$341$	−9.81052	−0.531269
$342$	16.9402	0.916020
$343$	−16.8035	−0.907301
$344$	23.2524	1.25368
$345$	0	0
$346$	9.12617	0.490626
$347$	23.9156	1.28386	0.641929	−	0.766764i	$-0.278134\pi$
$347$	23.9156	1.28386	0.641929	+	0.766764i	$0.278134\pi$
$348$	−2.80354	−0.150285
$349$	−12.3584	−0.661531	−0.330765	−	0.943713i	$-0.607307\pi$
$349$	−12.3584	−0.661531	−0.330765	+	0.943713i	$0.607307\pi$
$350$	0	0
$351$	−24.7772	−1.32251
$352$	3.35338	0.178736
$353$	−2.25458	−0.119999	−0.0599996	−	0.998198i	$-0.519110\pi$
$353$	−2.25458	−0.119999	−0.0599996	+	0.998198i	$0.519110\pi$
$354$	−6.03650	−0.320837
$355$	0	0
$356$	3.42329	0.181434
$357$	27.3520	1.44762
$358$	−26.6217	−1.40700
$359$	21.5837	1.13914	0.569571	−	0.821942i	$-0.307109\pi$
$359$	21.5837	1.13914	0.569571	+	0.821942i	$0.307109\pi$
$360$	0	0
$361$	−13.5621	−0.713796
$362$	9.16997	0.481963
$363$	21.7263	1.14033
$364$	−1.43218	−0.0750667
$365$	0	0
$366$	51.3412	2.68365
$367$	15.0318	0.784654	0.392327	−	0.919826i	$-0.371670\pi$
$367$	15.0318	0.784654	0.392327	+	0.919826i	$0.371670\pi$
$368$	5.20569	0.271365
$369$	43.9592	2.28842
$370$	0	0
$371$	−17.7113	−0.919524
$372$	−4.79690	−0.248708
$373$	−6.05672	−0.313605	−0.156803	−	0.987630i	$-0.550119\pi$
$373$	−6.05672	−0.313605	−0.156803	+	0.987630i	$0.550119\pi$
$374$	−16.4597	−0.851111
$375$	0	0
$376$	−3.00544	−0.154994
$377$	−9.84200	−0.506889
$378$	−13.7760	−0.708563
$379$	−11.6087	−0.596297	−0.298148	−	0.954520i	$-0.596369\pi$
$379$	−11.6087	−0.596297	−0.298148	+	0.954520i	$0.596369\pi$
$380$	0	0
$381$	18.6144	0.953645
$382$	−34.1964	−1.74964
$383$	−20.8061	−1.06314	−0.531572	−	0.847013i	$-0.678399\pi$
$383$	−20.8061	−1.06314	−0.531572	+	0.847013i	$0.678399\pi$
$384$	−23.2324	−1.18558
$385$	0	0
$386$	−22.1921	−1.12955
$387$	−43.3100	−2.20157
$388$	−0.640905	−0.0325370
$389$	−13.4090	−0.679866	−0.339933	−	0.940450i	$-0.610404\pi$
$389$	−13.4090	−0.679866	−0.339933	+	0.940450i	$0.610404\pi$
$390$	0	0
$391$	10.6619	0.539198
$392$	15.2016	0.767795
$393$	16.2020	0.817282
$394$	21.1337	1.06470
$395$	0	0
$396$	−3.35164	−0.168426
$397$	7.17418	0.360062	0.180031	−	0.983661i	$-0.442380\pi$
$397$	7.17418	0.360062	0.180031	+	0.983661i	$0.442380\pi$
$398$	−4.66093	−0.233632
$399$	−9.52873	−0.477033
$400$	0	0
$401$	−22.4252	−1.11986	−0.559931	−	0.828539i	$-0.689172\pi$
$401$	−22.4252	−1.11986	−0.559931	+	0.828539i	$0.689172\pi$
$402$	41.6903	2.07932
$403$	−16.8398	−0.838852
$404$	−3.35316	−0.166826
$405$	0	0
$406$	−5.47212	−0.271577
$407$	−12.6743	−0.628243
$408$	−58.9894	−2.92041
$409$	7.18162	0.355108	0.177554	−	0.984111i	$-0.443182\pi$
$409$	7.18162	0.355108	0.177554	+	0.984111i	$0.443182\pi$
$410$	0	0
$411$	29.3018	1.44535
$412$	−4.25742	−0.209748
$413$	2.21073	0.108783
$414$	−11.5710	−0.568684
$415$	0	0
$416$	5.75610	0.282216
$417$	−37.9943	−1.86059
$418$	5.73414	0.280466
$419$	−32.9500	−1.60971	−0.804857	−	0.593469i	$-0.797758\pi$
$419$	−32.9500	−1.60971	−0.804857	+	0.593469i	$0.797758\pi$
$420$	0	0
$421$	2.55607	0.124575	0.0622876	−	0.998058i	$-0.480160\pi$
$421$	2.55607	0.124575	0.0622876	+	0.998058i	$0.480160\pi$
$422$	25.8062	1.25623
$423$	5.59794	0.272181
$424$	38.1975	1.85504
$425$	0	0
$426$	−13.9964	−0.678126
$427$	−18.8026	−0.909920
$428$	−3.06245	−0.148029
$429$	−18.0718	−0.872514
$430$	0	0
$431$	0.389062	0.0187405	0.00937023	−	0.999956i	$-0.497017\pi$
$431$	0.389062	0.0187405	0.00937023	+	0.999956i	$0.497017\pi$
$432$	24.8965	1.19783
$433$	18.1300	0.871273	0.435637	−	0.900123i	$-0.356523\pi$
$433$	18.1300	0.871273	0.435637	+	0.900123i	$0.356523\pi$
$434$	−9.36290	−0.449434
$435$	0	0
$436$	−1.49070	−0.0713916
$437$	−3.71435	−0.177681
$438$	57.2621	2.73609
$439$	4.40463	0.210222	0.105111	−	0.994461i	$-0.466480\pi$
$439$	4.40463	0.210222	0.105111	+	0.994461i	$0.466480\pi$
$440$	0	0
$441$	−28.3145	−1.34831
$442$	−28.2532	−1.34387
$443$	−14.4495	−0.686515	−0.343257	−	0.939241i	$-0.611530\pi$
$443$	−14.4495	−0.686515	−0.343257	+	0.939241i	$0.611530\pi$
$444$	−6.19717	−0.294105
$445$	0	0
$446$	−0.633558	−0.0299999
$447$	−36.6682	−1.73435
$448$	12.3092	0.581556
$449$	−29.9345	−1.41270	−0.706349	−	0.707864i	$-0.749659\pi$
$449$	−29.9345	−1.41270	−0.706349	+	0.707864i	$0.749659\pi$
$450$	0	0
$451$	14.8799	0.700667
$452$	−3.06433	−0.144134
$453$	45.0343	2.11590
$454$	7.10681	0.333539
$455$	0	0
$456$	20.5504	0.962360
$457$	5.87957	0.275035	0.137517	−	0.990499i	$-0.456088\pi$
$457$	5.87957	0.275035	0.137517	+	0.990499i	$0.456088\pi$
$458$	−36.2740	−1.69497
$459$	50.9913	2.38007
$460$	0	0
$461$	6.69236	0.311694	0.155847	−	0.987781i	$-0.450189\pi$
$461$	6.69236	0.311694	0.155847	+	0.987781i	$0.450189\pi$
$462$	−10.0479	−0.467469
$463$	0.108136	0.00502551	0.00251275	−	0.999997i	$-0.499200\pi$
$463$	0.108136	0.00502551	0.00251275	+	0.999997i	$0.499200\pi$
$464$	9.88938	0.459103
$465$	0	0
$466$	−9.51985	−0.440999
$467$	−12.7113	−0.588209	−0.294104	−	0.955773i	$-0.595021\pi$
$467$	−12.7113	−0.588209	−0.294104	+	0.955773i	$0.595021\pi$
$468$	−5.75313	−0.265938
$469$	−15.2681	−0.705017
$470$	0	0
$471$	1.95254	0.0899681
$472$	−4.76784	−0.219458
$473$	−14.6601	−0.674074
$474$	−13.7915	−0.633462
$475$	0	0
$476$	2.94742	0.135095
$477$	−71.1469	−3.25759
$478$	21.6712	0.991220
$479$	21.0716	0.962787	0.481394	−	0.876505i	$-0.340131\pi$
$479$	21.0716	0.962787	0.481394	+	0.876505i	$0.340131\pi$
$480$	0	0
$481$	−21.7556	−0.991970
$482$	−18.7047	−0.851975
$483$	6.50861	0.296152
$484$	2.34120	0.106418
$485$	0	0
$486$	8.56420	0.388480
$487$	−3.53445	−0.160161	−0.0800805	−	0.996788i	$-0.525518\pi$
$487$	−3.53445	−0.160161	−0.0800805	+	0.996788i	$0.525518\pi$
$488$	40.5511	1.83566
$489$	36.7050	1.65986
$490$	0	0
$491$	4.77004	0.215269	0.107634	−	0.994191i	$-0.465672\pi$
$491$	4.77004	0.215269	0.107634	+	0.994191i	$0.465672\pi$
$492$	7.27560	0.328009
$493$	20.2548	0.912229
$494$	9.84270	0.442844
$495$	0	0
$496$	16.9209	0.759771
$497$	5.12585	0.229926
$498$	−44.7368	−2.00471
$499$	6.63631	0.297082	0.148541	−	0.988906i	$-0.452542\pi$
$499$	6.63631	0.297082	0.148541	+	0.988906i	$0.452542\pi$
$500$	0	0
$501$	24.3208	1.08657
$502$	−7.62209	−0.340191
$503$	15.0437	0.670767	0.335384	−	0.942082i	$-0.391134\pi$
$503$	15.0437	0.670767	0.335384	+	0.942082i	$0.391134\pi$
$504$	−23.4455	−1.04435
$505$	0	0
$506$	−3.91671	−0.174119
$507$	7.09855	0.315258
$508$	2.00587	0.0889960
$509$	26.1240	1.15793	0.578963	−	0.815354i	$-0.303458\pi$
$509$	26.1240	1.15793	0.578963	+	0.815354i	$0.303458\pi$
$510$	0	0
$511$	−20.9710	−0.927701
$512$	−25.4287	−1.12380
$513$	−17.7640	−0.784302
$514$	33.0480	1.45769
$515$	0	0
$516$	−7.16815	−0.315560
$517$	1.89487	0.0833362
$518$	−12.0960	−0.531470
$519$	−20.6211	−0.905165
$520$	0	0
$521$	12.6034	0.552167	0.276084	−	0.961134i	$-0.410963\pi$
$521$	12.6034	0.552167	0.276084	+	0.961134i	$0.410963\pi$
$522$	−21.9817	−0.962114
$523$	33.0171	1.44374	0.721869	−	0.692029i	$-0.243283\pi$
$523$	33.0171	1.44374	0.721869	+	0.692029i	$0.243283\pi$
$524$	1.74591	0.0762703
$525$	0	0
$526$	7.43544	0.324201
$527$	34.6563	1.50965
$528$	18.1588	0.790260
$529$	−20.4629	−0.889692
$530$	0	0
$531$	8.88060	0.385385
$532$	−1.02681	−0.0445176
$533$	25.5415	1.10632
$534$	41.2254	1.78400
$535$	0	0
$536$	32.9284	1.42229
$537$	60.1533	2.59580
$538$	−17.4528	−0.752445
$539$	−9.58427	−0.412824
$540$	0	0
$541$	27.6119	1.18713	0.593565	−	0.804786i	$-0.297720\pi$
$541$	27.6119	1.18713	0.593565	+	0.804786i	$0.297720\pi$
$542$	−15.0783	−0.647668
$543$	−20.7201	−0.889183
$544$	−11.8460	−0.507894
$545$	0	0
$546$	−17.2472	−0.738114
$547$	8.86100	0.378869	0.189435	−	0.981893i	$-0.439335\pi$
$547$	8.86100	0.378869	0.189435	+	0.981893i	$0.439335\pi$
$548$	3.15753	0.134883
$549$	−75.5306	−3.22357
$550$	0	0
$551$	−7.05624	−0.300606
$552$	−14.0370	−0.597453
$553$	5.05081	0.214782
$554$	−6.15790	−0.261624
$555$	0	0
$556$	−4.09422	−0.173634
$557$	31.3684	1.32912	0.664561	−	0.747234i	$-0.268619\pi$
$557$	31.3684	1.32912	0.664561	+	0.747234i	$0.268619\pi$
$558$	−37.6111	−1.59221
$559$	−25.1643	−1.06433
$560$	0	0
$561$	37.1916	1.57023
$562$	−15.0983	−0.636884
$563$	−24.1623	−1.01832	−0.509160	−	0.860672i	$-0.670044\pi$
$563$	−24.1623	−1.01832	−0.509160	+	0.860672i	$0.670044\pi$
$564$	0.926505	0.0390129
$565$	0	0
$566$	37.8914	1.59270
$567$	7.72465	0.324405
$568$	−11.0548	−0.463850
$569$	5.01744	0.210342	0.105171	−	0.994454i	$-0.466461\pi$
$569$	5.01744	0.210342	0.105171	+	0.994454i	$0.466461\pi$
$570$	0	0
$571$	26.7388	1.11898	0.559491	−	0.828836i	$-0.310997\pi$
$571$	26.7388	1.11898	0.559491	+	0.828836i	$0.310997\pi$
$572$	−1.94740	−0.0814247
$573$	77.2687	3.22795
$574$	14.2010	0.592737
$575$	0	0
$576$	49.4466	2.06027
$577$	−6.92070	−0.288113	−0.144056	−	0.989569i	$-0.546015\pi$
$577$	−6.92070	−0.288113	−0.144056	+	0.989569i	$0.546015\pi$
$578$	36.0840	1.50090
$579$	50.1444	2.08393
$580$	0	0
$581$	16.3839	0.679717
$582$	−7.71818	−0.319929
$583$	−24.0828	−0.997406
$584$	45.2276	1.87153
$585$	0	0
$586$	27.0326	1.11671
$587$	46.4635	1.91775	0.958877	−	0.283822i	$-0.0916025\pi$
$587$	46.4635	1.91775	0.958877	+	0.283822i	$0.0916025\pi$
$588$	−4.68628	−0.193259
$589$	−12.0734	−0.497474
$590$	0	0
$591$	−47.7527	−1.96428
$592$	21.8603	0.898454
$593$	32.1098	1.31859	0.659295	−	0.751884i	$-0.270855\pi$
$593$	32.1098	1.31859	0.659295	+	0.751884i	$0.270855\pi$
$594$	−18.7318	−0.768577
$595$	0	0
$596$	−3.95133	−0.161853
$597$	10.5316	0.431031
$598$	−6.72306	−0.274926
$599$	−3.11099	−0.127112	−0.0635558	−	0.997978i	$-0.520244\pi$
$599$	−3.11099	−0.127112	−0.0635558	+	0.997978i	$0.520244\pi$
$600$	0	0
$601$	2.48083	0.101195	0.0505975	−	0.998719i	$-0.483887\pi$
$601$	2.48083	0.101195	0.0505975	+	0.998719i	$0.483887\pi$
$602$	−13.9912	−0.570241
$603$	−61.3326	−2.49766
$604$	4.85285	0.197460
$605$	0	0
$606$	−40.3808	−1.64036
$607$	−37.9571	−1.54063	−0.770315	−	0.637664i	$-0.779901\pi$
$607$	−37.9571	−1.54063	−0.770315	+	0.637664i	$0.779901\pi$
$608$	4.12685	0.167366
$609$	12.3646	0.501037
$610$	0	0
$611$	3.25256	0.131584
$612$	11.8399	0.478599
$613$	−29.1282	−1.17648	−0.588239	−	0.808687i	$-0.700178\pi$
$613$	−29.1282	−1.17648	−0.588239	+	0.808687i	$0.700178\pi$
$614$	34.9088	1.40881
$615$	0	0
$616$	−7.93615	−0.319757
$617$	7.32433	0.294866	0.147433	−	0.989072i	$-0.452899\pi$
$617$	7.32433	0.294866	0.147433	+	0.989072i	$0.452899\pi$
$618$	−51.2706	−2.06240
$619$	2.53651	0.101951	0.0509755	−	0.998700i	$-0.483767\pi$
$619$	2.53651	0.101951	0.0509755	+	0.998700i	$0.483767\pi$
$620$	0	0
$621$	12.1337	0.486910
$622$	22.5546	0.904356
$623$	−15.0979	−0.604884
$624$	31.1697	1.24779
$625$	0	0
$626$	−4.48586	−0.179291
$627$	−12.9566	−0.517437
$628$	0.210403	0.00839600
$629$	44.7728	1.78521
$630$	0	0
$631$	1.06954	0.0425778	0.0212889	−	0.999773i	$-0.493223\pi$
$631$	1.06954	0.0425778	0.0212889	+	0.999773i	$0.493223\pi$
$632$	−10.8930	−0.433299
$633$	−58.3105	−2.31763
$634$	−11.4285	−0.453882
$635$	0	0
$636$	−11.7754	−0.466924
$637$	−16.4515	−0.651832
$638$	−7.44067	−0.294579
$639$	20.5907	0.814557
$640$	0	0
$641$	40.4792	1.59883	0.799417	−	0.600777i	$-0.205142\pi$
$641$	40.4792	1.59883	0.799417	+	0.600777i	$0.205142\pi$
$642$	−36.8800	−1.45554
$643$	−24.5046	−0.966368	−0.483184	−	0.875519i	$-0.660520\pi$
$643$	−24.5046	−0.966368	−0.483184	+	0.875519i	$0.660520\pi$
$644$	0.701360	0.0276375
$645$	0	0
$646$	−20.2562	−0.796969
$647$	1.49656	0.0588359	0.0294180	−	0.999567i	$-0.490635\pi$
$647$	1.49656	0.0588359	0.0294180	+	0.999567i	$0.490635\pi$
$648$	−16.6596	−0.654450
$649$	3.00602	0.117997
$650$	0	0
$651$	21.1560	0.829168
$652$	3.95529	0.154901
$653$	4.27935	0.167464	0.0837320	−	0.996488i	$-0.473316\pi$
$653$	4.27935	0.167464	0.0837320	+	0.996488i	$0.473316\pi$
$654$	−17.9520	−0.701977
$655$	0	0
$656$	−25.6644	−1.00203
$657$	−84.2411	−3.28656
$658$	1.80841	0.0704992
$659$	−14.3314	−0.558271	−0.279135	−	0.960252i	$-0.590048\pi$
$659$	−14.3314	−0.558271	−0.279135	+	0.960252i	$0.590048\pi$
$660$	0	0
$661$	19.4239	0.755501	0.377751	−	0.925907i	$-0.376698\pi$
$661$	19.4239	0.755501	0.377751	+	0.925907i	$0.376698\pi$
$662$	22.1772	0.861940
$663$	63.8397	2.47933
$664$	−35.3347	−1.37125
$665$	0	0
$666$	−48.5902	−1.88283
$667$	4.81977	0.186622
$668$	2.62078	0.101401
$669$	1.43156	0.0553473
$670$	0	0
$671$	−25.5666	−0.986988
$672$	−7.23142	−0.278958
$673$	−29.3933	−1.13303	−0.566513	−	0.824053i	$-0.691708\pi$
$673$	−29.3933	−1.13303	−0.566513	+	0.824053i	$0.691708\pi$
$674$	−13.2297	−0.509589
$675$	0	0
$676$	0.764932	0.0294205
$677$	−36.2514	−1.39325	−0.696626	−	0.717434i	$-0.745316\pi$
$677$	−36.2514	−1.39325	−0.696626	+	0.717434i	$0.745316\pi$
$678$	−36.9026	−1.41723
$679$	2.82661	0.108475
$680$	0	0
$681$	−16.0582	−0.615353
$682$	−12.7311	−0.487500
$683$	27.2333	1.04205	0.521027	−	0.853540i	$-0.325549\pi$
$683$	27.2333	1.04205	0.521027	+	0.853540i	$0.325549\pi$
$684$	−4.12471	−0.157712
$685$	0	0
$686$	−21.8059	−0.832552
$687$	81.9630	3.12709
$688$	25.2854	0.963997
$689$	−41.3383	−1.57486
$690$	0	0
$691$	−20.9110	−0.795493	−0.397747	−	0.917495i	$-0.630208\pi$
$691$	−20.9110	−0.795493	−0.397747	+	0.917495i	$0.630208\pi$
$692$	−2.22211	−0.0844718
$693$	14.7819	0.561518
$694$	31.0353	1.17808
$695$	0	0
$696$	−26.6664	−1.01079
$697$	−52.5641	−1.99101
$698$	−16.0375	−0.607029
$699$	21.5106	0.813607
$700$	0	0
$701$	−10.0458	−0.379425	−0.189712	−	0.981840i	$-0.560756\pi$
$701$	−10.0458	−0.379425	−0.189712	+	0.981840i	$0.560756\pi$
$702$	−32.1534	−1.21355
$703$	−15.5977	−0.588279
$704$	16.7373	0.630813
$705$	0	0
$706$	−2.92577	−0.110113
$707$	14.7886	0.556182
$708$	1.46981	0.0552389
$709$	44.6066	1.67524	0.837619	−	0.546255i	$-0.183947\pi$
$709$	44.6066	1.67524	0.837619	+	0.546255i	$0.183947\pi$
$710$	0	0
$711$	20.2893	0.760908
$712$	32.5613	1.22029
$713$	8.24671	0.308842
$714$	35.4947	1.32835
$715$	0	0
$716$	6.48205	0.242246
$717$	−48.9674	−1.82872
$718$	28.0091	1.04529
$719$	6.92265	0.258171	0.129086	−	0.991633i	$-0.458796\pi$
$719$	6.92265	0.258171	0.129086	+	0.991633i	$0.458796\pi$
$720$	0	0
$721$	18.7767	0.699280
$722$	−17.5996	−0.654988
$723$	42.2643	1.57182
$724$	−2.23277	−0.0829802
$725$	0	0
$726$	28.1942	1.04638
$727$	−1.23977	−0.0459805	−0.0229902	−	0.999736i	$-0.507319\pi$
$727$	−1.23977	−0.0459805	−0.0229902	+	0.999736i	$0.507319\pi$
$728$	−13.6225	−0.504882
$729$	−35.9807	−1.33262
$730$	0	0
$731$	51.7878	1.91544
$732$	−12.5009	−0.462047
$733$	−25.8685	−0.955474	−0.477737	−	0.878503i	$-0.658543\pi$
$733$	−25.8685	−0.955474	−0.477737	+	0.878503i	$0.658543\pi$
$734$	19.5068	0.720008
$735$	0	0
$736$	−2.81885	−0.103904
$737$	−20.7607	−0.764730
$738$	57.0458	2.09989
$739$	7.59657	0.279445	0.139722	−	0.990191i	$-0.455379\pi$
$739$	7.59657	0.279445	0.139722	+	0.990191i	$0.455379\pi$
$740$	0	0
$741$	−22.2401	−0.817011
$742$	−22.9839	−0.843767
$743$	−34.9507	−1.28222	−0.641108	−	0.767450i	$-0.721525\pi$
$743$	−34.9507	−1.28222	−0.641108	+	0.767450i	$0.721525\pi$
$744$	−45.6266	−1.67275
$745$	0	0
$746$	−7.85981	−0.287768
$747$	65.8146	2.40803
$748$	4.00772	0.146537
$749$	13.5065	0.493515
$750$	0	0
$751$	3.08275	0.112491	0.0562455	−	0.998417i	$-0.482087\pi$
$751$	3.08275	0.112491	0.0562455	+	0.998417i	$0.482087\pi$
$752$	−3.26821	−0.119180
$753$	17.2225	0.627624
$754$	−12.7720	−0.465128
$755$	0	0
$756$	3.35429	0.121994
$757$	−29.5454	−1.07385	−0.536923	−	0.843632i	$-0.680413\pi$
$757$	−29.5454	−1.07385	−0.536923	+	0.843632i	$0.680413\pi$
$758$	−15.0646	−0.547170
$759$	8.85001	0.321235
$760$	0	0
$761$	20.9087	0.757939	0.378970	−	0.925409i	$-0.376279\pi$
$761$	20.9087	0.757939	0.378970	+	0.925409i	$0.376279\pi$
$762$	24.1559	0.875077
$763$	6.57450	0.238013
$764$	8.32639	0.301238
$765$	0	0
$766$	−27.0001	−0.975555
$767$	5.15987	0.186312
$768$	21.6519	0.781295
$769$	17.0008	0.613066	0.306533	−	0.951860i	$-0.400831\pi$
$769$	17.0008	0.613066	0.306533	+	0.951860i	$0.400831\pi$
$770$	0	0
$771$	−74.6738	−2.68931
$772$	5.40350	0.194476
$773$	−6.51767	−0.234424	−0.117212	−	0.993107i	$-0.537396\pi$
$773$	−6.51767	−0.234424	−0.117212	+	0.993107i	$0.537396\pi$
$774$	−56.2034	−2.02019
$775$	0	0
$776$	−6.09609	−0.218837
$777$	27.3317	0.980518
$778$	−17.4009	−0.623853
$779$	18.3120	0.656095
$780$	0	0
$781$	6.96983	0.249400
$782$	13.8360	0.494775
$783$	23.0508	0.823768
$784$	16.5307	0.590381
$785$	0	0
$786$	21.0253	0.749948
$787$	4.22353	0.150553	0.0752763	−	0.997163i	$-0.476016\pi$
$787$	4.22353	0.150553	0.0752763	+	0.997163i	$0.476016\pi$
$788$	−5.14578	−0.183311
$789$	−16.8008	−0.598124
$790$	0	0
$791$	13.5147	0.480529
$792$	−31.8798	−1.13280
$793$	−43.8853	−1.55841
$794$	9.30994	0.330397
$795$	0	0
$796$	1.13488	0.0402247
$797$	0.0413582	0.00146498	0.000732491	−	1.00000i	$-0.499767\pi$
$797$	0.0413582	0.00146498	0.000732491		1.00000i	$0.499767\pi$
$798$	−12.3654	−0.437732
$799$	−6.69374	−0.236807
$800$	0	0
$801$	−60.6488	−2.14292
$802$	−29.1012	−1.02760
$803$	−28.5151	−1.00628
$804$	−10.1510	−0.358000
$805$	0	0
$806$	−21.8531	−0.769742
$807$	39.4356	1.38820
$808$	−31.8942	−1.12203
$809$	30.8971	1.08628	0.543142	−	0.839641i	$-0.317235\pi$
$809$	30.8971	1.08628	0.543142	+	0.839641i	$0.317235\pi$
$810$	0	0
$811$	20.6037	0.723493	0.361746	−	0.932277i	$-0.382181\pi$
$811$	20.6037	0.723493	0.361746	+	0.932277i	$0.382181\pi$
$812$	1.33239	0.0467578
$813$	34.0702	1.19490
$814$	−16.4475	−0.576484
$815$	0	0
$816$	−64.1470	−2.24559
$817$	−18.0416	−0.631194
$818$	9.31959	0.325852
$819$	25.3733	0.886613
$820$	0	0
$821$	36.2733	1.26595	0.632974	−	0.774173i	$-0.281834\pi$
$821$	36.2733	1.26595	0.632974	+	0.774173i	$0.281834\pi$
$822$	38.0250	1.32627
$823$	51.4134	1.79216	0.896078	−	0.443896i	$-0.146404\pi$
$823$	51.4134	1.79216	0.896078	+	0.443896i	$0.146404\pi$
$824$	−40.4953	−1.41072
$825$	0	0
$826$	2.86887	0.0998208
$827$	24.4313	0.849558	0.424779	−	0.905297i	$-0.360352\pi$
$827$	24.4313	0.849558	0.424779	+	0.905297i	$0.360352\pi$
$828$	2.81739	0.0979110
$829$	−4.34631	−0.150954	−0.0754768	−	0.997148i	$-0.524048\pi$
$829$	−4.34631	−0.150954	−0.0754768	+	0.997148i	$0.524048\pi$
$830$	0	0
$831$	13.9141	0.482675
$832$	28.7298	0.996027
$833$	33.8570	1.17308
$834$	−49.3052	−1.70730
$835$	0	0
$836$	−1.39619	−0.0482882
$837$	39.4403	1.36326
$838$	−42.7592	−1.47709
$839$	−50.2417	−1.73454	−0.867268	−	0.497841i	$-0.834126\pi$
$839$	−50.2417	−1.73454	−0.867268	+	0.497841i	$0.834126\pi$
$840$	0	0
$841$	−19.8438	−0.684268
$842$	3.31701	0.114312
$843$	34.1155	1.17500
$844$	−6.28347	−0.216286
$845$	0	0
$846$	7.26445	0.249757
$847$	−10.3255	−0.354788
$848$	41.5373	1.42640
$849$	−85.6177	−2.93839
$850$	0	0
$851$	10.6540	0.365215
$852$	3.40793	0.116754
$853$	−21.5835	−0.739006	−0.369503	−	0.929230i	$-0.620472\pi$
$853$	−21.5835	−0.739006	−0.369503	+	0.929230i	$0.620472\pi$
$854$	−24.4001	−0.834954
$855$	0	0
$856$	−29.1291	−0.995612
$857$	−28.6381	−0.978258	−0.489129	−	0.872211i	$-0.662685\pi$
$857$	−28.6381	−0.978258	−0.489129	+	0.872211i	$0.662685\pi$
$858$	−23.4518	−0.800630
$859$	−16.2773	−0.555374	−0.277687	−	0.960672i	$-0.589568\pi$
$859$	−16.2773	−0.555374	−0.277687	+	0.960672i	$0.589568\pi$
$860$	0	0
$861$	−32.0879	−1.09355
$862$	0.504886	0.0171965
$863$	−28.4598	−0.968782	−0.484391	−	0.874852i	$-0.660959\pi$
$863$	−28.4598	−0.968782	−0.484391	+	0.874852i	$0.660959\pi$
$864$	−13.4813	−0.458642
$865$	0	0
$866$	23.5273	0.799491
$867$	−81.5338	−2.76903
$868$	2.27975	0.0773796
$869$	6.86779	0.232974
$870$	0	0
$871$	−35.6359	−1.20748
$872$	−14.1791	−0.480164
$873$	11.3546	0.384295
$874$	−4.82011	−0.163043
$875$	0	0
$876$	−13.9426	−0.471076
$877$	3.33339	0.112561	0.0562804	−	0.998415i	$-0.482076\pi$
$877$	3.33339	0.112561	0.0562804	+	0.998415i	$0.482076\pi$
$878$	5.71590	0.192902
$879$	−61.0817	−2.06023
$880$	0	0
$881$	9.45635	0.318593	0.159296	−	0.987231i	$-0.449077\pi$
$881$	9.45635	0.318593	0.159296	+	0.987231i	$0.449077\pi$
$882$	−36.7437	−1.23723
$883$	−2.82689	−0.0951323	−0.0475662	−	0.998868i	$-0.515146\pi$
$883$	−2.82689	−0.0951323	−0.0475662	+	0.998868i	$0.515146\pi$
$884$	6.87929	0.231376
$885$	0	0
$886$	−18.7511	−0.629955
$887$	−22.3355	−0.749952	−0.374976	−	0.927035i	$-0.622349\pi$
$887$	−22.3355	−0.749952	−0.374976	+	0.927035i	$0.622349\pi$
$888$	−58.9456	−1.97808
$889$	−8.84657	−0.296704
$890$	0	0
$891$	10.5035	0.351881
$892$	0.154263	0.00516512
$893$	2.33193	0.0780349
$894$	−47.5844	−1.59146
$895$	0	0
$896$	11.0413	0.368864
$897$	15.1911	0.507217
$898$	−38.8461	−1.29631
$899$	15.6665	0.522507
$900$	0	0
$901$	85.0738	2.83422
$902$	19.3096	0.642941
$903$	31.6140	1.05205
$904$	−29.1469	−0.969412
$905$	0	0
$906$	58.4411	1.94158
$907$	−17.1828	−0.570545	−0.285272	−	0.958446i	$-0.592084\pi$
$907$	−17.1828	−0.570545	−0.285272	+	0.958446i	$0.592084\pi$
$908$	−1.73042	−0.0574259
$909$	59.4062	1.97038
$910$	0	0
$911$	−20.7182	−0.686425	−0.343213	−	0.939258i	$-0.611515\pi$
$911$	−20.7182	−0.686425	−0.343213	+	0.939258i	$0.611515\pi$
$912$	22.3472	0.739989
$913$	22.2778	0.737288
$914$	7.62992	0.252375
$915$	0	0
$916$	8.83225	0.291826
$917$	−7.70005	−0.254278
$918$	66.1714	2.18398
$919$	−40.9712	−1.35151	−0.675757	−	0.737125i	$-0.736183\pi$
$919$	−40.9712	−1.35151	−0.675757	+	0.737125i	$0.736183\pi$
$920$	0	0
$921$	−78.8784	−2.59913
$922$	8.68468	0.286015
$923$	11.9638	0.393792
$924$	2.44652	0.0804847
$925$	0	0
$926$	0.140328	0.00461147
$927$	75.4266	2.47734
$928$	−5.35503	−0.175788
$929$	43.5119	1.42758	0.713790	−	0.700360i	$-0.246977\pi$
$929$	43.5119	1.42758	0.713790	+	0.700360i	$0.246977\pi$
$930$	0	0
$931$	−11.7949	−0.386563
$932$	2.31796	0.0759274
$933$	−50.9633	−1.66846
$934$	−16.4955	−0.539748
$935$	0	0
$936$	−54.7219	−1.78864
$937$	38.2212	1.24863	0.624316	−	0.781172i	$-0.285378\pi$
$937$	38.2212	1.24863	0.624316	+	0.781172i	$0.285378\pi$
$938$	−19.8135	−0.646933
$939$	10.1360	0.330777
$940$	0	0
$941$	−15.5248	−0.506095	−0.253048	−	0.967454i	$-0.581433\pi$
$941$	−15.5248	−0.506095	−0.253048	+	0.967454i	$0.581433\pi$
$942$	2.53381	0.0825559
$943$	−12.5080	−0.407317
$944$	−5.18471	−0.168748
$945$	0	0
$946$	−19.0245	−0.618539
$947$	12.9251	0.420008	0.210004	−	0.977701i	$-0.432652\pi$
$947$	12.9251	0.420008	0.210004	+	0.977701i	$0.432652\pi$
$948$	3.35804	0.109064
$949$	−48.9464	−1.58887
$950$	0	0
$951$	25.8232	0.837375
$952$	28.0349	0.908617
$953$	6.03650	0.195542	0.0977708	−	0.995209i	$-0.468829\pi$
$953$	6.03650	0.195542	0.0977708	+	0.995209i	$0.468829\pi$
$954$	−92.3273	−2.98921
$955$	0	0
$956$	−5.27667	−0.170660
$957$	16.8126	0.543474
$958$	27.3447	0.883466
$959$	−13.9258	−0.449688
$960$	0	0
$961$	−4.19435	−0.135302
$962$	−28.2322	−0.910244
$963$	54.2560	1.74837
$964$	4.55435	0.146686
$965$	0	0
$966$	8.44622	0.271753
$967$	56.7615	1.82533	0.912664	−	0.408711i	$-0.134021\pi$
$967$	56.7615	1.82533	0.912664	+	0.408711i	$0.134021\pi$
$968$	22.2687	0.715744
$969$	45.7700	1.47034
$970$	0	0
$971$	−23.7181	−0.761149	−0.380574	−	0.924750i	$-0.624274\pi$
$971$	−23.7181	−0.761149	−0.380574	+	0.924750i	$0.624274\pi$
$972$	−2.08527	−0.0668852
$973$	18.0569	0.578879
$974$	−4.58665	−0.146966
$975$	0	0
$976$	44.0966	1.41150
$977$	−47.6492	−1.52443	−0.762217	−	0.647322i	$-0.775889\pi$
$977$	−47.6492	−1.52443	−0.762217	+	0.647322i	$0.775889\pi$
$978$	47.6321	1.52311
$979$	−20.5292	−0.656117
$980$	0	0
$981$	26.4100	0.843206
$982$	6.19008	0.197533
$983$	44.8564	1.43070	0.715348	−	0.698769i	$-0.246268\pi$
$983$	44.8564	1.43070	0.715348	+	0.698769i	$0.246268\pi$
$984$	69.2032	2.20612
$985$	0	0
$986$	26.2846	0.837073
$987$	−4.08620	−0.130065
$988$	−2.39657	−0.0762450
$989$	12.3233	0.391858
$990$	0	0
$991$	−51.3548	−1.63134	−0.815670	−	0.578517i	$-0.803632\pi$
$991$	−51.3548	−1.63134	−0.815670	+	0.578517i	$0.803632\pi$
$992$	−9.16256	−0.290912
$993$	−50.1105	−1.59021
$994$	6.65182	0.210983
$995$	0	0
$996$	10.8928	0.345153
$997$	17.4060	0.551255	0.275627	−	0.961265i	$-0.411114\pi$
$997$	17.4060	0.551255	0.275627	+	0.961265i	$0.411114\pi$
$998$	8.61195	0.272606
$999$	50.9534	1.61209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.i.1.9		11
5.2	odd	4		235.2.c.a.189.16	yes	22
5.3	odd	4		235.2.c.a.189.7	✓	22
5.4	even	2		1175.2.a.j.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.c.a.189.7	✓	22	5.3	odd	4
235.2.c.a.189.16	yes	22	5.2	odd	4
1175.2.a.i.1.9		11	1.1	even	1	trivial
1175.2.a.j.1.3		11	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q+1.29770 q^{2} -2.93223 q^{3} -0.315973 q^{4} -3.80515 q^{6} +1.39355 q^{7} -3.00544 q^{8} +5.59794 q^{9} +O(q^{10})\)	\(q+1.29770 q^{2} -2.93223 q^{3} -0.315973 q^{4} -3.80515 q^{6} +1.39355 q^{7} -3.00544 q^{8} +5.59794 q^{9} +1.89487 q^{11} +0.926505 q^{12} +3.25256 q^{13} +1.80841 q^{14} -3.26821 q^{16} -6.69374 q^{17} +7.26445 q^{18} +2.33193 q^{19} -4.08620 q^{21} +2.45897 q^{22} -1.59282 q^{23} +8.81263 q^{24} +4.22084 q^{26} -7.61776 q^{27} -0.440325 q^{28} -3.02593 q^{29} -5.17742 q^{31} +1.76972 q^{32} -5.55618 q^{33} -8.68647 q^{34} -1.76880 q^{36} -6.68877 q^{37} +3.02614 q^{38} -9.53723 q^{39} +7.85273 q^{41} -5.30267 q^{42} -7.73676 q^{43} -0.598728 q^{44} -2.06701 q^{46} +1.00000 q^{47} +9.58314 q^{48} -5.05802 q^{49} +19.6275 q^{51} -1.02772 q^{52} -12.7095 q^{53} -9.88557 q^{54} -4.18823 q^{56} -6.83773 q^{57} -3.92675 q^{58} +1.58640 q^{59} -13.4926 q^{61} -6.71874 q^{62} +7.80102 q^{63} +8.83299 q^{64} -7.21026 q^{66} -10.9563 q^{67} +2.11504 q^{68} +4.67052 q^{69} +3.67827 q^{71} -16.8243 q^{72} -15.0486 q^{73} -8.68002 q^{74} -0.736826 q^{76} +2.64059 q^{77} -12.3765 q^{78} +3.62442 q^{79} +5.54314 q^{81} +10.1905 q^{82} +11.7569 q^{83} +1.29113 q^{84} -10.0400 q^{86} +8.87270 q^{87} -5.69491 q^{88} -10.8341 q^{89} +4.53260 q^{91} +0.503290 q^{92} +15.1814 q^{93} +1.29770 q^{94} -5.18921 q^{96} +2.02835 q^{97} -6.56379 q^{98} +10.6074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{2} - 4 q^{3} + 10 q^{4} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q - 4 * q^2 - 4 * q^3 + 10 * q^4 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 9 * q^9	\( 11 q - 4 q^{2} - 4 q^{3} + 10 q^{4} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 9 q^{9} - 12 q^{12} - 19 q^{13} + 12 q^{16} - 16 q^{17} + 10 q^{18} - 6 q^{21} - 22 q^{22} - 3 q^{23} - 12 q^{24} + 6 q^{26} - 16 q^{27} - 18 q^{28} + 4 q^{29} + 2 q^{31} - 28 q^{32} - 18 q^{33} - 16 q^{34} - 8 q^{36} - 40 q^{37} + 14 q^{38} - 10 q^{39} + 4 q^{41} - 16 q^{42} - 23 q^{43} + 24 q^{44} - 16 q^{46} + 11 q^{47} + 18 q^{48} + 5 q^{49} + 12 q^{51} - 46 q^{52} - 16 q^{53} + 26 q^{56} - 42 q^{57} - 16 q^{58} + 7 q^{59} - 7 q^{61} - 14 q^{63} + 24 q^{64} + 12 q^{66} - 32 q^{67} + 58 q^{68} - 2 q^{69} - 17 q^{71} - 57 q^{73} - 16 q^{74} - 10 q^{76} - 8 q^{77} + 22 q^{78} - 13 q^{79} - 25 q^{81} - 12 q^{82} - 8 q^{83} - 4 q^{84} - 6 q^{86} + 10 q^{87} - 26 q^{88} - 37 q^{89} + 32 q^{91} - 4 q^{92} + 10 q^{93} - 4 q^{94} - 6 q^{96} - 32 q^{97} + 20 q^{98} - 8 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 - 4 * q^3 + 10 * q^4 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 9 * q^9 - 12 * q^12 - 19 * q^13 + 12 * q^16 - 16 * q^17 + 10 * q^18 - 6 * q^21 - 22 * q^22 - 3 * q^23 - 12 * q^24 + 6 * q^26 - 16 * q^27 - 18 * q^28 + 4 * q^29 + 2 * q^31 - 28 * q^32 - 18 * q^33 - 16 * q^34 - 8 * q^36 - 40 * q^37 + 14 * q^38 - 10 * q^39 + 4 * q^41 - 16 * q^42 - 23 * q^43 + 24 * q^44 - 16 * q^46 + 11 * q^47 + 18 * q^48 + 5 * q^49 + 12 * q^51 - 46 * q^52 - 16 * q^53 + 26 * q^56 - 42 * q^57 - 16 * q^58 + 7 * q^59 - 7 * q^61 - 14 * q^63 + 24 * q^64 + 12 * q^66 - 32 * q^67 + 58 * q^68 - 2 * q^69 - 17 * q^71 - 57 * q^73 - 16 * q^74 - 10 * q^76 - 8 * q^77 + 22 * q^78 - 13 * q^79 - 25 * q^81 - 12 * q^82 - 8 * q^83 - 4 * q^84 - 6 * q^86 + 10 * q^87 - 26 * q^88 - 37 * q^89 + 32 * q^91 - 4 * q^92 + 10 * q^93 - 4 * q^94 - 6 * q^96 - 32 * q^97 + 20 * q^98 - 8 * q^99

Introduction

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