LMFDB - Embedded newform 1075.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$8.58391821729$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 13x^{4} + 15x^{3} - 7x^{2} - 4x + 1 $ x^7 - 3x^6 - 6x^5 + 13x^4 + 15x^3 - 7x^2 - 4x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.25270$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25270 q^{2} +2.38208 q^{3} +3.07465 q^{4} -5.36611 q^{6} +3.07793 q^{7} -2.42085 q^{8} +2.67432 q^{9} +O(q^{10})$	\(q-2.25270 q^{2} +2.38208 q^{3} +3.07465 q^{4} -5.36611 q^{6} +3.07793 q^{7} -2.42085 q^{8} +2.67432 q^{9} +4.46001 q^{11} +7.32406 q^{12} +1.59968 q^{13} -6.93364 q^{14} -0.695842 q^{16} +7.07060 q^{17} -6.02444 q^{18} -4.61958 q^{19} +7.33188 q^{21} -10.0471 q^{22} -0.363843 q^{23} -5.76668 q^{24} -3.60359 q^{26} -0.775792 q^{27} +9.46353 q^{28} +0.297542 q^{29} -9.19492 q^{31} +6.40923 q^{32} +10.6241 q^{33} -15.9279 q^{34} +8.22260 q^{36} +5.91510 q^{37} +10.4065 q^{38} +3.81056 q^{39} -1.41529 q^{41} -16.5165 q^{42} -1.00000 q^{43} +13.7130 q^{44} +0.819628 q^{46} -5.47092 q^{47} -1.65755 q^{48} +2.47363 q^{49} +16.8428 q^{51} +4.91844 q^{52} +6.36882 q^{53} +1.74762 q^{54} -7.45121 q^{56} -11.0042 q^{57} -0.670272 q^{58} -0.464984 q^{59} -3.41781 q^{61} +20.7134 q^{62} +8.23136 q^{63} -13.0464 q^{64} -23.9329 q^{66} -12.0697 q^{67} +21.7396 q^{68} -0.866704 q^{69} +11.6085 q^{71} -6.47414 q^{72} -10.8922 q^{73} -13.3249 q^{74} -14.2036 q^{76} +13.7276 q^{77} -8.58404 q^{78} -6.89981 q^{79} -9.87097 q^{81} +3.18821 q^{82} -13.4456 q^{83} +22.5429 q^{84} +2.25270 q^{86} +0.708770 q^{87} -10.7970 q^{88} +4.02816 q^{89} +4.92368 q^{91} -1.11869 q^{92} -21.9031 q^{93} +12.3243 q^{94} +15.2673 q^{96} +17.4706 q^{97} -5.57233 q^{98} +11.9275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 5 q^{3} + 8 q^{4} + 4 q^{6} + 3 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 5 * q^3 + 8 * q^4 + 4 * q^6 + 3 * q^7 + 3 * q^8 + 8 * q^9	$ 7 q + 4 q^{2} + 5 q^{3} + 8 q^{4} + 4 q^{6} + 3 q^{7} + 3 q^{8} + 8 q^{9} + q^{11} + 23 q^{12} + 14 q^{13} - 17 q^{14} + 2 q^{16} + 12 q^{17} + 15 q^{18} - 4 q^{21} - 17 q^{22} + 18 q^{23} + 17 q^{24} + 12 q^{26} + 8 q^{27} - 2 q^{28} + 10 q^{29} - 15 q^{31} + 15 q^{32} + 20 q^{33} - 8 q^{34} + 32 q^{36} + 5 q^{37} + 4 q^{38} + 10 q^{39} - 21 q^{41} - 47 q^{42} - 7 q^{43} + 13 q^{44} + 4 q^{46} + 2 q^{47} + 33 q^{48} + 16 q^{49} + 16 q^{51} + 2 q^{52} + 42 q^{53} + 3 q^{54} - 28 q^{56} - 8 q^{57} + 30 q^{58} + 9 q^{59} + 4 q^{61} + 35 q^{62} - 8 q^{63} - 11 q^{64} - 24 q^{66} - 28 q^{67} + 30 q^{68} - 38 q^{69} + 2 q^{71} + 9 q^{72} + 11 q^{73} - 17 q^{74} - 36 q^{76} + 58 q^{77} - 2 q^{78} - 9 q^{79} - 25 q^{81} - 28 q^{82} + 12 q^{83} - 46 q^{84} - 4 q^{86} + 20 q^{87} - 14 q^{88} + 6 q^{89} - 42 q^{93} + 20 q^{94} + 40 q^{96} + 26 q^{97} + 13 q^{98} + 7 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 + 5 * q^3 + 8 * q^4 + 4 * q^6 + 3 * q^7 + 3 * q^8 + 8 * q^9 + q^11 + 23 * q^12 + 14 * q^13 - 17 * q^14 + 2 * q^16 + 12 * q^17 + 15 * q^18 - 4 * q^21 - 17 * q^22 + 18 * q^23 + 17 * q^24 + 12 * q^26 + 8 * q^27 - 2 * q^28 + 10 * q^29 - 15 * q^31 + 15 * q^32 + 20 * q^33 - 8 * q^34 + 32 * q^36 + 5 * q^37 + 4 * q^38 + 10 * q^39 - 21 * q^41 - 47 * q^42 - 7 * q^43 + 13 * q^44 + 4 * q^46 + 2 * q^47 + 33 * q^48 + 16 * q^49 + 16 * q^51 + 2 * q^52 + 42 * q^53 + 3 * q^54 - 28 * q^56 - 8 * q^57 + 30 * q^58 + 9 * q^59 + 4 * q^61 + 35 * q^62 - 8 * q^63 - 11 * q^64 - 24 * q^66 - 28 * q^67 + 30 * q^68 - 38 * q^69 + 2 * q^71 + 9 * q^72 + 11 * q^73 - 17 * q^74 - 36 * q^76 + 58 * q^77 - 2 * q^78 - 9 * q^79 - 25 * q^81 - 28 * q^82 + 12 * q^83 - 46 * q^84 - 4 * q^86 + 20 * q^87 - 14 * q^88 + 6 * q^89 - 42 * q^93 + 20 * q^94 + 40 * q^96 + 26 * q^97 + 13 * q^98 + 7 * 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 $

$2$	−2.25270	−1.59290	−0.796449	−	0.604706i	$-0.793291\pi$
$2$	−2.25270	−1.59290	−0.796449	+	0.604706i	$0.793291\pi$
$3$	2.38208	1.37530	0.687648	−	0.726044i	$-0.258643\pi$
$3$	2.38208	1.37530	0.687648	+	0.726044i	$0.258643\pi$
$4$	3.07465	1.53732
$5$	0	0
$5$	0	0
$6$	−5.36611	−2.19071
$7$	3.07793	1.16335	0.581673	−	0.813423i	$-0.302398\pi$
$7$	3.07793	1.16335	0.581673	+	0.813423i	$0.302398\pi$
$8$	−2.42085	−0.855901
$9$	2.67432	0.891441
$10$	0	0
$11$	4.46001	1.34474	0.672372	−	0.740214i	$-0.265276\pi$
$11$	4.46001	1.34474	0.672372	+	0.740214i	$0.265276\pi$
$12$	7.32406	2.11428
$13$	1.59968	0.443670	0.221835	−	0.975084i	$-0.428795\pi$
$13$	1.59968	0.443670	0.221835	+	0.975084i	$0.428795\pi$
$14$	−6.93364	−1.85309
$15$	0	0
$16$	−0.695842	−0.173961
$17$	7.07060	1.71487	0.857436	−	0.514591i	$-0.172056\pi$
$17$	7.07060	1.71487	0.857436	+	0.514591i	$0.172056\pi$
$18$	−6.02444	−1.41997
$19$	−4.61958	−1.05980	−0.529902	−	0.848059i	$-0.677771\pi$
$19$	−4.61958	−1.05980	−0.529902	+	0.848059i	$0.677771\pi$
$20$	0	0
$21$	7.33188	1.59995
$22$	−10.0471	−2.14204
$23$	−0.363843	−0.0758665	−0.0379332	−	0.999280i	$-0.512077\pi$
$23$	−0.363843	−0.0758665	−0.0379332	+	0.999280i	$0.512077\pi$
$24$	−5.76668	−1.17712
$25$	0	0
$26$	−3.60359	−0.706721
$27$	−0.775792	−0.149301
$28$	9.46353	1.78844
$29$	0.297542	0.0552521	0.0276261	−	0.999618i	$-0.491205\pi$
$29$	0.297542	0.0552521	0.0276261	+	0.999618i	$0.491205\pi$
$30$	0	0
$31$	−9.19492	−1.65146	−0.825728	−	0.564069i	$-0.809235\pi$
$31$	−9.19492	−1.65146	−0.825728	+	0.564069i	$0.809235\pi$
$32$	6.40923	1.13300
$33$	10.6241	1.84942
$34$	−15.9279	−2.73161
$35$	0	0
$36$	8.22260	1.37043
$37$	5.91510	0.972437	0.486218	−	0.873837i	$-0.338376\pi$
$37$	5.91510	0.972437	0.486218	+	0.873837i	$0.338376\pi$
$38$	10.4065	1.68816
$39$	3.81056	0.610178
$40$	0	0
$41$	−1.41529	−0.221031	−0.110515	−	0.993874i	$-0.535250\pi$
$41$	−1.41529	−0.221031	−0.110515	+	0.993874i	$0.535250\pi$
$42$	−16.5165	−2.54855
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	13.7130	2.06731
$45$	0	0
$46$	0.819628	0.120848
$47$	−5.47092	−0.798016	−0.399008	−	0.916947i	$-0.630645\pi$
$47$	−5.47092	−0.798016	−0.399008	+	0.916947i	$0.630645\pi$
$48$	−1.65755	−0.239247
$49$	2.47363	0.353375
$50$	0	0
$51$	16.8428	2.35846
$52$	4.91844	0.682065
$53$	6.36882	0.874825	0.437412	−	0.899261i	$-0.355895\pi$
$53$	6.36882	0.874825	0.437412	+	0.899261i	$0.355895\pi$
$54$	1.74762	0.237822
$55$	0	0
$56$	−7.45121	−0.995709
$57$	−11.0042	−1.45755
$58$	−0.670272	−0.0880110
$59$	−0.464984	−0.0605358	−0.0302679	−	0.999542i	$-0.509636\pi$
$59$	−0.464984	−0.0605358	−0.0302679	+	0.999542i	$0.509636\pi$
$60$	0	0
$61$	−3.41781	−0.437606	−0.218803	−	0.975769i	$-0.570215\pi$
$61$	−3.41781	−0.437606	−0.218803	+	0.975769i	$0.570215\pi$
$62$	20.7134	2.63060
$63$	8.23136	1.03705
$64$	−13.0464	−1.63080
$65$	0	0
$66$	−23.9329	−2.94594
$67$	−12.0697	−1.47455	−0.737274	−	0.675594i	$-0.763887\pi$
$67$	−12.0697	−1.47455	−0.737274	+	0.675594i	$0.763887\pi$
$68$	21.7396	2.63631
$69$	−0.866704	−0.104339
$70$	0	0
$71$	11.6085	1.37768	0.688838	−	0.724916i	$-0.258121\pi$
$71$	11.6085	1.37768	0.688838	+	0.724916i	$0.258121\pi$
$72$	−6.47414	−0.762985
$73$	−10.8922	−1.27483	−0.637417	−	0.770519i	$-0.719997\pi$
$73$	−10.8922	−1.27483	−0.637417	+	0.770519i	$0.719997\pi$
$74$	−13.3249	−1.54899
$75$	0	0
$76$	−14.2036	−1.62926
$77$	13.7276	1.56440
$78$	−8.58404	−0.971951
$79$	−6.89981	−0.776289	−0.388145	−	0.921598i	$-0.626884\pi$
$79$	−6.89981	−0.776289	−0.388145	+	0.921598i	$0.626884\pi$
$80$	0	0
$81$	−9.87097	−1.09677
$82$	3.18821	0.352079
$83$	−13.4456	−1.47585	−0.737924	−	0.674884i	$-0.764194\pi$
$83$	−13.4456	−1.47585	−0.737924	+	0.674884i	$0.764194\pi$
$84$	22.5429	2.45964
$85$	0	0
$86$	2.25270	0.242915
$87$	0.708770	0.0759881
$88$	−10.7970	−1.15097
$89$	4.02816	0.426984	0.213492	−	0.976945i	$-0.431516\pi$
$89$	4.02816	0.426984	0.213492	+	0.976945i	$0.431516\pi$
$90$	0	0
$91$	4.92368	0.516142
$92$	−1.11869	−0.116631
$93$	−21.9031	−2.27124
$94$	12.3243	1.27116
$95$	0	0
$96$	15.2673	1.55821
$97$	17.4706	1.77387	0.886933	−	0.461897i	$-0.152831\pi$
$97$	17.4706	1.77387	0.886933	+	0.461897i	$0.152831\pi$
$98$	−5.57233	−0.562891
$99$	11.9275	1.19876
$100$	0	0
$101$	−1.79111	−0.178222	−0.0891109	−	0.996022i	$-0.528403\pi$
$101$	−1.79111	−0.178222	−0.0891109	+	0.996022i	$0.528403\pi$
$102$	−37.9416	−3.75678
$103$	15.1408	1.49187	0.745934	−	0.666020i	$-0.232003\pi$
$103$	15.1408	1.49187	0.745934	+	0.666020i	$0.232003\pi$
$104$	−3.87258	−0.379738
$105$	0	0
$106$	−14.3470	−1.39351
$107$	−2.32537	−0.224802	−0.112401	−	0.993663i	$-0.535854\pi$
$107$	−2.32537	−0.224802	−0.112401	+	0.993663i	$0.535854\pi$
$108$	−2.38529	−0.229524
$109$	4.41609	0.422985	0.211492	−	0.977380i	$-0.432168\pi$
$109$	4.41609	0.422985	0.211492	+	0.977380i	$0.432168\pi$
$110$	0	0
$111$	14.0903	1.33739
$112$	−2.14175	−0.202376
$113$	−11.9809	−1.12706	−0.563532	−	0.826094i	$-0.690558\pi$
$113$	−11.9809	−1.12706	−0.563532	+	0.826094i	$0.690558\pi$
$114$	24.7892	2.32172
$115$	0	0
$116$	0.914836	0.0849404
$117$	4.27805	0.395506
$118$	1.04747	0.0964273
$119$	21.7628	1.99499
$120$	0	0
$121$	8.89168	0.808335
$122$	7.69930	0.697061
$123$	−3.37133	−0.303982
$124$	−28.2711	−2.53882
$125$	0	0
$126$	−18.5428	−1.65192
$127$	4.15791	0.368955	0.184477	−	0.982837i	$-0.440941\pi$
$127$	4.15791	0.368955	0.184477	+	0.982837i	$0.440941\pi$
$128$	16.5711	1.46469
$129$	−2.38208	−0.209731
$130$	0	0
$131$	18.1982	1.58998	0.794991	−	0.606621i	$-0.207476\pi$
$131$	18.1982	1.58998	0.794991	+	0.606621i	$0.207476\pi$
$132$	32.6654	2.84316
$133$	−14.2187	−1.23292
$134$	27.1894	2.34880
$135$	0	0
$136$	−17.1169	−1.46776
$137$	9.00594	0.769429	0.384715	−	0.923036i	$-0.374300\pi$
$137$	9.00594	0.769429	0.384715	+	0.923036i	$0.374300\pi$
$138$	1.95242	0.166201
$139$	5.34436	0.453303	0.226651	−	0.973976i	$-0.427222\pi$
$139$	5.34436	0.453303	0.226651	+	0.973976i	$0.427222\pi$
$140$	0	0
$141$	−13.0322	−1.09751
$142$	−26.1504	−2.19450
$143$	7.13457	0.596623
$144$	−1.86091	−0.155075
$145$	0	0
$146$	24.5368	2.03068
$147$	5.89239	0.485996
$148$	18.1868	1.49495
$149$	7.70678	0.631364	0.315682	−	0.948865i	$-0.397767\pi$
$149$	7.70678	0.631364	0.315682	+	0.948865i	$0.397767\pi$
$150$	0	0
$151$	3.32048	0.270217	0.135108	−	0.990831i	$-0.456862\pi$
$151$	3.32048	0.270217	0.135108	+	0.990831i	$0.456862\pi$
$152$	11.1833	0.907088
$153$	18.9091	1.52871
$154$	−30.9241	−2.49193
$155$	0	0
$156$	11.7161	0.938041
$157$	−11.3760	−0.907902	−0.453951	−	0.891027i	$-0.649986\pi$
$157$	−11.3760	−0.907902	−0.453951	+	0.891027i	$0.649986\pi$
$158$	15.5432	1.23655
$159$	15.1711	1.20314
$160$	0	0
$161$	−1.11988	−0.0882590
$162$	22.2363	1.74705
$163$	17.5360	1.37353	0.686764	−	0.726881i	$-0.259031\pi$
$163$	17.5360	1.37353	0.686764	+	0.726881i	$0.259031\pi$
$164$	−4.35150	−0.339795
$165$	0	0
$166$	30.2889	2.35087
$167$	−1.31455	−0.101723	−0.0508616	−	0.998706i	$-0.516197\pi$
$167$	−1.31455	−0.101723	−0.0508616	+	0.998706i	$0.516197\pi$
$168$	−17.7494	−1.36940
$169$	−10.4410	−0.803157
$170$	0	0
$171$	−12.3543	−0.944753
$172$	−3.07465	−0.234440
$173$	18.7477	1.42536	0.712681	−	0.701488i	$-0.247481\pi$
$173$	18.7477	1.42536	0.712681	+	0.701488i	$0.247481\pi$
$174$	−1.59664	−0.121041
$175$	0	0
$176$	−3.10346	−0.233932
$177$	−1.10763	−0.0832547
$178$	−9.07423	−0.680143
$179$	−14.7930	−1.10568	−0.552842	−	0.833286i	$-0.686457\pi$
$179$	−14.7930	−1.10568	−0.552842	+	0.833286i	$0.686457\pi$
$180$	0	0
$181$	−12.4465	−0.925141	−0.462570	−	0.886583i	$-0.653073\pi$
$181$	−12.4465	−0.925141	−0.462570	+	0.886583i	$0.653073\pi$
$182$	−11.0916	−0.822162
$183$	−8.14151	−0.601838
$184$	0.880810	0.0649342
$185$	0	0
$186$	49.3410	3.61786
$187$	31.5349	2.30606
$188$	−16.8211	−1.22681
$189$	−2.38783	−0.173689
$190$	0	0
$191$	−5.24115	−0.379236	−0.189618	−	0.981858i	$-0.560725\pi$
$191$	−5.24115	−0.379236	−0.189618	+	0.981858i	$0.560725\pi$
$192$	−31.0775	−2.24283
$193$	0.562987	0.0405247	0.0202623	−	0.999795i	$-0.493550\pi$
$193$	0.562987	0.0405247	0.0202623	+	0.999795i	$0.493550\pi$
$194$	−39.3559	−2.82559
$195$	0	0
$196$	7.60553	0.543252
$197$	−7.23855	−0.515725	−0.257863	−	0.966182i	$-0.583018\pi$
$197$	−7.23855	−0.515725	−0.257863	+	0.966182i	$0.583018\pi$
$198$	−26.8691	−1.90950
$199$	25.5395	1.81045	0.905223	−	0.424937i	$-0.139704\pi$
$199$	25.5395	1.81045	0.905223	+	0.424937i	$0.139704\pi$
$200$	0	0
$201$	−28.7510	−2.02794
$202$	4.03482	0.283889
$203$	0.915812	0.0642774
$204$	51.7855	3.62571
$205$	0	0
$206$	−34.1077	−2.37639
$207$	−0.973033	−0.0676305
$208$	−1.11312	−0.0771811
$209$	−20.6034	−1.42517
$210$	0	0
$211$	−8.23946	−0.567228	−0.283614	−	0.958939i	$-0.591533\pi$
$211$	−8.23946	−0.567228	−0.283614	+	0.958939i	$0.591533\pi$
$212$	19.5819	1.34489
$213$	27.6524	1.89471
$214$	5.23836	0.358087
$215$	0	0
$216$	1.87808	0.127787
$217$	−28.3013	−1.92122
$218$	−9.94811	−0.673771
$219$	−25.9461	−1.75327
$220$	0	0
$221$	11.3107	0.760837
$222$	−31.7411	−2.13032
$223$	−9.48879	−0.635417	−0.317708	−	0.948189i	$-0.602913\pi$
$223$	−9.48879	−0.635417	−0.317708	+	0.948189i	$0.602913\pi$
$224$	19.7271	1.31807
$225$	0	0
$226$	26.9893	1.79530
$227$	−13.3748	−0.887713	−0.443857	−	0.896098i	$-0.646390\pi$
$227$	−13.3748	−0.887713	−0.443857	+	0.896098i	$0.646390\pi$
$228$	−33.8341	−2.24072
$229$	10.3251	0.682302	0.341151	−	0.940008i	$-0.389183\pi$
$229$	10.3251	0.682302	0.341151	+	0.940008i	$0.389183\pi$
$230$	0	0
$231$	32.7002	2.15152
$232$	−0.720305	−0.0472904
$233$	−12.4866	−0.818023	−0.409011	−	0.912529i	$-0.634126\pi$
$233$	−12.4866	−0.818023	−0.409011	+	0.912529i	$0.634126\pi$
$234$	−9.63715	−0.630000
$235$	0	0
$236$	−1.42966	−0.0930631
$237$	−16.4359	−1.06763
$238$	−49.0249	−3.17781
$239$	−24.1810	−1.56414	−0.782071	−	0.623190i	$-0.785836\pi$
$239$	−24.1810	−1.56414	−0.782071	+	0.623190i	$0.785836\pi$
$240$	0	0
$241$	−18.5935	−1.19772	−0.598858	−	0.800855i	$-0.704379\pi$
$241$	−18.5935	−1.19772	−0.598858	+	0.800855i	$0.704379\pi$
$242$	−20.0303	−1.28759
$243$	−21.1861	−1.35909
$244$	−10.5086	−0.672742
$245$	0	0
$246$	7.59458	0.484213
$247$	−7.38983	−0.470204
$248$	22.2595	1.41348
$249$	−32.0286	−2.02973
$250$	0	0
$251$	−3.11663	−0.196720	−0.0983600	−	0.995151i	$-0.531360\pi$
$251$	−3.11663	−0.196720	−0.0983600	+	0.995151i	$0.531360\pi$
$252$	25.3085	1.59429
$253$	−1.62274	−0.102021
$254$	−9.36651	−0.587707
$255$	0	0
$256$	−11.2369	−0.702304
$257$	16.2781	1.01540	0.507701	−	0.861533i	$-0.330495\pi$
$257$	16.2781	1.01540	0.507701	+	0.861533i	$0.330495\pi$
$258$	5.36611	0.334080
$259$	18.2062	1.13128
$260$	0	0
$261$	0.795723	0.0492540
$262$	−40.9950	−2.53268
$263$	−7.64726	−0.471551	−0.235775	−	0.971808i	$-0.575763\pi$
$263$	−7.64726	−0.471551	−0.235775	+	0.971808i	$0.575763\pi$
$264$	−25.7194	−1.58292
$265$	0	0
$266$	32.0305	1.96392
$267$	9.59542	0.587230
$268$	−37.1100	−2.26686
$269$	−0.0523794	−0.00319363	−0.00159682	−	0.999999i	$-0.500508\pi$
$269$	−0.0523794	−0.00319363	−0.00159682	+	0.999999i	$0.500508\pi$
$270$	0	0
$271$	−22.1828	−1.34751	−0.673755	−	0.738955i	$-0.735320\pi$
$271$	−22.1828	−1.34751	−0.673755	+	0.738955i	$0.735320\pi$
$272$	−4.92002	−0.298320
$273$	11.7286	0.709849
$274$	−20.2877	−1.22562
$275$	0	0
$276$	−2.66481	−0.160403
$277$	20.1542	1.21095	0.605475	−	0.795864i	$-0.292983\pi$
$277$	20.1542	1.21095	0.605475	+	0.795864i	$0.292983\pi$
$278$	−12.0392	−0.722065
$279$	−24.5902	−1.47217
$280$	0	0
$281$	−11.3898	−0.679460	−0.339730	−	0.940523i	$-0.610336\pi$
$281$	−11.3898	−0.679460	−0.339730	+	0.940523i	$0.610336\pi$
$282$	29.3576	1.74822
$283$	−24.0107	−1.42729	−0.713645	−	0.700507i	$-0.752957\pi$
$283$	−24.0107	−1.42729	−0.713645	+	0.700507i	$0.752957\pi$
$284$	35.6920	2.11793
$285$	0	0
$286$	−16.0720	−0.950359
$287$	−4.35614	−0.257135
$288$	17.1403	1.01000
$289$	32.9933	1.94078
$290$	0	0
$291$	41.6163	2.43959
$292$	−33.4896	−1.95983
$293$	19.3772	1.13203	0.566013	−	0.824396i	$-0.308485\pi$
$293$	19.3772	1.13203	0.566013	+	0.824396i	$0.308485\pi$
$294$	−13.2738	−0.774142
$295$	0	0
$296$	−14.3196	−0.832309
$297$	−3.46004	−0.200772
$298$	−17.3610	−1.00570
$299$	−0.582031	−0.0336597
$300$	0	0
$301$	−3.07793	−0.177409
$302$	−7.48004	−0.430428
$303$	−4.26657	−0.245108
$304$	3.21450	0.184364
$305$	0	0
$306$	−42.5964	−2.43507
$307$	10.0830	0.575469	0.287734	−	0.957710i	$-0.407098\pi$
$307$	10.0830	0.575469	0.287734	+	0.957710i	$0.407098\pi$
$308$	42.2074	2.40499
$309$	36.0667	2.05176
$310$	0	0
$311$	−0.627419	−0.0355777	−0.0177888	−	0.999842i	$-0.505663\pi$
$311$	−0.627419	−0.0355777	−0.0177888	+	0.999842i	$0.505663\pi$
$312$	−9.22481	−0.522252
$313$	29.3950	1.66150	0.830752	−	0.556643i	$-0.187911\pi$
$313$	29.3950	1.66150	0.830752	+	0.556643i	$0.187911\pi$
$314$	25.6266	1.44619
$315$	0	0
$316$	−21.2145	−1.19341
$317$	15.4962	0.870351	0.435176	−	0.900346i	$-0.356686\pi$
$317$	15.4962	0.870351	0.435176	+	0.900346i	$0.356686\pi$
$318$	−34.1758	−1.91648
$319$	1.32704	0.0742999
$320$	0	0
$321$	−5.53923	−0.309169
$322$	2.52275	0.140588
$323$	−32.6632	−1.81743
$324$	−30.3497	−1.68610
$325$	0	0
$326$	−39.5034	−2.18789
$327$	10.5195	0.581729
$328$	3.42620	0.189180
$329$	−16.8391	−0.928369
$330$	0	0
$331$	−19.3377	−1.06290	−0.531449	−	0.847091i	$-0.678352\pi$
$331$	−19.3377	−1.06290	−0.531449	+	0.847091i	$0.678352\pi$
$332$	−41.3405	−2.26886
$333$	15.8189	0.866870
$334$	2.96129	0.162035
$335$	0	0
$336$	−5.10183	−0.278328
$337$	−22.5075	−1.22606	−0.613032	−	0.790058i	$-0.710050\pi$
$337$	−22.5075	−1.22606	−0.613032	+	0.790058i	$0.710050\pi$
$338$	23.5205	1.27935
$339$	−28.5394	−1.55005
$340$	0	0
$341$	−41.0094	−2.22078
$342$	27.8304	1.50490
$343$	−13.9318	−0.752249
$344$	2.42085	0.130524
$345$	0	0
$346$	−42.2329	−2.27046
$347$	−8.86650	−0.475979	−0.237989	−	0.971268i	$-0.576488\pi$
$347$	−8.86650	−0.475979	−0.237989	+	0.971268i	$0.576488\pi$
$348$	2.17922	0.116818
$349$	−25.1490	−1.34620	−0.673098	−	0.739553i	$-0.735037\pi$
$349$	−25.1490	−1.34620	−0.673098	+	0.739553i	$0.735037\pi$
$350$	0	0
$351$	−1.24102	−0.0662405
$352$	28.5852	1.52360
$353$	−13.8602	−0.737706	−0.368853	−	0.929488i	$-0.620249\pi$
$353$	−13.8602	−0.737706	−0.368853	+	0.929488i	$0.620249\pi$
$354$	2.49516	0.132616
$355$	0	0
$356$	12.3852	0.656413
$357$	51.8407	2.74370
$358$	33.3242	1.76124
$359$	−12.3782	−0.653298	−0.326649	−	0.945146i	$-0.605920\pi$
$359$	−12.3782	−0.653298	−0.326649	+	0.945146i	$0.605920\pi$
$360$	0	0
$361$	2.34054	0.123187
$362$	28.0382	1.47365
$363$	21.1807	1.11170
$364$	15.1386	0.793477
$365$	0	0
$366$	18.3404	0.958666
$367$	−11.8884	−0.620571	−0.310285	−	0.950643i	$-0.600425\pi$
$367$	−11.8884	−0.620571	−0.310285	+	0.950643i	$0.600425\pi$
$368$	0.253177	0.0131978
$369$	−3.78493	−0.197036
$370$	0	0
$371$	19.6028	1.01772
$372$	−67.3442	−3.49163
$373$	0.192676	0.00997636	0.00498818	−	0.999988i	$-0.498412\pi$
$373$	0.192676	0.00997636	0.00498818	+	0.999988i	$0.498412\pi$
$374$	−71.0386	−3.67332
$375$	0	0
$376$	13.2443	0.683022
$377$	0.475970	0.0245137
$378$	5.37906	0.276669
$379$	−4.99652	−0.256654	−0.128327	−	0.991732i	$-0.540961\pi$
$379$	−4.99652	−0.256654	−0.128327	+	0.991732i	$0.540961\pi$
$380$	0	0
$381$	9.90448	0.507422
$382$	11.8067	0.604084
$383$	22.8420	1.16717	0.583587	−	0.812051i	$-0.301649\pi$
$383$	22.8420	1.16717	0.583587	+	0.812051i	$0.301649\pi$
$384$	39.4737	2.01438
$385$	0	0
$386$	−1.26824	−0.0645516
$387$	−2.67432	−0.135943
$388$	53.7158	2.72701
$389$	−5.25228	−0.266301	−0.133151	−	0.991096i	$-0.542509\pi$
$389$	−5.25228	−0.266301	−0.133151	+	0.991096i	$0.542509\pi$
$390$	0	0
$391$	−2.57259	−0.130101
$392$	−5.98829	−0.302454
$393$	43.3496	2.18670
$394$	16.3063	0.821497
$395$	0	0
$396$	36.6729	1.84288
$397$	−2.71264	−0.136143	−0.0680717	−	0.997680i	$-0.521685\pi$
$397$	−2.71264	−0.136143	−0.0680717	+	0.997680i	$0.521685\pi$
$398$	−57.5327	−2.88386
$399$	−33.8702	−1.69563
$400$	0	0
$401$	2.11946	0.105841	0.0529204	−	0.998599i	$-0.483147\pi$
$401$	2.11946	0.105841	0.0529204	+	0.998599i	$0.483147\pi$
$402$	64.7674	3.23030
$403$	−14.7089	−0.732702
$404$	−5.50702	−0.273984
$405$	0	0
$406$	−2.06305	−0.102387
$407$	26.3814	1.30768
$408$	−40.7738	−2.01861
$409$	−12.4427	−0.615250	−0.307625	−	0.951508i	$-0.599534\pi$
$409$	−12.4427	−0.615250	−0.307625	+	0.951508i	$0.599534\pi$
$410$	0	0
$411$	21.4529	1.05819
$412$	46.5526	2.29348
$413$	−1.43119	−0.0704241
$414$	2.19195	0.107728
$415$	0	0
$416$	10.2527	0.502679
$417$	12.7307	0.623426
$418$	46.4132	2.27014
$419$	29.8761	1.45954	0.729772	−	0.683690i	$-0.239626\pi$
$419$	29.8761	1.45954	0.729772	+	0.683690i	$0.239626\pi$
$420$	0	0
$421$	16.0091	0.780237	0.390118	−	0.920765i	$-0.372434\pi$
$421$	16.0091	0.780237	0.390118	+	0.920765i	$0.372434\pi$
$422$	18.5610	0.903536
$423$	−14.6310	−0.711384
$424$	−15.4180	−0.748763
$425$	0	0
$426$	−62.2925	−3.01808
$427$	−10.5198	−0.509087
$428$	−7.14969	−0.345593
$429$	16.9951	0.820533
$430$	0	0
$431$	6.81141	0.328094	0.164047	−	0.986453i	$-0.447545\pi$
$431$	6.81141	0.328094	0.164047	+	0.986453i	$0.447545\pi$
$432$	0.539829	0.0259725
$433$	−8.40157	−0.403754	−0.201877	−	0.979411i	$-0.564704\pi$
$433$	−8.40157	−0.403754	−0.201877	+	0.979411i	$0.564704\pi$
$434$	63.7542	3.06030
$435$	0	0
$436$	13.5779	0.650264
$437$	1.68080	0.0804037
$438$	58.4487	2.79279
$439$	38.4432	1.83480	0.917398	−	0.397971i	$-0.130286\pi$
$439$	38.4432	1.83480	0.917398	+	0.397971i	$0.130286\pi$
$440$	0	0
$441$	6.61527	0.315013
$442$	−25.4795	−1.21194
$443$	−7.18191	−0.341223	−0.170612	−	0.985338i	$-0.554574\pi$
$443$	−7.18191	−0.341223	−0.170612	+	0.985338i	$0.554574\pi$
$444$	43.3226	2.05600
$445$	0	0
$446$	21.3754	1.01215
$447$	18.3582	0.868313
$448$	−40.1558	−1.89718
$449$	−9.91300	−0.467823	−0.233912	−	0.972258i	$-0.575153\pi$
$449$	−9.91300	−0.467823	−0.233912	+	0.972258i	$0.575153\pi$
$450$	0	0
$451$	−6.31219	−0.297229
$452$	−36.8369	−1.73266
$453$	7.90966	0.371628
$454$	30.1293	1.41404
$455$	0	0
$456$	26.6396	1.24752
$457$	−3.33017	−0.155779	−0.0778894	−	0.996962i	$-0.524818\pi$
$457$	−3.33017	−0.155779	−0.0778894	+	0.996962i	$0.524818\pi$
$458$	−23.2594	−1.08684
$459$	−5.48531	−0.256032
$460$	0	0
$461$	−30.2585	−1.40928	−0.704639	−	0.709566i	$-0.748891\pi$
$461$	−30.2585	−1.40928	−0.704639	+	0.709566i	$0.748891\pi$
$462$	−73.6637	−3.42715
$463$	−36.8740	−1.71368	−0.856839	−	0.515583i	$-0.827575\pi$
$463$	−36.8740	−1.71368	−0.856839	+	0.515583i	$0.827575\pi$
$464$	−0.207042	−0.00961169
$465$	0	0
$466$	28.1285	1.30303
$467$	27.1848	1.25796	0.628981	−	0.777420i	$-0.283472\pi$
$467$	27.1848	1.25796	0.628981	+	0.777420i	$0.283472\pi$
$468$	13.1535	0.608020
$469$	−37.1496	−1.71541
$470$	0	0
$471$	−27.0985	−1.24863
$472$	1.12566	0.0518126
$473$	−4.46001	−0.205071
$474$	37.0252	1.70062
$475$	0	0
$476$	66.9128	3.06694
$477$	17.0323	0.779854
$478$	54.4726	2.49152
$479$	−8.41358	−0.384426	−0.192213	−	0.981353i	$-0.561567\pi$
$479$	−8.41358	−0.384426	−0.192213	+	0.981353i	$0.561567\pi$
$480$	0	0
$481$	9.46224	0.431441
$482$	41.8856	1.90784
$483$	−2.66765	−0.121382
$484$	27.3388	1.24267
$485$	0	0
$486$	47.7259	2.16489
$487$	19.4022	0.879199	0.439599	−	0.898194i	$-0.355120\pi$
$487$	19.4022	0.879199	0.439599	+	0.898194i	$0.355120\pi$
$488$	8.27402	0.374547
$489$	41.7723	1.88901
$490$	0	0
$491$	4.09336	0.184731	0.0923653	−	0.995725i	$-0.470557\pi$
$491$	4.09336	0.184731	0.0923653	+	0.995725i	$0.470557\pi$
$492$	−10.3656	−0.467319
$493$	2.10380	0.0947503
$494$	16.6471	0.748987
$495$	0	0
$496$	6.39821	0.287288
$497$	35.7301	1.60271
$498$	72.1507	3.23315
$499$	−39.9936	−1.79036	−0.895180	−	0.445705i	$-0.852953\pi$
$499$	−39.9936	−1.79036	−0.895180	+	0.445705i	$0.852953\pi$
$500$	0	0
$501$	−3.13138	−0.139900
$502$	7.02083	0.313355
$503$	10.2376	0.456470	0.228235	−	0.973606i	$-0.426705\pi$
$503$	10.2376	0.456470	0.228235	+	0.973606i	$0.426705\pi$
$504$	−19.9269	−0.887616
$505$	0	0
$506$	3.65555	0.162509
$507$	−24.8714	−1.10458
$508$	12.7841	0.567203
$509$	−22.2236	−0.985042	−0.492521	−	0.870301i	$-0.663925\pi$
$509$	−22.2236	−0.985042	−0.492521	+	0.870301i	$0.663925\pi$
$510$	0	0
$511$	−33.5253	−1.48307
$512$	−7.82887	−0.345991
$513$	3.58383	0.158230
$514$	−36.6697	−1.61743
$515$	0	0
$516$	−7.32406	−0.322424
$517$	−24.4004	−1.07313
$518$	−41.0132	−1.80201
$519$	44.6586	1.96030
$520$	0	0
$521$	35.6625	1.56240	0.781202	−	0.624279i	$-0.214607\pi$
$521$	35.6625	1.56240	0.781202	+	0.624279i	$0.214607\pi$
$522$	−1.79252	−0.0784566
$523$	30.7263	1.34357	0.671784	−	0.740747i	$-0.265528\pi$
$523$	30.7263	1.34357	0.671784	+	0.740747i	$0.265528\pi$
$524$	55.9529	2.44432
$525$	0	0
$526$	17.2270	0.751132
$527$	−65.0135	−2.83203
$528$	−7.39271	−0.321726
$529$	−22.8676	−0.994244
$530$	0	0
$531$	−1.24352	−0.0539641
$532$	−43.7176	−1.89540
$533$	−2.26400	−0.0980647
$534$	−21.6156	−0.935398
$535$	0	0
$536$	29.2190	1.26207
$537$	−35.2383	−1.52064
$538$	0.117995	0.00508713
$539$	11.0324	0.475199
$540$	0	0
$541$	−25.6717	−1.10371	−0.551855	−	0.833940i	$-0.686080\pi$
$541$	−25.6717	−1.10371	−0.551855	+	0.833940i	$0.686080\pi$
$542$	49.9712	2.14645
$543$	−29.6486	−1.27234
$544$	45.3171	1.94295
$545$	0	0
$546$	−26.4210	−1.13072
$547$	−5.72318	−0.244705	−0.122353	−	0.992487i	$-0.539044\pi$
$547$	−5.72318	−0.244705	−0.122353	+	0.992487i	$0.539044\pi$
$548$	27.6901	1.18286
$549$	−9.14033	−0.390100
$550$	0	0
$551$	−1.37452	−0.0585565
$552$	2.09816	0.0893038
$553$	−21.2371	−0.903094
$554$	−45.4014	−1.92892
$555$	0	0
$556$	16.4320	0.696873
$557$	−2.88038	−0.122045	−0.0610227	−	0.998136i	$-0.519436\pi$
$557$	−2.88038	−0.122045	−0.0610227	+	0.998136i	$0.519436\pi$
$558$	55.3942	2.34502
$559$	−1.59968	−0.0676591
$560$	0	0
$561$	75.1188	3.17152
$562$	25.6578	1.08231
$563$	34.8003	1.46666	0.733329	−	0.679873i	$-0.237965\pi$
$563$	34.8003	1.46666	0.733329	+	0.679873i	$0.237965\pi$
$564$	−40.0694	−1.68723
$565$	0	0
$566$	54.0889	2.27353
$567$	−30.3821	−1.27593
$568$	−28.1025	−1.17915
$569$	9.54483	0.400140	0.200070	−	0.979782i	$-0.435883\pi$
$569$	9.54483	0.400140	0.200070	+	0.979782i	$0.435883\pi$
$570$	0	0
$571$	−33.9094	−1.41907	−0.709533	−	0.704672i	$-0.751094\pi$
$571$	−33.9094	−1.41907	−0.709533	+	0.704672i	$0.751094\pi$
$572$	21.9363	0.917202
$573$	−12.4848	−0.521562
$574$	9.81308	0.409590
$575$	0	0
$576$	−34.8902	−1.45376
$577$	−38.9664	−1.62219	−0.811095	−	0.584914i	$-0.801128\pi$
$577$	−38.9664	−1.62219	−0.811095	+	0.584914i	$0.801128\pi$
$578$	−74.3240	−3.09147
$579$	1.34108	0.0557334
$580$	0	0
$581$	−41.3846	−1.71692
$582$	−93.7490	−3.88602
$583$	28.4050	1.17641
$584$	26.3684	1.09113
$585$	0	0
$586$	−43.6509	−1.80320
$587$	−23.8879	−0.985959	−0.492980	−	0.870041i	$-0.664092\pi$
$587$	−23.8879	−0.985959	−0.492980	+	0.870041i	$0.664092\pi$
$588$	18.1170	0.747133
$589$	42.4767	1.75022
$590$	0	0
$591$	−17.2428	−0.709275
$592$	−4.11598	−0.169166
$593$	0.170990	0.00702173	0.00351086	−	0.999994i	$-0.498882\pi$
$593$	0.170990	0.00702173	0.00351086	+	0.999994i	$0.498882\pi$
$594$	7.79442	0.319809
$595$	0	0
$596$	23.6956	0.970610
$597$	60.8372	2.48990
$598$	1.31114	0.0536165
$599$	−9.94929	−0.406517	−0.203258	−	0.979125i	$-0.565153\pi$
$599$	−9.94929	−0.406517	−0.203258	+	0.979125i	$0.565153\pi$
$600$	0	0
$601$	15.4446	0.629997	0.314998	−	0.949092i	$-0.397996\pi$
$601$	15.4446	0.629997	0.314998	+	0.949092i	$0.397996\pi$
$602$	6.93364	0.282594
$603$	−32.2783	−1.31447
$604$	10.2093	0.415411
$605$	0	0
$606$	9.61128	0.390432
$607$	11.6488	0.472811	0.236405	−	0.971654i	$-0.424031\pi$
$607$	11.6488	0.472811	0.236405	+	0.971654i	$0.424031\pi$
$608$	−29.6080	−1.20076
$609$	2.18154	0.0884005
$610$	0	0
$611$	−8.75170	−0.354056
$612$	58.1386	2.35012
$613$	13.0576	0.527391	0.263696	−	0.964606i	$-0.415059\pi$
$613$	13.0576	0.527391	0.263696	+	0.964606i	$0.415059\pi$
$614$	−22.7140	−0.916663
$615$	0	0
$616$	−33.2325	−1.33897
$617$	−4.65693	−0.187481	−0.0937404	−	0.995597i	$-0.529882\pi$
$617$	−4.65693	−0.187481	−0.0937404	+	0.995597i	$0.529882\pi$
$618$	−81.2473	−3.26825
$619$	−8.18981	−0.329176	−0.164588	−	0.986362i	$-0.552629\pi$
$619$	−8.18981	−0.329176	−0.164588	+	0.986362i	$0.552629\pi$
$620$	0	0
$621$	0.282266	0.0113270
$622$	1.41338	0.0566716
$623$	12.3984	0.496731
$624$	−2.65155	−0.106147
$625$	0	0
$626$	−66.2180	−2.64660
$627$	−49.0790	−1.96003
$628$	−34.9771	−1.39574
$629$	41.8233	1.66760
$630$	0	0
$631$	1.71791	0.0683890	0.0341945	−	0.999415i	$-0.489113\pi$
$631$	1.71791	0.0683890	0.0341945	+	0.999415i	$0.489113\pi$
$632$	16.7034	0.664427
$633$	−19.6271	−0.780106
$634$	−34.9082	−1.38638
$635$	0	0
$636$	46.6457	1.84962
$637$	3.95700	0.156782
$638$	−2.98942	−0.118352
$639$	31.0449	1.22812
$640$	0	0
$641$	39.4310	1.55743	0.778716	−	0.627377i	$-0.215871\pi$
$641$	39.4310	1.55743	0.778716	+	0.627377i	$0.215871\pi$
$642$	12.4782	0.492475
$643$	27.4242	1.08150	0.540752	−	0.841182i	$-0.318140\pi$
$643$	27.4242	1.08150	0.540752	+	0.841182i	$0.318140\pi$
$644$	−3.44324	−0.135683
$645$	0	0
$646$	73.5803	2.89498
$647$	0.435658	0.0171275	0.00856375	−	0.999963i	$-0.497274\pi$
$647$	0.435658	0.0171275	0.00856375	+	0.999963i	$0.497274\pi$
$648$	23.8962	0.938730
$649$	−2.07383	−0.0814051
$650$	0	0
$651$	−67.4160	−2.64224
$652$	53.9171	2.11156
$653$	19.3248	0.756238	0.378119	−	0.925757i	$-0.376571\pi$
$653$	19.3248	0.756238	0.378119	+	0.925757i	$0.376571\pi$
$654$	−23.6972	−0.926635
$655$	0	0
$656$	0.984815	0.0384506
$657$	−29.1292	−1.13644
$658$	37.9334	1.47880
$659$	−18.0955	−0.704900	−0.352450	−	0.935831i	$-0.614651\pi$
$659$	−18.0955	−0.704900	−0.352450	+	0.935831i	$0.614651\pi$
$660$	0	0
$661$	−6.61568	−0.257320	−0.128660	−	0.991689i	$-0.541068\pi$
$661$	−6.61568	−0.257320	−0.128660	+	0.991689i	$0.541068\pi$
$662$	43.5620	1.69309
$663$	26.9429	1.04638
$664$	32.5499	1.26318
$665$	0	0
$666$	−35.6352	−1.38083
$667$	−0.108258	−0.00419179
$668$	−4.04179	−0.156382
$669$	−22.6031	−0.873886
$670$	0	0
$671$	−15.2435	−0.588468
$672$	46.9917	1.81274
$673$	−40.6612	−1.56738	−0.783688	−	0.621155i	$-0.786664\pi$
$673$	−40.6612	−1.56738	−0.783688	+	0.621155i	$0.786664\pi$
$674$	50.7027	1.95299
$675$	0	0
$676$	−32.1025	−1.23471
$677$	15.1509	0.582298	0.291149	−	0.956678i	$-0.405962\pi$
$677$	15.1509	0.582298	0.291149	+	0.956678i	$0.405962\pi$
$678$	64.2907	2.46907
$679$	53.7731	2.06362
$680$	0	0
$681$	−31.8598	−1.22087
$682$	92.3818	3.53748
$683$	18.9663	0.725725	0.362862	−	0.931843i	$-0.381799\pi$
$683$	18.9663	0.725725	0.362862	+	0.931843i	$0.381799\pi$
$684$	−37.9850	−1.45239
$685$	0	0
$686$	31.3842	1.19826
$687$	24.5953	0.938368
$688$	0.695842	0.0265287
$689$	10.1880	0.388134
$690$	0	0
$691$	3.52541	0.134113	0.0670564	−	0.997749i	$-0.478639\pi$
$691$	3.52541	0.134113	0.0670564	+	0.997749i	$0.478639\pi$
$692$	57.6426	2.19124
$693$	36.7120	1.39457
$694$	19.9736	0.758186
$695$	0	0
$696$	−1.71583	−0.0650383
$697$	−10.0069	−0.379039
$698$	56.6531	2.14435
$699$	−29.7441	−1.12502
$700$	0	0
$701$	5.73305	0.216534	0.108267	−	0.994122i	$-0.465470\pi$
$701$	5.73305	0.216534	0.108267	+	0.994122i	$0.465470\pi$
$702$	2.79563	0.105514
$703$	−27.3253	−1.03059
$704$	−58.1869	−2.19300
$705$	0	0
$706$	31.2229	1.17509
$707$	−5.51289	−0.207334
$708$	−3.40557	−0.127989
$709$	45.8360	1.72141	0.860703	−	0.509107i	$-0.170024\pi$
$709$	45.8360	1.72141	0.860703	+	0.509107i	$0.170024\pi$
$710$	0	0
$711$	−18.4523	−0.692016
$712$	−9.75159	−0.365456
$713$	3.34550	0.125290
$714$	−116.782	−4.37044
$715$	0	0
$716$	−45.4834	−1.69979
$717$	−57.6012	−2.15116
$718$	27.8844	1.04064
$719$	−15.1819	−0.566188	−0.283094	−	0.959092i	$-0.591361\pi$
$719$	−15.1819	−0.566188	−0.283094	+	0.959092i	$0.591361\pi$
$720$	0	0
$721$	46.6023	1.73556
$722$	−5.27254	−0.196224
$723$	−44.2914	−1.64721
$724$	−38.2686	−1.42224
$725$	0	0
$726$	−47.7138	−1.77082
$727$	29.4997	1.09408	0.547042	−	0.837105i	$-0.315754\pi$
$727$	29.4997	1.09408	0.547042	+	0.837105i	$0.315754\pi$
$728$	−11.9195	−0.441767
$729$	−20.8541	−0.772376
$730$	0	0
$731$	−7.07060	−0.261515
$732$	−25.0323	−0.925219
$733$	15.8755	0.586376	0.293188	−	0.956055i	$-0.405284\pi$
$733$	15.8755	0.586376	0.293188	+	0.956055i	$0.405284\pi$
$734$	26.7810	0.988506
$735$	0	0
$736$	−2.33195	−0.0859569
$737$	−53.8310	−1.98289
$738$	8.52630	0.313858
$739$	2.73588	0.100641	0.0503204	−	0.998733i	$-0.483976\pi$
$739$	2.73588	0.100641	0.0503204	+	0.998733i	$0.483976\pi$
$740$	0	0
$741$	−17.6032	−0.646670
$742$	−44.1591	−1.62113
$743$	−30.0086	−1.10091	−0.550455	−	0.834865i	$-0.685546\pi$
$743$	−30.0086	−1.10091	−0.550455	+	0.834865i	$0.685546\pi$
$744$	53.0241	1.94396
$745$	0	0
$746$	−0.434040	−0.0158913
$747$	−35.9579	−1.31563
$748$	96.9587	3.54516
$749$	−7.15732	−0.261523
$750$	0	0
$751$	31.2002	1.13851	0.569255	−	0.822161i	$-0.307232\pi$
$751$	31.2002	1.13851	0.569255	+	0.822161i	$0.307232\pi$
$752$	3.80690	0.138823
$753$	−7.42408	−0.270548
$754$	−1.07222	−0.0390479
$755$	0	0
$756$	−7.34173	−0.267016
$757$	−0.147557	−0.00536306	−0.00268153	−	0.999996i	$-0.500854\pi$
$757$	−0.147557	−0.00536306	−0.00268153	+	0.999996i	$0.500854\pi$
$758$	11.2556	0.408823
$759$	−3.86551	−0.140309
$760$	0	0
$761$	−14.2442	−0.516353	−0.258177	−	0.966098i	$-0.583122\pi$
$761$	−14.2442	−0.516353	−0.258177	+	0.966098i	$0.583122\pi$
$762$	−22.3118	−0.808271
$763$	13.5924	0.492078
$764$	−16.1147	−0.583008
$765$	0	0
$766$	−51.4562	−1.85919
$767$	−0.743824	−0.0268579
$768$	−26.7672	−0.965877
$769$	29.5204	1.06453	0.532266	−	0.846577i	$-0.321341\pi$
$769$	29.5204	1.06453	0.532266	+	0.846577i	$0.321341\pi$
$770$	0	0
$771$	38.7759	1.39648
$772$	1.73098	0.0622995
$773$	33.1908	1.19379	0.596894	−	0.802320i	$-0.296401\pi$
$773$	33.1908	1.19379	0.596894	+	0.802320i	$0.296401\pi$
$774$	6.02444	0.216544
$775$	0	0
$776$	−42.2937	−1.51825
$777$	43.3688	1.55585
$778$	11.8318	0.424190
$779$	6.53803	0.234249
$780$	0	0
$781$	51.7740	1.85262
$782$	5.79526	0.207238
$783$	−0.230831	−0.00824921
$784$	−1.72125	−0.0614733
$785$	0	0
$786$	−97.6535	−3.48318
$787$	−41.6467	−1.48454	−0.742272	−	0.670099i	$-0.766252\pi$
$787$	−41.6467	−1.48454	−0.742272	+	0.670099i	$0.766252\pi$
$788$	−22.2560	−0.792836
$789$	−18.2164	−0.648522
$790$	0	0
$791$	−36.8762	−1.31117
$792$	−28.8747	−1.02602
$793$	−5.46739	−0.194153
$794$	6.11076	0.216863
$795$	0	0
$796$	78.5249	2.78324
$797$	18.9260	0.670392	0.335196	−	0.942148i	$-0.391197\pi$
$797$	18.9260	0.670392	0.335196	+	0.942148i	$0.391197\pi$
$798$	76.2993	2.70097
$799$	−38.6827	−1.36849
$800$	0	0
$801$	10.7726	0.380631
$802$	−4.77451	−0.168594
$803$	−48.5793	−1.71432
$804$	−88.3992	−3.11760
$805$	0	0
$806$	33.1347	1.16712
$807$	−0.124772	−0.00439219
$808$	4.33601	0.152540
$809$	−14.1088	−0.496038	−0.248019	−	0.968755i	$-0.579780\pi$
$809$	−14.1088	−0.496038	−0.248019	+	0.968755i	$0.579780\pi$
$810$	0	0
$811$	8.04618	0.282540	0.141270	−	0.989971i	$-0.454881\pi$
$811$	8.04618	0.282540	0.141270	+	0.989971i	$0.454881\pi$
$812$	2.81580	0.0988151
$813$	−52.8413	−1.85323
$814$	−59.4293	−2.08300
$815$	0	0
$816$	−11.7199	−0.410278
$817$	4.61958	0.161619
$818$	28.0296	0.980031
$819$	13.1675	0.460110
$820$	0	0
$821$	−29.8027	−1.04012	−0.520060	−	0.854130i	$-0.674090\pi$
$821$	−29.8027	−1.04012	−0.520060	+	0.854130i	$0.674090\pi$
$822$	−48.3269	−1.68559
$823$	−5.76716	−0.201030	−0.100515	−	0.994936i	$-0.532049\pi$
$823$	−5.76716	−0.201030	−0.100515	+	0.994936i	$0.532049\pi$
$824$	−36.6537	−1.27689
$825$	0	0
$826$	3.22403	0.112178
$827$	15.3285	0.533025	0.266512	−	0.963832i	$-0.414129\pi$
$827$	15.3285	0.533025	0.266512	+	0.963832i	$0.414129\pi$
$828$	−2.99173	−0.103970
$829$	32.1807	1.11768	0.558840	−	0.829275i	$-0.311247\pi$
$829$	32.1807	1.11768	0.558840	+	0.829275i	$0.311247\pi$
$830$	0	0
$831$	48.0090	1.66541
$832$	−20.8700	−0.723536
$833$	17.4900	0.605993
$834$	−28.6784	−0.993053
$835$	0	0
$836$	−63.3481	−2.19094
$837$	7.13334	0.246564
$838$	−67.3019	−2.32491
$839$	3.61340	0.124749	0.0623743	−	0.998053i	$-0.480133\pi$
$839$	3.61340	0.124749	0.0623743	+	0.998053i	$0.480133\pi$
$840$	0	0
$841$	−28.9115	−0.996947
$842$	−36.0637	−1.24284
$843$	−27.1315	−0.934459
$844$	−25.3334	−0.872012
$845$	0	0
$846$	32.9592	1.13316
$847$	27.3679	0.940373
$848$	−4.43169	−0.152185
$849$	−57.1956	−1.96295
$850$	0	0
$851$	−2.15217	−0.0737753
$852$	85.0214	2.91279
$853$	−11.7530	−0.402415	−0.201207	−	0.979549i	$-0.564487\pi$
$853$	−11.7530	−0.402415	−0.201207	+	0.979549i	$0.564487\pi$
$854$	23.6979	0.810924
$855$	0	0
$856$	5.62938	0.192408
$857$	−25.5265	−0.871969	−0.435985	−	0.899954i	$-0.643600\pi$
$857$	−25.5265	−0.871969	−0.435985	+	0.899954i	$0.643600\pi$
$858$	−38.2849	−1.30703
$859$	−8.44228	−0.288047	−0.144024	−	0.989574i	$-0.546004\pi$
$859$	−8.44228	−0.288047	−0.144024	+	0.989574i	$0.546004\pi$
$860$	0	0
$861$	−10.3767	−0.353637
$862$	−15.3440	−0.522620
$863$	5.81237	0.197855	0.0989277	−	0.995095i	$-0.468459\pi$
$863$	5.81237	0.197855	0.0989277	+	0.995095i	$0.468459\pi$
$864$	−4.97223	−0.169159
$865$	0	0
$866$	18.9262	0.643138
$867$	78.5929	2.66915
$868$	−87.0164	−2.95353
$869$	−30.7732	−1.04391
$870$	0	0
$871$	−19.3076	−0.654213
$872$	−10.6907	−0.362033
$873$	46.7219	1.58130
$874$	−3.78634	−0.128075
$875$	0	0
$876$	−79.7751	−2.69535
$877$	−25.0904	−0.847242	−0.423621	−	0.905840i	$-0.639241\pi$
$877$	−25.0904	−0.847242	−0.423621	+	0.905840i	$0.639241\pi$
$878$	−86.6010	−2.92264
$879$	46.1580	1.55687
$880$	0	0
$881$	11.3274	0.381630	0.190815	−	0.981626i	$-0.438887\pi$
$881$	11.3274	0.381630	0.190815	+	0.981626i	$0.438887\pi$
$882$	−14.9022	−0.501784
$883$	−30.0666	−1.01182	−0.505911	−	0.862586i	$-0.668844\pi$
$883$	−30.0666	−1.01182	−0.505911	+	0.862586i	$0.668844\pi$
$884$	34.7763	1.16965
$885$	0	0
$886$	16.1787	0.543533
$887$	−15.2679	−0.512645	−0.256323	−	0.966591i	$-0.582511\pi$
$887$	−15.2679	−0.512645	−0.256323	+	0.966591i	$0.582511\pi$
$888$	−34.1105	−1.14467
$889$	12.7977	0.429222
$890$	0	0
$891$	−44.0246	−1.47488
$892$	−29.1747	−0.976841
$893$	25.2734	0.845741
$894$	−41.3555	−1.38313
$895$	0	0
$896$	51.0045	1.70394
$897$	−1.38645	−0.0462921
$898$	22.3310	0.745195
$899$	−2.73587	−0.0912465
$900$	0	0
$901$	45.0314	1.50021
$902$	14.2194	0.473456
$903$	−7.33188	−0.243990
$904$	29.0039	0.964656
$905$	0	0
$906$	−17.8181	−0.591966
$907$	39.6584	1.31684	0.658418	−	0.752652i	$-0.271226\pi$
$907$	39.6584	1.31684	0.658418	+	0.752652i	$0.271226\pi$
$908$	−41.1226	−1.36470
$909$	−4.79000	−0.158874
$910$	0	0
$911$	26.1451	0.866227	0.433114	−	0.901339i	$-0.357415\pi$
$911$	26.1451	0.866227	0.433114	+	0.901339i	$0.357415\pi$
$912$	7.65721	0.253555
$913$	−59.9676	−1.98464
$914$	7.50187	0.248140
$915$	0	0
$916$	31.7461	1.04892
$917$	56.0126	1.84970
$918$	12.3567	0.407833
$919$	23.1670	0.764207	0.382104	−	0.924119i	$-0.375200\pi$
$919$	23.1670	0.764207	0.382104	+	0.924119i	$0.375200\pi$
$920$	0	0
$921$	24.0186	0.791441
$922$	68.1632	2.24484
$923$	18.5698	0.611234
$924$	100.542	3.30758
$925$	0	0
$926$	83.0659	2.72971
$927$	40.4914	1.32991
$928$	1.90701	0.0626008
$929$	35.8082	1.17483	0.587414	−	0.809287i	$-0.300146\pi$
$929$	35.8082	1.17483	0.587414	+	0.809287i	$0.300146\pi$
$930$	0	0
$931$	−11.4271	−0.374509
$932$	−38.3918	−1.25757
$933$	−1.49456	−0.0489298
$934$	−61.2391	−2.00381
$935$	0	0
$936$	−10.3565	−0.338514
$937$	17.4587	0.570352	0.285176	−	0.958475i	$-0.407948\pi$
$937$	17.4587	0.570352	0.285176	+	0.958475i	$0.407948\pi$
$938$	83.6869	2.73247
$939$	70.0213	2.28506
$940$	0	0
$941$	11.5748	0.377327	0.188663	−	0.982042i	$-0.439584\pi$
$941$	11.5748	0.377327	0.188663	+	0.982042i	$0.439584\pi$
$942$	61.0448	1.98895
$943$	0.514942	0.0167688
$944$	0.323556	0.0105308
$945$	0	0
$946$	10.0471	0.326658
$947$	−23.3964	−0.760282	−0.380141	−	0.924929i	$-0.624125\pi$
$947$	−23.3964	−0.760282	−0.380141	+	0.924929i	$0.624125\pi$
$948$	−50.5347	−1.64129
$949$	−17.4240	−0.565606
$950$	0	0
$951$	36.9132	1.19699
$952$	−52.6845	−1.70751
$953$	46.0867	1.49290	0.746448	−	0.665444i	$-0.231758\pi$
$953$	46.0867	1.49290	0.746448	+	0.665444i	$0.231758\pi$
$954$	−38.3686	−1.24223
$955$	0	0
$956$	−74.3481	−2.40459
$957$	3.16112	0.102184
$958$	18.9533	0.612352
$959$	27.7196	0.895113
$960$	0	0
$961$	53.5465	1.72731
$962$	−21.3156	−0.687242
$963$	−6.21879	−0.200398
$964$	−57.1686	−1.84128
$965$	0	0
$966$	6.00941	0.193350
$967$	−38.7607	−1.24646	−0.623230	−	0.782039i	$-0.714180\pi$
$967$	−38.7607	−1.24646	−0.623230	+	0.782039i	$0.714180\pi$
$968$	−21.5255	−0.691855
$969$	−77.8065	−2.49950
$970$	0	0
$971$	−32.8623	−1.05460	−0.527300	−	0.849679i	$-0.676796\pi$
$971$	−32.8623	−1.05460	−0.527300	+	0.849679i	$0.676796\pi$
$972$	−65.1397	−2.08936
$973$	16.4495	0.527348
$974$	−43.7074	−1.40047
$975$	0	0
$976$	2.37826	0.0761262
$977$	−32.1944	−1.02999	−0.514996	−	0.857193i	$-0.672206\pi$
$977$	−32.1944	−1.02999	−0.514996	+	0.857193i	$0.672206\pi$
$978$	−94.1003	−3.00900
$979$	17.9656	0.574185
$980$	0	0
$981$	11.8100	0.377066
$982$	−9.22110	−0.294257
$983$	14.2582	0.454766	0.227383	−	0.973805i	$-0.426983\pi$
$983$	14.2582	0.454766	0.227383	+	0.973805i	$0.426983\pi$
$984$	8.16149	0.260179
$985$	0	0
$986$	−4.73922	−0.150928
$987$	−40.1121	−1.27678
$988$	−22.7211	−0.722855
$989$	0.363843	0.0115695
$990$	0	0
$991$	22.0055	0.699028	0.349514	−	0.936931i	$-0.386347\pi$
$991$	22.0055	0.699028	0.349514	+	0.936931i	$0.386347\pi$
$992$	−58.9323	−1.87110
$993$	−46.0641	−1.46180
$994$	−80.4891	−2.55296
$995$	0	0
$996$	−98.4766	−3.12035
$997$	22.6958	0.718783	0.359392	−	0.933187i	$-0.382984\pi$
$997$	22.6958	0.718783	0.359392	+	0.933187i	$0.382984\pi$
$998$	90.0935	2.85186
$999$	−4.58889	−0.145186

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.t.1.1		7
3.2	odd	2		9675.2.a.cm.1.7		7
5.2	odd	4		215.2.b.b.44.3	✓	14
5.3	odd	4		215.2.b.b.44.12	yes	14
5.4	even	2		1075.2.a.s.1.7		7
15.2	even	4		1935.2.b.d.1549.12		14
15.8	even	4		1935.2.b.d.1549.3		14
15.14	odd	2		9675.2.a.cn.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.b.b.44.3	✓	14	5.2	odd	4
215.2.b.b.44.12	yes	14	5.3	odd	4
1075.2.a.s.1.7		7	5.4	even	2
1075.2.a.t.1.1		7	1.1	even	1	trivial
1935.2.b.d.1549.3		14	15.8	even	4
1935.2.b.d.1549.12		14	15.2	even	4
9675.2.a.cm.1.7		7	3.2	odd	2
9675.2.a.cn.1.1		7	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25270 q^{2} +2.38208 q^{3} +3.07465 q^{4} -5.36611 q^{6} +3.07793 q^{7} -2.42085 q^{8} +2.67432 q^{9} +O(q^{10})\)	\(q-2.25270 q^{2} +2.38208 q^{3} +3.07465 q^{4} -5.36611 q^{6} +3.07793 q^{7} -2.42085 q^{8} +2.67432 q^{9} +4.46001 q^{11} +7.32406 q^{12} +1.59968 q^{13} -6.93364 q^{14} -0.695842 q^{16} +7.07060 q^{17} -6.02444 q^{18} -4.61958 q^{19} +7.33188 q^{21} -10.0471 q^{22} -0.363843 q^{23} -5.76668 q^{24} -3.60359 q^{26} -0.775792 q^{27} +9.46353 q^{28} +0.297542 q^{29} -9.19492 q^{31} +6.40923 q^{32} +10.6241 q^{33} -15.9279 q^{34} +8.22260 q^{36} +5.91510 q^{37} +10.4065 q^{38} +3.81056 q^{39} -1.41529 q^{41} -16.5165 q^{42} -1.00000 q^{43} +13.7130 q^{44} +0.819628 q^{46} -5.47092 q^{47} -1.65755 q^{48} +2.47363 q^{49} +16.8428 q^{51} +4.91844 q^{52} +6.36882 q^{53} +1.74762 q^{54} -7.45121 q^{56} -11.0042 q^{57} -0.670272 q^{58} -0.464984 q^{59} -3.41781 q^{61} +20.7134 q^{62} +8.23136 q^{63} -13.0464 q^{64} -23.9329 q^{66} -12.0697 q^{67} +21.7396 q^{68} -0.866704 q^{69} +11.6085 q^{71} -6.47414 q^{72} -10.8922 q^{73} -13.3249 q^{74} -14.2036 q^{76} +13.7276 q^{77} -8.58404 q^{78} -6.89981 q^{79} -9.87097 q^{81} +3.18821 q^{82} -13.4456 q^{83} +22.5429 q^{84} +2.25270 q^{86} +0.708770 q^{87} -10.7970 q^{88} +4.02816 q^{89} +4.92368 q^{91} -1.11869 q^{92} -21.9031 q^{93} +12.3243 q^{94} +15.2673 q^{96} +17.4706 q^{97} -5.57233 q^{98} +11.9275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 5 q^{3} + 8 q^{4} + 4 q^{6} + 3 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 5 * q^3 + 8 * q^4 + 4 * q^6 + 3 * q^7 + 3 * q^8 + 8 * q^9	\( 7 q + 4 q^{2} + 5 q^{3} + 8 q^{4} + 4 q^{6} + 3 q^{7} + 3 q^{8} + 8 q^{9} + q^{11} + 23 q^{12} + 14 q^{13} - 17 q^{14} + 2 q^{16} + 12 q^{17} + 15 q^{18} - 4 q^{21} - 17 q^{22} + 18 q^{23} + 17 q^{24} + 12 q^{26} + 8 q^{27} - 2 q^{28} + 10 q^{29} - 15 q^{31} + 15 q^{32} + 20 q^{33} - 8 q^{34} + 32 q^{36} + 5 q^{37} + 4 q^{38} + 10 q^{39} - 21 q^{41} - 47 q^{42} - 7 q^{43} + 13 q^{44} + 4 q^{46} + 2 q^{47} + 33 q^{48} + 16 q^{49} + 16 q^{51} + 2 q^{52} + 42 q^{53} + 3 q^{54} - 28 q^{56} - 8 q^{57} + 30 q^{58} + 9 q^{59} + 4 q^{61} + 35 q^{62} - 8 q^{63} - 11 q^{64} - 24 q^{66} - 28 q^{67} + 30 q^{68} - 38 q^{69} + 2 q^{71} + 9 q^{72} + 11 q^{73} - 17 q^{74} - 36 q^{76} + 58 q^{77} - 2 q^{78} - 9 q^{79} - 25 q^{81} - 28 q^{82} + 12 q^{83} - 46 q^{84} - 4 q^{86} + 20 q^{87} - 14 q^{88} + 6 q^{89} - 42 q^{93} + 20 q^{94} + 40 q^{96} + 26 q^{97} + 13 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 5 * q^3 + 8 * q^4 + 4 * q^6 + 3 * q^7 + 3 * q^8 + 8 * q^9 + q^11 + 23 * q^12 + 14 * q^13 - 17 * q^14 + 2 * q^16 + 12 * q^17 + 15 * q^18 - 4 * q^21 - 17 * q^22 + 18 * q^23 + 17 * q^24 + 12 * q^26 + 8 * q^27 - 2 * q^28 + 10 * q^29 - 15 * q^31 + 15 * q^32 + 20 * q^33 - 8 * q^34 + 32 * q^36 + 5 * q^37 + 4 * q^38 + 10 * q^39 - 21 * q^41 - 47 * q^42 - 7 * q^43 + 13 * q^44 + 4 * q^46 + 2 * q^47 + 33 * q^48 + 16 * q^49 + 16 * q^51 + 2 * q^52 + 42 * q^53 + 3 * q^54 - 28 * q^56 - 8 * q^57 + 30 * q^58 + 9 * q^59 + 4 * q^61 + 35 * q^62 - 8 * q^63 - 11 * q^64 - 24 * q^66 - 28 * q^67 + 30 * q^68 - 38 * q^69 + 2 * q^71 + 9 * q^72 + 11 * q^73 - 17 * q^74 - 36 * q^76 + 58 * q^77 - 2 * q^78 - 9 * q^79 - 25 * q^81 - 28 * q^82 + 12 * q^83 - 46 * q^84 - 4 * q^86 + 20 * q^87 - 14 * q^88 + 6 * q^89 - 42 * q^93 + 20 * q^94 + 40 * q^96 + 26 * q^97 + 13 * q^98 + 7 * q^99

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