LMFDB - Embedded newform 1475.2.a.p.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1475, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1475.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1475 = 5^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1475.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$11.7779342981$
Analytic rank:	$0$
Dimension:	$7$
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} - 9x^{5} - 3x^{4} + 15x^{3} + 8x^{2} - 2x - 1 $ x^7 - 9x^5 - 3x^4 + 15x^3 + 8x^2 - 2*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.47071$ of defining polynomial
Character	$\chi$	$=$	1475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.790770 q^{2} +0.679943 q^{3} -1.37468 q^{4} +0.537678 q^{6} -0.861107 q^{7} -2.66860 q^{8} -2.53768 q^{9} +O(q^{10})$	\(q+0.790770 q^{2} +0.679943 q^{3} -1.37468 q^{4} +0.537678 q^{6} -0.861107 q^{7} -2.66860 q^{8} -2.53768 q^{9} +3.45500 q^{11} -0.934706 q^{12} +0.891165 q^{13} -0.680937 q^{14} +0.639120 q^{16} +5.08773 q^{17} -2.00672 q^{18} -1.07538 q^{19} -0.585503 q^{21} +2.73211 q^{22} +4.17476 q^{23} -1.81449 q^{24} +0.704707 q^{26} -3.76530 q^{27} +1.18375 q^{28} +10.3391 q^{29} +1.93703 q^{31} +5.84259 q^{32} +2.34920 q^{33} +4.02323 q^{34} +3.48850 q^{36} -5.52397 q^{37} -0.850378 q^{38} +0.605941 q^{39} +7.95661 q^{41} -0.462998 q^{42} -2.93367 q^{43} -4.74953 q^{44} +3.30127 q^{46} +9.93214 q^{47} +0.434565 q^{48} -6.25849 q^{49} +3.45937 q^{51} -1.22507 q^{52} +6.53281 q^{53} -2.97749 q^{54} +2.29795 q^{56} -0.731197 q^{57} +8.17584 q^{58} -1.00000 q^{59} -1.77106 q^{61} +1.53175 q^{62} +2.18521 q^{63} +3.34191 q^{64} +1.85768 q^{66} +13.8550 q^{67} -6.99402 q^{68} +2.83860 q^{69} -13.2277 q^{71} +6.77204 q^{72} +13.2432 q^{73} -4.36819 q^{74} +1.47831 q^{76} -2.97513 q^{77} +0.479160 q^{78} -5.50286 q^{79} +5.05284 q^{81} +6.29184 q^{82} -0.578922 q^{83} +0.804882 q^{84} -2.31986 q^{86} +7.02999 q^{87} -9.22001 q^{88} -16.4135 q^{89} -0.767389 q^{91} -5.73897 q^{92} +1.31707 q^{93} +7.85403 q^{94} +3.97263 q^{96} -11.2488 q^{97} -4.94903 q^{98} -8.76768 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 13 q^{6} + q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 13 * q^6 + q^7 + 6 * q^8 - q^9	$ 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 13 q^{6} + q^{7} + 6 q^{8} - q^{9} - 9 q^{11} - 3 q^{12} + 17 q^{13} + 16 q^{16} + 6 q^{17} + 3 q^{18} + 3 q^{19} - 5 q^{21} + 12 q^{22} + 8 q^{23} - 31 q^{24} + 21 q^{26} + q^{27} + 27 q^{28} + 2 q^{29} - q^{31} + 34 q^{32} + 12 q^{33} - 21 q^{34} + 37 q^{36} + 26 q^{37} - 9 q^{38} - 3 q^{39} + 16 q^{41} - 8 q^{42} + 36 q^{43} - 23 q^{44} + 5 q^{46} + 8 q^{47} - 32 q^{48} - 14 q^{49} - 4 q^{51} + 60 q^{52} + 5 q^{53} - 42 q^{54} + 41 q^{56} + 31 q^{57} + 34 q^{58} - 7 q^{59} - 7 q^{61} - 5 q^{62} + 6 q^{63} - 8 q^{64} + 53 q^{66} + 32 q^{67} - 14 q^{68} + 34 q^{69} - 14 q^{71} + 26 q^{72} + 9 q^{73} - 7 q^{74} + 28 q^{76} - 2 q^{77} - 84 q^{78} + 6 q^{79} + 23 q^{81} - 7 q^{83} - 54 q^{84} + 44 q^{86} - 28 q^{87} - 3 q^{88} - 9 q^{89} - 17 q^{91} + 4 q^{92} - 37 q^{96} + 36 q^{97} - 3 q^{98} - 35 q^{99}+O(q^{100}) $ 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 13 * q^6 + q^7 + 6 * q^8 - q^9 - 9 * q^11 - 3 * q^12 + 17 * q^13 + 16 * q^16 + 6 * q^17 + 3 * q^18 + 3 * q^19 - 5 * q^21 + 12 * q^22 + 8 * q^23 - 31 * q^24 + 21 * q^26 + q^27 + 27 * q^28 + 2 * q^29 - q^31 + 34 * q^32 + 12 * q^33 - 21 * q^34 + 37 * q^36 + 26 * q^37 - 9 * q^38 - 3 * q^39 + 16 * q^41 - 8 * q^42 + 36 * q^43 - 23 * q^44 + 5 * q^46 + 8 * q^47 - 32 * q^48 - 14 * q^49 - 4 * q^51 + 60 * q^52 + 5 * q^53 - 42 * q^54 + 41 * q^56 + 31 * q^57 + 34 * q^58 - 7 * q^59 - 7 * q^61 - 5 * q^62 + 6 * q^63 - 8 * q^64 + 53 * q^66 + 32 * q^67 - 14 * q^68 + 34 * q^69 - 14 * q^71 + 26 * q^72 + 9 * q^73 - 7 * q^74 + 28 * q^76 - 2 * q^77 - 84 * q^78 + 6 * q^79 + 23 * q^81 - 7 * q^83 - 54 * q^84 + 44 * q^86 - 28 * q^87 - 3 * q^88 - 9 * q^89 - 17 * q^91 + 4 * q^92 - 37 * q^96 + 36 * q^97 - 3 * q^98 - 35 * 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 $

$2$	0.790770	0.559159	0.279579	−	0.960123i	$-0.409805\pi$
$2$	0.790770	0.559159	0.279579	+	0.960123i	$0.409805\pi$
$3$	0.679943	0.392565	0.196283	−	0.980547i	$-0.437113\pi$
$3$	0.679943	0.392565	0.196283	+	0.980547i	$0.437113\pi$
$4$	−1.37468	−0.687342
$5$	0	0
$5$	0	0
$6$	0.537678	0.219506
$7$	−0.861107	−0.325468	−0.162734	−	0.986670i	$-0.552031\pi$
$7$	−0.861107	−0.325468	−0.162734	+	0.986670i	$0.552031\pi$
$8$	−2.66860	−0.943492
$9$	−2.53768	−0.845893
$10$	0	0
$11$	3.45500	1.04172	0.520861	−	0.853642i	$-0.325611\pi$
$11$	3.45500	1.04172	0.520861	+	0.853642i	$0.325611\pi$
$12$	−0.934706	−0.269826
$13$	0.891165	0.247165	0.123582	−	0.992334i	$-0.460562\pi$
$13$	0.891165	0.247165	0.123582	+	0.992334i	$0.460562\pi$
$14$	−0.680937	−0.181988
$15$	0	0
$16$	0.639120	0.159780
$17$	5.08773	1.23396	0.616978	−	0.786980i	$-0.288357\pi$
$17$	5.08773	1.23396	0.616978	+	0.786980i	$0.288357\pi$
$18$	−2.00672	−0.472988
$19$	−1.07538	−0.246709	−0.123355	−	0.992363i	$-0.539365\pi$
$19$	−1.07538	−0.246709	−0.123355	+	0.992363i	$0.539365\pi$
$20$	0	0
$21$	−0.585503	−0.127767
$22$	2.73211	0.582488
$23$	4.17476	0.870497	0.435249	−	0.900310i	$-0.356661\pi$
$23$	4.17476	0.870497	0.435249	+	0.900310i	$0.356661\pi$
$24$	−1.81449	−0.370382
$25$	0	0
$26$	0.704707	0.138204
$27$	−3.76530	−0.724633
$28$	1.18375	0.223708
$29$	10.3391	1.91992	0.959961	−	0.280135i	$-0.0903793\pi$
$29$	10.3391	1.91992	0.959961	+	0.280135i	$0.0903793\pi$
$30$	0	0
$31$	1.93703	0.347901	0.173951	−	0.984754i	$-0.444347\pi$
$31$	1.93703	0.347901	0.173951	+	0.984754i	$0.444347\pi$
$32$	5.84259	1.03283
$33$	2.34920	0.408944
$34$	4.02323	0.689978
$35$	0	0
$36$	3.48850	0.581417
$37$	−5.52397	−0.908136	−0.454068	−	0.890967i	$-0.650028\pi$
$37$	−5.52397	−0.908136	−0.454068	+	0.890967i	$0.650028\pi$
$38$	−0.850378	−0.137950
$39$	0.605941	0.0970283
$40$	0	0
$41$	7.95661	1.24261	0.621307	−	0.783568i	$-0.286602\pi$
$41$	7.95661	1.24261	0.621307	+	0.783568i	$0.286602\pi$
$42$	−0.462998	−0.0714422
$43$	−2.93367	−0.447381	−0.223691	−	0.974660i	$-0.571810\pi$
$43$	−2.93367	−0.447381	−0.223691	+	0.974660i	$0.571810\pi$
$44$	−4.74953	−0.716019
$45$	0	0
$46$	3.30127	0.486746
$47$	9.93214	1.44875	0.724375	−	0.689406i	$-0.242128\pi$
$47$	9.93214	1.44875	0.724375	+	0.689406i	$0.242128\pi$
$48$	0.434565	0.0627240
$49$	−6.25849	−0.894071
$50$	0	0
$51$	3.45937	0.484408
$52$	−1.22507	−0.169887
$53$	6.53281	0.897350	0.448675	−	0.893695i	$-0.351896\pi$
$53$	6.53281	0.897350	0.448675	+	0.893695i	$0.351896\pi$
$54$	−2.97749	−0.405185
$55$	0	0
$56$	2.29795	0.307076
$57$	−0.731197	−0.0968494
$58$	8.17584	1.07354
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0	0
$61$	−1.77106	−0.226761	−0.113381	−	0.993552i	$-0.536168\pi$
$61$	−1.77106	−0.226761	−0.113381	+	0.993552i	$0.536168\pi$
$62$	1.53175	0.194532
$63$	2.18521	0.275311
$64$	3.34191	0.417738
$65$	0	0
$66$	1.85768	0.228664
$67$	13.8550	1.69265	0.846326	−	0.532665i	$-0.178809\pi$
$67$	13.8550	1.69265	0.846326	+	0.532665i	$0.178809\pi$
$68$	−6.99402	−0.848150
$69$	2.83860	0.341727
$70$	0	0
$71$	−13.2277	−1.56984	−0.784918	−	0.619600i	$-0.787295\pi$
$71$	−13.2277	−1.56984	−0.784918	+	0.619600i	$0.787295\pi$
$72$	6.77204	0.798093
$73$	13.2432	1.55000	0.774998	−	0.631964i	$-0.217751\pi$
$73$	13.2432	1.55000	0.774998	+	0.631964i	$0.217751\pi$
$74$	−4.36819	−0.507792
$75$	0	0
$76$	1.47831	0.169573
$77$	−2.97513	−0.339047
$78$	0.479160	0.0542542
$79$	−5.50286	−0.619120	−0.309560	−	0.950880i	$-0.600182\pi$
$79$	−5.50286	−0.619120	−0.309560	+	0.950880i	$0.600182\pi$
$80$	0	0
$81$	5.05284	0.561427
$82$	6.29184	0.694818
$83$	−0.578922	−0.0635449	−0.0317725	−	0.999495i	$-0.510115\pi$
$83$	−0.578922	−0.0635449	−0.0317725	+	0.999495i	$0.510115\pi$
$84$	0.804882	0.0878198
$85$	0	0
$86$	−2.31986	−0.250157
$87$	7.02999	0.753694
$88$	−9.22001	−0.982856
$89$	−16.4135	−1.73982	−0.869911	−	0.493208i	$-0.835824\pi$
$89$	−16.4135	−1.73982	−0.869911	+	0.493208i	$0.835824\pi$
$90$	0	0
$91$	−0.767389	−0.0804442
$92$	−5.73897	−0.598329
$93$	1.31707	0.136574
$94$	7.85403	0.810082
$95$	0	0
$96$	3.97263	0.405455
$97$	−11.2488	−1.14215	−0.571073	−	0.820900i	$-0.693473\pi$
$97$	−11.2488	−1.14215	−0.571073	+	0.820900i	$0.693473\pi$
$98$	−4.94903	−0.499927
$99$	−8.76768	−0.881185
$100$	0	0
$101$	0.162448	0.0161642	0.00808210	−	0.999967i	$-0.497427\pi$
$101$	0.162448	0.0161642	0.00808210	+	0.999967i	$0.497427\pi$
$102$	2.73556	0.270861
$103$	4.97654	0.490353	0.245176	−	0.969478i	$-0.421154\pi$
$103$	4.97654	0.490353	0.245176	+	0.969478i	$0.421154\pi$
$104$	−2.37816	−0.233198
$105$	0	0
$106$	5.16595	0.501761
$107$	2.34309	0.226515	0.113257	−	0.993566i	$-0.463872\pi$
$107$	2.34309	0.226515	0.113257	+	0.993566i	$0.463872\pi$
$108$	5.17610	0.498070
$109$	−5.53391	−0.530053	−0.265026	−	0.964241i	$-0.585381\pi$
$109$	−5.53391	−0.530053	−0.265026	+	0.964241i	$0.585381\pi$
$110$	0	0
$111$	−3.75598	−0.356502
$112$	−0.550351	−0.0520033
$113$	6.06119	0.570189	0.285094	−	0.958499i	$-0.407975\pi$
$113$	6.06119	0.570189	0.285094	+	0.958499i	$0.407975\pi$
$114$	−0.578208	−0.0541542
$115$	0	0
$116$	−14.2130	−1.31964
$117$	−2.26149	−0.209075
$118$	−0.790770	−0.0727963
$119$	−4.38108	−0.401613
$120$	0	0
$121$	0.937031	0.0851846
$122$	−1.40050	−0.126795
$123$	5.41004	0.487807
$124$	−2.66280	−0.239127
$125$	0	0
$126$	1.72800	0.153942
$127$	−2.36743	−0.210076	−0.105038	−	0.994468i	$-0.533496\pi$
$127$	−2.36743	−0.210076	−0.105038	+	0.994468i	$0.533496\pi$
$128$	−9.04251	−0.799252
$129$	−1.99473	−0.175626
$130$	0	0
$131$	4.69969	0.410614	0.205307	−	0.978698i	$-0.434181\pi$
$131$	4.69969	0.410614	0.205307	+	0.978698i	$0.434181\pi$
$132$	−3.22941	−0.281084
$133$	0.926017	0.0802959
$134$	10.9561	0.946462
$135$	0	0
$136$	−13.5771	−1.16423
$137$	23.0171	1.96648	0.983242	−	0.182305i	$-0.0583557\pi$
$137$	23.0171	1.96648	0.983242	+	0.182305i	$0.0583557\pi$
$138$	2.24468	0.191079
$139$	5.83521	0.494936	0.247468	−	0.968896i	$-0.420401\pi$
$139$	5.83521	0.494936	0.247468	+	0.968896i	$0.420401\pi$
$140$	0	0
$141$	6.75328	0.568729
$142$	−10.4600	−0.877787
$143$	3.07898	0.257477
$144$	−1.62188	−0.135157
$145$	0	0
$146$	10.4723	0.866694
$147$	−4.25542	−0.350981
$148$	7.59371	0.624199
$149$	12.8020	1.04878	0.524389	−	0.851479i	$-0.324294\pi$
$149$	12.8020	1.04878	0.524389	+	0.851479i	$0.324294\pi$
$150$	0	0
$151$	−12.5549	−1.02170	−0.510850	−	0.859670i	$-0.670669\pi$
$151$	−12.5549	−1.02170	−0.510850	+	0.859670i	$0.670669\pi$
$152$	2.86976	0.232768
$153$	−12.9110	−1.04380
$154$	−2.35264	−0.189581
$155$	0	0
$156$	−0.832977	−0.0666916
$157$	1.38996	0.110931	0.0554656	−	0.998461i	$-0.482336\pi$
$157$	1.38996	0.110931	0.0554656	+	0.998461i	$0.482336\pi$
$158$	−4.35149	−0.346186
$159$	4.44193	0.352268
$160$	0	0
$161$	−3.59491	−0.283319
$162$	3.99564	0.313927
$163$	8.40043	0.657973	0.328986	−	0.944335i	$-0.393293\pi$
$163$	8.40043	0.657973	0.328986	+	0.944335i	$0.393293\pi$
$164$	−10.9378	−0.854100
$165$	0	0
$166$	−0.457794	−0.0355317
$167$	−1.65476	−0.128049	−0.0640246	−	0.997948i	$-0.520394\pi$
$167$	−1.65476	−0.128049	−0.0640246	+	0.997948i	$0.520394\pi$
$168$	1.56247	0.120547
$169$	−12.2058	−0.938910
$170$	0	0
$171$	2.72897	0.208689
$172$	4.03287	0.307504
$173$	−11.4718	−0.872183	−0.436092	−	0.899902i	$-0.643638\pi$
$173$	−11.4718	−0.872183	−0.436092	+	0.899902i	$0.643638\pi$
$174$	5.55910	0.421434
$175$	0	0
$176$	2.20816	0.166446
$177$	−0.679943	−0.0511076
$178$	−12.9793	−0.972837
$179$	17.5951	1.31512	0.657561	−	0.753401i	$-0.271588\pi$
$179$	17.5951	1.31512	0.657561	+	0.753401i	$0.271588\pi$
$180$	0	0
$181$	−20.1797	−1.49994	−0.749972	−	0.661469i	$-0.769933\pi$
$181$	−20.1797	−1.49994	−0.749972	+	0.661469i	$0.769933\pi$
$182$	−0.606828	−0.0449811
$183$	−1.20422	−0.0890185
$184$	−11.1407	−0.821307
$185$	0	0
$186$	1.04150	0.0763664
$187$	17.5781	1.28544
$188$	−13.6535	−0.995787
$189$	3.24233	0.235845
$190$	0	0
$191$	4.91971	0.355977	0.177989	−	0.984033i	$-0.443041\pi$
$191$	4.91971	0.355977	0.177989	+	0.984033i	$0.443041\pi$
$192$	2.27230	0.163989
$193$	−11.0953	−0.798655	−0.399327	−	0.916808i	$-0.630756\pi$
$193$	−11.0953	−0.798655	−0.399327	+	0.916808i	$0.630756\pi$
$194$	−8.89523	−0.638640
$195$	0	0
$196$	8.60345	0.614532
$197$	10.2680	0.731566	0.365783	−	0.930700i	$-0.380801\pi$
$197$	10.2680	0.731566	0.365783	+	0.930700i	$0.380801\pi$
$198$	−6.93322	−0.492722
$199$	18.4716	1.30942	0.654709	−	0.755881i	$-0.272791\pi$
$199$	18.4716	1.30942	0.654709	+	0.755881i	$0.272791\pi$
$200$	0	0
$201$	9.42058	0.664476
$202$	0.128459	0.00903835
$203$	−8.90306	−0.624873
$204$	−4.75553	−0.332954
$205$	0	0
$206$	3.93529	0.274185
$207$	−10.5942	−0.736347
$208$	0.569562	0.0394920
$209$	−3.71544	−0.257002
$210$	0	0
$211$	−26.6668	−1.83582	−0.917910	−	0.396788i	$-0.870125\pi$
$211$	−26.6668	−1.83582	−0.917910	+	0.396788i	$0.870125\pi$
$212$	−8.98054	−0.616786
$213$	−8.99406	−0.616263
$214$	1.85284	0.126658
$215$	0	0
$216$	10.0481	0.683685
$217$	−1.66799	−0.113231
$218$	−4.37605	−0.296384
$219$	9.00460	0.608474
$220$	0	0
$221$	4.53401	0.304991
$222$	−2.97012	−0.199341
$223$	16.9572	1.13554	0.567768	−	0.823189i	$-0.307807\pi$
$223$	16.9572	1.13554	0.567768	+	0.823189i	$0.307807\pi$
$224$	−5.03110	−0.336154
$225$	0	0
$226$	4.79300	0.318826
$227$	−22.1161	−1.46790	−0.733950	−	0.679204i	$-0.762325\pi$
$227$	−22.1161	−1.46790	−0.733950	+	0.679204i	$0.762325\pi$
$228$	1.00516	0.0665686
$229$	13.3767	0.883956	0.441978	−	0.897026i	$-0.354277\pi$
$229$	13.3767	0.883956	0.441978	+	0.897026i	$0.354277\pi$
$230$	0	0
$231$	−2.02291	−0.133098
$232$	−27.5909	−1.81143
$233$	12.5226	0.820385	0.410193	−	0.911999i	$-0.365461\pi$
$233$	12.5226	0.820385	0.410193	+	0.911999i	$0.365461\pi$
$234$	−1.78832	−0.116906
$235$	0	0
$236$	1.37468	0.0894842
$237$	−3.74163	−0.243045
$238$	−3.46443	−0.224566
$239$	−7.06197	−0.456801	−0.228400	−	0.973567i	$-0.573350\pi$
$239$	−7.06197	−0.456801	−0.228400	+	0.973567i	$0.573350\pi$
$240$	0	0
$241$	8.04837	0.518441	0.259221	−	0.965818i	$-0.416534\pi$
$241$	8.04837	0.518441	0.259221	+	0.965818i	$0.416534\pi$
$242$	0.740976	0.0476317
$243$	14.7316	0.945030
$244$	2.43465	0.155862
$245$	0	0
$246$	4.27809	0.272761
$247$	−0.958342	−0.0609778
$248$	−5.16916	−0.328242
$249$	−0.393634	−0.0249455
$250$	0	0
$251$	14.2281	0.898070	0.449035	−	0.893514i	$-0.351768\pi$
$251$	14.2281	0.898070	0.449035	+	0.893514i	$0.351768\pi$
$252$	−3.00397	−0.189233
$253$	14.4238	0.906816
$254$	−1.87210	−0.117466
$255$	0	0
$256$	−13.8344	−0.864647
$257$	−8.17431	−0.509899	−0.254950	−	0.966954i	$-0.582059\pi$
$257$	−8.17431	−0.509899	−0.254950	+	0.966954i	$0.582059\pi$
$258$	−1.57737	−0.0982029
$259$	4.75673	0.295569
$260$	0	0
$261$	−26.2373	−1.62405
$262$	3.71637	0.229598
$263$	−11.4939	−0.708747	−0.354373	−	0.935104i	$-0.615306\pi$
$263$	−11.4939	−0.708747	−0.354373	+	0.935104i	$0.615306\pi$
$264$	−6.26908	−0.385835
$265$	0	0
$266$	0.732267	0.0448981
$267$	−11.1602	−0.682994
$268$	−19.0462	−1.16343
$269$	−13.7108	−0.835961	−0.417981	−	0.908456i	$-0.637262\pi$
$269$	−13.7108	−0.835961	−0.417981	+	0.908456i	$0.637262\pi$
$270$	0	0
$271$	−17.6820	−1.07410	−0.537051	−	0.843549i	$-0.680462\pi$
$271$	−17.6820	−1.07410	−0.537051	+	0.843549i	$0.680462\pi$
$272$	3.25167	0.197162
$273$	−0.521780	−0.0315796
$274$	18.2012	1.09958
$275$	0	0
$276$	−3.90217	−0.234883
$277$	10.5559	0.634242	0.317121	−	0.948385i	$-0.397284\pi$
$277$	10.5559	0.634242	0.317121	+	0.948385i	$0.397284\pi$
$278$	4.61431	0.276748
$279$	−4.91556	−0.294287
$280$	0	0
$281$	−17.4146	−1.03887	−0.519435	−	0.854510i	$-0.673857\pi$
$281$	−17.4146	−1.03887	−0.519435	+	0.854510i	$0.673857\pi$
$282$	5.34029	0.318010
$283$	−2.68771	−0.159768	−0.0798840	−	0.996804i	$-0.525455\pi$
$283$	−2.68771	−0.159768	−0.0798840	+	0.996804i	$0.525455\pi$
$284$	18.1839	1.07901
$285$	0	0
$286$	2.43476	0.143971
$287$	−6.85149	−0.404431
$288$	−14.8266	−0.873667
$289$	8.88504	0.522649
$290$	0	0
$291$	−7.64856	−0.448366
$292$	−18.2052	−1.06538
$293$	−17.2120	−1.00553	−0.502767	−	0.864422i	$-0.667685\pi$
$293$	−17.2120	−1.00553	−0.502767	+	0.864422i	$0.667685\pi$
$294$	−3.36506	−0.196254
$295$	0	0
$296$	14.7413	0.856818
$297$	−13.0091	−0.754866
$298$	10.1234	0.586434
$299$	3.72040	0.215156
$300$	0	0
$301$	2.52621	0.145608
$302$	−9.92800	−0.571292
$303$	0.110455	0.00634550
$304$	−0.687297	−0.0394192
$305$	0	0
$306$	−10.2097	−0.583647
$307$	−14.1961	−0.810215	−0.405107	−	0.914269i	$-0.632766\pi$
$307$	−14.1961	−0.810215	−0.405107	+	0.914269i	$0.632766\pi$
$308$	4.08985	0.233041
$309$	3.38376	0.192495
$310$	0	0
$311$	3.78796	0.214796	0.107398	−	0.994216i	$-0.465748\pi$
$311$	3.78796	0.214796	0.107398	+	0.994216i	$0.465748\pi$
$312$	−1.61701	−0.0915454
$313$	26.5907	1.50300	0.751499	−	0.659734i	$-0.229331\pi$
$313$	26.5907	1.50300	0.751499	+	0.659734i	$0.229331\pi$
$314$	1.09914	0.0620282
$315$	0	0
$316$	7.56469	0.425547
$317$	2.16873	0.121808	0.0609041	−	0.998144i	$-0.480602\pi$
$317$	2.16873	0.121808	0.0609041	+	0.998144i	$0.480602\pi$
$318$	3.51255	0.196974
$319$	35.7216	2.00002
$320$	0	0
$321$	1.59316	0.0889217
$322$	−2.84275	−0.158420
$323$	−5.47125	−0.304428
$324$	−6.94606	−0.385892
$325$	0	0
$326$	6.64281	0.367911
$327$	−3.76274	−0.208080
$328$	−21.2330	−1.17240
$329$	−8.55263	−0.471522
$330$	0	0
$331$	−20.6814	−1.13675	−0.568375	−	0.822769i	$-0.692428\pi$
$331$	−20.6814	−1.13675	−0.568375	+	0.822769i	$0.692428\pi$
$332$	0.795834	0.0436771
$333$	14.0181	0.768185
$334$	−1.30854	−0.0715999
$335$	0	0
$336$	−0.374207	−0.0204147
$337$	19.9920	1.08903	0.544516	−	0.838750i	$-0.316713\pi$
$337$	19.9920	1.08903	0.544516	+	0.838750i	$0.316713\pi$
$338$	−9.65200	−0.524999
$339$	4.12126	0.223836
$340$	0	0
$341$	6.69244	0.362416
$342$	2.15799	0.116691
$343$	11.4170	0.616459
$344$	7.82879	0.422100
$345$	0	0
$346$	−9.07154	−0.487689
$347$	−14.3201	−0.768744	−0.384372	−	0.923178i	$-0.625582\pi$
$347$	−14.3201	−0.768744	−0.384372	+	0.923178i	$0.625582\pi$
$348$	−9.66401	−0.518045
$349$	30.8464	1.65117	0.825584	−	0.564280i	$-0.190846\pi$
$349$	30.8464	1.65117	0.825584	+	0.564280i	$0.190846\pi$
$350$	0	0
$351$	−3.35551	−0.179104
$352$	20.1862	1.07593
$353$	5.75557	0.306338	0.153169	−	0.988200i	$-0.451052\pi$
$353$	5.75557	0.306338	0.153169	+	0.988200i	$0.451052\pi$
$354$	−0.537678	−0.0285773
$355$	0	0
$356$	22.5633	1.19585
$357$	−2.97889	−0.157659
$358$	13.9137	0.735362
$359$	32.5206	1.71637	0.858185	−	0.513341i	$-0.171592\pi$
$359$	32.5206	1.71637	0.858185	+	0.513341i	$0.171592\pi$
$360$	0	0
$361$	−17.8436	−0.939135
$362$	−15.9575	−0.838707
$363$	0.637127	0.0334405
$364$	1.05492	0.0552927
$365$	0	0
$366$	−0.952261	−0.0497755
$367$	−17.5121	−0.914123	−0.457062	−	0.889435i	$-0.651098\pi$
$367$	−17.5121	−0.914123	−0.457062	+	0.889435i	$0.651098\pi$
$368$	2.66817	0.139088
$369$	−20.1913	−1.05112
$370$	0	0
$371$	−5.62545	−0.292059
$372$	−1.81055	−0.0938728
$373$	0.478332	0.0247671	0.0123835	−	0.999923i	$-0.496058\pi$
$373$	0.478332	0.0247671	0.0123835	+	0.999923i	$0.496058\pi$
$374$	13.9003	0.718765
$375$	0	0
$376$	−26.5049	−1.36688
$377$	9.21384	0.474537
$378$	2.56394	0.131875
$379$	−14.9271	−0.766753	−0.383376	−	0.923592i	$-0.625239\pi$
$379$	−14.9271	−0.766753	−0.383376	+	0.923592i	$0.625239\pi$
$380$	0	0
$381$	−1.60972	−0.0824684
$382$	3.89035	0.199048
$383$	12.7960	0.653844	0.326922	−	0.945051i	$-0.393989\pi$
$383$	12.7960	0.653844	0.326922	+	0.945051i	$0.393989\pi$
$384$	−6.14838	−0.313758
$385$	0	0
$386$	−8.77380	−0.446575
$387$	7.44472	0.378436
$388$	15.4636	0.785044
$389$	−10.7195	−0.543499	−0.271749	−	0.962368i	$-0.587602\pi$
$389$	−10.7195	−0.543499	−0.271749	+	0.962368i	$0.587602\pi$
$390$	0	0
$391$	21.2401	1.07416
$392$	16.7014	0.843548
$393$	3.19552	0.161193
$394$	8.11964	0.409062
$395$	0	0
$396$	12.0528	0.605675
$397$	7.80889	0.391917	0.195958	−	0.980612i	$-0.437218\pi$
$397$	7.80889	0.391917	0.195958	+	0.980612i	$0.437218\pi$
$398$	14.6068	0.732172
$399$	0.629639	0.0315214
$400$	0	0
$401$	−2.17245	−0.108487	−0.0542435	−	0.998528i	$-0.517275\pi$
$401$	−2.17245	−0.108487	−0.0542435	+	0.998528i	$0.517275\pi$
$402$	7.44951	0.371548
$403$	1.72622	0.0859889
$404$	−0.223315	−0.0111103
$405$	0	0
$406$	−7.04027	−0.349403
$407$	−19.0853	−0.946025
$408$	−9.23166	−0.457035
$409$	−8.35204	−0.412982	−0.206491	−	0.978449i	$-0.566204\pi$
$409$	−8.35204	−0.412982	−0.206491	+	0.978449i	$0.566204\pi$
$410$	0	0
$411$	15.6503	0.771973
$412$	−6.84116	−0.337040
$413$	0.861107	0.0423723
$414$	−8.37756	−0.411735
$415$	0	0
$416$	5.20672	0.255280
$417$	3.96761	0.194295
$418$	−2.93806	−0.143705
$419$	21.8454	1.06722	0.533610	−	0.845731i	$-0.320835\pi$
$419$	21.8454	1.06722	0.533610	+	0.845731i	$0.320835\pi$
$420$	0	0
$421$	−20.4579	−0.997055	−0.498528	−	0.866874i	$-0.666126\pi$
$421$	−20.4579	−0.997055	−0.498528	+	0.866874i	$0.666126\pi$
$422$	−21.0873	−1.02652
$423$	−25.2046	−1.22549
$424$	−17.4334	−0.846642
$425$	0	0
$426$	−7.11223	−0.344589
$427$	1.52507	0.0738035
$428$	−3.22100	−0.155693
$429$	2.09353	0.101076
$430$	0	0
$431$	−12.7329	−0.613324	−0.306662	−	0.951818i	$-0.599212\pi$
$431$	−12.7329	−0.613324	−0.306662	+	0.951818i	$0.599212\pi$
$432$	−2.40648	−0.115782
$433$	34.5852	1.66206	0.831030	−	0.556227i	$-0.187752\pi$
$433$	34.5852	1.66206	0.831030	+	0.556227i	$0.187752\pi$
$434$	−1.31900	−0.0633139
$435$	0	0
$436$	7.60738	0.364327
$437$	−4.48945	−0.214760
$438$	7.12056	0.340234
$439$	−3.76112	−0.179509	−0.0897543	−	0.995964i	$-0.528608\pi$
$439$	−3.76112	−0.179509	−0.0897543	+	0.995964i	$0.528608\pi$
$440$	0	0
$441$	15.8820	0.756288
$442$	3.58536	0.170538
$443$	−35.3659	−1.68029	−0.840143	−	0.542365i	$-0.817529\pi$
$443$	−35.3659	−1.68029	−0.840143	+	0.542365i	$0.817529\pi$
$444$	5.16329	0.245039
$445$	0	0
$446$	13.4092	0.634945
$447$	8.70461	0.411714
$448$	−2.87774	−0.135960
$449$	35.4576	1.67335	0.836673	−	0.547702i	$-0.184497\pi$
$449$	35.4576	1.67335	0.836673	+	0.547702i	$0.184497\pi$
$450$	0	0
$451$	27.4901	1.29446
$452$	−8.33221	−0.391914
$453$	−8.53658	−0.401083
$454$	−17.4888	−0.820789
$455$	0	0
$456$	1.95127	0.0913766
$457$	−18.7701	−0.878026	−0.439013	−	0.898481i	$-0.644672\pi$
$457$	−18.7701	−0.878026	−0.439013	+	0.898481i	$0.644672\pi$
$458$	10.5779	0.494272
$459$	−19.1569	−0.894166
$460$	0	0
$461$	38.5357	1.79479	0.897394	−	0.441230i	$-0.145458\pi$
$461$	38.5357	1.79479	0.897394	+	0.441230i	$0.145458\pi$
$462$	−1.59966	−0.0744229
$463$	−16.8365	−0.782456	−0.391228	−	0.920294i	$-0.627950\pi$
$463$	−16.8365	−0.782456	−0.391228	+	0.920294i	$0.627950\pi$
$464$	6.60792	0.306765
$465$	0	0
$466$	9.90252	0.458726
$467$	−31.7197	−1.46781	−0.733907	−	0.679250i	$-0.762305\pi$
$467$	−31.7197	−1.46781	−0.733907	+	0.679250i	$0.762305\pi$
$468$	3.10883	0.143706
$469$	−11.9306	−0.550904
$470$	0	0
$471$	0.945096	0.0435477
$472$	2.66860	0.122832
$473$	−10.1358	−0.466047
$474$	−2.95877	−0.135901
$475$	0	0
$476$	6.02260	0.276046
$477$	−16.5782	−0.759062
$478$	−5.58439	−0.255424
$479$	19.8967	0.909102	0.454551	−	0.890721i	$-0.349800\pi$
$479$	19.8967	0.909102	0.454551	+	0.890721i	$0.349800\pi$
$480$	0	0
$481$	−4.92277	−0.224459
$482$	6.36441	0.289891
$483$	−2.44433	−0.111221
$484$	−1.28812	−0.0585509
$485$	0	0
$486$	11.6493	0.528422
$487$	−23.6377	−1.07112	−0.535562	−	0.844496i	$-0.679900\pi$
$487$	−23.6377	−1.07112	−0.535562	+	0.844496i	$0.679900\pi$
$488$	4.72625	0.213947
$489$	5.71181	0.258297
$490$	0	0
$491$	−38.2047	−1.72416	−0.862078	−	0.506776i	$-0.830837\pi$
$491$	−38.2047	−1.72416	−0.862078	+	0.506776i	$0.830837\pi$
$492$	−7.43709	−0.335290
$493$	52.6026	2.36910
$494$	−0.757828	−0.0340963
$495$	0	0
$496$	1.23800	0.0555876
$497$	11.3904	0.510931
$498$	−0.311274	−0.0139485
$499$	10.7471	0.481105	0.240552	−	0.970636i	$-0.422671\pi$
$499$	10.7471	0.481105	0.240552	+	0.970636i	$0.422671\pi$
$500$	0	0
$501$	−1.12514	−0.0502677
$502$	11.2512	0.502164
$503$	−17.0270	−0.759196	−0.379598	−	0.925151i	$-0.623938\pi$
$503$	−17.0270	−0.759196	−0.379598	+	0.925151i	$0.623938\pi$
$504$	−5.83145	−0.259754
$505$	0	0
$506$	11.4059	0.507054
$507$	−8.29926	−0.368583
$508$	3.25447	0.144394
$509$	−31.6748	−1.40396	−0.701979	−	0.712197i	$-0.747700\pi$
$509$	−31.6748	−1.40396	−0.701979	+	0.712197i	$0.747700\pi$
$510$	0	0
$511$	−11.4038	−0.504474
$512$	7.14522	0.315777
$513$	4.04913	0.178774
$514$	−6.46400	−0.285115
$515$	0	0
$516$	2.74212	0.120715
$517$	34.3155	1.50920
$518$	3.76148	0.165270
$519$	−7.80015	−0.342389
$520$	0	0
$521$	−6.99510	−0.306461	−0.153231	−	0.988190i	$-0.548968\pi$
$521$	−6.99510	−0.306461	−0.153231	+	0.988190i	$0.548968\pi$
$522$	−20.7477	−0.908100
$523$	−43.1667	−1.88755	−0.943773	−	0.330594i	$-0.892751\pi$
$523$	−43.1667	−1.88755	−0.943773	+	0.330594i	$0.892751\pi$
$524$	−6.46059	−0.282232
$525$	0	0
$526$	−9.08906	−0.396302
$527$	9.85510	0.429295
$528$	1.50142	0.0653410
$529$	−5.57140	−0.242235
$530$	0	0
$531$	2.53768	0.110126
$532$	−1.27298	−0.0551907
$533$	7.09065	0.307130
$534$	−8.82515	−0.381902
$535$	0	0
$536$	−36.9733	−1.59700
$537$	11.9637	0.516271
$538$	−10.8421	−0.467435
$539$	−21.6231	−0.931373
$540$	0	0
$541$	8.51269	0.365989	0.182994	−	0.983114i	$-0.441421\pi$
$541$	8.51269	0.365989	0.182994	+	0.983114i	$0.441421\pi$
$542$	−13.9824	−0.600594
$543$	−13.7210	−0.588826
$544$	29.7256	1.27447
$545$	0	0
$546$	−0.412608	−0.0176580
$547$	6.74939	0.288583	0.144292	−	0.989535i	$-0.453910\pi$
$547$	6.74939	0.288583	0.144292	+	0.989535i	$0.453910\pi$
$548$	−31.6412	−1.35165
$549$	4.49438	0.191816
$550$	0	0
$551$	−11.1185	−0.473662
$552$	−7.57507	−0.322416
$553$	4.73855	0.201504
$554$	8.34729	0.354642
$555$	0	0
$556$	−8.02157	−0.340190
$557$	2.70750	0.114720	0.0573601	−	0.998354i	$-0.481732\pi$
$557$	2.70750	0.114720	0.0573601	+	0.998354i	$0.481732\pi$
$558$	−3.88708	−0.164553
$559$	−2.61439	−0.110577
$560$	0	0
$561$	11.9521	0.504619
$562$	−13.7710	−0.580893
$563$	−4.83213	−0.203650	−0.101825	−	0.994802i	$-0.532468\pi$
$563$	−4.83213	−0.203650	−0.101825	+	0.994802i	$0.532468\pi$
$564$	−9.28362	−0.390911
$565$	0	0
$566$	−2.12536	−0.0893357
$567$	−4.35104	−0.182726
$568$	35.2993	1.48113
$569$	−9.01151	−0.377782	−0.188891	−	0.981998i	$-0.560489\pi$
$569$	−9.01151	−0.377782	−0.188891	+	0.981998i	$0.560489\pi$
$570$	0	0
$571$	−14.3558	−0.600773	−0.300386	−	0.953818i	$-0.597116\pi$
$571$	−14.3558	−0.600773	−0.300386	+	0.953818i	$0.597116\pi$
$572$	−4.23262	−0.176975
$573$	3.34512	0.139744
$574$	−5.41795	−0.226141
$575$	0	0
$576$	−8.48068	−0.353362
$577$	6.28329	0.261577	0.130788	−	0.991410i	$-0.458249\pi$
$577$	6.28329	0.261577	0.130788	+	0.991410i	$0.458249\pi$
$578$	7.02602	0.292244
$579$	−7.54415	−0.313524
$580$	0	0
$581$	0.498514	0.0206818
$582$	−6.04825	−0.250708
$583$	22.5709	0.934789
$584$	−35.3407	−1.46241
$585$	0	0
$586$	−13.6107	−0.562253
$587$	2.29423	0.0946930	0.0473465	−	0.998879i	$-0.484923\pi$
$587$	2.29423	0.0946930	0.0473465	+	0.998879i	$0.484923\pi$
$588$	5.84985	0.241244
$589$	−2.08304	−0.0858304
$590$	0	0
$591$	6.98167	0.287187
$592$	−3.53048	−0.145102
$593$	−37.2400	−1.52926	−0.764632	−	0.644468i	$-0.777079\pi$
$593$	−37.2400	−1.52926	−0.764632	+	0.644468i	$0.777079\pi$
$594$	−10.2872	−0.422090
$595$	0	0
$596$	−17.5987	−0.720869
$597$	12.5596	0.514031
$598$	2.94198	0.120306
$599$	1.11017	0.0453605	0.0226802	−	0.999743i	$-0.492780\pi$
$599$	1.11017	0.0453605	0.0226802	+	0.999743i	$0.492780\pi$
$600$	0	0
$601$	22.2450	0.907391	0.453695	−	0.891157i	$-0.350105\pi$
$601$	22.2450	0.907391	0.453695	+	0.891157i	$0.350105\pi$
$602$	1.99765	0.0814181
$603$	−35.1594	−1.43180
$604$	17.2589	0.702256
$605$	0	0
$606$	0.0873448	0.00354814
$607$	42.0085	1.70507	0.852537	−	0.522667i	$-0.175063\pi$
$607$	42.0085	1.70507	0.852537	+	0.522667i	$0.175063\pi$
$608$	−6.28301	−0.254810
$609$	−6.05357	−0.245303
$610$	0	0
$611$	8.85118	0.358080
$612$	17.7486	0.717444
$613$	32.8737	1.32776	0.663879	−	0.747840i	$-0.268909\pi$
$613$	32.8737	1.32776	0.663879	+	0.747840i	$0.268909\pi$
$614$	−11.2259	−0.453039
$615$	0	0
$616$	7.93941	0.319888
$617$	32.6437	1.31419	0.657093	−	0.753809i	$-0.271786\pi$
$617$	32.6437	1.31419	0.657093	+	0.753809i	$0.271786\pi$
$618$	2.67577	0.107635
$619$	−26.7567	−1.07544	−0.537721	−	0.843123i	$-0.680715\pi$
$619$	−26.7567	−1.07544	−0.537721	+	0.843123i	$0.680715\pi$
$620$	0	0
$621$	−15.7192	−0.630791
$622$	2.99541	0.120105
$623$	14.1337	0.566256
$624$	0.387269	0.0155032
$625$	0	0
$626$	21.0272	0.840414
$627$	−2.52629	−0.100890
$628$	−1.91076	−0.0762477
$629$	−28.1045	−1.12060
$630$	0	0
$631$	49.8897	1.98608	0.993039	−	0.117783i	$-0.0375788\pi$
$631$	49.8897	1.98608	0.993039	+	0.117783i	$0.0375788\pi$
$632$	14.6849	0.584135
$633$	−18.1319	−0.720679
$634$	1.71497	0.0681101
$635$	0	0
$636$	−6.10625	−0.242129
$637$	−5.57735	−0.220983
$638$	28.2475	1.11833
$639$	33.5676	1.32791
$640$	0	0
$641$	10.6727	0.421546	0.210773	−	0.977535i	$-0.432402\pi$
$641$	10.6727	0.421546	0.210773	+	0.977535i	$0.432402\pi$
$642$	1.25983	0.0497214
$643$	23.6471	0.932551	0.466275	−	0.884640i	$-0.345596\pi$
$643$	23.6471	0.932551	0.466275	+	0.884640i	$0.345596\pi$
$644$	4.94187	0.194737
$645$	0	0
$646$	−4.32650	−0.170224
$647$	36.5812	1.43816	0.719078	−	0.694929i	$-0.244564\pi$
$647$	36.5812	1.43816	0.719078	+	0.694929i	$0.244564\pi$
$648$	−13.4840	−0.529702
$649$	−3.45500	−0.135621
$650$	0	0
$651$	−1.13414	−0.0444504
$652$	−11.5479	−0.452252
$653$	−6.96251	−0.272464	−0.136232	−	0.990677i	$-0.543499\pi$
$653$	−6.96251	−0.272464	−0.136232	+	0.990677i	$0.543499\pi$
$654$	−2.97546	−0.116350
$655$	0	0
$656$	5.08523	0.198545
$657$	−33.6069	−1.31113
$658$	−6.76316	−0.263656
$659$	10.2575	0.399577	0.199789	−	0.979839i	$-0.435974\pi$
$659$	10.2575	0.399577	0.199789	+	0.979839i	$0.435974\pi$
$660$	0	0
$661$	9.24211	0.359476	0.179738	−	0.983714i	$-0.442475\pi$
$661$	9.24211	0.359476	0.179738	+	0.983714i	$0.442475\pi$
$662$	−16.3542	−0.635624
$663$	3.08287	0.119729
$664$	1.54491	0.0599541
$665$	0	0
$666$	11.0851	0.429537
$667$	43.1632	1.67129
$668$	2.27477	0.0880136
$669$	11.5299	0.445772
$670$	0	0
$671$	−6.11902	−0.236222
$672$	−3.42086	−0.131962
$673$	−17.8092	−0.686494	−0.343247	−	0.939245i	$-0.611527\pi$
$673$	−17.8092	−0.686494	−0.343247	+	0.939245i	$0.611527\pi$
$674$	15.8090	0.608942
$675$	0	0
$676$	16.7791	0.645352
$677$	41.4483	1.59299	0.796495	−	0.604646i	$-0.206685\pi$
$677$	41.4483	1.59299	0.796495	+	0.604646i	$0.206685\pi$
$678$	3.25897	0.125160
$679$	9.68644	0.371732
$680$	0	0
$681$	−15.0377	−0.576246
$682$	5.29218	0.202648
$683$	17.6980	0.677194	0.338597	−	0.940931i	$-0.390048\pi$
$683$	17.6980	0.677194	0.338597	+	0.940931i	$0.390048\pi$
$684$	−3.75147	−0.143441
$685$	0	0
$686$	9.02821	0.344698
$687$	9.09538	0.347010
$688$	−1.87497	−0.0714825
$689$	5.82181	0.221793
$690$	0	0
$691$	−5.31800	−0.202306	−0.101153	−	0.994871i	$-0.532253\pi$
$691$	−5.31800	−0.202306	−0.101153	+	0.994871i	$0.532253\pi$
$692$	15.7701	0.599488
$693$	7.54991	0.286797
$694$	−11.3239	−0.429850
$695$	0	0
$696$	−18.7602	−0.711104
$697$	40.4811	1.53333
$698$	24.3924	0.923265
$699$	8.51468	0.322055
$700$	0	0
$701$	16.0075	0.604594	0.302297	−	0.953214i	$-0.402247\pi$
$701$	16.0075	0.604594	0.302297	+	0.953214i	$0.402247\pi$
$702$	−2.65343	−0.100147
$703$	5.94037	0.224045
$704$	11.5463	0.435167
$705$	0	0
$706$	4.55133	0.171292
$707$	−0.139885	−0.00526093
$708$	0.934706	0.0351284
$709$	−16.9598	−0.636939	−0.318469	−	0.947933i	$-0.603169\pi$
$709$	−16.9598	−0.636939	−0.318469	+	0.947933i	$0.603169\pi$
$710$	0	0
$711$	13.9645	0.523709
$712$	43.8009	1.64151
$713$	8.08663	0.302847
$714$	−2.35561	−0.0881566
$715$	0	0
$716$	−24.1877	−0.903938
$717$	−4.80173	−0.179324
$718$	25.7163	0.959723
$719$	−1.09644	−0.0408904	−0.0204452	−	0.999791i	$-0.506508\pi$
$719$	−1.09644	−0.0408904	−0.0204452	+	0.999791i	$0.506508\pi$
$720$	0	0
$721$	−4.28533	−0.159594
$722$	−14.1101	−0.525125
$723$	5.47243	0.203522
$724$	27.7407	1.03097
$725$	0	0
$726$	0.503821	0.0186986
$727$	−5.50729	−0.204254	−0.102127	−	0.994771i	$-0.532565\pi$
$727$	−5.50729	−0.204254	−0.102127	+	0.994771i	$0.532565\pi$
$728$	2.04785	0.0758984
$729$	−5.14192	−0.190442
$730$	0	0
$731$	−14.9258	−0.552049
$732$	1.65542	0.0611861
$733$	−8.46048	−0.312495	−0.156247	−	0.987718i	$-0.549940\pi$
$733$	−8.46048	−0.312495	−0.156247	+	0.987718i	$0.549940\pi$
$734$	−13.8480	−0.511140
$735$	0	0
$736$	24.3914	0.899079
$737$	47.8689	1.76327
$738$	−15.9667	−0.587741
$739$	−21.3671	−0.786000	−0.393000	−	0.919538i	$-0.628563\pi$
$739$	−21.3671	−0.786000	−0.393000	+	0.919538i	$0.628563\pi$
$740$	0	0
$741$	−0.651617	−0.0239378
$742$	−4.44843	−0.163307
$743$	−24.4657	−0.897559	−0.448780	−	0.893643i	$-0.648141\pi$
$743$	−24.4657	−0.897559	−0.448780	+	0.893643i	$0.648141\pi$
$744$	−3.51473	−0.128856
$745$	0	0
$746$	0.378250	0.0138487
$747$	1.46912	0.0537522
$748$	−24.1644	−0.883536
$749$	−2.01765	−0.0737232
$750$	0	0
$751$	−41.5193	−1.51506	−0.757530	−	0.652801i	$-0.773594\pi$
$751$	−41.5193	−1.51506	−0.757530	+	0.652801i	$0.773594\pi$
$752$	6.34783	0.231481
$753$	9.67430	0.352551
$754$	7.28603	0.265341
$755$	0	0
$756$	−4.45718	−0.162106
$757$	19.3301	0.702565	0.351283	−	0.936269i	$-0.385746\pi$
$757$	19.3301	0.702565	0.351283	+	0.936269i	$0.385746\pi$
$758$	−11.8039	−0.428736
$759$	9.80735	0.355984
$760$	0	0
$761$	17.7320	0.642783	0.321391	−	0.946946i	$-0.395849\pi$
$761$	17.7320	0.642783	0.321391	+	0.946946i	$0.395849\pi$
$762$	−1.27292	−0.0461129
$763$	4.76529	0.172515
$764$	−6.76304	−0.244678
$765$	0	0
$766$	10.1187	0.365603
$767$	−0.891165	−0.0321781
$768$	−9.40656	−0.339430
$769$	−22.3156	−0.804723	−0.402361	−	0.915481i	$-0.631810\pi$
$769$	−22.3156	−0.804723	−0.402361	+	0.915481i	$0.631810\pi$
$770$	0	0
$771$	−5.55806	−0.200169
$772$	15.2525	0.548949
$773$	10.7368	0.386175	0.193087	−	0.981182i	$-0.438150\pi$
$773$	10.7368	0.386175	0.193087	+	0.981182i	$0.438150\pi$
$774$	5.88706	0.211606
$775$	0	0
$776$	30.0186	1.07760
$777$	3.23431	0.116030
$778$	−8.47664	−0.303902
$779$	−8.55638	−0.306564
$780$	0	0
$781$	−45.7016	−1.63533
$782$	16.7960	0.600624
$783$	−38.9298	−1.39124
$784$	−3.99993	−0.142855
$785$	0	0
$786$	2.52692	0.0901323
$787$	−23.3749	−0.833225	−0.416612	−	0.909084i	$-0.636783\pi$
$787$	−23.3749	−0.833225	−0.416612	+	0.909084i	$0.636783\pi$
$788$	−14.1153	−0.502836
$789$	−7.81522	−0.278229
$790$	0	0
$791$	−5.21933	−0.185578
$792$	23.3974	0.831391
$793$	−1.57831	−0.0560474
$794$	6.17503	0.219144
$795$	0	0
$796$	−25.3926	−0.900017
$797$	−18.0595	−0.639700	−0.319850	−	0.947468i	$-0.603633\pi$
$797$	−18.0595	−0.639700	−0.319850	+	0.947468i	$0.603633\pi$
$798$	0.497899	0.0176254
$799$	50.5321	1.78770
$800$	0	0
$801$	41.6521	1.47170
$802$	−1.71791	−0.0606615
$803$	45.7552	1.61466
$804$	−12.9503	−0.456722
$805$	0	0
$806$	1.36504	0.0480814
$807$	−9.32254	−0.328169
$808$	−0.433509	−0.0152508
$809$	−41.1777	−1.44773	−0.723866	−	0.689941i	$-0.757637\pi$
$809$	−41.1777	−1.44773	−0.723866	+	0.689941i	$0.757637\pi$
$810$	0	0
$811$	−3.00079	−0.105372	−0.0526859	−	0.998611i	$-0.516778\pi$
$811$	−3.00079	−0.105372	−0.0526859	+	0.998611i	$0.516778\pi$
$812$	12.2389	0.429501
$813$	−12.0227	−0.421655
$814$	−15.0921	−0.528978
$815$	0	0
$816$	2.21095	0.0773988
$817$	3.15481	0.110373
$818$	−6.60454	−0.230922
$819$	1.94739	0.0680472
$820$	0	0
$821$	24.8692	0.867941	0.433970	−	0.900927i	$-0.357112\pi$
$821$	24.8692	0.867941	0.433970	+	0.900927i	$0.357112\pi$
$822$	12.3758	0.431655
$823$	22.9543	0.800137	0.400068	−	0.916485i	$-0.368986\pi$
$823$	22.9543	0.800137	0.400068	+	0.916485i	$0.368986\pi$
$824$	−13.2804	−0.462644
$825$	0	0
$826$	0.680937	0.0236928
$827$	−40.8811	−1.42158	−0.710788	−	0.703407i	$-0.751661\pi$
$827$	−40.8811	−1.42158	−0.710788	+	0.703407i	$0.751661\pi$
$828$	14.5637	0.506122
$829$	33.3120	1.15697	0.578487	−	0.815691i	$-0.303643\pi$
$829$	33.3120	1.15697	0.578487	+	0.815691i	$0.303643\pi$
$830$	0	0
$831$	7.17741	0.248981
$832$	2.97819	0.103250
$833$	−31.8416	−1.10324
$834$	3.13746	0.108642
$835$	0	0
$836$	5.10755	0.176648
$837$	−7.29351	−0.252101
$838$	17.2747	0.596745
$839$	−27.7659	−0.958587	−0.479294	−	0.877655i	$-0.659107\pi$
$839$	−27.7659	−0.958587	−0.479294	+	0.877655i	$0.659107\pi$
$840$	0	0
$841$	77.8968	2.68610
$842$	−16.1775	−0.557512
$843$	−11.8409	−0.407824
$844$	36.6584	1.26184
$845$	0	0
$846$	−19.9310	−0.685242
$847$	−0.806884	−0.0277249
$848$	4.17525	0.143379
$849$	−1.82749	−0.0627193
$850$	0	0
$851$	−23.0612	−0.790529
$852$	12.3640	0.423583
$853$	16.2968	0.557992	0.278996	−	0.960292i	$-0.409998\pi$
$853$	16.2968	0.557992	0.278996	+	0.960292i	$0.409998\pi$
$854$	1.20598	0.0412679
$855$	0	0
$856$	−6.25275	−0.213715
$857$	−34.3174	−1.17226	−0.586130	−	0.810217i	$-0.699349\pi$
$857$	−34.3174	−1.17226	−0.586130	+	0.810217i	$0.699349\pi$
$858$	1.65550	0.0565178
$859$	−8.01569	−0.273492	−0.136746	−	0.990606i	$-0.543664\pi$
$859$	−8.01569	−0.273492	−0.136746	+	0.990606i	$0.543664\pi$
$860$	0	0
$861$	−4.65862	−0.158765
$862$	−10.0688	−0.342946
$863$	30.0282	1.02217	0.511085	−	0.859530i	$-0.329244\pi$
$863$	30.0282	1.02217	0.511085	+	0.859530i	$0.329244\pi$
$864$	−21.9991	−0.748426
$865$	0	0
$866$	27.3490	0.929356
$867$	6.04132	0.205174
$868$	2.29296	0.0778281
$869$	−19.0124	−0.644951
$870$	0	0
$871$	12.3471	0.418364
$872$	14.7678	0.500100
$873$	28.5459	0.966132
$874$	−3.55012	−0.120085
$875$	0	0
$876$	−12.3785	−0.418230
$877$	46.0763	1.55589	0.777943	−	0.628335i	$-0.216263\pi$
$877$	46.0763	1.55589	0.777943	+	0.628335i	$0.216263\pi$
$878$	−2.97418	−0.100374
$879$	−11.7032	−0.394738
$880$	0	0
$881$	−15.1336	−0.509864	−0.254932	−	0.966959i	$-0.582053\pi$
$881$	−15.1336	−0.509864	−0.254932	+	0.966959i	$0.582053\pi$
$882$	12.5590	0.422885
$883$	−41.8835	−1.40949	−0.704746	−	0.709459i	$-0.748939\pi$
$883$	−41.8835	−1.40949	−0.704746	+	0.709459i	$0.748939\pi$
$884$	−6.23283	−0.209633
$885$	0	0
$886$	−27.9663	−0.939547
$887$	−36.1083	−1.21240	−0.606198	−	0.795313i	$-0.707306\pi$
$887$	−36.1083	−1.21240	−0.606198	+	0.795313i	$0.707306\pi$
$888$	10.0232	0.336357
$889$	2.03861	0.0683729
$890$	0	0
$891$	17.4576	0.584851
$892$	−23.3107	−0.780501
$893$	−10.6808	−0.357420
$894$	6.88334	0.230213
$895$	0	0
$896$	7.78657	0.260131
$897$	2.52966	0.0844628
$898$	28.0388	0.935666
$899$	20.0271	0.667943
$900$	0	0
$901$	33.2372	1.10729
$902$	21.7383	0.723807
$903$	1.71768	0.0571607
$904$	−16.1749	−0.537968
$905$	0	0
$906$	−6.75047	−0.224269
$907$	−16.3071	−0.541469	−0.270734	−	0.962654i	$-0.587266\pi$
$907$	−16.3071	−0.541469	−0.270734	+	0.962654i	$0.587266\pi$
$908$	30.4027	1.00895
$909$	−0.412241	−0.0136732
$910$	0	0
$911$	−9.41052	−0.311784	−0.155892	−	0.987774i	$-0.549825\pi$
$911$	−9.41052	−0.311784	−0.155892	+	0.987774i	$0.549825\pi$
$912$	−0.467322	−0.0154746
$913$	−2.00018	−0.0661961
$914$	−14.8428	−0.490956
$915$	0	0
$916$	−18.3887	−0.607580
$917$	−4.04694	−0.133642
$918$	−15.1487	−0.499981
$919$	37.1431	1.22524	0.612619	−	0.790379i	$-0.290116\pi$
$919$	37.1431	1.22524	0.612619	+	0.790379i	$0.290116\pi$
$920$	0	0
$921$	−9.65254	−0.318062
$922$	30.4729	1.00357
$923$	−11.7880	−0.388008
$924$	2.78087	0.0914838
$925$	0	0
$926$	−13.3138	−0.437517
$927$	−12.6288	−0.414786
$928$	60.4071	1.98296
$929$	55.4770	1.82014	0.910071	−	0.414451i	$-0.136026\pi$
$929$	55.4770	1.82014	0.910071	+	0.414451i	$0.136026\pi$
$930$	0	0
$931$	6.73026	0.220575
$932$	−17.2147	−0.563885
$933$	2.57560	0.0843212
$934$	−25.0830	−0.820740
$935$	0	0
$936$	6.03501	0.197260
$937$	28.9939	0.947190	0.473595	−	0.880743i	$-0.342956\pi$
$937$	28.9939	0.947190	0.473595	+	0.880743i	$0.342956\pi$
$938$	−9.43436	−0.308043
$939$	18.0802	0.590024
$940$	0	0
$941$	−19.1867	−0.625468	−0.312734	−	0.949841i	$-0.601245\pi$
$941$	−19.1867	−0.625468	−0.312734	+	0.949841i	$0.601245\pi$
$942$	0.747353	0.0243501
$943$	33.2169	1.08169
$944$	−0.639120	−0.0208016
$945$	0	0
$946$	−8.01512	−0.260594
$947$	35.4003	1.15036	0.575178	−	0.818028i	$-0.304933\pi$
$947$	35.4003	1.15036	0.575178	+	0.818028i	$0.304933\pi$
$948$	5.14355	0.167055
$949$	11.8019	0.383105
$950$	0	0
$951$	1.47461	0.0478177
$952$	11.6913	0.378919
$953$	−31.1586	−1.00933	−0.504664	−	0.863316i	$-0.668384\pi$
$953$	−31.1586	−1.00933	−0.504664	+	0.863316i	$0.668384\pi$
$954$	−13.1095	−0.424436
$955$	0	0
$956$	9.70797	0.313978
$957$	24.2886	0.785139
$958$	15.7337	0.508332
$959$	−19.8202	−0.640027
$960$	0	0
$961$	−27.2479	−0.878965
$962$	−3.89278	−0.125508
$963$	−5.94600	−0.191607
$964$	−11.0640	−0.356346
$965$	0	0
$966$	−1.93291	−0.0621902
$967$	−28.8739	−0.928521	−0.464261	−	0.885699i	$-0.653680\pi$
$967$	−28.8739	−0.928521	−0.464261	+	0.885699i	$0.653680\pi$
$968$	−2.50056	−0.0803710
$969$	−3.72013	−0.119508
$970$	0	0
$971$	−32.4911	−1.04269	−0.521344	−	0.853347i	$-0.674569\pi$
$971$	−32.4911	−1.04269	−0.521344	+	0.853347i	$0.674569\pi$
$972$	−20.2512	−0.649558
$973$	−5.02474	−0.161086
$974$	−18.6919	−0.598928
$975$	0	0
$976$	−1.13192	−0.0362319
$977$	−4.14512	−0.132614	−0.0663071	−	0.997799i	$-0.521122\pi$
$977$	−4.14512	−0.132614	−0.0663071	+	0.997799i	$0.521122\pi$
$978$	4.51673	0.144429
$979$	−56.7085	−1.81241
$980$	0	0
$981$	14.0433	0.448368
$982$	−30.2111	−0.964076
$983$	43.7310	1.39480	0.697401	−	0.716682i	$-0.254340\pi$
$983$	43.7310	1.39480	0.697401	+	0.716682i	$0.254340\pi$
$984$	−14.4372	−0.460241
$985$	0	0
$986$	41.5965	1.32470
$987$	−5.81530	−0.185103
$988$	1.31742	0.0419126
$989$	−12.2474	−0.389444
$990$	0	0
$991$	56.0591	1.78078	0.890388	−	0.455202i	$-0.150433\pi$
$991$	56.0591	1.78078	0.890388	+	0.455202i	$0.150433\pi$
$992$	11.3173	0.359324
$993$	−14.0621	−0.446249
$994$	9.00722	0.285692
$995$	0	0
$996$	0.541121	0.0171461
$997$	34.2938	1.08610	0.543048	−	0.839702i	$-0.317270\pi$
$997$	34.2938	1.08610	0.543048	+	0.839702i	$0.317270\pi$
$998$	8.49846	0.269014
$999$	20.7994	0.658065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1475.2.a.p.1.4	yes	7
5.2	odd	4		1475.2.b.g.1299.9		14
5.3	odd	4		1475.2.b.g.1299.6		14
5.4	even	2		1475.2.a.n.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1475.2.a.n.1.4	✓	7	5.4	even	2
1475.2.a.p.1.4	yes	7	1.1	even	1	trivial
1475.2.b.g.1299.6		14	5.3	odd	4
1475.2.b.g.1299.9		14	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1475 = 5^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1475.a (trivial)

\(f(q)\)	\(=\)	\(q+0.790770 q^{2} +0.679943 q^{3} -1.37468 q^{4} +0.537678 q^{6} -0.861107 q^{7} -2.66860 q^{8} -2.53768 q^{9} +O(q^{10})\)	\(q+0.790770 q^{2} +0.679943 q^{3} -1.37468 q^{4} +0.537678 q^{6} -0.861107 q^{7} -2.66860 q^{8} -2.53768 q^{9} +3.45500 q^{11} -0.934706 q^{12} +0.891165 q^{13} -0.680937 q^{14} +0.639120 q^{16} +5.08773 q^{17} -2.00672 q^{18} -1.07538 q^{19} -0.585503 q^{21} +2.73211 q^{22} +4.17476 q^{23} -1.81449 q^{24} +0.704707 q^{26} -3.76530 q^{27} +1.18375 q^{28} +10.3391 q^{29} +1.93703 q^{31} +5.84259 q^{32} +2.34920 q^{33} +4.02323 q^{34} +3.48850 q^{36} -5.52397 q^{37} -0.850378 q^{38} +0.605941 q^{39} +7.95661 q^{41} -0.462998 q^{42} -2.93367 q^{43} -4.74953 q^{44} +3.30127 q^{46} +9.93214 q^{47} +0.434565 q^{48} -6.25849 q^{49} +3.45937 q^{51} -1.22507 q^{52} +6.53281 q^{53} -2.97749 q^{54} +2.29795 q^{56} -0.731197 q^{57} +8.17584 q^{58} -1.00000 q^{59} -1.77106 q^{61} +1.53175 q^{62} +2.18521 q^{63} +3.34191 q^{64} +1.85768 q^{66} +13.8550 q^{67} -6.99402 q^{68} +2.83860 q^{69} -13.2277 q^{71} +6.77204 q^{72} +13.2432 q^{73} -4.36819 q^{74} +1.47831 q^{76} -2.97513 q^{77} +0.479160 q^{78} -5.50286 q^{79} +5.05284 q^{81} +6.29184 q^{82} -0.578922 q^{83} +0.804882 q^{84} -2.31986 q^{86} +7.02999 q^{87} -9.22001 q^{88} -16.4135 q^{89} -0.767389 q^{91} -5.73897 q^{92} +1.31707 q^{93} +7.85403 q^{94} +3.97263 q^{96} -11.2488 q^{97} -4.94903 q^{98} -8.76768 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 13 q^{6} + q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 13 * q^6 + q^7 + 6 * q^8 - q^9	\( 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 13 q^{6} + q^{7} + 6 q^{8} - q^{9} - 9 q^{11} - 3 q^{12} + 17 q^{13} + 16 q^{16} + 6 q^{17} + 3 q^{18} + 3 q^{19} - 5 q^{21} + 12 q^{22} + 8 q^{23} - 31 q^{24} + 21 q^{26} + q^{27} + 27 q^{28} + 2 q^{29} - q^{31} + 34 q^{32} + 12 q^{33} - 21 q^{34} + 37 q^{36} + 26 q^{37} - 9 q^{38} - 3 q^{39} + 16 q^{41} - 8 q^{42} + 36 q^{43} - 23 q^{44} + 5 q^{46} + 8 q^{47} - 32 q^{48} - 14 q^{49} - 4 q^{51} + 60 q^{52} + 5 q^{53} - 42 q^{54} + 41 q^{56} + 31 q^{57} + 34 q^{58} - 7 q^{59} - 7 q^{61} - 5 q^{62} + 6 q^{63} - 8 q^{64} + 53 q^{66} + 32 q^{67} - 14 q^{68} + 34 q^{69} - 14 q^{71} + 26 q^{72} + 9 q^{73} - 7 q^{74} + 28 q^{76} - 2 q^{77} - 84 q^{78} + 6 q^{79} + 23 q^{81} - 7 q^{83} - 54 q^{84} + 44 q^{86} - 28 q^{87} - 3 q^{88} - 9 q^{89} - 17 q^{91} + 4 q^{92} - 37 q^{96} + 36 q^{97} - 3 q^{98} - 35 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 13 * q^6 + q^7 + 6 * q^8 - q^9 - 9 * q^11 - 3 * q^12 + 17 * q^13 + 16 * q^16 + 6 * q^17 + 3 * q^18 + 3 * q^19 - 5 * q^21 + 12 * q^22 + 8 * q^23 - 31 * q^24 + 21 * q^26 + q^27 + 27 * q^28 + 2 * q^29 - q^31 + 34 * q^32 + 12 * q^33 - 21 * q^34 + 37 * q^36 + 26 * q^37 - 9 * q^38 - 3 * q^39 + 16 * q^41 - 8 * q^42 + 36 * q^43 - 23 * q^44 + 5 * q^46 + 8 * q^47 - 32 * q^48 - 14 * q^49 - 4 * q^51 + 60 * q^52 + 5 * q^53 - 42 * q^54 + 41 * q^56 + 31 * q^57 + 34 * q^58 - 7 * q^59 - 7 * q^61 - 5 * q^62 + 6 * q^63 - 8 * q^64 + 53 * q^66 + 32 * q^67 - 14 * q^68 + 34 * q^69 - 14 * q^71 + 26 * q^72 + 9 * q^73 - 7 * q^74 + 28 * q^76 - 2 * q^77 - 84 * q^78 + 6 * q^79 + 23 * q^81 - 7 * q^83 - 54 * q^84 + 44 * q^86 - 28 * q^87 - 3 * q^88 - 9 * q^89 - 17 * q^91 + 4 * q^92 - 37 * q^96 + 36 * q^97 - 3 * q^98 - 35 * q^99

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