LMFDB - Embedded newform 6275.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6275,2,Mod(1,6275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6275, 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("6275.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6275 = 5^{2} \cdot 251 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6275.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:	$50.1061272684$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 28 x^{15} + 54 x^{14} + 317 x^{13} - 582 x^{12} - 1867 x^{11} + 3178 x^{10} + \cdots + 256 $ x^17 - 2x^16 - 28x^15 + 54x^14 + 317x^13 - 582x^12 - 1867x^11 + 3178x^10 + 6186x^9 - 9216x^8 - 11921x^7 + 13680x^6 + 13752x^5 - 9400x^4 - 8800x^3 + 1920x^2 + 2240x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 251)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.622810$ of defining polynomial
Character	$\chi$	$=$	6275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.622810 q^{2} +1.30185 q^{3} -1.61211 q^{4} +0.810802 q^{6} -3.93205 q^{7} -2.24966 q^{8} -1.30520 q^{9} +O(q^{10})$	\(q+0.622810 q^{2} +1.30185 q^{3} -1.61211 q^{4} +0.810802 q^{6} -3.93205 q^{7} -2.24966 q^{8} -1.30520 q^{9} -3.01556 q^{11} -2.09871 q^{12} -6.58110 q^{13} -2.44892 q^{14} +1.82311 q^{16} -2.00738 q^{17} -0.812891 q^{18} +5.92036 q^{19} -5.11892 q^{21} -1.87812 q^{22} -5.10129 q^{23} -2.92871 q^{24} -4.09877 q^{26} -5.60470 q^{27} +6.33889 q^{28} +3.88820 q^{29} -8.26372 q^{31} +5.63476 q^{32} -3.92580 q^{33} -1.25022 q^{34} +2.10412 q^{36} +3.68109 q^{37} +3.68726 q^{38} -8.56757 q^{39} +1.89627 q^{41} -3.18812 q^{42} -7.00055 q^{43} +4.86141 q^{44} -3.17714 q^{46} +9.72137 q^{47} +2.37340 q^{48} +8.46101 q^{49} -2.61330 q^{51} +10.6094 q^{52} -6.65232 q^{53} -3.49067 q^{54} +8.84576 q^{56} +7.70740 q^{57} +2.42161 q^{58} +9.91108 q^{59} +10.5438 q^{61} -5.14673 q^{62} +5.13211 q^{63} -0.136826 q^{64} -2.44502 q^{66} +2.42143 q^{67} +3.23611 q^{68} -6.64110 q^{69} -15.6398 q^{71} +2.93625 q^{72} -10.8434 q^{73} +2.29262 q^{74} -9.54426 q^{76} +11.8573 q^{77} -5.33597 q^{78} +6.40419 q^{79} -3.38086 q^{81} +1.18101 q^{82} +6.22959 q^{83} +8.25225 q^{84} -4.36002 q^{86} +5.06183 q^{87} +6.78398 q^{88} +3.23865 q^{89} +25.8772 q^{91} +8.22383 q^{92} -10.7581 q^{93} +6.05457 q^{94} +7.33559 q^{96} -5.85568 q^{97} +5.26960 q^{98} +3.93591 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9	$ 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9} - q^{11} + 9 q^{12} - 22 q^{13} - 7 q^{14} + 40 q^{16} + q^{17} + 7 q^{18} + 13 q^{19} + 25 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} - 9 q^{26} + 15 q^{27} + 10 q^{28} + 28 q^{29} + 12 q^{31} - 4 q^{32} + 16 q^{33} - 21 q^{34} + 21 q^{36} - 27 q^{37} + 37 q^{38} + 13 q^{39} - q^{41} + 56 q^{42} - 9 q^{43} - 43 q^{44} + 4 q^{46} + 20 q^{47} + 79 q^{48} + 32 q^{49} - 2 q^{51} + q^{52} - q^{53} - 65 q^{54} - 61 q^{56} + 24 q^{57} + 46 q^{58} - 20 q^{59} + 59 q^{61} + 73 q^{62} + 41 q^{63} + 54 q^{64} - 43 q^{66} - 15 q^{67} + 20 q^{68} + 38 q^{69} - 26 q^{71} + 2 q^{72} - 8 q^{73} + 2 q^{74} + 38 q^{76} + 33 q^{79} + 29 q^{81} - 10 q^{82} + 63 q^{84} + 11 q^{86} + 11 q^{87} - 27 q^{88} + 11 q^{89} - 2 q^{91} - 28 q^{92} - 28 q^{93} + 29 q^{94} - 17 q^{96} + 10 q^{97} - 22 q^{98} - 36 q^{99}+O(q^{100}) $ 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9 - q^11 + 9 * q^12 - 22 * q^13 - 7 * q^14 + 40 * q^16 + q^17 + 7 * q^18 + 13 * q^19 + 25 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 - 9 * q^26 + 15 * q^27 + 10 * q^28 + 28 * q^29 + 12 * q^31 - 4 * q^32 + 16 * q^33 - 21 * q^34 + 21 * q^36 - 27 * q^37 + 37 * q^38 + 13 * q^39 - q^41 + 56 * q^42 - 9 * q^43 - 43 * q^44 + 4 * q^46 + 20 * q^47 + 79 * q^48 + 32 * q^49 - 2 * q^51 + q^52 - q^53 - 65 * q^54 - 61 * q^56 + 24 * q^57 + 46 * q^58 - 20 * q^59 + 59 * q^61 + 73 * q^62 + 41 * q^63 + 54 * q^64 - 43 * q^66 - 15 * q^67 + 20 * q^68 + 38 * q^69 - 26 * q^71 + 2 * q^72 - 8 * q^73 + 2 * q^74 + 38 * q^76 + 33 * q^79 + 29 * q^81 - 10 * q^82 + 63 * q^84 + 11 * q^86 + 11 * q^87 - 27 * q^88 + 11 * q^89 - 2 * q^91 - 28 * q^92 - 28 * q^93 + 29 * q^94 - 17 * q^96 + 10 * q^97 - 22 * q^98 - 36 * 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 $

$2$	0.622810	0.440393	0.220197	−	0.975456i	$-0.429330\pi$
$2$	0.622810	0.440393	0.220197	+	0.975456i	$0.429330\pi$
$3$	1.30185	0.751621	0.375810	−	0.926697i	$-0.377364\pi$
$3$	1.30185	0.751621	0.375810	+	0.926697i	$0.377364\pi$
$4$	−1.61211	−0.806054
$5$	0	0
$5$	0	0
$6$	0.810802	0.331009
$7$	−3.93205	−1.48618	−0.743088	−	0.669194i	$-0.766639\pi$
$7$	−3.93205	−1.48618	−0.743088	+	0.669194i	$0.766639\pi$
$8$	−2.24966	−0.795374
$9$	−1.30520	−0.435066
$10$	0	0
$11$	−3.01556	−0.909226	−0.454613	−	0.890689i	$-0.650222\pi$
$11$	−3.01556	−0.909226	−0.454613	+	0.890689i	$0.650222\pi$
$12$	−2.09871	−0.605847
$13$	−6.58110	−1.82527	−0.912634	−	0.408778i	$-0.865955\pi$
$13$	−6.58110	−1.82527	−0.912634	+	0.408778i	$0.865955\pi$
$14$	−2.44892	−0.654501
$15$	0	0
$16$	1.82311	0.455777
$17$	−2.00738	−0.486861	−0.243431	−	0.969918i	$-0.578273\pi$
$17$	−2.00738	−0.486861	−0.243431	+	0.969918i	$0.578273\pi$
$18$	−0.812891	−0.191600
$19$	5.92036	1.35822	0.679112	−	0.734034i	$-0.262365\pi$
$19$	5.92036	1.35822	0.679112	+	0.734034i	$0.262365\pi$
$20$	0	0
$21$	−5.11892	−1.11704
$22$	−1.87812	−0.400417
$23$	−5.10129	−1.06369	−0.531847	−	0.846841i	$-0.678502\pi$
$23$	−5.10129	−1.06369	−0.531847	+	0.846841i	$0.678502\pi$
$24$	−2.92871	−0.597819
$25$	0	0
$26$	−4.09877	−0.803836
$27$	−5.60470	−1.07863
$28$	6.33889	1.19794
$29$	3.88820	0.722020	0.361010	−	0.932562i	$-0.382432\pi$
$29$	3.88820	0.722020	0.361010	+	0.932562i	$0.382432\pi$
$30$	0	0
$31$	−8.26372	−1.48421	−0.742104	−	0.670285i	$-0.766172\pi$
$31$	−8.26372	−1.48421	−0.742104	+	0.670285i	$0.766172\pi$
$32$	5.63476	0.996095
$33$	−3.92580	−0.683393
$34$	−1.25022	−0.214410
$35$	0	0
$36$	2.10412	0.350687
$37$	3.68109	0.605168	0.302584	−	0.953123i	$-0.402151\pi$
$37$	3.68109	0.605168	0.302584	+	0.953123i	$0.402151\pi$
$38$	3.68726	0.598153
$39$	−8.56757	−1.37191
$40$	0	0
$41$	1.89627	0.296147	0.148073	−	0.988976i	$-0.452693\pi$
$41$	1.89627	0.296147	0.148073	+	0.988976i	$0.452693\pi$
$42$	−3.18812	−0.491937
$43$	−7.00055	−1.06757	−0.533787	−	0.845619i	$-0.679232\pi$
$43$	−7.00055	−1.06757	−0.533787	+	0.845619i	$0.679232\pi$
$44$	4.86141	0.732885
$45$	0	0
$46$	−3.17714	−0.468443
$47$	9.72137	1.41801	0.709004	−	0.705205i	$-0.249145\pi$
$47$	9.72137	1.41801	0.709004	+	0.705205i	$0.249145\pi$
$48$	2.37340	0.342571
$49$	8.46101	1.20872
$50$	0	0
$51$	−2.61330	−0.365935
$52$	10.6094	1.47126
$53$	−6.65232	−0.913766	−0.456883	−	0.889527i	$-0.651034\pi$
$53$	−6.65232	−0.913766	−0.456883	+	0.889527i	$0.651034\pi$
$54$	−3.49067	−0.475019
$55$	0	0
$56$	8.84576	1.18206
$57$	7.70740	1.02087
$58$	2.42161	0.317973
$59$	9.91108	1.29031	0.645156	−	0.764050i	$-0.276792\pi$
$59$	9.91108	1.29031	0.645156	+	0.764050i	$0.276792\pi$
$60$	0	0
$61$	10.5438	1.34999	0.674995	−	0.737822i	$-0.264146\pi$
$61$	10.5438	1.34999	0.674995	+	0.737822i	$0.264146\pi$
$62$	−5.14673	−0.653635
$63$	5.13211	0.646585
$64$	−0.136826	−0.0171032
$65$	0	0
$66$	−2.44502	−0.300962
$67$	2.42143	0.295825	0.147912	−	0.989000i	$-0.452745\pi$
$67$	2.42143	0.295825	0.147912	+	0.989000i	$0.452745\pi$
$68$	3.23611	0.392436
$69$	−6.64110	−0.799494
$70$	0	0
$71$	−15.6398	−1.85610	−0.928050	−	0.372456i	$-0.878516\pi$
$71$	−15.6398	−1.85610	−0.928050	+	0.372456i	$0.878516\pi$
$72$	2.93625	0.346040
$73$	−10.8434	−1.26912	−0.634562	−	0.772872i	$-0.718819\pi$
$73$	−10.8434	−1.26912	−0.634562	+	0.772872i	$0.718819\pi$
$74$	2.29262	0.266512
$75$	0	0
$76$	−9.54426	−1.09480
$77$	11.8573	1.35127
$78$	−5.33597	−0.604179
$79$	6.40419	0.720528	0.360264	−	0.932850i	$-0.382687\pi$
$79$	6.40419	0.720528	0.360264	+	0.932850i	$0.382687\pi$
$80$	0	0
$81$	−3.38086	−0.375651
$82$	1.18101	0.130421
$83$	6.22959	0.683786	0.341893	−	0.939739i	$-0.388932\pi$
$83$	6.22959	0.683786	0.341893	+	0.939739i	$0.388932\pi$
$84$	8.25225	0.900394
$85$	0	0
$86$	−4.36002	−0.470153
$87$	5.06183	0.542686
$88$	6.78398	0.723175
$89$	3.23865	0.343296	0.171648	−	0.985158i	$-0.445091\pi$
$89$	3.23865	0.343296	0.171648	+	0.985158i	$0.445091\pi$
$90$	0	0
$91$	25.8772	2.71267
$92$	8.22383	0.857394
$93$	−10.7581	−1.11556
$94$	6.05457	0.624481
$95$	0	0
$96$	7.33559	0.748685
$97$	−5.85568	−0.594554	−0.297277	−	0.954791i	$-0.596078\pi$
$97$	−5.85568	−0.594554	−0.297277	+	0.954791i	$0.596078\pi$
$98$	5.26960	0.532310
$99$	3.93591	0.395574
$100$	0	0
$101$	6.73240	0.669899	0.334949	−	0.942236i	$-0.391281\pi$
$101$	6.73240	0.669899	0.334949	+	0.942236i	$0.391281\pi$
$102$	−1.62759	−0.161155
$103$	1.87998	0.185240	0.0926199	−	0.995702i	$-0.470476\pi$
$103$	1.87998	0.185240	0.0926199	+	0.995702i	$0.470476\pi$
$104$	14.8052	1.45177
$105$	0	0
$106$	−4.14313	−0.402417
$107$	−16.6182	−1.60654	−0.803271	−	0.595613i	$-0.796909\pi$
$107$	−16.6182	−1.60654	−0.803271	+	0.595613i	$0.796909\pi$
$108$	9.03538	0.869430
$109$	0.834566	0.0799369	0.0399685	−	0.999201i	$-0.487274\pi$
$109$	0.834566	0.0799369	0.0399685	+	0.999201i	$0.487274\pi$
$110$	0	0
$111$	4.79222	0.454857
$112$	−7.16854	−0.677364
$113$	5.91577	0.556509	0.278254	−	0.960507i	$-0.410244\pi$
$113$	5.91577	0.556509	0.278254	+	0.960507i	$0.410244\pi$
$114$	4.80025	0.449584
$115$	0	0
$116$	−6.26820	−0.581987
$117$	8.58964	0.794112
$118$	6.17272	0.568245
$119$	7.89312	0.723561
$120$	0	0
$121$	−1.90639	−0.173308
$122$	6.56676	0.594526
$123$	2.46864	0.222590
$124$	13.3220	1.19635
$125$	0	0
$126$	3.19633	0.284751
$127$	10.5329	0.934643	0.467322	−	0.884087i	$-0.345219\pi$
$127$	10.5329	0.934643	0.467322	+	0.884087i	$0.345219\pi$
$128$	−11.3547	−1.00363
$129$	−9.11364	−0.802411
$130$	0	0
$131$	−17.3283	−1.51398	−0.756992	−	0.653424i	$-0.773332\pi$
$131$	−17.3283	−1.51398	−0.756992	+	0.653424i	$0.773332\pi$
$132$	6.32880	0.550852
$133$	−23.2792	−2.01856
$134$	1.50809	0.130279
$135$	0	0
$136$	4.51592	0.387237
$137$	−13.8693	−1.18493	−0.592466	−	0.805596i	$-0.701845\pi$
$137$	−13.8693	−1.18493	−0.592466	+	0.805596i	$0.701845\pi$
$138$	−4.13614	−0.352092
$139$	−19.6739	−1.66872	−0.834361	−	0.551218i	$-0.814163\pi$
$139$	−19.6739	−1.66872	−0.834361	+	0.551218i	$0.814163\pi$
$140$	0	0
$141$	12.6557	1.06580
$142$	−9.74061	−0.817414
$143$	19.8457	1.65958
$144$	−2.37952	−0.198293
$145$	0	0
$146$	−6.75338	−0.558913
$147$	11.0149	0.908496
$148$	−5.93432	−0.487798
$149$	−0.0299644	−0.00245478	−0.00122739	−	0.999999i	$-0.500391\pi$
$149$	−0.0299644	−0.00245478	−0.00122739	+	0.999999i	$0.500391\pi$
$150$	0	0
$151$	−0.462488	−0.0376367	−0.0188184	−	0.999823i	$-0.505990\pi$
$151$	−0.462488	−0.0376367	−0.0188184	+	0.999823i	$0.505990\pi$
$152$	−13.3188	−1.08030
$153$	2.62003	0.211817
$154$	7.38487	0.595090
$155$	0	0
$156$	13.8118	1.10583
$157$	5.93306	0.473510	0.236755	−	0.971569i	$-0.423916\pi$
$157$	5.93306	0.473510	0.236755	+	0.971569i	$0.423916\pi$
$158$	3.98860	0.317316
$159$	−8.66029	−0.686806
$160$	0	0
$161$	20.0585	1.58083
$162$	−2.10563	−0.165434
$163$	5.34504	0.418656	0.209328	−	0.977845i	$-0.432872\pi$
$163$	5.34504	0.418656	0.209328	+	0.977845i	$0.432872\pi$
$164$	−3.05698	−0.238710
$165$	0	0
$166$	3.87985	0.301135
$167$	16.6417	1.28777	0.643887	−	0.765121i	$-0.277321\pi$
$167$	16.6417	1.28777	0.643887	+	0.765121i	$0.277321\pi$
$168$	11.5158	0.888464
$169$	30.3108	2.33160
$170$	0	0
$171$	−7.72725	−0.590918
$172$	11.2856	0.860522
$173$	18.7115	1.42261	0.711304	−	0.702884i	$-0.248105\pi$
$173$	18.7115	1.42261	0.711304	+	0.702884i	$0.248105\pi$
$174$	3.15256	0.238995
$175$	0	0
$176$	−5.49769	−0.414404
$177$	12.9027	0.969826
$178$	2.01707	0.151185
$179$	5.50738	0.411641	0.205821	−	0.978590i	$-0.434014\pi$
$179$	5.50738	0.411641	0.205821	+	0.978590i	$0.434014\pi$
$180$	0	0
$181$	22.3213	1.65913	0.829563	−	0.558413i	$-0.188589\pi$
$181$	22.3213	1.65913	0.829563	+	0.558413i	$0.188589\pi$
$182$	16.1166	1.19464
$183$	13.7263	1.01468
$184$	11.4762	0.846034
$185$	0	0
$186$	−6.70025	−0.491286
$187$	6.05338	0.442667
$188$	−15.6719	−1.14299
$189$	22.0380	1.60303
$190$	0	0
$191$	9.45994	0.684497	0.342249	−	0.939609i	$-0.388811\pi$
$191$	9.45994	0.684497	0.342249	+	0.939609i	$0.388811\pi$
$192$	−0.178126	−0.0128551
$193$	13.3834	0.963356	0.481678	−	0.876348i	$-0.340028\pi$
$193$	13.3834	0.963356	0.481678	+	0.876348i	$0.340028\pi$
$194$	−3.64697	−0.261837
$195$	0	0
$196$	−13.6401	−0.974290
$197$	−5.83822	−0.415956	−0.207978	−	0.978134i	$-0.566688\pi$
$197$	−5.83822	−0.415956	−0.207978	+	0.978134i	$0.566688\pi$
$198$	2.45132	0.174208
$199$	−11.2099	−0.794652	−0.397326	−	0.917678i	$-0.630062\pi$
$199$	−11.2099	−0.794652	−0.397326	+	0.917678i	$0.630062\pi$
$200$	0	0
$201$	3.15233	0.222348
$202$	4.19301	0.295019
$203$	−15.2886	−1.07305
$204$	4.21292	0.294963
$205$	0	0
$206$	1.17087	0.0815784
$207$	6.65820	0.462777
$208$	−11.9980	−0.831914
$209$	−17.8532	−1.23493
$210$	0	0
$211$	−9.99147	−0.687841	−0.343921	−	0.938999i	$-0.611755\pi$
$211$	−9.99147	−0.687841	−0.343921	+	0.938999i	$0.611755\pi$
$212$	10.7243	0.736545
$213$	−20.3606	−1.39508
$214$	−10.3500	−0.707511
$215$	0	0
$216$	12.6087	0.857911
$217$	32.4934	2.20579
$218$	0.519776	0.0352037
$219$	−14.1164	−0.953899
$220$	0	0
$221$	13.2108	0.888652
$222$	2.98464	0.200316
$223$	−2.52198	−0.168884	−0.0844421	−	0.996428i	$-0.526911\pi$
$223$	−2.52198	−0.168884	−0.0844421	+	0.996428i	$0.526911\pi$
$224$	−22.1562	−1.48037
$225$	0	0
$226$	3.68440	0.245083
$227$	20.9064	1.38761	0.693805	−	0.720163i	$-0.255933\pi$
$227$	20.9064	1.38761	0.693805	+	0.720163i	$0.255933\pi$
$228$	−12.4252	−0.822876
$229$	−11.3615	−0.750786	−0.375393	−	0.926866i	$-0.622492\pi$
$229$	−11.3615	−0.750786	−0.375393	+	0.926866i	$0.622492\pi$
$230$	0	0
$231$	15.4364	1.01564
$232$	−8.74711	−0.574276
$233$	−6.49404	−0.425439	−0.212719	−	0.977113i	$-0.568232\pi$
$233$	−6.49404	−0.425439	−0.212719	+	0.977113i	$0.568232\pi$
$234$	5.34971	0.349722
$235$	0	0
$236$	−15.9777	−1.04006
$237$	8.33727	0.541564
$238$	4.91591	0.318651
$239$	−9.49990	−0.614497	−0.307249	−	0.951629i	$-0.599408\pi$
$239$	−9.49990	−0.614497	−0.307249	+	0.951629i	$0.599408\pi$
$240$	0	0
$241$	−5.85361	−0.377064	−0.188532	−	0.982067i	$-0.560373\pi$
$241$	−5.85361	−0.377064	−0.188532	+	0.982067i	$0.560373\pi$
$242$	−1.18732	−0.0763236
$243$	12.4128	0.796278
$244$	−16.9977	−1.08816
$245$	0	0
$246$	1.53750	0.0980272
$247$	−38.9625	−2.47912
$248$	18.5905	1.18050
$249$	8.10996	0.513948
$250$	0	0
$251$	1.00000	0.0631194
$251$	1.00000	0.0631194
$252$	−8.27351	−0.521182
$253$	15.3833	0.967138
$254$	6.55999	0.411610
$255$	0	0
$256$	−6.79820	−0.424887
$257$	19.9382	1.24371	0.621856	−	0.783131i	$-0.286379\pi$
$257$	19.9382	1.24371	0.621856	+	0.783131i	$0.286379\pi$
$258$	−5.67607	−0.353376
$259$	−14.4742	−0.899386
$260$	0	0
$261$	−5.07487	−0.314127
$262$	−10.7923	−0.666748
$263$	−30.5342	−1.88282	−0.941409	−	0.337267i	$-0.890498\pi$
$263$	−30.5342	−1.88282	−0.941409	+	0.337267i	$0.890498\pi$
$264$	8.83169	0.543553
$265$	0	0
$266$	−14.4985	−0.888960
$267$	4.21622	0.258029
$268$	−3.90361	−0.238451
$269$	−5.26126	−0.320785	−0.160392	−	0.987053i	$-0.551276\pi$
$269$	−5.26126	−0.320785	−0.160392	+	0.987053i	$0.551276\pi$
$270$	0	0
$271$	18.5566	1.12724	0.563618	−	0.826036i	$-0.309409\pi$
$271$	18.5566	1.12724	0.563618	+	0.826036i	$0.309409\pi$
$272$	−3.65967	−0.221900
$273$	33.6881	2.03890
$274$	−8.63792	−0.521836
$275$	0	0
$276$	10.7062	0.644435
$277$	−10.6839	−0.641931	−0.320966	−	0.947091i	$-0.604007\pi$
$277$	−10.6839	−0.641931	−0.320966	+	0.947091i	$0.604007\pi$
$278$	−12.2531	−0.734894
$279$	10.7858	0.645729
$280$	0	0
$281$	−22.1411	−1.32083	−0.660415	−	0.750901i	$-0.729620\pi$
$281$	−22.1411	−1.32083	−0.660415	+	0.750901i	$0.729620\pi$
$282$	7.88211	0.469373
$283$	2.25692	0.134160	0.0670799	−	0.997748i	$-0.478632\pi$
$283$	2.25692	0.134160	0.0670799	+	0.997748i	$0.478632\pi$
$284$	25.2130	1.49612
$285$	0	0
$286$	12.3601	0.730868
$287$	−7.45621	−0.440126
$288$	−7.35449	−0.433367
$289$	−12.9704	−0.762966
$290$	0	0
$291$	−7.62319	−0.446879
$292$	17.4807	1.02298
$293$	−18.1554	−1.06065	−0.530326	−	0.847794i	$-0.677931\pi$
$293$	−18.1554	−1.06065	−0.530326	+	0.847794i	$0.677931\pi$
$294$	6.86021	0.400096
$295$	0	0
$296$	−8.28120	−0.481335
$297$	16.9013	0.980715
$298$	−0.0186621	−0.00108107
$299$	33.5721	1.94153
$300$	0	0
$301$	27.5265	1.58660
$302$	−0.288042	−0.0165749
$303$	8.76454	0.503510
$304$	10.7935	0.619047
$305$	0	0
$306$	1.63178	0.0932827
$307$	−3.85685	−0.220122	−0.110061	−	0.993925i	$-0.535105\pi$
$307$	−3.85685	−0.220122	−0.110061	+	0.993925i	$0.535105\pi$
$308$	−19.1153	−1.08920
$309$	2.44744	0.139230
$310$	0	0
$311$	−14.5608	−0.825667	−0.412833	−	0.910807i	$-0.635461\pi$
$311$	−14.5608	−0.825667	−0.412833	+	0.910807i	$0.635461\pi$
$312$	19.2741	1.09118
$313$	−1.26227	−0.0713480	−0.0356740	−	0.999363i	$-0.511358\pi$
$313$	−1.26227	−0.0713480	−0.0356740	+	0.999363i	$0.511358\pi$
$314$	3.69517	0.208530
$315$	0	0
$316$	−10.3242	−0.580784
$317$	−4.21550	−0.236766	−0.118383	−	0.992968i	$-0.537771\pi$
$317$	−4.21550	−0.236766	−0.118383	+	0.992968i	$0.537771\pi$
$318$	−5.39372	−0.302465
$319$	−11.7251	−0.656480
$320$	0	0
$321$	−21.6343	−1.20751
$322$	12.4927	0.696189
$323$	−11.8844	−0.661267
$324$	5.45031	0.302795
$325$	0	0
$326$	3.32895	0.184373
$327$	1.08648	0.0600823
$328$	−4.26595	−0.235548
$329$	−38.2249	−2.10741
$330$	0	0
$331$	−20.2826	−1.11483	−0.557415	−	0.830234i	$-0.688207\pi$
$331$	−20.2826	−1.11483	−0.557415	+	0.830234i	$0.688207\pi$
$332$	−10.0428	−0.551168
$333$	−4.80456	−0.263288
$334$	10.3646	0.567127
$335$	0	0
$336$	−9.33234	−0.509121
$337$	−34.1915	−1.86253	−0.931266	−	0.364340i	$-0.881294\pi$
$337$	−34.1915	−1.86253	−0.931266	+	0.364340i	$0.881294\pi$
$338$	18.8779	1.02682
$339$	7.70141	0.418283
$340$	0	0
$341$	24.9198	1.34948
$342$	−4.81261	−0.260236
$343$	−5.74478	−0.310189
$344$	15.7488	0.849121
$345$	0	0
$346$	11.6537	0.626507
$347$	−13.9320	−0.747910	−0.373955	−	0.927447i	$-0.621999\pi$
$347$	−13.9320	−0.747910	−0.373955	+	0.927447i	$0.621999\pi$
$348$	−8.16022	−0.437434
$349$	−8.42095	−0.450763	−0.225382	−	0.974271i	$-0.572363\pi$
$349$	−8.42095	−0.450763	−0.225382	+	0.974271i	$0.572363\pi$
$350$	0	0
$351$	36.8851	1.96878
$352$	−16.9920	−0.905675
$353$	5.19599	0.276555	0.138277	−	0.990394i	$-0.455843\pi$
$353$	5.19599	0.276555	0.138277	+	0.990394i	$0.455843\pi$
$354$	8.03593	0.427105
$355$	0	0
$356$	−5.22106	−0.276715
$357$	10.2756	0.543844
$358$	3.43005	0.181284
$359$	36.3620	1.91911	0.959556	−	0.281517i	$-0.0908375\pi$
$359$	36.3620	1.91911	0.959556	+	0.281517i	$0.0908375\pi$
$360$	0	0
$361$	16.0507	0.844774
$362$	13.9019	0.730668
$363$	−2.48182	−0.130262
$364$	−41.7168	−2.18656
$365$	0	0
$366$	8.54890	0.446858
$367$	4.87935	0.254700	0.127350	−	0.991858i	$-0.459353\pi$
$367$	4.87935	0.254700	0.127350	+	0.991858i	$0.459353\pi$
$368$	−9.30020	−0.484806
$369$	−2.47500	−0.128844
$370$	0	0
$371$	26.1572	1.35802
$372$	17.3432	0.899203
$373$	16.3744	0.847833	0.423917	−	0.905701i	$-0.360655\pi$
$373$	16.3744	0.847833	0.423917	+	0.905701i	$0.360655\pi$
$374$	3.77011	0.194948
$375$	0	0
$376$	−21.8697	−1.12785
$377$	−25.5886	−1.31788
$378$	13.7255	0.705962
$379$	−12.4364	−0.638815	−0.319408	−	0.947617i	$-0.603484\pi$
$379$	−12.4364	−0.638815	−0.319408	+	0.947617i	$0.603484\pi$
$380$	0	0
$381$	13.7122	0.702497
$382$	5.89175	0.301448
$383$	16.0441	0.819817	0.409908	−	0.912127i	$-0.365561\pi$
$383$	16.0441	0.819817	0.409908	+	0.912127i	$0.365561\pi$
$384$	−14.7821	−0.754347
$385$	0	0
$386$	8.33529	0.424255
$387$	9.13711	0.464466
$388$	9.43998	0.479242
$389$	8.27219	0.419417	0.209708	−	0.977764i	$-0.432749\pi$
$389$	8.27219	0.419417	0.209708	+	0.977764i	$0.432749\pi$
$390$	0	0
$391$	10.2402	0.517871
$392$	−19.0344	−0.961381
$393$	−22.5588	−1.13794
$394$	−3.63610	−0.183184
$395$	0	0
$396$	−6.34511	−0.318854
$397$	26.5169	1.33084	0.665422	−	0.746468i	$-0.268252\pi$
$397$	26.5169	1.33084	0.665422	+	0.746468i	$0.268252\pi$
$398$	−6.98167	−0.349959
$399$	−30.3059	−1.51719
$400$	0	0
$401$	23.4292	1.17000	0.585000	−	0.811033i	$-0.301094\pi$
$401$	23.4292	1.17000	0.585000	+	0.811033i	$0.301094\pi$
$402$	1.96330	0.0979206
$403$	54.3844	2.70908
$404$	−10.8534	−0.539975
$405$	0	0
$406$	−9.52189	−0.472563
$407$	−11.1006	−0.550235
$408$	5.87903	0.291055
$409$	−8.61597	−0.426032	−0.213016	−	0.977049i	$-0.568329\pi$
$409$	−8.61597	−0.426032	−0.213016	+	0.977049i	$0.568329\pi$
$410$	0	0
$411$	−18.0556	−0.890619
$412$	−3.03073	−0.149313
$413$	−38.9709	−1.91763
$414$	4.14680	0.203804
$415$	0	0
$416$	−37.0829	−1.81814
$417$	−25.6124	−1.25425
$418$	−11.1192	−0.543856
$419$	−12.2314	−0.597545	−0.298772	−	0.954324i	$-0.596577\pi$
$419$	−12.2314	−0.597545	−0.298772	+	0.954324i	$0.596577\pi$
$420$	0	0
$421$	−17.9483	−0.874745	−0.437372	−	0.899281i	$-0.644091\pi$
$421$	−17.9483	−0.874745	−0.437372	+	0.899281i	$0.644091\pi$
$422$	−6.22279	−0.302921
$423$	−12.6883	−0.616927
$424$	14.9654	0.726786
$425$	0	0
$426$	−12.6808	−0.614385
$427$	−41.4586	−2.00632
$428$	26.7903	1.29496
$429$	25.8360	1.24738
$430$	0	0
$431$	−2.70538	−0.130314	−0.0651569	−	0.997875i	$-0.520755\pi$
$431$	−2.70538	−0.130314	−0.0651569	+	0.997875i	$0.520755\pi$
$432$	−10.2180	−0.491612
$433$	−30.0233	−1.44283	−0.721415	−	0.692503i	$-0.756508\pi$
$433$	−30.0233	−1.44283	−0.721415	+	0.692503i	$0.756508\pi$
$434$	20.2372	0.971416
$435$	0	0
$436$	−1.34541	−0.0644335
$437$	−30.2015	−1.44473
$438$	−8.79185	−0.420091
$439$	−0.941071	−0.0449149	−0.0224574	−	0.999748i	$-0.507149\pi$
$439$	−0.941071	−0.0449149	−0.0224574	+	0.999748i	$0.507149\pi$
$440$	0	0
$441$	−11.0433	−0.525872
$442$	8.22780	0.391356
$443$	−5.00333	−0.237715	−0.118858	−	0.992911i	$-0.537923\pi$
$443$	−5.00333	−0.237715	−0.118858	+	0.992911i	$0.537923\pi$
$444$	−7.72557	−0.366639
$445$	0	0
$446$	−1.57071	−0.0743755
$447$	−0.0390090	−0.00184506
$448$	0.538005	0.0254183
$449$	−5.34829	−0.252401	−0.126201	−	0.992005i	$-0.540278\pi$
$449$	−5.34829	−0.252401	−0.126201	+	0.992005i	$0.540278\pi$
$450$	0	0
$451$	−5.71831	−0.269265
$452$	−9.53685	−0.448576
$453$	−0.602087	−0.0282885
$454$	13.0207	0.611094
$455$	0	0
$456$	−17.3390	−0.811973
$457$	31.1015	1.45487	0.727434	−	0.686178i	$-0.240713\pi$
$457$	31.1015	1.45487	0.727434	+	0.686178i	$0.240713\pi$
$458$	−7.07603	−0.330641
$459$	11.2508	0.525141
$460$	0	0
$461$	7.48123	0.348436	0.174218	−	0.984707i	$-0.444260\pi$
$461$	7.48123	0.348436	0.174218	+	0.984707i	$0.444260\pi$
$462$	9.61396	0.447282
$463$	−5.06565	−0.235421	−0.117710	−	0.993048i	$-0.537555\pi$
$463$	−5.06565	−0.235421	−0.117710	+	0.993048i	$0.537555\pi$
$464$	7.08860	0.329080
$465$	0	0
$466$	−4.04455	−0.187360
$467$	10.7910	0.499347	0.249673	−	0.968330i	$-0.419677\pi$
$467$	10.7910	0.499347	0.249673	+	0.968330i	$0.419677\pi$
$468$	−13.8474	−0.640097
$469$	−9.52119	−0.439648
$470$	0	0
$471$	7.72392	0.355900
$472$	−22.2965	−1.02628
$473$	21.1106	0.970667
$474$	5.19253	0.238501
$475$	0	0
$476$	−12.7246	−0.583229
$477$	8.68260	0.397549
$478$	−5.91663	−0.270620
$479$	37.2246	1.70084	0.850418	−	0.526107i	$-0.176349\pi$
$479$	37.2246	1.70084	0.850418	+	0.526107i	$0.176349\pi$
$480$	0	0
$481$	−24.2256	−1.10459
$482$	−3.64569	−0.166056
$483$	26.1131	1.18819
$484$	3.07330	0.139695
$485$	0	0
$486$	7.73079	0.350676
$487$	1.19893	0.0543288	0.0271644	−	0.999631i	$-0.491352\pi$
$487$	1.19893	0.0543288	0.0271644	+	0.999631i	$0.491352\pi$
$488$	−23.7198	−1.07375
$489$	6.95842	0.314670
$490$	0	0
$491$	10.7598	0.485584	0.242792	−	0.970078i	$-0.421937\pi$
$491$	10.7598	0.485584	0.242792	+	0.970078i	$0.421937\pi$
$492$	−3.97972	−0.179420
$493$	−7.80510	−0.351524
$494$	−24.2662	−1.09179
$495$	0	0
$496$	−15.0656	−0.676467
$497$	61.4964	2.75849
$498$	5.05096	0.226339
$499$	32.5779	1.45839	0.729194	−	0.684307i	$-0.239895\pi$
$499$	32.5779	1.45839	0.729194	+	0.684307i	$0.239895\pi$
$500$	0	0
$501$	21.6649	0.967918
$502$	0.622810	0.0277974
$503$	−0.566614	−0.0252641	−0.0126320	−	0.999920i	$-0.504021\pi$
$503$	−0.566614	−0.0252641	−0.0126320	+	0.999920i	$0.504021\pi$
$504$	−11.5455	−0.514276
$505$	0	0
$506$	9.58085	0.425921
$507$	39.4600	1.75248
$508$	−16.9802	−0.753373
$509$	−6.97468	−0.309147	−0.154574	−	0.987981i	$-0.549400\pi$
$509$	−6.97468	−0.309147	−0.154574	+	0.987981i	$0.549400\pi$
$510$	0	0
$511$	42.6368	1.88614
$512$	18.4755	0.816509
$513$	−33.1819	−1.46502
$514$	12.4177	0.547723
$515$	0	0
$516$	14.6922	0.646786
$517$	−29.3154	−1.28929
$518$	−9.01471	−0.396083
$519$	24.3595	1.06926
$520$	0	0
$521$	−15.1642	−0.664355	−0.332177	−	0.943217i	$-0.607783\pi$
$521$	−15.1642	−0.664355	−0.332177	+	0.943217i	$0.607783\pi$
$522$	−3.16068	−0.138339
$523$	18.2532	0.798158	0.399079	−	0.916917i	$-0.369330\pi$
$523$	18.2532	0.798158	0.399079	+	0.916917i	$0.369330\pi$
$524$	27.9351	1.22035
$525$	0	0
$526$	−19.0170	−0.829180
$527$	16.5884	0.722604
$528$	−7.15714	−0.311475
$529$	3.02320	0.131443
$530$	0	0
$531$	−12.9359	−0.561372
$532$	37.5285	1.62707
$533$	−12.4795	−0.540548
$534$	2.62591	0.113634
$535$	0	0
$536$	−5.44739	−0.235291
$537$	7.16976	0.309398
$538$	−3.27677	−0.141271
$539$	−25.5147	−1.09900
$540$	0	0
$541$	−0.347914	−0.0149580	−0.00747899	−	0.999972i	$-0.502381\pi$
$541$	−0.347914	−0.0149580	−0.00747899	+	0.999972i	$0.502381\pi$
$542$	11.5573	0.496427
$543$	29.0588	1.24703
$544$	−11.3111	−0.484960
$545$	0	0
$546$	20.9813	0.897916
$547$	−29.1298	−1.24550	−0.622749	−	0.782422i	$-0.713984\pi$
$547$	−29.1298	−1.24550	−0.622749	+	0.782422i	$0.713984\pi$
$548$	22.3588	0.955119
$549$	−13.7617	−0.587335
$550$	0	0
$551$	23.0196	0.980666
$552$	14.9402	0.635897
$553$	−25.1816	−1.07083
$554$	−6.65402	−0.282702
$555$	0	0
$556$	31.7165	1.34508
$557$	20.2253	0.856973	0.428487	−	0.903548i	$-0.359047\pi$
$557$	20.2253	0.856973	0.428487	+	0.903548i	$0.359047\pi$
$558$	6.71750	0.284375
$559$	46.0713	1.94861
$560$	0	0
$561$	7.88057	0.332718
$562$	−13.7897	−0.581685
$563$	3.71784	0.156688	0.0783440	−	0.996926i	$-0.475037\pi$
$563$	3.71784	0.156688	0.0783440	+	0.996926i	$0.475037\pi$
$564$	−20.4024	−0.859095
$565$	0	0
$566$	1.40563	0.0590831
$567$	13.2937	0.558283
$568$	35.1841	1.47629
$569$	33.5532	1.40662	0.703311	−	0.710883i	$-0.251704\pi$
$569$	33.5532	1.40662	0.703311	+	0.710883i	$0.251704\pi$
$570$	0	0
$571$	−25.5578	−1.06956	−0.534780	−	0.844992i	$-0.679605\pi$
$571$	−25.5578	−1.06956	−0.534780	+	0.844992i	$0.679605\pi$
$572$	−31.9934	−1.33771
$573$	12.3154	0.514482
$574$	−4.64380	−0.193829
$575$	0	0
$576$	0.178584	0.00744102
$577$	−13.3016	−0.553753	−0.276876	−	0.960906i	$-0.589299\pi$
$577$	−13.3016	−0.553753	−0.276876	+	0.960906i	$0.589299\pi$
$578$	−8.07811	−0.336005
$579$	17.4231	0.724078
$580$	0	0
$581$	−24.4950	−1.01623
$582$	−4.74780	−0.196802
$583$	20.0605	0.830820
$584$	24.3939	1.00943
$585$	0	0
$586$	−11.3074	−0.467104
$587$	−32.4672	−1.34006	−0.670032	−	0.742332i	$-0.733720\pi$
$587$	−32.4672	−1.34006	−0.670032	+	0.742332i	$0.733720\pi$
$588$	−17.7573	−0.732297
$589$	−48.9242	−2.01589
$590$	0	0
$591$	−7.60046	−0.312641
$592$	6.71103	0.275821
$593$	5.79919	0.238144	0.119072	−	0.992886i	$-0.462008\pi$
$593$	5.79919	0.238144	0.119072	+	0.992886i	$0.462008\pi$
$594$	10.5263	0.431900
$595$	0	0
$596$	0.0483058	0.00197868
$597$	−14.5936	−0.597277
$598$	20.9090	0.855034
$599$	−3.07138	−0.125493	−0.0627465	−	0.998029i	$-0.519986\pi$
$599$	−3.07138	−0.125493	−0.0627465	+	0.998029i	$0.519986\pi$
$600$	0	0
$601$	23.0372	0.939707	0.469854	−	0.882744i	$-0.344307\pi$
$601$	23.0372	0.939707	0.469854	+	0.882744i	$0.344307\pi$
$602$	17.1438	0.698729
$603$	−3.16045	−0.128703
$604$	0.745580	0.0303372
$605$	0	0
$606$	5.45865	0.221742
$607$	48.7294	1.97786	0.988932	−	0.148368i	$-0.0474020\pi$
$607$	48.7294	1.97786	0.988932	+	0.148368i	$0.0474020\pi$
$608$	33.3598	1.35292
$609$	−19.9034	−0.806526
$610$	0	0
$611$	−63.9773	−2.58824
$612$	−4.22377	−0.170736
$613$	1.69828	0.0685929	0.0342964	−	0.999412i	$-0.489081\pi$
$613$	1.69828	0.0685929	0.0342964	+	0.999412i	$0.489081\pi$
$614$	−2.40208	−0.0969402
$615$	0	0
$616$	−26.6749	−1.07476
$617$	42.6700	1.71783	0.858914	−	0.512119i	$-0.171139\pi$
$617$	42.6700	1.71783	0.858914	+	0.512119i	$0.171139\pi$
$618$	1.52429	0.0613160
$619$	−31.9703	−1.28500	−0.642498	−	0.766288i	$-0.722102\pi$
$619$	−31.9703	−1.28500	−0.642498	+	0.766288i	$0.722102\pi$
$620$	0	0
$621$	28.5912	1.14733
$622$	−9.06861	−0.363618
$623$	−12.7345	−0.510199
$624$	−15.6196	−0.625284
$625$	0	0
$626$	−0.786157	−0.0314212
$627$	−23.2421	−0.928202
$628$	−9.56473	−0.381674
$629$	−7.38936	−0.294633
$630$	0	0
$631$	−5.18897	−0.206570	−0.103285	−	0.994652i	$-0.532935\pi$
$631$	−5.18897	−0.206570	−0.103285	+	0.994652i	$0.532935\pi$
$632$	−14.4072	−0.573089
$633$	−13.0074	−0.516996
$634$	−2.62546	−0.104270
$635$	0	0
$636$	13.9613	0.553602
$637$	−55.6827	−2.20623
$638$	−7.30251	−0.289109
$639$	20.4130	0.807526
$640$	0	0
$641$	19.3638	0.764822	0.382411	−	0.923992i	$-0.375094\pi$
$641$	19.3638	0.764822	0.382411	+	0.923992i	$0.375094\pi$
$642$	−13.4741	−0.531780
$643$	−21.5916	−0.851489	−0.425744	−	0.904844i	$-0.639988\pi$
$643$	−21.5916	−0.851489	−0.425744	+	0.904844i	$0.639988\pi$
$644$	−32.3365	−1.27424
$645$	0	0
$646$	−7.40174	−0.291218
$647$	40.6062	1.59639	0.798196	−	0.602397i	$-0.205788\pi$
$647$	40.6062	1.59639	0.798196	+	0.602397i	$0.205788\pi$
$648$	7.60577	0.298783
$649$	−29.8875	−1.17319
$650$	0	0
$651$	42.3013	1.65792
$652$	−8.61678	−0.337459
$653$	−8.37874	−0.327886	−0.163943	−	0.986470i	$-0.552421\pi$
$653$	−8.37874	−0.327886	−0.163943	+	0.986470i	$0.552421\pi$
$654$	0.676668	0.0264598
$655$	0	0
$656$	3.45709	0.134977
$657$	14.1528	0.552153
$658$	−23.8069	−0.928088
$659$	2.74672	0.106997	0.0534985	−	0.998568i	$-0.482963\pi$
$659$	2.74672	0.106997	0.0534985	+	0.998568i	$0.482963\pi$
$660$	0	0
$661$	2.29053	0.0890912	0.0445456	−	0.999007i	$-0.485816\pi$
$661$	2.29053	0.0890912	0.0445456	+	0.999007i	$0.485816\pi$
$662$	−12.6322	−0.490964
$663$	17.1984	0.667930
$664$	−14.0144	−0.543866
$665$	0	0
$666$	−2.99233	−0.115950
$667$	−19.8348	−0.768008
$668$	−26.8282	−1.03802
$669$	−3.28323	−0.126937
$670$	0	0
$671$	−31.7954	−1.22745
$672$	−28.8439	−1.11268
$673$	−3.55591	−0.137070	−0.0685352	−	0.997649i	$-0.521833\pi$
$673$	−3.55591	−0.137070	−0.0685352	+	0.997649i	$0.521833\pi$
$674$	−21.2948	−0.820246
$675$	0	0
$676$	−48.8643	−1.87940
$677$	49.2272	1.89195	0.945977	−	0.324232i	$-0.105106\pi$
$677$	49.2272	1.89195	0.945977	+	0.324232i	$0.105106\pi$
$678$	4.79652	0.184209
$679$	23.0248	0.883611
$680$	0	0
$681$	27.2170	1.04296
$682$	15.5203	0.594302
$683$	2.75471	0.105406	0.0527030	−	0.998610i	$-0.483216\pi$
$683$	2.75471	0.105406	0.0527030	+	0.998610i	$0.483216\pi$
$684$	12.4572	0.476312
$685$	0	0
$686$	−3.57790	−0.136605
$687$	−14.7909	−0.564306
$688$	−12.7628	−0.486575
$689$	43.7796	1.66787
$690$	0	0
$691$	−4.74172	−0.180384	−0.0901918	−	0.995924i	$-0.528748\pi$
$691$	−4.74172	−0.180384	−0.0901918	+	0.995924i	$0.528748\pi$
$692$	−30.1649	−1.14670
$693$	−15.4762	−0.587892
$694$	−8.67700	−0.329374
$695$	0	0
$696$	−11.3874	−0.431638
$697$	−3.80653	−0.144183
$698$	−5.24466	−0.198513
$699$	−8.45423	−0.319768
$700$	0	0
$701$	28.7187	1.08469	0.542345	−	0.840156i	$-0.317536\pi$
$701$	28.7187	1.08469	0.542345	+	0.840156i	$0.317536\pi$
$702$	22.9724	0.867038
$703$	21.7934	0.821954
$704$	0.412606	0.0155507
$705$	0	0
$706$	3.23612	0.121793
$707$	−26.4721	−0.995587
$708$	−20.8005	−0.781732
$709$	−13.3937	−0.503009	−0.251505	−	0.967856i	$-0.580925\pi$
$709$	−13.3937	−0.503009	−0.251505	+	0.967856i	$0.580925\pi$
$710$	0	0
$711$	−8.35875	−0.313477
$712$	−7.28586	−0.273049
$713$	42.1557	1.57874
$714$	6.39976	0.239505
$715$	0	0
$716$	−8.87849	−0.331805
$717$	−12.3674	−0.461869
$718$	22.6466	0.845164
$719$	51.9716	1.93821	0.969107	−	0.246640i	$-0.0793265\pi$
$719$	51.9716	1.93821	0.969107	+	0.246640i	$0.0793265\pi$
$720$	0	0
$721$	−7.39217	−0.275299
$722$	9.99655	0.372033
$723$	−7.62049	−0.283409
$724$	−35.9843	−1.33735
$725$	0	0
$726$	−1.54570	−0.0573664
$727$	5.26831	0.195391	0.0976954	−	0.995216i	$-0.468853\pi$
$727$	5.26831	0.195391	0.0976954	+	0.995216i	$0.468853\pi$
$728$	−58.2148	−2.15758
$729$	26.3021	0.974150
$730$	0	0
$731$	14.0528	0.519761
$732$	−22.1283	−0.817887
$733$	−26.1445	−0.965669	−0.482835	−	0.875712i	$-0.660393\pi$
$733$	−26.1445	−0.965669	−0.482835	+	0.875712i	$0.660393\pi$
$734$	3.03891	0.112168
$735$	0	0
$736$	−28.7446	−1.05954
$737$	−7.30198	−0.268972
$738$	−1.54146	−0.0567418
$739$	11.7217	0.431189	0.215594	−	0.976483i	$-0.430831\pi$
$739$	11.7217	0.431189	0.215594	+	0.976483i	$0.430831\pi$
$740$	0	0
$741$	−50.7231	−1.86336
$742$	16.2910	0.598061
$743$	−18.3220	−0.672167	−0.336084	−	0.941832i	$-0.609102\pi$
$743$	−18.3220	−0.672167	−0.336084	+	0.941832i	$0.609102\pi$
$744$	24.2020	0.887289
$745$	0	0
$746$	10.1981	0.373380
$747$	−8.13085	−0.297492
$748$	−9.75870	−0.356813
$749$	65.3436	2.38760
$750$	0	0
$751$	23.5394	0.858965	0.429482	−	0.903075i	$-0.358696\pi$
$751$	23.5394	0.858965	0.429482	+	0.903075i	$0.358696\pi$
$752$	17.7231	0.646294
$753$	1.30185	0.0474419
$754$	−15.9368	−0.580386
$755$	0	0
$756$	−35.5276	−1.29213
$757$	35.5799	1.29317	0.646587	−	0.762840i	$-0.276196\pi$
$757$	35.5799	1.29317	0.646587	+	0.762840i	$0.276196\pi$
$758$	−7.74552	−0.281330
$759$	20.0266	0.726921
$760$	0	0
$761$	−12.1130	−0.439097	−0.219549	−	0.975602i	$-0.570458\pi$
$761$	−12.1130	−0.439097	−0.219549	+	0.975602i	$0.570458\pi$
$762$	8.54009	0.309375
$763$	−3.28156	−0.118800
$764$	−15.2504	−0.551742
$765$	0	0
$766$	9.99245	0.361042
$767$	−65.2258	−2.35517
$768$	−8.85020	−0.319354
$769$	10.1118	0.364640	0.182320	−	0.983239i	$-0.441639\pi$
$769$	10.1118	0.364640	0.182320	+	0.983239i	$0.441639\pi$
$770$	0	0
$771$	25.9565	0.934800
$772$	−21.5754	−0.776516
$773$	6.19658	0.222875	0.111438	−	0.993771i	$-0.464454\pi$
$773$	6.19658	0.222875	0.111438	+	0.993771i	$0.464454\pi$
$774$	5.69069	0.204548
$775$	0	0
$776$	13.1733	0.472893
$777$	−18.8432	−0.675997
$778$	5.15200	0.184708
$779$	11.2266	0.402234
$780$	0	0
$781$	47.1627	1.68761
$782$	6.37772	0.228067
$783$	−21.7922	−0.778790
$784$	15.4253	0.550905
$785$	0	0
$786$	−14.0499	−0.501142
$787$	12.0316	0.428881	0.214441	−	0.976737i	$-0.431207\pi$
$787$	12.0316	0.428881	0.214441	+	0.976737i	$0.431207\pi$
$788$	9.41184	0.335283
$789$	−39.7508	−1.41517
$790$	0	0
$791$	−23.2611	−0.827069
$792$	−8.85444	−0.314629
$793$	−69.3895	−2.46409
$794$	16.5150	0.586094
$795$	0	0
$796$	18.0716	0.640532
$797$	−5.35261	−0.189599	−0.0947996	−	0.995496i	$-0.530221\pi$
$797$	−5.35261	−0.189599	−0.0947996	+	0.995496i	$0.530221\pi$
$798$	−18.8748	−0.668161
$799$	−19.5145	−0.690373
$800$	0	0
$801$	−4.22709	−0.149357
$802$	14.5920	0.515260
$803$	32.6989	1.15392
$804$	−5.08189	−0.179225
$805$	0	0
$806$	33.8711	1.19306
$807$	−6.84935	−0.241108
$808$	−15.1456	−0.532820
$809$	29.2497	1.02836	0.514182	−	0.857681i	$-0.328096\pi$
$809$	29.2497	1.02836	0.514182	+	0.857681i	$0.328096\pi$
$810$	0	0
$811$	−30.7220	−1.07879	−0.539397	−	0.842052i	$-0.681348\pi$
$811$	−30.7220	−1.07879	−0.539397	+	0.842052i	$0.681348\pi$
$812$	24.6469	0.864935
$813$	24.1579	0.847254
$814$	−6.91355	−0.242320
$815$	0	0
$816$	−4.76432	−0.166785
$817$	−41.4458	−1.45001
$818$	−5.36611	−0.187622
$819$	−33.7749	−1.18019
$820$	0	0
$821$	−10.6846	−0.372894	−0.186447	−	0.982465i	$-0.559697\pi$
$821$	−10.6846	−0.372894	−0.186447	+	0.982465i	$0.559697\pi$
$822$	−11.2452	−0.392223
$823$	31.9198	1.11266	0.556328	−	0.830963i	$-0.312210\pi$
$823$	31.9198	1.11266	0.556328	+	0.830963i	$0.312210\pi$
$824$	−4.22931	−0.147335
$825$	0	0
$826$	−24.2714	−0.844512
$827$	−32.2088	−1.12001	−0.560005	−	0.828489i	$-0.689201\pi$
$827$	−32.2088	−1.12001	−0.560005	+	0.828489i	$0.689201\pi$
$828$	−10.7337	−0.373023
$829$	4.54003	0.157682	0.0788408	−	0.996887i	$-0.474878\pi$
$829$	4.54003	0.157682	0.0788408	+	0.996887i	$0.474878\pi$
$830$	0	0
$831$	−13.9087	−0.482489
$832$	0.900462	0.0312179
$833$	−16.9845	−0.588477
$834$	−15.9517	−0.552362
$835$	0	0
$836$	28.7813	0.995423
$837$	46.3157	1.60090
$838$	−7.61786	−0.263155
$839$	−3.51756	−0.121440	−0.0607198	−	0.998155i	$-0.519340\pi$
$839$	−3.51756	−0.121440	−0.0607198	+	0.998155i	$0.519340\pi$
$840$	0	0
$841$	−13.8819	−0.478686
$842$	−11.1784	−0.385232
$843$	−28.8243	−0.992763
$844$	16.1073	0.554437
$845$	0	0
$846$	−7.90241	−0.271691
$847$	7.49600	0.257566
$848$	−12.1279	−0.416473
$849$	2.93816	0.100837
$850$	0	0
$851$	−18.7783	−0.643713
$852$	32.8234	1.12451
$853$	41.4217	1.41825	0.709127	−	0.705081i	$-0.249089\pi$
$853$	41.4217	1.41825	0.709127	+	0.705081i	$0.249089\pi$
$854$	−25.8208	−0.883570
$855$	0	0
$856$	37.3853	1.27780
$857$	−6.59439	−0.225260	−0.112630	−	0.993637i	$-0.535927\pi$
$857$	−6.59439	−0.225260	−0.112630	+	0.993637i	$0.535927\pi$
$858$	16.0909	0.549336
$859$	−54.3859	−1.85562	−0.927811	−	0.373050i	$-0.878312\pi$
$859$	−54.3859	−1.85562	−0.927811	+	0.373050i	$0.878312\pi$
$860$	0	0
$861$	−9.70683	−0.330808
$862$	−1.68494	−0.0573893
$863$	32.2610	1.09818	0.549089	−	0.835764i	$-0.314975\pi$
$863$	32.2610	1.09818	0.549089	+	0.835764i	$0.314975\pi$
$864$	−31.5812	−1.07441
$865$	0	0
$866$	−18.6988	−0.635412
$867$	−16.8855	−0.573461
$868$	−52.3828	−1.77799
$869$	−19.3122	−0.655123
$870$	0	0
$871$	−15.9357	−0.539960
$872$	−1.87749	−0.0635798
$873$	7.64282	0.258670
$874$	−18.8098	−0.636251
$875$	0	0
$876$	22.7572	0.768894
$877$	−25.0725	−0.846637	−0.423318	−	0.905981i	$-0.639135\pi$
$877$	−25.0725	−0.846637	−0.423318	+	0.905981i	$0.639135\pi$
$878$	−0.586108	−0.0197802
$879$	−23.6356	−0.797209
$880$	0	0
$881$	−39.8888	−1.34389	−0.671944	−	0.740602i	$-0.734540\pi$
$881$	−39.8888	−1.34389	−0.671944	+	0.740602i	$0.734540\pi$
$882$	−6.87788	−0.231590
$883$	28.2464	0.950566	0.475283	−	0.879833i	$-0.342346\pi$
$883$	28.2464	0.950566	0.475283	+	0.879833i	$0.342346\pi$
$884$	−21.2972	−0.716302
$885$	0	0
$886$	−3.11612	−0.104688
$887$	−1.88012	−0.0631283	−0.0315642	−	0.999502i	$-0.510049\pi$
$887$	−1.88012	−0.0631283	−0.0315642	+	0.999502i	$0.510049\pi$
$888$	−10.7808	−0.361781
$889$	−41.4159	−1.38904
$890$	0	0
$891$	10.1952	0.341552
$892$	4.06570	0.136130
$893$	57.5540	1.92597
$894$	−0.0242952	−0.000812553 0
$895$	0	0
$896$	44.6474	1.49157
$897$	43.7057	1.45929
$898$	−3.33097	−0.111156
$899$	−32.1310	−1.07163
$900$	0	0
$901$	13.3537	0.444877
$902$	−3.56142	−0.118582
$903$	35.8353	1.19252
$904$	−13.3084	−0.442632
$905$	0	0
$906$	−0.374986	−0.0124581
$907$	12.9333	0.429443	0.214722	−	0.976675i	$-0.431116\pi$
$907$	12.9333	0.429443	0.214722	+	0.976675i	$0.431116\pi$
$908$	−33.7034	−1.11849
$909$	−8.78712	−0.291450
$910$	0	0
$911$	−20.9733	−0.694875	−0.347438	−	0.937703i	$-0.612948\pi$
$911$	−20.9733	−0.694875	−0.347438	+	0.937703i	$0.612948\pi$
$912$	14.0514	0.465289
$913$	−18.7857	−0.621716
$914$	19.3703	0.640714
$915$	0	0
$916$	18.3159	0.605174
$917$	68.1359	2.25004
$918$	7.00709	0.231269
$919$	−59.2829	−1.95556	−0.977781	−	0.209630i	$-0.932774\pi$
$919$	−59.2829	−1.95556	−0.977781	+	0.209630i	$0.932774\pi$
$920$	0	0
$921$	−5.02102	−0.165448
$922$	4.65939	0.153449
$923$	102.927	3.38788
$924$	−24.8852	−0.818662
$925$	0	0
$926$	−3.15494	−0.103678
$927$	−2.45375	−0.0805916
$928$	21.9091	0.719201
$929$	−52.9155	−1.73610	−0.868050	−	0.496476i	$-0.834627\pi$
$929$	−52.9155	−1.73610	−0.868050	+	0.496476i	$0.834627\pi$
$930$	0	0
$931$	50.0923	1.64171
$932$	10.4691	0.342926
$933$	−18.9559	−0.620588
$934$	6.72073	0.219909
$935$	0	0
$936$	−19.3237	−0.631616
$937$	14.9951	0.489869	0.244934	−	0.969540i	$-0.421234\pi$
$937$	14.9951	0.489869	0.244934	+	0.969540i	$0.421234\pi$
$938$	−5.92989	−0.193618
$939$	−1.64329	−0.0536266
$940$	0	0
$941$	1.41283	0.0460568	0.0230284	−	0.999735i	$-0.492669\pi$
$941$	1.41283	0.0460568	0.0230284	+	0.999735i	$0.492669\pi$
$942$	4.81054	0.156736
$943$	−9.67341	−0.315010
$944$	18.0690	0.588094
$945$	0	0
$946$	13.1479	0.427475
$947$	1.95072	0.0633898	0.0316949	−	0.999498i	$-0.489910\pi$
$947$	1.95072	0.0633898	0.0316949	+	0.999498i	$0.489910\pi$
$948$	−13.4406	−0.436530
$949$	71.3614	2.31649
$950$	0	0
$951$	−5.48793	−0.177958
$952$	−17.7568	−0.575502
$953$	−4.60766	−0.149257	−0.0746284	−	0.997211i	$-0.523777\pi$
$953$	−4.60766	−0.149257	−0.0746284	+	0.997211i	$0.523777\pi$
$954$	5.40761	0.175078
$955$	0	0
$956$	15.3149	0.495318
$957$	−15.2643	−0.493424
$958$	23.1839	0.749037
$959$	54.5347	1.76102
$960$	0	0
$961$	37.2891	1.20287
$962$	−15.0880	−0.486456
$963$	21.6901	0.698953
$964$	9.43664	0.303934
$965$	0	0
$966$	16.2635	0.523270
$967$	21.2940	0.684768	0.342384	−	0.939560i	$-0.388766\pi$
$967$	21.2940	0.684768	0.342384	+	0.939560i	$0.388766\pi$
$968$	4.28871	0.137844
$969$	−15.4717	−0.497022
$970$	0	0
$971$	28.6035	0.917930	0.458965	−	0.888454i	$-0.348220\pi$
$971$	28.6035	0.917930	0.458965	+	0.888454i	$0.348220\pi$
$972$	−20.0107	−0.641843
$973$	77.3589	2.48001
$974$	0.746707	0.0239260
$975$	0	0
$976$	19.2224	0.615294
$977$	−33.4519	−1.07022	−0.535110	−	0.844783i	$-0.679730\pi$
$977$	−33.4519	−1.07022	−0.535110	+	0.844783i	$0.679730\pi$
$978$	4.33377	0.138579
$979$	−9.76636	−0.312134
$980$	0	0
$981$	−1.08927	−0.0347779
$982$	6.70133	0.213848
$983$	−45.8996	−1.46397	−0.731985	−	0.681321i	$-0.761406\pi$
$983$	−45.8996	−1.46397	−0.731985	+	0.681321i	$0.761406\pi$
$984$	−5.55360	−0.177042
$985$	0	0
$986$	−4.86109	−0.154809
$987$	−49.7629	−1.58397
$988$	62.8117	1.99831
$989$	35.7119	1.13557
$990$	0	0
$991$	−15.4162	−0.489713	−0.244856	−	0.969559i	$-0.578741\pi$
$991$	−15.4162	−0.489713	−0.244856	+	0.969559i	$0.578741\pi$
$992$	−46.5641	−1.47841
$993$	−26.4047	−0.837929
$994$	38.3006	1.21482
$995$	0	0
$996$	−13.0741	−0.414270
$997$	−39.3302	−1.24560	−0.622800	−	0.782381i	$-0.714005\pi$
$997$	−39.3302	−1.24560	−0.622800	+	0.782381i	$0.714005\pi$
$998$	20.2899	0.642264
$999$	−20.6314	−0.652750

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6275.2.a.e.1.10		17
5.4	even	2		251.2.a.b.1.8	✓	17
15.14	odd	2		2259.2.a.k.1.10		17
20.19	odd	2		4016.2.a.k.1.13		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
251.2.a.b.1.8	✓	17	5.4	even	2
2259.2.a.k.1.10		17	15.14	odd	2
4016.2.a.k.1.13		17	20.19	odd	2
6275.2.a.e.1.10		17	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6275 = 5^{2} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6275.a (trivial)

\(f(q)\)	\(=\)	\(q+0.622810 q^{2} +1.30185 q^{3} -1.61211 q^{4} +0.810802 q^{6} -3.93205 q^{7} -2.24966 q^{8} -1.30520 q^{9} +O(q^{10})\)	\(q+0.622810 q^{2} +1.30185 q^{3} -1.61211 q^{4} +0.810802 q^{6} -3.93205 q^{7} -2.24966 q^{8} -1.30520 q^{9} -3.01556 q^{11} -2.09871 q^{12} -6.58110 q^{13} -2.44892 q^{14} +1.82311 q^{16} -2.00738 q^{17} -0.812891 q^{18} +5.92036 q^{19} -5.11892 q^{21} -1.87812 q^{22} -5.10129 q^{23} -2.92871 q^{24} -4.09877 q^{26} -5.60470 q^{27} +6.33889 q^{28} +3.88820 q^{29} -8.26372 q^{31} +5.63476 q^{32} -3.92580 q^{33} -1.25022 q^{34} +2.10412 q^{36} +3.68109 q^{37} +3.68726 q^{38} -8.56757 q^{39} +1.89627 q^{41} -3.18812 q^{42} -7.00055 q^{43} +4.86141 q^{44} -3.17714 q^{46} +9.72137 q^{47} +2.37340 q^{48} +8.46101 q^{49} -2.61330 q^{51} +10.6094 q^{52} -6.65232 q^{53} -3.49067 q^{54} +8.84576 q^{56} +7.70740 q^{57} +2.42161 q^{58} +9.91108 q^{59} +10.5438 q^{61} -5.14673 q^{62} +5.13211 q^{63} -0.136826 q^{64} -2.44502 q^{66} +2.42143 q^{67} +3.23611 q^{68} -6.64110 q^{69} -15.6398 q^{71} +2.93625 q^{72} -10.8434 q^{73} +2.29262 q^{74} -9.54426 q^{76} +11.8573 q^{77} -5.33597 q^{78} +6.40419 q^{79} -3.38086 q^{81} +1.18101 q^{82} +6.22959 q^{83} +8.25225 q^{84} -4.36002 q^{86} +5.06183 q^{87} +6.78398 q^{88} +3.23865 q^{89} +25.8772 q^{91} +8.22383 q^{92} -10.7581 q^{93} +6.05457 q^{94} +7.33559 q^{96} -5.85568 q^{97} +5.26960 q^{98} +3.93591 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9	\( 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9} - q^{11} + 9 q^{12} - 22 q^{13} - 7 q^{14} + 40 q^{16} + q^{17} + 7 q^{18} + 13 q^{19} + 25 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} - 9 q^{26} + 15 q^{27} + 10 q^{28} + 28 q^{29} + 12 q^{31} - 4 q^{32} + 16 q^{33} - 21 q^{34} + 21 q^{36} - 27 q^{37} + 37 q^{38} + 13 q^{39} - q^{41} + 56 q^{42} - 9 q^{43} - 43 q^{44} + 4 q^{46} + 20 q^{47} + 79 q^{48} + 32 q^{49} - 2 q^{51} + q^{52} - q^{53} - 65 q^{54} - 61 q^{56} + 24 q^{57} + 46 q^{58} - 20 q^{59} + 59 q^{61} + 73 q^{62} + 41 q^{63} + 54 q^{64} - 43 q^{66} - 15 q^{67} + 20 q^{68} + 38 q^{69} - 26 q^{71} + 2 q^{72} - 8 q^{73} + 2 q^{74} + 38 q^{76} + 33 q^{79} + 29 q^{81} - 10 q^{82} + 63 q^{84} + 11 q^{86} + 11 q^{87} - 27 q^{88} + 11 q^{89} - 2 q^{91} - 28 q^{92} - 28 q^{93} + 29 q^{94} - 17 q^{96} + 10 q^{97} - 22 q^{98} - 36 q^{99}+O(q^{100}) \) 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9 - q^11 + 9 * q^12 - 22 * q^13 - 7 * q^14 + 40 * q^16 + q^17 + 7 * q^18 + 13 * q^19 + 25 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 - 9 * q^26 + 15 * q^27 + 10 * q^28 + 28 * q^29 + 12 * q^31 - 4 * q^32 + 16 * q^33 - 21 * q^34 + 21 * q^36 - 27 * q^37 + 37 * q^38 + 13 * q^39 - q^41 + 56 * q^42 - 9 * q^43 - 43 * q^44 + 4 * q^46 + 20 * q^47 + 79 * q^48 + 32 * q^49 - 2 * q^51 + q^52 - q^53 - 65 * q^54 - 61 * q^56 + 24 * q^57 + 46 * q^58 - 20 * q^59 + 59 * q^61 + 73 * q^62 + 41 * q^63 + 54 * q^64 - 43 * q^66 - 15 * q^67 + 20 * q^68 + 38 * q^69 - 26 * q^71 + 2 * q^72 - 8 * q^73 + 2 * q^74 + 38 * q^76 + 33 * q^79 + 29 * q^81 - 10 * q^82 + 63 * q^84 + 11 * q^86 + 11 * q^87 - 27 * q^88 + 11 * q^89 - 2 * q^91 - 28 * q^92 - 28 * q^93 + 29 * q^94 - 17 * q^96 + 10 * q^97 - 22 * q^98 - 36 * q^99

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