LMFDB - Embedded newform 775.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, 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("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.205225.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 3x^{2} + 7x - 3 $ x^5 - x^4 - 6x^3 + 3x^2 + 7*x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.77799$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.77799 q^{2} -2.60920 q^{3} +5.71723 q^{4} -7.24833 q^{6} +3.19118 q^{7} +10.3264 q^{8} +3.80792 q^{9} +O(q^{10})$	\(q+2.77799 q^{2} -2.60920 q^{3} +5.71723 q^{4} -7.24833 q^{6} +3.19118 q^{7} +10.3264 q^{8} +3.80792 q^{9} -3.35726 q^{11} -14.9174 q^{12} -1.19118 q^{13} +8.86507 q^{14} +17.2523 q^{16} +5.02239 q^{17} +10.5784 q^{18} -5.30909 q^{19} -8.32643 q^{21} -9.32643 q^{22} +5.19601 q^{23} -26.9437 q^{24} -3.30909 q^{26} -2.10803 q^{27} +18.2447 q^{28} -1.49129 q^{29} +1.00000 q^{31} +27.2738 q^{32} +8.75976 q^{33} +13.9522 q^{34} +21.7708 q^{36} +5.51769 q^{37} -14.7486 q^{38} +3.10803 q^{39} -0.707433 q^{41} -23.1307 q^{42} -4.47012 q^{43} -19.1942 q^{44} +14.4345 q^{46} -8.34567 q^{47} -45.0146 q^{48} +3.18364 q^{49} -13.1044 q^{51} -6.81026 q^{52} -1.50027 q^{53} -5.85609 q^{54} +32.9535 q^{56} +13.8525 q^{57} -4.14279 q^{58} -0.830984 q^{59} -9.68912 q^{61} +2.77799 q^{62} +12.1518 q^{63} +41.2617 q^{64} +24.3345 q^{66} -11.0996 q^{67} +28.7142 q^{68} -13.5574 q^{69} -4.53593 q^{71} +39.3222 q^{72} -5.69900 q^{73} +15.3281 q^{74} -30.3533 q^{76} -10.7136 q^{77} +8.63408 q^{78} +8.77256 q^{79} -5.92349 q^{81} -1.96524 q^{82} -7.26575 q^{83} -47.6041 q^{84} -12.4179 q^{86} +3.89107 q^{87} -34.6685 q^{88} -13.3681 q^{89} -3.80128 q^{91} +29.7068 q^{92} -2.60920 q^{93} -23.1842 q^{94} -71.1627 q^{96} +10.3272 q^{97} +8.84412 q^{98} -12.7842 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 4 q^{2} + q^{3} + 6 q^{4} - q^{6} + 6 q^{7} + 15 q^{8} + 2 q^{9}+O(q^{10}) $ 5 * q + 4 * q^2 + q^3 + 6 * q^4 - q^6 + 6 * q^7 + 15 * q^8 + 2 * q^9	$ 5 q + 4 q^{2} + q^{3} + 6 q^{4} - q^{6} + 6 q^{7} + 15 q^{8} + 2 q^{9} - 11 q^{12} + 4 q^{13} + 2 q^{14} + 20 q^{16} + 11 q^{17} + 19 q^{18} - 4 q^{19} - 5 q^{21} - 10 q^{22} + 12 q^{23} - 26 q^{24} + 6 q^{26} - 2 q^{27} + 18 q^{28} - 6 q^{29} + 5 q^{31} + 29 q^{32} + 21 q^{33} - 5 q^{34} + 23 q^{36} - 2 q^{37} - 6 q^{38} + 7 q^{39} - 2 q^{41} - 24 q^{42} + 7 q^{43} - 28 q^{44} + 27 q^{46} + 8 q^{47} - 39 q^{48} - q^{49} - 19 q^{51} - 6 q^{52} + 25 q^{53} - 18 q^{54} + 35 q^{56} + 20 q^{57} - q^{58} + 4 q^{59} - 17 q^{61} + 4 q^{62} + 10 q^{63} + 27 q^{64} + 27 q^{66} - 13 q^{67} + 18 q^{68} - 10 q^{69} - 6 q^{71} + 26 q^{72} + 7 q^{73} + 6 q^{74} - 5 q^{76} + 7 q^{77} + 22 q^{78} + 12 q^{79} - 11 q^{81} - 21 q^{82} - 4 q^{83} - 63 q^{84} - 41 q^{86} + q^{87} - 49 q^{88} - 3 q^{89} - 22 q^{91} + 34 q^{92} + q^{93} - 34 q^{94} - 64 q^{96} + 25 q^{97} - 22 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q + 4 * q^2 + q^3 + 6 * q^4 - q^6 + 6 * q^7 + 15 * q^8 + 2 * q^9 - 11 * q^12 + 4 * q^13 + 2 * q^14 + 20 * q^16 + 11 * q^17 + 19 * q^18 - 4 * q^19 - 5 * q^21 - 10 * q^22 + 12 * q^23 - 26 * q^24 + 6 * q^26 - 2 * q^27 + 18 * q^28 - 6 * q^29 + 5 * q^31 + 29 * q^32 + 21 * q^33 - 5 * q^34 + 23 * q^36 - 2 * q^37 - 6 * q^38 + 7 * q^39 - 2 * q^41 - 24 * q^42 + 7 * q^43 - 28 * q^44 + 27 * q^46 + 8 * q^47 - 39 * q^48 - q^49 - 19 * q^51 - 6 * q^52 + 25 * q^53 - 18 * q^54 + 35 * q^56 + 20 * q^57 - q^58 + 4 * q^59 - 17 * q^61 + 4 * q^62 + 10 * q^63 + 27 * q^64 + 27 * q^66 - 13 * q^67 + 18 * q^68 - 10 * q^69 - 6 * q^71 + 26 * q^72 + 7 * q^73 + 6 * q^74 - 5 * q^76 + 7 * q^77 + 22 * q^78 + 12 * q^79 - 11 * q^81 - 21 * q^82 - 4 * q^83 - 63 * q^84 - 41 * q^86 + q^87 - 49 * q^88 - 3 * q^89 - 22 * q^91 + 34 * q^92 + q^93 - 34 * q^94 - 64 * q^96 + 25 * q^97 - 22 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.77799	1.96434	0.982168	−	0.188006i	$-0.0602024\pi$
$2$	2.77799	1.96434	0.982168	+	0.188006i	$0.0602024\pi$
$3$	−2.60920	−1.50642	−0.753211	−	0.657779i	$-0.771496\pi$
$3$	−2.60920	−1.50642	−0.753211	+	0.657779i	$0.771496\pi$
$4$	5.71723	2.85862
$5$	0	0
$5$	0	0
$6$	−7.24833	−2.95912
$7$	3.19118	1.20615	0.603077	−	0.797683i	$-0.293941\pi$
$7$	3.19118	1.20615	0.603077	+	0.797683i	$0.293941\pi$
$8$	10.3264	3.65094
$9$	3.80792	1.26931
$10$	0	0
$11$	−3.35726	−1.01225	−0.506126	−	0.862460i	$-0.668923\pi$
$11$	−3.35726	−1.01225	−0.506126	+	0.862460i	$0.668923\pi$
$12$	−14.9174	−4.30628
$13$	−1.19118	−0.330374	−0.165187	−	0.986262i	$-0.552823\pi$
$13$	−1.19118	−0.330374	−0.165187	+	0.986262i	$0.552823\pi$
$14$	8.86507	2.36929
$15$	0	0
$16$	17.2523	4.31307
$17$	5.02239	1.21811	0.609054	−	0.793128i	$-0.291549\pi$
$17$	5.02239	1.21811	0.609054	+	0.793128i	$0.291549\pi$
$18$	10.5784	2.49335
$19$	−5.30909	−1.21799	−0.608995	−	0.793174i	$-0.708427\pi$
$19$	−5.30909	−1.21799	−0.608995	+	0.793174i	$0.708427\pi$
$20$	0	0
$21$	−8.32643	−1.81698
$22$	−9.32643	−1.98840
$23$	5.19601	1.08344	0.541721	−	0.840558i	$-0.317773\pi$
$23$	5.19601	1.08344	0.541721	+	0.840558i	$0.317773\pi$
$24$	−26.9437	−5.49986
$25$	0	0
$26$	−3.30909	−0.648966
$27$	−2.10803	−0.405691
$28$	18.2447	3.44793
$29$	−1.49129	−0.276926	−0.138463	−	0.990368i	$-0.544216\pi$
$29$	−1.49129	−0.276926	−0.138463	+	0.990368i	$0.544216\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	27.2738	4.82136
$33$	8.75976	1.52488
$34$	13.9522	2.39277
$35$	0	0
$36$	21.7708	3.62846
$37$	5.51769	0.907103	0.453552	−	0.891230i	$-0.350157\pi$
$37$	5.51769	0.907103	0.453552	+	0.891230i	$0.350157\pi$
$38$	−14.7486	−2.39254
$39$	3.10803	0.497683
$40$	0	0
$41$	−0.707433	−0.110482	−0.0552412	−	0.998473i	$-0.517593\pi$
$41$	−0.707433	−0.110482	−0.0552412	+	0.998473i	$0.517593\pi$
$42$	−23.1307	−3.56915
$43$	−4.47012	−0.681686	−0.340843	−	0.940120i	$-0.610712\pi$
$43$	−4.47012	−0.681686	−0.340843	+	0.940120i	$0.610712\pi$
$44$	−19.1942	−2.89364
$45$	0	0
$46$	14.4345	2.12825
$47$	−8.34567	−1.21734	−0.608670	−	0.793423i	$-0.708297\pi$
$47$	−8.34567	−1.21734	−0.608670	+	0.793423i	$0.708297\pi$
$48$	−45.0146	−6.49730
$49$	3.18364	0.454806
$50$	0	0
$51$	−13.1044	−1.83499
$52$	−6.81026	−0.944413
$53$	−1.50027	−0.206078	−0.103039	−	0.994677i	$-0.532857\pi$
$53$	−1.50027	−0.206078	−0.103039	+	0.994677i	$0.532857\pi$
$54$	−5.85609	−0.796913
$55$	0	0
$56$	32.9535	4.40360
$57$	13.8525	1.83481
$58$	−4.14279	−0.543975
$59$	−0.830984	−0.108185	−0.0540924	−	0.998536i	$-0.517227\pi$
$59$	−0.830984	−0.108185	−0.0540924	+	0.998536i	$0.517227\pi$
$60$	0	0
$61$	−9.68912	−1.24056	−0.620282	−	0.784379i	$-0.712982\pi$
$61$	−9.68912	−1.24056	−0.620282	+	0.784379i	$0.712982\pi$
$62$	2.77799	0.352805
$63$	12.1518	1.53098
$64$	41.2617	5.15771
$65$	0	0
$66$	24.3345	2.99537
$67$	−11.0996	−1.35603	−0.678016	−	0.735048i	$-0.737160\pi$
$67$	−11.0996	−1.35603	−0.678016	+	0.735048i	$0.737160\pi$
$68$	28.7142	3.48210
$69$	−13.5574	−1.63212
$70$	0	0
$71$	−4.53593	−0.538316	−0.269158	−	0.963096i	$-0.586745\pi$
$71$	−4.53593	−0.538316	−0.269158	+	0.963096i	$0.586745\pi$
$72$	39.3222	4.63417
$73$	−5.69900	−0.667017	−0.333508	−	0.942747i	$-0.608233\pi$
$73$	−5.69900	−0.667017	−0.333508	+	0.942747i	$0.608233\pi$
$74$	15.3281	1.78186
$75$	0	0
$76$	−30.3533	−3.48176
$77$	−10.7136	−1.22093
$78$	8.63408	0.977617
$79$	8.77256	0.986990	0.493495	−	0.869749i	$-0.335719\pi$
$79$	8.77256	0.986990	0.493495	+	0.869749i	$0.335719\pi$
$80$	0	0
$81$	−5.92349	−0.658166
$82$	−1.96524	−0.217025
$83$	−7.26575	−0.797520	−0.398760	−	0.917055i	$-0.630559\pi$
$83$	−7.26575	−0.797520	−0.398760	+	0.917055i	$0.630559\pi$
$84$	−47.6041	−5.19404
$85$	0	0
$86$	−12.4179	−1.33906
$87$	3.89107	0.417167
$88$	−34.6685	−3.69567
$89$	−13.3681	−1.41701	−0.708506	−	0.705705i	$-0.750630\pi$
$89$	−13.3681	−1.41701	−0.708506	+	0.705705i	$0.750630\pi$
$90$	0	0
$91$	−3.80128	−0.398482
$92$	29.7068	3.09715
$93$	−2.60920	−0.270561
$94$	−23.1842	−2.39127
$95$	0	0
$96$	−71.1627	−7.26301
$97$	10.3272	1.04857	0.524286	−	0.851542i	$-0.324332\pi$
$97$	10.3272	1.04857	0.524286	+	0.851542i	$0.324332\pi$
$98$	8.84412	0.893391
$99$	−12.7842	−1.28486
$100$	0	0
$101$	10.2429	1.01921	0.509603	−	0.860409i	$-0.329792\pi$
$101$	10.2429	1.01921	0.509603	+	0.860409i	$0.329792\pi$
$102$	−36.4040	−3.60453
$103$	−11.6234	−1.14529	−0.572643	−	0.819805i	$-0.694082\pi$
$103$	−11.6234	−1.14529	−0.572643	+	0.819805i	$0.694082\pi$
$104$	−12.3007	−1.20618
$105$	0	0
$106$	−4.16774	−0.404807
$107$	−5.07683	−0.490795	−0.245398	−	0.969423i	$-0.578919\pi$
$107$	−5.07683	−0.490795	−0.245398	+	0.969423i	$0.578919\pi$
$108$	−12.0521	−1.15971
$109$	−3.08315	−0.295312	−0.147656	−	0.989039i	$-0.547173\pi$
$109$	−3.08315	−0.295312	−0.147656	+	0.989039i	$0.547173\pi$
$110$	0	0
$111$	−14.3968	−1.36648
$112$	55.0551	5.20222
$113$	20.0404	1.88524	0.942622	−	0.333861i	$-0.108352\pi$
$113$	20.0404	1.88524	0.942622	+	0.333861i	$0.108352\pi$
$114$	38.4821	3.60417
$115$	0	0
$116$	−8.52605	−0.791624
$117$	−4.53593	−0.419347
$118$	−2.30846	−0.212511
$119$	16.0274	1.46923
$120$	0	0
$121$	0.271180	0.0246528
$122$	−26.9163	−2.43688
$123$	1.84583	0.166433
$124$	5.71723	0.513422
$125$	0	0
$126$	33.7575	3.00736
$127$	−15.3484	−1.36195	−0.680977	−	0.732305i	$-0.738445\pi$
$127$	−15.3484	−1.36195	−0.680977	+	0.732305i	$0.738445\pi$
$128$	60.0771	5.31012
$129$	11.6634	1.02691
$130$	0	0
$131$	−5.04253	−0.440567	−0.220284	−	0.975436i	$-0.570698\pi$
$131$	−5.04253	−0.440567	−0.220284	+	0.975436i	$0.570698\pi$
$132$	50.0815	4.35904
$133$	−16.9423	−1.46908
$134$	−30.8346	−2.66370
$135$	0	0
$136$	51.8634	4.44725
$137$	4.40068	0.375975	0.187988	−	0.982171i	$-0.439803\pi$
$137$	4.40068	0.375975	0.187988	+	0.982171i	$0.439803\pi$
$138$	−37.6624	−3.20604
$139$	−3.16247	−0.268237	−0.134118	−	0.990965i	$-0.542820\pi$
$139$	−3.16247	−0.268237	−0.134118	+	0.990965i	$0.542820\pi$
$140$	0	0
$141$	21.7755	1.83383
$142$	−12.6008	−1.05743
$143$	3.99910	0.334422
$144$	65.6953	5.47461
$145$	0	0
$146$	−15.8318	−1.31025
$147$	−8.30675	−0.685129
$148$	31.5459	2.59306
$149$	7.07940	0.579967	0.289983	−	0.957032i	$-0.406350\pi$
$149$	7.07940	0.579967	0.289983	+	0.957032i	$0.406350\pi$
$150$	0	0
$151$	−1.71059	−0.139205	−0.0696027	−	0.997575i	$-0.522173\pi$
$151$	−1.71059	−0.139205	−0.0696027	+	0.997575i	$0.522173\pi$
$152$	−54.8240	−4.44681
$153$	19.1249	1.54615
$154$	−29.7623	−2.39832
$155$	0	0
$156$	17.7693	1.42268
$157$	11.5607	0.922646	0.461323	−	0.887232i	$-0.347375\pi$
$157$	11.5607	0.922646	0.461323	+	0.887232i	$0.347375\pi$
$158$	24.3701	1.93878
$159$	3.91451	0.310441
$160$	0	0
$161$	16.5814	1.30680
$162$	−16.4554	−1.29286
$163$	17.3496	1.35893	0.679463	−	0.733710i	$-0.262213\pi$
$163$	17.3496	1.35893	0.679463	+	0.733710i	$0.262213\pi$
$164$	−4.04456	−0.315827
$165$	0	0
$166$	−20.1842	−1.56660
$167$	2.73202	0.211410	0.105705	−	0.994398i	$-0.466290\pi$
$167$	2.73202	0.211410	0.105705	+	0.994398i	$0.466290\pi$
$168$	−85.9823	−6.63368
$169$	−11.5811	−0.890853
$170$	0	0
$171$	−20.2166	−1.54600
$172$	−25.5567	−1.94868
$173$	5.79374	0.440490	0.220245	−	0.975445i	$-0.429314\pi$
$173$	5.79374	0.440490	0.220245	+	0.975445i	$0.429314\pi$
$174$	10.8094	0.819456
$175$	0	0
$176$	−57.9203	−4.36591
$177$	2.16820	0.162972
$178$	−37.1363	−2.78349
$179$	5.25284	0.392616	0.196308	−	0.980542i	$-0.437105\pi$
$179$	5.25284	0.392616	0.196308	+	0.980542i	$0.437105\pi$
$180$	0	0
$181$	11.3965	0.847099	0.423549	−	0.905873i	$-0.360784\pi$
$181$	11.3965	0.847099	0.423549	+	0.905873i	$0.360784\pi$
$182$	−10.5599	−0.782753
$183$	25.2808	1.86881
$184$	53.6562	3.95559
$185$	0	0
$186$	−7.24833	−0.531473
$187$	−16.8615	−1.23303
$188$	−47.7141	−3.47991
$189$	−6.72711	−0.489325
$190$	0	0
$191$	6.06453	0.438814	0.219407	−	0.975633i	$-0.429588\pi$
$191$	6.06453	0.438814	0.219407	+	0.975633i	$0.429588\pi$
$192$	−107.660	−7.76969
$193$	−19.3484	−1.39273	−0.696366	−	0.717687i	$-0.745201\pi$
$193$	−19.3484	−1.39273	−0.696366	+	0.717687i	$0.745201\pi$
$194$	28.6890	2.05975
$195$	0	0
$196$	18.2016	1.30011
$197$	21.3254	1.51937	0.759685	−	0.650291i	$-0.225353\pi$
$197$	21.3254	1.51937	0.759685	+	0.650291i	$0.225353\pi$
$198$	−35.5143	−2.52389
$199$	−7.63085	−0.540936	−0.270468	−	0.962729i	$-0.587178\pi$
$199$	−7.63085	−0.540936	−0.270468	+	0.962729i	$0.587178\pi$
$200$	0	0
$201$	28.9611	2.04276
$202$	28.4547	2.00206
$203$	−4.75898	−0.334015
$204$	−74.9210	−5.24552
$205$	0	0
$206$	−32.2897	−2.24973
$207$	19.7860	1.37522
$208$	−20.5506	−1.42493
$209$	17.8240	1.23291
$210$	0	0
$211$	−26.0480	−1.79322	−0.896611	−	0.442820i	$-0.853978\pi$
$211$	−26.0480	−1.79322	−0.896611	+	0.442820i	$0.853978\pi$
$212$	−8.57741	−0.589099
$213$	11.8351	0.810930
$214$	−14.1034	−0.964087
$215$	0	0
$216$	−21.7684	−1.48115
$217$	3.19118	0.216632
$218$	−8.56496	−0.580093
$219$	14.8698	1.00481
$220$	0	0
$221$	−5.98258	−0.402432
$222$	−39.9941	−2.68423
$223$	7.16391	0.479731	0.239865	−	0.970806i	$-0.422897\pi$
$223$	7.16391	0.479731	0.239865	+	0.970806i	$0.422897\pi$
$224$	87.0355	5.81530
$225$	0	0
$226$	55.6721	3.70325
$227$	13.9109	0.923299	0.461649	−	0.887062i	$-0.347258\pi$
$227$	13.9109	0.923299	0.461649	+	0.887062i	$0.347258\pi$
$228$	79.1978	5.24500
$229$	−10.7572	−0.710855	−0.355428	−	0.934704i	$-0.615665\pi$
$229$	−10.7572	−0.710855	−0.355428	+	0.934704i	$0.615665\pi$
$230$	0	0
$231$	27.9540	1.83924
$232$	−15.3997	−1.01104
$233$	−10.1804	−0.666937	−0.333468	−	0.942761i	$-0.608219\pi$
$233$	−10.1804	−0.666937	−0.333468	+	0.942761i	$0.608219\pi$
$234$	−12.6008	−0.823738
$235$	0	0
$236$	−4.75092	−0.309259
$237$	−22.8894	−1.48682
$238$	44.5239	2.88605
$239$	15.6571	1.01277	0.506387	−	0.862306i	$-0.330981\pi$
$239$	15.6571	1.01277	0.506387	+	0.862306i	$0.330981\pi$
$240$	0	0
$241$	11.3588	0.731687	0.365844	−	0.930676i	$-0.380780\pi$
$241$	11.3588	0.731687	0.365844	+	0.930676i	$0.380780\pi$
$242$	0.753336	0.0484263
$243$	21.7797	1.39717
$244$	−55.3949	−3.54630
$245$	0	0
$246$	5.12771	0.326931
$247$	6.32409	0.402392
$248$	10.3264	0.655729
$249$	18.9578	1.20140
$250$	0	0
$251$	27.4648	1.73356	0.866781	−	0.498689i	$-0.166185\pi$
$251$	27.4648	1.73356	0.866781	+	0.498689i	$0.166185\pi$
$252$	69.4745	4.37648
$253$	−17.4443	−1.09672
$254$	−42.6378	−2.67534
$255$	0	0
$256$	84.3702	5.27314
$257$	6.22692	0.388424	0.194212	−	0.980960i	$-0.437785\pi$
$257$	6.22692	0.388424	0.194212	+	0.980960i	$0.437785\pi$
$258$	32.4009	2.01719
$259$	17.6080	1.09411
$260$	0	0
$261$	−5.67872	−0.351504
$262$	−14.0081	−0.865423
$263$	−3.62420	−0.223478	−0.111739	−	0.993738i	$-0.535642\pi$
$263$	−3.62420	−0.223478	−0.111739	+	0.993738i	$0.535642\pi$
$264$	90.4570	5.56724
$265$	0	0
$266$	−47.0655	−2.88577
$267$	34.8799	2.13462
$268$	−63.4589	−3.87637
$269$	23.6812	1.44387	0.721935	−	0.691961i	$-0.243253\pi$
$269$	23.6812	1.44387	0.721935	+	0.691961i	$0.243253\pi$
$270$	0	0
$271$	−15.5530	−0.944776	−0.472388	−	0.881391i	$-0.656608\pi$
$271$	−15.5530	−0.944776	−0.472388	+	0.881391i	$0.656608\pi$
$272$	86.6476	5.25378
$273$	9.91829	0.600282
$274$	12.2250	0.738542
$275$	0	0
$276$	−77.5109	−4.66561
$277$	21.4909	1.29127	0.645633	−	0.763648i	$-0.276594\pi$
$277$	21.4909	1.29127	0.645633	+	0.763648i	$0.276594\pi$
$278$	−8.78530	−0.526907
$279$	3.80792	0.227974
$280$	0	0
$281$	−19.7705	−1.17941	−0.589704	−	0.807620i	$-0.700756\pi$
$281$	−19.7705	−1.17941	−0.589704	+	0.807620i	$0.700756\pi$
$282$	60.4922	3.60226
$283$	−17.7784	−1.05682	−0.528408	−	0.848991i	$-0.677211\pi$
$283$	−17.7784	−1.05682	−0.528408	+	0.848991i	$0.677211\pi$
$284$	−25.9329	−1.53884
$285$	0	0
$286$	11.1095	0.656917
$287$	−2.25755	−0.133259
$288$	103.856	6.11979
$289$	8.22441	0.483789
$290$	0	0
$291$	−26.9458	−1.57959
$292$	−32.5825	−1.90674
$293$	−3.97574	−0.232265	−0.116132	−	0.993234i	$-0.537050\pi$
$293$	−3.97574	−0.232265	−0.116132	+	0.993234i	$0.537050\pi$
$294$	−23.0761	−1.34582
$295$	0	0
$296$	56.9781	3.31178
$297$	7.07720	0.410661
$298$	19.6665	1.13925
$299$	−6.18939	−0.357942
$300$	0	0
$301$	−14.2649	−0.822218
$302$	−4.75199	−0.273446
$303$	−26.7258	−1.53536
$304$	−91.5938	−5.25327
$305$	0	0
$306$	53.1287	3.03717
$307$	27.7757	1.58524	0.792622	−	0.609714i	$-0.208716\pi$
$307$	27.7757	1.58524	0.792622	+	0.609714i	$0.208716\pi$
$308$	−61.2522	−3.49017
$309$	30.3277	1.72528
$310$	0	0
$311$	3.70517	0.210101	0.105050	−	0.994467i	$-0.466500\pi$
$311$	3.70517	0.210101	0.105050	+	0.994467i	$0.466500\pi$
$312$	32.0949	1.81701
$313$	−3.42377	−0.193523	−0.0967614	−	0.995308i	$-0.530848\pi$
$313$	−3.42377	−0.193523	−0.0967614	+	0.995308i	$0.530848\pi$
$314$	32.1156	1.81239
$315$	0	0
$316$	50.1548	2.82143
$317$	−24.3820	−1.36943	−0.684715	−	0.728811i	$-0.740073\pi$
$317$	−24.3820	−1.36943	−0.684715	+	0.728811i	$0.740073\pi$
$318$	10.8745	0.609810
$319$	5.00665	0.280318
$320$	0	0
$321$	13.2465	0.739345
$322$	46.0630	2.56699
$323$	−26.6643	−1.48364
$324$	−33.8660	−1.88144
$325$	0	0
$326$	48.1970	2.66939
$327$	8.04456	0.444865
$328$	−7.30525	−0.403365
$329$	−26.6325	−1.46830
$330$	0	0
$331$	−8.78756	−0.483008	−0.241504	−	0.970400i	$-0.577641\pi$
$331$	−8.78756	−0.483008	−0.241504	+	0.970400i	$0.577641\pi$
$332$	−41.5400	−2.27980
$333$	21.0109	1.15139
$334$	7.58952	0.415280
$335$	0	0
$336$	−143.650	−7.83674
$337$	35.5824	1.93830	0.969148	−	0.246478i	$-0.0792734\pi$
$337$	35.5824	1.93830	0.969148	+	0.246478i	$0.0792734\pi$
$338$	−32.1721	−1.74993
$339$	−52.2895	−2.83997
$340$	0	0
$341$	−3.35726	−0.181806
$342$	−56.1615	−3.03687
$343$	−12.1787	−0.657588
$344$	−46.1603	−2.48880
$345$	0	0
$346$	16.0949	0.865269
$347$	−36.0910	−1.93747	−0.968734	−	0.248102i	$-0.920193\pi$
$347$	−36.0910	−1.93747	−0.968734	+	0.248102i	$0.920193\pi$
$348$	22.2462	1.19252
$349$	26.5580	1.42162	0.710810	−	0.703384i	$-0.248329\pi$
$349$	26.5580	1.42162	0.710810	+	0.703384i	$0.248329\pi$
$350$	0	0
$351$	2.51105	0.134030
$352$	−91.5650	−4.88043
$353$	6.87575	0.365959	0.182980	−	0.983117i	$-0.441426\pi$
$353$	6.87575	0.365959	0.182980	+	0.983117i	$0.441426\pi$
$354$	6.02324	0.320132
$355$	0	0
$356$	−76.4283	−4.05069
$357$	−41.8186	−2.21327
$358$	14.5923	0.771229
$359$	29.0331	1.53231	0.766153	−	0.642658i	$-0.222168\pi$
$359$	29.0331	1.53231	0.766153	+	0.642658i	$0.222168\pi$
$360$	0	0
$361$	9.18645	0.483497
$362$	31.6595	1.66399
$363$	−0.707564	−0.0371375
$364$	−21.7328	−1.13911
$365$	0	0
$366$	70.2299	3.67098
$367$	24.1543	1.26084	0.630422	−	0.776253i	$-0.282882\pi$
$367$	24.1543	1.26084	0.630422	+	0.776253i	$0.282882\pi$
$368$	89.6429	4.67296
$369$	−2.69385	−0.140236
$370$	0	0
$371$	−4.78764	−0.248562
$372$	−14.9174	−0.773431
$373$	2.64196	0.136796	0.0683979	−	0.997658i	$-0.478211\pi$
$373$	2.64196	0.136796	0.0683979	+	0.997658i	$0.478211\pi$
$374$	−46.8410	−2.42209
$375$	0	0
$376$	−86.1810	−4.44444
$377$	1.77640	0.0914891
$378$	−18.6878	−0.961199
$379$	−14.6438	−0.752201	−0.376101	−	0.926579i	$-0.622735\pi$
$379$	−14.6438	−0.752201	−0.376101	+	0.926579i	$0.622735\pi$
$380$	0	0
$381$	40.0472	2.05168
$382$	16.8472	0.861978
$383$	−13.9914	−0.714927	−0.357464	−	0.933927i	$-0.616358\pi$
$383$	−13.9914	−0.714927	−0.357464	+	0.933927i	$0.616358\pi$
$384$	−156.753	−7.99928
$385$	0	0
$386$	−53.7498	−2.73579
$387$	−17.0219	−0.865269
$388$	59.0432	2.99747
$389$	1.05263	0.0533705	0.0266852	−	0.999644i	$-0.491505\pi$
$389$	1.05263	0.0533705	0.0266852	+	0.999644i	$0.491505\pi$
$390$	0	0
$391$	26.0964	1.31975
$392$	32.8756	1.66047
$393$	13.1570	0.663681
$394$	59.2417	2.98455
$395$	0	0
$396$	−73.0901	−3.67292
$397$	16.6848	0.837388	0.418694	−	0.908127i	$-0.362488\pi$
$397$	16.6848	0.837388	0.418694	+	0.908127i	$0.362488\pi$
$398$	−21.1984	−1.06258
$399$	44.2058	2.21306
$400$	0	0
$401$	14.1409	0.706161	0.353080	−	0.935593i	$-0.385134\pi$
$401$	14.1409	0.706161	0.353080	+	0.935593i	$0.385134\pi$
$402$	80.4535	4.01266
$403$	−1.19118	−0.0593370
$404$	58.5610	2.91352
$405$	0	0
$406$	−13.2204	−0.656117
$407$	−18.5243	−0.918216
$408$	−135.322	−6.69943
$409$	13.1425	0.649856	0.324928	−	0.945739i	$-0.394660\pi$
$409$	13.1425	0.649856	0.324928	+	0.945739i	$0.394660\pi$
$410$	0	0
$411$	−11.4823	−0.566378
$412$	−66.4536	−3.27393
$413$	−2.65182	−0.130488
$414$	54.9653	2.70140
$415$	0	0
$416$	−32.4880	−1.59286
$417$	8.25150	0.404078
$418$	49.5149	2.42185
$419$	−22.9312	−1.12026	−0.560130	−	0.828404i	$-0.689249\pi$
$419$	−22.9312	−1.12026	−0.560130	+	0.828404i	$0.689249\pi$
$420$	0	0
$421$	5.65061	0.275394	0.137697	−	0.990474i	$-0.456030\pi$
$421$	5.65061	0.275394	0.137697	+	0.990474i	$0.456030\pi$
$422$	−72.3612	−3.52249
$423$	−31.7797	−1.54518
$424$	−15.4925	−0.752381
$425$	0	0
$426$	32.8779	1.59294
$427$	−30.9197	−1.49631
$428$	−29.0254	−1.40299
$429$	−10.4345	−0.503781
$430$	0	0
$431$	6.67802	0.321669	0.160835	−	0.986981i	$-0.448581\pi$
$431$	6.67802	0.321669	0.160835	+	0.986981i	$0.448581\pi$
$432$	−36.3683	−1.74977
$433$	−21.4170	−1.02923	−0.514617	−	0.857420i	$-0.672066\pi$
$433$	−21.4170	−1.02923	−0.514617	+	0.857420i	$0.672066\pi$
$434$	8.86507	0.425537
$435$	0	0
$436$	−17.6271	−0.844184
$437$	−27.5861	−1.31962
$438$	41.3082	1.97378
$439$	−32.2056	−1.53709	−0.768544	−	0.639797i	$-0.779018\pi$
$439$	−32.2056	−1.53709	−0.768544	+	0.639797i	$0.779018\pi$
$440$	0	0
$441$	12.1231	0.577288
$442$	−16.6195	−0.790511
$443$	−21.7717	−1.03440	−0.517202	−	0.855863i	$-0.673026\pi$
$443$	−21.7717	−1.03440	−0.517202	+	0.855863i	$0.673026\pi$
$444$	−82.3096	−3.90624
$445$	0	0
$446$	19.9013	0.942352
$447$	−18.4716	−0.873675
$448$	131.674	6.22099
$449$	−24.4073	−1.15185	−0.575927	−	0.817501i	$-0.695359\pi$
$449$	−24.4073	−1.15185	−0.575927	+	0.817501i	$0.695359\pi$
$450$	0	0
$451$	2.37503	0.111836
$452$	114.576	5.38919
$453$	4.46326	0.209702
$454$	38.6443	1.81367
$455$	0	0
$456$	143.047	6.69877
$457$	−23.0753	−1.07942	−0.539708	−	0.841853i	$-0.681465\pi$
$457$	−23.0753	−1.07942	−0.539708	+	0.841853i	$0.681465\pi$
$458$	−29.8834	−1.39636
$459$	−10.5874	−0.494175
$460$	0	0
$461$	41.0943	1.91395	0.956977	−	0.290163i	$-0.0937097\pi$
$461$	41.0943	1.91395	0.956977	+	0.290163i	$0.0937097\pi$
$462$	77.6559	3.61288
$463$	−5.39931	−0.250927	−0.125464	−	0.992098i	$-0.540042\pi$
$463$	−5.39931	−0.250927	−0.125464	+	0.992098i	$0.540042\pi$
$464$	−25.7281	−1.19440
$465$	0	0
$466$	−28.2809	−1.31009
$467$	13.1326	0.607705	0.303852	−	0.952719i	$-0.401727\pi$
$467$	13.1326	0.607705	0.303852	+	0.952719i	$0.401727\pi$
$468$	−25.9329	−1.19875
$469$	−35.4208	−1.63558
$470$	0	0
$471$	−30.1642	−1.38989
$472$	−8.58109	−0.394977
$473$	15.0073	0.690038
$474$	−63.5864	−2.92062
$475$	0	0
$476$	91.6321	4.19995
$477$	−5.71292	−0.261577
$478$	43.4953	1.98943
$479$	25.0400	1.14411	0.572053	−	0.820217i	$-0.306147\pi$
$479$	25.0400	1.14411	0.572053	+	0.820217i	$0.306147\pi$
$480$	0	0
$481$	−6.57257	−0.299684
$482$	31.5548	1.43728
$483$	−43.2642	−1.96859
$484$	1.55040	0.0704727
$485$	0	0
$486$	60.5037	2.74450
$487$	−27.6734	−1.25400	−0.627001	−	0.779019i	$-0.715718\pi$
$487$	−27.6734	−1.25400	−0.627001	+	0.779019i	$0.715718\pi$
$488$	−100.054	−4.52923
$489$	−45.2686	−2.04712
$490$	0	0
$491$	29.6311	1.33723	0.668617	−	0.743607i	$-0.266887\pi$
$491$	29.6311	1.33723	0.668617	+	0.743607i	$0.266887\pi$
$492$	10.5531	0.475768
$493$	−7.48984	−0.337325
$494$	17.5683	0.790434
$495$	0	0
$496$	17.2523	0.774649
$497$	−14.4750	−0.649291
$498$	52.6646	2.35996
$499$	−29.5793	−1.32415	−0.662076	−	0.749437i	$-0.730324\pi$
$499$	−29.5793	−1.32415	−0.662076	+	0.749437i	$0.730324\pi$
$500$	0	0
$501$	−7.12838	−0.318472
$502$	76.2969	3.40530
$503$	34.7648	1.55009	0.775044	−	0.631907i	$-0.217728\pi$
$503$	34.7648	1.55009	0.775044	+	0.631907i	$0.217728\pi$
$504$	125.484	5.58952
$505$	0	0
$506$	−48.4602	−2.15432
$507$	30.2174	1.34200
$508$	−87.7506	−3.89330
$509$	−17.3248	−0.767908	−0.383954	−	0.923352i	$-0.625438\pi$
$509$	−17.3248	−0.767908	−0.383954	+	0.923352i	$0.625438\pi$
$510$	0	0
$511$	−18.1865	−0.804525
$512$	114.225	5.04810
$513$	11.1917	0.494127
$514$	17.2983	0.762996
$515$	0	0
$516$	66.6825	2.93553
$517$	28.0186	1.23225
$518$	48.9147	2.14919
$519$	−15.1170	−0.663563
$520$	0	0
$521$	−9.15645	−0.401151	−0.200576	−	0.979678i	$-0.564281\pi$
$521$	−9.15645	−0.401151	−0.200576	+	0.979678i	$0.564281\pi$
$522$	−15.7754	−0.690471
$523$	2.52071	0.110223	0.0551116	−	0.998480i	$-0.482449\pi$
$523$	2.52071	0.110223	0.0551116	+	0.998480i	$0.482449\pi$
$524$	−28.8293	−1.25941
$525$	0	0
$526$	−10.0680	−0.438985
$527$	5.02239	0.218779
$528$	151.126	6.57690
$529$	3.99850	0.173848
$530$	0	0
$531$	−3.16432	−0.137320
$532$	−96.8629	−4.19954
$533$	0.842681	0.0365006
$534$	96.8961	4.19311
$535$	0	0
$536$	−114.619	−4.95079
$537$	−13.7057	−0.591445
$538$	65.7862	2.83625
$539$	−10.6883	−0.460378
$540$	0	0
$541$	13.9861	0.601308	0.300654	−	0.953733i	$-0.402795\pi$
$541$	13.9861	0.601308	0.300654	+	0.953733i	$0.402795\pi$
$542$	−43.2060	−1.85586
$543$	−29.7359	−1.27609
$544$	136.979	5.87295
$545$	0	0
$546$	27.5529	1.17916
$547$	40.0333	1.71170	0.855850	−	0.517224i	$-0.173035\pi$
$547$	40.0333	1.71170	0.855850	+	0.517224i	$0.173035\pi$
$548$	25.1597	1.07477
$549$	−36.8954	−1.57466
$550$	0	0
$551$	7.91739	0.337292
$552$	−140.000	−5.95879
$553$	27.9948	1.19046
$554$	59.7016	2.53648
$555$	0	0
$556$	−18.0805	−0.766786
$557$	26.5806	1.12626	0.563128	−	0.826370i	$-0.309598\pi$
$557$	26.5806	1.12626	0.563128	+	0.826370i	$0.309598\pi$
$558$	10.5784	0.447818
$559$	5.32472	0.225212
$560$	0	0
$561$	43.9949	1.85747
$562$	−54.9222	−2.31675
$563$	27.1232	1.14310	0.571552	−	0.820566i	$-0.306341\pi$
$563$	27.1232	1.14310	0.571552	+	0.820566i	$0.306341\pi$
$564$	124.496	5.24221
$565$	0	0
$566$	−49.3882	−2.07594
$567$	−18.9029	−0.793849
$568$	−46.8399	−1.96536
$569$	−10.8914	−0.456593	−0.228296	−	0.973592i	$-0.573316\pi$
$569$	−10.8914	−0.456593	−0.228296	+	0.973592i	$0.573316\pi$
$570$	0	0
$571$	−19.9840	−0.836306	−0.418153	−	0.908377i	$-0.637322\pi$
$571$	−19.9840	−0.836306	−0.418153	+	0.908377i	$0.637322\pi$
$572$	22.8638	0.955983
$573$	−15.8236	−0.661039
$574$	−6.27144	−0.261765
$575$	0	0
$576$	157.121	6.54672
$577$	−9.85602	−0.410312	−0.205156	−	0.978729i	$-0.565770\pi$
$577$	−9.85602	−0.410312	−0.205156	+	0.978729i	$0.565770\pi$
$578$	22.8473	0.950324
$579$	50.4840	2.09804
$580$	0	0
$581$	−23.1863	−0.961931
$582$	−74.8553	−3.10285
$583$	5.03680	0.208603
$584$	−58.8503	−2.43524
$585$	0	0
$586$	−11.0446	−0.456246
$587$	−9.32567	−0.384912	−0.192456	−	0.981306i	$-0.561645\pi$
$587$	−9.32567	−0.384912	−0.192456	+	0.981306i	$0.561645\pi$
$588$	−47.4916	−1.95852
$589$	−5.30909	−0.218757
$590$	0	0
$591$	−55.6422	−2.28881
$592$	95.1927	3.91240
$593$	20.9174	0.858975	0.429487	−	0.903073i	$-0.358694\pi$
$593$	20.9174	0.858975	0.429487	+	0.903073i	$0.358694\pi$
$594$	19.6604	0.806676
$595$	0	0
$596$	40.4745	1.65790
$597$	19.9104	0.814878
$598$	−17.1941	−0.703118
$599$	−0.703114	−0.0287285	−0.0143642	−	0.999897i	$-0.504572\pi$
$599$	−0.703114	−0.0287285	−0.0143642	+	0.999897i	$0.504572\pi$
$600$	0	0
$601$	−11.8938	−0.485158	−0.242579	−	0.970132i	$-0.577993\pi$
$601$	−11.8938	−0.485158	−0.242579	+	0.970132i	$0.577993\pi$
$602$	−39.6279	−1.61511
$603$	−42.2664	−1.72122
$604$	−9.77981	−0.397935
$605$	0	0
$606$	−74.2439	−3.01595
$607$	−2.61874	−0.106292	−0.0531458	−	0.998587i	$-0.516925\pi$
$607$	−2.61874	−0.106292	−0.0531458	+	0.998587i	$0.516925\pi$
$608$	−144.799	−5.87237
$609$	12.4171	0.503167
$610$	0	0
$611$	9.94121	0.402178
$612$	109.341	4.41986
$613$	−2.46746	−0.0996598	−0.0498299	−	0.998758i	$-0.515868\pi$
$613$	−2.46746	−0.0996598	−0.0498299	+	0.998758i	$0.515868\pi$
$614$	77.1606	3.11395
$615$	0	0
$616$	−110.633	−4.45755
$617$	16.0271	0.645225	0.322613	−	0.946531i	$-0.395439\pi$
$617$	16.0271	0.645225	0.322613	+	0.946531i	$0.395439\pi$
$618$	84.2502	3.38904
$619$	9.96434	0.400501	0.200250	−	0.979745i	$-0.435824\pi$
$619$	9.96434	0.400501	0.200250	+	0.979745i	$0.435824\pi$
$620$	0	0
$621$	−10.9533	−0.439543
$622$	10.2929	0.412709
$623$	−42.6599	−1.70913
$624$	53.6206	2.14654
$625$	0	0
$626$	−9.51119	−0.380144
$627$	−46.5063	−1.85728
$628$	66.0953	2.63749
$629$	27.7120	1.10495
$630$	0	0
$631$	11.7749	0.468750	0.234375	−	0.972146i	$-0.424696\pi$
$631$	11.7749	0.468750	0.234375	+	0.972146i	$0.424696\pi$
$632$	90.5892	3.60345
$633$	67.9645	2.70135
$634$	−67.7330	−2.69002
$635$	0	0
$636$	22.3802	0.887431
$637$	−3.79229	−0.150256
$638$	13.9084	0.550639
$639$	−17.2725	−0.683288
$640$	0	0
$641$	−26.2117	−1.03530	−0.517650	−	0.855592i	$-0.673193\pi$
$641$	−26.2117	−1.03530	−0.517650	+	0.855592i	$0.673193\pi$
$642$	36.7985	1.45232
$643$	−3.32247	−0.131026	−0.0655128	−	0.997852i	$-0.520868\pi$
$643$	−3.32247	−0.131026	−0.0655128	+	0.997852i	$0.520868\pi$
$644$	94.7997	3.73563
$645$	0	0
$646$	−74.0733	−2.91437
$647$	−39.2327	−1.54240	−0.771198	−	0.636596i	$-0.780342\pi$
$647$	−39.2327	−1.54240	−0.771198	+	0.636596i	$0.780342\pi$
$648$	−61.1685	−2.40293
$649$	2.78983	0.109510
$650$	0	0
$651$	−8.32643	−0.326339
$652$	99.1917	3.88464
$653$	45.6087	1.78481	0.892403	−	0.451240i	$-0.149018\pi$
$653$	45.6087	1.78481	0.892403	+	0.451240i	$0.149018\pi$
$654$	22.3477	0.873864
$655$	0	0
$656$	−12.2048	−0.476518
$657$	−21.7013	−0.846650
$658$	−73.9850	−2.88423
$659$	−34.5552	−1.34608	−0.673040	−	0.739606i	$-0.735012\pi$
$659$	−34.5552	−1.34608	−0.673040	+	0.739606i	$0.735012\pi$
$660$	0	0
$661$	10.7019	0.416257	0.208129	−	0.978101i	$-0.433263\pi$
$661$	10.7019	0.416257	0.208129	+	0.978101i	$0.433263\pi$
$662$	−24.4117	−0.948789
$663$	15.6097	0.606232
$664$	−75.0293	−2.91170
$665$	0	0
$666$	58.3682	2.26172
$667$	−7.74876	−0.300033
$668$	15.6196	0.604339
$669$	−18.6921	−0.722677
$670$	0	0
$671$	32.5289	1.25576
$672$	−227.093	−8.76030
$673$	1.33908	0.0516177	0.0258088	−	0.999667i	$-0.491784\pi$
$673$	1.33908	0.0516177	0.0258088	+	0.999667i	$0.491784\pi$
$674$	98.8476	3.80747
$675$	0	0
$676$	−66.2117	−2.54661
$677$	−12.5652	−0.482919	−0.241459	−	0.970411i	$-0.577626\pi$
$677$	−12.5652	−0.482919	−0.241459	+	0.970411i	$0.577626\pi$
$678$	−145.260	−5.57866
$679$	32.9561	1.26474
$680$	0	0
$681$	−36.2963	−1.39088
$682$	−9.32643	−0.357127
$683$	−15.5212	−0.593904	−0.296952	−	0.954892i	$-0.595970\pi$
$683$	−15.5212	−0.593904	−0.296952	+	0.954892i	$0.595970\pi$
$684$	−115.583	−4.41943
$685$	0	0
$686$	−33.8323	−1.29172
$687$	28.0677	1.07085
$688$	−77.1196	−2.94016
$689$	1.78710	0.0680830
$690$	0	0
$691$	41.0105	1.56011	0.780057	−	0.625708i	$-0.215190\pi$
$691$	41.0105	1.56011	0.780057	+	0.625708i	$0.215190\pi$
$692$	33.1241	1.25919
$693$	−40.7966	−1.54974
$694$	−100.261	−3.80584
$695$	0	0
$696$	40.1809	1.52305
$697$	−3.55300	−0.134580
$698$	73.7780	2.79254
$699$	26.5626	1.00469
$700$	0	0
$701$	10.9024	0.411777	0.205888	−	0.978575i	$-0.433992\pi$
$701$	10.9024	0.411777	0.205888	+	0.978575i	$0.433992\pi$
$702$	6.97567	0.263280
$703$	−29.2939	−1.10484
$704$	−138.526	−5.22090
$705$	0	0
$706$	19.1008	0.718867
$707$	32.6870	1.22932
$708$	12.3961	0.465874
$709$	−26.2569	−0.986099	−0.493050	−	0.870001i	$-0.664118\pi$
$709$	−26.2569	−0.986099	−0.493050	+	0.870001i	$0.664118\pi$
$710$	0	0
$711$	33.4052	1.25279
$712$	−138.044	−5.17343
$713$	5.19601	0.194592
$714$	−116.172	−4.34761
$715$	0	0
$716$	30.0317	1.12234
$717$	−40.8525	−1.52566
$718$	80.6535	3.00996
$719$	43.0645	1.60603	0.803017	−	0.595956i	$-0.203227\pi$
$719$	43.0645	1.60603	0.803017	+	0.595956i	$0.203227\pi$
$720$	0	0
$721$	−37.0923	−1.38139
$722$	25.5199	0.949751
$723$	−29.6375	−1.10223
$724$	65.1567	2.42153
$725$	0	0
$726$	−1.96560	−0.0729504
$727$	−21.9542	−0.814236	−0.407118	−	0.913376i	$-0.633466\pi$
$727$	−21.9542	−0.814236	−0.407118	+	0.913376i	$0.633466\pi$
$728$	−39.2536	−1.45484
$729$	−39.0570	−1.44656
$730$	0	0
$731$	−22.4507	−0.830368
$732$	144.536	5.34222
$733$	53.7742	1.98620	0.993098	−	0.117284i	$-0.0374188\pi$
$733$	53.7742	1.98620	0.993098	+	0.117284i	$0.0374188\pi$
$734$	67.1004	2.47672
$735$	0	0
$736$	141.715	5.22367
$737$	37.2642	1.37264
$738$	−7.48349	−0.275471
$739$	13.8724	0.510306	0.255153	−	0.966901i	$-0.417874\pi$
$739$	13.8724	0.510306	0.255153	+	0.966901i	$0.417874\pi$
$740$	0	0
$741$	−16.5008	−0.606173
$742$	−13.3000	−0.488259
$743$	48.9020	1.79404	0.897020	−	0.441989i	$-0.145727\pi$
$743$	48.9020	1.79404	0.897020	+	0.441989i	$0.145727\pi$
$744$	−26.9437	−0.987805
$745$	0	0
$746$	7.33935	0.268713
$747$	−27.6674	−1.01230
$748$	−96.4009	−3.52476
$749$	−16.2011	−0.591974
$750$	0	0
$751$	2.81020	0.102546	0.0512729	−	0.998685i	$-0.483672\pi$
$751$	2.81020	0.102546	0.0512729	+	0.998685i	$0.483672\pi$
$752$	−143.982	−5.25047
$753$	−71.6611	−2.61148
$754$	4.93481	0.179715
$755$	0	0
$756$	−38.4604	−1.39879
$757$	42.5260	1.54563	0.772817	−	0.634629i	$-0.218847\pi$
$757$	42.5260	1.54563	0.772817	+	0.634629i	$0.218847\pi$
$758$	−40.6803	−1.47758
$759$	45.5158	1.65212
$760$	0	0
$761$	3.71370	0.134622	0.0673108	−	0.997732i	$-0.478558\pi$
$761$	3.71370	0.134622	0.0673108	+	0.997732i	$0.478558\pi$
$762$	111.251	4.03018
$763$	−9.83889	−0.356192
$764$	34.6723	1.25440
$765$	0	0
$766$	−38.8680	−1.40436
$767$	0.989852	0.0357415
$768$	−220.139	−7.94357
$769$	6.16375	0.222270	0.111135	−	0.993805i	$-0.464551\pi$
$769$	6.16375	0.222270	0.111135	+	0.993805i	$0.464551\pi$
$770$	0	0
$771$	−16.2473	−0.585131
$772$	−110.620	−3.98128
$773$	−10.3694	−0.372960	−0.186480	−	0.982459i	$-0.559708\pi$
$773$	−10.3694	−0.372960	−0.186480	+	0.982459i	$0.559708\pi$
$774$	−47.2865	−1.69968
$775$	0	0
$776$	106.644	3.82828
$777$	−45.9427	−1.64818
$778$	2.92420	0.104837
$779$	3.75583	0.134566
$780$	0	0
$781$	15.2283	0.544911
$782$	72.4955	2.59243
$783$	3.14369	0.112346
$784$	54.9250	1.96161
$785$	0	0
$786$	36.5499	1.30369
$787$	36.1061	1.28704	0.643522	−	0.765428i	$-0.277473\pi$
$787$	36.1061	1.28704	0.643522	+	0.765428i	$0.277473\pi$
$788$	121.922	4.34330
$789$	9.45626	0.336652
$790$	0	0
$791$	63.9526	2.27389
$792$	−132.015	−4.69095
$793$	11.5415	0.409851
$794$	46.3503	1.64491
$795$	0	0
$796$	−43.6273	−1.54633
$797$	40.4141	1.43154	0.715770	−	0.698336i	$-0.246076\pi$
$797$	40.4141	1.43154	0.715770	+	0.698336i	$0.246076\pi$
$798$	122.803	4.34719
$799$	−41.9152	−1.48285
$800$	0	0
$801$	−50.9045	−1.79862
$802$	39.2832	1.38714
$803$	19.1330	0.675189
$804$	165.577	5.83945
$805$	0	0
$806$	−3.30909	−0.116558
$807$	−61.7891	−2.17508
$808$	105.773	3.72107
$809$	−29.4474	−1.03532	−0.517658	−	0.855588i	$-0.673196\pi$
$809$	−29.4474	−1.03532	−0.517658	+	0.855588i	$0.673196\pi$
$810$	0	0
$811$	−38.1714	−1.34038	−0.670189	−	0.742190i	$-0.733787\pi$
$811$	−38.1714	−1.34038	−0.670189	+	0.742190i	$0.733787\pi$
$812$	−27.2082	−0.954820
$813$	40.5808	1.42323
$814$	−51.4604	−1.80369
$815$	0	0
$816$	−226.081	−7.91441
$817$	23.7322	0.830286
$818$	36.5098	1.27654
$819$	−14.4750	−0.505796
$820$	0	0
$821$	24.1008	0.841123	0.420561	−	0.907264i	$-0.361833\pi$
$821$	24.1008	0.841123	0.420561	+	0.907264i	$0.361833\pi$
$822$	−31.8976	−1.11256
$823$	−25.0974	−0.874841	−0.437421	−	0.899257i	$-0.644108\pi$
$823$	−25.0974	−0.874841	−0.437421	+	0.899257i	$0.644108\pi$
$824$	−120.028	−4.18138
$825$	0	0
$826$	−7.36673	−0.256321
$827$	24.2885	0.844593	0.422297	−	0.906458i	$-0.361224\pi$
$827$	24.2885	0.844593	0.422297	+	0.906458i	$0.361224\pi$
$828$	113.121	3.93123
$829$	−56.3057	−1.95558	−0.977788	−	0.209595i	$-0.932786\pi$
$829$	−56.3057	−1.95558	−0.977788	+	0.209595i	$0.932786\pi$
$830$	0	0
$831$	−56.0742	−1.94519
$832$	−49.1502	−1.70398
$833$	15.9895	0.554003
$834$	22.9226	0.793745
$835$	0	0
$836$	101.904	3.52442
$837$	−2.10803	−0.0728642
$838$	−63.7026	−2.20057
$839$	20.3241	0.701666	0.350833	−	0.936438i	$-0.385898\pi$
$839$	20.3241	0.701666	0.350833	+	0.936438i	$0.385898\pi$
$840$	0	0
$841$	−26.7761	−0.923312
$842$	15.6973	0.540966
$843$	51.5851	1.77669
$844$	−148.923	−5.12613
$845$	0	0
$846$	−88.2836	−3.03525
$847$	0.865386	0.0297350
$848$	−25.8831	−0.888829
$849$	46.3874	1.59201
$850$	0	0
$851$	28.6700	0.982794
$852$	67.6642	2.31814
$853$	−15.9337	−0.545559	−0.272779	−	0.962077i	$-0.587943\pi$
$853$	−15.9337	−0.545559	−0.272779	+	0.962077i	$0.587943\pi$
$854$	−85.8947	−2.93926
$855$	0	0
$856$	−52.4255	−1.79187
$857$	−12.0574	−0.411872	−0.205936	−	0.978565i	$-0.566024\pi$
$857$	−12.0574	−0.411872	−0.205936	+	0.978565i	$0.566024\pi$
$858$	−28.9868	−0.989594
$859$	−42.7955	−1.46017	−0.730083	−	0.683359i	$-0.760518\pi$
$859$	−42.7955	−1.46017	−0.730083	+	0.683359i	$0.760518\pi$
$860$	0	0
$861$	5.89039	0.200744
$862$	18.5515	0.631866
$863$	6.38290	0.217276	0.108638	−	0.994081i	$-0.465351\pi$
$863$	6.38290	0.217276	0.108638	+	0.994081i	$0.465351\pi$
$864$	−57.4939	−1.95598
$865$	0	0
$866$	−59.4962	−2.02176
$867$	−21.4591	−0.728790
$868$	18.2447	0.619266
$869$	−29.4517	−0.999082
$870$	0	0
$871$	13.2216	0.447998
$872$	−31.8379	−1.07817
$873$	39.3253	1.33096
$874$	−76.6339	−2.59218
$875$	0	0
$876$	85.0142	2.87236
$877$	−39.0506	−1.31865	−0.659323	−	0.751860i	$-0.729157\pi$
$877$	−39.0506	−1.31865	−0.659323	+	0.751860i	$0.729157\pi$
$878$	−89.4667	−3.01936
$879$	10.3735	0.349889
$880$	0	0
$881$	−53.3955	−1.79894	−0.899471	−	0.436981i	$-0.856048\pi$
$881$	−53.3955	−1.79894	−0.899471	+	0.436981i	$0.856048\pi$
$882$	33.6777	1.13399
$883$	−5.54925	−0.186747	−0.0933736	−	0.995631i	$-0.529765\pi$
$883$	−5.54925	−0.186747	−0.0933736	+	0.995631i	$0.529765\pi$
$884$	−34.2038	−1.15040
$885$	0	0
$886$	−60.4816	−2.03192
$887$	−2.10386	−0.0706407	−0.0353204	−	0.999376i	$-0.511245\pi$
$887$	−2.10386	−0.0706407	−0.0353204	+	0.999376i	$0.511245\pi$
$888$	−148.667	−4.98894
$889$	−48.9797	−1.64273
$890$	0	0
$891$	19.8867	0.666229
$892$	40.9577	1.37137
$893$	44.3079	1.48271
$894$	−51.3138	−1.71619
$895$	0	0
$896$	191.717	6.40482
$897$	16.1494	0.539211
$898$	−67.8033	−2.26263
$899$	−1.49129	−0.0497373
$900$	0	0
$901$	−7.53496	−0.251026
$902$	6.59782	0.219683
$903$	37.2201	1.23861
$904$	206.946	6.88292
$905$	0	0
$906$	12.3989	0.411925
$907$	−11.5899	−0.384835	−0.192417	−	0.981313i	$-0.561633\pi$
$907$	−11.5899	−0.384835	−0.192417	+	0.981313i	$0.561633\pi$
$908$	79.5318	2.63936
$909$	39.0042	1.29369
$910$	0	0
$911$	3.29305	0.109104	0.0545518	−	0.998511i	$-0.482627\pi$
$911$	3.29305	0.109104	0.0545518	+	0.998511i	$0.482627\pi$
$912$	238.987	7.91364
$913$	24.3930	0.807290
$914$	−64.1028	−2.12033
$915$	0	0
$916$	−61.5013	−2.03206
$917$	−16.0916	−0.531392
$918$	−29.4116	−0.970726
$919$	−25.3918	−0.837598	−0.418799	−	0.908079i	$-0.637549\pi$
$919$	−25.3918	−0.837598	−0.418799	+	0.908079i	$0.637549\pi$
$920$	0	0
$921$	−72.4724	−2.38805
$922$	114.160	3.75965
$923$	5.40311	0.177846
$924$	159.819	5.25767
$925$	0	0
$926$	−14.9992	−0.492905
$927$	−44.2610	−1.45372
$928$	−40.6731	−1.33516
$929$	27.3497	0.897313	0.448657	−	0.893704i	$-0.351903\pi$
$929$	27.3497	0.897313	0.448657	+	0.893704i	$0.351903\pi$
$930$	0	0
$931$	−16.9022	−0.553948
$932$	−58.2034	−1.90652
$933$	−9.66753	−0.316501
$934$	36.4823	1.19374
$935$	0	0
$936$	−46.8399	−1.53101
$937$	−46.6566	−1.52420	−0.762102	−	0.647457i	$-0.775833\pi$
$937$	−46.6566	−1.52420	−0.762102	+	0.647457i	$0.775833\pi$
$938$	−98.3987	−3.21283
$939$	8.93329	0.291527
$940$	0	0
$941$	−51.0338	−1.66366	−0.831828	−	0.555034i	$-0.812705\pi$
$941$	−51.0338	−1.66366	−0.831828	+	0.555034i	$0.812705\pi$
$942$	−83.7960	−2.73022
$943$	−3.67583	−0.119701
$944$	−14.3363	−0.466608
$945$	0	0
$946$	41.6902	1.35547
$947$	22.3659	0.726795	0.363398	−	0.931634i	$-0.381617\pi$
$947$	22.3659	0.726795	0.363398	+	0.931634i	$0.381617\pi$
$948$	−130.864	−4.25026
$949$	6.78854	0.220365
$950$	0	0
$951$	63.6175	2.06294
$952$	165.505	5.36406
$953$	−20.0703	−0.650141	−0.325070	−	0.945690i	$-0.605388\pi$
$953$	−20.0703	−0.650141	−0.325070	+	0.945690i	$0.605388\pi$
$954$	−15.8704	−0.513825
$955$	0	0
$956$	89.5152	2.89513
$957$	−13.0633	−0.422278
$958$	69.5608	2.24741
$959$	14.0434	0.453484
$960$	0	0
$961$	1.00000	0.0322581
$962$	−18.2585	−0.588679
$963$	−19.3322	−0.622970
$964$	64.9411	2.09161
$965$	0	0
$966$	−120.188	−3.86697
$967$	33.9313	1.09116	0.545578	−	0.838060i	$-0.316310\pi$
$967$	33.9313	1.09116	0.545578	+	0.838060i	$0.316310\pi$
$968$	2.80032	0.0900058
$969$	69.5726	2.23499
$970$	0	0
$971$	39.5272	1.26849	0.634244	−	0.773133i	$-0.281311\pi$
$971$	39.5272	1.26849	0.634244	+	0.773133i	$0.281311\pi$
$972$	124.519	3.99396
$973$	−10.0920	−0.323535
$974$	−76.8764	−2.46328
$975$	0	0
$976$	−167.159	−5.35064
$977$	−39.6785	−1.26943	−0.634714	−	0.772747i	$-0.718882\pi$
$977$	−39.6785	−1.26943	−0.634714	+	0.772747i	$0.718882\pi$
$978$	−125.756	−4.02122
$979$	44.8800	1.43437
$980$	0	0
$981$	−11.7404	−0.374842
$982$	82.3150	2.62678
$983$	−10.5874	−0.337687	−0.168844	−	0.985643i	$-0.554003\pi$
$983$	−10.5874	−0.337687	−0.168844	+	0.985643i	$0.554003\pi$
$984$	19.0609	0.607638
$985$	0	0
$986$	−20.8067	−0.662621
$987$	69.4896	2.21188
$988$	36.1563	1.15028
$989$	−23.2268	−0.738568
$990$	0	0
$991$	39.8120	1.26467	0.632335	−	0.774695i	$-0.282096\pi$
$991$	39.8120	1.26467	0.632335	+	0.774695i	$0.282096\pi$
$992$	27.2738	0.865943
$993$	22.9285	0.727614
$994$	−40.2113	−1.27543
$995$	0	0
$996$	108.386	3.43434
$997$	−5.51347	−0.174613	−0.0873066	−	0.996181i	$-0.527826\pi$
$997$	−5.51347	−0.174613	−0.0873066	+	0.996181i	$0.527826\pi$
$998$	−82.1711	−2.60108
$999$	−11.6315	−0.368003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.j.1.5	yes	5
3.2	odd	2		6975.2.a.bq.1.1		5
5.2	odd	4		775.2.b.h.249.10		10
5.3	odd	4		775.2.b.h.249.1		10
5.4	even	2		775.2.a.i.1.1	✓	5
15.14	odd	2		6975.2.a.bx.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.a.i.1.1	✓	5	5.4	even	2
775.2.a.j.1.5	yes	5	1.1	even	1	trivial
775.2.b.h.249.1		10	5.3	odd	4
775.2.b.h.249.10		10	5.2	odd	4
6975.2.a.bq.1.1		5	3.2	odd	2
6975.2.a.bx.1.5		5	15.14	odd	2

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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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q+2.77799 q^{2} -2.60920 q^{3} +5.71723 q^{4} -7.24833 q^{6} +3.19118 q^{7} +10.3264 q^{8} +3.80792 q^{9} +O(q^{10})\)	\(q+2.77799 q^{2} -2.60920 q^{3} +5.71723 q^{4} -7.24833 q^{6} +3.19118 q^{7} +10.3264 q^{8} +3.80792 q^{9} -3.35726 q^{11} -14.9174 q^{12} -1.19118 q^{13} +8.86507 q^{14} +17.2523 q^{16} +5.02239 q^{17} +10.5784 q^{18} -5.30909 q^{19} -8.32643 q^{21} -9.32643 q^{22} +5.19601 q^{23} -26.9437 q^{24} -3.30909 q^{26} -2.10803 q^{27} +18.2447 q^{28} -1.49129 q^{29} +1.00000 q^{31} +27.2738 q^{32} +8.75976 q^{33} +13.9522 q^{34} +21.7708 q^{36} +5.51769 q^{37} -14.7486 q^{38} +3.10803 q^{39} -0.707433 q^{41} -23.1307 q^{42} -4.47012 q^{43} -19.1942 q^{44} +14.4345 q^{46} -8.34567 q^{47} -45.0146 q^{48} +3.18364 q^{49} -13.1044 q^{51} -6.81026 q^{52} -1.50027 q^{53} -5.85609 q^{54} +32.9535 q^{56} +13.8525 q^{57} -4.14279 q^{58} -0.830984 q^{59} -9.68912 q^{61} +2.77799 q^{62} +12.1518 q^{63} +41.2617 q^{64} +24.3345 q^{66} -11.0996 q^{67} +28.7142 q^{68} -13.5574 q^{69} -4.53593 q^{71} +39.3222 q^{72} -5.69900 q^{73} +15.3281 q^{74} -30.3533 q^{76} -10.7136 q^{77} +8.63408 q^{78} +8.77256 q^{79} -5.92349 q^{81} -1.96524 q^{82} -7.26575 q^{83} -47.6041 q^{84} -12.4179 q^{86} +3.89107 q^{87} -34.6685 q^{88} -13.3681 q^{89} -3.80128 q^{91} +29.7068 q^{92} -2.60920 q^{93} -23.1842 q^{94} -71.1627 q^{96} +10.3272 q^{97} +8.84412 q^{98} -12.7842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 4 q^{2} + q^{3} + 6 q^{4} - q^{6} + 6 q^{7} + 15 q^{8} + 2 q^{9}+O(q^{10}) \) 5 * q + 4 * q^2 + q^3 + 6 * q^4 - q^6 + 6 * q^7 + 15 * q^8 + 2 * q^9	\( 5 q + 4 q^{2} + q^{3} + 6 q^{4} - q^{6} + 6 q^{7} + 15 q^{8} + 2 q^{9} - 11 q^{12} + 4 q^{13} + 2 q^{14} + 20 q^{16} + 11 q^{17} + 19 q^{18} - 4 q^{19} - 5 q^{21} - 10 q^{22} + 12 q^{23} - 26 q^{24} + 6 q^{26} - 2 q^{27} + 18 q^{28} - 6 q^{29} + 5 q^{31} + 29 q^{32} + 21 q^{33} - 5 q^{34} + 23 q^{36} - 2 q^{37} - 6 q^{38} + 7 q^{39} - 2 q^{41} - 24 q^{42} + 7 q^{43} - 28 q^{44} + 27 q^{46} + 8 q^{47} - 39 q^{48} - q^{49} - 19 q^{51} - 6 q^{52} + 25 q^{53} - 18 q^{54} + 35 q^{56} + 20 q^{57} - q^{58} + 4 q^{59} - 17 q^{61} + 4 q^{62} + 10 q^{63} + 27 q^{64} + 27 q^{66} - 13 q^{67} + 18 q^{68} - 10 q^{69} - 6 q^{71} + 26 q^{72} + 7 q^{73} + 6 q^{74} - 5 q^{76} + 7 q^{77} + 22 q^{78} + 12 q^{79} - 11 q^{81} - 21 q^{82} - 4 q^{83} - 63 q^{84} - 41 q^{86} + q^{87} - 49 q^{88} - 3 q^{89} - 22 q^{91} + 34 q^{92} + q^{93} - 34 q^{94} - 64 q^{96} + 25 q^{97} - 22 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + 4 * q^2 + q^3 + 6 * q^4 - q^6 + 6 * q^7 + 15 * q^8 + 2 * q^9 - 11 * q^12 + 4 * q^13 + 2 * q^14 + 20 * q^16 + 11 * q^17 + 19 * q^18 - 4 * q^19 - 5 * q^21 - 10 * q^22 + 12 * q^23 - 26 * q^24 + 6 * q^26 - 2 * q^27 + 18 * q^28 - 6 * q^29 + 5 * q^31 + 29 * q^32 + 21 * q^33 - 5 * q^34 + 23 * q^36 - 2 * q^37 - 6 * q^38 + 7 * q^39 - 2 * q^41 - 24 * q^42 + 7 * q^43 - 28 * q^44 + 27 * q^46 + 8 * q^47 - 39 * q^48 - q^49 - 19 * q^51 - 6 * q^52 + 25 * q^53 - 18 * q^54 + 35 * q^56 + 20 * q^57 - q^58 + 4 * q^59 - 17 * q^61 + 4 * q^62 + 10 * q^63 + 27 * q^64 + 27 * q^66 - 13 * q^67 + 18 * q^68 - 10 * q^69 - 6 * q^71 + 26 * q^72 + 7 * q^73 + 6 * q^74 - 5 * q^76 + 7 * q^77 + 22 * q^78 + 12 * q^79 - 11 * q^81 - 21 * q^82 - 4 * q^83 - 63 * q^84 - 41 * q^86 + q^87 - 49 * q^88 - 3 * q^89 - 22 * q^91 + 34 * q^92 + q^93 - 34 * q^94 - 64 * q^96 + 25 * q^97 - 22 * q^98 + 5 * q^99

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