LMFDB - Embedded newform 525.4.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{41}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 10 $ x^2 - x - 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.70156$ of defining polynomial
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.70156 q^{2} -3.00000 q^{3} +14.1047 q^{4} +14.1047 q^{6} -7.00000 q^{7} -28.7016 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.70156 q^{2} -3.00000 q^{3} +14.1047 q^{4} +14.1047 q^{6} -7.00000 q^{7} -28.7016 q^{8} +9.00000 q^{9} +24.5969 q^{11} -42.3141 q^{12} +35.0156 q^{13} +32.9109 q^{14} +22.1047 q^{16} +18.4187 q^{17} -42.3141 q^{18} -67.4031 q^{19} +21.0000 q^{21} -115.644 q^{22} +145.675 q^{23} +86.1047 q^{24} -164.628 q^{26} -27.0000 q^{27} -98.7328 q^{28} +214.419 q^{29} -88.6594 q^{31} +125.686 q^{32} -73.7906 q^{33} -86.5969 q^{34} +126.942 q^{36} -162.125 q^{37} +316.900 q^{38} -105.047 q^{39} -337.769 q^{41} -98.7328 q^{42} -122.156 q^{43} +346.931 q^{44} -684.900 q^{46} -354.219 q^{47} -66.3141 q^{48} +49.0000 q^{49} -55.2562 q^{51} +493.884 q^{52} -676.691 q^{53} +126.942 q^{54} +200.911 q^{56} +202.209 q^{57} -1008.10 q^{58} +501.319 q^{59} -708.931 q^{61} +416.837 q^{62} -63.0000 q^{63} -767.758 q^{64} +346.931 q^{66} +907.956 q^{67} +259.791 q^{68} -437.025 q^{69} +430.334 q^{71} -258.314 q^{72} -41.3406 q^{73} +762.241 q^{74} -950.700 q^{76} -172.178 q^{77} +493.884 q^{78} +890.388 q^{79} +81.0000 q^{81} +1588.04 q^{82} +1057.15 q^{83} +296.198 q^{84} +574.325 q^{86} -643.256 q^{87} -705.969 q^{88} +1473.72 q^{89} -245.109 q^{91} +2054.70 q^{92} +265.978 q^{93} +1665.38 q^{94} -377.058 q^{96} -555.034 q^{97} -230.377 q^{98} +221.372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 9 q^{6} - 14 q^{7} - 51 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 9 * q^6 - 14 * q^7 - 51 * q^8 + 18 * q^9	$ 2 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 9 q^{6} - 14 q^{7} - 51 q^{8} + 18 q^{9} + 62 q^{11} - 27 q^{12} + 6 q^{13} + 21 q^{14} + 25 q^{16} - 40 q^{17} - 27 q^{18} - 122 q^{19} + 42 q^{21} - 52 q^{22} - 16 q^{23} + 153 q^{24} - 214 q^{26} - 54 q^{27} - 63 q^{28} + 352 q^{29} + 66 q^{31} + 309 q^{32} - 186 q^{33} - 186 q^{34} + 81 q^{36} + 188 q^{37} + 224 q^{38} - 18 q^{39} + 16 q^{41} - 63 q^{42} + 396 q^{43} + 156 q^{44} - 960 q^{46} + 188 q^{47} - 75 q^{48} + 98 q^{49} + 120 q^{51} + 642 q^{52} - 982 q^{53} + 81 q^{54} + 357 q^{56} + 366 q^{57} - 774 q^{58} + 516 q^{59} - 880 q^{61} + 680 q^{62} - 126 q^{63} - 479 q^{64} + 156 q^{66} + 356 q^{67} + 558 q^{68} + 48 q^{69} + 310 q^{71} - 459 q^{72} - 326 q^{73} + 1358 q^{74} - 672 q^{76} - 434 q^{77} + 642 q^{78} + 1832 q^{79} + 162 q^{81} + 2190 q^{82} + 680 q^{83} + 189 q^{84} + 1456 q^{86} - 1056 q^{87} - 1540 q^{88} + 796 q^{89} - 42 q^{91} + 2880 q^{92} - 198 q^{93} + 2588 q^{94} - 927 q^{96} + 670 q^{97} - 147 q^{98} + 558 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 9 * q^6 - 14 * q^7 - 51 * q^8 + 18 * q^9 + 62 * q^11 - 27 * q^12 + 6 * q^13 + 21 * q^14 + 25 * q^16 - 40 * q^17 - 27 * q^18 - 122 * q^19 + 42 * q^21 - 52 * q^22 - 16 * q^23 + 153 * q^24 - 214 * q^26 - 54 * q^27 - 63 * q^28 + 352 * q^29 + 66 * q^31 + 309 * q^32 - 186 * q^33 - 186 * q^34 + 81 * q^36 + 188 * q^37 + 224 * q^38 - 18 * q^39 + 16 * q^41 - 63 * q^42 + 396 * q^43 + 156 * q^44 - 960 * q^46 + 188 * q^47 - 75 * q^48 + 98 * q^49 + 120 * q^51 + 642 * q^52 - 982 * q^53 + 81 * q^54 + 357 * q^56 + 366 * q^57 - 774 * q^58 + 516 * q^59 - 880 * q^61 + 680 * q^62 - 126 * q^63 - 479 * q^64 + 156 * q^66 + 356 * q^67 + 558 * q^68 + 48 * q^69 + 310 * q^71 - 459 * q^72 - 326 * q^73 + 1358 * q^74 - 672 * q^76 - 434 * q^77 + 642 * q^78 + 1832 * q^79 + 162 * q^81 + 2190 * q^82 + 680 * q^83 + 189 * q^84 + 1456 * q^86 - 1056 * q^87 - 1540 * q^88 + 796 * q^89 - 42 * q^91 + 2880 * q^92 - 198 * q^93 + 2588 * q^94 - 927 * q^96 + 670 * q^97 - 147 * q^98 + 558 * 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 $

$2$	−4.70156	−1.66225	−0.831127	−	0.556083i	$-0.812304\pi$
$2$	−4.70156	−1.66225	−0.831127	+	0.556083i	$0.812304\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	14.1047	1.76309
$5$	0	0
$5$	0	0
$6$	14.1047	0.959702
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−28.7016	−1.26844
$9$	9.00000	0.333333
$10$	0	0
$11$	24.5969	0.674203	0.337102	−	0.941468i	$-0.390553\pi$
$11$	24.5969	0.674203	0.337102	+	0.941468i	$0.390553\pi$
$12$	−42.3141	−1.01792
$13$	35.0156	0.747045	0.373523	−	0.927621i	$-0.378150\pi$
$13$	35.0156	0.747045	0.373523	+	0.927621i	$0.378150\pi$
$14$	32.9109	0.628273
$15$	0	0
$16$	22.1047	0.345386
$17$	18.4187	0.262777	0.131388	−	0.991331i	$-0.458057\pi$
$17$	18.4187	0.262777	0.131388	+	0.991331i	$0.458057\pi$
$18$	−42.3141	−0.554084
$19$	−67.4031	−0.813860	−0.406930	−	0.913459i	$-0.633401\pi$
$19$	−67.4031	−0.813860	−0.406930	+	0.913459i	$0.633401\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	−115.644	−1.12070
$23$	145.675	1.32067	0.660333	−	0.750973i	$-0.270415\pi$
$23$	145.675	1.32067	0.660333	+	0.750973i	$0.270415\pi$
$24$	86.1047	0.732335
$25$	0	0
$26$	−164.628	−1.24178
$27$	−27.0000	−0.192450
$28$	−98.7328	−0.666384
$29$	214.419	1.37298	0.686492	−	0.727137i	$-0.259149\pi$
$29$	214.419	1.37298	0.686492	+	0.727137i	$0.259149\pi$
$30$	0	0
$31$	−88.6594	−0.513667	−0.256834	−	0.966456i	$-0.582679\pi$
$31$	−88.6594	−0.513667	−0.256834	+	0.966456i	$0.582679\pi$
$32$	125.686	0.694323
$33$	−73.7906	−0.389251
$34$	−86.5969	−0.436801
$35$	0	0
$36$	126.942	0.587695
$37$	−162.125	−0.720356	−0.360178	−	0.932884i	$-0.617284\pi$
$37$	−162.125	−0.720356	−0.360178	+	0.932884i	$0.617284\pi$
$38$	316.900	1.35284
$39$	−105.047	−0.431307
$40$	0	0
$41$	−337.769	−1.28660	−0.643300	−	0.765614i	$-0.722435\pi$
$41$	−337.769	−1.28660	−0.643300	+	0.765614i	$0.722435\pi$
$42$	−98.7328	−0.362733
$43$	−122.156	−0.433224	−0.216612	−	0.976258i	$-0.569501\pi$
$43$	−122.156	−0.433224	−0.216612	+	0.976258i	$0.569501\pi$
$44$	346.931	1.18868
$45$	0	0
$46$	−684.900	−2.19528
$47$	−354.219	−1.09932	−0.549661	−	0.835388i	$-0.685243\pi$
$47$	−354.219	−1.09932	−0.549661	+	0.835388i	$0.685243\pi$
$48$	−66.3141	−0.199409
$49$	49.0000	0.142857
$50$	0	0
$51$	−55.2562	−0.151714
$52$	493.884	1.31710
$53$	−676.691	−1.75378	−0.876892	−	0.480687i	$-0.840387\pi$
$53$	−676.691	−1.75378	−0.876892	+	0.480687i	$0.840387\pi$
$54$	126.942	0.319901
$55$	0	0
$56$	200.911	0.479426
$57$	202.209	0.469882
$58$	−1008.10	−2.28225
$59$	501.319	1.10621	0.553103	−	0.833113i	$-0.313444\pi$
$59$	501.319	1.10621	0.553103	+	0.833113i	$0.313444\pi$
$60$	0	0
$61$	−708.931	−1.48802	−0.744011	−	0.668167i	$-0.767079\pi$
$61$	−708.931	−1.48802	−0.744011	+	0.668167i	$0.767079\pi$
$62$	416.837	0.853845
$63$	−63.0000	−0.125988
$64$	−767.758	−1.49953
$65$	0	0
$66$	346.931	0.647035
$67$	907.956	1.65559	0.827795	−	0.561031i	$-0.189595\pi$
$67$	907.956	1.65559	0.827795	+	0.561031i	$0.189595\pi$
$68$	259.791	0.463298
$69$	−437.025	−0.762487
$70$	0	0
$71$	430.334	0.719314	0.359657	−	0.933085i	$-0.382894\pi$
$71$	430.334	0.719314	0.359657	+	0.933085i	$0.382894\pi$
$72$	−258.314	−0.422814
$73$	−41.3406	−0.0662816	−0.0331408	−	0.999451i	$-0.510551\pi$
$73$	−41.3406	−0.0662816	−0.0331408	+	0.999451i	$0.510551\pi$
$74$	762.241	1.19741
$75$	0	0
$76$	−950.700	−1.43490
$77$	−172.178	−0.254825
$78$	493.884	0.716941
$79$	890.388	1.26806	0.634028	−	0.773310i	$-0.281400\pi$
$79$	890.388	1.26806	0.634028	+	0.773310i	$0.281400\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1588.04	2.13866
$83$	1057.15	1.39804	0.699020	−	0.715102i	$-0.253620\pi$
$83$	1057.15	1.39804	0.699020	+	0.715102i	$0.253620\pi$
$84$	296.198	0.384737
$85$	0	0
$86$	574.325	0.720129
$87$	−643.256	−0.792693
$88$	−705.969	−0.855188
$89$	1473.72	1.75522	0.877610	−	0.479376i	$-0.159137\pi$
$89$	1473.72	1.75522	0.877610	+	0.479376i	$0.159137\pi$
$90$	0	0
$91$	−245.109	−0.282356
$92$	2054.70	2.32845
$93$	265.978	0.296566
$94$	1665.38	1.82735
$95$	0	0
$96$	−377.058	−0.400868
$97$	−555.034	−0.580981	−0.290491	−	0.956878i	$-0.593819\pi$
$97$	−555.034	−0.580981	−0.290491	+	0.956878i	$0.593819\pi$
$98$	−230.377	−0.237465
$99$	221.372	0.224734
$100$	0	0
$101$	1890.14	1.86214	0.931071	−	0.364838i	$-0.118876\pi$
$101$	1890.14	1.86214	0.931071	+	0.364838i	$0.118876\pi$
$102$	259.791	0.252187
$103$	−662.700	−0.633959	−0.316979	−	0.948432i	$-0.602669\pi$
$103$	−662.700	−0.633959	−0.316979	+	0.948432i	$0.602669\pi$
$104$	−1005.00	−0.947583
$105$	0	0
$106$	3181.50	2.91523
$107$	−1614.53	−1.45872	−0.729358	−	0.684132i	$-0.760181\pi$
$107$	−1614.53	−1.45872	−0.729358	+	0.684132i	$0.760181\pi$
$108$	−380.827	−0.339306
$109$	217.206	0.190868	0.0954339	−	0.995436i	$-0.469576\pi$
$109$	217.206	0.190868	0.0954339	+	0.995436i	$0.469576\pi$
$110$	0	0
$111$	486.375	0.415898
$112$	−154.733	−0.130544
$113$	1658.20	1.38044	0.690221	−	0.723598i	$-0.257513\pi$
$113$	1658.20	1.38044	0.690221	+	0.723598i	$0.257513\pi$
$114$	−950.700	−0.781063
$115$	0	0
$116$	3024.31	2.42069
$117$	315.141	0.249015
$118$	−2356.98	−1.83879
$119$	−128.931	−0.0993202
$120$	0	0
$121$	−725.994	−0.545450
$122$	3333.08	2.47347
$123$	1013.31	0.742819
$124$	−1250.51	−0.905640
$125$	0	0
$126$	296.198	0.209424
$127$	1108.81	0.774734	0.387367	−	0.921926i	$-0.373385\pi$
$127$	1108.81	0.774734	0.387367	+	0.921926i	$0.373385\pi$
$128$	2604.17	1.79827
$129$	366.469	0.250122
$130$	0	0
$131$	185.488	0.123711	0.0618554	−	0.998085i	$-0.480298\pi$
$131$	185.488	0.123711	0.0618554	+	0.998085i	$0.480298\pi$
$132$	−1040.79	−0.686284
$133$	471.822	0.307610
$134$	−4268.81	−2.75201
$135$	0	0
$136$	−528.647	−0.333317
$137$	37.9907	0.0236917	0.0118458	−	0.999930i	$-0.496229\pi$
$137$	37.9907	0.0236917	0.0118458	+	0.999930i	$0.496229\pi$
$138$	2054.70	1.26745
$139$	183.609	0.112040	0.0560199	−	0.998430i	$-0.482159\pi$
$139$	183.609	0.112040	0.0560199	+	0.998430i	$0.482159\pi$
$140$	0	0
$141$	1062.66	0.634694
$142$	−2023.24	−1.19568
$143$	861.275	0.503660
$144$	198.942	0.115129
$145$	0	0
$146$	194.366	0.110177
$147$	−147.000	−0.0824786
$148$	−2286.72	−1.27005
$149$	−1383.34	−0.760587	−0.380293	−	0.924866i	$-0.624177\pi$
$149$	−1383.34	−0.760587	−0.380293	+	0.924866i	$0.624177\pi$
$150$	0	0
$151$	765.256	0.412422	0.206211	−	0.978508i	$-0.433887\pi$
$151$	765.256	0.412422	0.206211	+	0.978508i	$0.433887\pi$
$152$	1934.57	1.03233
$153$	165.769	0.0875922
$154$	809.506	0.423584
$155$	0	0
$156$	−1481.65	−0.760431
$157$	2366.76	1.20311	0.601554	−	0.798832i	$-0.294548\pi$
$157$	2366.76	1.20311	0.601554	+	0.798832i	$0.294548\pi$
$158$	−4186.21	−2.10783
$159$	2030.07	1.01255
$160$	0	0
$161$	−1019.72	−0.499165
$162$	−380.827	−0.184695
$163$	3137.69	1.50775	0.753875	−	0.657018i	$-0.228183\pi$
$163$	3137.69	1.50775	0.753875	+	0.657018i	$0.228183\pi$
$164$	−4764.12	−2.26839
$165$	0	0
$166$	−4970.26	−2.32390
$167$	−146.469	−0.0678688	−0.0339344	−	0.999424i	$-0.510804\pi$
$167$	−146.469	−0.0678688	−0.0339344	+	0.999424i	$0.510804\pi$
$168$	−602.733	−0.276797
$169$	−970.906	−0.441924
$170$	0	0
$171$	−606.628	−0.271287
$172$	−1722.98	−0.763812
$173$	1424.12	0.625860	0.312930	−	0.949776i	$-0.398689\pi$
$173$	1424.12	0.625860	0.312930	+	0.949776i	$0.398689\pi$
$174$	3024.31	1.31766
$175$	0	0
$176$	543.706	0.232860
$177$	−1503.96	−0.638668
$178$	−6928.81	−2.91762
$179$	1244.70	0.519737	0.259869	−	0.965644i	$-0.416321\pi$
$179$	1244.70	0.519737	0.259869	+	0.965644i	$0.416321\pi$
$180$	0	0
$181$	−3879.09	−1.59299	−0.796493	−	0.604648i	$-0.793314\pi$
$181$	−3879.09	−1.59299	−0.796493	+	0.604648i	$0.793314\pi$
$182$	1152.40	0.469348
$183$	2126.79	0.859110
$184$	−4181.10	−1.67519
$185$	0	0
$186$	−1250.51	−0.492968
$187$	453.044	0.177165
$188$	−4996.14	−1.93820
$189$	189.000	0.0727393
$190$	0	0
$191$	1574.90	0.596628	0.298314	−	0.954468i	$-0.403576\pi$
$191$	1574.90	0.596628	0.298314	+	0.954468i	$0.403576\pi$
$192$	2303.27	0.865752
$193$	4775.67	1.78114	0.890572	−	0.454843i	$-0.150305\pi$
$193$	4775.67	1.78114	0.890572	+	0.454843i	$0.150305\pi$
$194$	2609.53	0.965738
$195$	0	0
$196$	691.130	0.251869
$197$	2803.58	1.01394	0.506971	−	0.861963i	$-0.330765\pi$
$197$	2803.58	1.01394	0.506971	+	0.861963i	$0.330765\pi$
$198$	−1040.79	−0.373566
$199$	4102.92	1.46155	0.730774	−	0.682620i	$-0.239159\pi$
$199$	4102.92	1.46155	0.730774	+	0.682620i	$0.239159\pi$
$200$	0	0
$201$	−2723.87	−0.955855
$202$	−8886.63	−3.09535
$203$	−1500.93	−0.518940
$204$	−779.372	−0.267485
$205$	0	0
$206$	3115.72	1.05380
$207$	1311.07	0.440222
$208$	774.009	0.258019
$209$	−1657.91	−0.548707
$210$	0	0
$211$	−823.512	−0.268687	−0.134343	−	0.990935i	$-0.542893\pi$
$211$	−823.512	−0.268687	−0.134343	+	0.990935i	$0.542893\pi$
$212$	−9544.51	−3.09207
$213$	−1291.00	−0.415296
$214$	7590.82	2.42476
$215$	0	0
$216$	774.942	0.244112
$217$	620.616	0.194148
$218$	−1021.21	−0.317271
$219$	124.022	0.0382677
$220$	0	0
$221$	644.944	0.196306
$222$	−2286.72	−0.691328
$223$	−817.194	−0.245396	−0.122698	−	0.992444i	$-0.539155\pi$
$223$	−817.194	−0.245396	−0.122698	+	0.992444i	$0.539155\pi$
$224$	−879.802	−0.262430
$225$	0	0
$226$	−7796.12	−2.29465
$227$	−3655.85	−1.06893	−0.534465	−	0.845190i	$-0.679487\pi$
$227$	−3655.85	−1.06893	−0.534465	+	0.845190i	$0.679487\pi$
$228$	2852.10	0.828443
$229$	939.393	0.271078	0.135539	−	0.990772i	$-0.456723\pi$
$229$	939.393	0.271078	0.135539	+	0.990772i	$0.456723\pi$
$230$	0	0
$231$	516.534	0.147123
$232$	−6154.15	−1.74155
$233$	7.64701	0.00215010	0.00107505	−	0.999999i	$-0.499658\pi$
$233$	7.64701	0.00215010	0.00107505	+	0.999999i	$0.499658\pi$
$234$	−1481.65	−0.413926
$235$	0	0
$236$	7070.94	1.95034
$237$	−2671.16	−0.732112
$238$	606.178	0.165095
$239$	−889.115	−0.240636	−0.120318	−	0.992735i	$-0.538391\pi$
$239$	−889.115	−0.240636	−0.120318	+	0.992735i	$0.538391\pi$
$240$	0	0
$241$	2140.23	0.572051	0.286026	−	0.958222i	$-0.407666\pi$
$241$	2140.23	0.572051	0.286026	+	0.958222i	$0.407666\pi$
$242$	3413.30	0.906676
$243$	−243.000	−0.0641500
$244$	−9999.25	−2.62351
$245$	0	0
$246$	−4764.12	−1.23475
$247$	−2360.16	−0.607990
$248$	2544.66	0.651557
$249$	−3171.45	−0.807158
$250$	0	0
$251$	−6749.81	−1.69739	−0.848693	−	0.528886i	$-0.822610\pi$
$251$	−6749.81	−1.69739	−0.848693	+	0.528886i	$0.822610\pi$
$252$	−888.595	−0.222128
$253$	3583.15	0.890398
$254$	−5213.15	−1.28780
$255$	0	0
$256$	−6101.62	−1.48965
$257$	−3068.64	−0.744811	−0.372405	−	0.928070i	$-0.621467\pi$
$257$	−3068.64	−0.744811	−0.372405	+	0.928070i	$0.621467\pi$
$258$	−1722.98	−0.415766
$259$	1134.87	0.272269
$260$	0	0
$261$	1929.77	0.457662
$262$	−872.081	−0.205639
$263$	4674.12	1.09589	0.547944	−	0.836515i	$-0.315411\pi$
$263$	4674.12	1.09589	0.547944	+	0.836515i	$0.315411\pi$
$264$	2117.91	0.493743
$265$	0	0
$266$	−2218.30	−0.511326
$267$	−4421.17	−1.01338
$268$	12806.4	2.91895
$269$	2417.38	0.547919	0.273960	−	0.961741i	$-0.411667\pi$
$269$	2417.38	0.547919	0.273960	+	0.961741i	$0.411667\pi$
$270$	0	0
$271$	7724.30	1.73143	0.865715	−	0.500537i	$-0.166864\pi$
$271$	7724.30	1.73143	0.865715	+	0.500537i	$0.166864\pi$
$272$	407.141	0.0907593
$273$	735.328	0.163019
$274$	−178.616	−0.0393816
$275$	0	0
$276$	−6164.10	−1.34433
$277$	4576.17	0.992620	0.496310	−	0.868145i	$-0.334688\pi$
$277$	4576.17	0.992620	0.496310	+	0.868145i	$0.334688\pi$
$278$	−863.250	−0.186239
$279$	−797.934	−0.171222
$280$	0	0
$281$	−1358.56	−0.288415	−0.144208	−	0.989547i	$-0.546063\pi$
$281$	−1358.56	−0.288415	−0.144208	+	0.989547i	$0.546063\pi$
$282$	−4996.14	−1.05502
$283$	−3885.04	−0.816048	−0.408024	−	0.912971i	$-0.633782\pi$
$283$	−3885.04	−0.816048	−0.408024	+	0.912971i	$0.633782\pi$
$284$	6069.73	1.26821
$285$	0	0
$286$	−4049.34	−0.837211
$287$	2364.38	0.486289
$288$	1131.17	0.231441
$289$	−4573.75	−0.930948
$290$	0	0
$291$	1665.10	0.335430
$292$	−583.097	−0.116860
$293$	4033.91	0.804312	0.402156	−	0.915571i	$-0.368261\pi$
$293$	4033.91	0.804312	0.402156	+	0.915571i	$0.368261\pi$
$294$	691.130	0.137100
$295$	0	0
$296$	4653.24	0.913730
$297$	−664.116	−0.129750
$298$	6503.85	1.26429
$299$	5100.90	0.986598
$300$	0	0
$301$	855.093	0.163743
$302$	−3597.90	−0.685549
$303$	−5670.43	−1.07511
$304$	−1489.92	−0.281096
$305$	0	0
$306$	−779.372	−0.145600
$307$	4620.36	0.858950	0.429475	−	0.903079i	$-0.358699\pi$
$307$	4620.36	0.858950	0.429475	+	0.903079i	$0.358699\pi$
$308$	−2428.52	−0.449278
$309$	1988.10	0.366016
$310$	0	0
$311$	6675.89	1.21722	0.608609	−	0.793470i	$-0.291728\pi$
$311$	6675.89	1.21722	0.608609	+	0.793470i	$0.291728\pi$
$312$	3015.01	0.547087
$313$	−2836.78	−0.512283	−0.256141	−	0.966639i	$-0.582451\pi$
$313$	−2836.78	−0.512283	−0.256141	+	0.966639i	$0.582451\pi$
$314$	−11127.5	−1.99987
$315$	0	0
$316$	12558.6	2.23569
$317$	−4010.63	−0.710597	−0.355299	−	0.934753i	$-0.615621\pi$
$317$	−4010.63	−0.710597	−0.355299	+	0.934753i	$0.615621\pi$
$318$	−9544.51	−1.68311
$319$	5274.03	0.925671
$320$	0	0
$321$	4843.59	0.842190
$322$	4794.30	0.829739
$323$	−1241.48	−0.213863
$324$	1142.48	0.195898
$325$	0	0
$326$	−14752.1	−2.50626
$327$	−651.619	−0.110198
$328$	9694.49	1.63198
$329$	2479.53	0.415504
$330$	0	0
$331$	11087.5	1.84117	0.920583	−	0.390546i	$-0.127714\pi$
$331$	11087.5	1.84117	0.920583	+	0.390546i	$0.127714\pi$
$332$	14910.8	2.46486
$333$	−1459.12	−0.240119
$334$	688.631	0.112815
$335$	0	0
$336$	464.198	0.0753693
$337$	−12118.7	−1.95890	−0.979450	−	0.201689i	$-0.935357\pi$
$337$	−12118.7	−1.95890	−0.979450	+	0.201689i	$0.935357\pi$
$338$	4564.78	0.734589
$339$	−4974.59	−0.796999
$340$	0	0
$341$	−2180.74	−0.346316
$342$	2852.10	0.450947
$343$	−343.000	−0.0539949
$344$	3506.07	0.549520
$345$	0	0
$346$	−6695.58	−1.04034
$347$	6361.22	0.984116	0.492058	−	0.870562i	$-0.336245\pi$
$347$	6361.22	0.984116	0.492058	+	0.870562i	$0.336245\pi$
$348$	−9072.93	−1.39759
$349$	−3115.18	−0.477799	−0.238899	−	0.971044i	$-0.576787\pi$
$349$	−3115.18	−0.477799	−0.238899	+	0.971044i	$0.576787\pi$
$350$	0	0
$351$	−945.422	−0.143769
$352$	3091.48	0.468115
$353$	11927.4	1.79839	0.899194	−	0.437550i	$-0.144154\pi$
$353$	11927.4	1.79839	0.899194	+	0.437550i	$0.144154\pi$
$354$	7070.94	1.06163
$355$	0	0
$356$	20786.4	3.09460
$357$	386.794	0.0573426
$358$	−5852.02	−0.863935
$359$	−6143.95	−0.903245	−0.451623	−	0.892209i	$-0.649155\pi$
$359$	−6143.95	−0.903245	−0.451623	+	0.892209i	$0.649155\pi$
$360$	0	0
$361$	−2315.82	−0.337632
$362$	18237.8	2.64794
$363$	2177.98	0.314916
$364$	−3457.19	−0.497819
$365$	0	0
$366$	−9999.25	−1.42806
$367$	1927.67	0.274178	0.137089	−	0.990559i	$-0.456225\pi$
$367$	1927.67	0.274178	0.137089	+	0.990559i	$0.456225\pi$
$368$	3220.10	0.456139
$369$	−3039.92	−0.428867
$370$	0	0
$371$	4736.83	0.662868
$372$	3751.54	0.522871
$373$	−10452.0	−1.45090	−0.725449	−	0.688276i	$-0.758368\pi$
$373$	−10452.0	−1.45090	−0.725449	+	0.688276i	$0.758368\pi$
$374$	−2130.01	−0.294493
$375$	0	0
$376$	10166.6	1.39443
$377$	7508.01	1.02568
$378$	−888.595	−0.120911
$379$	7066.43	0.957726	0.478863	−	0.877890i	$-0.341049\pi$
$379$	7066.43	0.957726	0.478863	+	0.877890i	$0.341049\pi$
$380$	0	0
$381$	−3326.44	−0.447293
$382$	−7404.51	−0.991747
$383$	−7168.04	−0.956318	−0.478159	−	0.878273i	$-0.658696\pi$
$383$	−7168.04	−0.956318	−0.478159	+	0.878273i	$0.658696\pi$
$384$	−7812.52	−1.03823
$385$	0	0
$386$	−22453.1	−2.96071
$387$	−1099.41	−0.144408
$388$	−7828.58	−1.02432
$389$	−7414.06	−0.966344	−0.483172	−	0.875525i	$-0.660515\pi$
$389$	−7414.06	−0.966344	−0.483172	+	0.875525i	$0.660515\pi$
$390$	0	0
$391$	2683.15	0.347040
$392$	−1406.38	−0.181206
$393$	−556.463	−0.0714245
$394$	−13181.2	−1.68543
$395$	0	0
$396$	3122.38	0.396226
$397$	8936.01	1.12969	0.564843	−	0.825198i	$-0.308937\pi$
$397$	8936.01	1.12969	0.564843	+	0.825198i	$0.308937\pi$
$398$	−19290.1	−2.42946
$399$	−1415.47	−0.177599
$400$	0	0
$401$	1782.91	0.222031	0.111015	−	0.993819i	$-0.464590\pi$
$401$	1782.91	0.222031	0.111015	+	0.993819i	$0.464590\pi$
$402$	12806.4	1.58887
$403$	−3104.46	−0.383733
$404$	26659.9	3.28312
$405$	0	0
$406$	7056.72	0.862609
$407$	−3987.77	−0.485667
$408$	1585.94	0.192441
$409$	−8759.92	−1.05905	−0.529524	−	0.848295i	$-0.677629\pi$
$409$	−8759.92	−1.05905	−0.529524	+	0.848295i	$0.677629\pi$
$410$	0	0
$411$	−113.972	−0.0136784
$412$	−9347.17	−1.11772
$413$	−3509.23	−0.418106
$414$	−6164.10	−0.731761
$415$	0	0
$416$	4400.97	0.518691
$417$	−550.828	−0.0646862
$418$	7794.75	0.912090
$419$	−3212.74	−0.374588	−0.187294	−	0.982304i	$-0.559972\pi$
$419$	−3212.74	−0.374588	−0.187294	+	0.982304i	$0.559972\pi$
$420$	0	0
$421$	15757.8	1.82420	0.912101	−	0.409965i	$-0.134459\pi$
$421$	15757.8	1.82420	0.912101	+	0.409965i	$0.134459\pi$
$422$	3871.79	0.446626
$423$	−3187.97	−0.366440
$424$	19422.1	2.22457
$425$	0	0
$426$	6069.73	0.690327
$427$	4962.52	0.562419
$428$	−22772.5	−2.57184
$429$	−2583.82	−0.290788
$430$	0	0
$431$	−405.917	−0.0453650	−0.0226825	−	0.999743i	$-0.507221\pi$
$431$	−405.917	−0.0453650	−0.0226825	+	0.999743i	$0.507221\pi$
$432$	−596.827	−0.0664695
$433$	7845.25	0.870713	0.435357	−	0.900258i	$-0.356622\pi$
$433$	7845.25	0.870713	0.435357	+	0.900258i	$0.356622\pi$
$434$	−2917.86	−0.322723
$435$	0	0
$436$	3063.63	0.336516
$437$	−9818.95	−1.07484
$438$	−583.097	−0.0636106
$439$	423.029	0.0459911	0.0229955	−	0.999736i	$-0.492680\pi$
$439$	423.029	0.0459911	0.0229955	+	0.999736i	$0.492680\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	−3032.24	−0.326310
$443$	16058.7	1.72229	0.861143	−	0.508362i	$-0.169749\pi$
$443$	16058.7	1.72229	0.861143	+	0.508362i	$0.169749\pi$
$444$	6860.17	0.733264
$445$	0	0
$446$	3842.09	0.407911
$447$	4150.01	0.439125
$448$	5374.30	0.566768
$449$	2186.75	0.229842	0.114921	−	0.993375i	$-0.463338\pi$
$449$	2186.75	0.229842	0.114921	+	0.993375i	$0.463338\pi$
$450$	0	0
$451$	−8308.05	−0.867430
$452$	23388.3	2.43384
$453$	−2295.77	−0.238112
$454$	17188.2	1.77683
$455$	0	0
$456$	−5803.72	−0.596018
$457$	5799.22	0.593602	0.296801	−	0.954939i	$-0.404080\pi$
$457$	5799.22	0.593602	0.296801	+	0.954939i	$0.404080\pi$
$458$	−4416.62	−0.450600
$459$	−497.306	−0.0505714
$460$	0	0
$461$	9873.35	0.997500	0.498750	−	0.866746i	$-0.333793\pi$
$461$	9873.35	0.997500	0.498750	+	0.866746i	$0.333793\pi$
$462$	−2428.52	−0.244556
$463$	6181.84	0.620506	0.310253	−	0.950654i	$-0.399586\pi$
$463$	6181.84	0.620506	0.310253	+	0.950654i	$0.399586\pi$
$464$	4739.66	0.474209
$465$	0	0
$466$	−35.9529	−0.00357400
$467$	−6145.50	−0.608950	−0.304475	−	0.952520i	$-0.598481\pi$
$467$	−6145.50	−0.608950	−0.304475	+	0.952520i	$0.598481\pi$
$468$	4444.96	0.439035
$469$	−6355.69	−0.625754
$470$	0	0
$471$	−7100.28	−0.694615
$472$	−14388.6	−1.40316
$473$	−3004.66	−0.292081
$474$	12558.6	1.21696
$475$	0	0
$476$	−1818.53	−0.175110
$477$	−6090.22	−0.584595
$478$	4180.23	0.399999
$479$	10879.4	1.03777	0.518887	−	0.854843i	$-0.326347\pi$
$479$	10879.4	1.03777	0.518887	+	0.854843i	$0.326347\pi$
$480$	0	0
$481$	−5676.91	−0.538139
$482$	−10062.4	−0.950894
$483$	3059.17	0.288193
$484$	−10239.9	−0.961675
$485$	0	0
$486$	1142.48	0.106634
$487$	−8087.51	−0.752526	−0.376263	−	0.926513i	$-0.622791\pi$
$487$	−8087.51	−0.752526	−0.376263	+	0.926513i	$0.622791\pi$
$488$	20347.4	1.88747
$489$	−9413.08	−0.870499
$490$	0	0
$491$	−6959.90	−0.639707	−0.319853	−	0.947467i	$-0.603634\pi$
$491$	−6959.90	−0.639707	−0.319853	+	0.947467i	$0.603634\pi$
$492$	14292.4	1.30965
$493$	3949.32	0.360788
$494$	11096.4	1.01063
$495$	0	0
$496$	−1959.79	−0.177413
$497$	−3012.34	−0.271875
$498$	14910.8	1.34170
$499$	18632.0	1.67151	0.835756	−	0.549101i	$-0.185030\pi$
$499$	18632.0	1.67151	0.835756	+	0.549101i	$0.185030\pi$
$500$	0	0
$501$	439.406	0.0391840
$502$	31734.6	2.82149
$503$	−4627.62	−0.410209	−0.205105	−	0.978740i	$-0.565753\pi$
$503$	−4627.62	−0.410209	−0.205105	+	0.978740i	$0.565753\pi$
$504$	1808.20	0.159809
$505$	0	0
$506$	−16846.4	−1.48007
$507$	2912.72	0.255145
$508$	15639.4	1.36592
$509$	−11351.8	−0.988528	−0.494264	−	0.869312i	$-0.664562\pi$
$509$	−11351.8	−0.988528	−0.494264	+	0.869312i	$0.664562\pi$
$510$	0	0
$511$	289.384	0.0250521
$512$	7853.76	0.677911
$513$	1819.88	0.156627
$514$	14427.4	1.23806
$515$	0	0
$516$	5168.93	0.440987
$517$	−8712.67	−0.741166
$518$	−5335.68	−0.452580
$519$	−4272.36	−0.361340
$520$	0	0
$521$	19096.1	1.60579	0.802893	−	0.596123i	$-0.203293\pi$
$521$	19096.1	1.60579	0.802893	+	0.596123i	$0.203293\pi$
$522$	−9072.93	−0.760750
$523$	3145.11	0.262956	0.131478	−	0.991319i	$-0.458028\pi$
$523$	3145.11	0.262956	0.131478	+	0.991319i	$0.458028\pi$
$524$	2616.24	0.218113
$525$	0	0
$526$	−21975.7	−1.82164
$527$	−1632.99	−0.134980
$528$	−1631.12	−0.134442
$529$	9054.20	0.744160
$530$	0	0
$531$	4511.87	0.368735
$532$	6654.90	0.542343
$533$	−11827.2	−0.961148
$534$	20786.4	1.68449
$535$	0	0
$536$	−26059.8	−2.10002
$537$	−3734.09	−0.300071
$538$	−11365.5	−0.910781
$539$	1205.25	0.0963148
$540$	0	0
$541$	8776.12	0.697440	0.348720	−	0.937227i	$-0.386616\pi$
$541$	8776.12	0.697440	0.348720	+	0.937227i	$0.386616\pi$
$542$	−36316.3	−2.87808
$543$	11637.3	0.919710
$544$	2314.98	0.182452
$545$	0	0
$546$	−3457.19	−0.270978
$547$	13695.1	1.07049	0.535247	−	0.844696i	$-0.320219\pi$
$547$	13695.1	1.07049	0.535247	+	0.844696i	$0.320219\pi$
$548$	535.847	0.0417705
$549$	−6380.38	−0.496007
$550$	0	0
$551$	−14452.5	−1.11742
$552$	12543.3	0.967171
$553$	−6232.71	−0.479280
$554$	−21515.2	−1.64999
$555$	0	0
$556$	2589.75	0.197536
$557$	−7850.44	−0.597188	−0.298594	−	0.954380i	$-0.596518\pi$
$557$	−7850.44	−0.597188	−0.298594	+	0.954380i	$0.596518\pi$
$558$	3751.54	0.284615
$559$	−4277.38	−0.323638
$560$	0	0
$561$	−1359.13	−0.102286
$562$	6387.33	0.479419
$563$	4948.81	0.370457	0.185229	−	0.982695i	$-0.440697\pi$
$563$	4948.81	0.370457	0.185229	+	0.982695i	$0.440697\pi$
$564$	14988.4	1.11902
$565$	0	0
$566$	18265.7	1.35648
$567$	−567.000	−0.0419961
$568$	−12351.3	−0.912408
$569$	−8115.76	−0.597945	−0.298972	−	0.954262i	$-0.596644\pi$
$569$	−8115.76	−0.597945	−0.298972	+	0.954262i	$0.596644\pi$
$570$	0	0
$571$	5656.42	0.414560	0.207280	−	0.978282i	$-0.433539\pi$
$571$	5656.42	0.414560	0.207280	+	0.978282i	$0.433539\pi$
$572$	12148.0	0.887996
$573$	−4724.71	−0.344463
$574$	−11116.3	−0.808336
$575$	0	0
$576$	−6909.82	−0.499842
$577$	9536.77	0.688078	0.344039	−	0.938955i	$-0.388205\pi$
$577$	9536.77	0.688078	0.344039	+	0.938955i	$0.388205\pi$
$578$	21503.8	1.54747
$579$	−14327.0	−1.02834
$580$	0	0
$581$	−7400.05	−0.528409
$582$	−7828.58	−0.557569
$583$	−16644.5	−1.18241
$584$	1186.54	0.0840743
$585$	0	0
$586$	−18965.7	−1.33697
$587$	13089.6	0.920383	0.460191	−	0.887820i	$-0.347781\pi$
$587$	13089.6	0.920383	0.460191	+	0.887820i	$0.347781\pi$
$588$	−2073.39	−0.145417
$589$	5975.92	0.418053
$590$	0	0
$591$	−8410.73	−0.585400
$592$	−3583.72	−0.248801
$593$	−4281.96	−0.296524	−0.148262	−	0.988948i	$-0.547368\pi$
$593$	−4281.96	−0.296524	−0.148262	+	0.988948i	$0.547368\pi$
$594$	3122.38	0.215678
$595$	0	0
$596$	−19511.5	−1.34098
$597$	−12308.7	−0.843825
$598$	−23982.2	−1.63997
$599$	3699.92	0.252378	0.126189	−	0.992006i	$-0.459725\pi$
$599$	3699.92	0.252378	0.126189	+	0.992006i	$0.459725\pi$
$600$	0	0
$601$	−17286.1	−1.17323	−0.586616	−	0.809865i	$-0.699540\pi$
$601$	−17286.1	−1.17323	−0.586616	+	0.809865i	$0.699540\pi$
$602$	−4020.28	−0.272183
$603$	8171.61	0.551863
$604$	10793.7	0.727135
$605$	0	0
$606$	26659.9	1.78710
$607$	−14456.7	−0.966689	−0.483344	−	0.875430i	$-0.660578\pi$
$607$	−14456.7	−0.966689	−0.483344	+	0.875430i	$0.660578\pi$
$608$	−8471.63	−0.565082
$609$	4502.79	0.299610
$610$	0	0
$611$	−12403.2	−0.821243
$612$	2338.12	0.154433
$613$	−17981.9	−1.18480	−0.592400	−	0.805644i	$-0.701819\pi$
$613$	−17981.9	−1.18480	−0.592400	+	0.805644i	$0.701819\pi$
$614$	−21722.9	−1.42779
$615$	0	0
$616$	4941.78	0.323231
$617$	−19614.7	−1.27983	−0.639916	−	0.768445i	$-0.721031\pi$
$617$	−19614.7	−1.27983	−0.639916	+	0.768445i	$0.721031\pi$
$618$	−9347.17	−0.608412
$619$	−10462.9	−0.679385	−0.339692	−	0.940537i	$-0.610323\pi$
$619$	−10462.9	−0.679385	−0.339692	+	0.940537i	$0.610323\pi$
$620$	0	0
$621$	−3933.22	−0.254162
$622$	−31387.1	−2.02332
$623$	−10316.1	−0.663411
$624$	−2322.03	−0.148967
$625$	0	0
$626$	13337.3	0.851544
$627$	4973.72	0.316796
$628$	33382.4	2.12118
$629$	−2986.14	−0.189293
$630$	0	0
$631$	24481.9	1.54454	0.772272	−	0.635292i	$-0.219120\pi$
$631$	24481.9	1.54454	0.772272	+	0.635292i	$0.219120\pi$
$632$	−25555.5	−1.60846
$633$	2470.54	0.155126
$634$	18856.2	1.18119
$635$	0	0
$636$	28633.5	1.78521
$637$	1715.77	0.106721
$638$	−24796.2	−1.53870
$639$	3873.01	0.239771
$640$	0	0
$641$	−1109.39	−0.0683595	−0.0341797	−	0.999416i	$-0.510882\pi$
$641$	−1109.39	−0.0683595	−0.0341797	+	0.999416i	$0.510882\pi$
$642$	−22772.5	−1.39993
$643$	−30112.5	−1.84684	−0.923422	−	0.383787i	$-0.874620\pi$
$643$	−30112.5	−1.84684	−0.923422	+	0.383787i	$0.874620\pi$
$644$	−14382.9	−0.880071
$645$	0	0
$646$	5836.90	0.355495
$647$	4260.27	0.258869	0.129435	−	0.991588i	$-0.458684\pi$
$647$	4260.27	0.258869	0.129435	+	0.991588i	$0.458684\pi$
$648$	−2324.83	−0.140938
$649$	12330.9	0.745808
$650$	0	0
$651$	−1861.85	−0.112091
$652$	44256.2	2.65829
$653$	10576.8	0.633844	0.316922	−	0.948452i	$-0.397351\pi$
$653$	10576.8	0.633844	0.316922	+	0.948452i	$0.397351\pi$
$654$	3063.63	0.183176
$655$	0	0
$656$	−7466.27	−0.444373
$657$	−372.066	−0.0220939
$658$	−11657.7	−0.690674
$659$	3394.70	0.200666	0.100333	−	0.994954i	$-0.468009\pi$
$659$	3394.70	0.200666	0.100333	+	0.994954i	$0.468009\pi$
$660$	0	0
$661$	−33174.4	−1.95210	−0.976048	−	0.217554i	$-0.930192\pi$
$661$	−33174.4	−1.95210	−0.976048	+	0.217554i	$0.930192\pi$
$662$	−52128.7	−3.06048
$663$	−1934.83	−0.113337
$664$	−30341.9	−1.77333
$665$	0	0
$666$	6860.17	0.399138
$667$	31235.4	1.81326
$668$	−2065.89	−0.119658
$669$	2451.58	0.141680
$670$	0	0
$671$	−17437.5	−1.00323
$672$	2639.40	0.151514
$673$	−753.881	−0.0431797	−0.0215899	−	0.999767i	$-0.506873\pi$
$673$	−753.881	−0.0431797	−0.0215899	+	0.999767i	$0.506873\pi$
$674$	56976.9	3.25619
$675$	0	0
$676$	−13694.3	−0.779149
$677$	−15668.8	−0.889511	−0.444756	−	0.895652i	$-0.646709\pi$
$677$	−15668.8	−0.889511	−0.444756	+	0.895652i	$0.646709\pi$
$678$	23388.3	1.32481
$679$	3885.24	0.219590
$680$	0	0
$681$	10967.5	0.617147
$682$	10252.9	0.575665
$683$	11557.4	0.647485	0.323742	−	0.946145i	$-0.395059\pi$
$683$	11557.4	0.647485	0.323742	+	0.946145i	$0.395059\pi$
$684$	−8556.30	−0.478302
$685$	0	0
$686$	1612.64	0.0897532
$687$	−2818.18	−0.156507
$688$	−2700.22	−0.149630
$689$	−23694.7	−1.31016
$690$	0	0
$691$	−18503.1	−1.01866	−0.509328	−	0.860572i	$-0.670106\pi$
$691$	−18503.1	−1.01866	−0.509328	+	0.860572i	$0.670106\pi$
$692$	20086.8	1.10344
$693$	−1549.60	−0.0849416
$694$	−29907.7	−1.63585
$695$	0	0
$696$	18462.5	1.00549
$697$	−6221.28	−0.338088
$698$	14646.2	0.794223
$699$	−22.9410	−0.00124136
$700$	0	0
$701$	22580.4	1.21662	0.608311	−	0.793699i	$-0.291847\pi$
$701$	22580.4	1.21662	0.608311	+	0.793699i	$0.291847\pi$
$702$	4444.96	0.238980
$703$	10927.7	0.586269
$704$	−18884.4	−1.01099
$705$	0	0
$706$	−56077.4	−2.98938
$707$	−13231.0	−0.703823
$708$	−21212.8	−1.12603
$709$	−27426.6	−1.45279	−0.726394	−	0.687278i	$-0.758805\pi$
$709$	−27426.6	−1.45279	−0.726394	+	0.687278i	$0.758805\pi$
$710$	0	0
$711$	8013.49	0.422685
$712$	−42298.2	−2.22639
$713$	−12915.5	−0.678383
$714$	−1818.53	−0.0953178
$715$	0	0
$716$	17556.1	0.916342
$717$	2667.35	0.138931
$718$	28886.1	1.50142
$719$	19383.0	1.00538	0.502688	−	0.864468i	$-0.332344\pi$
$719$	19383.0	1.00538	0.502688	+	0.864468i	$0.332344\pi$
$720$	0	0
$721$	4638.90	0.239614
$722$	10888.0	0.561230
$723$	−6420.69	−0.330274
$724$	−54713.3	−2.80857
$725$	0	0
$726$	−10239.9	−0.523469
$727$	12317.3	0.628368	0.314184	−	0.949362i	$-0.398269\pi$
$727$	12317.3	0.628368	0.314184	+	0.949362i	$0.398269\pi$
$728$	7035.02	0.358153
$729$	729.000	0.0370370
$730$	0	0
$731$	−2249.96	−0.113841
$732$	29997.8	1.51468
$733$	−1234.02	−0.0621822	−0.0310911	−	0.999517i	$-0.509898\pi$
$733$	−1234.02	−0.0621822	−0.0310911	+	0.999517i	$0.509898\pi$
$734$	−9063.05	−0.455754
$735$	0	0
$736$	18309.3	0.916970
$737$	22332.9	1.11620
$738$	14292.4	0.712885
$739$	−15257.3	−0.759473	−0.379736	−	0.925095i	$-0.623985\pi$
$739$	−15257.3	−0.759473	−0.379736	+	0.925095i	$0.623985\pi$
$740$	0	0
$741$	7080.49	0.351023
$742$	−22270.5	−1.10186
$743$	35565.1	1.75606	0.878032	−	0.478602i	$-0.158856\pi$
$743$	35565.1	1.75606	0.878032	+	0.478602i	$0.158856\pi$
$744$	−7633.99	−0.376177
$745$	0	0
$746$	49140.8	2.41176
$747$	9514.35	0.466013
$748$	6390.04	0.312357
$749$	11301.7	0.551343
$750$	0	0
$751$	14266.7	0.693209	0.346605	−	0.938011i	$-0.387335\pi$
$751$	14266.7	0.693209	0.346605	+	0.938011i	$0.387335\pi$
$752$	−7829.89	−0.379690
$753$	20249.4	0.979986
$754$	−35299.4	−1.70494
$755$	0	0
$756$	2665.79	0.128246
$757$	15927.9	0.764744	0.382372	−	0.924009i	$-0.375107\pi$
$757$	15927.9	0.764744	0.382372	+	0.924009i	$0.375107\pi$
$758$	−33223.3	−1.59198
$759$	−10749.4	−0.514071
$760$	0	0
$761$	−2566.48	−0.122253	−0.0611266	−	0.998130i	$-0.519469\pi$
$761$	−2566.48	−0.122253	−0.0611266	+	0.998130i	$0.519469\pi$
$762$	15639.4	0.743514
$763$	−1520.44	−0.0721413
$764$	22213.5	1.05191
$765$	0	0
$766$	33701.0	1.58964
$767$	17554.0	0.826386
$768$	18304.9	0.860052
$769$	14433.1	0.676816	0.338408	−	0.940999i	$-0.390112\pi$
$769$	14433.1	0.676816	0.338408	+	0.940999i	$0.390112\pi$
$770$	0	0
$771$	9205.91	0.430017
$772$	67359.4	3.14031
$773$	29443.2	1.36999	0.684993	−	0.728550i	$-0.259805\pi$
$773$	29443.2	1.36999	0.684993	+	0.728550i	$0.259805\pi$
$774$	5168.93	0.240043
$775$	0	0
$776$	15930.4	0.736941
$777$	−3404.62	−0.157195
$778$	34857.7	1.60631
$779$	22766.7	1.04711
$780$	0	0
$781$	10584.9	0.484964
$782$	−12615.0	−0.576869
$783$	−5789.31	−0.264231
$784$	1083.13	0.0493408
$785$	0	0
$786$	2616.24	0.118726
$787$	−26390.6	−1.19533	−0.597664	−	0.801747i	$-0.703904\pi$
$787$	−26390.6	−1.19533	−0.597664	+	0.801747i	$0.703904\pi$
$788$	39543.6	1.78767
$789$	−14022.4	−0.632711
$790$	0	0
$791$	−11607.4	−0.521758
$792$	−6353.72	−0.285063
$793$	−24823.7	−1.11162
$794$	−42013.2	−1.87783
$795$	0	0
$796$	57870.3	2.57683
$797$	3738.33	0.166146	0.0830730	−	0.996543i	$-0.473527\pi$
$797$	3738.33	0.166146	0.0830730	+	0.996543i	$0.473527\pi$
$798$	6654.90	0.295214
$799$	−6524.26	−0.288876
$800$	0	0
$801$	13263.5	0.585073
$802$	−8382.48	−0.369072
$803$	−1016.85	−0.0446873
$804$	−38419.3	−1.68525
$805$	0	0
$806$	14595.8	0.637861
$807$	−7252.14	−0.316341
$808$	−54250.1	−2.36202
$809$	43204.1	1.87760	0.938798	−	0.344468i	$-0.111941\pi$
$809$	43204.1	1.87760	0.938798	+	0.344468i	$0.111941\pi$
$810$	0	0
$811$	−30192.4	−1.30727	−0.653637	−	0.756809i	$-0.726758\pi$
$811$	−30192.4	−1.30727	−0.653637	+	0.756809i	$0.726758\pi$
$812$	−21170.2	−0.914935
$813$	−23172.9	−0.999642
$814$	18748.7	0.807301
$815$	0	0
$816$	−1221.42	−0.0523999
$817$	8233.71	0.352584
$818$	41185.3	1.76041
$819$	−2205.98	−0.0941188
$820$	0	0
$821$	−40274.7	−1.71206	−0.856028	−	0.516929i	$-0.827075\pi$
$821$	−40274.7	−1.71206	−0.856028	+	0.516929i	$0.827075\pi$
$822$	535.847	0.0227370
$823$	−25184.2	−1.06667	−0.533334	−	0.845905i	$-0.679061\pi$
$823$	−25184.2	−1.06667	−0.533334	+	0.845905i	$0.679061\pi$
$824$	19020.5	0.804140
$825$	0	0
$826$	16498.9	0.694999
$827$	38941.7	1.63741	0.818703	−	0.574218i	$-0.194694\pi$
$827$	38941.7	1.63741	0.818703	+	0.574218i	$0.194694\pi$
$828$	18492.3	0.776150
$829$	−8327.05	−0.348867	−0.174433	−	0.984669i	$-0.555809\pi$
$829$	−8327.05	−0.348867	−0.174433	+	0.984669i	$0.555809\pi$
$830$	0	0
$831$	−13728.5	−0.573089
$832$	−26883.5	−1.12021
$833$	902.519	0.0375395
$834$	2589.75	0.107525
$835$	0	0
$836$	−23384.2	−0.967418
$837$	2393.80	0.0988553
$838$	15104.9	0.622660
$839$	8784.41	0.361468	0.180734	−	0.983532i	$-0.442153\pi$
$839$	8784.41	0.361468	0.180734	+	0.983532i	$0.442153\pi$
$840$	0	0
$841$	21586.4	0.885087
$842$	−74086.4	−3.03229
$843$	4075.67	0.166517
$844$	−11615.4	−0.473718
$845$	0	0
$846$	14988.4	0.609117
$847$	5081.96	0.206161
$848$	−14958.0	−0.605732
$849$	11655.1	0.471145
$850$	0	0
$851$	−23617.6	−0.951350
$852$	−18209.2	−0.732203
$853$	9076.15	0.364316	0.182158	−	0.983269i	$-0.441692\pi$
$853$	9076.15	0.364316	0.182158	+	0.983269i	$0.441692\pi$
$854$	−23331.6	−0.934884
$855$	0	0
$856$	46339.6	1.85030
$857$	−36396.7	−1.45074	−0.725372	−	0.688357i	$-0.758332\pi$
$857$	−36396.7	−1.45074	−0.725372	+	0.688357i	$0.758332\pi$
$858$	12148.0	0.483364
$859$	8915.27	0.354115	0.177058	−	0.984200i	$-0.443342\pi$
$859$	8915.27	0.354115	0.177058	+	0.984200i	$0.443342\pi$
$860$	0	0
$861$	−7093.14	−0.280759
$862$	1908.44	0.0754081
$863$	6148.26	0.242514	0.121257	−	0.992621i	$-0.461308\pi$
$863$	6148.26	0.242514	0.121257	+	0.992621i	$0.461308\pi$
$864$	−3393.52	−0.133623
$865$	0	0
$866$	−36884.9	−1.44735
$867$	13721.2	0.537483
$868$	8753.59	0.342300
$869$	21900.8	0.854928
$870$	0	0
$871$	31792.6	1.23680
$872$	−6234.16	−0.242105
$873$	−4995.31	−0.193660
$874$	46164.4	1.78665
$875$	0	0
$876$	1749.29	0.0674692
$877$	14287.0	0.550101	0.275050	−	0.961430i	$-0.411306\pi$
$877$	14287.0	0.550101	0.275050	+	0.961430i	$0.411306\pi$
$878$	−1988.90	−0.0764488
$879$	−12101.7	−0.464370
$880$	0	0
$881$	−13315.9	−0.509221	−0.254610	−	0.967044i	$-0.581947\pi$
$881$	−13315.9	−0.509221	−0.254610	+	0.967044i	$0.581947\pi$
$882$	−2073.39	−0.0791549
$883$	5271.78	0.200917	0.100458	−	0.994941i	$-0.467969\pi$
$883$	5271.78	0.200917	0.100458	+	0.994941i	$0.467969\pi$
$884$	9096.73	0.346104
$885$	0	0
$886$	−75501.1	−2.86288
$887$	−2606.07	−0.0986507	−0.0493253	−	0.998783i	$-0.515707\pi$
$887$	−2606.07	−0.0986507	−0.0493253	+	0.998783i	$0.515707\pi$
$888$	−13959.7	−0.527542
$889$	−7761.69	−0.292822
$890$	0	0
$891$	1992.35	0.0749115
$892$	−11526.3	−0.432654
$893$	23875.4	0.894694
$894$	−19511.5	−0.729937
$895$	0	0
$896$	−18229.2	−0.679682
$897$	−15302.7	−0.569612
$898$	−10281.1	−0.382056
$899$	−19010.2	−0.705258
$900$	0	0
$901$	−12463.8	−0.460854
$902$	39060.8	1.44189
$903$	−2565.28	−0.0945373
$904$	−47592.8	−1.75101
$905$	0	0
$906$	10793.7	0.395802
$907$	−18610.6	−0.681317	−0.340659	−	0.940187i	$-0.610650\pi$
$907$	−18610.6	−0.681317	−0.340659	+	0.940187i	$0.610650\pi$
$908$	−51564.6	−1.88462
$909$	17011.3	0.620714
$910$	0	0
$911$	41091.7	1.49443	0.747216	−	0.664581i	$-0.231390\pi$
$911$	41091.7	1.49443	0.747216	+	0.664581i	$0.231390\pi$
$912$	4469.77	0.162291
$913$	26002.6	0.942563
$914$	−27265.4	−0.986716
$915$	0	0
$916$	13249.8	0.477934
$917$	−1298.41	−0.0467583
$918$	2338.12	0.0840624
$919$	38891.3	1.39598	0.697990	−	0.716107i	$-0.254078\pi$
$919$	38891.3	1.39598	0.697990	+	0.716107i	$0.254078\pi$
$920$	0	0
$921$	−13861.1	−0.495915
$922$	−46420.2	−1.65810
$923$	15068.4	0.537360
$924$	7285.56	0.259391
$925$	0	0
$926$	−29064.3	−1.03144
$927$	−5964.30	−0.211320
$928$	26949.4	0.953295
$929$	18699.4	0.660396	0.330198	−	0.943912i	$-0.392885\pi$
$929$	18699.4	0.660396	0.330198	+	0.943912i	$0.392885\pi$
$930$	0	0
$931$	−3302.75	−0.116266
$932$	107.859	0.00379080
$933$	−20027.7	−0.702761
$934$	28893.4	1.01223
$935$	0	0
$936$	−9045.03	−0.315861
$937$	−21509.6	−0.749933	−0.374967	−	0.927038i	$-0.622346\pi$
$937$	−21509.6	−0.749933	−0.374967	+	0.927038i	$0.622346\pi$
$938$	29881.7	1.04016
$939$	8510.35	0.295767
$940$	0	0
$941$	−11241.7	−0.389448	−0.194724	−	0.980858i	$-0.562381\pi$
$941$	−11241.7	−0.389448	−0.194724	+	0.980858i	$0.562381\pi$
$942$	33382.4	1.15463
$943$	−49204.5	−1.69917
$944$	11081.5	0.382068
$945$	0	0
$946$	14126.6	0.485513
$947$	36556.3	1.25441	0.627203	−	0.778856i	$-0.284200\pi$
$947$	36556.3	1.25441	0.627203	+	0.778856i	$0.284200\pi$
$948$	−37675.9	−1.29078
$949$	−1447.57	−0.0495153
$950$	0	0
$951$	12031.9	0.410263
$952$	3700.53	0.125982
$953$	36633.4	1.24520	0.622598	−	0.782542i	$-0.286077\pi$
$953$	36633.4	1.24520	0.622598	+	0.782542i	$0.286077\pi$
$954$	28633.5	0.971745
$955$	0	0
$956$	−12540.7	−0.424263
$957$	−15822.1	−0.534436
$958$	−51150.3	−1.72504
$959$	−265.935	−0.00895462
$960$	0	0
$961$	−21930.5	−0.736146
$962$	26690.3	0.894523
$963$	−14530.8	−0.486239
$964$	30187.3	1.00858
$965$	0	0
$966$	−14382.9	−0.479050
$967$	35515.8	1.18109	0.590544	−	0.807006i	$-0.298913\pi$
$967$	35515.8	1.18109	0.590544	+	0.807006i	$0.298913\pi$
$968$	20837.2	0.691871
$969$	3724.44	0.123474
$970$	0	0
$971$	−39661.0	−1.31080	−0.655398	−	0.755283i	$-0.727499\pi$
$971$	−39661.0	−1.31080	−0.655398	+	0.755283i	$0.727499\pi$
$972$	−3427.44	−0.113102
$973$	−1285.26	−0.0423471
$974$	38023.9	1.25089
$975$	0	0
$976$	−15670.7	−0.513942
$977$	−50325.3	−1.64795	−0.823977	−	0.566624i	$-0.808249\pi$
$977$	−50325.3	−1.64795	−0.823977	+	0.566624i	$0.808249\pi$
$978$	44256.2	1.44699
$979$	36249.0	1.18337
$980$	0	0
$981$	1954.86	0.0636226
$982$	32722.4	1.06335
$983$	−51189.0	−1.66091	−0.830456	−	0.557084i	$-0.811920\pi$
$983$	−51189.0	−1.66091	−0.830456	+	0.557084i	$0.811920\pi$
$984$	−29083.5	−0.942223
$985$	0	0
$986$	−18568.0	−0.599721
$987$	−7438.59	−0.239892
$988$	−33289.3	−1.07194
$989$	−17795.1	−0.572145
$990$	0	0
$991$	−55137.3	−1.76740	−0.883700	−	0.468054i	$-0.844955\pi$
$991$	−55137.3	−1.76740	−0.883700	+	0.468054i	$0.844955\pi$
$992$	−11143.2	−0.356651
$993$	−33262.6	−1.06300
$994$	14162.7	0.451925
$995$	0	0
$996$	−44732.3	−1.42309
$997$	−41606.5	−1.32166	−0.660828	−	0.750537i	$-0.729795\pi$
$997$	−41606.5	−1.32166	−0.660828	+	0.750537i	$0.729795\pi$
$998$	−87599.6	−2.77848
$999$	4377.37	0.138633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.i.1.1		2
3.2	odd	2		1575.4.a.y.1.2		2
5.2	odd	4		525.4.d.j.274.1		4
5.3	odd	4		525.4.d.j.274.4		4
5.4	even	2		105.4.a.g.1.2	✓	2
15.14	odd	2		315.4.a.g.1.1		2
20.19	odd	2		1680.4.a.y.1.2		2
35.34	odd	2		735.4.a.q.1.2		2
105.104	even	2		2205.4.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.g.1.2	✓	2	5.4	even	2
315.4.a.g.1.1		2	15.14	odd	2
525.4.a.i.1.1		2	1.1	even	1	trivial
525.4.d.j.274.1		4	5.2	odd	4
525.4.d.j.274.4		4	5.3	odd	4
735.4.a.q.1.2		2	35.34	odd	2
1575.4.a.y.1.2		2	3.2	odd	2
1680.4.a.y.1.2		2	20.19	odd	2
2205.4.a.v.1.1		2	105.104	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

\(f(q)\)	\(=\)	\(q-4.70156 q^{2} -3.00000 q^{3} +14.1047 q^{4} +14.1047 q^{6} -7.00000 q^{7} -28.7016 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.70156 q^{2} -3.00000 q^{3} +14.1047 q^{4} +14.1047 q^{6} -7.00000 q^{7} -28.7016 q^{8} +9.00000 q^{9} +24.5969 q^{11} -42.3141 q^{12} +35.0156 q^{13} +32.9109 q^{14} +22.1047 q^{16} +18.4187 q^{17} -42.3141 q^{18} -67.4031 q^{19} +21.0000 q^{21} -115.644 q^{22} +145.675 q^{23} +86.1047 q^{24} -164.628 q^{26} -27.0000 q^{27} -98.7328 q^{28} +214.419 q^{29} -88.6594 q^{31} +125.686 q^{32} -73.7906 q^{33} -86.5969 q^{34} +126.942 q^{36} -162.125 q^{37} +316.900 q^{38} -105.047 q^{39} -337.769 q^{41} -98.7328 q^{42} -122.156 q^{43} +346.931 q^{44} -684.900 q^{46} -354.219 q^{47} -66.3141 q^{48} +49.0000 q^{49} -55.2562 q^{51} +493.884 q^{52} -676.691 q^{53} +126.942 q^{54} +200.911 q^{56} +202.209 q^{57} -1008.10 q^{58} +501.319 q^{59} -708.931 q^{61} +416.837 q^{62} -63.0000 q^{63} -767.758 q^{64} +346.931 q^{66} +907.956 q^{67} +259.791 q^{68} -437.025 q^{69} +430.334 q^{71} -258.314 q^{72} -41.3406 q^{73} +762.241 q^{74} -950.700 q^{76} -172.178 q^{77} +493.884 q^{78} +890.388 q^{79} +81.0000 q^{81} +1588.04 q^{82} +1057.15 q^{83} +296.198 q^{84} +574.325 q^{86} -643.256 q^{87} -705.969 q^{88} +1473.72 q^{89} -245.109 q^{91} +2054.70 q^{92} +265.978 q^{93} +1665.38 q^{94} -377.058 q^{96} -555.034 q^{97} -230.377 q^{98} +221.372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 9 q^{6} - 14 q^{7} - 51 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 9 * q^6 - 14 * q^7 - 51 * q^8 + 18 * q^9	\( 2 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 9 q^{6} - 14 q^{7} - 51 q^{8} + 18 q^{9} + 62 q^{11} - 27 q^{12} + 6 q^{13} + 21 q^{14} + 25 q^{16} - 40 q^{17} - 27 q^{18} - 122 q^{19} + 42 q^{21} - 52 q^{22} - 16 q^{23} + 153 q^{24} - 214 q^{26} - 54 q^{27} - 63 q^{28} + 352 q^{29} + 66 q^{31} + 309 q^{32} - 186 q^{33} - 186 q^{34} + 81 q^{36} + 188 q^{37} + 224 q^{38} - 18 q^{39} + 16 q^{41} - 63 q^{42} + 396 q^{43} + 156 q^{44} - 960 q^{46} + 188 q^{47} - 75 q^{48} + 98 q^{49} + 120 q^{51} + 642 q^{52} - 982 q^{53} + 81 q^{54} + 357 q^{56} + 366 q^{57} - 774 q^{58} + 516 q^{59} - 880 q^{61} + 680 q^{62} - 126 q^{63} - 479 q^{64} + 156 q^{66} + 356 q^{67} + 558 q^{68} + 48 q^{69} + 310 q^{71} - 459 q^{72} - 326 q^{73} + 1358 q^{74} - 672 q^{76} - 434 q^{77} + 642 q^{78} + 1832 q^{79} + 162 q^{81} + 2190 q^{82} + 680 q^{83} + 189 q^{84} + 1456 q^{86} - 1056 q^{87} - 1540 q^{88} + 796 q^{89} - 42 q^{91} + 2880 q^{92} - 198 q^{93} + 2588 q^{94} - 927 q^{96} + 670 q^{97} - 147 q^{98} + 558 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 9 * q^6 - 14 * q^7 - 51 * q^8 + 18 * q^9 + 62 * q^11 - 27 * q^12 + 6 * q^13 + 21 * q^14 + 25 * q^16 - 40 * q^17 - 27 * q^18 - 122 * q^19 + 42 * q^21 - 52 * q^22 - 16 * q^23 + 153 * q^24 - 214 * q^26 - 54 * q^27 - 63 * q^28 + 352 * q^29 + 66 * q^31 + 309 * q^32 - 186 * q^33 - 186 * q^34 + 81 * q^36 + 188 * q^37 + 224 * q^38 - 18 * q^39 + 16 * q^41 - 63 * q^42 + 396 * q^43 + 156 * q^44 - 960 * q^46 + 188 * q^47 - 75 * q^48 + 98 * q^49 + 120 * q^51 + 642 * q^52 - 982 * q^53 + 81 * q^54 + 357 * q^56 + 366 * q^57 - 774 * q^58 + 516 * q^59 - 880 * q^61 + 680 * q^62 - 126 * q^63 - 479 * q^64 + 156 * q^66 + 356 * q^67 + 558 * q^68 + 48 * q^69 + 310 * q^71 - 459 * q^72 - 326 * q^73 + 1358 * q^74 - 672 * q^76 - 434 * q^77 + 642 * q^78 + 1832 * q^79 + 162 * q^81 + 2190 * q^82 + 680 * q^83 + 189 * q^84 + 1456 * q^86 - 1056 * q^87 - 1540 * q^88 + 796 * q^89 - 42 * q^91 + 2880 * q^92 - 198 * q^93 + 2588 * q^94 - 927 * q^96 + 670 * q^97 - 147 * q^98 + 558 * q^99

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