LMFDB - Embedded newform 175.4.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(1,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 32x^{2} - 35x + 120 $ x^4 - 32x^2 - 35x + 120
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			1.4
Root			$-3.84167$ of defining polynomial
Character	$\chi$	$=$	175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.84167 q^{2} -9.58084 q^{3} +15.4418 q^{4} -46.3873 q^{6} +7.00000 q^{7} +36.0308 q^{8} +64.7926 q^{9} +O(q^{10})$	\(q+4.84167 q^{2} -9.58084 q^{3} +15.4418 q^{4} -46.3873 q^{6} +7.00000 q^{7} +36.0308 q^{8} +64.7926 q^{9} +62.1962 q^{11} -147.945 q^{12} +14.0934 q^{13} +33.8917 q^{14} +50.9148 q^{16} +63.5104 q^{17} +313.704 q^{18} +48.7094 q^{19} -67.0659 q^{21} +301.134 q^{22} -99.3784 q^{23} -345.205 q^{24} +68.2354 q^{26} -362.085 q^{27} +108.093 q^{28} -69.0571 q^{29} -9.68658 q^{31} -41.7334 q^{32} -595.892 q^{33} +307.497 q^{34} +1000.51 q^{36} +240.290 q^{37} +235.835 q^{38} -135.026 q^{39} +335.306 q^{41} -324.711 q^{42} +51.2582 q^{43} +960.421 q^{44} -481.158 q^{46} -451.564 q^{47} -487.806 q^{48} +49.0000 q^{49} -608.484 q^{51} +217.627 q^{52} -180.014 q^{53} -1753.10 q^{54} +252.215 q^{56} -466.677 q^{57} -334.352 q^{58} +268.600 q^{59} -323.925 q^{61} -46.8992 q^{62} +453.548 q^{63} -609.378 q^{64} -2885.12 q^{66} -541.910 q^{67} +980.715 q^{68} +952.129 q^{69} -161.433 q^{71} +2334.53 q^{72} +305.751 q^{73} +1163.40 q^{74} +752.161 q^{76} +435.373 q^{77} -653.753 q^{78} -504.722 q^{79} +1719.68 q^{81} +1623.44 q^{82} -513.838 q^{83} -1035.62 q^{84} +248.176 q^{86} +661.625 q^{87} +2240.98 q^{88} +543.158 q^{89} +98.6535 q^{91} -1534.58 q^{92} +92.8056 q^{93} -2186.32 q^{94} +399.842 q^{96} +1863.06 q^{97} +237.242 q^{98} +4029.85 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 3 q^{3} + 36 q^{4} + q^{6} + 28 q^{7} + 27 q^{8} + 61 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 3 * q^3 + 36 * q^4 + q^6 + 28 * q^7 + 27 * q^8 + 61 * q^9	\( 4 q + 4 q^{2} - 3 q^{3} + 36 q^{4} + q^{6} + 28 q^{7} + 27 q^{8} + 61 q^{9} + 100 q^{11} - 165 q^{12} + 44 q^{13} + 28 q^{14} + 160 q^{16} - 53 q^{17} + 433 q^{18} - 29 q^{19} - 21 q^{21} - 152 q^{22} + 295 q^{23} - 21 q^{24} + 700 q^{26} - 441 q^{27} + 252 q^{28} + 129 q^{29} + 114 q^{31} - 310 q^{32} - 865 q^{33} + 203 q^{34} + 1101 q^{36} + 403 q^{37} + 555 q^{38} + 674 q^{39} + 671 q^{41} + 7 q^{42} - 411 q^{43} + 438 q^{44} - 997 q^{46} - 8 q^{47} - 523 q^{48} + 196 q^{49} - 885 q^{51} + 74 q^{52} + 90 q^{53} - 2777 q^{54} + 189 q^{56} + 233 q^{57} + 673 q^{58} + 1018 q^{59} + 50 q^{61} - 1626 q^{62} + 427 q^{63} - 2421 q^{64} - 3841 q^{66} + 424 q^{67} - 617 q^{68} + 1080 q^{69} + 215 q^{71} + 2940 q^{72} - 1207 q^{73} + 623 q^{74} - 3257 q^{76} + 700 q^{77} + 278 q^{78} - 951 q^{79} + 28 q^{81} + 1695 q^{82} - 3035 q^{83} - 1155 q^{84} - 99 q^{86} + 2210 q^{87} + 163 q^{88} + 2819 q^{89} + 308 q^{91} + 3073 q^{92} - 852 q^{93} - 3056 q^{94} - 1345 q^{96} - 1100 q^{97} + 196 q^{98} + 2383 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 3 * q^3 + 36 * q^4 + q^6 + 28 * q^7 + 27 * q^8 + 61 * q^9 + 100 * q^11 - 165 * q^12 + 44 * q^13 + 28 * q^14 + 160 * q^16 - 53 * q^17 + 433 * q^18 - 29 * q^19 - 21 * q^21 - 152 * q^22 + 295 * q^23 - 21 * q^24 + 700 * q^26 - 441 * q^27 + 252 * q^28 + 129 * q^29 + 114 * q^31 - 310 * q^32 - 865 * q^33 + 203 * q^34 + 1101 * q^36 + 403 * q^37 + 555 * q^38 + 674 * q^39 + 671 * q^41 + 7 * q^42 - 411 * q^43 + 438 * q^44 - 997 * q^46 - 8 * q^47 - 523 * q^48 + 196 * q^49 - 885 * q^51 + 74 * q^52 + 90 * q^53 - 2777 * q^54 + 189 * q^56 + 233 * q^57 + 673 * q^58 + 1018 * q^59 + 50 * q^61 - 1626 * q^62 + 427 * q^63 - 2421 * q^64 - 3841 * q^66 + 424 * q^67 - 617 * q^68 + 1080 * q^69 + 215 * q^71 + 2940 * q^72 - 1207 * q^73 + 623 * q^74 - 3257 * q^76 + 700 * q^77 + 278 * q^78 - 951 * q^79 + 28 * q^81 + 1695 * q^82 - 3035 * q^83 - 1155 * q^84 - 99 * q^86 + 2210 * q^87 + 163 * q^88 + 2819 * q^89 + 308 * q^91 + 3073 * q^92 - 852 * q^93 - 3056 * q^94 - 1345 * q^96 - 1100 * q^97 + 196 * q^98 + 2383 * 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 $

$2$	4.84167	1.71179	0.855895	−	0.517150i	$-0.173007\pi$
$2$	4.84167	1.71179	0.855895	+	0.517150i	$0.173007\pi$
$3$	−9.58084	−1.84383	−0.921917	−	0.387387i	$-0.873378\pi$
$3$	−9.58084	−1.84383	−0.921917	+	0.387387i	$0.873378\pi$
$4$	15.4418	1.93022
$5$	0	0
$5$	0	0
$6$	−46.3873	−3.15626
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	36.0308	1.59235
$9$	64.7926	2.39972
$10$	0	0
$11$	62.1962	1.70481	0.852403	−	0.522886i	$-0.175145\pi$
$11$	62.1962	1.70481	0.852403	+	0.522886i	$0.175145\pi$
$12$	−147.945	−3.55901
$13$	14.0934	0.300676	0.150338	−	0.988635i	$-0.451964\pi$
$13$	14.0934	0.300676	0.150338	+	0.988635i	$0.451964\pi$
$14$	33.8917	0.646996
$15$	0	0
$16$	50.9148	0.795543
$17$	63.5104	0.906091	0.453045	−	0.891487i	$-0.350338\pi$
$17$	63.5104	0.906091	0.453045	+	0.891487i	$0.350338\pi$
$18$	313.704	4.10782
$19$	48.7094	0.588143	0.294071	−	0.955783i	$-0.404990\pi$
$19$	48.7094	0.588143	0.294071	+	0.955783i	$0.404990\pi$
$20$	0	0
$21$	−67.0659	−0.696904
$22$	301.134	2.91827
$23$	−99.3784	−0.900949	−0.450475	−	0.892789i	$-0.648745\pi$
$23$	−99.3784	−0.900949	−0.450475	+	0.892789i	$0.648745\pi$
$24$	−345.205	−2.93603
$25$	0	0
$26$	68.2354	0.514695
$27$	−362.085	−2.58086
$28$	108.093	0.729556
$29$	−69.0571	−0.442193	−0.221096	−	0.975252i	$-0.570964\pi$
$29$	−69.0571	−0.442193	−0.221096	+	0.975252i	$0.570964\pi$
$30$	0	0
$31$	−9.68658	−0.0561213	−0.0280607	−	0.999606i	$-0.508933\pi$
$31$	−9.68658	−0.0561213	−0.0280607	+	0.999606i	$0.508933\pi$
$32$	−41.7334	−0.230547
$33$	−595.892	−3.14338
$34$	307.497	1.55104
$35$	0	0
$36$	1000.51	4.63201
$37$	240.290	1.06766	0.533829	−	0.845592i	$-0.320752\pi$
$37$	240.290	1.06766	0.533829	+	0.845592i	$0.320752\pi$
$38$	235.835	1.00678
$39$	−135.026	−0.554398
$40$	0	0
$41$	335.306	1.27722	0.638610	−	0.769531i	$-0.279510\pi$
$41$	335.306	1.27722	0.638610	+	0.769531i	$0.279510\pi$
$42$	−324.711	−1.19295
$43$	51.2582	0.181786	0.0908931	−	0.995861i	$-0.471028\pi$
$43$	51.2582	0.181786	0.0908931	+	0.995861i	$0.471028\pi$
$44$	960.421	3.29066
$45$	0	0
$46$	−481.158	−1.54224
$47$	−451.564	−1.40143	−0.700716	−	0.713440i	$-0.747136\pi$
$47$	−451.564	−1.40143	−0.700716	+	0.713440i	$0.747136\pi$
$48$	−487.806	−1.46685
$49$	49.0000	0.142857
$50$	0	0
$51$	−608.484	−1.67068
$52$	217.627	0.580373
$53$	−180.014	−0.466545	−0.233273	−	0.972411i	$-0.574943\pi$
$53$	−180.014	−0.466545	−0.233273	+	0.972411i	$0.574943\pi$
$54$	−1753.10	−4.41789
$55$	0	0
$56$	252.215	0.601852
$57$	−466.677	−1.08444
$58$	−334.352	−0.756941
$59$	268.600	0.592691	0.296345	−	0.955081i	$-0.404232\pi$
$59$	268.600	0.592691	0.296345	+	0.955081i	$0.404232\pi$
$60$	0	0
$61$	−323.925	−0.679906	−0.339953	−	0.940442i	$-0.610411\pi$
$61$	−323.925	−0.679906	−0.339953	+	0.940442i	$0.610411\pi$
$62$	−46.8992	−0.0960679
$63$	453.548	0.907011
$64$	−609.378	−1.19019
$65$	0	0
$66$	−2885.12	−5.38080
$67$	−541.910	−0.988132	−0.494066	−	0.869424i	$-0.664490\pi$
$67$	−541.910	−0.988132	−0.494066	+	0.869424i	$0.664490\pi$
$68$	980.715	1.74896
$69$	952.129	1.66120
$70$	0	0
$71$	−161.433	−0.269839	−0.134919	−	0.990857i	$-0.543078\pi$
$71$	−161.433	−0.269839	−0.134919	+	0.990857i	$0.543078\pi$
$72$	2334.53	3.82120
$73$	305.751	0.490212	0.245106	−	0.969496i	$-0.421177\pi$
$73$	305.751	0.490212	0.245106	+	0.969496i	$0.421177\pi$
$74$	1163.40	1.82761
$75$	0	0
$76$	752.161	1.13525
$77$	435.373	0.644356
$78$	−653.753	−0.949012
$79$	−504.722	−0.718805	−0.359403	−	0.933183i	$-0.617020\pi$
$79$	−504.722	−0.718805	−0.359403	+	0.933183i	$0.617020\pi$
$80$	0	0
$81$	1719.68	2.35895
$82$	1623.44	2.18633
$83$	−513.838	−0.679531	−0.339766	−	0.940510i	$-0.610348\pi$
$83$	−513.838	−0.679531	−0.339766	+	0.940510i	$0.610348\pi$
$84$	−1035.62	−1.34518
$85$	0	0
$86$	248.176	0.311180
$87$	661.625	0.815330
$88$	2240.98	2.71465
$89$	543.158	0.646907	0.323453	−	0.946244i	$-0.395156\pi$
$89$	543.158	0.646907	0.323453	+	0.946244i	$0.395156\pi$
$90$	0	0
$91$	98.6535	0.113645
$92$	−1534.58	−1.73903
$93$	92.8056	0.103478
$94$	−2186.32	−2.39896
$95$	0	0
$96$	399.842	0.425090
$97$	1863.06	1.95016	0.975079	−	0.221857i	$-0.0712118\pi$
$97$	1863.06	1.95016	0.975079	+	0.221857i	$0.0712118\pi$
$98$	237.242	0.244541
$99$	4029.85	4.09106
$100$	0	0
$101$	−1685.70	−1.66073	−0.830365	−	0.557221i	$-0.811868\pi$
$101$	−1685.70	−1.66073	−0.830365	+	0.557221i	$0.811868\pi$
$102$	−2946.08	−2.85986
$103$	−1014.19	−0.970203	−0.485102	−	0.874458i	$-0.661217\pi$
$103$	−1014.19	−0.970203	−0.485102	+	0.874458i	$0.661217\pi$
$104$	507.794	0.478782
$105$	0	0
$106$	−871.571	−0.798627
$107$	913.161	0.825033	0.412517	−	0.910950i	$-0.364650\pi$
$107$	913.161	0.825033	0.412517	+	0.910950i	$0.364650\pi$
$108$	−5591.24	−4.98164
$109$	−1397.13	−1.22772	−0.613859	−	0.789416i	$-0.710383\pi$
$109$	−1397.13	−1.22772	−0.613859	+	0.789416i	$0.710383\pi$
$110$	0	0
$111$	−2302.18	−1.96859
$112$	356.403	0.300687
$113$	2082.49	1.73366	0.866831	−	0.498603i	$-0.166153\pi$
$113$	2082.49	1.73366	0.866831	+	0.498603i	$0.166153\pi$
$114$	−2259.50	−1.85633
$115$	0	0
$116$	−1066.37	−0.853531
$117$	913.145	0.721541
$118$	1300.47	1.01456
$119$	444.573	0.342470
$120$	0	0
$121$	2537.37	1.90636
$122$	−1568.34	−1.16386
$123$	−3212.51	−2.35498
$124$	−149.578	−0.108327
$125$	0	0
$126$	2195.93	1.55261
$127$	−230.691	−0.161185	−0.0805925	−	0.996747i	$-0.525681\pi$
$127$	−230.691	−0.161185	−0.0805925	+	0.996747i	$0.525681\pi$
$128$	−2616.54	−1.80681
$129$	−491.097	−0.335184
$130$	0	0
$131$	−973.877	−0.649527	−0.324764	−	0.945795i	$-0.605285\pi$
$131$	−973.877	−0.649527	−0.324764	+	0.945795i	$0.605285\pi$
$132$	−9201.65	−6.06743
$133$	340.966	0.222297
$134$	−2623.75	−1.69148
$135$	0	0
$136$	2288.33	1.44281
$137$	695.734	0.433873	0.216936	−	0.976186i	$-0.430394\pi$
$137$	695.734	0.433873	0.216936	+	0.976186i	$0.430394\pi$
$138$	4609.90	2.84363
$139$	−298.530	−0.182165	−0.0910826	−	0.995843i	$-0.529033\pi$
$139$	−298.530	−0.182165	−0.0910826	+	0.995843i	$0.529033\pi$
$140$	0	0
$141$	4326.36	2.58401
$142$	−781.605	−0.461908
$143$	876.553	0.512595
$144$	3298.90	1.90908
$145$	0	0
$146$	1480.35	0.839140
$147$	−469.461	−0.263405
$148$	3710.50	2.06082
$149$	−1792.02	−0.985290	−0.492645	−	0.870230i	$-0.663970\pi$
$149$	−1792.02	−0.985290	−0.492645	+	0.870230i	$0.663970\pi$
$150$	0	0
$151$	1201.27	0.647403	0.323701	−	0.946159i	$-0.395073\pi$
$151$	1201.27	0.647403	0.323701	+	0.946159i	$0.395073\pi$
$152$	1755.04	0.936529
$153$	4115.00	2.17437
$154$	2107.94	1.10300
$155$	0	0
$156$	−2085.05	−1.07011
$157$	409.798	0.208315	0.104158	−	0.994561i	$-0.466785\pi$
$157$	409.798	0.208315	0.104158	+	0.994561i	$0.466785\pi$
$158$	−2443.70	−1.23044
$159$	1724.69	0.860232
$160$	0	0
$161$	−695.649	−0.340527
$162$	8326.12	4.03803
$163$	−2030.71	−0.975811	−0.487905	−	0.872896i	$-0.662239\pi$
$163$	−2030.71	−0.975811	−0.487905	+	0.872896i	$0.662239\pi$
$164$	5177.73	2.46532
$165$	0	0
$166$	−2487.84	−1.16321
$167$	520.014	0.240958	0.120479	−	0.992716i	$-0.461557\pi$
$167$	520.014	0.240958	0.120479	+	0.992716i	$0.461557\pi$
$168$	−2416.44	−1.10971
$169$	−1998.38	−0.909594
$170$	0	0
$171$	3156.01	1.41138
$172$	791.520	0.350888
$173$	−2561.90	−1.12588	−0.562942	−	0.826497i	$-0.690331\pi$
$173$	−2561.90	−1.12588	−0.562942	+	0.826497i	$0.690331\pi$
$174$	3203.37	1.39567
$175$	0	0
$176$	3166.71	1.35625
$177$	−2573.42	−1.09282
$178$	2629.80	1.10737
$179$	−3042.08	−1.27025	−0.635127	−	0.772408i	$-0.719052\pi$
$179$	−3042.08	−1.27025	−0.635127	+	0.772408i	$0.719052\pi$
$180$	0	0
$181$	−3648.02	−1.49809	−0.749047	−	0.662516i	$-0.769488\pi$
$181$	−3648.02	−1.49809	−0.749047	+	0.662516i	$0.769488\pi$
$182$	477.648	0.194536
$183$	3103.47	1.25363
$184$	−3580.68	−1.43463
$185$	0	0
$186$	449.334	0.177133
$187$	3950.11	1.54471
$188$	−6972.95	−2.70508
$189$	−2534.59	−0.975474
$190$	0	0
$191$	−4091.12	−1.54986	−0.774929	−	0.632049i	$-0.782214\pi$
$191$	−4091.12	−1.54986	−0.774929	+	0.632049i	$0.782214\pi$
$192$	5838.35	2.19451
$193$	3051.70	1.13817	0.569084	−	0.822280i	$-0.307298\pi$
$193$	3051.70	1.13817	0.569084	+	0.822280i	$0.307298\pi$
$194$	9020.34	3.33826
$195$	0	0
$196$	756.648	0.275746
$197$	3011.44	1.08912	0.544560	−	0.838722i	$-0.316697\pi$
$197$	3011.44	1.08912	0.544560	+	0.838722i	$0.316697\pi$
$198$	19511.2	7.00304
$199$	199.943	0.0712239	0.0356119	−	0.999366i	$-0.488662\pi$
$199$	199.943	0.0712239	0.0356119	+	0.999366i	$0.488662\pi$
$200$	0	0
$201$	5191.96	1.82195
$202$	−8161.62	−2.84282
$203$	−483.400	−0.167133
$204$	−9396.08	−3.22479
$205$	0	0
$206$	−4910.37	−1.66078
$207$	−6438.98	−2.16203
$208$	717.560	0.239201
$209$	3029.54	1.00267
$210$	0	0
$211$	−297.442	−0.0970461	−0.0485231	−	0.998822i	$-0.515451\pi$
$211$	−297.442	−0.0970461	−0.0485231	+	0.998822i	$0.515451\pi$
$212$	−2779.75	−0.900537
$213$	1546.66	0.497538
$214$	4421.23	1.41228
$215$	0	0
$216$	−13046.2	−4.10963
$217$	−67.8061	−0.0212119
$218$	−6764.47	−2.10159
$219$	−2929.36	−0.903870
$220$	0	0
$221$	895.075	0.272440
$222$	−11146.4	−3.36981
$223$	−6282.68	−1.88663	−0.943317	−	0.331894i	$-0.892312\pi$
$223$	−6282.68	−1.88663	−0.943317	+	0.331894i	$0.892312\pi$
$224$	−292.134	−0.0871385
$225$	0	0
$226$	10082.7	2.96766
$227$	−2357.28	−0.689243	−0.344621	−	0.938742i	$-0.611993\pi$
$227$	−2357.28	−0.689243	−0.344621	+	0.938742i	$0.611993\pi$
$228$	−7206.34	−2.09321
$229$	−2476.81	−0.714727	−0.357363	−	0.933965i	$-0.616324\pi$
$229$	−2476.81	−0.714727	−0.357363	+	0.933965i	$0.616324\pi$
$230$	0	0
$231$	−4171.25	−1.18809
$232$	−2488.18	−0.704125
$233$	−5142.47	−1.44590	−0.722950	−	0.690900i	$-0.757214\pi$
$233$	−5142.47	−1.44590	−0.722950	+	0.690900i	$0.757214\pi$
$234$	4421.15	1.23513
$235$	0	0
$236$	4147.67	1.14403
$237$	4835.66	1.32536
$238$	2152.48	0.586237
$239$	−831.250	−0.224975	−0.112488	−	0.993653i	$-0.535882\pi$
$239$	−831.250	−0.224975	−0.112488	+	0.993653i	$0.535882\pi$
$240$	0	0
$241$	4538.85	1.21317	0.606584	−	0.795020i	$-0.292540\pi$
$241$	4538.85	1.21317	0.606584	+	0.795020i	$0.292540\pi$
$242$	12285.1	3.26329
$243$	−6699.68	−1.76866
$244$	−5001.98	−1.31237
$245$	0	0
$246$	−15553.9	−4.03123
$247$	686.479	0.176841
$248$	−349.015	−0.0893648
$249$	4923.01	1.25294
$250$	0	0
$251$	7232.00	1.81865	0.909323	−	0.416091i	$-0.136600\pi$
$251$	7232.00	1.81865	0.909323	+	0.416091i	$0.136600\pi$
$252$	7003.60	1.75073
$253$	−6180.96	−1.53594
$254$	−1116.93	−0.275915
$255$	0	0
$256$	−7793.41	−1.90269
$257$	4242.66	1.02977	0.514883	−	0.857260i	$-0.327835\pi$
$257$	4242.66	1.02977	0.514883	+	0.857260i	$0.327835\pi$
$258$	−2377.73	−0.573764
$259$	1682.03	0.403537
$260$	0	0
$261$	−4474.39	−1.06114
$262$	−4715.20	−1.11185
$263$	6604.75	1.54854	0.774271	−	0.632855i	$-0.218117\pi$
$263$	6604.75	1.54854	0.774271	+	0.632855i	$0.218117\pi$
$264$	−21470.4	−5.00536
$265$	0	0
$266$	1650.85	0.380526
$267$	−5203.92	−1.19279
$268$	−8368.07	−1.90732
$269$	4612.29	1.04541	0.522707	−	0.852512i	$-0.324922\pi$
$269$	4612.29	1.04541	0.522707	+	0.852512i	$0.324922\pi$
$270$	0	0
$271$	−3542.29	−0.794018	−0.397009	−	0.917815i	$-0.629952\pi$
$271$	−3542.29	−0.794018	−0.397009	+	0.917815i	$0.629952\pi$
$272$	3233.62	0.720834
$273$	−945.184	−0.209543
$274$	3368.52	0.742699
$275$	0	0
$276$	14702.6	3.20649
$277$	19.5351	0.00423737	0.00211868	−	0.999998i	$-0.499326\pi$
$277$	19.5351	0.00423737	0.00211868	+	0.999998i	$0.499326\pi$
$278$	−1445.38	−0.311829
$279$	−627.618	−0.134676
$280$	0	0
$281$	6769.20	1.43707	0.718535	−	0.695491i	$-0.244813\pi$
$281$	6769.20	1.43707	0.718535	+	0.695491i	$0.244813\pi$
$282$	20946.8	4.42328
$283$	1269.89	0.266740	0.133370	−	0.991066i	$-0.457420\pi$
$283$	1269.89	0.266740	0.133370	+	0.991066i	$0.457420\pi$
$284$	−2492.81	−0.520850
$285$	0	0
$286$	4243.98	0.877455
$287$	2347.14	0.482743
$288$	−2704.02	−0.553249
$289$	−879.424	−0.178999
$290$	0	0
$291$	−17849.7	−3.59577
$292$	4721.35	0.946220
$293$	6349.74	1.26606	0.633030	−	0.774127i	$-0.281811\pi$
$293$	6349.74	1.26606	0.633030	+	0.774127i	$0.281811\pi$
$294$	−2272.98	−0.450894
$295$	0	0
$296$	8657.82	1.70009
$297$	−22520.3	−4.39987
$298$	−8676.39	−1.68661
$299$	−1400.58	−0.270894
$300$	0	0
$301$	358.808	0.0687087
$302$	5816.15	1.10822
$303$	16150.4	3.06211
$304$	2480.03	0.467893
$305$	0	0
$306$	19923.5	3.72206
$307$	−4772.37	−0.887211	−0.443605	−	0.896222i	$-0.646301\pi$
$307$	−4772.37	−0.887211	−0.443605	+	0.896222i	$0.646301\pi$
$308$	6722.95	1.24375
$309$	9716.78	1.78889
$310$	0	0
$311$	740.703	0.135053	0.0675264	−	0.997717i	$-0.478489\pi$
$311$	740.703	0.135053	0.0675264	+	0.997717i	$0.478489\pi$
$312$	−4865.10	−0.882795
$313$	−2279.68	−0.411678	−0.205839	−	0.978586i	$-0.565992\pi$
$313$	−2279.68	−0.411678	−0.205839	+	0.978586i	$0.565992\pi$
$314$	1984.11	0.356592
$315$	0	0
$316$	−7793.81	−1.38746
$317$	−10198.1	−1.80689	−0.903446	−	0.428702i	$-0.858971\pi$
$317$	−10198.1	−1.80689	−0.903446	+	0.428702i	$0.858971\pi$
$318$	8350.39	1.47254
$319$	−4295.09	−0.753852
$320$	0	0
$321$	−8748.85	−1.52122
$322$	−3368.10	−0.582910
$323$	3093.56	0.532911
$324$	26554.9	4.55331
$325$	0	0
$326$	−9832.01	−1.67038
$327$	13385.7	2.26371
$328$	12081.3	2.03378
$329$	−3160.95	−0.529692
$330$	0	0
$331$	−78.0380	−0.0129588	−0.00647939	−	0.999979i	$-0.502062\pi$
$331$	−78.0380	−0.0129588	−0.00647939	+	0.999979i	$0.502062\pi$
$332$	−7934.59	−1.31165
$333$	15569.0	2.56209
$334$	2517.74	0.412469
$335$	0	0
$336$	−3414.64	−0.554417
$337$	−4164.73	−0.673196	−0.336598	−	0.941648i	$-0.609276\pi$
$337$	−4164.73	−0.673196	−0.336598	+	0.941648i	$0.609276\pi$
$338$	−9675.49	−1.55703
$339$	−19952.0	−3.19658
$340$	0	0
$341$	−602.468	−0.0956759
$342$	15280.4	2.41599
$343$	343.000	0.0539949
$344$	1846.87	0.289467
$345$	0	0
$346$	−12403.9	−1.92728
$347$	1795.19	0.277726	0.138863	−	0.990312i	$-0.455655\pi$
$347$	1795.19	0.277726	0.138863	+	0.990312i	$0.455655\pi$
$348$	10216.7	1.57377
$349$	−11751.4	−1.80241	−0.901203	−	0.433398i	$-0.857314\pi$
$349$	−11751.4	−1.80241	−0.901203	+	0.433398i	$0.857314\pi$
$350$	0	0
$351$	−5102.99	−0.776004
$352$	−2595.66	−0.393038
$353$	2882.32	0.434590	0.217295	−	0.976106i	$-0.430277\pi$
$353$	2882.32	0.434590	0.217295	+	0.976106i	$0.430277\pi$
$354$	−12459.6	−1.87069
$355$	0	0
$356$	8387.34	1.24868
$357$	−4259.39	−0.631458
$358$	−14728.7	−2.17441
$359$	−1193.78	−0.175503	−0.0877513	−	0.996142i	$-0.527968\pi$
$359$	−1193.78	−0.175503	−0.0877513	+	0.996142i	$0.527968\pi$
$360$	0	0
$361$	−4486.39	−0.654088
$362$	−17662.5	−2.56442
$363$	−24310.1	−3.51502
$364$	1523.39	0.219360
$365$	0	0
$366$	15026.0	2.14596
$367$	8858.80	1.26001	0.630007	−	0.776589i	$-0.283052\pi$
$367$	8858.80	1.26001	0.630007	+	0.776589i	$0.283052\pi$
$368$	−5059.83	−0.716744
$369$	21725.3	3.06497
$370$	0	0
$371$	−1260.10	−0.176337
$372$	1433.09	0.199737
$373$	−2287.78	−0.317578	−0.158789	−	0.987313i	$-0.550759\pi$
$373$	−2287.78	−0.317578	−0.158789	+	0.987313i	$0.550759\pi$
$374$	19125.1	2.64422
$375$	0	0
$376$	−16270.2	−2.23157
$377$	−973.246	−0.132957
$378$	−12271.7	−1.66981
$379$	8870.18	1.20219	0.601095	−	0.799177i	$-0.294731\pi$
$379$	8870.18	1.20219	0.601095	+	0.799177i	$0.294731\pi$
$380$	0	0
$381$	2210.21	0.297198
$382$	−19807.8	−2.65303
$383$	13359.2	1.78231	0.891155	−	0.453700i	$-0.149896\pi$
$383$	13359.2	1.78231	0.891155	+	0.453700i	$0.149896\pi$
$384$	25068.7	3.33146
$385$	0	0
$386$	14775.3	1.94830
$387$	3321.15	0.436237
$388$	28769.0	3.76424
$389$	11324.7	1.47605	0.738025	−	0.674773i	$-0.235759\pi$
$389$	11324.7	1.47605	0.738025	+	0.674773i	$0.235759\pi$
$390$	0	0
$391$	−6311.57	−0.816342
$392$	1765.51	0.227479
$393$	9330.57	1.19762
$394$	14580.4	1.86434
$395$	0	0
$396$	62228.2	7.89667
$397$	−13242.8	−1.67415	−0.837076	−	0.547087i	$-0.815737\pi$
$397$	−13242.8	−1.67415	−0.837076	+	0.547087i	$0.815737\pi$
$398$	968.056	0.121920
$399$	−3266.74	−0.409879
$400$	0	0
$401$	1952.96	0.243207	0.121604	−	0.992579i	$-0.461196\pi$
$401$	1952.96	0.243207	0.121604	+	0.992579i	$0.461196\pi$
$402$	25137.8	3.11880
$403$	−136.516	−0.0168744
$404$	−26030.3	−3.20558
$405$	0	0
$406$	−2340.46	−0.286097
$407$	14945.1	1.82015
$408$	−21924.1	−2.66031
$409$	−10597.8	−1.28124	−0.640618	−	0.767860i	$-0.721322\pi$
$409$	−10597.8	−1.28124	−0.640618	+	0.767860i	$0.721322\pi$
$410$	0	0
$411$	−6665.72	−0.799989
$412$	−15660.9	−1.87271
$413$	1880.20	0.224016
$414$	−31175.5	−3.70094
$415$	0	0
$416$	−588.164	−0.0693200
$417$	2860.17	0.335882
$418$	14668.1	1.71636
$419$	−1631.18	−0.190187	−0.0950935	−	0.995468i	$-0.530315\pi$
$419$	−1631.18	−0.190187	−0.0950935	+	0.995468i	$0.530315\pi$
$420$	0	0
$421$	13181.2	1.52592	0.762961	−	0.646445i	$-0.223745\pi$
$421$	13181.2	1.52592	0.762961	+	0.646445i	$0.223745\pi$
$422$	−1440.12	−0.166123
$423$	−29258.0	−3.36305
$424$	−6486.06	−0.742903
$425$	0	0
$426$	7488.44	0.851681
$427$	−2267.47	−0.256980
$428$	14100.8	1.59250
$429$	−8398.12	−0.945140
$430$	0	0
$431$	9159.40	1.02365	0.511825	−	0.859090i	$-0.328970\pi$
$431$	9159.40	1.02365	0.511825	+	0.859090i	$0.328970\pi$
$432$	−18435.5	−2.05319
$433$	270.519	0.0300238	0.0150119	−	0.999887i	$-0.495221\pi$
$433$	270.519	0.0300238	0.0150119	+	0.999887i	$0.495221\pi$
$434$	−328.295	−0.0363103
$435$	0	0
$436$	−21574.3	−2.36977
$437$	−4840.67	−0.529887
$438$	−14183.0	−1.54724
$439$	17008.0	1.84908	0.924541	−	0.381082i	$-0.124448\pi$
$439$	17008.0	1.84908	0.924541	+	0.381082i	$0.124448\pi$
$440$	0	0
$441$	3174.84	0.342818
$442$	4333.66	0.466360
$443$	3968.12	0.425578	0.212789	−	0.977098i	$-0.431745\pi$
$443$	3968.12	0.425578	0.212789	+	0.977098i	$0.431745\pi$
$444$	−35549.8	−3.79981
$445$	0	0
$446$	−30418.7	−3.22952
$447$	17169.1	1.81671
$448$	−4265.64	−0.449850
$449$	−12480.3	−1.31177	−0.655884	−	0.754862i	$-0.727704\pi$
$449$	−12480.3	−1.31177	−0.655884	+	0.754862i	$0.727704\pi$
$450$	0	0
$451$	20854.8	2.17741
$452$	32157.3	3.34636
$453$	−11509.2	−1.19370
$454$	−11413.2	−1.17984
$455$	0	0
$456$	−16814.7	−1.72680
$457$	5782.90	0.591932	0.295966	−	0.955199i	$-0.404359\pi$
$457$	5782.90	0.591932	0.295966	+	0.955199i	$0.404359\pi$
$458$	−11991.9	−1.22346
$459$	−22996.2	−2.33849
$460$	0	0
$461$	10049.6	1.01531	0.507653	−	0.861562i	$-0.330513\pi$
$461$	10049.6	1.01531	0.507653	+	0.861562i	$0.330513\pi$
$462$	−20195.8	−2.03375
$463$	−659.842	−0.0662321	−0.0331161	−	0.999452i	$-0.510543\pi$
$463$	−659.842	−0.0662321	−0.0331161	+	0.999452i	$0.510543\pi$
$464$	−3516.03	−0.351783
$465$	0	0
$466$	−24898.2	−2.47508
$467$	−4467.60	−0.442690	−0.221345	−	0.975196i	$-0.571045\pi$
$467$	−4467.60	−0.442690	−0.221345	+	0.975196i	$0.571045\pi$
$468$	14100.6	1.39274
$469$	−3793.37	−0.373479
$470$	0	0
$471$	−3926.21	−0.384099
$472$	9677.87	0.943771
$473$	3188.07	0.309910
$474$	23412.7	2.26873
$475$	0	0
$476$	6865.01	0.661044
$477$	−11663.6	−1.11958
$478$	−4024.64	−0.385110
$479$	7633.87	0.728185	0.364092	−	0.931363i	$-0.381379\pi$
$479$	7633.87	0.728185	0.364092	+	0.931363i	$0.381379\pi$
$480$	0	0
$481$	3386.49	0.321020
$482$	21975.6	2.07669
$483$	6664.90	0.627875
$484$	39181.5	3.67971
$485$	0	0
$486$	−32437.6	−3.02758
$487$	6289.84	0.585256	0.292628	−	0.956226i	$-0.405470\pi$
$487$	6289.84	0.585256	0.292628	+	0.956226i	$0.405470\pi$
$488$	−11671.2	−1.08265
$489$	19455.9	1.79923
$490$	0	0
$491$	3562.54	0.327445	0.163722	−	0.986506i	$-0.447650\pi$
$491$	3562.54	0.327445	0.163722	+	0.986506i	$0.447650\pi$
$492$	−49607.0	−4.54564
$493$	−4385.85	−0.400667
$494$	3323.71	0.302714
$495$	0	0
$496$	−493.190	−0.0446469
$497$	−1130.03	−0.101990
$498$	23835.6	2.14478
$499$	−18916.9	−1.69706	−0.848532	−	0.529144i	$-0.822513\pi$
$499$	−18916.9	−1.69706	−0.848532	+	0.529144i	$0.822513\pi$
$500$	0	0
$501$	−4982.17	−0.444286
$502$	35015.0	3.11314
$503$	2565.91	0.227452	0.113726	−	0.993512i	$-0.463721\pi$
$503$	2565.91	0.227452	0.113726	+	0.993512i	$0.463721\pi$
$504$	16341.7	1.44428
$505$	0	0
$506$	−29926.2	−2.62921
$507$	19146.1	1.67714
$508$	−3562.28	−0.311123
$509$	5447.84	0.474403	0.237202	−	0.971460i	$-0.423770\pi$
$509$	5447.84	0.474403	0.237202	+	0.971460i	$0.423770\pi$
$510$	0	0
$511$	2140.26	0.185283
$512$	−16800.8	−1.45019
$513$	−17636.9	−1.51791
$514$	20541.6	1.76274
$515$	0	0
$516$	−7583.42	−0.646980
$517$	−28085.5	−2.38917
$518$	8143.83	0.690771
$519$	24545.2	2.07594
$520$	0	0
$521$	−4732.95	−0.397993	−0.198997	−	0.980000i	$-0.563768\pi$
$521$	−4732.95	−0.397993	−0.198997	+	0.980000i	$0.563768\pi$
$522$	−21663.5	−1.81645
$523$	−9182.96	−0.767769	−0.383884	−	0.923381i	$-0.625414\pi$
$523$	−9182.96	−0.767769	−0.383884	+	0.923381i	$0.625414\pi$
$524$	−15038.4	−1.25373
$525$	0	0
$526$	31978.0	2.65078
$527$	−615.199	−0.0508510
$528$	−30339.7	−2.50069
$529$	−2290.93	−0.188290
$530$	0	0
$531$	17403.3	1.42230
$532$	5265.13	0.429083
$533$	4725.59	0.384030
$534$	−25195.7	−2.04180
$535$	0	0
$536$	−19525.4	−1.57345
$537$	29145.7	2.34214
$538$	22331.2	1.78953
$539$	3047.61	0.243544
$540$	0	0
$541$	14572.9	1.15811	0.579055	−	0.815288i	$-0.303422\pi$
$541$	14572.9	1.15811	0.579055	+	0.815288i	$0.303422\pi$
$542$	−17150.6	−1.35919
$543$	34951.1	2.76224
$544$	−2650.51	−0.208896
$545$	0	0
$546$	−4576.27	−0.358693
$547$	11290.3	0.882519	0.441260	−	0.897380i	$-0.354532\pi$
$547$	11290.3	0.882519	0.441260	+	0.897380i	$0.354532\pi$
$548$	10743.4	0.837472
$549$	−20987.9	−1.63159
$550$	0	0
$551$	−3363.73	−0.260072
$552$	34305.9	2.64521
$553$	−3533.05	−0.271683
$554$	94.5826	0.00725349
$555$	0	0
$556$	−4609.84	−0.351620
$557$	3919.93	0.298191	0.149096	−	0.988823i	$-0.452364\pi$
$557$	3919.93	0.298191	0.149096	+	0.988823i	$0.452364\pi$
$558$	−3038.72	−0.230537
$559$	722.401	0.0546588
$560$	0	0
$561$	−37845.4	−2.84819
$562$	32774.2	2.45996
$563$	−7444.71	−0.557295	−0.278647	−	0.960393i	$-0.589886\pi$
$563$	−7444.71	−0.557295	−0.278647	+	0.960393i	$0.589886\pi$
$564$	66806.8	4.98772
$565$	0	0
$566$	6148.41	0.456602
$567$	12037.7	0.891601
$568$	−5816.55	−0.429678
$569$	8529.24	0.628408	0.314204	−	0.949355i	$-0.398262\pi$
$569$	8529.24	0.628408	0.314204	+	0.949355i	$0.398262\pi$
$570$	0	0
$571$	10324.8	0.756706	0.378353	−	0.925661i	$-0.376491\pi$
$571$	10324.8	0.756706	0.378353	+	0.925661i	$0.376491\pi$
$572$	13535.6	0.989423
$573$	39196.3	2.85768
$574$	11364.1	0.826355
$575$	0	0
$576$	−39483.1	−2.85613
$577$	6467.10	0.466601	0.233301	−	0.972405i	$-0.425047\pi$
$577$	6467.10	0.466601	0.233301	+	0.972405i	$0.425047\pi$
$578$	−4257.88	−0.306409
$579$	−29237.9	−2.09859
$580$	0	0
$581$	−3596.87	−0.256839
$582$	−86422.5	−6.15520
$583$	−11196.2	−0.795369
$584$	11016.5	0.780589
$585$	0	0
$586$	30743.4	2.16723
$587$	7114.68	0.500263	0.250131	−	0.968212i	$-0.419526\pi$
$587$	7114.68	0.500263	0.250131	+	0.968212i	$0.419526\pi$
$588$	−7249.33	−0.508431
$589$	−471.828	−0.0330073
$590$	0	0
$591$	−28852.2	−2.00816
$592$	12234.3	0.849369
$593$	−21270.8	−1.47299	−0.736497	−	0.676441i	$-0.763522\pi$
$593$	−21270.8	−1.47299	−0.736497	+	0.676441i	$0.763522\pi$
$594$	−109036.	−7.53165
$595$	0	0
$596$	−27672.1	−1.90183
$597$	−1915.62	−0.131325
$598$	−6781.13	−0.463714
$599$	−4697.43	−0.320420	−0.160210	−	0.987083i	$-0.551217\pi$
$599$	−4697.43	−0.320420	−0.160210	+	0.987083i	$0.551217\pi$
$600$	0	0
$601$	8719.81	0.591828	0.295914	−	0.955215i	$-0.404376\pi$
$601$	8719.81	0.591828	0.295914	+	0.955215i	$0.404376\pi$
$602$	1737.23	0.117615
$603$	−35111.8	−2.37125
$604$	18549.7	1.24963
$605$	0	0
$606$	78195.2	5.24169
$607$	−23097.1	−1.54445	−0.772227	−	0.635347i	$-0.780857\pi$
$607$	−23097.1	−1.54445	−0.772227	+	0.635347i	$0.780857\pi$
$608$	−2032.81	−0.135594
$609$	4631.38	0.308166
$610$	0	0
$611$	−6364.05	−0.421378
$612$	63543.1	4.19702
$613$	−16846.2	−1.10997	−0.554986	−	0.831860i	$-0.687276\pi$
$613$	−16846.2	−1.10997	−0.554986	+	0.831860i	$0.687276\pi$
$614$	−23106.3	−1.51872
$615$	0	0
$616$	15686.8	1.02604
$617$	3476.46	0.226834	0.113417	−	0.993547i	$-0.463820\pi$
$617$	3476.46	0.226834	0.113417	+	0.993547i	$0.463820\pi$
$618$	47045.5	3.06221
$619$	−5407.16	−0.351102	−0.175551	−	0.984470i	$-0.556171\pi$
$619$	−5407.16	−0.351102	−0.175551	+	0.984470i	$0.556171\pi$
$620$	0	0
$621$	35983.4	2.32522
$622$	3586.24	0.231182
$623$	3802.11	0.244508
$624$	−6874.83	−0.441047
$625$	0	0
$626$	−11037.5	−0.704706
$627$	−29025.6	−1.84876
$628$	6328.02	0.402095
$629$	15260.9	0.967396
$630$	0	0
$631$	−10498.7	−0.662358	−0.331179	−	0.943568i	$-0.607446\pi$
$631$	−10498.7	−0.662358	−0.331179	+	0.943568i	$0.607446\pi$
$632$	−18185.5	−1.14459
$633$	2849.74	0.178937
$634$	−49376.1	−3.09302
$635$	0	0
$636$	26632.3	1.66044
$637$	690.574	0.0429538
$638$	−20795.4	−1.29044
$639$	−10459.7	−0.647539
$640$	0	0
$641$	14363.3	0.885050	0.442525	−	0.896756i	$-0.354083\pi$
$641$	14363.3	0.885050	0.442525	+	0.896756i	$0.354083\pi$
$642$	−42359.1	−2.60402
$643$	16883.3	1.03548	0.517739	−	0.855539i	$-0.326774\pi$
$643$	16883.3	1.03548	0.517739	+	0.855539i	$0.326774\pi$
$644$	−10742.1	−0.657293
$645$	0	0
$646$	14978.0	0.912231
$647$	−27365.2	−1.66281	−0.831404	−	0.555668i	$-0.812462\pi$
$647$	−27365.2	−1.66281	−0.831404	+	0.555668i	$0.812462\pi$
$648$	61961.3	3.75628
$649$	16705.9	1.01042
$650$	0	0
$651$	649.639	0.0391112
$652$	−31357.8	−1.88353
$653$	28643.3	1.71654	0.858269	−	0.513200i	$-0.171540\pi$
$653$	28643.3	1.71654	0.858269	+	0.513200i	$0.171540\pi$
$654$	64809.3	3.87499
$655$	0	0
$656$	17072.0	1.01608
$657$	19810.4	1.17637
$658$	−15304.3	−0.906721
$659$	−4102.07	−0.242480	−0.121240	−	0.992623i	$-0.538687\pi$
$659$	−4102.07	−0.242480	−0.121240	+	0.992623i	$0.538687\pi$
$660$	0	0
$661$	−13784.0	−0.811098	−0.405549	−	0.914073i	$-0.632920\pi$
$661$	−13784.0	−0.811098	−0.405549	+	0.914073i	$0.632920\pi$
$662$	−377.834	−0.0221827
$663$	−8575.58	−0.502334
$664$	−18514.0	−1.08205
$665$	0	0
$666$	75379.9	4.38576
$667$	6862.79	0.398393
$668$	8029.95	0.465102
$669$	60193.4	3.47864
$670$	0	0
$671$	−20146.9	−1.15911
$672$	2798.89	0.160669
$673$	4676.98	0.267882	0.133941	−	0.990989i	$-0.457237\pi$
$673$	4676.98	0.267882	0.133941	+	0.990989i	$0.457237\pi$
$674$	−20164.2	−1.15237
$675$	0	0
$676$	−30858.5	−1.75572
$677$	3849.54	0.218537	0.109269	−	0.994012i	$-0.465149\pi$
$677$	3849.54	0.218537	0.109269	+	0.994012i	$0.465149\pi$
$678$	−96600.9	−5.47188
$679$	13041.4	0.737091
$680$	0	0
$681$	22584.7	1.27085
$682$	−2916.96	−0.163777
$683$	−10647.5	−0.596508	−0.298254	−	0.954487i	$-0.596404\pi$
$683$	−10647.5	−0.596508	−0.298254	+	0.954487i	$0.596404\pi$
$684$	48734.5	2.72428
$685$	0	0
$686$	1660.69	0.0924280
$687$	23730.0	1.31784
$688$	2609.80	0.144619
$689$	−2537.01	−0.140279
$690$	0	0
$691$	22410.8	1.23379	0.616894	−	0.787046i	$-0.288391\pi$
$691$	22410.8	1.23379	0.616894	+	0.787046i	$0.288391\pi$
$692$	−39560.4	−2.17321
$693$	28209.0	1.54628
$694$	8691.72	0.475408
$695$	0	0
$696$	23838.9	1.29829
$697$	21295.4	1.15728
$698$	−56896.6	−3.08534
$699$	49269.2	2.66600
$700$	0	0
$701$	6040.55	0.325461	0.162731	−	0.986671i	$-0.447970\pi$
$701$	6040.55	0.325461	0.162731	+	0.986671i	$0.447970\pi$
$702$	−24707.0	−1.32836
$703$	11704.4	0.627936
$704$	−37901.0	−2.02904
$705$	0	0
$706$	13955.2	0.743926
$707$	−11799.9	−0.627697
$708$	−39738.2	−2.10940
$709$	19582.2	1.03727	0.518634	−	0.854996i	$-0.326441\pi$
$709$	19582.2	1.03727	0.518634	+	0.854996i	$0.326441\pi$
$710$	0	0
$711$	−32702.2	−1.72493
$712$	19570.4	1.03010
$713$	962.637	0.0505625
$714$	−20622.6	−1.08092
$715$	0	0
$716$	−46975.2	−2.45188
$717$	7964.07	0.414817
$718$	−5779.91	−0.300424
$719$	9257.31	0.480166	0.240083	−	0.970752i	$-0.422825\pi$
$719$	9257.31	0.480166	0.240083	+	0.970752i	$0.422825\pi$
$720$	0	0
$721$	−7099.32	−0.366702
$722$	−21721.6	−1.11966
$723$	−43486.1	−2.23688
$724$	−56332.0	−2.89166
$725$	0	0
$726$	−117702.	−6.01697
$727$	11915.5	0.607870	0.303935	−	0.952693i	$-0.401699\pi$
$727$	11915.5	0.607870	0.303935	+	0.952693i	$0.401699\pi$
$728$	3554.56	0.180963
$729$	17757.3	0.902162
$730$	0	0
$731$	3255.43	0.164715
$732$	47923.2	2.41980
$733$	−15608.0	−0.786486	−0.393243	−	0.919435i	$-0.628647\pi$
$733$	−15608.0	−0.786486	−0.393243	+	0.919435i	$0.628647\pi$
$734$	42891.4	2.15688
$735$	0	0
$736$	4147.40	0.207711
$737$	−33704.8	−1.68457
$738$	105187.	5.24659
$739$	−26189.9	−1.30367	−0.651835	−	0.758361i	$-0.726000\pi$
$739$	−26189.9	−1.30367	−0.651835	+	0.758361i	$0.726000\pi$
$740$	0	0
$741$	−6577.05	−0.326065
$742$	−6101.00	−0.301853
$743$	37914.9	1.87209	0.936044	−	0.351882i	$-0.114458\pi$
$743$	37914.9	1.87209	0.936044	+	0.351882i	$0.114458\pi$
$744$	3343.86	0.164774
$745$	0	0
$746$	−11076.7	−0.543627
$747$	−33292.9	−1.63069
$748$	60996.8	2.98164
$749$	6392.12	0.311833
$750$	0	0
$751$	−21401.6	−1.03989	−0.519944	−	0.854200i	$-0.674047\pi$
$751$	−21401.6	−1.03989	−0.519944	+	0.854200i	$0.674047\pi$
$752$	−22991.3	−1.11490
$753$	−69288.7	−3.35328
$754$	−4712.14	−0.227594
$755$	0	0
$756$	−39138.7	−1.88288
$757$	24094.8	1.15686	0.578428	−	0.815734i	$-0.303667\pi$
$757$	24094.8	1.15686	0.578428	+	0.815734i	$0.303667\pi$
$758$	42946.5	2.05790
$759$	59218.8	2.83203
$760$	0	0
$761$	19101.1	0.909872	0.454936	−	0.890524i	$-0.349662\pi$
$761$	19101.1	0.909872	0.454936	+	0.890524i	$0.349662\pi$
$762$	10701.1	0.508741
$763$	−9779.94	−0.464033
$764$	−63174.2	−2.99157
$765$	0	0
$766$	64681.0	3.05094
$767$	3785.48	0.178208
$768$	74667.5	3.50824
$769$	−32718.1	−1.53426	−0.767129	−	0.641493i	$-0.778315\pi$
$769$	−32718.1	−1.53426	−0.767129	+	0.641493i	$0.778315\pi$
$770$	0	0
$771$	−40648.3	−1.89872
$772$	47123.8	2.19692
$773$	−4707.97	−0.219061	−0.109530	−	0.993983i	$-0.534935\pi$
$773$	−4707.97	−0.219061	−0.109530	+	0.993983i	$0.534935\pi$
$774$	16079.9	0.746746
$775$	0	0
$776$	67127.6	3.10533
$777$	−16115.2	−0.744056
$778$	54830.3	2.52669
$779$	16332.6	0.751187
$780$	0	0
$781$	−10040.5	−0.460023
$782$	−30558.5	−1.39741
$783$	25004.5	1.14124
$784$	2494.82	0.113649
$785$	0	0
$786$	45175.6	2.05007
$787$	3218.47	0.145776	0.0728882	−	0.997340i	$-0.476778\pi$
$787$	3218.47	0.145776	0.0728882	+	0.997340i	$0.476778\pi$
$788$	46502.1	2.10224
$789$	−63279.1	−2.85525
$790$	0	0
$791$	14577.4	0.655262
$792$	145199.	6.51440
$793$	−4565.18	−0.204432
$794$	−64117.4	−2.86580
$795$	0	0
$796$	3087.47	0.137478
$797$	−15548.9	−0.691054	−0.345527	−	0.938409i	$-0.612300\pi$
$797$	−15548.9	−0.691054	−0.345527	+	0.938409i	$0.612300\pi$
$798$	−15816.5	−0.701627
$799$	−28679.0	−1.26982
$800$	0	0
$801$	35192.6	1.55240
$802$	9455.58	0.416319
$803$	19016.6	0.835717
$804$	80173.2	3.51678
$805$	0	0
$806$	−660.968	−0.0288854
$807$	−44189.6	−1.92757
$808$	−60737.1	−2.64446
$809$	−3106.83	−0.135019	−0.0675095	−	0.997719i	$-0.521505\pi$
$809$	−3106.83	−0.135019	−0.0675095	+	0.997719i	$0.521505\pi$
$810$	0	0
$811$	−44061.1	−1.90776	−0.953882	−	0.300183i	$-0.902952\pi$
$811$	−44061.1	−1.90776	−0.953882	+	0.300183i	$0.902952\pi$
$812$	−7464.56	−0.322604
$813$	33938.1	1.46404
$814$	72359.3	3.11572
$815$	0	0
$816$	−30980.8	−1.32910
$817$	2496.76	0.106916
$818$	−51310.9	−2.19321
$819$	6392.01	0.272717
$820$	0	0
$821$	13977.3	0.594169	0.297084	−	0.954851i	$-0.403986\pi$
$821$	13977.3	0.594169	0.297084	+	0.954851i	$0.403986\pi$
$822$	−32273.2	−1.36941
$823$	3287.14	0.139225	0.0696127	−	0.997574i	$-0.477824\pi$
$823$	3287.14	0.139225	0.0696127	+	0.997574i	$0.477824\pi$
$824$	−36542.0	−1.54490
$825$	0	0
$826$	9103.32	0.383469
$827$	−2454.69	−0.103214	−0.0516069	−	0.998667i	$-0.516434\pi$
$827$	−2454.69	−0.103214	−0.0516069	+	0.998667i	$0.516434\pi$
$828$	−99429.5	−4.17320
$829$	−38510.6	−1.61342	−0.806711	−	0.590946i	$-0.798755\pi$
$829$	−38510.6	−1.61342	−0.806711	+	0.590946i	$0.798755\pi$
$830$	0	0
$831$	−187.163	−0.00781301
$832$	−8588.18	−0.357862
$833$	3112.01	0.129442
$834$	13848.0	0.574960
$835$	0	0
$836$	46781.6	1.93538
$837$	3507.36	0.144841
$838$	−7897.64	−0.325560
$839$	32983.5	1.35723	0.678616	−	0.734493i	$-0.262580\pi$
$839$	32983.5	1.35723	0.678616	+	0.734493i	$0.262580\pi$
$840$	0	0
$841$	−19620.1	−0.804466
$842$	63819.1	2.61206
$843$	−64854.6	−2.64972
$844$	−4593.04	−0.187321
$845$	0	0
$846$	−141658.	−5.75684
$847$	17761.6	0.720537
$848$	−9165.39	−0.371157
$849$	−12166.7	−0.491824
$850$	0	0
$851$	−23879.6	−0.961906
$852$	23883.3	0.960361
$853$	−13620.1	−0.546710	−0.273355	−	0.961913i	$-0.588133\pi$
$853$	−13620.1	−0.546710	−0.273355	+	0.961913i	$0.588133\pi$
$854$	−10978.4	−0.439897
$855$	0	0
$856$	32901.9	1.31374
$857$	24493.2	0.976279	0.488139	−	0.872766i	$-0.337676\pi$
$857$	24493.2	0.976279	0.488139	+	0.872766i	$0.337676\pi$
$858$	−40661.0	−1.61788
$859$	3742.34	0.148646	0.0743231	−	0.997234i	$-0.476320\pi$
$859$	3742.34	0.148646	0.0743231	+	0.997234i	$0.476320\pi$
$860$	0	0
$861$	−22487.6	−0.890099
$862$	44346.8	1.75227
$863$	165.238	0.00651770	0.00325885	−	0.999995i	$-0.498963\pi$
$863$	165.238	0.00651770	0.00325885	+	0.999995i	$0.498963\pi$
$864$	15111.0	0.595009
$865$	0	0
$866$	1309.77	0.0513945
$867$	8425.63	0.330045
$868$	−1047.05	−0.0409437
$869$	−31391.8	−1.22542
$870$	0	0
$871$	−7637.33	−0.297108
$872$	−50339.8	−1.95495
$873$	120713.	4.67984
$874$	−23436.9	−0.907055
$875$	0	0
$876$	−45234.5	−1.74467
$877$	7230.06	0.278383	0.139192	−	0.990265i	$-0.455550\pi$
$877$	7230.06	0.278383	0.139192	+	0.990265i	$0.455550\pi$
$878$	82347.2	3.16524
$879$	−60835.9	−2.33441
$880$	0	0
$881$	−18707.9	−0.715422	−0.357711	−	0.933832i	$-0.616443\pi$
$881$	−18707.9	−0.715422	−0.357711	+	0.933832i	$0.616443\pi$
$882$	15371.5	0.586832
$883$	−28766.9	−1.09636	−0.548179	−	0.836361i	$-0.684679\pi$
$883$	−28766.9	−1.09636	−0.548179	+	0.836361i	$0.684679\pi$
$884$	13821.6	0.525871
$885$	0	0
$886$	19212.3	0.728500
$887$	−33980.4	−1.28630	−0.643152	−	0.765738i	$-0.722374\pi$
$887$	−33980.4	−1.28630	−0.643152	+	0.765738i	$0.722374\pi$
$888$	−82949.2	−3.13468
$889$	−1614.84	−0.0609222
$890$	0	0
$891$	106957.	4.02156
$892$	−97015.8	−3.64163
$893$	−21995.4	−0.824242
$894$	83127.1	3.10983
$895$	0	0
$896$	−18315.8	−0.682910
$897$	13418.7	0.499484
$898$	−60425.7	−2.24547
$899$	668.927	0.0248164
$900$	0	0
$901$	−11432.8	−0.422732
$902$	100972.	3.72727
$903$	−3437.68	−0.126688
$904$	75033.5	2.76059
$905$	0	0
$906$	−55723.6	−2.04337
$907$	−35753.2	−1.30889	−0.654446	−	0.756109i	$-0.727098\pi$
$907$	−35753.2	−1.30889	−0.654446	+	0.756109i	$0.727098\pi$
$908$	−36400.6	−1.33039
$909$	−109221.	−3.98529
$910$	0	0
$911$	16039.7	0.583334	0.291667	−	0.956520i	$-0.405790\pi$
$911$	16039.7	0.583334	0.291667	+	0.956520i	$0.405790\pi$
$912$	−23760.8	−0.862717
$913$	−31958.8	−1.15847
$914$	27998.9	1.01326
$915$	0	0
$916$	−38246.5	−1.37958
$917$	−6817.14	−0.245498
$918$	−111340.	−4.00301
$919$	22104.9	0.793441	0.396720	−	0.917940i	$-0.370148\pi$
$919$	22104.9	0.793441	0.396720	+	0.917940i	$0.370148\pi$
$920$	0	0
$921$	45723.3	1.63587
$922$	48656.8	1.73799
$923$	−2275.13	−0.0811342
$924$	−64411.5	−2.29327
$925$	0	0
$926$	−3194.74	−0.113376
$927$	−65711.9	−2.32822
$928$	2881.99	0.101946
$929$	20234.8	0.714621	0.357310	−	0.933986i	$-0.383694\pi$
$929$	20234.8	0.714621	0.357310	+	0.933986i	$0.383694\pi$
$930$	0	0
$931$	2386.76	0.0840204
$932$	−79409.1	−2.79091
$933$	−7096.56	−0.249015
$934$	−21630.7	−0.757792
$935$	0	0
$936$	32901.3	1.14894
$937$	−37551.2	−1.30923	−0.654614	−	0.755964i	$-0.727169\pi$
$937$	−37551.2	−1.30923	−0.654614	+	0.755964i	$0.727169\pi$
$938$	−18366.3	−0.639318
$939$	21841.3	0.759066
$940$	0	0
$941$	19093.3	0.661449	0.330725	−	0.943727i	$-0.392707\pi$
$941$	19093.3	0.661449	0.330725	+	0.943727i	$0.392707\pi$
$942$	−19009.4	−0.657496
$943$	−33322.2	−1.15071
$944$	13675.7	0.471511
$945$	0	0
$946$	15435.6	0.530501
$947$	−10117.0	−0.347158	−0.173579	−	0.984820i	$-0.555533\pi$
$947$	−10117.0	−0.347158	−0.173579	+	0.984820i	$0.555533\pi$
$948$	74671.3	2.55824
$949$	4309.06	0.147395
$950$	0	0
$951$	97706.8	3.33161
$952$	16018.3	0.545332
$953$	6272.48	0.213206	0.106603	−	0.994302i	$-0.466003\pi$
$953$	6272.48	0.213206	0.106603	+	0.994302i	$0.466003\pi$
$954$	−56471.3	−1.91649
$955$	0	0
$956$	−12836.0	−0.434253
$957$	41150.6	1.38998
$958$	36960.7	1.24650
$959$	4870.14	0.163988
$960$	0	0
$961$	−29697.2	−0.996850
$962$	16396.3	0.549519
$963$	59166.0	1.97985
$964$	70088.1	2.34169
$965$	0	0
$966$	32269.3	1.07479
$967$	26660.8	0.886613	0.443307	−	0.896370i	$-0.353805\pi$
$967$	26660.8	0.886613	0.443307	+	0.896370i	$0.353805\pi$
$968$	91423.3	3.03560
$969$	−29638.9	−0.982599
$970$	0	0
$971$	−461.190	−0.0152423	−0.00762116	−	0.999971i	$-0.502426\pi$
$971$	−461.190	−0.0152423	−0.00762116	+	0.999971i	$0.502426\pi$
$972$	−103455.	−3.41391
$973$	−2089.71	−0.0688520
$974$	30453.3	1.00184
$975$	0	0
$976$	−16492.5	−0.540895
$977$	−4058.08	−0.132886	−0.0664429	−	0.997790i	$-0.521165\pi$
$977$	−4058.08	−0.132886	−0.0664429	+	0.997790i	$0.521165\pi$
$978$	94199.0	3.07991
$979$	33782.4	1.10285
$980$	0	0
$981$	−90523.9	−2.94618
$982$	17248.7	0.560517
$983$	3259.92	0.105773	0.0528867	−	0.998601i	$-0.483158\pi$
$983$	3259.92	0.105773	0.0528867	+	0.998601i	$0.483158\pi$
$984$	−115749.	−3.74995
$985$	0	0
$986$	−21234.8	−0.685857
$987$	30284.5	0.976664
$988$	10600.5	0.341342
$989$	−5093.96	−0.163780
$990$	0	0
$991$	−21398.9	−0.685933	−0.342967	−	0.939348i	$-0.611432\pi$
$991$	−21398.9	−0.685933	−0.342967	+	0.939348i	$0.611432\pi$
$992$	404.254	0.0129386
$993$	747.669	0.0238938
$994$	−5471.24	−0.174585
$995$	0	0
$996$	76020.1	2.41846
$997$	−28609.5	−0.908798	−0.454399	−	0.890798i	$-0.650146\pi$
$997$	−28609.5	−0.908798	−0.454399	+	0.890798i	$0.650146\pi$
$998$	−91589.2	−2.90502
$999$	−87005.2	−2.75548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.a.h.1.4	yes	4
3.2	odd	2		1575.4.a.bg.1.1		4
5.2	odd	4		175.4.b.f.99.7		8
5.3	odd	4		175.4.b.f.99.2		8
5.4	even	2		175.4.a.g.1.1	✓	4
7.6	odd	2		1225.4.a.bd.1.4		4
15.14	odd	2		1575.4.a.bl.1.4		4
35.34	odd	2		1225.4.a.z.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.a.g.1.1	✓	4	5.4	even	2
175.4.a.h.1.4	yes	4	1.1	even	1	trivial
175.4.b.f.99.2		8	5.3	odd	4
175.4.b.f.99.7		8	5.2	odd	4
1225.4.a.z.1.1		4	35.34	odd	2
1225.4.a.bd.1.4		4	7.6	odd	2
1575.4.a.bg.1.1		4	3.2	odd	2
1575.4.a.bl.1.4		4	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

\(f(q)\)	\(=\)	\(q+4.84167 q^{2} -9.58084 q^{3} +15.4418 q^{4} -46.3873 q^{6} +7.00000 q^{7} +36.0308 q^{8} +64.7926 q^{9} +O(q^{10})\)	\(q+4.84167 q^{2} -9.58084 q^{3} +15.4418 q^{4} -46.3873 q^{6} +7.00000 q^{7} +36.0308 q^{8} +64.7926 q^{9} +62.1962 q^{11} -147.945 q^{12} +14.0934 q^{13} +33.8917 q^{14} +50.9148 q^{16} +63.5104 q^{17} +313.704 q^{18} +48.7094 q^{19} -67.0659 q^{21} +301.134 q^{22} -99.3784 q^{23} -345.205 q^{24} +68.2354 q^{26} -362.085 q^{27} +108.093 q^{28} -69.0571 q^{29} -9.68658 q^{31} -41.7334 q^{32} -595.892 q^{33} +307.497 q^{34} +1000.51 q^{36} +240.290 q^{37} +235.835 q^{38} -135.026 q^{39} +335.306 q^{41} -324.711 q^{42} +51.2582 q^{43} +960.421 q^{44} -481.158 q^{46} -451.564 q^{47} -487.806 q^{48} +49.0000 q^{49} -608.484 q^{51} +217.627 q^{52} -180.014 q^{53} -1753.10 q^{54} +252.215 q^{56} -466.677 q^{57} -334.352 q^{58} +268.600 q^{59} -323.925 q^{61} -46.8992 q^{62} +453.548 q^{63} -609.378 q^{64} -2885.12 q^{66} -541.910 q^{67} +980.715 q^{68} +952.129 q^{69} -161.433 q^{71} +2334.53 q^{72} +305.751 q^{73} +1163.40 q^{74} +752.161 q^{76} +435.373 q^{77} -653.753 q^{78} -504.722 q^{79} +1719.68 q^{81} +1623.44 q^{82} -513.838 q^{83} -1035.62 q^{84} +248.176 q^{86} +661.625 q^{87} +2240.98 q^{88} +543.158 q^{89} +98.6535 q^{91} -1534.58 q^{92} +92.8056 q^{93} -2186.32 q^{94} +399.842 q^{96} +1863.06 q^{97} +237.242 q^{98} +4029.85 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 3 q^{3} + 36 q^{4} + q^{6} + 28 q^{7} + 27 q^{8} + 61 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 3 * q^3 + 36 * q^4 + q^6 + 28 * q^7 + 27 * q^8 + 61 * q^9	\( 4 q + 4 q^{2} - 3 q^{3} + 36 q^{4} + q^{6} + 28 q^{7} + 27 q^{8} + 61 q^{9} + 100 q^{11} - 165 q^{12} + 44 q^{13} + 28 q^{14} + 160 q^{16} - 53 q^{17} + 433 q^{18} - 29 q^{19} - 21 q^{21} - 152 q^{22} + 295 q^{23} - 21 q^{24} + 700 q^{26} - 441 q^{27} + 252 q^{28} + 129 q^{29} + 114 q^{31} - 310 q^{32} - 865 q^{33} + 203 q^{34} + 1101 q^{36} + 403 q^{37} + 555 q^{38} + 674 q^{39} + 671 q^{41} + 7 q^{42} - 411 q^{43} + 438 q^{44} - 997 q^{46} - 8 q^{47} - 523 q^{48} + 196 q^{49} - 885 q^{51} + 74 q^{52} + 90 q^{53} - 2777 q^{54} + 189 q^{56} + 233 q^{57} + 673 q^{58} + 1018 q^{59} + 50 q^{61} - 1626 q^{62} + 427 q^{63} - 2421 q^{64} - 3841 q^{66} + 424 q^{67} - 617 q^{68} + 1080 q^{69} + 215 q^{71} + 2940 q^{72} - 1207 q^{73} + 623 q^{74} - 3257 q^{76} + 700 q^{77} + 278 q^{78} - 951 q^{79} + 28 q^{81} + 1695 q^{82} - 3035 q^{83} - 1155 q^{84} - 99 q^{86} + 2210 q^{87} + 163 q^{88} + 2819 q^{89} + 308 q^{91} + 3073 q^{92} - 852 q^{93} - 3056 q^{94} - 1345 q^{96} - 1100 q^{97} + 196 q^{98} + 2383 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 3 * q^3 + 36 * q^4 + q^6 + 28 * q^7 + 27 * q^8 + 61 * q^9 + 100 * q^11 - 165 * q^12 + 44 * q^13 + 28 * q^14 + 160 * q^16 - 53 * q^17 + 433 * q^18 - 29 * q^19 - 21 * q^21 - 152 * q^22 + 295 * q^23 - 21 * q^24 + 700 * q^26 - 441 * q^27 + 252 * q^28 + 129 * q^29 + 114 * q^31 - 310 * q^32 - 865 * q^33 + 203 * q^34 + 1101 * q^36 + 403 * q^37 + 555 * q^38 + 674 * q^39 + 671 * q^41 + 7 * q^42 - 411 * q^43 + 438 * q^44 - 997 * q^46 - 8 * q^47 - 523 * q^48 + 196 * q^49 - 885 * q^51 + 74 * q^52 + 90 * q^53 - 2777 * q^54 + 189 * q^56 + 233 * q^57 + 673 * q^58 + 1018 * q^59 + 50 * q^61 - 1626 * q^62 + 427 * q^63 - 2421 * q^64 - 3841 * q^66 + 424 * q^67 - 617 * q^68 + 1080 * q^69 + 215 * q^71 + 2940 * q^72 - 1207 * q^73 + 623 * q^74 - 3257 * q^76 + 700 * q^77 + 278 * q^78 - 951 * q^79 + 28 * q^81 + 1695 * q^82 - 3035 * q^83 - 1155 * q^84 - 99 * q^86 + 2210 * q^87 + 163 * q^88 + 2819 * q^89 + 308 * q^91 + 3073 * q^92 - 852 * q^93 - 3056 * q^94 - 1345 * q^96 - 1100 * q^97 + 196 * q^98 + 2383 * q^99

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