LMFDB - Embedded newform 3525.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 $ x^8 - 3x^7 - 7x^6 + 24x^5 + 8x^4 - 47x^3 + 8x^2 + 13*x + 2
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			1.2
Root			$-1.60641$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.60641 q^{2} -1.00000 q^{3} +0.580562 q^{4} +1.60641 q^{6} +2.35394 q^{7} +2.28020 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.60641 q^{2} -1.00000 q^{3} +0.580562 q^{4} +1.60641 q^{6} +2.35394 q^{7} +2.28020 q^{8} +1.00000 q^{9} +1.21821 q^{11} -0.580562 q^{12} -1.28767 q^{13} -3.78140 q^{14} -4.82407 q^{16} +2.46057 q^{17} -1.60641 q^{18} -0.168892 q^{19} -2.35394 q^{21} -1.95695 q^{22} +8.96026 q^{23} -2.28020 q^{24} +2.06852 q^{26} -1.00000 q^{27} +1.36661 q^{28} -2.39692 q^{29} +6.32953 q^{31} +3.18904 q^{32} -1.21821 q^{33} -3.95270 q^{34} +0.580562 q^{36} +9.44703 q^{37} +0.271311 q^{38} +1.28767 q^{39} -1.59177 q^{41} +3.78140 q^{42} +1.20123 q^{43} +0.707246 q^{44} -14.3939 q^{46} +1.00000 q^{47} +4.82407 q^{48} -1.45896 q^{49} -2.46057 q^{51} -0.747570 q^{52} +5.14255 q^{53} +1.60641 q^{54} +5.36746 q^{56} +0.168892 q^{57} +3.85044 q^{58} -11.9036 q^{59} +14.0274 q^{61} -10.1678 q^{62} +2.35394 q^{63} +4.52522 q^{64} +1.95695 q^{66} +8.76052 q^{67} +1.42852 q^{68} -8.96026 q^{69} -6.83248 q^{71} +2.28020 q^{72} +0.476914 q^{73} -15.1758 q^{74} -0.0980525 q^{76} +2.86759 q^{77} -2.06852 q^{78} -5.18222 q^{79} +1.00000 q^{81} +2.55704 q^{82} -13.6149 q^{83} -1.36661 q^{84} -1.92967 q^{86} +2.39692 q^{87} +2.77776 q^{88} -12.0162 q^{89} -3.03109 q^{91} +5.20199 q^{92} -6.32953 q^{93} -1.60641 q^{94} -3.18904 q^{96} +13.4808 q^{97} +2.34370 q^{98} +1.21821 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * 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 $

$2$	−1.60641	−1.13591	−0.567953	−	0.823061i	$-0.692264\pi$
$2$	−1.60641	−1.13591	−0.567953	+	0.823061i	$0.692264\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.580562	0.290281
$5$	0	0
$5$	0	0
$6$	1.60641	0.655815
$7$	2.35394	0.889706	0.444853	−	0.895604i	$-0.353256\pi$
$7$	2.35394	0.889706	0.444853	+	0.895604i	$0.353256\pi$
$8$	2.28020	0.806174
$9$	1.00000	0.333333
$10$	0	0
$11$	1.21821	0.367304	0.183652	−	0.982991i	$-0.441208\pi$
$11$	1.21821	0.367304	0.183652	+	0.982991i	$0.441208\pi$
$12$	−0.580562	−0.167594
$13$	−1.28767	−0.357134	−0.178567	−	0.983928i	$-0.557146\pi$
$13$	−1.28767	−0.357134	−0.178567	+	0.983928i	$0.557146\pi$
$14$	−3.78140	−1.01062
$15$	0	0
$16$	−4.82407	−1.20602
$17$	2.46057	0.596777	0.298388	−	0.954445i	$-0.403551\pi$
$17$	2.46057	0.596777	0.298388	+	0.954445i	$0.403551\pi$
$18$	−1.60641	−0.378635
$19$	−0.168892	−0.0387466	−0.0193733	−	0.999812i	$-0.506167\pi$
$19$	−0.168892	−0.0387466	−0.0193733	+	0.999812i	$0.506167\pi$
$20$	0	0
$21$	−2.35394	−0.513672
$22$	−1.95695	−0.417222
$23$	8.96026	1.86834	0.934172	−	0.356823i	$-0.116140\pi$
$23$	8.96026	1.86834	0.934172	+	0.356823i	$0.116140\pi$
$24$	−2.28020	−0.465445
$25$	0	0
$26$	2.06852	0.405671
$27$	−1.00000	−0.192450
$28$	1.36661	0.258265
$29$	−2.39692	−0.445097	−0.222548	−	0.974922i	$-0.571437\pi$
$29$	−2.39692	−0.445097	−0.222548	+	0.974922i	$0.571437\pi$
$30$	0	0
$31$	6.32953	1.13682	0.568409	−	0.822746i	$-0.307559\pi$
$31$	6.32953	1.13682	0.568409	+	0.822746i	$0.307559\pi$
$32$	3.18904	0.563749
$33$	−1.21821	−0.212063
$34$	−3.95270	−0.677882
$35$	0	0
$36$	0.580562	0.0967603
$37$	9.44703	1.55308	0.776541	−	0.630066i	$-0.216972\pi$
$37$	9.44703	1.55308	0.776541	+	0.630066i	$0.216972\pi$
$38$	0.271311	0.0440124
$39$	1.28767	0.206191
$40$	0	0
$41$	−1.59177	−0.248593	−0.124296	−	0.992245i	$-0.539667\pi$
$41$	−1.59177	−0.248593	−0.124296	+	0.992245i	$0.539667\pi$
$42$	3.78140	0.583483
$43$	1.20123	0.183186	0.0915928	−	0.995797i	$-0.470804\pi$
$43$	1.20123	0.183186	0.0915928	+	0.995797i	$0.470804\pi$
$44$	0.707246	0.106621
$45$	0	0
$46$	−14.3939	−2.12226
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	4.82407	0.696295
$49$	−1.45896	−0.208423
$50$	0	0
$51$	−2.46057	−0.344549
$52$	−0.747570	−0.103669
$53$	5.14255	0.706384	0.353192	−	0.935551i	$-0.385096\pi$
$53$	5.14255	0.706384	0.353192	+	0.935551i	$0.385096\pi$
$54$	1.60641	0.218605
$55$	0	0
$56$	5.36746	0.717257
$57$	0.168892	0.0223703
$58$	3.85044	0.505588
$59$	−11.9036	−1.54972	−0.774861	−	0.632131i	$-0.782180\pi$
$59$	−11.9036	−1.54972	−0.774861	+	0.632131i	$0.782180\pi$
$60$	0	0
$61$	14.0274	1.79602	0.898009	−	0.439977i	$-0.145013\pi$
$61$	14.0274	1.79602	0.898009	+	0.439977i	$0.145013\pi$
$62$	−10.1678	−1.29132
$63$	2.35394	0.296569
$64$	4.52522	0.565653
$65$	0	0
$66$	1.95695	0.240884
$67$	8.76052	1.07027	0.535134	−	0.844767i	$-0.320261\pi$
$67$	8.76052	1.07027	0.535134	+	0.844767i	$0.320261\pi$
$68$	1.42852	0.173233
$69$	−8.96026	−1.07869
$70$	0	0
$71$	−6.83248	−0.810866	−0.405433	−	0.914125i	$-0.632879\pi$
$71$	−6.83248	−0.810866	−0.405433	+	0.914125i	$0.632879\pi$
$72$	2.28020	0.268725
$73$	0.476914	0.0558185	0.0279093	−	0.999610i	$-0.491115\pi$
$73$	0.476914	0.0558185	0.0279093	+	0.999610i	$0.491115\pi$
$74$	−15.1758	−1.76415
$75$	0	0
$76$	−0.0980525	−0.0112474
$77$	2.86759	0.326792
$78$	−2.06852	−0.234214
$79$	−5.18222	−0.583045	−0.291523	−	0.956564i	$-0.594162\pi$
$79$	−5.18222	−0.583045	−0.291523	+	0.956564i	$0.594162\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.55704	0.282378
$83$	−13.6149	−1.49443	−0.747214	−	0.664583i	$-0.768609\pi$
$83$	−13.6149	−1.49443	−0.747214	+	0.664583i	$0.768609\pi$
$84$	−1.36661	−0.149109
$85$	0	0
$86$	−1.92967	−0.208082
$87$	2.39692	0.256977
$88$	2.77776	0.296111
$89$	−12.0162	−1.27371	−0.636855	−	0.770984i	$-0.719765\pi$
$89$	−12.0162	−1.27371	−0.636855	+	0.770984i	$0.719765\pi$
$90$	0	0
$91$	−3.03109	−0.317744
$92$	5.20199	0.542345
$93$	−6.32953	−0.656342
$94$	−1.60641	−0.165689
$95$	0	0
$96$	−3.18904	−0.325480
$97$	13.4808	1.36876	0.684381	−	0.729124i	$-0.260072\pi$
$97$	13.4808	1.36876	0.684381	+	0.729124i	$0.260072\pi$
$98$	2.34370	0.236749
$99$	1.21821	0.122435
$100$	0	0
$101$	5.27825	0.525206	0.262603	−	0.964904i	$-0.415419\pi$
$101$	5.27825	0.525206	0.262603	+	0.964904i	$0.415419\pi$
$102$	3.95270	0.391375
$103$	−9.08889	−0.895555	−0.447778	−	0.894145i	$-0.647784\pi$
$103$	−9.08889	−0.895555	−0.447778	+	0.894145i	$0.647784\pi$
$104$	−2.93614	−0.287912
$105$	0	0
$106$	−8.26107	−0.802386
$107$	−5.74384	−0.555278	−0.277639	−	0.960686i	$-0.589552\pi$
$107$	−5.74384	−0.555278	−0.277639	+	0.960686i	$0.589552\pi$
$108$	−0.580562	−0.0558646
$109$	5.71806	0.547691	0.273846	−	0.961774i	$-0.411704\pi$
$109$	5.71806	0.547691	0.273846	+	0.961774i	$0.411704\pi$
$110$	0	0
$111$	−9.44703	−0.896673
$112$	−11.3556	−1.07300
$113$	−10.9763	−1.03257	−0.516283	−	0.856418i	$-0.672685\pi$
$113$	−10.9763	−1.03257	−0.516283	+	0.856418i	$0.672685\pi$
$114$	−0.271311	−0.0254106
$115$	0	0
$116$	−1.39156	−0.129203
$117$	−1.28767	−0.119045
$118$	19.1222	1.76034
$119$	5.79205	0.530956
$120$	0	0
$121$	−9.51597	−0.865088
$122$	−22.5337	−2.04011
$123$	1.59177	0.143525
$124$	3.67468	0.329996
$125$	0	0
$126$	−3.78140	−0.336874
$127$	−3.75661	−0.333345	−0.166673	−	0.986012i	$-0.553302\pi$
$127$	−3.75661	−0.333345	−0.166673	+	0.986012i	$0.553302\pi$
$128$	−13.6475	−1.20628
$129$	−1.20123	−0.105762
$130$	0	0
$131$	6.15566	0.537823	0.268911	−	0.963165i	$-0.413336\pi$
$131$	6.15566	0.537823	0.268911	+	0.963165i	$0.413336\pi$
$132$	−0.707246	−0.0615579
$133$	−0.397563	−0.0344731
$134$	−14.0730	−1.21572
$135$	0	0
$136$	5.61061	0.481106
$137$	1.52211	0.130043	0.0650213	−	0.997884i	$-0.479288\pi$
$137$	1.52211	0.130043	0.0650213	+	0.997884i	$0.479288\pi$
$138$	14.3939	1.22529
$139$	0.241574	0.0204900	0.0102450	−	0.999948i	$-0.496739\pi$
$139$	0.241574	0.0204900	0.0102450	+	0.999948i	$0.496739\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	10.9758	0.921067
$143$	−1.56865	−0.131177
$144$	−4.82407	−0.402006
$145$	0	0
$146$	−0.766120	−0.0634046
$147$	1.45896	0.120333
$148$	5.48459	0.450830
$149$	−6.91605	−0.566585	−0.283292	−	0.959034i	$-0.591427\pi$
$149$	−6.91605	−0.566585	−0.283292	+	0.959034i	$0.591427\pi$
$150$	0	0
$151$	−13.1690	−1.07168	−0.535838	−	0.844321i	$-0.680004\pi$
$151$	−13.1690	−1.07168	−0.535838	+	0.844321i	$0.680004\pi$
$152$	−0.385109	−0.0312365
$153$	2.46057	0.198926
$154$	−4.60654	−0.371205
$155$	0	0
$156$	0.747570	0.0598535
$157$	−7.97672	−0.636612	−0.318306	−	0.947988i	$-0.603114\pi$
$157$	−7.97672	−0.636612	−0.318306	+	0.947988i	$0.603114\pi$
$158$	8.32478	0.662284
$159$	−5.14255	−0.407831
$160$	0	0
$161$	21.0919	1.66228
$162$	−1.60641	−0.126212
$163$	18.1440	1.42114	0.710572	−	0.703624i	$-0.248436\pi$
$163$	18.1440	1.42114	0.710572	+	0.703624i	$0.248436\pi$
$164$	−0.924122	−0.0721618
$165$	0	0
$166$	21.8711	1.69753
$167$	15.5428	1.20273	0.601367	−	0.798973i	$-0.294623\pi$
$167$	15.5428	1.20273	0.601367	+	0.798973i	$0.294623\pi$
$168$	−5.36746	−0.414109
$169$	−11.3419	−0.872455
$170$	0	0
$171$	−0.168892	−0.0129155
$172$	0.697388	0.0531753
$173$	9.13465	0.694494	0.347247	−	0.937774i	$-0.387116\pi$
$173$	9.13465	0.694494	0.347247	+	0.937774i	$0.387116\pi$
$174$	−3.85044	−0.291901
$175$	0	0
$176$	−5.87673	−0.442975
$177$	11.9036	0.894733
$178$	19.3029	1.44681
$179$	−12.1271	−0.906422	−0.453211	−	0.891403i	$-0.649722\pi$
$179$	−12.1271	−0.906422	−0.453211	+	0.891403i	$0.649722\pi$
$180$	0	0
$181$	21.3726	1.58861	0.794305	−	0.607519i	$-0.207835\pi$
$181$	21.3726	1.58861	0.794305	+	0.607519i	$0.207835\pi$
$182$	4.86918	0.360928
$183$	−14.0274	−1.03693
$184$	20.4312	1.50621
$185$	0	0
$186$	10.1678	0.745542
$187$	2.99749	0.219199
$188$	0.580562	0.0423418
$189$	−2.35394	−0.171224
$190$	0	0
$191$	13.4979	0.976673	0.488336	−	0.872655i	$-0.337604\pi$
$191$	13.4979	0.976673	0.488336	+	0.872655i	$0.337604\pi$
$192$	−4.52522	−0.326580
$193$	8.03065	0.578059	0.289030	−	0.957320i	$-0.406667\pi$
$193$	8.03065	0.578059	0.289030	+	0.957320i	$0.406667\pi$
$194$	−21.6557	−1.55479
$195$	0	0
$196$	−0.847019	−0.0605013
$197$	17.2888	1.23178	0.615888	−	0.787833i	$-0.288797\pi$
$197$	17.2888	1.23178	0.615888	+	0.787833i	$0.288797\pi$
$198$	−1.95695	−0.139074
$199$	5.14079	0.364421	0.182211	−	0.983260i	$-0.441675\pi$
$199$	5.14079	0.364421	0.182211	+	0.983260i	$0.441675\pi$
$200$	0	0
$201$	−8.76052	−0.617919
$202$	−8.47905	−0.596584
$203$	−5.64220	−0.396005
$204$	−1.42852	−0.100016
$205$	0	0
$206$	14.6005	1.01727
$207$	8.96026	0.622781
$208$	6.21179	0.430710
$209$	−0.205746	−0.0142318
$210$	0	0
$211$	6.07830	0.418448	0.209224	−	0.977868i	$-0.432906\pi$
$211$	6.07830	0.418448	0.209224	+	0.977868i	$0.432906\pi$
$212$	2.98557	0.205050
$213$	6.83248	0.468154
$214$	9.22697	0.630743
$215$	0	0
$216$	−2.28020	−0.155148
$217$	14.8993	1.01143
$218$	−9.18557	−0.622125
$219$	−0.476914	−0.0322268
$220$	0	0
$221$	−3.16840	−0.213129
$222$	15.1758	1.01854
$223$	−12.8780	−0.862372	−0.431186	−	0.902263i	$-0.641905\pi$
$223$	−12.8780	−0.862372	−0.431186	+	0.902263i	$0.641905\pi$
$224$	7.50682	0.501571
$225$	0	0
$226$	17.6325	1.17290
$227$	−13.8756	−0.920957	−0.460478	−	0.887671i	$-0.652322\pi$
$227$	−13.8756	−0.920957	−0.460478	+	0.887671i	$0.652322\pi$
$228$	0.0980525	0.00649369
$229$	24.1014	1.59266	0.796331	−	0.604861i	$-0.206771\pi$
$229$	24.1014	1.59266	0.796331	+	0.604861i	$0.206771\pi$
$230$	0	0
$231$	−2.86759	−0.188674
$232$	−5.46546	−0.358825
$233$	−26.5063	−1.73648	−0.868241	−	0.496142i	$-0.834750\pi$
$233$	−26.5063	−1.73648	−0.868241	+	0.496142i	$0.834750\pi$
$234$	2.06852	0.135224
$235$	0	0
$236$	−6.91081	−0.449855
$237$	5.18222	0.336621
$238$	−9.30442	−0.603116
$239$	−5.89635	−0.381403	−0.190702	−	0.981648i	$-0.561076\pi$
$239$	−5.89635	−0.381403	−0.190702	+	0.981648i	$0.561076\pi$
$240$	0	0
$241$	4.50808	0.290391	0.145195	−	0.989403i	$-0.453619\pi$
$241$	4.50808	0.290391	0.145195	+	0.989403i	$0.453619\pi$
$242$	15.2866	0.982658
$243$	−1.00000	−0.0641500
$244$	8.14375	0.521350
$245$	0	0
$246$	−2.55704	−0.163031
$247$	0.217477	0.0138377
$248$	14.4326	0.916472
$249$	13.6149	0.862809
$250$	0	0
$251$	9.71575	0.613253	0.306626	−	0.951830i	$-0.400800\pi$
$251$	9.71575	0.613253	0.306626	+	0.951830i	$0.400800\pi$
$252$	1.36661	0.0860882
$253$	10.9155	0.686250
$254$	6.03466	0.378649
$255$	0	0
$256$	12.8730	0.804563
$257$	−22.1299	−1.38043	−0.690213	−	0.723607i	$-0.742483\pi$
$257$	−22.1299	−1.38043	−0.690213	+	0.723607i	$0.742483\pi$
$258$	1.92967	0.120136
$259$	22.2378	1.38179
$260$	0	0
$261$	−2.39692	−0.148366
$262$	−9.88854	−0.610916
$263$	24.7388	1.52546	0.762729	−	0.646719i	$-0.223859\pi$
$263$	24.7388	1.52546	0.762729	+	0.646719i	$0.223859\pi$
$264$	−2.77776	−0.170960
$265$	0	0
$266$	0.638650	0.0391581
$267$	12.0162	0.735377
$268$	5.08602	0.310678
$269$	24.4078	1.48817	0.744086	−	0.668084i	$-0.232885\pi$
$269$	24.4078	1.48817	0.744086	+	0.668084i	$0.232885\pi$
$270$	0	0
$271$	20.3632	1.23698	0.618488	−	0.785795i	$-0.287746\pi$
$271$	20.3632	1.23698	0.618488	+	0.785795i	$0.287746\pi$
$272$	−11.8700	−0.719724
$273$	3.03109	0.183450
$274$	−2.44513	−0.147716
$275$	0	0
$276$	−5.20199	−0.313123
$277$	−10.2127	−0.613621	−0.306811	−	0.951771i	$-0.599262\pi$
$277$	−10.2127	−0.613621	−0.306811	+	0.951771i	$0.599262\pi$
$278$	−0.388067	−0.0232747
$279$	6.32953	0.378939
$280$	0	0
$281$	9.12961	0.544627	0.272314	−	0.962209i	$-0.412211\pi$
$281$	9.12961	0.544627	0.272314	+	0.962209i	$0.412211\pi$
$282$	1.60641	0.0956605
$283$	20.4947	1.21828	0.609141	−	0.793062i	$-0.291514\pi$
$283$	20.4947	1.21828	0.609141	+	0.793062i	$0.291514\pi$
$284$	−3.96668	−0.235379
$285$	0	0
$286$	2.51989	0.149004
$287$	−3.74694	−0.221175
$288$	3.18904	0.187916
$289$	−10.9456	−0.643857
$290$	0	0
$291$	−13.4808	−0.790256
$292$	0.276878	0.0162031
$293$	21.4658	1.25405	0.627023	−	0.779000i	$-0.284273\pi$
$293$	21.4658	1.25405	0.627023	+	0.779000i	$0.284273\pi$
$294$	−2.34370	−0.136687
$295$	0	0
$296$	21.5412	1.25205
$297$	−1.21821	−0.0706877
$298$	11.1100	0.643586
$299$	−11.5378	−0.667249
$300$	0	0
$301$	2.82762	0.162981
$302$	21.1548	1.21732
$303$	−5.27825	−0.303228
$304$	0.814749	0.0467291
$305$	0	0
$306$	−3.95270	−0.225961
$307$	11.4104	0.651226	0.325613	−	0.945503i	$-0.394429\pi$
$307$	11.4104	0.651226	0.325613	+	0.945503i	$0.394429\pi$
$308$	1.66482	0.0948616
$309$	9.08889	0.517049
$310$	0	0
$311$	7.47198	0.423697	0.211849	−	0.977303i	$-0.432052\pi$
$311$	7.47198	0.423697	0.211849	+	0.977303i	$0.432052\pi$
$312$	2.93614	0.166226
$313$	−15.3336	−0.866707	−0.433353	−	0.901224i	$-0.642670\pi$
$313$	−15.3336	−0.866707	−0.433353	+	0.901224i	$0.642670\pi$
$314$	12.8139	0.723131
$315$	0	0
$316$	−3.00860	−0.169247
$317$	−18.8478	−1.05860	−0.529298	−	0.848436i	$-0.677545\pi$
$317$	−18.8478	−1.05860	−0.529298	+	0.848436i	$0.677545\pi$
$318$	8.26107	0.463258
$319$	−2.91995	−0.163486
$320$	0	0
$321$	5.74384	0.320590
$322$	−33.8823	−1.88819
$323$	−0.415572	−0.0231231
$324$	0.580562	0.0322534
$325$	0	0
$326$	−29.1467	−1.61429
$327$	−5.71806	−0.316210
$328$	−3.62956	−0.200409
$329$	2.35394	0.129777
$330$	0	0
$331$	−3.60922	−0.198380	−0.0991902	−	0.995068i	$-0.531625\pi$
$331$	−3.60922	−0.198380	−0.0991902	+	0.995068i	$0.531625\pi$
$332$	−7.90429	−0.433804
$333$	9.44703	0.517694
$334$	−24.9681	−1.36619
$335$	0	0
$336$	11.3556	0.619498
$337$	−18.5074	−1.00816	−0.504082	−	0.863656i	$-0.668169\pi$
$337$	−18.5074	−1.00816	−0.504082	+	0.863656i	$0.668169\pi$
$338$	18.2198	0.991027
$339$	10.9763	0.596152
$340$	0	0
$341$	7.71069	0.417557
$342$	0.271311	0.0146708
$343$	−19.9119	−1.07514
$344$	2.73905	0.147679
$345$	0	0
$346$	−14.6740	−0.788880
$347$	1.05799	0.0567958	0.0283979	−	0.999597i	$-0.490959\pi$
$347$	1.05799	0.0567958	0.0283979	+	0.999597i	$0.490959\pi$
$348$	1.39156	0.0745954
$349$	27.1342	1.45246	0.726230	−	0.687452i	$-0.241271\pi$
$349$	27.1342	1.45246	0.726230	+	0.687452i	$0.241271\pi$
$350$	0	0
$351$	1.28767	0.0687305
$352$	3.88492	0.207067
$353$	4.09521	0.217966	0.108983	−	0.994044i	$-0.465241\pi$
$353$	4.09521	0.217966	0.108983	+	0.994044i	$0.465241\pi$
$354$	−19.1222	−1.01633
$355$	0	0
$356$	−6.97612	−0.369734
$357$	−5.79205	−0.306548
$358$	19.4811	1.02961
$359$	25.4872	1.34516	0.672580	−	0.740024i	$-0.265186\pi$
$359$	25.4872	1.34516	0.672580	+	0.740024i	$0.265186\pi$
$360$	0	0
$361$	−18.9715	−0.998499
$362$	−34.3332	−1.80451
$363$	9.51597	0.499459
$364$	−1.75973	−0.0922352
$365$	0	0
$366$	22.5337	1.17786
$367$	18.1282	0.946284	0.473142	−	0.880986i	$-0.343120\pi$
$367$	18.1282	0.946284	0.473142	+	0.880986i	$0.343120\pi$
$368$	−43.2249	−2.25326
$369$	−1.59177	−0.0828643
$370$	0	0
$371$	12.1053	0.628474
$372$	−3.67468	−0.190524
$373$	6.22180	0.322153	0.161076	−	0.986942i	$-0.448503\pi$
$373$	6.22180	0.322153	0.161076	+	0.986942i	$0.448503\pi$
$374$	−4.81521	−0.248989
$375$	0	0
$376$	2.28020	0.117593
$377$	3.08643	0.158959
$378$	3.78140	0.194494
$379$	5.23729	0.269021	0.134511	−	0.990912i	$-0.457054\pi$
$379$	5.23729	0.269021	0.134511	+	0.990912i	$0.457054\pi$
$380$	0	0
$381$	3.75661	0.192457
$382$	−21.6832	−1.10941
$383$	11.0477	0.564512	0.282256	−	0.959339i	$-0.408917\pi$
$383$	11.0477	0.564512	0.282256	+	0.959339i	$0.408917\pi$
$384$	13.6475	0.696444
$385$	0	0
$386$	−12.9005	−0.656621
$387$	1.20123	0.0610619
$388$	7.82641	0.397326
$389$	9.44478	0.478869	0.239435	−	0.970913i	$-0.423038\pi$
$389$	9.44478	0.478869	0.239435	+	0.970913i	$0.423038\pi$
$390$	0	0
$391$	22.0474	1.11498
$392$	−3.32673	−0.168025
$393$	−6.15566	−0.310512
$394$	−27.7730	−1.39918
$395$	0	0
$396$	0.707246	0.0355404
$397$	3.00343	0.150738	0.0753689	−	0.997156i	$-0.475987\pi$
$397$	3.00343	0.150738	0.0753689	+	0.997156i	$0.475987\pi$
$398$	−8.25823	−0.413948
$399$	0.397563	0.0199030
$400$	0	0
$401$	−29.6585	−1.48107	−0.740537	−	0.672015i	$-0.765429\pi$
$401$	−29.6585	−1.48107	−0.740537	+	0.672015i	$0.765429\pi$
$402$	14.0730	0.701898
$403$	−8.15032	−0.405996
$404$	3.06435	0.152457
$405$	0	0
$406$	9.06371	0.449824
$407$	11.5085	0.570453
$408$	−5.61061	−0.277767
$409$	10.5918	0.523730	0.261865	−	0.965105i	$-0.415663\pi$
$409$	10.5918	0.523730	0.261865	+	0.965105i	$0.415663\pi$
$410$	0	0
$411$	−1.52211	−0.0750801
$412$	−5.27667	−0.259963
$413$	−28.0205	−1.37880
$414$	−14.3939	−0.707421
$415$	0	0
$416$	−4.10642	−0.201334
$417$	−0.241574	−0.0118299
$418$	0.330513	0.0161659
$419$	−21.2794	−1.03957	−0.519783	−	0.854298i	$-0.673987\pi$
$419$	−21.2794	−1.03957	−0.519783	+	0.854298i	$0.673987\pi$
$420$	0	0
$421$	−18.4416	−0.898789	−0.449395	−	0.893333i	$-0.648360\pi$
$421$	−18.4416	−0.898789	−0.449395	+	0.893333i	$0.648360\pi$
$422$	−9.76426	−0.475317
$423$	1.00000	0.0486217
$424$	11.7261	0.569468
$425$	0	0
$426$	−10.9758	−0.531778
$427$	33.0195	1.59793
$428$	−3.33465	−0.161187
$429$	1.56865	0.0757349
$430$	0	0
$431$	−1.32450	−0.0637991	−0.0318995	−	0.999491i	$-0.510156\pi$
$431$	−1.32450	−0.0637991	−0.0318995	+	0.999491i	$0.510156\pi$
$432$	4.82407	0.232098
$433$	27.9318	1.34232	0.671159	−	0.741313i	$-0.265797\pi$
$433$	27.9318	1.34232	0.671159	+	0.741313i	$0.265797\pi$
$434$	−23.9345	−1.14889
$435$	0	0
$436$	3.31969	0.158984
$437$	−1.51332	−0.0723919
$438$	0.766120	0.0366066
$439$	18.3491	0.875756	0.437878	−	0.899034i	$-0.355730\pi$
$439$	18.3491	0.875756	0.437878	+	0.899034i	$0.355730\pi$
$440$	0	0
$441$	−1.45896	−0.0694745
$442$	5.08975	0.242095
$443$	13.7771	0.654569	0.327285	−	0.944926i	$-0.393866\pi$
$443$	13.7771	0.654569	0.327285	+	0.944926i	$0.393866\pi$
$444$	−5.48459	−0.260287
$445$	0	0
$446$	20.6873	0.979573
$447$	6.91605	0.327118
$448$	10.6521	0.503265
$449$	−9.08241	−0.428625	−0.214313	−	0.976765i	$-0.568751\pi$
$449$	−9.08241	−0.428625	−0.214313	+	0.976765i	$0.568751\pi$
$450$	0	0
$451$	−1.93911	−0.0913092
$452$	−6.37244	−0.299734
$453$	13.1690	0.618732
$454$	22.2900	1.04612
$455$	0	0
$456$	0.385109	0.0180344
$457$	−28.8025	−1.34732	−0.673662	−	0.739039i	$-0.735280\pi$
$457$	−28.8025	−1.34732	−0.673662	+	0.739039i	$0.735280\pi$
$458$	−38.7167	−1.80911
$459$	−2.46057	−0.114850
$460$	0	0
$461$	−29.5937	−1.37831	−0.689157	−	0.724612i	$-0.742019\pi$
$461$	−29.5937	−1.37831	−0.689157	+	0.724612i	$0.742019\pi$
$462$	4.60654	0.214315
$463$	17.0730	0.793447	0.396724	−	0.917938i	$-0.370147\pi$
$463$	17.0730	0.793447	0.396724	+	0.917938i	$0.370147\pi$
$464$	11.5629	0.536794
$465$	0	0
$466$	42.5800	1.97248
$467$	26.7895	1.23967	0.619834	−	0.784733i	$-0.287200\pi$
$467$	26.7895	1.23967	0.619834	+	0.784733i	$0.287200\pi$
$468$	−0.747570	−0.0345564
$469$	20.6217	0.952223
$470$	0	0
$471$	7.97672	0.367548
$472$	−27.1427	−1.24935
$473$	1.46335	0.0672848
$474$	−8.32478	−0.382370
$475$	0	0
$476$	3.36264	0.154126
$477$	5.14255	0.235461
$478$	9.47198	0.433238
$479$	−30.0981	−1.37522	−0.687609	−	0.726081i	$-0.741340\pi$
$479$	−30.0981	−1.37522	−0.687609	+	0.726081i	$0.741340\pi$
$480$	0	0
$481$	−12.1646	−0.554659
$482$	−7.24184	−0.329857
$483$	−21.0919	−0.959716
$484$	−5.52461	−0.251119
$485$	0	0
$486$	1.60641	0.0728684
$487$	10.5069	0.476114	0.238057	−	0.971251i	$-0.423490\pi$
$487$	10.5069	0.476114	0.238057	+	0.971251i	$0.423490\pi$
$488$	31.9852	1.44790
$489$	−18.1440	−0.820498
$490$	0	0
$491$	17.5258	0.790928	0.395464	−	0.918481i	$-0.370584\pi$
$491$	17.5258	0.790928	0.395464	+	0.918481i	$0.370584\pi$
$492$	0.924122	0.0416626
$493$	−5.89780	−0.265623
$494$	−0.349358	−0.0157183
$495$	0	0
$496$	−30.5341	−1.37102
$497$	−16.0833	−0.721432
$498$	−21.8711	−0.980069
$499$	3.44802	0.154354	0.0771772	−	0.997017i	$-0.475409\pi$
$499$	3.44802	0.154354	0.0771772	+	0.997017i	$0.475409\pi$
$500$	0	0
$501$	−15.5428	−0.694399
$502$	−15.6075	−0.696597
$503$	−1.65374	−0.0737367	−0.0368684	−	0.999320i	$-0.511738\pi$
$503$	−1.65374	−0.0737367	−0.0368684	+	0.999320i	$0.511738\pi$
$504$	5.36746	0.239086
$505$	0	0
$506$	−17.5348	−0.779515
$507$	11.3419	0.503712
$508$	−2.18094	−0.0967638
$509$	23.3010	1.03280	0.516399	−	0.856348i	$-0.327272\pi$
$509$	23.3010	1.03280	0.516399	+	0.856348i	$0.327272\pi$
$510$	0	0
$511$	1.12263	0.0496621
$512$	6.61555	0.292369
$513$	0.168892	0.00745678
$514$	35.5498	1.56803
$515$	0	0
$516$	−0.697388	−0.0307008
$517$	1.21821	0.0535768
$518$	−35.7230	−1.56958
$519$	−9.13465	−0.400967
$520$	0	0
$521$	−12.6319	−0.553415	−0.276707	−	0.960954i	$-0.589243\pi$
$521$	−12.6319	−0.553415	−0.276707	+	0.960954i	$0.589243\pi$
$522$	3.85044	0.168529
$523$	29.1509	1.27468	0.637340	−	0.770583i	$-0.280035\pi$
$523$	29.1509	1.27468	0.637340	+	0.770583i	$0.280035\pi$
$524$	3.57374	0.156120
$525$	0	0
$526$	−39.7407	−1.73278
$527$	15.5743	0.678426
$528$	5.87673	0.255752
$529$	57.2863	2.49071
$530$	0	0
$531$	−11.9036	−0.516574
$532$	−0.230810	−0.0100069
$533$	2.04967	0.0887810
$534$	−19.3029	−0.835319
$535$	0	0
$536$	19.9758	0.862821
$537$	12.1271	0.523323
$538$	−39.2091	−1.69042
$539$	−1.77732	−0.0765547
$540$	0	0
$541$	26.2586	1.12894	0.564472	−	0.825452i	$-0.309080\pi$
$541$	26.2586	1.12894	0.564472	+	0.825452i	$0.309080\pi$
$542$	−32.7117	−1.40509
$543$	−21.3726	−0.917184
$544$	7.84688	0.336432
$545$	0	0
$546$	−4.86918	−0.208382
$547$	22.9028	0.979253	0.489626	−	0.871932i	$-0.337133\pi$
$547$	22.9028	0.979253	0.489626	+	0.871932i	$0.337133\pi$
$548$	0.883679	0.0377489
$549$	14.0274	0.598673
$550$	0	0
$551$	0.404821	0.0172460
$552$	−20.4312	−0.869610
$553$	−12.1986	−0.518739
$554$	16.4058	0.697016
$555$	0	0
$556$	0.140249	0.00594787
$557$	−5.02429	−0.212886	−0.106443	−	0.994319i	$-0.533946\pi$
$557$	−5.02429	−0.212886	−0.106443	+	0.994319i	$0.533946\pi$
$558$	−10.1678	−0.430439
$559$	−1.54678	−0.0654219
$560$	0	0
$561$	−2.99749	−0.126554
$562$	−14.6659	−0.618645
$563$	22.6970	0.956564	0.478282	−	0.878206i	$-0.341260\pi$
$563$	22.6970	0.956564	0.478282	+	0.878206i	$0.341260\pi$
$564$	−0.580562	−0.0244461
$565$	0	0
$566$	−32.9229	−1.38385
$567$	2.35394	0.0988562
$568$	−15.5794	−0.653699
$569$	−17.3367	−0.726791	−0.363395	−	0.931635i	$-0.618383\pi$
$569$	−17.3367	−0.726791	−0.363395	+	0.931635i	$0.618383\pi$
$570$	0	0
$571$	−9.39051	−0.392981	−0.196490	−	0.980506i	$-0.562954\pi$
$571$	−9.39051	−0.392981	−0.196490	+	0.980506i	$0.562954\pi$
$572$	−0.910696	−0.0380781
$573$	−13.4979	−0.563882
$574$	6.01913	0.251233
$575$	0	0
$576$	4.52522	0.188551
$577$	−18.8942	−0.786576	−0.393288	−	0.919415i	$-0.628663\pi$
$577$	−18.8942	−0.786576	−0.393288	+	0.919415i	$0.628663\pi$
$578$	17.5831	0.731361
$579$	−8.03065	−0.333743
$580$	0	0
$581$	−32.0487	−1.32960
$582$	21.6557	0.897656
$583$	6.26471	0.259458
$584$	1.08746	0.0449994
$585$	0	0
$586$	−34.4830	−1.42448
$587$	44.8632	1.85170	0.925851	−	0.377889i	$-0.123350\pi$
$587$	44.8632	1.85170	0.925851	+	0.377889i	$0.123350\pi$
$588$	0.847019	0.0349305
$589$	−1.06901	−0.0440478
$590$	0	0
$591$	−17.2888	−0.711167
$592$	−45.5732	−1.87305
$593$	2.66127	0.109285	0.0546425	−	0.998506i	$-0.482598\pi$
$593$	2.66127	0.109285	0.0546425	+	0.998506i	$0.482598\pi$
$594$	1.95695	0.0802945
$595$	0	0
$596$	−4.01519	−0.164469
$597$	−5.14079	−0.210399
$598$	18.5345	0.757932
$599$	−12.2072	−0.498771	−0.249386	−	0.968404i	$-0.580229\pi$
$599$	−12.2072	−0.498771	−0.249386	+	0.968404i	$0.580229\pi$
$600$	0	0
$601$	−6.16119	−0.251320	−0.125660	−	0.992073i	$-0.540105\pi$
$601$	−6.16119	−0.251320	−0.125660	+	0.992073i	$0.540105\pi$
$602$	−4.54233	−0.185131
$603$	8.76052	0.356756
$604$	−7.64540	−0.311087
$605$	0	0
$606$	8.47905	0.344438
$607$	11.0117	0.446952	0.223476	−	0.974709i	$-0.428260\pi$
$607$	11.0117	0.446952	0.223476	+	0.974709i	$0.428260\pi$
$608$	−0.538605	−0.0218433
$609$	5.64220	0.228634
$610$	0	0
$611$	−1.28767	−0.0520934
$612$	1.42852	0.0577443
$613$	24.1631	0.975938	0.487969	−	0.872861i	$-0.337738\pi$
$613$	24.1631	0.975938	0.487969	+	0.872861i	$0.337738\pi$
$614$	−18.3298	−0.739731
$615$	0	0
$616$	6.53869	0.263451
$617$	28.8522	1.16155	0.580773	−	0.814066i	$-0.302750\pi$
$617$	28.8522	1.16155	0.580773	+	0.814066i	$0.302750\pi$
$618$	−14.6005	−0.587319
$619$	1.78397	0.0717037	0.0358519	−	0.999357i	$-0.488586\pi$
$619$	1.78397	0.0717037	0.0358519	+	0.999357i	$0.488586\pi$
$620$	0	0
$621$	−8.96026	−0.359563
$622$	−12.0031	−0.481280
$623$	−28.2853	−1.13323
$624$	−6.21179	−0.248671
$625$	0	0
$626$	24.6321	0.984497
$627$	0.205746	0.00821671
$628$	−4.63098	−0.184796
$629$	23.2451	0.926844
$630$	0	0
$631$	12.2661	0.488306	0.244153	−	0.969737i	$-0.421490\pi$
$631$	12.2661	0.488306	0.244153	+	0.969737i	$0.421490\pi$
$632$	−11.8165	−0.470036
$633$	−6.07830	−0.241591
$634$	30.2773	1.20246
$635$	0	0
$636$	−2.98557	−0.118386
$637$	1.87866	0.0744351
$638$	4.69064	0.185704
$639$	−6.83248	−0.270289
$640$	0	0
$641$	−31.0075	−1.22472	−0.612362	−	0.790578i	$-0.709780\pi$
$641$	−31.0075	−1.22472	−0.612362	+	0.790578i	$0.709780\pi$
$642$	−9.22697	−0.364160
$643$	−23.9013	−0.942574	−0.471287	−	0.881980i	$-0.656210\pi$
$643$	−23.9013	−0.942574	−0.471287	+	0.881980i	$0.656210\pi$
$644$	12.2452	0.482527
$645$	0	0
$646$	0.667581	0.0262656
$647$	−28.8735	−1.13513	−0.567566	−	0.823328i	$-0.692115\pi$
$647$	−28.8735	−1.13513	−0.567566	+	0.823328i	$0.692115\pi$
$648$	2.28020	0.0895748
$649$	−14.5011	−0.569219
$650$	0	0
$651$	−14.8993	−0.583951
$652$	10.5337	0.412531
$653$	−36.1118	−1.41316	−0.706582	−	0.707631i	$-0.749764\pi$
$653$	−36.1118	−1.41316	−0.706582	+	0.707631i	$0.749764\pi$
$654$	9.18557	0.359184
$655$	0	0
$656$	7.67882	0.299808
$657$	0.476914	0.0186062
$658$	−3.78140	−0.147414
$659$	31.4095	1.22354	0.611770	−	0.791036i	$-0.290458\pi$
$659$	31.4095	1.22354	0.611770	+	0.791036i	$0.290458\pi$
$660$	0	0
$661$	10.1647	0.395361	0.197681	−	0.980266i	$-0.436659\pi$
$661$	10.1647	0.395361	0.197681	+	0.980266i	$0.436659\pi$
$662$	5.79789	0.225341
$663$	3.16840	0.123050
$664$	−31.0447	−1.20477
$665$	0	0
$666$	−15.1758	−0.588052
$667$	−21.4770	−0.831593
$668$	9.02353	0.349131
$669$	12.8780	0.497891
$670$	0	0
$671$	17.0882	0.659684
$672$	−7.50682	−0.289582
$673$	−13.4744	−0.519400	−0.259700	−	0.965689i	$-0.583624\pi$
$673$	−13.4744	−0.519400	−0.259700	+	0.965689i	$0.583624\pi$
$674$	29.7306	1.14518
$675$	0	0
$676$	−6.58469	−0.253257
$677$	1.48122	0.0569281	0.0284640	−	0.999595i	$-0.490938\pi$
$677$	1.48122	0.0569281	0.0284640	+	0.999595i	$0.490938\pi$
$678$	−17.6325	−0.677172
$679$	31.7329	1.21780
$680$	0	0
$681$	13.8756	0.531715
$682$	−12.3866	−0.474306
$683$	−14.5690	−0.557469	−0.278734	−	0.960368i	$-0.589915\pi$
$683$	−14.5690	−0.557469	−0.278734	+	0.960368i	$0.589915\pi$
$684$	−0.0980525	−0.00374913
$685$	0	0
$686$	31.9867	1.22126
$687$	−24.1014	−0.919524
$688$	−5.79481	−0.220925
$689$	−6.62189	−0.252274
$690$	0	0
$691$	−25.4543	−0.968327	−0.484163	−	0.874978i	$-0.660876\pi$
$691$	−25.4543	−0.968327	−0.484163	+	0.874978i	$0.660876\pi$
$692$	5.30323	0.201599
$693$	2.86759	0.108931
$694$	−1.69957	−0.0645146
$695$	0	0
$696$	5.46546	0.207168
$697$	−3.91667	−0.148355
$698$	−43.5887	−1.64986
$699$	26.5063	1.00256
$700$	0	0
$701$	47.1753	1.78179	0.890894	−	0.454211i	$-0.150079\pi$
$701$	47.1753	1.78179	0.890894	+	0.454211i	$0.150079\pi$
$702$	−2.06852	−0.0780713
$703$	−1.59553	−0.0601766
$704$	5.51267	0.207766
$705$	0	0
$706$	−6.57860	−0.247589
$707$	12.4247	0.467279
$708$	6.91081	0.259724
$709$	−37.8007	−1.41964	−0.709818	−	0.704385i	$-0.751223\pi$
$709$	−37.8007	−1.41964	−0.709818	+	0.704385i	$0.751223\pi$
$710$	0	0
$711$	−5.18222	−0.194348
$712$	−27.3993	−1.02683
$713$	56.7142	2.12397
$714$	9.30442	0.348209
$715$	0	0
$716$	−7.04053	−0.263117
$717$	5.89635	0.220203
$718$	−40.9429	−1.52797
$719$	−13.3382	−0.497431	−0.248716	−	0.968577i	$-0.580008\pi$
$719$	−13.3382	−0.497431	−0.248716	+	0.968577i	$0.580008\pi$
$720$	0	0
$721$	−21.3947	−0.796781
$722$	30.4760	1.13420
$723$	−4.50808	−0.167657
$724$	12.4081	0.461143
$725$	0	0
$726$	−15.2866	−0.567338
$727$	−0.000763187 0	−2.83050e−5 0	−1.41525e−5	−	1.00000i	$-0.500005\pi$
$727$	−0.000763187 0	−2.83050e−5 0	−1.41525e−5		1.00000i	$0.500005\pi$
$728$	−6.91150	−0.256157
$729$	1.00000	0.0370370
$730$	0	0
$731$	2.95571	0.109321
$732$	−8.14375	−0.301002
$733$	−39.7135	−1.46685	−0.733425	−	0.679770i	$-0.762080\pi$
$733$	−39.7135	−1.46685	−0.733425	+	0.679770i	$0.762080\pi$
$734$	−29.1214	−1.07489
$735$	0	0
$736$	28.5747	1.05328
$737$	10.6721	0.393113
$738$	2.55704	0.0941260
$739$	20.0290	0.736777	0.368389	−	0.929672i	$-0.379910\pi$
$739$	20.0290	0.736777	0.368389	+	0.929672i	$0.379910\pi$
$740$	0	0
$741$	−0.217477	−0.00798921
$742$	−19.4461	−0.713887
$743$	−12.4716	−0.457539	−0.228769	−	0.973481i	$-0.573470\pi$
$743$	−12.4716	−0.457539	−0.228769	+	0.973481i	$0.573470\pi$
$744$	−14.4326	−0.529125
$745$	0	0
$746$	−9.99478	−0.365935
$747$	−13.6149	−0.498143
$748$	1.74023	0.0636292
$749$	−13.5207	−0.494034
$750$	0	0
$751$	−21.9589	−0.801291	−0.400646	−	0.916233i	$-0.631214\pi$
$751$	−21.9589	−0.801291	−0.400646	+	0.916233i	$0.631214\pi$
$752$	−4.82407	−0.175916
$753$	−9.71575	−0.354062
$754$	−4.95808	−0.180563
$755$	0	0
$756$	−1.36661	−0.0497031
$757$	26.4162	0.960113	0.480056	−	0.877238i	$-0.340616\pi$
$757$	26.4162	0.960113	0.480056	+	0.877238i	$0.340616\pi$
$758$	−8.41325	−0.305583
$759$	−10.9155	−0.396207
$760$	0	0
$761$	−36.2026	−1.31234	−0.656172	−	0.754611i	$-0.727826\pi$
$761$	−36.2026	−1.31234	−0.656172	+	0.754611i	$0.727826\pi$
$762$	−6.03466	−0.218613
$763$	13.4600	0.487284
$764$	7.83636	0.283510
$765$	0	0
$766$	−17.7472	−0.641232
$767$	15.3279	0.553459
$768$	−12.8730	−0.464515
$769$	34.8533	1.25684	0.628422	−	0.777873i	$-0.283701\pi$
$769$	34.8533	1.25684	0.628422	+	0.777873i	$0.283701\pi$
$770$	0	0
$771$	22.1299	0.796989
$772$	4.66229	0.167800
$773$	−9.23266	−0.332076	−0.166038	−	0.986119i	$-0.553097\pi$
$773$	−9.23266	−0.332076	−0.166038	+	0.986119i	$0.553097\pi$
$774$	−1.92967	−0.0693605
$775$	0	0
$776$	30.7389	1.10346
$777$	−22.2378	−0.797775
$778$	−15.1722	−0.543950
$779$	0.268838	0.00963212
$780$	0	0
$781$	−8.32339	−0.297834
$782$	−35.4172	−1.26652
$783$	2.39692	0.0856589
$784$	7.03814	0.251362
$785$	0	0
$786$	9.88854	0.352712
$787$	17.2217	0.613886	0.306943	−	0.951728i	$-0.400694\pi$
$787$	17.2217	0.613886	0.306943	+	0.951728i	$0.400694\pi$
$788$	10.0372	0.357561
$789$	−24.7388	−0.880723
$790$	0	0
$791$	−25.8376	−0.918680
$792$	2.77776	0.0987036
$793$	−18.0625	−0.641419
$794$	−4.82475	−0.171224
$795$	0	0
$796$	2.98455	0.105785
$797$	2.93899	0.104105	0.0520523	−	0.998644i	$-0.483424\pi$
$797$	2.93899	0.104105	0.0520523	+	0.998644i	$0.483424\pi$
$798$	−0.638650	−0.0226080
$799$	2.46057	0.0870489
$800$	0	0
$801$	−12.0162	−0.424570
$802$	47.6438	1.68236
$803$	0.580981	0.0205024
$804$	−5.08602	−0.179370
$805$	0	0
$806$	13.0928	0.461173
$807$	−24.4078	−0.859196
$808$	12.0355	0.423407
$809$	−47.0667	−1.65478	−0.827389	−	0.561629i	$-0.810175\pi$
$809$	−47.0667	−1.65478	−0.827389	+	0.561629i	$0.810175\pi$
$810$	0	0
$811$	12.1936	0.428176	0.214088	−	0.976814i	$-0.431322\pi$
$811$	12.1936	0.428176	0.214088	+	0.976814i	$0.431322\pi$
$812$	−3.27565	−0.114953
$813$	−20.3632	−0.714168
$814$	−18.4873	−0.647981
$815$	0	0
$816$	11.8700	0.415533
$817$	−0.202878	−0.00709782
$818$	−17.0148	−0.594907
$819$	−3.03109	−0.105915
$820$	0	0
$821$	−27.8694	−0.972647	−0.486324	−	0.873779i	$-0.661662\pi$
$821$	−27.8694	−0.972647	−0.486324	+	0.873779i	$0.661662\pi$
$822$	2.44513	0.0852839
$823$	−26.1727	−0.912323	−0.456161	−	0.889897i	$-0.650776\pi$
$823$	−26.1727	−0.912323	−0.456161	+	0.889897i	$0.650776\pi$
$824$	−20.7245	−0.721973
$825$	0	0
$826$	45.0125	1.56618
$827$	−6.25176	−0.217395	−0.108697	−	0.994075i	$-0.534668\pi$
$827$	−6.25176	−0.217395	−0.108697	+	0.994075i	$0.534668\pi$
$828$	5.20199	0.180782
$829$	−2.54642	−0.0884409	−0.0442205	−	0.999022i	$-0.514080\pi$
$829$	−2.54642	−0.0884409	−0.0442205	+	0.999022i	$0.514080\pi$
$830$	0	0
$831$	10.2127	0.354274
$832$	−5.82697	−0.202014
$833$	−3.58989	−0.124382
$834$	0.388067	0.0134377
$835$	0	0
$836$	−0.119448	−0.00413121
$837$	−6.32953	−0.218781
$838$	34.1835	1.18085
$839$	6.20012	0.214052	0.107026	−	0.994256i	$-0.465867\pi$
$839$	6.20012	0.214052	0.107026	+	0.994256i	$0.465867\pi$
$840$	0	0
$841$	−23.2548	−0.801889
$842$	29.6248	1.02094
$843$	−9.12961	−0.314441
$844$	3.52883	0.121467
$845$	0	0
$846$	−1.60641	−0.0552296
$847$	−22.4000	−0.769674
$848$	−24.8081	−0.851912
$849$	−20.4947	−0.703375
$850$	0	0
$851$	84.6479	2.90169
$852$	3.96668	0.135896
$853$	30.5276	1.04525	0.522623	−	0.852564i	$-0.324953\pi$
$853$	30.5276	1.04525	0.522623	+	0.852564i	$0.324953\pi$
$854$	−53.0430	−1.81509
$855$	0	0
$856$	−13.0971	−0.447650
$857$	18.2826	0.624522	0.312261	−	0.949996i	$-0.398914\pi$
$857$	18.2826	0.624522	0.312261	+	0.949996i	$0.398914\pi$
$858$	−2.51989	−0.0860277
$859$	42.6716	1.45594	0.727969	−	0.685610i	$-0.240465\pi$
$859$	42.6716	1.45594	0.727969	+	0.685610i	$0.240465\pi$
$860$	0	0
$861$	3.74694	0.127695
$862$	2.12770	0.0724697
$863$	3.21332	0.109383	0.0546913	−	0.998503i	$-0.482583\pi$
$863$	3.21332	0.109383	0.0546913	+	0.998503i	$0.482583\pi$
$864$	−3.18904	−0.108493
$865$	0	0
$866$	−44.8701	−1.52475
$867$	10.9456	0.371731
$868$	8.64999	0.293600
$869$	−6.31303	−0.214155
$870$	0	0
$871$	−11.2806	−0.382229
$872$	13.0383	0.441534
$873$	13.4808	0.456254
$874$	2.43102	0.0822304
$875$	0	0
$876$	−0.276878	−0.00935484
$877$	−48.8397	−1.64920	−0.824600	−	0.565717i	$-0.808600\pi$
$877$	−48.8397	−1.64920	−0.824600	+	0.565717i	$0.808600\pi$
$878$	−29.4763	−0.994776
$879$	−21.4658	−0.724024
$880$	0	0
$881$	−29.2473	−0.985367	−0.492684	−	0.870209i	$-0.663984\pi$
$881$	−29.2473	−0.985367	−0.492684	+	0.870209i	$0.663984\pi$
$882$	2.34370	0.0789164
$883$	37.5839	1.26480	0.632400	−	0.774642i	$-0.282070\pi$
$883$	37.5839	1.26480	0.632400	+	0.774642i	$0.282070\pi$
$884$	−1.83945	−0.0618674
$885$	0	0
$886$	−22.1317	−0.743529
$887$	−10.7876	−0.362211	−0.181106	−	0.983464i	$-0.557968\pi$
$887$	−10.7876	−0.362211	−0.181106	+	0.983464i	$0.557968\pi$
$888$	−21.5412	−0.722874
$889$	−8.84283	−0.296579
$890$	0	0
$891$	1.21821	0.0408115
$892$	−7.47645	−0.250330
$893$	−0.168892	−0.00565177
$894$	−11.1100	−0.371575
$895$	0	0
$896$	−32.1253	−1.07323
$897$	11.5378	0.385237
$898$	14.5901	0.486878
$899$	−15.1714	−0.505993
$900$	0	0
$901$	12.6536	0.421554
$902$	3.11501	0.103719
$903$	−2.82762	−0.0940973
$904$	−25.0282	−0.832427
$905$	0	0
$906$	−21.1548	−0.702821
$907$	−35.2429	−1.17022	−0.585111	−	0.810953i	$-0.698949\pi$
$907$	−35.2429	−1.17022	−0.585111	+	0.810953i	$0.698949\pi$
$908$	−8.05565	−0.267336
$909$	5.27825	0.175069
$910$	0	0
$911$	−11.1069	−0.367987	−0.183993	−	0.982927i	$-0.558903\pi$
$911$	−11.1069	−0.367987	−0.183993	+	0.982927i	$0.558903\pi$
$912$	−0.814749	−0.0269790
$913$	−16.5858	−0.548910
$914$	46.2687	1.53043
$915$	0	0
$916$	13.9923	0.462320
$917$	14.4901	0.478504
$918$	3.95270	0.130458
$919$	−47.4809	−1.56625	−0.783126	−	0.621863i	$-0.786376\pi$
$919$	−47.4809	−1.56625	−0.783126	+	0.621863i	$0.786376\pi$
$920$	0	0
$921$	−11.4104	−0.375985
$922$	47.5396	1.56563
$923$	8.79795	0.289588
$924$	−1.66482	−0.0547684
$925$	0	0
$926$	−27.4262	−0.901281
$927$	−9.08889	−0.298518
$928$	−7.64388	−0.250923
$929$	32.0236	1.05066	0.525331	−	0.850898i	$-0.323942\pi$
$929$	32.0236	1.05066	0.525331	+	0.850898i	$0.323942\pi$
$930$	0	0
$931$	0.246408	0.00807569
$932$	−15.3885	−0.504068
$933$	−7.47198	−0.244622
$934$	−43.0350	−1.40815
$935$	0	0
$936$	−2.93614	−0.0959707
$937$	29.3965	0.960342	0.480171	−	0.877175i	$-0.340575\pi$
$937$	29.3965	0.960342	0.480171	+	0.877175i	$0.340575\pi$
$938$	−33.1270	−1.08164
$939$	15.3336	0.500394
$940$	0	0
$941$	−27.5767	−0.898976	−0.449488	−	0.893286i	$-0.648393\pi$
$941$	−27.5767	−0.898976	−0.449488	+	0.893286i	$0.648393\pi$
$942$	−12.8139	−0.417500
$943$	−14.2627	−0.464457
$944$	57.4240	1.86899
$945$	0	0
$946$	−2.35074	−0.0764292
$947$	6.49455	0.211044	0.105522	−	0.994417i	$-0.466349\pi$
$947$	6.49455	0.211044	0.105522	+	0.994417i	$0.466349\pi$
$948$	3.00860	0.0977147
$949$	−0.614105	−0.0199347
$950$	0	0
$951$	18.8478	0.611181
$952$	13.2070	0.428043
$953$	54.1799	1.75506	0.877530	−	0.479522i	$-0.159190\pi$
$953$	54.1799	1.75506	0.877530	+	0.479522i	$0.159190\pi$
$954$	−8.26107	−0.267462
$955$	0	0
$956$	−3.42320	−0.110714
$957$	2.91995	0.0943885
$958$	48.3500	1.56212
$959$	3.58295	0.115700
$960$	0	0
$961$	9.06294	0.292353
$962$	19.5414	0.630040
$963$	−5.74384	−0.185093
$964$	2.61722	0.0842950
$965$	0	0
$966$	33.8823	1.09015
$967$	49.7977	1.60139	0.800693	−	0.599075i	$-0.204465\pi$
$967$	49.7977	1.60139	0.800693	+	0.599075i	$0.204465\pi$
$968$	−21.6983	−0.697411
$969$	0.415572	0.0133501
$970$	0	0
$971$	−43.9456	−1.41028	−0.705140	−	0.709068i	$-0.749116\pi$
$971$	−43.9456	−1.41028	−0.705140	+	0.709068i	$0.749116\pi$
$972$	−0.580562	−0.0186215
$973$	0.568651	0.0182301
$974$	−16.8784	−0.540820
$975$	0	0
$976$	−67.6689	−2.16603
$977$	23.1730	0.741371	0.370685	−	0.928758i	$-0.379123\pi$
$977$	23.1730	0.741371	0.370685	+	0.928758i	$0.379123\pi$
$978$	29.1467	0.932008
$979$	−14.6382	−0.467839
$980$	0	0
$981$	5.71806	0.182564
$982$	−28.1537	−0.898420
$983$	61.2466	1.95346	0.976732	−	0.214465i	$-0.0688009\pi$
$983$	61.2466	1.95346	0.976732	+	0.214465i	$0.0688009\pi$
$984$	3.62956	0.115706
$985$	0	0
$986$	9.47429	0.301723
$987$	−2.35394	−0.0749268
$988$	0.126259	0.00401683
$989$	10.7633	0.342254
$990$	0	0
$991$	57.7571	1.83471	0.917357	−	0.398064i	$-0.130318\pi$
$991$	57.7571	1.83471	0.917357	+	0.398064i	$0.130318\pi$
$992$	20.1851	0.640879
$993$	3.60922	0.114535
$994$	25.8363	0.819479
$995$	0	0
$996$	7.90429	0.250457
$997$	−37.2895	−1.18097	−0.590486	−	0.807048i	$-0.701064\pi$
$997$	−37.2895	−1.18097	−0.590486	+	0.807048i	$0.701064\pi$
$998$	−5.53894	−0.175332
$999$	−9.44703	−0.298891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.be.1.2	yes	8
5.4	even	2		3525.2.a.bd.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.bd.1.7	✓	8	5.4	even	2
3525.2.a.be.1.2	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q-1.60641 q^{2} -1.00000 q^{3} +0.580562 q^{4} +1.60641 q^{6} +2.35394 q^{7} +2.28020 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.60641 q^{2} -1.00000 q^{3} +0.580562 q^{4} +1.60641 q^{6} +2.35394 q^{7} +2.28020 q^{8} +1.00000 q^{9} +1.21821 q^{11} -0.580562 q^{12} -1.28767 q^{13} -3.78140 q^{14} -4.82407 q^{16} +2.46057 q^{17} -1.60641 q^{18} -0.168892 q^{19} -2.35394 q^{21} -1.95695 q^{22} +8.96026 q^{23} -2.28020 q^{24} +2.06852 q^{26} -1.00000 q^{27} +1.36661 q^{28} -2.39692 q^{29} +6.32953 q^{31} +3.18904 q^{32} -1.21821 q^{33} -3.95270 q^{34} +0.580562 q^{36} +9.44703 q^{37} +0.271311 q^{38} +1.28767 q^{39} -1.59177 q^{41} +3.78140 q^{42} +1.20123 q^{43} +0.707246 q^{44} -14.3939 q^{46} +1.00000 q^{47} +4.82407 q^{48} -1.45896 q^{49} -2.46057 q^{51} -0.747570 q^{52} +5.14255 q^{53} +1.60641 q^{54} +5.36746 q^{56} +0.168892 q^{57} +3.85044 q^{58} -11.9036 q^{59} +14.0274 q^{61} -10.1678 q^{62} +2.35394 q^{63} +4.52522 q^{64} +1.95695 q^{66} +8.76052 q^{67} +1.42852 q^{68} -8.96026 q^{69} -6.83248 q^{71} +2.28020 q^{72} +0.476914 q^{73} -15.1758 q^{74} -0.0980525 q^{76} +2.86759 q^{77} -2.06852 q^{78} -5.18222 q^{79} +1.00000 q^{81} +2.55704 q^{82} -13.6149 q^{83} -1.36661 q^{84} -1.92967 q^{86} +2.39692 q^{87} +2.77776 q^{88} -12.0162 q^{89} -3.03109 q^{91} +5.20199 q^{92} -6.32953 q^{93} -1.60641 q^{94} -3.18904 q^{96} +13.4808 q^{97} +2.34370 q^{98} +1.21821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * q^99

Introduction

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