LMFDB - Embedded newform 3525.2.a.bg.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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 $ x^10 - 3x^9 - 9x^8 + 29x^7 + 25x^6 - 91x^5 - 21x^4 + 101x^3 + 6x^2 - 30*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.88719$ 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)

$f(q)$	$=$	$q-1.88719 q^{2} -1.00000 q^{3} +1.56149 q^{4} +1.88719 q^{6} +1.44822 q^{7} +0.827559 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.88719 q^{2} -1.00000 q^{3} +1.56149 q^{4} +1.88719 q^{6} +1.44822 q^{7} +0.827559 q^{8} +1.00000 q^{9} +0.859846 q^{11} -1.56149 q^{12} +2.84255 q^{13} -2.73307 q^{14} -4.68473 q^{16} +5.63243 q^{17} -1.88719 q^{18} -6.59805 q^{19} -1.44822 q^{21} -1.62269 q^{22} -0.190099 q^{23} -0.827559 q^{24} -5.36442 q^{26} -1.00000 q^{27} +2.26138 q^{28} -10.3976 q^{29} +7.02308 q^{31} +7.18586 q^{32} -0.859846 q^{33} -10.6295 q^{34} +1.56149 q^{36} -5.67710 q^{37} +12.4518 q^{38} -2.84255 q^{39} -8.12459 q^{41} +2.73307 q^{42} -4.91032 q^{43} +1.34264 q^{44} +0.358753 q^{46} +1.00000 q^{47} +4.68473 q^{48} -4.90265 q^{49} -5.63243 q^{51} +4.43860 q^{52} -3.85125 q^{53} +1.88719 q^{54} +1.19849 q^{56} +6.59805 q^{57} +19.6222 q^{58} +15.1067 q^{59} -10.1814 q^{61} -13.2539 q^{62} +1.44822 q^{63} -4.19162 q^{64} +1.62269 q^{66} -10.1209 q^{67} +8.79496 q^{68} +0.190099 q^{69} -0.840275 q^{71} +0.827559 q^{72} +4.72701 q^{73} +10.7138 q^{74} -10.3028 q^{76} +1.24525 q^{77} +5.36442 q^{78} -13.2708 q^{79} +1.00000 q^{81} +15.3326 q^{82} -0.110350 q^{83} -2.26138 q^{84} +9.26671 q^{86} +10.3976 q^{87} +0.711573 q^{88} +14.5928 q^{89} +4.11663 q^{91} -0.296837 q^{92} -7.02308 q^{93} -1.88719 q^{94} -7.18586 q^{96} +1.88445 q^{97} +9.25224 q^{98} +0.859846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9	$ 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9} - 16 q^{11} - 7 q^{12} + q^{13} - 12 q^{14} - 3 q^{16} + 14 q^{17} + 3 q^{18} - 26 q^{19} + 7 q^{23} - 9 q^{24} - 10 q^{26} - 10 q^{27} - 24 q^{28} - 14 q^{29} - 22 q^{31} + 11 q^{32} + 16 q^{33} - 12 q^{34} + 7 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 22 q^{41} + 12 q^{42} - 11 q^{43} - 36 q^{44} - 14 q^{46} + 10 q^{47} + 3 q^{48} + 2 q^{49} - 14 q^{51} + 14 q^{52} + 22 q^{53} - 3 q^{54} - 48 q^{56} + 26 q^{57} - 20 q^{58} - 37 q^{59} - 25 q^{61} - 2 q^{62} - 7 q^{64} - 4 q^{67} + 8 q^{68} - 7 q^{69} - 27 q^{71} + 9 q^{72} + q^{73} + 4 q^{74} - 42 q^{76} + 34 q^{77} + 10 q^{78} + 5 q^{79} + 10 q^{81} - 32 q^{82} + 2 q^{83} + 24 q^{84} - 6 q^{86} + 14 q^{87} - 58 q^{88} + 9 q^{89} - 64 q^{91} + 34 q^{92} + 22 q^{93} + 3 q^{94} - 11 q^{96} - 40 q^{97} + 29 q^{98} - 16 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9 - 16 * q^11 - 7 * q^12 + q^13 - 12 * q^14 - 3 * q^16 + 14 * q^17 + 3 * q^18 - 26 * q^19 + 7 * q^23 - 9 * q^24 - 10 * q^26 - 10 * q^27 - 24 * q^28 - 14 * q^29 - 22 * q^31 + 11 * q^32 + 16 * q^33 - 12 * q^34 + 7 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 22 * q^41 + 12 * q^42 - 11 * q^43 - 36 * q^44 - 14 * q^46 + 10 * q^47 + 3 * q^48 + 2 * q^49 - 14 * q^51 + 14 * q^52 + 22 * q^53 - 3 * q^54 - 48 * q^56 + 26 * q^57 - 20 * q^58 - 37 * q^59 - 25 * q^61 - 2 * q^62 - 7 * q^64 - 4 * q^67 + 8 * q^68 - 7 * q^69 - 27 * q^71 + 9 * q^72 + q^73 + 4 * q^74 - 42 * q^76 + 34 * q^77 + 10 * q^78 + 5 * q^79 + 10 * q^81 - 32 * q^82 + 2 * q^83 + 24 * q^84 - 6 * q^86 + 14 * q^87 - 58 * q^88 + 9 * q^89 - 64 * q^91 + 34 * q^92 + 22 * q^93 + 3 * q^94 - 11 * q^96 - 40 * q^97 + 29 * q^98 - 16 * 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 $

$2$	−1.88719	−1.33444	−0.667222	−	0.744859i	$-0.732517\pi$
$2$	−1.88719	−1.33444	−0.667222	+	0.744859i	$0.732517\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.56149	0.780743
$5$	0	0
$5$	0	0
$6$	1.88719	0.770442
$7$	1.44822	0.547376	0.273688	−	0.961818i	$-0.411756\pi$
$7$	1.44822	0.547376	0.273688	+	0.961818i	$0.411756\pi$
$8$	0.827559	0.292586
$9$	1.00000	0.333333
$10$	0	0
$11$	0.859846	0.259253	0.129627	−	0.991563i	$-0.458622\pi$
$11$	0.859846	0.259253	0.129627	+	0.991563i	$0.458622\pi$
$12$	−1.56149	−0.450762
$13$	2.84255	0.788380	0.394190	−	0.919029i	$-0.371025\pi$
$13$	2.84255	0.788380	0.394190	+	0.919029i	$0.371025\pi$
$14$	−2.73307	−0.730443
$15$	0	0
$16$	−4.68473	−1.17118
$17$	5.63243	1.36606	0.683032	−	0.730389i	$-0.260661\pi$
$17$	5.63243	1.36606	0.683032	+	0.730389i	$0.260661\pi$
$18$	−1.88719	−0.444815
$19$	−6.59805	−1.51370	−0.756848	−	0.653590i	$-0.773262\pi$
$19$	−6.59805	−1.51370	−0.756848	+	0.653590i	$0.773262\pi$
$20$	0	0
$21$	−1.44822	−0.316028
$22$	−1.62269	−0.345959
$23$	−0.190099	−0.0396384	−0.0198192	−	0.999804i	$-0.506309\pi$
$23$	−0.190099	−0.0396384	−0.0198192	+	0.999804i	$0.506309\pi$
$24$	−0.827559	−0.168925
$25$	0	0
$26$	−5.36442	−1.05205
$27$	−1.00000	−0.192450
$28$	2.26138	0.427360
$29$	−10.3976	−1.93078	−0.965391	−	0.260807i	$-0.916011\pi$
$29$	−10.3976	−1.93078	−0.965391	+	0.260807i	$0.916011\pi$
$30$	0	0
$31$	7.02308	1.26138	0.630692	−	0.776034i	$-0.282771\pi$
$31$	7.02308	1.26138	0.630692	+	0.776034i	$0.282771\pi$
$32$	7.18586	1.27029
$33$	−0.859846	−0.149680
$34$	−10.6295	−1.82294
$35$	0	0
$36$	1.56149	0.260248
$37$	−5.67710	−0.933309	−0.466655	−	0.884440i	$-0.654541\pi$
$37$	−5.67710	−0.933309	−0.466655	+	0.884440i	$0.654541\pi$
$38$	12.4518	2.01994
$39$	−2.84255	−0.455172
$40$	0	0
$41$	−8.12459	−1.26885	−0.634424	−	0.772986i	$-0.718762\pi$
$41$	−8.12459	−1.26885	−0.634424	+	0.772986i	$0.718762\pi$
$42$	2.73307	0.421722
$43$	−4.91032	−0.748817	−0.374409	−	0.927264i	$-0.622154\pi$
$43$	−4.91032	−0.748817	−0.374409	+	0.927264i	$0.622154\pi$
$44$	1.34264	0.202410
$45$	0	0
$46$	0.358753	0.0528952
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	4.68473	0.676183
$49$	−4.90265	−0.700379
$50$	0	0
$51$	−5.63243	−0.788697
$52$	4.43860	0.615522
$53$	−3.85125	−0.529010	−0.264505	−	0.964384i	$-0.585209\pi$
$53$	−3.85125	−0.529010	−0.264505	+	0.964384i	$0.585209\pi$
$54$	1.88719	0.256814
$55$	0	0
$56$	1.19849	0.160155
$57$	6.59805	0.873933
$58$	19.6222	2.57652
$59$	15.1067	1.96672	0.983360	−	0.181665i	$-0.0581487\pi$
$59$	15.1067	1.96672	0.983360	+	0.181665i	$0.0581487\pi$
$60$	0	0
$61$	−10.1814	−1.30359	−0.651796	−	0.758395i	$-0.725984\pi$
$61$	−10.1814	−1.30359	−0.651796	+	0.758395i	$0.725984\pi$
$62$	−13.2539	−1.68325
$63$	1.44822	0.182459
$64$	−4.19162	−0.523953
$65$	0	0
$66$	1.62269	0.199740
$67$	−10.1209	−1.23646	−0.618230	−	0.785998i	$-0.712150\pi$
$67$	−10.1209	−1.23646	−0.618230	+	0.785998i	$0.712150\pi$
$68$	8.79496	1.06654
$69$	0.190099	0.0228852
$70$	0	0
$71$	−0.840275	−0.0997223	−0.0498611	−	0.998756i	$-0.515878\pi$
$71$	−0.840275	−0.0997223	−0.0498611	+	0.998756i	$0.515878\pi$
$72$	0.827559	0.0975287
$73$	4.72701	0.553254	0.276627	−	0.960977i	$-0.410783\pi$
$73$	4.72701	0.553254	0.276627	+	0.960977i	$0.410783\pi$
$74$	10.7138	1.24545
$75$	0	0
$76$	−10.3028	−1.18181
$77$	1.24525	0.141909
$78$	5.36442	0.607401
$79$	−13.2708	−1.49308	−0.746541	−	0.665340i	$-0.768287\pi$
$79$	−13.2708	−1.49308	−0.746541	+	0.665340i	$0.768287\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	15.3326	1.69321
$83$	−0.110350	−0.0121125	−0.00605624	−	0.999982i	$-0.501928\pi$
$83$	−0.110350	−0.0121125	−0.00605624	+	0.999982i	$0.501928\pi$
$84$	−2.26138	−0.246737
$85$	0	0
$86$	9.26671	0.999255
$87$	10.3976	1.11474
$88$	0.711573	0.0758539
$89$	14.5928	1.54683	0.773416	−	0.633899i	$-0.218546\pi$
$89$	14.5928	1.54683	0.773416	+	0.633899i	$0.218546\pi$
$90$	0	0
$91$	4.11663	0.431541
$92$	−0.296837	−0.0309474
$93$	−7.02308	−0.728260
$94$	−1.88719	−0.194649
$95$	0	0
$96$	−7.18586	−0.733404
$97$	1.88445	0.191337	0.0956685	−	0.995413i	$-0.469501\pi$
$97$	1.88445	0.191337	0.0956685	+	0.995413i	$0.469501\pi$
$98$	9.25224	0.934617
$99$	0.859846	0.0864177
$100$	0	0
$101$	−3.61387	−0.359594	−0.179797	−	0.983704i	$-0.557544\pi$
$101$	−3.61387	−0.359594	−0.179797	+	0.983704i	$0.557544\pi$
$102$	10.6295	1.05247
$103$	−1.46000	−0.143858	−0.0719289	−	0.997410i	$-0.522915\pi$
$103$	−1.46000	−0.143858	−0.0719289	+	0.997410i	$0.522915\pi$
$104$	2.35237	0.230669
$105$	0	0
$106$	7.26805	0.705935
$107$	−15.0739	−1.45724	−0.728622	−	0.684916i	$-0.759839\pi$
$107$	−15.0739	−1.45724	−0.728622	+	0.684916i	$0.759839\pi$
$108$	−1.56149	−0.150254
$109$	5.90985	0.566061	0.283031	−	0.959111i	$-0.408660\pi$
$109$	5.90985	0.566061	0.283031	+	0.959111i	$0.408660\pi$
$110$	0	0
$111$	5.67710	0.538846
$112$	−6.78453	−0.641078
$113$	20.3228	1.91181	0.955904	−	0.293678i	$-0.0948794\pi$
$113$	20.3228	1.91181	0.955904	+	0.293678i	$0.0948794\pi$
$114$	−12.4518	−1.16622
$115$	0	0
$116$	−16.2357	−1.50744
$117$	2.84255	0.262793
$118$	−28.5092	−2.62448
$119$	8.15700	0.747751
$120$	0	0
$121$	−10.2607	−0.932788
$122$	19.2142	1.73957
$123$	8.12459	0.732569
$124$	10.9665	0.984816
$125$	0	0
$126$	−2.73307	−0.243481
$127$	−4.27301	−0.379169	−0.189584	−	0.981864i	$-0.560714\pi$
$127$	−4.27301	−0.379169	−0.189584	+	0.981864i	$0.560714\pi$
$128$	−6.46134	−0.571107
$129$	4.91032	0.432330
$130$	0	0
$131$	−12.5152	−1.09346	−0.546730	−	0.837309i	$-0.684127\pi$
$131$	−12.5152	−1.09346	−0.546730	+	0.837309i	$0.684127\pi$
$132$	−1.34264	−0.116862
$133$	−9.55544	−0.828562
$134$	19.1000	1.64999
$135$	0	0
$136$	4.66116	0.399691
$137$	7.69232	0.657200	0.328600	−	0.944469i	$-0.393423\pi$
$137$	7.69232	0.657200	0.328600	+	0.944469i	$0.393423\pi$
$138$	−0.358753	−0.0305391
$139$	−6.47935	−0.549571	−0.274786	−	0.961505i	$-0.588607\pi$
$139$	−6.47935	−0.549571	−0.274786	+	0.961505i	$0.588607\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	1.58576	0.133074
$143$	2.44415	0.204390
$144$	−4.68473	−0.390394
$145$	0	0
$146$	−8.92076	−0.738287
$147$	4.90265	0.404364
$148$	−8.86471	−0.728675
$149$	16.7246	1.37013	0.685066	−	0.728481i	$-0.259773\pi$
$149$	16.7246	1.37013	0.685066	+	0.728481i	$0.259773\pi$
$150$	0	0
$151$	16.0916	1.30951	0.654757	−	0.755839i	$-0.272771\pi$
$151$	16.0916	1.30951	0.654757	+	0.755839i	$0.272771\pi$
$152$	−5.46028	−0.442887
$153$	5.63243	0.455355
$154$	−2.35002	−0.189370
$155$	0	0
$156$	−4.43860	−0.355372
$157$	−7.85429	−0.626840	−0.313420	−	0.949615i	$-0.601475\pi$
$157$	−7.85429	−0.626840	−0.313420	+	0.949615i	$0.601475\pi$
$158$	25.0445	1.99244
$159$	3.85125	0.305424
$160$	0	0
$161$	−0.275305	−0.0216971
$162$	−1.88719	−0.148272
$163$	−2.33379	−0.182797	−0.0913983	−	0.995814i	$-0.529134\pi$
$163$	−2.33379	−0.182797	−0.0913983	+	0.995814i	$0.529134\pi$
$164$	−12.6864	−0.990644
$165$	0	0
$166$	0.208251	0.0161634
$167$	10.0546	0.778052	0.389026	−	0.921227i	$-0.372812\pi$
$167$	10.0546	0.778052	0.389026	+	0.921227i	$0.372812\pi$
$168$	−1.19849	−0.0924654
$169$	−4.91994	−0.378457
$170$	0	0
$171$	−6.59805	−0.504566
$172$	−7.66740	−0.584634
$173$	2.50875	0.190737	0.0953684	−	0.995442i	$-0.469597\pi$
$173$	2.50875	0.190737	0.0953684	+	0.995442i	$0.469597\pi$
$174$	−19.6222	−1.48756
$175$	0	0
$176$	−4.02815	−0.303633
$177$	−15.1067	−1.13549
$178$	−27.5394	−2.06416
$179$	−15.3483	−1.14718	−0.573592	−	0.819141i	$-0.694450\pi$
$179$	−15.3483	−1.14718	−0.573592	+	0.819141i	$0.694450\pi$
$180$	0	0
$181$	−17.0869	−1.27006	−0.635028	−	0.772489i	$-0.719012\pi$
$181$	−17.0869	−1.27006	−0.635028	+	0.772489i	$0.719012\pi$
$182$	−7.76887	−0.575867
$183$	10.1814	0.752629
$184$	−0.157318	−0.0115976
$185$	0	0
$186$	13.2539	0.971823
$187$	4.84302	0.354156
$188$	1.56149	0.113883
$189$	−1.44822	−0.105343
$190$	0	0
$191$	2.59051	0.187443	0.0937213	−	0.995598i	$-0.470124\pi$
$191$	2.59051	0.187443	0.0937213	+	0.995598i	$0.470124\pi$
$192$	4.19162	0.302504
$193$	−10.1692	−0.731994	−0.365997	−	0.930616i	$-0.619272\pi$
$193$	−10.1692	−0.731994	−0.365997	+	0.930616i	$0.619272\pi$
$194$	−3.55632	−0.255329
$195$	0	0
$196$	−7.65543	−0.546816
$197$	19.8628	1.41517	0.707584	−	0.706629i	$-0.249785\pi$
$197$	19.8628	1.41517	0.707584	+	0.706629i	$0.249785\pi$
$198$	−1.62269	−0.115320
$199$	−4.72329	−0.334825	−0.167413	−	0.985887i	$-0.553541\pi$
$199$	−4.72329	−0.334825	−0.167413	+	0.985887i	$0.553541\pi$
$200$	0	0
$201$	10.1209	0.713870
$202$	6.82007	0.479858
$203$	−15.0580	−1.05686
$204$	−8.79496	−0.615770
$205$	0	0
$206$	2.75529	0.191970
$207$	−0.190099	−0.0132128
$208$	−13.3166	−0.923338
$209$	−5.67331	−0.392431
$210$	0	0
$211$	−17.7581	−1.22252	−0.611261	−	0.791429i	$-0.709337\pi$
$211$	−17.7581	−1.22252	−0.611261	+	0.791429i	$0.709337\pi$
$212$	−6.01368	−0.413021
$213$	0.840275	0.0575747
$214$	28.4472	1.94461
$215$	0	0
$216$	−0.827559	−0.0563082
$217$	10.1710	0.690451
$218$	−11.1530	−0.755377
$219$	−4.72701	−0.319421
$220$	0	0
$221$	16.0104	1.07698
$222$	−10.7138	−0.719061
$223$	27.7580	1.85882	0.929408	−	0.369053i	$-0.120318\pi$
$223$	27.7580	1.85882	0.929408	+	0.369053i	$0.120318\pi$
$224$	10.4067	0.695328
$225$	0	0
$226$	−38.3530	−2.55120
$227$	−19.9112	−1.32155	−0.660775	−	0.750584i	$-0.729772\pi$
$227$	−19.9112	−1.32155	−0.660775	+	0.750584i	$0.729772\pi$
$228$	10.3028	0.682317
$229$	15.9729	1.05552	0.527760	−	0.849394i	$-0.323032\pi$
$229$	15.9729	1.05552	0.527760	+	0.849394i	$0.323032\pi$
$230$	0	0
$231$	−1.24525	−0.0819312
$232$	−8.60461	−0.564920
$233$	−15.9896	−1.04752	−0.523758	−	0.851867i	$-0.675470\pi$
$233$	−15.9896	−1.04752	−0.523758	+	0.851867i	$0.675470\pi$
$234$	−5.36442	−0.350683
$235$	0	0
$236$	23.5889	1.53550
$237$	13.2708	0.862031
$238$	−15.3938	−0.997832
$239$	−16.2400	−1.05048	−0.525239	−	0.850955i	$-0.676024\pi$
$239$	−16.2400	−1.05048	−0.525239	+	0.850955i	$0.676024\pi$
$240$	0	0
$241$	−1.73011	−0.111446	−0.0557231	−	0.998446i	$-0.517746\pi$
$241$	−1.73011	−0.111446	−0.0557231	+	0.998446i	$0.517746\pi$
$242$	19.3638	1.24475
$243$	−1.00000	−0.0641500
$244$	−15.8981	−1.01777
$245$	0	0
$246$	−15.3326	−0.977573
$247$	−18.7553	−1.19337
$248$	5.81202	0.369063
$249$	0.110350	0.00699315
$250$	0	0
$251$	−0.650330	−0.0410484	−0.0205242	−	0.999789i	$-0.506534\pi$
$251$	−0.650330	−0.0410484	−0.0205242	+	0.999789i	$0.506534\pi$
$252$	2.26138	0.142453
$253$	−0.163456	−0.0102764
$254$	8.06399	0.505980
$255$	0	0
$256$	20.5770	1.28606
$257$	30.7586	1.91867	0.959336	−	0.282268i	$-0.0910867\pi$
$257$	30.7586	1.91867	0.959336	+	0.282268i	$0.0910867\pi$
$258$	−9.26671	−0.576920
$259$	−8.22170	−0.510871
$260$	0	0
$261$	−10.3976	−0.643594
$262$	23.6186	1.45916
$263$	−11.7992	−0.727569	−0.363784	−	0.931483i	$-0.618515\pi$
$263$	−11.7992	−0.727569	−0.363784	+	0.931483i	$0.618515\pi$
$264$	−0.711573	−0.0437943
$265$	0	0
$266$	18.0329	1.10567
$267$	−14.5928	−0.893064
$268$	−15.8036	−0.965357
$269$	10.7027	0.652555	0.326278	−	0.945274i	$-0.394206\pi$
$269$	10.7027	0.652555	0.326278	+	0.945274i	$0.394206\pi$
$270$	0	0
$271$	−18.8506	−1.14509	−0.572547	−	0.819872i	$-0.694045\pi$
$271$	−18.8506	−1.14509	−0.572547	+	0.819872i	$0.694045\pi$
$272$	−26.3864	−1.59991
$273$	−4.11663	−0.249150
$274$	−14.5169	−0.876997
$275$	0	0
$276$	0.296837	0.0178675
$277$	−20.6129	−1.23851	−0.619255	−	0.785190i	$-0.712565\pi$
$277$	−20.6129	−1.23851	−0.619255	+	0.785190i	$0.712565\pi$
$278$	12.2278	0.733373
$279$	7.02308	0.420461
$280$	0	0
$281$	−11.2673	−0.672149	−0.336074	−	0.941835i	$-0.609099\pi$
$281$	−11.2673	−0.672149	−0.336074	+	0.941835i	$0.609099\pi$
$282$	1.88719	0.112381
$283$	12.1394	0.721615	0.360808	−	0.932640i	$-0.382501\pi$
$283$	12.1394	0.721615	0.360808	+	0.932640i	$0.382501\pi$
$284$	−1.31208	−0.0778575
$285$	0	0
$286$	−4.61258	−0.272747
$287$	−11.7662	−0.694537
$288$	7.18586	0.423431
$289$	14.7242	0.866131
$290$	0	0
$291$	−1.88445	−0.110468
$292$	7.38115	0.431949
$293$	4.03918	0.235971	0.117986	−	0.993015i	$-0.462356\pi$
$293$	4.03918	0.235971	0.117986	+	0.993015i	$0.462356\pi$
$294$	−9.25224	−0.539602
$295$	0	0
$296$	−4.69813	−0.273073
$297$	−0.859846	−0.0498933
$298$	−31.5625	−1.82837
$299$	−0.540365	−0.0312501
$300$	0	0
$301$	−7.11123	−0.409885
$302$	−30.3679	−1.74747
$303$	3.61387	0.207612
$304$	30.9101	1.77282
$305$	0	0
$306$	−10.6295	−0.607646
$307$	−15.3270	−0.874756	−0.437378	−	0.899278i	$-0.644093\pi$
$307$	−15.3270	−0.874756	−0.437378	+	0.899278i	$0.644093\pi$
$308$	1.94444	0.110795
$309$	1.46000	0.0830563
$310$	0	0
$311$	−7.92368	−0.449311	−0.224655	−	0.974438i	$-0.572126\pi$
$311$	−7.92368	−0.449311	−0.224655	+	0.974438i	$0.572126\pi$
$312$	−2.35237	−0.133177
$313$	−6.41853	−0.362797	−0.181398	−	0.983410i	$-0.558062\pi$
$313$	−6.41853	−0.362797	−0.181398	+	0.983410i	$0.558062\pi$
$314$	14.8225	0.836484
$315$	0	0
$316$	−20.7222	−1.16571
$317$	−24.5794	−1.38052	−0.690260	−	0.723562i	$-0.742504\pi$
$317$	−24.5794	−1.38052	−0.690260	+	0.723562i	$0.742504\pi$
$318$	−7.26805	−0.407572
$319$	−8.94031	−0.500561
$320$	0	0
$321$	15.0739	0.841341
$322$	0.519553	0.0289536
$323$	−37.1630	−2.06781
$324$	1.56149	0.0867492
$325$	0	0
$326$	4.40431	0.243932
$327$	−5.90985	−0.326815
$328$	−6.72357	−0.371247
$329$	1.44822	0.0798430
$330$	0	0
$331$	9.57831	0.526472	0.263236	−	0.964732i	$-0.415210\pi$
$331$	9.57831	0.526472	0.263236	+	0.964732i	$0.415210\pi$
$332$	−0.172310	−0.00945674
$333$	−5.67710	−0.311103
$334$	−18.9750	−1.03827
$335$	0	0
$336$	6.78453	0.370127
$337$	−25.0697	−1.36563	−0.682816	−	0.730590i	$-0.739245\pi$
$337$	−25.0697	−1.36563	−0.682816	+	0.730590i	$0.739245\pi$
$338$	9.28486	0.505030
$339$	−20.3228	−1.10378
$340$	0	0
$341$	6.03877	0.327018
$342$	12.4518	0.673315
$343$	−17.2377	−0.930747
$344$	−4.06358	−0.219094
$345$	0	0
$346$	−4.73449	−0.254528
$347$	−13.1076	−0.703651	−0.351825	−	0.936066i	$-0.614439\pi$
$347$	−13.1076	−0.703651	−0.351825	+	0.936066i	$0.614439\pi$
$348$	16.2357	0.870324
$349$	5.51525	0.295225	0.147612	−	0.989045i	$-0.452841\pi$
$349$	5.51525	0.295225	0.147612	+	0.989045i	$0.452841\pi$
$350$	0	0
$351$	−2.84255	−0.151724
$352$	6.17873	0.329328
$353$	2.08998	0.111238	0.0556191	−	0.998452i	$-0.482287\pi$
$353$	2.08998	0.111238	0.0556191	+	0.998452i	$0.482287\pi$
$354$	28.5092	1.51524
$355$	0	0
$356$	22.7864	1.20768
$357$	−8.15700	−0.431714
$358$	28.9651	1.53085
$359$	13.2830	0.701048	0.350524	−	0.936554i	$-0.386004\pi$
$359$	13.2830	0.701048	0.350524	+	0.936554i	$0.386004\pi$
$360$	0	0
$361$	24.5343	1.29128
$362$	32.2462	1.69482
$363$	10.2607	0.538545
$364$	6.42807	0.336922
$365$	0	0
$366$	−19.2142	−1.00434
$367$	0.628588	0.0328120	0.0164060	−	0.999865i	$-0.494778\pi$
$367$	0.628588	0.0328120	0.0164060	+	0.999865i	$0.494778\pi$
$368$	0.890563	0.0464238
$369$	−8.12459	−0.422949
$370$	0	0
$371$	−5.57747	−0.289568
$372$	−10.9665	−0.568584
$373$	2.38412	0.123445	0.0617225	−	0.998093i	$-0.480341\pi$
$373$	2.38412	0.123445	0.0617225	+	0.998093i	$0.480341\pi$
$374$	−9.13969	−0.472602
$375$	0	0
$376$	0.827559	0.0426781
$377$	−29.5556	−1.52219
$378$	2.73307	0.140574
$379$	−23.4179	−1.20290	−0.601449	−	0.798911i	$-0.705410\pi$
$379$	−23.4179	−1.20290	−0.601449	+	0.798911i	$0.705410\pi$
$380$	0	0
$381$	4.27301	0.218913
$382$	−4.88878	−0.250132
$383$	−27.1633	−1.38798	−0.693989	−	0.719986i	$-0.744148\pi$
$383$	−27.1633	−1.38798	−0.693989	+	0.719986i	$0.744148\pi$
$384$	6.46134	0.329729
$385$	0	0
$386$	19.1912	0.976806
$387$	−4.91032	−0.249606
$388$	2.94254	0.149385
$389$	−23.7025	−1.20176	−0.600882	−	0.799338i	$-0.705184\pi$
$389$	−23.7025	−1.20176	−0.600882	+	0.799338i	$0.705184\pi$
$390$	0	0
$391$	−1.07072	−0.0541485
$392$	−4.05724	−0.204921
$393$	12.5152	0.631309
$394$	−37.4849	−1.88846
$395$	0	0
$396$	1.34264	0.0674701
$397$	3.84692	0.193072	0.0965358	−	0.995330i	$-0.469224\pi$
$397$	3.84692	0.193072	0.0965358	+	0.995330i	$0.469224\pi$
$398$	8.91374	0.446806
$399$	9.55544	0.478370
$400$	0	0
$401$	−16.9168	−0.844786	−0.422393	−	0.906413i	$-0.638810\pi$
$401$	−16.9168	−0.844786	−0.422393	+	0.906413i	$0.638810\pi$
$402$	−19.1000	−0.952620
$403$	19.9634	0.994450
$404$	−5.64302	−0.280750
$405$	0	0
$406$	28.4173	1.41033
$407$	−4.88143	−0.241964
$408$	−4.66116	−0.230762
$409$	25.8955	1.28045	0.640224	−	0.768188i	$-0.278842\pi$
$409$	25.8955	1.28045	0.640224	+	0.768188i	$0.278842\pi$
$410$	0	0
$411$	−7.69232	−0.379434
$412$	−2.27976	−0.112316
$413$	21.8778	1.07654
$414$	0.358753	0.0176317
$415$	0	0
$416$	20.4261	1.00147
$417$	6.47935	0.317295
$418$	10.7066	0.523677
$419$	−36.2498	−1.77092	−0.885460	−	0.464716i	$-0.846156\pi$
$419$	−36.2498	−1.77092	−0.885460	+	0.464716i	$0.846156\pi$
$420$	0	0
$421$	35.1728	1.71422	0.857108	−	0.515137i	$-0.172259\pi$
$421$	35.1728	1.71422	0.857108	+	0.515137i	$0.172259\pi$
$422$	33.5130	1.63139
$423$	1.00000	0.0486217
$424$	−3.18714	−0.154781
$425$	0	0
$426$	−1.58576	−0.0768303
$427$	−14.7449	−0.713555
$428$	−23.5376	−1.13773
$429$	−2.44415	−0.118005
$430$	0	0
$431$	−27.3100	−1.31548	−0.657739	−	0.753246i	$-0.728487\pi$
$431$	−27.3100	−1.31548	−0.657739	+	0.753246i	$0.728487\pi$
$432$	4.68473	0.225394
$433$	16.1935	0.778211	0.389105	−	0.921193i	$-0.372784\pi$
$433$	16.1935	0.778211	0.389105	+	0.921193i	$0.372784\pi$
$434$	−19.1946	−0.921369
$435$	0	0
$436$	9.22815	0.441948
$437$	1.25428	0.0600005
$438$	8.92076	0.426250
$439$	−12.2351	−0.583948	−0.291974	−	0.956426i	$-0.594312\pi$
$439$	−12.2351	−0.583948	−0.291974	+	0.956426i	$0.594312\pi$
$440$	0	0
$441$	−4.90265	−0.233460
$442$	−30.2147	−1.43717
$443$	23.1034	1.09768	0.548838	−	0.835929i	$-0.315070\pi$
$443$	23.1034	1.09768	0.548838	+	0.835929i	$0.315070\pi$
$444$	8.86471	0.420701
$445$	0	0
$446$	−52.3847	−2.48049
$447$	−16.7246	−0.791046
$448$	−6.07040	−0.286799
$449$	−11.6166	−0.548223	−0.274112	−	0.961698i	$-0.588384\pi$
$449$	−11.6166	−0.548223	−0.274112	+	0.961698i	$0.588384\pi$
$450$	0	0
$451$	−6.98589	−0.328953
$452$	31.7338	1.49263
$453$	−16.0916	−0.756048
$454$	37.5761	1.76353
$455$	0	0
$456$	5.46028	0.255701
$457$	−2.55111	−0.119336	−0.0596680	−	0.998218i	$-0.519004\pi$
$457$	−2.55111	−0.119336	−0.0596680	+	0.998218i	$0.519004\pi$
$458$	−30.1439	−1.40853
$459$	−5.63243	−0.262899
$460$	0	0
$461$	2.45274	0.114235	0.0571176	−	0.998367i	$-0.481809\pi$
$461$	2.45274	0.114235	0.0571176	+	0.998367i	$0.481809\pi$
$462$	2.35002	0.109333
$463$	−36.6395	−1.70278	−0.851392	−	0.524530i	$-0.824241\pi$
$463$	−36.6395	−1.70278	−0.851392	+	0.524530i	$0.824241\pi$
$464$	48.7099	2.26130
$465$	0	0
$466$	30.1755	1.39785
$467$	27.2894	1.26280	0.631401	−	0.775457i	$-0.282480\pi$
$467$	27.2894	1.26280	0.631401	+	0.775457i	$0.282480\pi$
$468$	4.43860	0.205174
$469$	−14.6572	−0.676808
$470$	0	0
$471$	7.85429	0.361906
$472$	12.5017	0.575435
$473$	−4.22212	−0.194133
$474$	−25.0445	−1.15033
$475$	0	0
$476$	12.7370	0.583801
$477$	−3.85125	−0.176337
$478$	30.6479	1.40180
$479$	−8.83826	−0.403831	−0.201915	−	0.979403i	$-0.564717\pi$
$479$	−8.83826	−0.403831	−0.201915	+	0.979403i	$0.564717\pi$
$480$	0	0
$481$	−16.1374	−0.735803
$482$	3.26505	0.148719
$483$	0.275305	0.0125268
$484$	−16.0219	−0.728268
$485$	0	0
$486$	1.88719	0.0856047
$487$	3.60971	0.163572	0.0817858	−	0.996650i	$-0.473938\pi$
$487$	3.60971	0.163572	0.0817858	+	0.996650i	$0.473938\pi$
$488$	−8.42569	−0.381413
$489$	2.33379	0.105538
$490$	0	0
$491$	28.7874	1.29916	0.649578	−	0.760295i	$-0.274946\pi$
$491$	28.7874	1.29916	0.649578	+	0.760295i	$0.274946\pi$
$492$	12.6864	0.571948
$493$	−58.5636	−2.63757
$494$	35.3947	1.59248
$495$	0	0
$496$	−32.9013	−1.47731
$497$	−1.21690	−0.0545856
$498$	−0.208251	−0.00933197
$499$	3.94447	0.176579	0.0882893	−	0.996095i	$-0.471860\pi$
$499$	3.94447	0.176579	0.0882893	+	0.996095i	$0.471860\pi$
$500$	0	0
$501$	−10.0546	−0.449208
$502$	1.22730	0.0547769
$503$	16.5560	0.738198	0.369099	−	0.929390i	$-0.379666\pi$
$503$	16.5560	0.738198	0.369099	+	0.929390i	$0.379666\pi$
$504$	1.19849	0.0533849
$505$	0	0
$506$	0.308472	0.0137133
$507$	4.91994	0.218502
$508$	−6.67225	−0.296033
$509$	−8.73370	−0.387115	−0.193557	−	0.981089i	$-0.562003\pi$
$509$	−8.73370	−0.387115	−0.193557	+	0.981089i	$0.562003\pi$
$510$	0	0
$511$	6.84575	0.302838
$512$	−25.9101	−1.14507
$513$	6.59805	0.291311
$514$	−58.0474	−2.56036
$515$	0	0
$516$	7.66740	0.337539
$517$	0.859846	0.0378160
$518$	15.5159	0.681730
$519$	−2.50875	−0.110122
$520$	0	0
$521$	13.1791	0.577388	0.288694	−	0.957421i	$-0.406779\pi$
$521$	13.1791	0.577388	0.288694	+	0.957421i	$0.406779\pi$
$522$	19.6222	0.858841
$523$	2.57258	0.112491	0.0562454	−	0.998417i	$-0.482087\pi$
$523$	2.57258	0.112491	0.0562454	+	0.998417i	$0.482087\pi$
$524$	−19.5423	−0.853711
$525$	0	0
$526$	22.2673	0.970900
$527$	39.5570	1.72313
$528$	4.02815	0.175303
$529$	−22.9639	−0.998429
$530$	0	0
$531$	15.1067	0.655574
$532$	−14.9207	−0.646894
$533$	−23.0945	−1.00033
$534$	27.5394	1.19174
$535$	0	0
$536$	−8.37560	−0.361771
$537$	15.3483	0.662327
$538$	−20.1980	−0.870799
$539$	−4.21553	−0.181576
$540$	0	0
$541$	−20.2219	−0.869407	−0.434704	−	0.900574i	$-0.643147\pi$
$541$	−20.2219	−0.869407	−0.434704	+	0.900574i	$0.643147\pi$
$542$	35.5747	1.52807
$543$	17.0869	0.733268
$544$	40.4738	1.73530
$545$	0	0
$546$	7.76887	0.332477
$547$	15.1716	0.648693	0.324346	−	0.945938i	$-0.394856\pi$
$547$	15.1716	0.648693	0.324346	+	0.945938i	$0.394856\pi$
$548$	12.0115	0.513104
$549$	−10.1814	−0.434531
$550$	0	0
$551$	68.6038	2.92262
$552$	0.157318	0.00669590
$553$	−19.2191	−0.817277
$554$	38.9005	1.65272
$555$	0	0
$556$	−10.1174	−0.429074
$557$	11.8437	0.501835	0.250918	−	0.968008i	$-0.419268\pi$
$557$	11.8437	0.501835	0.250918	+	0.968008i	$0.419268\pi$
$558$	−13.2539	−0.561082
$559$	−13.9578	−0.590353
$560$	0	0
$561$	−4.84302	−0.204472
$562$	21.2635	0.896945
$563$	16.0440	0.676174	0.338087	−	0.941115i	$-0.390220\pi$
$563$	16.0440	0.676174	0.338087	+	0.941115i	$0.390220\pi$
$564$	−1.56149	−0.0657504
$565$	0	0
$566$	−22.9094	−0.962956
$567$	1.44822	0.0608196
$568$	−0.695377	−0.0291774
$569$	25.6910	1.07702	0.538511	−	0.842619i	$-0.318987\pi$
$569$	25.6910	1.07702	0.538511	+	0.842619i	$0.318987\pi$
$570$	0	0
$571$	−10.8543	−0.454239	−0.227119	−	0.973867i	$-0.572931\pi$
$571$	−10.8543	−0.454239	−0.227119	+	0.973867i	$0.572931\pi$
$572$	3.81651	0.159576
$573$	−2.59051	−0.108220
$574$	22.2051	0.926821
$575$	0	0
$576$	−4.19162	−0.174651
$577$	10.2698	0.427536	0.213768	−	0.976884i	$-0.431426\pi$
$577$	10.2698	0.427536	0.213768	+	0.976884i	$0.431426\pi$
$578$	−27.7874	−1.15580
$579$	10.1692	0.422617
$580$	0	0
$581$	−0.159811	−0.00663009
$582$	3.55632	0.147414
$583$	−3.31148	−0.137148
$584$	3.91187	0.161875
$585$	0	0
$586$	−7.62270	−0.314891
$587$	−6.33798	−0.261596	−0.130798	−	0.991409i	$-0.541754\pi$
$587$	−6.33798	−0.261596	−0.130798	+	0.991409i	$0.541754\pi$
$588$	7.65543	0.315705
$589$	−46.3387	−1.90935
$590$	0	0
$591$	−19.8628	−0.817048
$592$	26.5957	1.09308
$593$	−22.6796	−0.931339	−0.465669	−	0.884959i	$-0.654186\pi$
$593$	−22.6796	−0.931339	−0.465669	+	0.884959i	$0.654186\pi$
$594$	1.62269	0.0665799
$595$	0	0
$596$	26.1152	1.06972
$597$	4.72329	0.193311
$598$	1.01977	0.0417015
$599$	6.52930	0.266780	0.133390	−	0.991064i	$-0.457414\pi$
$599$	6.52930	0.266780	0.133390	+	0.991064i	$0.457414\pi$
$600$	0	0
$601$	9.56925	0.390338	0.195169	−	0.980770i	$-0.437474\pi$
$601$	9.56925	0.390338	0.195169	+	0.980770i	$0.437474\pi$
$602$	13.4203	0.546969
$603$	−10.1209	−0.412153
$604$	25.1268	1.02239
$605$	0	0
$606$	−6.82007	−0.277046
$607$	−40.9145	−1.66067	−0.830334	−	0.557266i	$-0.811850\pi$
$607$	−40.9145	−1.66067	−0.830334	+	0.557266i	$0.811850\pi$
$608$	−47.4127	−1.92284
$609$	15.0580	0.610181
$610$	0	0
$611$	2.84255	0.114997
$612$	8.79496	0.355515
$613$	−25.6984	−1.03795	−0.518973	−	0.854790i	$-0.673686\pi$
$613$	−25.6984	−1.03795	−0.518973	+	0.854790i	$0.673686\pi$
$614$	28.9249	1.16731
$615$	0	0
$616$	1.03052	0.0415206
$617$	20.1936	0.812963	0.406481	−	0.913659i	$-0.366756\pi$
$617$	20.1936	0.812963	0.406481	+	0.913659i	$0.366756\pi$
$618$	−2.75529	−0.110834
$619$	−20.4156	−0.820572	−0.410286	−	0.911957i	$-0.634571\pi$
$619$	−20.4156	−0.820572	−0.410286	+	0.911957i	$0.634571\pi$
$620$	0	0
$621$	0.190099	0.00762841
$622$	14.9535	0.599580
$623$	21.1336	0.846699
$624$	13.3166	0.533089
$625$	0	0
$626$	12.1130	0.484132
$627$	5.67331	0.226570
$628$	−12.2644	−0.489401
$629$	−31.9758	−1.27496
$630$	0	0
$631$	−22.2092	−0.884135	−0.442067	−	0.896982i	$-0.645755\pi$
$631$	−22.2092	−0.884135	−0.442067	+	0.896982i	$0.645755\pi$
$632$	−10.9824	−0.436855
$633$	17.7581	0.705823
$634$	46.3861	1.84223
$635$	0	0
$636$	6.01368	0.238458
$637$	−13.9360	−0.552165
$638$	16.8721	0.667972
$639$	−0.840275	−0.0332408
$640$	0	0
$641$	21.0709	0.832249	0.416124	−	0.909308i	$-0.363388\pi$
$641$	21.0709	0.832249	0.416124	+	0.909308i	$0.363388\pi$
$642$	−28.4472	−1.12272
$643$	−25.6183	−1.01029	−0.505144	−	0.863035i	$-0.668561\pi$
$643$	−25.6183	−1.01029	−0.505144	+	0.863035i	$0.668561\pi$
$644$	−0.429885	−0.0169399
$645$	0	0
$646$	70.1337	2.75937
$647$	−37.3646	−1.46896	−0.734478	−	0.678633i	$-0.762573\pi$
$647$	−37.3646	−1.46896	−0.734478	+	0.678633i	$0.762573\pi$
$648$	0.827559	0.0325096
$649$	12.9894	0.509879
$650$	0	0
$651$	−10.1710	−0.398632
$652$	−3.64418	−0.142717
$653$	42.1304	1.64869	0.824344	−	0.566089i	$-0.191544\pi$
$653$	42.1304	1.64869	0.824344	+	0.566089i	$0.191544\pi$
$654$	11.1530	0.436117
$655$	0	0
$656$	38.0615	1.48605
$657$	4.72701	0.184418
$658$	−2.73307	−0.106546
$659$	−37.4208	−1.45771	−0.728853	−	0.684670i	$-0.759946\pi$
$659$	−37.4208	−1.45771	−0.728853	+	0.684670i	$0.759946\pi$
$660$	0	0
$661$	3.81349	0.148328	0.0741639	−	0.997246i	$-0.476371\pi$
$661$	3.81349	0.148328	0.0741639	+	0.997246i	$0.476371\pi$
$662$	−18.0761	−0.702547
$663$	−16.0104	−0.621793
$664$	−0.0913211	−0.00354395
$665$	0	0
$666$	10.7138	0.415150
$667$	1.97657	0.0765330
$668$	15.7002	0.607458
$669$	−27.7580	−1.07319
$670$	0	0
$671$	−8.75441	−0.337960
$672$	−10.4067	−0.401448
$673$	16.5907	0.639524	0.319762	−	0.947498i	$-0.396397\pi$
$673$	16.5907	0.639524	0.319762	+	0.947498i	$0.396397\pi$
$674$	47.3113	1.82236
$675$	0	0
$676$	−7.68241	−0.295477
$677$	44.5604	1.71260	0.856298	−	0.516482i	$-0.172759\pi$
$677$	44.5604	1.71260	0.856298	+	0.516482i	$0.172759\pi$
$678$	38.3530	1.47294
$679$	2.72910	0.104733
$680$	0	0
$681$	19.9112	0.762997
$682$	−11.3963	−0.436387
$683$	7.32263	0.280193	0.140096	−	0.990138i	$-0.455259\pi$
$683$	7.32263	0.280193	0.140096	+	0.990138i	$0.455259\pi$
$684$	−10.3028	−0.393936
$685$	0	0
$686$	32.5308	1.24203
$687$	−15.9729	−0.609404
$688$	23.0036	0.877002
$689$	−10.9474	−0.417061
$690$	0	0
$691$	33.4388	1.27207	0.636037	−	0.771659i	$-0.280573\pi$
$691$	33.4388	1.27207	0.636037	+	0.771659i	$0.280573\pi$
$692$	3.91738	0.148916
$693$	1.24525	0.0473030
$694$	24.7365	0.938983
$695$	0	0
$696$	8.60461	0.326157
$697$	−45.7611	−1.73333
$698$	−10.4083	−0.393961
$699$	15.9896	0.604783
$700$	0	0
$701$	−48.6669	−1.83812	−0.919062	−	0.394113i	$-0.871052\pi$
$701$	−48.6669	−1.83812	−0.919062	+	0.394113i	$0.871052\pi$
$702$	5.36442	0.202467
$703$	37.4578	1.41275
$704$	−3.60415	−0.135837
$705$	0	0
$706$	−3.94418	−0.148441
$707$	−5.23369	−0.196833
$708$	−23.5889	−0.886524
$709$	22.6001	0.848765	0.424382	−	0.905483i	$-0.360491\pi$
$709$	22.6001	0.848765	0.424382	+	0.905483i	$0.360491\pi$
$710$	0	0
$711$	−13.2708	−0.497694
$712$	12.0764	0.452582
$713$	−1.33508	−0.0499992
$714$	15.3938	0.576099
$715$	0	0
$716$	−23.9661	−0.895656
$717$	16.2400	0.606493
$718$	−25.0675	−0.935510
$719$	0.480330	0.0179133	0.00895665	−	0.999960i	$-0.497149\pi$
$719$	0.480330	0.0179133	0.00895665	+	0.999960i	$0.497149\pi$
$720$	0	0
$721$	−2.11440	−0.0787443
$722$	−46.3009	−1.72314
$723$	1.73011	0.0643435
$724$	−26.6809	−0.991588
$725$	0	0
$726$	−19.3638	−0.718659
$727$	14.6427	0.543067	0.271533	−	0.962429i	$-0.412469\pi$
$727$	14.6427	0.543067	0.271533	+	0.962429i	$0.412469\pi$
$728$	3.40676	0.126263
$729$	1.00000	0.0370370
$730$	0	0
$731$	−27.6570	−1.02293
$732$	15.8981	0.587610
$733$	40.2801	1.48778	0.743890	−	0.668302i	$-0.232979\pi$
$733$	40.2801	1.48778	0.743890	+	0.668302i	$0.232979\pi$
$734$	−1.18627	−0.0437859
$735$	0	0
$736$	−1.36602	−0.0503523
$737$	−8.70237	−0.320556
$738$	15.3326	0.564402
$739$	7.24682	0.266579	0.133289	−	0.991077i	$-0.457446\pi$
$739$	7.24682	0.266579	0.133289	+	0.991077i	$0.457446\pi$
$740$	0	0
$741$	18.7553	0.688992
$742$	10.5257	0.386412
$743$	21.4774	0.787930	0.393965	−	0.919126i	$-0.371103\pi$
$743$	21.4774	0.787930	0.393965	+	0.919126i	$0.371103\pi$
$744$	−5.81202	−0.213079
$745$	0	0
$746$	−4.49928	−0.164730
$747$	−0.110350	−0.00403750
$748$	7.56230	0.276505
$749$	−21.8303	−0.797661
$750$	0	0
$751$	−4.27938	−0.156157	−0.0780783	−	0.996947i	$-0.524878\pi$
$751$	−4.27938	−0.156157	−0.0780783	+	0.996947i	$0.524878\pi$
$752$	−4.68473	−0.170835
$753$	0.650330	0.0236993
$754$	55.7770	2.03128
$755$	0	0
$756$	−2.26138	−0.0822455
$757$	−30.3315	−1.10242	−0.551209	−	0.834367i	$-0.685833\pi$
$757$	−30.3315	−1.10242	−0.551209	+	0.834367i	$0.685833\pi$
$758$	44.1941	1.60520
$759$	0.163456	0.00593307
$760$	0	0
$761$	−24.5189	−0.888809	−0.444405	−	0.895826i	$-0.646585\pi$
$761$	−24.5189	−0.888809	−0.444405	+	0.895826i	$0.646585\pi$
$762$	−8.06399	−0.292128
$763$	8.55877	0.309848
$764$	4.04504	0.146345
$765$	0	0
$766$	51.2622	1.85218
$767$	42.9414	1.55052
$768$	−20.5770	−0.742509
$769$	38.6946	1.39536	0.697682	−	0.716408i	$-0.254215\pi$
$769$	38.6946	1.39536	0.697682	+	0.716408i	$0.254215\pi$
$770$	0	0
$771$	−30.7586	−1.10775
$772$	−15.8791	−0.571500
$773$	−17.7072	−0.636882	−0.318441	−	0.947943i	$-0.603159\pi$
$773$	−17.7072	−0.636882	−0.318441	+	0.947943i	$0.603159\pi$
$774$	9.26671	0.333085
$775$	0	0
$776$	1.55949	0.0559826
$777$	8.22170	0.294952
$778$	44.7311	1.60369
$779$	53.6064	1.92065
$780$	0	0
$781$	−0.722507	−0.0258533
$782$	2.02065	0.0722582
$783$	10.3976	0.371579
$784$	22.9676	0.820272
$785$	0	0
$786$	−23.6186	−0.842447
$787$	40.2262	1.43391	0.716954	−	0.697121i	$-0.245536\pi$
$787$	40.2262	1.43391	0.716954	+	0.697121i	$0.245536\pi$
$788$	31.0155	1.10488
$789$	11.7992	0.420062
$790$	0	0
$791$	29.4319	1.04648
$792$	0.711573	0.0252846
$793$	−28.9410	−1.02773
$794$	−7.25988	−0.257643
$795$	0	0
$796$	−7.37535	−0.261412
$797$	2.98055	0.105576	0.0527882	−	0.998606i	$-0.483189\pi$
$797$	2.98055	0.105576	0.0527882	+	0.998606i	$0.483189\pi$
$798$	−18.0329	−0.638359
$799$	5.63243	0.199261
$800$	0	0
$801$	14.5928	0.515611
$802$	31.9253	1.12732
$803$	4.06450	0.143433
$804$	15.8036	0.557349
$805$	0	0
$806$	−37.6748	−1.32704
$807$	−10.7027	−0.376753
$808$	−2.99069	−0.105212
$809$	−26.4486	−0.929883	−0.464941	−	0.885342i	$-0.653925\pi$
$809$	−26.4486	−0.929883	−0.464941	+	0.885342i	$0.653925\pi$
$810$	0	0
$811$	22.0553	0.774466	0.387233	−	0.921982i	$-0.373431\pi$
$811$	22.0553	0.774466	0.387233	+	0.921982i	$0.373431\pi$
$812$	−23.5129	−0.825139
$813$	18.8506	0.661121
$814$	9.21219	0.322887
$815$	0	0
$816$	26.3864	0.923709
$817$	32.3986	1.13348
$818$	−48.8696	−1.70869
$819$	4.11663	0.143847
$820$	0	0
$821$	−20.8576	−0.727936	−0.363968	−	0.931411i	$-0.618578\pi$
$821$	−20.8576	−0.727936	−0.363968	+	0.931411i	$0.618578\pi$
$822$	14.5169	0.506334
$823$	−46.5050	−1.62106	−0.810532	−	0.585695i	$-0.800822\pi$
$823$	−46.5050	−1.62106	−0.810532	+	0.585695i	$0.800822\pi$
$824$	−1.20823	−0.0420908
$825$	0	0
$826$	−41.2876	−1.43658
$827$	−10.7596	−0.374147	−0.187073	−	0.982346i	$-0.559900\pi$
$827$	−10.7596	−0.374147	−0.187073	+	0.982346i	$0.559900\pi$
$828$	−0.296837	−0.0103158
$829$	−11.8086	−0.410128	−0.205064	−	0.978749i	$-0.565740\pi$
$829$	−11.8086	−0.410128	−0.205064	+	0.978749i	$0.565740\pi$
$830$	0	0
$831$	20.6129	0.715054
$832$	−11.9149	−0.413074
$833$	−27.6138	−0.956763
$834$	−12.2278	−0.423413
$835$	0	0
$836$	−8.85879	−0.306388
$837$	−7.02308	−0.242753
$838$	68.4103	2.36319
$839$	−1.61587	−0.0557859	−0.0278930	−	0.999611i	$-0.508880\pi$
$839$	−1.61587	−0.0557859	−0.0278930	+	0.999611i	$0.508880\pi$
$840$	0	0
$841$	79.1097	2.72792
$842$	−66.3777	−2.28753
$843$	11.2673	0.388065
$844$	−27.7291	−0.954475
$845$	0	0
$846$	−1.88719	−0.0648829
$847$	−14.8597	−0.510586
$848$	18.0421	0.619568
$849$	−12.1394	−0.416625
$850$	0	0
$851$	1.07921	0.0369949
$852$	1.31208	0.0449510
$853$	−41.0468	−1.40542	−0.702708	−	0.711478i	$-0.748026\pi$
$853$	−41.0468	−1.40542	−0.702708	+	0.711478i	$0.748026\pi$
$854$	27.8264	0.952200
$855$	0	0
$856$	−12.4745	−0.426370
$857$	−10.9047	−0.372499	−0.186249	−	0.982503i	$-0.559633\pi$
$857$	−10.9047	−0.372499	−0.186249	+	0.982503i	$0.559633\pi$
$858$	4.61258	0.157471
$859$	4.70526	0.160541	0.0802707	−	0.996773i	$-0.474422\pi$
$859$	4.70526	0.160541	0.0802707	+	0.996773i	$0.474422\pi$
$860$	0	0
$861$	11.7662	0.400991
$862$	51.5392	1.75543
$863$	29.9360	1.01903	0.509517	−	0.860461i	$-0.329824\pi$
$863$	29.9360	1.01903	0.509517	+	0.860461i	$0.329824\pi$
$864$	−7.18586	−0.244468
$865$	0	0
$866$	−30.5602	−1.03848
$867$	−14.7242	−0.500061
$868$	15.8818	0.539065
$869$	−11.4108	−0.387086
$870$	0	0
$871$	−28.7690	−0.974800
$872$	4.89075	0.165622
$873$	1.88445	0.0637790
$874$	−2.36707	−0.0800673
$875$	0	0
$876$	−7.38115	−0.249386
$877$	31.0724	1.04924	0.524620	−	0.851336i	$-0.324207\pi$
$877$	31.0724	1.04924	0.524620	+	0.851336i	$0.324207\pi$
$878$	23.0899	0.779246
$879$	−4.03918	−0.136238
$880$	0	0
$881$	−4.98410	−0.167919	−0.0839593	−	0.996469i	$-0.526757\pi$
$881$	−4.98410	−0.167919	−0.0839593	+	0.996469i	$0.526757\pi$
$882$	9.25224	0.311539
$883$	40.1396	1.35080	0.675402	−	0.737450i	$-0.263970\pi$
$883$	40.1396	1.35080	0.675402	+	0.737450i	$0.263970\pi$
$884$	25.0001	0.840843
$885$	0	0
$886$	−43.6005	−1.46479
$887$	17.2649	0.579698	0.289849	−	0.957072i	$-0.406395\pi$
$887$	17.2649	0.579698	0.289849	+	0.957072i	$0.406395\pi$
$888$	4.69813	0.157659
$889$	−6.18827	−0.207548
$890$	0	0
$891$	0.859846	0.0288059
$892$	43.3438	1.45126
$893$	−6.59805	−0.220795
$894$	31.5625	1.05561
$895$	0	0
$896$	−9.35744	−0.312610
$897$	0.540365	0.0180423
$898$	21.9228	0.731574
$899$	−73.0231	−2.43546
$900$	0	0
$901$	−21.6919	−0.722662
$902$	13.1837	0.438969
$903$	7.11123	0.236647
$904$	16.8183	0.559369
$905$	0	0
$906$	30.3679	1.00890
$907$	19.9543	0.662571	0.331286	−	0.943531i	$-0.392518\pi$
$907$	19.9543	0.662571	0.331286	+	0.943531i	$0.392518\pi$
$908$	−31.0910	−1.03179
$909$	−3.61387	−0.119865
$910$	0	0
$911$	−51.6225	−1.71033	−0.855164	−	0.518357i	$-0.826544\pi$
$911$	−51.6225	−1.71033	−0.855164	+	0.518357i	$0.826544\pi$
$912$	−30.9101	−1.02354
$913$	−0.0948840	−0.00314020
$914$	4.81443	0.159247
$915$	0	0
$916$	24.9415	0.824089
$917$	−18.1248	−0.598534
$918$	10.6295	0.350824
$919$	51.2100	1.68926	0.844630	−	0.535350i	$-0.179820\pi$
$919$	51.2100	1.68926	0.844630	+	0.535350i	$0.179820\pi$
$920$	0	0
$921$	15.3270	0.505041
$922$	−4.62878	−0.152441
$923$	−2.38852	−0.0786191
$924$	−1.94444	−0.0639672
$925$	0	0
$926$	69.1458	2.27227
$927$	−1.46000	−0.0479526
$928$	−74.7156	−2.45266
$929$	8.78390	0.288190	0.144095	−	0.989564i	$-0.453973\pi$
$929$	8.78390	0.288190	0.144095	+	0.989564i	$0.453973\pi$
$930$	0	0
$931$	32.3480	1.06016
$932$	−24.9676	−0.817841
$933$	7.92368	0.259410
$934$	−51.5002	−1.68514
$935$	0	0
$936$	2.35237	0.0768897
$937$	−5.50915	−0.179976	−0.0899881	−	0.995943i	$-0.528683\pi$
$937$	−5.50915	−0.179976	−0.0899881	+	0.995943i	$0.528683\pi$
$938$	27.6610	0.903164
$939$	6.41853	0.209461
$940$	0	0
$941$	31.9819	1.04258	0.521290	−	0.853379i	$-0.325451\pi$
$941$	31.9819	1.04258	0.521290	+	0.853379i	$0.325451\pi$
$942$	−14.8225	−0.482944
$943$	1.54448	0.0502950
$944$	−70.7707	−2.30339
$945$	0	0
$946$	7.96794	0.259060
$947$	−14.9787	−0.486742	−0.243371	−	0.969933i	$-0.578253\pi$
$947$	−14.9787	−0.486742	−0.243371	+	0.969933i	$0.578253\pi$
$948$	20.7222	0.673025
$949$	13.4367	0.436175
$950$	0	0
$951$	24.5794	0.797043
$952$	6.75040	0.218782
$953$	25.8993	0.838961	0.419481	−	0.907764i	$-0.362212\pi$
$953$	25.8993	0.838961	0.419481	+	0.907764i	$0.362212\pi$
$954$	7.26805	0.235312
$955$	0	0
$956$	−25.3585	−0.820153
$957$	8.94031	0.288999
$958$	16.6795	0.538890
$959$	11.1402	0.359735
$960$	0	0
$961$	18.3237	0.591088
$962$	30.4544	0.981888
$963$	−15.0739	−0.485748
$964$	−2.70154	−0.0870109
$965$	0	0
$966$	−0.519553	−0.0167164
$967$	14.3077	0.460105	0.230053	−	0.973178i	$-0.426110\pi$
$967$	14.3077	0.460105	0.230053	+	0.973178i	$0.426110\pi$
$968$	−8.49130	−0.272921
$969$	37.1630	1.19385
$970$	0	0
$971$	6.01930	0.193168	0.0965842	−	0.995325i	$-0.469208\pi$
$971$	6.01930	0.193168	0.0965842	+	0.995325i	$0.469208\pi$
$972$	−1.56149	−0.0500847
$973$	−9.38353	−0.300822
$974$	−6.81221	−0.218277
$975$	0	0
$976$	47.6970	1.52674
$977$	−3.45052	−0.110392	−0.0551959	−	0.998476i	$-0.517578\pi$
$977$	−3.45052	−0.110392	−0.0551959	+	0.998476i	$0.517578\pi$
$978$	−4.40431	−0.140834
$979$	12.5475	0.401021
$980$	0	0
$981$	5.90985	0.188687
$982$	−54.3272	−1.73365
$983$	−20.5372	−0.655034	−0.327517	−	0.944845i	$-0.606212\pi$
$983$	−20.5372	−0.655034	−0.327517	+	0.944845i	$0.606212\pi$
$984$	6.72357	0.214340
$985$	0	0
$986$	110.521	3.51969
$987$	−1.44822	−0.0460974
$988$	−29.2861	−0.931714
$989$	0.933447	0.0296819
$990$	0	0
$991$	17.3370	0.550726	0.275363	−	0.961340i	$-0.411202\pi$
$991$	17.3370	0.550726	0.275363	+	0.961340i	$0.411202\pi$
$992$	50.4669	1.60233
$993$	−9.57831	−0.303958
$994$	2.29653	0.0728415
$995$	0	0
$996$	0.172310	0.00545985
$997$	60.2724	1.90884	0.954422	−	0.298459i	$-0.0964726\pi$
$997$	60.2724	1.90884	0.954422	+	0.298459i	$0.0964726\pi$
$998$	−7.44396	−0.235634
$999$	5.67710	0.179615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bg.1.2		10
5.2	odd	4		705.2.c.b.424.4	✓	20
5.3	odd	4		705.2.c.b.424.17	yes	20
5.4	even	2		3525.2.a.bf.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.4	✓	20	5.2	odd	4
705.2.c.b.424.17	yes	20	5.3	odd	4
3525.2.a.bf.1.9		10	5.4	even	2
3525.2.a.bg.1.2		10	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)

\(f(q)\)	\(=\)	\(q-1.88719 q^{2} -1.00000 q^{3} +1.56149 q^{4} +1.88719 q^{6} +1.44822 q^{7} +0.827559 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.88719 q^{2} -1.00000 q^{3} +1.56149 q^{4} +1.88719 q^{6} +1.44822 q^{7} +0.827559 q^{8} +1.00000 q^{9} +0.859846 q^{11} -1.56149 q^{12} +2.84255 q^{13} -2.73307 q^{14} -4.68473 q^{16} +5.63243 q^{17} -1.88719 q^{18} -6.59805 q^{19} -1.44822 q^{21} -1.62269 q^{22} -0.190099 q^{23} -0.827559 q^{24} -5.36442 q^{26} -1.00000 q^{27} +2.26138 q^{28} -10.3976 q^{29} +7.02308 q^{31} +7.18586 q^{32} -0.859846 q^{33} -10.6295 q^{34} +1.56149 q^{36} -5.67710 q^{37} +12.4518 q^{38} -2.84255 q^{39} -8.12459 q^{41} +2.73307 q^{42} -4.91032 q^{43} +1.34264 q^{44} +0.358753 q^{46} +1.00000 q^{47} +4.68473 q^{48} -4.90265 q^{49} -5.63243 q^{51} +4.43860 q^{52} -3.85125 q^{53} +1.88719 q^{54} +1.19849 q^{56} +6.59805 q^{57} +19.6222 q^{58} +15.1067 q^{59} -10.1814 q^{61} -13.2539 q^{62} +1.44822 q^{63} -4.19162 q^{64} +1.62269 q^{66} -10.1209 q^{67} +8.79496 q^{68} +0.190099 q^{69} -0.840275 q^{71} +0.827559 q^{72} +4.72701 q^{73} +10.7138 q^{74} -10.3028 q^{76} +1.24525 q^{77} +5.36442 q^{78} -13.2708 q^{79} +1.00000 q^{81} +15.3326 q^{82} -0.110350 q^{83} -2.26138 q^{84} +9.26671 q^{86} +10.3976 q^{87} +0.711573 q^{88} +14.5928 q^{89} +4.11663 q^{91} -0.296837 q^{92} -7.02308 q^{93} -1.88719 q^{94} -7.18586 q^{96} +1.88445 q^{97} +9.25224 q^{98} +0.859846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9} - 16 q^{11} - 7 q^{12} + q^{13} - 12 q^{14} - 3 q^{16} + 14 q^{17} + 3 q^{18} - 26 q^{19} + 7 q^{23} - 9 q^{24} - 10 q^{26} - 10 q^{27} - 24 q^{28} - 14 q^{29} - 22 q^{31} + 11 q^{32} + 16 q^{33} - 12 q^{34} + 7 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 22 q^{41} + 12 q^{42} - 11 q^{43} - 36 q^{44} - 14 q^{46} + 10 q^{47} + 3 q^{48} + 2 q^{49} - 14 q^{51} + 14 q^{52} + 22 q^{53} - 3 q^{54} - 48 q^{56} + 26 q^{57} - 20 q^{58} - 37 q^{59} - 25 q^{61} - 2 q^{62} - 7 q^{64} - 4 q^{67} + 8 q^{68} - 7 q^{69} - 27 q^{71} + 9 q^{72} + q^{73} + 4 q^{74} - 42 q^{76} + 34 q^{77} + 10 q^{78} + 5 q^{79} + 10 q^{81} - 32 q^{82} + 2 q^{83} + 24 q^{84} - 6 q^{86} + 14 q^{87} - 58 q^{88} + 9 q^{89} - 64 q^{91} + 34 q^{92} + 22 q^{93} + 3 q^{94} - 11 q^{96} - 40 q^{97} + 29 q^{98} - 16 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9 - 16 * q^11 - 7 * q^12 + q^13 - 12 * q^14 - 3 * q^16 + 14 * q^17 + 3 * q^18 - 26 * q^19 + 7 * q^23 - 9 * q^24 - 10 * q^26 - 10 * q^27 - 24 * q^28 - 14 * q^29 - 22 * q^31 + 11 * q^32 + 16 * q^33 - 12 * q^34 + 7 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 22 * q^41 + 12 * q^42 - 11 * q^43 - 36 * q^44 - 14 * q^46 + 10 * q^47 + 3 * q^48 + 2 * q^49 - 14 * q^51 + 14 * q^52 + 22 * q^53 - 3 * q^54 - 48 * q^56 + 26 * q^57 - 20 * q^58 - 37 * q^59 - 25 * q^61 - 2 * q^62 - 7 * q^64 - 4 * q^67 + 8 * q^68 - 7 * q^69 - 27 * q^71 + 9 * q^72 + q^73 + 4 * q^74 - 42 * q^76 + 34 * q^77 + 10 * q^78 + 5 * q^79 + 10 * q^81 - 32 * q^82 + 2 * q^83 + 24 * q^84 - 6 * q^86 + 14 * q^87 - 58 * q^88 + 9 * q^89 - 64 * q^91 + 34 * q^92 + 22 * q^93 + 3 * q^94 - 11 * q^96 - 40 * q^97 + 29 * q^98 - 16 * q^99

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