LMFDB - Embedded newform 6025.2.a.h.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 241)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-2.59703$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.59703 q^{2} +1.20534 q^{3} +4.74454 q^{4} +3.13029 q^{6} +0.744578 q^{7} +7.12764 q^{8} -1.54716 q^{9} +O(q^{10})$	\(q+2.59703 q^{2} +1.20534 q^{3} +4.74454 q^{4} +3.13029 q^{6} +0.744578 q^{7} +7.12764 q^{8} -1.54716 q^{9} +6.28793 q^{11} +5.71878 q^{12} +4.06994 q^{13} +1.93369 q^{14} +9.02158 q^{16} +1.60034 q^{17} -4.01801 q^{18} +2.14421 q^{19} +0.897468 q^{21} +16.3299 q^{22} -9.25572 q^{23} +8.59122 q^{24} +10.5697 q^{26} -5.48087 q^{27} +3.53268 q^{28} +3.13090 q^{29} -3.15223 q^{31} +9.17399 q^{32} +7.57908 q^{33} +4.15612 q^{34} -7.34056 q^{36} -4.19928 q^{37} +5.56857 q^{38} +4.90566 q^{39} -4.52694 q^{41} +2.33075 q^{42} -6.99535 q^{43} +29.8333 q^{44} -24.0373 q^{46} +4.82023 q^{47} +10.8741 q^{48} -6.44560 q^{49} +1.92895 q^{51} +19.3100 q^{52} -3.71179 q^{53} -14.2339 q^{54} +5.30708 q^{56} +2.58450 q^{57} +8.13103 q^{58} +3.34128 q^{59} +10.8630 q^{61} -8.18643 q^{62} -1.15198 q^{63} +5.78192 q^{64} +19.6831 q^{66} -5.80682 q^{67} +7.59287 q^{68} -11.1563 q^{69} +15.7805 q^{71} -11.0276 q^{72} +1.64682 q^{73} -10.9056 q^{74} +10.1733 q^{76} +4.68186 q^{77} +12.7401 q^{78} -11.4813 q^{79} -1.96482 q^{81} -11.7566 q^{82} +4.74454 q^{83} +4.25807 q^{84} -18.1671 q^{86} +3.77380 q^{87} +44.8181 q^{88} -7.95332 q^{89} +3.03039 q^{91} -43.9141 q^{92} -3.79951 q^{93} +12.5182 q^{94} +11.0578 q^{96} +5.49759 q^{97} -16.7394 q^{98} -9.72843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.59703	1.83637	0.918187	−	0.396147i	$-0.129653\pi$
$2$	2.59703	1.83637	0.918187	+	0.396147i	$0.129653\pi$
$3$	1.20534	0.695902	0.347951	−	0.937513i	$-0.386877\pi$
$3$	1.20534	0.695902	0.347951	+	0.937513i	$0.386877\pi$
$4$	4.74454	2.37227
$5$	0	0
$5$	0	0
$6$	3.13029	1.27794
$7$	0.744578	0.281424	0.140712	−	0.990051i	$-0.455061\pi$
$7$	0.744578	0.281424	0.140712	+	0.990051i	$0.455061\pi$
$8$	7.12764	2.52000
$9$	−1.54716	−0.515720
$10$	0	0
$11$	6.28793	1.89588	0.947941	−	0.318445i	$-0.103161\pi$
$11$	6.28793	1.89588	0.947941	+	0.318445i	$0.103161\pi$
$12$	5.71878	1.65087
$13$	4.06994	1.12880	0.564399	−	0.825502i	$-0.309108\pi$
$13$	4.06994	1.12880	0.564399	+	0.825502i	$0.309108\pi$
$14$	1.93369	0.516800
$15$	0	0
$16$	9.02158	2.25539
$17$	1.60034	0.388139	0.194070	−	0.980988i	$-0.437831\pi$
$17$	1.60034	0.388139	0.194070	+	0.980988i	$0.437831\pi$
$18$	−4.01801	−0.947055
$19$	2.14421	0.491916	0.245958	−	0.969280i	$-0.420897\pi$
$19$	2.14421	0.491916	0.245958	+	0.969280i	$0.420897\pi$
$20$	0	0
$21$	0.897468	0.195844
$22$	16.3299	3.48155
$23$	−9.25572	−1.92995	−0.964975	−	0.262340i	$-0.915506\pi$
$23$	−9.25572	−1.92995	−0.964975	+	0.262340i	$0.915506\pi$
$24$	8.59122	1.75367
$25$	0	0
$26$	10.5697	2.07290
$27$	−5.48087	−1.05479
$28$	3.53268	0.667614
$29$	3.13090	0.581394	0.290697	−	0.956815i	$-0.406113\pi$
$29$	3.13090	0.581394	0.290697	+	0.956815i	$0.406113\pi$
$30$	0	0
$31$	−3.15223	−0.566158	−0.283079	−	0.959097i	$-0.591356\pi$
$31$	−3.15223	−0.566158	−0.283079	+	0.959097i	$0.591356\pi$
$32$	9.17399	1.62175
$33$	7.57908	1.31935
$34$	4.15612	0.712769
$35$	0	0
$36$	−7.34056	−1.22343
$37$	−4.19928	−0.690358	−0.345179	−	0.938537i	$-0.612182\pi$
$37$	−4.19928	−0.690358	−0.345179	+	0.938537i	$0.612182\pi$
$38$	5.56857	0.903342
$39$	4.90566	0.785534
$40$	0	0
$41$	−4.52694	−0.706990	−0.353495	−	0.935436i	$-0.615007\pi$
$41$	−4.52694	−0.706990	−0.353495	+	0.935436i	$0.615007\pi$
$42$	2.33075	0.359642
$43$	−6.99535	−1.06678	−0.533391	−	0.845869i	$-0.679082\pi$
$43$	−6.99535	−1.06678	−0.533391	+	0.845869i	$0.679082\pi$
$44$	29.8333	4.49754
$45$	0	0
$46$	−24.0373	−3.54411
$47$	4.82023	0.703102	0.351551	−	0.936169i	$-0.385654\pi$
$47$	4.82023	0.703102	0.351551	+	0.936169i	$0.385654\pi$
$48$	10.8741	1.56953
$49$	−6.44560	−0.920800
$50$	0	0
$51$	1.92895	0.270107
$52$	19.3100	2.67782
$53$	−3.71179	−0.509853	−0.254927	−	0.966960i	$-0.582051\pi$
$53$	−3.71179	−0.509853	−0.254927	+	0.966960i	$0.582051\pi$
$54$	−14.2339	−1.93699
$55$	0	0
$56$	5.30708	0.709189
$57$	2.58450	0.342325
$58$	8.13103	1.06766
$59$	3.34128	0.434997	0.217499	−	0.976061i	$-0.430210\pi$
$59$	3.34128	0.434997	0.217499	+	0.976061i	$0.430210\pi$
$60$	0	0
$61$	10.8630	1.39087	0.695434	−	0.718590i	$-0.255212\pi$
$61$	10.8630	1.39087	0.695434	+	0.718590i	$0.255212\pi$
$62$	−8.18643	−1.03968
$63$	−1.15198	−0.145136
$64$	5.78192	0.722740
$65$	0	0
$66$	19.6831	2.42282
$67$	−5.80682	−0.709416	−0.354708	−	0.934977i	$-0.615420\pi$
$67$	−5.80682	−0.709416	−0.354708	+	0.934977i	$0.615420\pi$
$68$	7.59287	0.920771
$69$	−11.1563	−1.34306
$70$	0	0
$71$	15.7805	1.87281	0.936403	−	0.350927i	$-0.114134\pi$
$71$	15.7805	1.87281	0.936403	+	0.350927i	$0.114134\pi$
$72$	−11.0276	−1.29961
$73$	1.64682	0.192745	0.0963727	−	0.995345i	$-0.469276\pi$
$73$	1.64682	0.192745	0.0963727	+	0.995345i	$0.469276\pi$
$74$	−10.9056	−1.26775
$75$	0	0
$76$	10.1733	1.16696
$77$	4.68186	0.533547
$78$	12.7401	1.44253
$79$	−11.4813	−1.29174	−0.645872	−	0.763446i	$-0.723506\pi$
$79$	−11.4813	−1.29174	−0.645872	+	0.763446i	$0.723506\pi$
$80$	0	0
$81$	−1.96482	−0.218313
$82$	−11.7566	−1.29830
$83$	4.74454	0.520781	0.260390	−	0.965503i	$-0.416149\pi$
$83$	4.74454	0.520781	0.260390	+	0.965503i	$0.416149\pi$
$84$	4.25807	0.464594
$85$	0	0
$86$	−18.1671	−1.95901
$87$	3.77380	0.404594
$88$	44.8181	4.77762
$89$	−7.95332	−0.843050	−0.421525	−	0.906817i	$-0.638505\pi$
$89$	−7.95332	−0.843050	−0.421525	+	0.906817i	$0.638505\pi$
$90$	0	0
$91$	3.03039	0.317671
$92$	−43.9141	−4.57836
$93$	−3.79951	−0.393991
$94$	12.5182	1.29116
$95$	0	0
$96$	11.0578	1.12858
$97$	5.49759	0.558195	0.279098	−	0.960263i	$-0.409965\pi$
$97$	5.49759	0.558195	0.279098	+	0.960263i	$0.409965\pi$
$98$	−16.7394	−1.69093
$99$	−9.72843	−0.977744
$100$	0	0
$101$	−10.4008	−1.03492	−0.517459	−	0.855708i	$-0.673122\pi$
$101$	−10.4008	−1.03492	−0.517459	+	0.855708i	$0.673122\pi$
$102$	5.00953	0.496018
$103$	16.9464	1.66978	0.834888	−	0.550420i	$-0.185532\pi$
$103$	16.9464	1.66978	0.834888	+	0.550420i	$0.185532\pi$
$104$	29.0091	2.84457
$105$	0	0
$106$	−9.63961	−0.936281
$107$	0.873633	0.0844573	0.0422287	−	0.999108i	$-0.486554\pi$
$107$	0.873633	0.0844573	0.0422287	+	0.999108i	$0.486554\pi$
$108$	−26.0042	−2.50225
$109$	−9.90349	−0.948582	−0.474291	−	0.880368i	$-0.657296\pi$
$109$	−9.90349	−0.948582	−0.474291	+	0.880368i	$0.657296\pi$
$110$	0	0
$111$	−5.06155	−0.480421
$112$	6.71727	0.634722
$113$	−5.23192	−0.492177	−0.246089	−	0.969247i	$-0.579145\pi$
$113$	−5.23192	−0.492177	−0.246089	+	0.969247i	$0.579145\pi$
$114$	6.71201	0.628638
$115$	0	0
$116$	14.8547	1.37922
$117$	−6.29685	−0.582144
$118$	8.67738	0.798818
$119$	1.19158	0.109232
$120$	0	0
$121$	28.5381	2.59437
$122$	28.2115	2.55415
$123$	−5.45650	−0.491996
$124$	−14.9559	−1.34308
$125$	0	0
$126$	−2.99172	−0.266524
$127$	3.50226	0.310775	0.155388	−	0.987854i	$-0.450337\pi$
$127$	3.50226	0.310775	0.155388	+	0.987854i	$0.450337\pi$
$128$	−3.33219	−0.294527
$129$	−8.43177	−0.742376
$130$	0	0
$131$	−13.2883	−1.16100	−0.580500	−	0.814260i	$-0.697143\pi$
$131$	−13.2883	−1.16100	−0.580500	+	0.814260i	$0.697143\pi$
$132$	35.9593	3.12985
$133$	1.59653	0.138437
$134$	−15.0805	−1.30275
$135$	0	0
$136$	11.4066	0.978111
$137$	9.37803	0.801219	0.400610	−	0.916249i	$-0.368798\pi$
$137$	9.37803	0.801219	0.400610	+	0.916249i	$0.368798\pi$
$138$	−28.9731	−2.46636
$139$	3.48685	0.295751	0.147875	−	0.989006i	$-0.452757\pi$
$139$	3.48685	0.295751	0.147875	+	0.989006i	$0.452757\pi$
$140$	0	0
$141$	5.81000	0.489291
$142$	40.9825	3.43917
$143$	25.5915	2.14007
$144$	−13.9578	−1.16315
$145$	0	0
$146$	4.27683	0.353953
$147$	−7.76913	−0.640787
$148$	−19.9237	−1.63771
$149$	−8.39873	−0.688051	−0.344025	−	0.938960i	$-0.611791\pi$
$149$	−8.39873	−0.688051	−0.344025	+	0.938960i	$0.611791\pi$
$150$	0	0
$151$	−6.68837	−0.544292	−0.272146	−	0.962256i	$-0.587733\pi$
$151$	−6.68837	−0.544292	−0.272146	+	0.962256i	$0.587733\pi$
$152$	15.2832	1.23963
$153$	−2.47598	−0.200171
$154$	12.1589	0.979792
$155$	0	0
$156$	23.2751	1.86350
$157$	11.9755	0.955752	0.477876	−	0.878427i	$-0.341407\pi$
$157$	11.9755	0.955752	0.477876	+	0.878427i	$0.341407\pi$
$158$	−29.8171	−2.37213
$159$	−4.47396	−0.354808
$160$	0	0
$161$	−6.89161	−0.543135
$162$	−5.10268	−0.400905
$163$	13.7742	1.07888	0.539438	−	0.842025i	$-0.318637\pi$
$163$	13.7742	1.07888	0.539438	+	0.842025i	$0.318637\pi$
$164$	−21.4783	−1.67717
$165$	0	0
$166$	12.3217	0.956348
$167$	−7.34847	−0.568642	−0.284321	−	0.958729i	$-0.591768\pi$
$167$	−7.34847	−0.568642	−0.284321	+	0.958729i	$0.591768\pi$
$168$	6.39683	0.493526
$169$	3.56442	0.274187
$170$	0	0
$171$	−3.31744	−0.253691
$172$	−33.1897	−2.53069
$173$	−14.4542	−1.09893	−0.549467	−	0.835515i	$-0.685169\pi$
$173$	−14.4542	−1.09893	−0.549467	+	0.835515i	$0.685169\pi$
$174$	9.80065	0.742985
$175$	0	0
$176$	56.7270	4.27596
$177$	4.02737	0.302716
$178$	−20.6550	−1.54816
$179$	10.4351	0.779953	0.389976	−	0.920825i	$-0.372483\pi$
$179$	10.4351	0.779953	0.389976	+	0.920825i	$0.372483\pi$
$180$	0	0
$181$	25.3704	1.88577	0.942883	−	0.333125i	$-0.108103\pi$
$181$	25.3704	1.88577	0.942883	+	0.333125i	$0.108103\pi$
$182$	7.87000	0.583363
$183$	13.0936	0.967908
$184$	−65.9714	−4.86348
$185$	0	0
$186$	−9.86741	−0.723514
$187$	10.0628	0.735867
$188$	22.8698	1.66795
$189$	−4.08093	−0.296844
$190$	0	0
$191$	−16.4111	−1.18747	−0.593733	−	0.804662i	$-0.702346\pi$
$191$	−16.4111	−1.18747	−0.593733	+	0.804662i	$0.702346\pi$
$192$	6.96916	0.502956
$193$	8.05553	0.579850	0.289925	−	0.957049i	$-0.406370\pi$
$193$	8.05553	0.579850	0.289925	+	0.957049i	$0.406370\pi$
$194$	14.2774	1.02506
$195$	0	0
$196$	−30.5814	−2.18439
$197$	−1.16210	−0.0827963	−0.0413981	−	0.999143i	$-0.513181\pi$
$197$	−1.16210	−0.0827963	−0.0413981	+	0.999143i	$0.513181\pi$
$198$	−25.2650	−1.79550
$199$	−15.8123	−1.12090	−0.560451	−	0.828188i	$-0.689372\pi$
$199$	−15.8123	−1.12090	−0.560451	+	0.828188i	$0.689372\pi$
$200$	0	0
$201$	−6.99918	−0.493684
$202$	−27.0112	−1.90050
$203$	2.33120	0.163618
$204$	9.15198	0.640767
$205$	0	0
$206$	44.0102	3.06633
$207$	14.3201	0.995314
$208$	36.7173	2.54589
$209$	13.4827	0.932615
$210$	0	0
$211$	−6.41779	−0.441819	−0.220910	−	0.975294i	$-0.570903\pi$
$211$	−6.41779	−0.441819	−0.220910	+	0.975294i	$0.570903\pi$
$212$	−17.6107	−1.20951
$213$	19.0209	1.30329
$214$	2.26885	0.155095
$215$	0	0
$216$	−39.0656	−2.65808
$217$	−2.34708	−0.159330
$218$	−25.7196	−1.74195
$219$	1.98497	0.134132
$220$	0	0
$221$	6.51329	0.438131
$222$	−13.1450	−0.882234
$223$	−15.6352	−1.04701	−0.523506	−	0.852022i	$-0.675376\pi$
$223$	−15.6352	−1.04701	−0.523506	+	0.852022i	$0.675376\pi$
$224$	6.83075	0.456399
$225$	0	0
$226$	−13.5874	−0.903821
$227$	6.01020	0.398911	0.199456	−	0.979907i	$-0.436083\pi$
$227$	6.01020	0.398911	0.199456	+	0.979907i	$0.436083\pi$
$228$	12.2623	0.812088
$229$	−10.7079	−0.707595	−0.353798	−	0.935322i	$-0.615110\pi$
$229$	−10.7079	−0.707595	−0.353798	+	0.935322i	$0.615110\pi$
$230$	0	0
$231$	5.64322	0.371297
$232$	22.3159	1.46511
$233$	−2.77571	−0.181843	−0.0909214	−	0.995858i	$-0.528981\pi$
$233$	−2.77571	−0.181843	−0.0909214	+	0.995858i	$0.528981\pi$
$234$	−16.3531	−1.06903
$235$	0	0
$236$	15.8528	1.03193
$237$	−13.8388	−0.898928
$238$	3.09456	0.200590
$239$	9.74488	0.630344	0.315172	−	0.949035i	$-0.397938\pi$
$239$	9.74488	0.630344	0.315172	+	0.949035i	$0.397938\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	74.1141	4.76423
$243$	14.0743	0.902868
$244$	51.5400	3.29951
$245$	0	0
$246$	−14.1707	−0.903489
$247$	8.72682	0.555274
$248$	−22.4680	−1.42672
$249$	5.71877	0.362413
$250$	0	0
$251$	1.47018	0.0927970	0.0463985	−	0.998923i	$-0.485226\pi$
$251$	1.47018	0.0927970	0.0463985	+	0.998923i	$0.485226\pi$
$252$	−5.46562	−0.344302
$253$	−58.1993	−3.65896
$254$	9.09545	0.570699
$255$	0	0
$256$	−20.2176	−1.26360
$257$	−19.0717	−1.18966	−0.594829	−	0.803852i	$-0.702780\pi$
$257$	−19.0717	−1.18966	−0.594829	+	0.803852i	$0.702780\pi$
$258$	−21.8975	−1.36328
$259$	−3.12669	−0.194283
$260$	0	0
$261$	−4.84401	−0.299836
$262$	−34.5099	−2.13203
$263$	11.0150	0.679217	0.339608	−	0.940567i	$-0.389705\pi$
$263$	11.0150	0.679217	0.339608	+	0.940567i	$0.389705\pi$
$264$	54.0210	3.32476
$265$	0	0
$266$	4.14624	0.254222
$267$	−9.58644	−0.586681
$268$	−27.5507	−1.68293
$269$	−9.48636	−0.578393	−0.289197	−	0.957270i	$-0.593388\pi$
$269$	−9.48636	−0.578393	−0.289197	+	0.957270i	$0.593388\pi$
$270$	0	0
$271$	21.3477	1.29678	0.648390	−	0.761308i	$-0.275443\pi$
$271$	21.3477	1.29678	0.648390	+	0.761308i	$0.275443\pi$
$272$	14.4376	0.875407
$273$	3.65264	0.221068
$274$	24.3550	1.47134
$275$	0	0
$276$	−52.9314	−3.18609
$277$	18.2788	1.09827	0.549135	−	0.835734i	$-0.314957\pi$
$277$	18.2788	1.09827	0.549135	+	0.835734i	$0.314957\pi$
$278$	9.05544	0.543109
$279$	4.87701	0.291979
$280$	0	0
$281$	11.5147	0.686909	0.343454	−	0.939169i	$-0.388403\pi$
$281$	11.5147	0.686909	0.343454	+	0.939169i	$0.388403\pi$
$282$	15.0887	0.898521
$283$	−25.1735	−1.49641	−0.748205	−	0.663468i	$-0.769084\pi$
$283$	−25.1735	−1.49641	−0.748205	+	0.663468i	$0.769084\pi$
$284$	74.8714	4.44280
$285$	0	0
$286$	66.4618	3.92997
$287$	−3.37066	−0.198964
$288$	−14.1936	−0.836367
$289$	−14.4389	−0.849348
$290$	0	0
$291$	6.62645	0.388449
$292$	7.81339	0.457244
$293$	0.319785	0.0186820	0.00934102	−	0.999956i	$-0.497027\pi$
$293$	0.319785	0.0186820	0.00934102	+	0.999956i	$0.497027\pi$
$294$	−20.1766	−1.17673
$295$	0	0
$296$	−29.9310	−1.73970
$297$	−34.4633	−1.99976
$298$	−21.8117	−1.26352
$299$	−37.6702	−2.17853
$300$	0	0
$301$	−5.20859	−0.300218
$302$	−17.3699	−0.999523
$303$	−12.5365	−0.720202
$304$	19.3442	1.10946
$305$	0	0
$306$	−6.43018	−0.367589
$307$	8.24844	0.470763	0.235382	−	0.971903i	$-0.424366\pi$
$307$	8.24844	0.470763	0.235382	+	0.971903i	$0.424366\pi$
$308$	22.2132	1.26572
$309$	20.4261	1.16200
$310$	0	0
$311$	−11.0098	−0.624306	−0.312153	−	0.950032i	$-0.601050\pi$
$311$	−11.0098	−0.624306	−0.312153	+	0.950032i	$0.601050\pi$
$312$	34.9657	1.97955
$313$	10.3244	0.583570	0.291785	−	0.956484i	$-0.405751\pi$
$313$	10.3244	0.583570	0.291785	+	0.956484i	$0.405751\pi$
$314$	31.1008	1.75512
$315$	0	0
$316$	−54.4733	−3.06437
$317$	29.1691	1.63830	0.819149	−	0.573581i	$-0.194446\pi$
$317$	29.1691	1.63830	0.819149	+	0.573581i	$0.194446\pi$
$318$	−11.6190	−0.651560
$319$	19.6869	1.10225
$320$	0	0
$321$	1.05302	0.0587740
$322$	−17.8977	−0.997398
$323$	3.43147	0.190932
$324$	−9.32216	−0.517898
$325$	0	0
$326$	35.7719	1.98122
$327$	−11.9371	−0.660121
$328$	−32.2664	−1.78162
$329$	3.58903	0.197870
$330$	0	0
$331$	14.3362	0.787988	0.393994	−	0.919113i	$-0.371093\pi$
$331$	14.3362	0.787988	0.393994	+	0.919113i	$0.371093\pi$
$332$	22.5107	1.23543
$333$	6.49696	0.356031
$334$	−19.0842	−1.04424
$335$	0	0
$336$	8.09658	0.441705
$337$	−5.47393	−0.298184	−0.149092	−	0.988823i	$-0.547635\pi$
$337$	−5.47393	−0.298184	−0.149092	+	0.988823i	$0.547635\pi$
$338$	9.25690	0.503509
$339$	−6.30623	−0.342507
$340$	0	0
$341$	−19.8210	−1.07337
$342$	−8.61547	−0.465871
$343$	−10.0113	−0.540559
$344$	−49.8604	−2.68829
$345$	0	0
$346$	−37.5380	−2.01805
$347$	24.3460	1.30696	0.653480	−	0.756944i	$-0.273309\pi$
$347$	24.3460	1.30696	0.653480	+	0.756944i	$0.273309\pi$
$348$	17.9049	0.959805
$349$	−32.0868	−1.71757	−0.858783	−	0.512339i	$-0.828779\pi$
$349$	−32.0868	−1.71757	−0.858783	+	0.512339i	$0.828779\pi$
$350$	0	0
$351$	−22.3068	−1.19065
$352$	57.6854	3.07464
$353$	−13.4079	−0.713631	−0.356816	−	0.934175i	$-0.616138\pi$
$353$	−13.4079	−0.713631	−0.356816	+	0.934175i	$0.616138\pi$
$354$	10.4592	0.555899
$355$	0	0
$356$	−37.7348	−1.99994
$357$	1.43625	0.0760146
$358$	27.1001	1.43228
$359$	26.1416	1.37970	0.689851	−	0.723951i	$-0.257676\pi$
$359$	26.1416	1.37970	0.689851	+	0.723951i	$0.257676\pi$
$360$	0	0
$361$	−14.4024	−0.758019
$362$	65.8875	3.46297
$363$	34.3980	1.80543
$364$	14.3778	0.753602
$365$	0	0
$366$	34.0044	1.77744
$367$	−4.22872	−0.220737	−0.110369	−	0.993891i	$-0.535203\pi$
$367$	−4.22872	−0.220737	−0.110369	+	0.993891i	$0.535203\pi$
$368$	−83.5012	−4.35280
$369$	7.00391	0.364609
$370$	0	0
$371$	−2.76372	−0.143485
$372$	−18.0269	−0.934652
$373$	35.5776	1.84214	0.921070	−	0.389398i	$-0.127317\pi$
$373$	35.5776	1.84214	0.921070	+	0.389398i	$0.127317\pi$
$374$	26.1334	1.35133
$375$	0	0
$376$	34.3568	1.77182
$377$	12.7426	0.656277
$378$	−10.5983	−0.545117
$379$	−10.5187	−0.540310	−0.270155	−	0.962817i	$-0.587075\pi$
$379$	−10.5187	−0.540310	−0.270155	+	0.962817i	$0.587075\pi$
$380$	0	0
$381$	4.22140	0.216269
$382$	−42.6201	−2.18063
$383$	−14.8054	−0.756519	−0.378260	−	0.925700i	$-0.623477\pi$
$383$	−14.8054	−0.756519	−0.378260	+	0.925700i	$0.623477\pi$
$384$	−4.01641	−0.204962
$385$	0	0
$386$	20.9204	1.06482
$387$	10.8229	0.550160
$388$	26.0835	1.32419
$389$	−8.90749	−0.451628	−0.225814	−	0.974170i	$-0.572504\pi$
$389$	−8.90749	−0.451628	−0.225814	+	0.974170i	$0.572504\pi$
$390$	0	0
$391$	−14.8123	−0.749090
$392$	−45.9419	−2.32042
$393$	−16.0168	−0.807943
$394$	−3.01801	−0.152045
$395$	0	0
$396$	−46.1569	−2.31947
$397$	−32.7082	−1.64158	−0.820789	−	0.571232i	$-0.806466\pi$
$397$	−32.7082	−1.64158	−0.820789	+	0.571232i	$0.806466\pi$
$398$	−41.0648	−2.05839
$399$	1.92436	0.0963386
$400$	0	0
$401$	−16.3591	−0.816933	−0.408467	−	0.912773i	$-0.633936\pi$
$401$	−16.3591	−0.816933	−0.408467	+	0.912773i	$0.633936\pi$
$402$	−18.1771	−0.906589
$403$	−12.8294	−0.639078
$404$	−49.3470	−2.45511
$405$	0	0
$406$	6.05419	0.300464
$407$	−26.4048	−1.30884
$408$	13.7489	0.680670
$409$	−27.1198	−1.34099	−0.670494	−	0.741915i	$-0.733918\pi$
$409$	−27.1198	−1.34099	−0.670494	+	0.741915i	$0.733918\pi$
$410$	0	0
$411$	11.3037	0.557570
$412$	80.4028	3.96116
$413$	2.48784	0.122419
$414$	37.1896	1.82777
$415$	0	0
$416$	37.3376	1.83063
$417$	4.20284	0.205814
$418$	35.0148	1.71263
$419$	−1.69471	−0.0827921	−0.0413960	−	0.999143i	$-0.513181\pi$
$419$	−1.69471	−0.0827921	−0.0413960	+	0.999143i	$0.513181\pi$
$420$	0	0
$421$	6.27194	0.305676	0.152838	−	0.988251i	$-0.451159\pi$
$421$	6.27194	0.305676	0.152838	+	0.988251i	$0.451159\pi$
$422$	−16.6672	−0.811345
$423$	−7.45766	−0.362604
$424$	−26.4563	−1.28483
$425$	0	0
$426$	49.3977	2.39333
$427$	8.08837	0.391424
$428$	4.14499	0.200356
$429$	30.8464	1.48928
$430$	0	0
$431$	26.2043	1.26222	0.631108	−	0.775695i	$-0.282600\pi$
$431$	26.2043	1.26222	0.631108	+	0.775695i	$0.282600\pi$
$432$	−49.4460	−2.37897
$433$	1.61920	0.0778136	0.0389068	−	0.999243i	$-0.487612\pi$
$433$	1.61920	0.0778136	0.0389068	+	0.999243i	$0.487612\pi$
$434$	−6.09543	−0.292590
$435$	0	0
$436$	−46.9875	−2.25029
$437$	−19.8462	−0.949374
$438$	5.15502	0.246316
$439$	−35.8451	−1.71080	−0.855398	−	0.517972i	$-0.826687\pi$
$439$	−35.8451	−1.71080	−0.855398	+	0.517972i	$0.826687\pi$
$440$	0	0
$441$	9.97238	0.474875
$442$	16.9152	0.804573
$443$	−19.6847	−0.935250	−0.467625	−	0.883927i	$-0.654890\pi$
$443$	−19.6847	−0.935250	−0.467625	+	0.883927i	$0.654890\pi$
$444$	−24.0147	−1.13969
$445$	0	0
$446$	−40.6051	−1.92271
$447$	−10.1233	−0.478816
$448$	4.30509	0.203396
$449$	23.0445	1.08754	0.543769	−	0.839235i	$-0.316997\pi$
$449$	23.0445	1.08754	0.543769	+	0.839235i	$0.316997\pi$
$450$	0	0
$451$	−28.4651	−1.34037
$452$	−24.8230	−1.16758
$453$	−8.06175	−0.378774
$454$	15.6086	0.732550
$455$	0	0
$456$	18.4214	0.862660
$457$	−9.75545	−0.456341	−0.228170	−	0.973621i	$-0.573274\pi$
$457$	−9.75545	−0.456341	−0.228170	+	0.973621i	$0.573274\pi$
$458$	−27.8086	−1.29941
$459$	−8.77125	−0.409407
$460$	0	0
$461$	29.0597	1.35345	0.676724	−	0.736237i	$-0.263399\pi$
$461$	29.0597	1.35345	0.676724	+	0.736237i	$0.263399\pi$
$462$	14.6556	0.681839
$463$	−34.1246	−1.58591	−0.792953	−	0.609282i	$-0.791458\pi$
$463$	−34.1246	−1.58591	−0.792953	+	0.609282i	$0.791458\pi$
$464$	28.2457	1.31127
$465$	0	0
$466$	−7.20859	−0.333931
$467$	12.0061	0.555577	0.277789	−	0.960642i	$-0.410399\pi$
$467$	12.0061	0.555577	0.277789	+	0.960642i	$0.410399\pi$
$468$	−29.8757	−1.38100
$469$	−4.32363	−0.199647
$470$	0	0
$471$	14.4346	0.665110
$472$	23.8154	1.09619
$473$	−43.9863	−2.02249
$474$	−35.9398	−1.65077
$475$	0	0
$476$	5.65349	0.259127
$477$	5.74273	0.262941
$478$	25.3077	1.15755
$479$	7.47517	0.341549	0.170775	−	0.985310i	$-0.445373\pi$
$479$	7.47517	0.341549	0.170775	+	0.985310i	$0.445373\pi$
$480$	0	0
$481$	−17.0908	−0.779275
$482$	2.59703	0.118291
$483$	−8.30672	−0.377969
$484$	135.400	6.15455
$485$	0	0
$486$	36.5514	1.65800
$487$	−21.7985	−0.987783	−0.493891	−	0.869524i	$-0.664426\pi$
$487$	−21.7985	−0.987783	−0.493891	+	0.869524i	$0.664426\pi$
$488$	77.4277	3.50499
$489$	16.6025	0.750793
$490$	0	0
$491$	−12.8909	−0.581758	−0.290879	−	0.956760i	$-0.593948\pi$
$491$	−12.8909	−0.581758	−0.290879	+	0.956760i	$0.593948\pi$
$492$	−25.8886	−1.16715
$493$	5.01051	0.225662
$494$	22.6638	1.01969
$495$	0	0
$496$	−28.4381	−1.27691
$497$	11.7498	0.527053
$498$	14.8518	0.665525
$499$	−24.9744	−1.11801	−0.559004	−	0.829165i	$-0.688816\pi$
$499$	−24.9744	−1.11801	−0.559004	+	0.829165i	$0.688816\pi$
$500$	0	0
$501$	−8.85740	−0.395719
$502$	3.81810	0.170410
$503$	−11.1640	−0.497779	−0.248890	−	0.968532i	$-0.580066\pi$
$503$	−11.1640	−0.497779	−0.248890	+	0.968532i	$0.580066\pi$
$504$	−8.21090	−0.365743
$505$	0	0
$506$	−151.145	−6.71922
$507$	4.29634	0.190807
$508$	16.6166	0.737242
$509$	18.6656	0.827337	0.413668	−	0.910428i	$-0.364247\pi$
$509$	18.6656	0.827337	0.413668	+	0.910428i	$0.364247\pi$
$510$	0	0
$511$	1.22618	0.0542432
$512$	−45.8413	−2.02592
$513$	−11.7521	−0.518870
$514$	−49.5296	−2.18466
$515$	0	0
$516$	−40.0049	−1.76112
$517$	30.3092	1.33300
$518$	−8.12010	−0.356777
$519$	−17.4222	−0.764751
$520$	0	0
$521$	−37.9249	−1.66152	−0.830760	−	0.556631i	$-0.812094\pi$
$521$	−37.9249	−1.66152	−0.830760	+	0.556631i	$0.812094\pi$
$522$	−12.5800	−0.550612
$523$	−23.8400	−1.04245	−0.521225	−	0.853419i	$-0.674525\pi$
$523$	−23.8400	−1.04245	−0.521225	+	0.853419i	$0.674525\pi$
$524$	−63.0467	−2.75421
$525$	0	0
$526$	28.6063	1.24730
$527$	−5.04464	−0.219748
$528$	68.3753	2.97565
$529$	62.6683	2.72471
$530$	0	0
$531$	−5.16949	−0.224337
$532$	7.57482	0.328410
$533$	−18.4244	−0.798049
$534$	−24.8962	−1.07737
$535$	0	0
$536$	−41.3889	−1.78773
$537$	12.5778	0.542771
$538$	−24.6363	−1.06215
$539$	−40.5295	−1.74573
$540$	0	0
$541$	37.7424	1.62267	0.811337	−	0.584579i	$-0.198740\pi$
$541$	37.7424	1.62267	0.811337	+	0.584579i	$0.198740\pi$
$542$	55.4405	2.38137
$543$	30.5799	1.31231
$544$	14.6815	0.629464
$545$	0	0
$546$	9.48601	0.405964
$547$	22.1817	0.948423	0.474211	−	0.880411i	$-0.342733\pi$
$547$	22.1817	0.948423	0.474211	+	0.880411i	$0.342733\pi$
$548$	44.4944	1.90071
$549$	−16.8068	−0.717298
$550$	0	0
$551$	6.71332	0.285997
$552$	−79.5179	−3.38451
$553$	−8.54870	−0.363528
$554$	47.4706	2.01683
$555$	0	0
$556$	16.5435	0.701601
$557$	−4.36041	−0.184757	−0.0923783	−	0.995724i	$-0.529447\pi$
$557$	−4.36041	−0.184757	−0.0923783	+	0.995724i	$0.529447\pi$
$558$	12.6657	0.536182
$559$	−28.4707	−1.20418
$560$	0	0
$561$	12.1291	0.512091
$562$	29.9039	1.26142
$563$	−5.45151	−0.229754	−0.114877	−	0.993380i	$-0.536647\pi$
$563$	−5.45151	−0.229754	−0.114877	+	0.993380i	$0.536647\pi$
$564$	27.5658	1.16073
$565$	0	0
$566$	−65.3762	−2.74797
$567$	−1.46296	−0.0614386
$568$	112.478	4.71947
$569$	−17.0647	−0.715388	−0.357694	−	0.933839i	$-0.616437\pi$
$569$	−17.0647	−0.715388	−0.357694	+	0.933839i	$0.616437\pi$
$570$	0	0
$571$	−12.7567	−0.533853	−0.266926	−	0.963717i	$-0.586008\pi$
$571$	−12.7567	−0.533853	−0.266926	+	0.963717i	$0.586008\pi$
$572$	121.420	5.07682
$573$	−19.7809	−0.826360
$574$	−8.75370	−0.365372
$575$	0	0
$576$	−8.94555	−0.372731
$577$	28.2866	1.17759	0.588794	−	0.808283i	$-0.299603\pi$
$577$	28.2866	1.17759	0.588794	+	0.808283i	$0.299603\pi$
$578$	−37.4982	−1.55972
$579$	9.70964	0.403519
$580$	0	0
$581$	3.53268	0.146560
$582$	17.2091	0.713339
$583$	−23.3395	−0.966622
$584$	11.7379	0.485718
$585$	0	0
$586$	0.830490	0.0343072
$587$	−15.2711	−0.630308	−0.315154	−	0.949041i	$-0.602056\pi$
$587$	−15.2711	−0.630308	−0.315154	+	0.949041i	$0.602056\pi$
$588$	−36.8610	−1.52012
$589$	−6.75906	−0.278502
$590$	0	0
$591$	−1.40072	−0.0576181
$592$	−37.8841	−1.55703
$593$	−14.5819	−0.598808	−0.299404	−	0.954126i	$-0.596788\pi$
$593$	−14.5819	−0.598808	−0.299404	+	0.954126i	$0.596788\pi$
$594$	−89.5021	−3.67231
$595$	0	0
$596$	−39.8481	−1.63224
$597$	−19.0591	−0.780038
$598$	−97.8305	−4.00059
$599$	24.4860	1.00047	0.500235	−	0.865890i	$-0.333247\pi$
$599$	24.4860	1.00047	0.500235	+	0.865890i	$0.333247\pi$
$600$	0	0
$601$	10.0479	0.409863	0.204931	−	0.978776i	$-0.434303\pi$
$601$	10.0479	0.409863	0.204931	+	0.978776i	$0.434303\pi$
$602$	−13.5268	−0.551312
$603$	8.98408	0.365860
$604$	−31.7332	−1.29121
$605$	0	0
$606$	−32.5576	−1.32256
$607$	5.94024	0.241107	0.120553	−	0.992707i	$-0.461533\pi$
$607$	5.94024	0.241107	0.120553	+	0.992707i	$0.461533\pi$
$608$	19.6710	0.797763
$609$	2.80989	0.113862
$610$	0	0
$611$	19.6180	0.793661
$612$	−11.7474	−0.474860
$613$	−15.6857	−0.633539	−0.316769	−	0.948503i	$-0.602598\pi$
$613$	−15.6857	−0.633539	−0.316769	+	0.948503i	$0.602598\pi$
$614$	21.4214	0.864497
$615$	0	0
$616$	33.3706	1.34454
$617$	6.45067	0.259694	0.129847	−	0.991534i	$-0.458551\pi$
$617$	6.45067	0.259694	0.129847	+	0.991534i	$0.458551\pi$
$618$	53.0471	2.13387
$619$	−3.10687	−0.124876	−0.0624379	−	0.998049i	$-0.519888\pi$
$619$	−3.10687	−0.124876	−0.0624379	+	0.998049i	$0.519888\pi$
$620$	0	0
$621$	50.7294	2.03570
$622$	−28.5926	−1.14646
$623$	−5.92187	−0.237255
$624$	44.2568	1.77169
$625$	0	0
$626$	26.8127	1.07165
$627$	16.2512	0.649009
$628$	56.8184	2.26730
$629$	−6.72028	−0.267955
$630$	0	0
$631$	−29.4635	−1.17292	−0.586462	−	0.809976i	$-0.699480\pi$
$631$	−29.4635	−1.17292	−0.586462	+	0.809976i	$0.699480\pi$
$632$	−81.8343	−3.25520
$633$	−7.73561	−0.307463
$634$	75.7528	3.00853
$635$	0	0
$636$	−21.2269	−0.841700
$637$	−26.2332	−1.03940
$638$	51.1274	2.02415
$639$	−24.4150	−0.965843
$640$	0	0
$641$	−48.1471	−1.90169	−0.950847	−	0.309660i	$-0.899785\pi$
$641$	−48.1471	−1.90169	−0.950847	+	0.309660i	$0.899785\pi$
$642$	2.73473	0.107931
$643$	44.2183	1.74380	0.871899	−	0.489686i	$-0.162888\pi$
$643$	44.2183	1.74380	0.871899	+	0.489686i	$0.162888\pi$
$644$	−32.6975	−1.28846
$645$	0	0
$646$	8.91161	0.350622
$647$	−45.0000	−1.76913	−0.884566	−	0.466415i	$-0.845546\pi$
$647$	−45.0000	−1.76913	−0.884566	+	0.466415i	$0.845546\pi$
$648$	−14.0045	−0.550149
$649$	21.0097	0.824704
$650$	0	0
$651$	−2.82903	−0.110878
$652$	65.3521	2.55939
$653$	32.3117	1.26445	0.632227	−	0.774784i	$-0.282141\pi$
$653$	32.3117	1.26445	0.632227	+	0.774784i	$0.282141\pi$
$654$	−31.0008	−1.21223
$655$	0	0
$656$	−40.8402	−1.59454
$657$	−2.54789	−0.0994026
$658$	9.32081	0.363363
$659$	38.4217	1.49670	0.748349	−	0.663305i	$-0.230847\pi$
$659$	38.4217	1.49670	0.748349	+	0.663305i	$0.230847\pi$
$660$	0	0
$661$	18.8765	0.734210	0.367105	−	0.930179i	$-0.380349\pi$
$661$	18.8765	0.734210	0.367105	+	0.930179i	$0.380349\pi$
$662$	37.2315	1.44704
$663$	7.85072	0.304897
$664$	33.8174	1.31237
$665$	0	0
$666$	16.8728	0.653806
$667$	−28.9788	−1.12206
$668$	−34.8651	−1.34897
$669$	−18.8457	−0.728618
$670$	0	0
$671$	68.3059	2.63692
$672$	8.23336	0.317609
$673$	4.88197	0.188186	0.0940931	−	0.995563i	$-0.470005\pi$
$673$	4.88197	0.188186	0.0940931	+	0.995563i	$0.470005\pi$
$674$	−14.2159	−0.547577
$675$	0	0
$676$	16.9116	0.650444
$677$	14.1390	0.543405	0.271703	−	0.962381i	$-0.412413\pi$
$677$	14.1390	0.543405	0.271703	+	0.962381i	$0.412413\pi$
$678$	−16.3774	−0.628972
$679$	4.09338	0.157090
$680$	0	0
$681$	7.24433	0.277603
$682$	−51.4757	−1.97111
$683$	18.3055	0.700440	0.350220	−	0.936668i	$-0.386107\pi$
$683$	18.3055	0.700440	0.350220	+	0.936668i	$0.386107\pi$
$684$	−15.7397	−0.601823
$685$	0	0
$686$	−25.9996	−0.992669
$687$	−12.9066	−0.492417
$688$	−63.1091	−2.40601
$689$	−15.1068	−0.575522
$690$	0	0
$691$	12.6938	0.482895	0.241448	−	0.970414i	$-0.422378\pi$
$691$	12.6938	0.482895	0.241448	+	0.970414i	$0.422378\pi$
$692$	−68.5786	−2.60697
$693$	−7.24358	−0.275161
$694$	63.2271	2.40007
$695$	0	0
$696$	26.8983	1.01958
$697$	−7.24465	−0.274411
$698$	−83.3302	−3.15409
$699$	−3.34567	−0.126545
$700$	0	0
$701$	13.7325	0.518670	0.259335	−	0.965787i	$-0.416497\pi$
$701$	13.7325	0.518670	0.259335	+	0.965787i	$0.416497\pi$
$702$	−57.9313	−2.18648
$703$	−9.00415	−0.339598
$704$	36.3563	1.37023
$705$	0	0
$706$	−34.8207	−1.31049
$707$	−7.74421	−0.291251
$708$	19.1080	0.718123
$709$	37.0563	1.39168	0.695840	−	0.718197i	$-0.255032\pi$
$709$	37.0563	1.39168	0.695840	+	0.718197i	$0.255032\pi$
$710$	0	0
$711$	17.7634	0.666178
$712$	−56.6884	−2.12449
$713$	29.1762	1.09266
$714$	3.72999	0.139591
$715$	0	0
$716$	49.5095	1.85026
$717$	11.7459	0.438658
$718$	67.8905	2.53365
$719$	−21.7402	−0.810771	−0.405386	−	0.914146i	$-0.632863\pi$
$719$	−21.7402	−0.810771	−0.405386	+	0.914146i	$0.632863\pi$
$720$	0	0
$721$	12.6179	0.469915
$722$	−37.4033	−1.39201
$723$	1.20534	0.0448270
$724$	120.371	4.47354
$725$	0	0
$726$	89.3325	3.31544
$727$	−22.3166	−0.827679	−0.413839	−	0.910350i	$-0.635812\pi$
$727$	−22.3166	−0.827679	−0.413839	+	0.910350i	$0.635812\pi$
$728$	21.5995	0.800531
$729$	22.8588	0.846621
$730$	0	0
$731$	−11.1949	−0.414060
$732$	62.1232	2.29614
$733$	45.3568	1.67529	0.837645	−	0.546215i	$-0.183932\pi$
$733$	45.3568	1.67529	0.837645	+	0.546215i	$0.183932\pi$
$734$	−10.9821	−0.405356
$735$	0	0
$736$	−84.9118	−3.12989
$737$	−36.5129	−1.34497
$738$	18.1893	0.669558
$739$	−12.2783	−0.451663	−0.225831	−	0.974166i	$-0.572510\pi$
$739$	−12.2783	−0.451663	−0.225831	+	0.974166i	$0.572510\pi$
$740$	0	0
$741$	10.5188	0.386417
$742$	−7.17744	−0.263492
$743$	−23.7224	−0.870291	−0.435146	−	0.900360i	$-0.643303\pi$
$743$	−23.7224	−0.870291	−0.435146	+	0.900360i	$0.643303\pi$
$744$	−27.0815	−0.992856
$745$	0	0
$746$	92.3960	3.38286
$747$	−7.34056	−0.268577
$748$	47.7435	1.74567
$749$	0.650488	0.0237683
$750$	0	0
$751$	18.8204	0.686765	0.343383	−	0.939196i	$-0.388427\pi$
$751$	18.8204	0.686765	0.343383	+	0.939196i	$0.388427\pi$
$752$	43.4860	1.58577
$753$	1.77207	0.0645777
$754$	33.0928	1.20517
$755$	0	0
$756$	−19.3621	−0.704194
$757$	−20.4755	−0.744195	−0.372098	−	0.928194i	$-0.621361\pi$
$757$	−20.4755	−0.744195	−0.372098	+	0.928194i	$0.621361\pi$
$758$	−27.3173	−0.992210
$759$	−70.1499	−2.54628
$760$	0	0
$761$	6.54100	0.237111	0.118555	−	0.992947i	$-0.462174\pi$
$761$	6.54100	0.237111	0.118555	+	0.992947i	$0.462174\pi$
$762$	10.9631	0.397151
$763$	−7.37392	−0.266954
$764$	−77.8632	−2.81699
$765$	0	0
$766$	−38.4499	−1.38925
$767$	13.5988	0.491024
$768$	−24.3691	−0.879343
$769$	−10.7564	−0.387885	−0.193942	−	0.981013i	$-0.562127\pi$
$769$	−10.7564	−0.387885	−0.193942	+	0.981013i	$0.562127\pi$
$770$	0	0
$771$	−22.9878	−0.827886
$772$	38.2198	1.37556
$773$	24.6229	0.885624	0.442812	−	0.896614i	$-0.353981\pi$
$773$	24.6229	0.885624	0.442812	+	0.896614i	$0.353981\pi$
$774$	28.1074	1.01030
$775$	0	0
$776$	39.1848	1.40665
$777$	−3.76872	−0.135202
$778$	−23.1330	−0.829357
$779$	−9.70673	−0.347780
$780$	0	0
$781$	99.2269	3.55062
$782$	−38.4679	−1.37561
$783$	−17.1601	−0.613250
$784$	−58.1495	−2.07677
$785$	0	0
$786$	−41.5961	−1.48369
$787$	10.1240	0.360883	0.180441	−	0.983586i	$-0.442247\pi$
$787$	10.1240	0.360883	0.180441	+	0.983586i	$0.442247\pi$
$788$	−5.51363	−0.196415
$789$	13.2769	0.472669
$790$	0	0
$791$	−3.89557	−0.138511
$792$	−69.3407	−2.46392
$793$	44.2119	1.57001
$794$	−84.9440	−3.01455
$795$	0	0
$796$	−75.0219	−2.65908
$797$	8.60700	0.304876	0.152438	−	0.988313i	$-0.451288\pi$
$797$	8.60700	0.304876	0.152438	+	0.988313i	$0.451288\pi$
$798$	4.99762	0.176914
$799$	7.71400	0.272902
$800$	0	0
$801$	12.3051	0.434778
$802$	−42.4849	−1.50020
$803$	10.3551	0.365423
$804$	−33.2079	−1.17115
$805$	0	0
$806$	−33.3183	−1.17359
$807$	−11.4343	−0.402505
$808$	−74.1332	−2.60800
$809$	23.7331	0.834411	0.417205	−	0.908812i	$-0.363010\pi$
$809$	23.7331	0.834411	0.417205	+	0.908812i	$0.363010\pi$
$810$	0	0
$811$	35.1374	1.23384	0.616920	−	0.787026i	$-0.288380\pi$
$811$	35.1374	1.23384	0.616920	+	0.787026i	$0.288380\pi$
$812$	11.0605	0.388147
$813$	25.7312	0.902432
$814$	−68.5739	−2.40351
$815$	0	0
$816$	17.4022	0.609198
$817$	−14.9995	−0.524767
$818$	−70.4308	−2.46256
$819$	−4.68850	−0.163829
$820$	0	0
$821$	18.3525	0.640508	0.320254	−	0.947332i	$-0.396232\pi$
$821$	18.3525	0.640508	0.320254	+	0.947332i	$0.396232\pi$
$822$	29.3560	1.02391
$823$	0.411745	0.0143525	0.00717626	−	0.999974i	$-0.497716\pi$
$823$	0.411745	0.0143525	0.00717626	+	0.999974i	$0.497716\pi$
$824$	120.788	4.20784
$825$	0	0
$826$	6.46099	0.224807
$827$	10.9496	0.380756	0.190378	−	0.981711i	$-0.439029\pi$
$827$	10.9496	0.380756	0.190378	+	0.981711i	$0.439029\pi$
$828$	67.9422	2.36115
$829$	6.76398	0.234923	0.117461	−	0.993077i	$-0.462524\pi$
$829$	6.76398	0.234923	0.117461	+	0.993077i	$0.462524\pi$
$830$	0	0
$831$	22.0322	0.764288
$832$	23.5321	0.815827
$833$	−10.3152	−0.357399
$834$	10.9149	0.377951
$835$	0	0
$836$	63.9690	2.21241
$837$	17.2770	0.597179
$838$	−4.40121	−0.152037
$839$	3.28222	0.113315	0.0566574	−	0.998394i	$-0.481956\pi$
$839$	3.28222	0.113315	0.0566574	+	0.998394i	$0.481956\pi$
$840$	0	0
$841$	−19.1974	−0.661981
$842$	16.2884	0.561335
$843$	13.8791	0.478021
$844$	−30.4495	−1.04811
$845$	0	0
$846$	−19.3677	−0.665876
$847$	21.2488	0.730118
$848$	−33.4862	−1.14992
$849$	−30.3426	−1.04136
$850$	0	0
$851$	38.8674	1.33236
$852$	90.2454	3.09175
$853$	36.1823	1.23886	0.619429	−	0.785053i	$-0.287364\pi$
$853$	36.1823	1.23886	0.619429	+	0.785053i	$0.287364\pi$
$854$	21.0057	0.718800
$855$	0	0
$856$	6.22694	0.212832
$857$	25.4700	0.870037	0.435019	−	0.900421i	$-0.356742\pi$
$857$	25.4700	0.870037	0.435019	+	0.900421i	$0.356742\pi$
$858$	80.1089	2.73487
$859$	3.88904	0.132692	0.0663461	−	0.997797i	$-0.478866\pi$
$859$	3.88904	0.132692	0.0663461	+	0.997797i	$0.478866\pi$
$860$	0	0
$861$	−4.06279	−0.138459
$862$	68.0532	2.31790
$863$	4.43810	0.151075	0.0755373	−	0.997143i	$-0.475933\pi$
$863$	4.43810	0.151075	0.0755373	+	0.997143i	$0.475933\pi$
$864$	−50.2814	−1.71061
$865$	0	0
$866$	4.20509	0.142895
$867$	−17.4038	−0.591063
$868$	−11.1358	−0.377975
$869$	−72.1934	−2.44899
$870$	0	0
$871$	−23.6334	−0.800788
$872$	−70.5885	−2.39043
$873$	−8.50564	−0.287872
$874$	−51.5411	−1.74341
$875$	0	0
$876$	9.41778	0.318197
$877$	−29.5579	−0.998101	−0.499050	−	0.866573i	$-0.666318\pi$
$877$	−29.5579	−0.998101	−0.499050	+	0.866573i	$0.666318\pi$
$878$	−93.0907	−3.14166
$879$	0.385449	0.0130009
$880$	0	0
$881$	−48.9852	−1.65035	−0.825177	−	0.564874i	$-0.808925\pi$
$881$	−48.9852	−1.65035	−0.825177	+	0.564874i	$0.808925\pi$
$882$	25.8985	0.872048
$883$	−10.8101	−0.363790	−0.181895	−	0.983318i	$-0.558223\pi$
$883$	−10.8101	−0.363790	−0.181895	+	0.983318i	$0.558223\pi$
$884$	30.9026	1.03937
$885$	0	0
$886$	−51.1218	−1.71747
$887$	13.9186	0.467340	0.233670	−	0.972316i	$-0.424926\pi$
$887$	13.9186	0.467340	0.233670	+	0.972316i	$0.424926\pi$
$888$	−36.0769	−1.21066
$889$	2.60770	0.0874596
$890$	0	0
$891$	−12.3546	−0.413896
$892$	−74.1819	−2.48379
$893$	10.3356	0.345867
$894$	−26.2905	−0.879286
$895$	0	0
$896$	−2.48107	−0.0828869
$897$	−45.4054	−1.51604
$898$	59.8472	1.99713
$899$	−9.86933	−0.329161
$900$	0	0
$901$	−5.94012	−0.197894
$902$	−73.9246	−2.46142
$903$	−6.27811	−0.208922
$904$	−37.2912	−1.24029
$905$	0	0
$906$	−20.9366	−0.695571
$907$	45.3560	1.50602	0.753011	−	0.658008i	$-0.228601\pi$
$907$	45.3560	1.50602	0.753011	+	0.658008i	$0.228601\pi$
$908$	28.5156	0.946325
$909$	16.0917	0.533728
$910$	0	0
$911$	3.51366	0.116413	0.0582064	−	0.998305i	$-0.481462\pi$
$911$	3.51366	0.116413	0.0582064	+	0.998305i	$0.481462\pi$
$912$	23.3163	0.772079
$913$	29.8333	0.987339
$914$	−25.3352	−0.838013
$915$	0	0
$916$	−50.8039	−1.67861
$917$	−9.89414	−0.326733
$918$	−22.7791	−0.751824
$919$	22.3344	0.736743	0.368372	−	0.929679i	$-0.379915\pi$
$919$	22.3344	0.736743	0.368372	+	0.929679i	$0.379915\pi$
$920$	0	0
$921$	9.94216	0.327605
$922$	75.4689	2.48544
$923$	64.2259	2.11402
$924$	26.7745	0.880816
$925$	0	0
$926$	−88.6226	−2.91232
$927$	−26.2187	−0.861137
$928$	28.7229	0.942874
$929$	18.1496	0.595470	0.297735	−	0.954648i	$-0.403769\pi$
$929$	18.1496	0.595470	0.297735	+	0.954648i	$0.403769\pi$
$930$	0	0
$931$	−13.8207	−0.452956
$932$	−13.1695	−0.431380
$933$	−13.2705	−0.434456
$934$	31.1802	1.02025
$935$	0	0
$936$	−44.8817	−1.46700
$937$	−50.6507	−1.65469	−0.827343	−	0.561696i	$-0.810149\pi$
$937$	−50.6507	−1.65469	−0.827343	+	0.561696i	$0.810149\pi$
$938$	−11.2286	−0.366626
$939$	12.4444	0.406107
$940$	0	0
$941$	44.9519	1.46539	0.732695	−	0.680558i	$-0.238262\pi$
$941$	44.9519	1.46539	0.732695	+	0.680558i	$0.238262\pi$
$942$	37.4869	1.22139
$943$	41.9001	1.36446
$944$	30.1436	0.981090
$945$	0	0
$946$	−114.234	−3.71405
$947$	−18.5204	−0.601832	−0.300916	−	0.953651i	$-0.597292\pi$
$947$	−18.5204	−0.601832	−0.300916	+	0.953651i	$0.597292\pi$
$948$	−65.6588	−2.13250
$949$	6.70245	0.217571
$950$	0	0
$951$	35.1586	1.14010
$952$	8.49313	0.275264
$953$	−4.77064	−0.154536	−0.0772681	−	0.997010i	$-0.524620\pi$
$953$	−4.77064	−0.154536	−0.0772681	+	0.997010i	$0.524620\pi$
$954$	14.9140	0.482859
$955$	0	0
$956$	46.2350	1.49535
$957$	23.7294	0.767062
$958$	19.4132	0.627212
$959$	6.98268	0.225482
$960$	0	0
$961$	−21.0634	−0.679465
$962$	−44.3853	−1.43104
$963$	−1.35165	−0.0435563
$964$	4.74454	0.152811
$965$	0	0
$966$	−21.5727	−0.694092
$967$	42.9853	1.38231	0.691157	−	0.722705i	$-0.257102\pi$
$967$	42.9853	1.38231	0.691157	+	0.722705i	$0.257102\pi$
$968$	203.409	6.53781
$969$	4.13608	0.132870
$970$	0	0
$971$	38.4332	1.23338	0.616690	−	0.787206i	$-0.288473\pi$
$971$	38.4332	1.23338	0.616690	+	0.787206i	$0.288473\pi$
$972$	66.7762	2.14185
$973$	2.59623	0.0832314
$974$	−56.6112	−1.81394
$975$	0	0
$976$	98.0016	3.13695
$977$	−11.7197	−0.374948	−0.187474	−	0.982270i	$-0.560030\pi$
$977$	−11.7197	−0.374948	−0.187474	+	0.982270i	$0.560030\pi$
$978$	43.1172	1.37874
$979$	−50.0099	−1.59832
$980$	0	0
$981$	15.3223	0.489203
$982$	−33.4780	−1.06832
$983$	24.4745	0.780615	0.390307	−	0.920685i	$-0.372369\pi$
$983$	24.4745	0.780615	0.390307	+	0.920685i	$0.372369\pi$
$984$	−38.8920	−1.23983
$985$	0	0
$986$	13.0124	0.414400
$987$	4.32600	0.137698
$988$	41.4047	1.31726
$989$	64.7470	2.05884
$990$	0	0
$991$	22.7385	0.722313	0.361156	−	0.932505i	$-0.382382\pi$
$991$	22.7385	0.722313	0.361156	+	0.932505i	$0.382382\pi$
$992$	−28.9185	−0.918164
$993$	17.2800	0.548363
$994$	30.5146	0.967866
$995$	0	0
$996$	27.1329	0.859740
$997$	−51.7206	−1.63801	−0.819005	−	0.573787i	$-0.805474\pi$
$997$	−51.7206	−1.63801	−0.819005	+	0.573787i	$0.805474\pi$
$998$	−64.8592	−2.05308
$999$	23.0157	0.728184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.12		12
5.4	even	2		241.2.a.b.1.1	✓	12
15.14	odd	2		2169.2.a.h.1.12		12
20.19	odd	2		3856.2.a.n.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.1	✓	12	5.4	even	2
2169.2.a.h.1.12		12	15.14	odd	2
3856.2.a.n.1.9		12	20.19	odd	2
6025.2.a.h.1.12		12	1.1	even	1	trivial

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.59703 q^{2} +1.20534 q^{3} +4.74454 q^{4} +3.13029 q^{6} +0.744578 q^{7} +7.12764 q^{8} -1.54716 q^{9} +O(q^{10})\)	\(q+2.59703 q^{2} +1.20534 q^{3} +4.74454 q^{4} +3.13029 q^{6} +0.744578 q^{7} +7.12764 q^{8} -1.54716 q^{9} +6.28793 q^{11} +5.71878 q^{12} +4.06994 q^{13} +1.93369 q^{14} +9.02158 q^{16} +1.60034 q^{17} -4.01801 q^{18} +2.14421 q^{19} +0.897468 q^{21} +16.3299 q^{22} -9.25572 q^{23} +8.59122 q^{24} +10.5697 q^{26} -5.48087 q^{27} +3.53268 q^{28} +3.13090 q^{29} -3.15223 q^{31} +9.17399 q^{32} +7.57908 q^{33} +4.15612 q^{34} -7.34056 q^{36} -4.19928 q^{37} +5.56857 q^{38} +4.90566 q^{39} -4.52694 q^{41} +2.33075 q^{42} -6.99535 q^{43} +29.8333 q^{44} -24.0373 q^{46} +4.82023 q^{47} +10.8741 q^{48} -6.44560 q^{49} +1.92895 q^{51} +19.3100 q^{52} -3.71179 q^{53} -14.2339 q^{54} +5.30708 q^{56} +2.58450 q^{57} +8.13103 q^{58} +3.34128 q^{59} +10.8630 q^{61} -8.18643 q^{62} -1.15198 q^{63} +5.78192 q^{64} +19.6831 q^{66} -5.80682 q^{67} +7.59287 q^{68} -11.1563 q^{69} +15.7805 q^{71} -11.0276 q^{72} +1.64682 q^{73} -10.9056 q^{74} +10.1733 q^{76} +4.68186 q^{77} +12.7401 q^{78} -11.4813 q^{79} -1.96482 q^{81} -11.7566 q^{82} +4.74454 q^{83} +4.25807 q^{84} -18.1671 q^{86} +3.77380 q^{87} +44.8181 q^{88} -7.95332 q^{89} +3.03039 q^{91} -43.9141 q^{92} -3.79951 q^{93} +12.5182 q^{94} +11.0578 q^{96} +5.49759 q^{97} -16.7394 q^{98} -9.72843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * q^99

Introduction

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