LMFDB - Embedded newform 3525.2.a.bf.1.3

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			1.3
Root			$1.55802$ 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)

$f(q)$	$=$	$q-1.55802 q^{2} +1.00000 q^{3} +0.427425 q^{4} -1.55802 q^{6} -3.87455 q^{7} +2.45010 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.55802 q^{2} +1.00000 q^{3} +0.427425 q^{4} -1.55802 q^{6} -3.87455 q^{7} +2.45010 q^{8} +1.00000 q^{9} +1.67382 q^{11} +0.427425 q^{12} +2.12123 q^{13} +6.03662 q^{14} -4.67216 q^{16} +5.31859 q^{17} -1.55802 q^{18} -8.33742 q^{19} -3.87455 q^{21} -2.60785 q^{22} -0.669466 q^{23} +2.45010 q^{24} -3.30492 q^{26} +1.00000 q^{27} -1.65608 q^{28} +3.15855 q^{29} -2.86625 q^{31} +2.37911 q^{32} +1.67382 q^{33} -8.28647 q^{34} +0.427425 q^{36} -0.398041 q^{37} +12.9899 q^{38} +2.12123 q^{39} -11.3299 q^{41} +6.03662 q^{42} -1.82268 q^{43} +0.715434 q^{44} +1.04304 q^{46} -1.00000 q^{47} -4.67216 q^{48} +8.01211 q^{49} +5.31859 q^{51} +0.906669 q^{52} +2.61130 q^{53} -1.55802 q^{54} -9.49303 q^{56} -8.33742 q^{57} -4.92108 q^{58} -2.45585 q^{59} +12.4426 q^{61} +4.46567 q^{62} -3.87455 q^{63} +5.63762 q^{64} -2.60785 q^{66} -0.720799 q^{67} +2.27330 q^{68} -0.669466 q^{69} +8.17608 q^{71} +2.45010 q^{72} +14.1727 q^{73} +0.620156 q^{74} -3.56362 q^{76} -6.48530 q^{77} -3.30492 q^{78} -15.8007 q^{79} +1.00000 q^{81} +17.6522 q^{82} +5.57490 q^{83} -1.65608 q^{84} +2.83977 q^{86} +3.15855 q^{87} +4.10104 q^{88} -3.73868 q^{89} -8.21881 q^{91} -0.286147 q^{92} -2.86625 q^{93} +1.55802 q^{94} +2.37911 q^{96} +13.6442 q^{97} -12.4830 q^{98} +1.67382 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.55802	−1.10169	−0.550843	−	0.834609i	$-0.685694\pi$
$2$	−1.55802	−1.10169	−0.550843	+	0.834609i	$0.685694\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.427425	0.213713
$5$	0	0
$5$	0	0
$6$	−1.55802	−0.636059
$7$	−3.87455	−1.46444	−0.732220	−	0.681068i	$-0.761516\pi$
$7$	−3.87455	−1.46444	−0.732220	+	0.681068i	$0.761516\pi$
$8$	2.45010	0.866242
$9$	1.00000	0.333333
$10$	0	0
$11$	1.67382	0.504676	0.252338	−	0.967639i	$-0.418800\pi$
$11$	1.67382	0.504676	0.252338	+	0.967639i	$0.418800\pi$
$12$	0.427425	0.123387
$13$	2.12123	0.588324	0.294162	−	0.955756i	$-0.404959\pi$
$13$	2.12123	0.588324	0.294162	+	0.955756i	$0.404959\pi$
$14$	6.03662	1.61335
$15$	0	0
$16$	−4.67216	−1.16804
$17$	5.31859	1.28995	0.644974	−	0.764204i	$-0.276868\pi$
$17$	5.31859	1.28995	0.644974	+	0.764204i	$0.276868\pi$
$18$	−1.55802	−0.367229
$19$	−8.33742	−1.91273	−0.956367	−	0.292167i	$-0.905624\pi$
$19$	−8.33742	−1.91273	−0.956367	+	0.292167i	$0.905624\pi$
$20$	0	0
$21$	−3.87455	−0.845495
$22$	−2.60785	−0.555995
$23$	−0.669466	−0.139593	−0.0697967	−	0.997561i	$-0.522235\pi$
$23$	−0.669466	−0.139593	−0.0697967	+	0.997561i	$0.522235\pi$
$24$	2.45010	0.500125
$25$	0	0
$26$	−3.30492	−0.648149
$27$	1.00000	0.192450
$28$	−1.65608	−0.312970
$29$	3.15855	0.586528	0.293264	−	0.956032i	$-0.405259\pi$
$29$	3.15855	0.586528	0.293264	+	0.956032i	$0.405259\pi$
$30$	0	0
$31$	−2.86625	−0.514793	−0.257397	−	0.966306i	$-0.582865\pi$
$31$	−2.86625	−0.514793	−0.257397	+	0.966306i	$0.582865\pi$
$32$	2.37911	0.420571
$33$	1.67382	0.291375
$34$	−8.28647	−1.42112
$35$	0	0
$36$	0.427425	0.0712376
$37$	−0.398041	−0.0654376	−0.0327188	−	0.999465i	$-0.510417\pi$
$37$	−0.398041	−0.0654376	−0.0327188	+	0.999465i	$0.510417\pi$
$38$	12.9899	2.10723
$39$	2.12123	0.339669
$40$	0	0
$41$	−11.3299	−1.76943	−0.884714	−	0.466133i	$-0.845647\pi$
$41$	−11.3299	−1.76943	−0.884714	+	0.466133i	$0.845647\pi$
$42$	6.03662	0.931470
$43$	−1.82268	−0.277956	−0.138978	−	0.990295i	$-0.544382\pi$
$43$	−1.82268	−0.277956	−0.138978	+	0.990295i	$0.544382\pi$
$44$	0.715434	0.107856
$45$	0	0
$46$	1.04304	0.153788
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−4.67216	−0.674368
$49$	8.01211	1.14459
$50$	0	0
$51$	5.31859	0.744752
$52$	0.906669	0.125732
$53$	2.61130	0.358690	0.179345	−	0.983786i	$-0.442602\pi$
$53$	2.61130	0.358690	0.179345	+	0.983786i	$0.442602\pi$
$54$	−1.55802	−0.212020
$55$	0	0
$56$	−9.49303	−1.26856
$57$	−8.33742	−1.10432
$58$	−4.92108	−0.646170
$59$	−2.45585	−0.319724	−0.159862	−	0.987139i	$-0.551105\pi$
$59$	−2.45585	−0.319724	−0.159862	+	0.987139i	$0.551105\pi$
$60$	0	0
$61$	12.4426	1.59311	0.796555	−	0.604566i	$-0.206653\pi$
$61$	12.4426	1.59311	0.796555	+	0.604566i	$0.206653\pi$
$62$	4.46567	0.567141
$63$	−3.87455	−0.488147
$64$	5.63762	0.704702
$65$	0	0
$66$	−2.60785	−0.321004
$67$	−0.720799	−0.0880596	−0.0440298	−	0.999030i	$-0.514020\pi$
$67$	−0.720799	−0.0880596	−0.0440298	+	0.999030i	$0.514020\pi$
$68$	2.27330	0.275678
$69$	−0.669466	−0.0805943
$70$	0	0
$71$	8.17608	0.970322	0.485161	−	0.874425i	$-0.338761\pi$
$71$	8.17608	0.970322	0.485161	+	0.874425i	$0.338761\pi$
$72$	2.45010	0.288747
$73$	14.1727	1.65879	0.829397	−	0.558659i	$-0.188684\pi$
$73$	14.1727	1.65879	0.829397	+	0.558659i	$0.188684\pi$
$74$	0.620156	0.0720917
$75$	0	0
$76$	−3.56362	−0.408776
$77$	−6.48530	−0.739069
$78$	−3.30492	−0.374209
$79$	−15.8007	−1.77772	−0.888861	−	0.458177i	$-0.848502\pi$
$79$	−15.8007	−1.77772	−0.888861	+	0.458177i	$0.848502\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	17.6522	1.94936
$83$	5.57490	0.611925	0.305962	−	0.952044i	$-0.401022\pi$
$83$	5.57490	0.611925	0.305962	+	0.952044i	$0.401022\pi$
$84$	−1.65608	−0.180693
$85$	0	0
$86$	2.83977	0.306220
$87$	3.15855	0.338632
$88$	4.10104	0.437172
$89$	−3.73868	−0.396299	−0.198150	−	0.980172i	$-0.563493\pi$
$89$	−3.73868	−0.396299	−0.198150	+	0.980172i	$0.563493\pi$
$90$	0	0
$91$	−8.21881	−0.861566
$92$	−0.286147	−0.0298329
$93$	−2.86625	−0.297216
$94$	1.55802	0.160697
$95$	0	0
$96$	2.37911	0.242817
$97$	13.6442	1.38536	0.692680	−	0.721245i	$-0.256430\pi$
$97$	13.6442	1.38536	0.692680	+	0.721245i	$0.256430\pi$
$98$	−12.4830	−1.26098
$99$	1.67382	0.168225
$100$	0	0
$101$	−4.56073	−0.453810	−0.226905	−	0.973917i	$-0.572861\pi$
$101$	−4.56073	−0.453810	−0.226905	+	0.973917i	$0.572861\pi$
$102$	−8.28647	−0.820483
$103$	4.91561	0.484349	0.242175	−	0.970233i	$-0.422139\pi$
$103$	4.91561	0.484349	0.242175	+	0.970233i	$0.422139\pi$
$104$	5.19724	0.509631
$105$	0	0
$106$	−4.06846	−0.395164
$107$	2.44138	0.236017	0.118009	−	0.993013i	$-0.462349\pi$
$107$	2.44138	0.236017	0.118009	+	0.993013i	$0.462349\pi$
$108$	0.427425	0.0411290
$109$	−8.26373	−0.791522	−0.395761	−	0.918354i	$-0.629519\pi$
$109$	−8.26373	−0.791522	−0.395761	+	0.918354i	$0.629519\pi$
$110$	0	0
$111$	−0.398041	−0.0377804
$112$	18.1025	1.71052
$113$	−16.8631	−1.58635	−0.793175	−	0.608994i	$-0.791573\pi$
$113$	−16.8631	−1.58635	−0.793175	+	0.608994i	$0.791573\pi$
$114$	12.9899	1.21661
$115$	0	0
$116$	1.35004	0.125348
$117$	2.12123	0.196108
$118$	3.82626	0.352235
$119$	−20.6071	−1.88905
$120$	0	0
$121$	−8.19832	−0.745302
$122$	−19.3858	−1.75511
$123$	−11.3299	−1.02158
$124$	−1.22511	−0.110018
$125$	0	0
$126$	6.03662	0.537785
$127$	−19.2540	−1.70851	−0.854257	−	0.519850i	$-0.825988\pi$
$127$	−19.2540	−1.70851	−0.854257	+	0.519850i	$0.825988\pi$
$128$	−13.5417	−1.19693
$129$	−1.82268	−0.160478
$130$	0	0
$131$	−7.72157	−0.674637	−0.337318	−	0.941391i	$-0.609520\pi$
$131$	−7.72157	−0.674637	−0.337318	+	0.941391i	$0.609520\pi$
$132$	0.715434	0.0622705
$133$	32.3037	2.80109
$134$	1.12302	0.0970140
$135$	0	0
$136$	13.0311	1.11741
$137$	−19.9662	−1.70583	−0.852913	−	0.522053i	$-0.825166\pi$
$137$	−19.9662	−1.70583	−0.852913	+	0.522053i	$0.825166\pi$
$138$	1.04304	0.0887896
$139$	2.90594	0.246479	0.123239	−	0.992377i	$-0.460672\pi$
$139$	2.90594	0.246479	0.123239	+	0.992377i	$0.460672\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−12.7385	−1.06899
$143$	3.55057	0.296913
$144$	−4.67216	−0.389347
$145$	0	0
$146$	−22.0814	−1.82747
$147$	8.01211	0.660827
$148$	−0.170133	−0.0139848
$149$	−12.7231	−1.04232	−0.521158	−	0.853460i	$-0.674500\pi$
$149$	−12.7231	−1.04232	−0.521158	+	0.853460i	$0.674500\pi$
$150$	0	0
$151$	−19.0537	−1.55057	−0.775286	−	0.631611i	$-0.782394\pi$
$151$	−19.0537	−1.55057	−0.775286	+	0.631611i	$0.782394\pi$
$152$	−20.4275	−1.65689
$153$	5.31859	0.429983
$154$	10.1042	0.814222
$155$	0	0
$156$	0.906669	0.0725916
$157$	7.84774	0.626318	0.313159	−	0.949701i	$-0.398613\pi$
$157$	7.84774	0.626318	0.313159	+	0.949701i	$0.398613\pi$
$158$	24.6179	1.95849
$159$	2.61130	0.207090
$160$	0	0
$161$	2.59388	0.204426
$162$	−1.55802	−0.122410
$163$	−23.9243	−1.87389	−0.936946	−	0.349474i	$-0.886360\pi$
$163$	−23.9243	−1.87389	−0.936946	+	0.349474i	$0.886360\pi$
$164$	−4.84268	−0.378149
$165$	0	0
$166$	−8.68580	−0.674149
$167$	−7.87294	−0.609226	−0.304613	−	0.952476i	$-0.598527\pi$
$167$	−7.87294	−0.609226	−0.304613	+	0.952476i	$0.598527\pi$
$168$	−9.49303	−0.732403
$169$	−8.50037	−0.653875
$170$	0	0
$171$	−8.33742	−0.637578
$172$	−0.779059	−0.0594027
$173$	21.5863	1.64118	0.820589	−	0.571518i	$-0.193645\pi$
$173$	21.5863	1.64118	0.820589	+	0.571518i	$0.193645\pi$
$174$	−4.92108	−0.373066
$175$	0	0
$176$	−7.82036	−0.589482
$177$	−2.45585	−0.184593
$178$	5.82494	0.436597
$179$	−6.16737	−0.460971	−0.230486	−	0.973076i	$-0.574031\pi$
$179$	−6.16737	−0.460971	−0.230486	+	0.973076i	$0.574031\pi$
$180$	0	0
$181$	−20.4173	−1.51761	−0.758805	−	0.651318i	$-0.774216\pi$
$181$	−20.4173	−1.51761	−0.758805	+	0.651318i	$0.774216\pi$
$182$	12.8051	0.949175
$183$	12.4426	0.919783
$184$	−1.64026	−0.120922
$185$	0	0
$186$	4.46567	0.327439
$187$	8.90238	0.651006
$188$	−0.427425	−0.0311732
$189$	−3.87455	−0.281832
$190$	0	0
$191$	7.84659	0.567759	0.283880	−	0.958860i	$-0.408378\pi$
$191$	7.84659	0.567759	0.283880	+	0.958860i	$0.408378\pi$
$192$	5.63762	0.406860
$193$	11.2626	0.810700	0.405350	−	0.914161i	$-0.367150\pi$
$193$	11.2626	0.810700	0.405350	+	0.914161i	$0.367150\pi$
$194$	−21.2579	−1.52623
$195$	0	0
$196$	3.42458	0.244613
$197$	5.49967	0.391835	0.195918	−	0.980620i	$-0.437231\pi$
$197$	5.49967	0.391835	0.195918	+	0.980620i	$0.437231\pi$
$198$	−2.60785	−0.185332
$199$	14.9707	1.06125	0.530623	−	0.847608i	$-0.321958\pi$
$199$	14.9707	1.06125	0.530623	+	0.847608i	$0.321958\pi$
$200$	0	0
$201$	−0.720799	−0.0508412
$202$	7.10571	0.499956
$203$	−12.2379	−0.858935
$204$	2.27330	0.159163
$205$	0	0
$206$	−7.65862	−0.533601
$207$	−0.669466	−0.0465311
$208$	−9.91073	−0.687186
$209$	−13.9554	−0.965312
$210$	0	0
$211$	−2.58347	−0.177853	−0.0889267	−	0.996038i	$-0.528344\pi$
$211$	−2.58347	−0.177853	−0.0889267	+	0.996038i	$0.528344\pi$
$212$	1.11614	0.0766567
$213$	8.17608	0.560216
$214$	−3.80372	−0.260017
$215$	0	0
$216$	2.45010	0.166708
$217$	11.1054	0.753884
$218$	12.8751	0.872009
$219$	14.1727	0.957705
$220$	0	0
$221$	11.2820	0.758907
$222$	0.620156	0.0416222
$223$	−0.956824	−0.0640737	−0.0320368	−	0.999487i	$-0.510199\pi$
$223$	−0.956824	−0.0640737	−0.0320368	+	0.999487i	$0.510199\pi$
$224$	−9.21797	−0.615902
$225$	0	0
$226$	26.2731	1.74766
$227$	−2.45535	−0.162967	−0.0814836	−	0.996675i	$-0.525966\pi$
$227$	−2.45535	−0.162967	−0.0814836	+	0.996675i	$0.525966\pi$
$228$	−3.56362	−0.236007
$229$	−4.34066	−0.286839	−0.143419	−	0.989662i	$-0.545810\pi$
$229$	−4.34066	−0.286839	−0.143419	+	0.989662i	$0.545810\pi$
$230$	0	0
$231$	−6.48530	−0.426701
$232$	7.73877	0.508075
$233$	−5.97881	−0.391685	−0.195843	−	0.980635i	$-0.562744\pi$
$233$	−5.97881	−0.391685	−0.195843	+	0.980635i	$0.562744\pi$
$234$	−3.30492	−0.216050
$235$	0	0
$236$	−1.04969	−0.0683290
$237$	−15.8007	−1.02637
$238$	32.1063	2.08114
$239$	−22.8096	−1.47543	−0.737716	−	0.675111i	$-0.764096\pi$
$239$	−22.8096	−1.47543	−0.737716	+	0.675111i	$0.764096\pi$
$240$	0	0
$241$	5.79509	0.373295	0.186647	−	0.982427i	$-0.440238\pi$
$241$	5.79509	0.373295	0.186647	+	0.982427i	$0.440238\pi$
$242$	12.7731	0.821089
$243$	1.00000	0.0641500
$244$	5.31828	0.340468
$245$	0	0
$246$	17.6522	1.12546
$247$	−17.6856	−1.12531
$248$	−7.02260	−0.445935
$249$	5.57490	0.353295
$250$	0	0
$251$	−12.4869	−0.788164	−0.394082	−	0.919075i	$-0.628937\pi$
$251$	−12.4869	−0.788164	−0.394082	+	0.919075i	$0.628937\pi$
$252$	−1.65608	−0.104323
$253$	−1.12057	−0.0704495
$254$	29.9981	1.88225
$255$	0	0
$256$	9.82306	0.613941
$257$	−16.0155	−0.999019	−0.499509	−	0.866309i	$-0.666486\pi$
$257$	−16.0155	−0.999019	−0.499509	+	0.866309i	$0.666486\pi$
$258$	2.83977	0.176796
$259$	1.54223	0.0958294
$260$	0	0
$261$	3.15855	0.195509
$262$	12.0304	0.743238
$263$	−5.41400	−0.333841	−0.166921	−	0.985970i	$-0.553382\pi$
$263$	−5.41400	−0.333841	−0.166921	+	0.985970i	$0.553382\pi$
$264$	4.10104	0.252401
$265$	0	0
$266$	−50.3298	−3.08592
$267$	−3.73868	−0.228803
$268$	−0.308088	−0.0188195
$269$	29.6868	1.81004	0.905018	−	0.425372i	$-0.139857\pi$
$269$	29.6868	1.81004	0.905018	+	0.425372i	$0.139857\pi$
$270$	0	0
$271$	−4.27710	−0.259815	−0.129908	−	0.991526i	$-0.541468\pi$
$271$	−4.27710	−0.259815	−0.129908	+	0.991526i	$0.541468\pi$
$272$	−24.8493	−1.50671
$273$	−8.21881	−0.497425
$274$	31.1077	1.87928
$275$	0	0
$276$	−0.286147	−0.0172240
$277$	10.0695	0.605019	0.302510	−	0.953146i	$-0.402176\pi$
$277$	10.0695	0.605019	0.302510	+	0.953146i	$0.402176\pi$
$278$	−4.52752	−0.271542
$279$	−2.86625	−0.171598
$280$	0	0
$281$	18.4511	1.10070	0.550351	−	0.834933i	$-0.314494\pi$
$281$	18.4511	1.10070	0.550351	+	0.834933i	$0.314494\pi$
$282$	1.55802	0.0927787
$283$	−16.4247	−0.976349	−0.488174	−	0.872746i	$-0.662337\pi$
$283$	−16.4247	−0.976349	−0.488174	+	0.872746i	$0.662337\pi$
$284$	3.49466	0.207370
$285$	0	0
$286$	−5.53185	−0.327105
$287$	43.8981	2.59122
$288$	2.37911	0.140190
$289$	11.2874	0.663966
$290$	0	0
$291$	13.6442	0.799838
$292$	6.05779	0.354505
$293$	−25.6582	−1.49897	−0.749483	−	0.662023i	$-0.769698\pi$
$293$	−25.6582	−1.49897	−0.749483	+	0.662023i	$0.769698\pi$
$294$	−12.4830	−0.728024
$295$	0	0
$296$	−0.975242	−0.0566848
$297$	1.67382	0.0971250
$298$	19.8228	1.14831
$299$	−1.42009	−0.0821261
$300$	0	0
$301$	7.06205	0.407050
$302$	29.6861	1.70824
$303$	−4.56073	−0.262007
$304$	38.9537	2.23415
$305$	0	0
$306$	−8.28647	−0.473706
$307$	−7.82693	−0.446707	−0.223353	−	0.974738i	$-0.571700\pi$
$307$	−7.82693	−0.446707	−0.223353	+	0.974738i	$0.571700\pi$
$308$	−2.77198	−0.157948
$309$	4.91561	0.279639
$310$	0	0
$311$	−1.69175	−0.0959304	−0.0479652	−	0.998849i	$-0.515274\pi$
$311$	−1.69175	−0.0959304	−0.0479652	+	0.998849i	$0.515274\pi$
$312$	5.19724	0.294236
$313$	5.43076	0.306965	0.153482	−	0.988151i	$-0.450951\pi$
$313$	5.43076	0.306965	0.153482	+	0.988151i	$0.450951\pi$
$314$	−12.2269	−0.690006
$315$	0	0
$316$	−6.75364	−0.379922
$317$	−5.09510	−0.286169	−0.143085	−	0.989710i	$-0.545702\pi$
$317$	−5.09510	−0.286169	−0.143085	+	0.989710i	$0.545702\pi$
$318$	−4.06846	−0.228148
$319$	5.28685	0.296007
$320$	0	0
$321$	2.44138	0.136265
$322$	−4.04131	−0.225214
$323$	−44.3433	−2.46733
$324$	0.427425	0.0237459
$325$	0	0
$326$	37.2745	2.06444
$327$	−8.26373	−0.456985
$328$	−27.7593	−1.53275
$329$	3.87455	0.213611
$330$	0	0
$331$	−8.65332	−0.475629	−0.237815	−	0.971311i	$-0.576431\pi$
$331$	−8.65332	−0.475629	−0.237815	+	0.971311i	$0.576431\pi$
$332$	2.38285	0.130776
$333$	−0.398041	−0.0218125
$334$	12.2662	0.671176
$335$	0	0
$336$	18.1025	0.987572
$337$	−23.9207	−1.30304	−0.651521	−	0.758631i	$-0.725869\pi$
$337$	−23.9207	−1.30304	−0.651521	+	0.758631i	$0.725869\pi$
$338$	13.2437	0.720365
$339$	−16.8631	−0.915879
$340$	0	0
$341$	−4.79759	−0.259804
$342$	12.9899	0.702411
$343$	−3.92145	−0.211738
$344$	−4.46575	−0.240777
$345$	0	0
$346$	−33.6319	−1.80806
$347$	−3.91600	−0.210222	−0.105111	−	0.994461i	$-0.533520\pi$
$347$	−3.91600	−0.210222	−0.105111	+	0.994461i	$0.533520\pi$
$348$	1.35004	0.0723700
$349$	−25.6427	−1.37262	−0.686310	−	0.727309i	$-0.740771\pi$
$349$	−25.6427	−1.37262	−0.686310	+	0.727309i	$0.740771\pi$
$350$	0	0
$351$	2.12123	0.113223
$352$	3.98221	0.212252
$353$	−10.3163	−0.549081	−0.274540	−	0.961576i	$-0.588526\pi$
$353$	−10.3163	−0.549081	−0.274540	+	0.961576i	$0.588526\pi$
$354$	3.82626	0.203363
$355$	0	0
$356$	−1.59801	−0.0846942
$357$	−20.6071	−1.09064
$358$	9.60889	0.507845
$359$	−35.3075	−1.86346	−0.931730	−	0.363152i	$-0.881701\pi$
$359$	−35.3075	−1.86346	−0.931730	+	0.363152i	$0.881701\pi$
$360$	0	0
$361$	50.5125	2.65855
$362$	31.8106	1.67193
$363$	−8.19832	−0.430300
$364$	−3.51293	−0.184128
$365$	0	0
$366$	−19.3858	−1.01331
$367$	31.0761	1.62216	0.811081	−	0.584934i	$-0.198880\pi$
$367$	31.0761	1.62216	0.811081	+	0.584934i	$0.198880\pi$
$368$	3.12785	0.163051
$369$	−11.3299	−0.589810
$370$	0	0
$371$	−10.1176	−0.525281
$372$	−1.22511	−0.0635188
$373$	−12.2252	−0.632998	−0.316499	−	0.948593i	$-0.602507\pi$
$373$	−12.2252	−0.632998	−0.316499	+	0.948593i	$0.602507\pi$
$374$	−13.8701	−0.717205
$375$	0	0
$376$	−2.45010	−0.126354
$377$	6.70002	0.345069
$378$	6.03662	0.310490
$379$	13.7419	0.705873	0.352936	−	0.935647i	$-0.385183\pi$
$379$	13.7419	0.705873	0.352936	+	0.935647i	$0.385183\pi$
$380$	0	0
$381$	−19.2540	−0.986411
$382$	−12.2251	−0.625493
$383$	−31.2761	−1.59813	−0.799067	−	0.601242i	$-0.794673\pi$
$383$	−31.2761	−1.59813	−0.799067	+	0.601242i	$0.794673\pi$
$384$	−13.5417	−0.691049
$385$	0	0
$386$	−17.5474	−0.893138
$387$	−1.82268	−0.0926519
$388$	5.83188	0.296069
$389$	−28.1852	−1.42905	−0.714524	−	0.699611i	$-0.753357\pi$
$389$	−28.1852	−1.42905	−0.714524	+	0.699611i	$0.753357\pi$
$390$	0	0
$391$	−3.56062	−0.180068
$392$	19.6305	0.991489
$393$	−7.72157	−0.389502
$394$	−8.56859	−0.431679
$395$	0	0
$396$	0.715434	0.0359519
$397$	−7.43456	−0.373130	−0.186565	−	0.982443i	$-0.559736\pi$
$397$	−7.43456	−0.373130	−0.186565	+	0.982443i	$0.559736\pi$
$398$	−23.3247	−1.16916
$399$	32.3037	1.61721
$400$	0	0
$401$	−11.6308	−0.580815	−0.290408	−	0.956903i	$-0.593791\pi$
$401$	−11.6308	−0.580815	−0.290408	+	0.956903i	$0.593791\pi$
$402$	1.12302	0.0560111
$403$	−6.07998	−0.302865
$404$	−1.94937	−0.0969849
$405$	0	0
$406$	19.0670	0.946277
$407$	−0.666250	−0.0330248
$408$	13.0311	0.645135
$409$	−18.8108	−0.930135	−0.465067	−	0.885275i	$-0.653970\pi$
$409$	−18.8108	−0.930135	−0.465067	+	0.885275i	$0.653970\pi$
$410$	0	0
$411$	−19.9662	−0.984859
$412$	2.10106	0.103512
$413$	9.51529	0.468217
$414$	1.04304	0.0512627
$415$	0	0
$416$	5.04665	0.247432
$417$	2.90594	0.142305
$418$	21.7427	1.06347
$419$	5.76522	0.281650	0.140825	−	0.990035i	$-0.455025\pi$
$419$	5.76522	0.281650	0.140825	+	0.990035i	$0.455025\pi$
$420$	0	0
$421$	−8.44411	−0.411541	−0.205770	−	0.978600i	$-0.565970\pi$
$421$	−8.44411	−0.411541	−0.205770	+	0.978600i	$0.565970\pi$
$422$	4.02510	0.195939
$423$	−1.00000	−0.0486217
$424$	6.39796	0.310713
$425$	0	0
$426$	−12.7385	−0.617182
$427$	−48.2094	−2.33302
$428$	1.04351	0.0504398
$429$	3.55057	0.171423
$430$	0	0
$431$	22.0375	1.06151	0.530754	−	0.847526i	$-0.321909\pi$
$431$	22.0375	1.06151	0.530754	+	0.847526i	$0.321909\pi$
$432$	−4.67216	−0.224789
$433$	−35.5013	−1.70608	−0.853041	−	0.521843i	$-0.825245\pi$
$433$	−35.5013	−1.70608	−0.853041	+	0.521843i	$0.825245\pi$
$434$	−17.3024	−0.830544
$435$	0	0
$436$	−3.53213	−0.169158
$437$	5.58162	0.267005
$438$	−22.0814	−1.05509
$439$	32.1001	1.53205	0.766027	−	0.642808i	$-0.222231\pi$
$439$	32.1001	1.53205	0.766027	+	0.642808i	$0.222231\pi$
$440$	0	0
$441$	8.01211	0.381529
$442$	−17.5775	−0.836078
$443$	12.9184	0.613773	0.306886	−	0.951746i	$-0.400713\pi$
$443$	12.9184	0.613773	0.306886	+	0.951746i	$0.400713\pi$
$444$	−0.170133	−0.00807415
$445$	0	0
$446$	1.49075	0.0705891
$447$	−12.7231	−0.601782
$448$	−21.8432	−1.03199
$449$	16.8553	0.795451	0.397726	−	0.917504i	$-0.369800\pi$
$449$	16.8553	0.795451	0.397726	+	0.917504i	$0.369800\pi$
$450$	0	0
$451$	−18.9642	−0.892989
$452$	−7.20773	−0.339023
$453$	−19.0537	−0.895223
$454$	3.82548	0.179539
$455$	0	0
$456$	−20.4275	−0.956606
$457$	11.6787	0.546304	0.273152	−	0.961971i	$-0.411934\pi$
$457$	11.6787	0.546304	0.273152	+	0.961971i	$0.411934\pi$
$458$	6.76283	0.316006
$459$	5.31859	0.248251
$460$	0	0
$461$	14.0864	0.656067	0.328034	−	0.944666i	$-0.393614\pi$
$461$	14.0864	0.656067	0.328034	+	0.944666i	$0.393614\pi$
$462$	10.1042	0.470091
$463$	7.13177	0.331442	0.165721	−	0.986173i	$-0.447005\pi$
$463$	7.13177	0.331442	0.165721	+	0.986173i	$0.447005\pi$
$464$	−14.7572	−0.685088
$465$	0	0
$466$	9.31511	0.431514
$467$	−15.6100	−0.722342	−0.361171	−	0.932500i	$-0.617623\pi$
$467$	−15.6100	−0.722342	−0.361171	+	0.932500i	$0.617623\pi$
$468$	0.906669	0.0419108
$469$	2.79277	0.128958
$470$	0	0
$471$	7.84774	0.361605
$472$	−6.01707	−0.276958
$473$	−3.05084	−0.140278
$474$	24.6179	1.13074
$475$	0	0
$476$	−8.80801	−0.403714
$477$	2.61130	0.119563
$478$	35.5379	1.62546
$479$	1.56644	0.0715725	0.0357863	−	0.999359i	$-0.488606\pi$
$479$	1.56644	0.0715725	0.0357863	+	0.999359i	$0.488606\pi$
$480$	0	0
$481$	−0.844338	−0.0384985
$482$	−9.02887	−0.411254
$483$	2.59388	0.118026
$484$	−3.50417	−0.159280
$485$	0	0
$486$	−1.55802	−0.0706732
$487$	−6.76390	−0.306501	−0.153251	−	0.988187i	$-0.548974\pi$
$487$	−6.76390	−0.306501	−0.153251	+	0.988187i	$0.548974\pi$
$488$	30.4856	1.38002
$489$	−23.9243	−1.08189
$490$	0	0
$491$	1.29446	0.0584184	0.0292092	−	0.999573i	$-0.490701\pi$
$491$	1.29446	0.0584184	0.0292092	+	0.999573i	$0.490701\pi$
$492$	−4.84268	−0.218325
$493$	16.7990	0.756591
$494$	27.5545	1.23974
$495$	0	0
$496$	13.3916	0.601299
$497$	−31.6786	−1.42098
$498$	−8.68580	−0.389220
$499$	5.35126	0.239556	0.119778	−	0.992801i	$-0.461782\pi$
$499$	5.35126	0.239556	0.119778	+	0.992801i	$0.461782\pi$
$500$	0	0
$501$	−7.87294	−0.351737
$502$	19.4548	0.868309
$503$	−26.7676	−1.19351	−0.596754	−	0.802425i	$-0.703543\pi$
$503$	−26.7676	−1.19351	−0.596754	+	0.802425i	$0.703543\pi$
$504$	−9.49303	−0.422853
$505$	0	0
$506$	1.74587	0.0776132
$507$	−8.50037	−0.377515
$508$	−8.22964	−0.365131
$509$	16.3687	0.725530	0.362765	−	0.931881i	$-0.381833\pi$
$509$	16.3687	0.725530	0.362765	+	0.931881i	$0.381833\pi$
$510$	0	0
$511$	−54.9130	−2.42921
$512$	11.7790	0.520561
$513$	−8.33742	−0.368106
$514$	24.9524	1.10061
$515$	0	0
$516$	−0.779059	−0.0342962
$517$	−1.67382	−0.0736146
$518$	−2.40282	−0.105574
$519$	21.5863	0.947535
$520$	0	0
$521$	33.4809	1.46683	0.733413	−	0.679783i	$-0.237926\pi$
$521$	33.4809	1.46683	0.733413	+	0.679783i	$0.237926\pi$
$522$	−4.92108	−0.215390
$523$	28.6007	1.25062	0.625311	−	0.780376i	$-0.284972\pi$
$523$	28.6007	1.25062	0.625311	+	0.780376i	$0.284972\pi$
$524$	−3.30040	−0.144178
$525$	0	0
$526$	8.43511	0.367788
$527$	−15.2444	−0.664056
$528$	−7.82036	−0.340338
$529$	−22.5518	−0.980514
$530$	0	0
$531$	−2.45585	−0.106575
$532$	13.8074	0.598628
$533$	−24.0333	−1.04100
$534$	5.82494	0.252070
$535$	0	0
$536$	−1.76603	−0.0762809
$537$	−6.16737	−0.266142
$538$	−46.2526	−1.99409
$539$	13.4108	0.577646
$540$	0	0
$541$	44.5729	1.91634	0.958168	−	0.286205i	$-0.0923939\pi$
$541$	44.5729	1.91634	0.958168	+	0.286205i	$0.0923939\pi$
$542$	6.66380	0.286235
$543$	−20.4173	−0.876192
$544$	12.6535	0.542515
$545$	0	0
$546$	12.8051	0.548006
$547$	39.0348	1.66901	0.834504	−	0.551002i	$-0.185754\pi$
$547$	39.0348	1.66901	0.834504	+	0.551002i	$0.185754\pi$
$548$	−8.53405	−0.364557
$549$	12.4426	0.531037
$550$	0	0
$551$	−26.3341	−1.12187
$552$	−1.64026	−0.0698141
$553$	61.2207	2.60337
$554$	−15.6885	−0.666542
$555$	0	0
$556$	1.24207	0.0526757
$557$	−5.19235	−0.220007	−0.110003	−	0.993931i	$-0.535086\pi$
$557$	−5.19235	−0.220007	−0.110003	+	0.993931i	$0.535086\pi$
$558$	4.46567	0.189047
$559$	−3.86632	−0.163528
$560$	0	0
$561$	8.90238	0.375859
$562$	−28.7472	−1.21263
$563$	−31.0460	−1.30843	−0.654217	−	0.756307i	$-0.727002\pi$
$563$	−31.0460	−1.30843	−0.654217	+	0.756307i	$0.727002\pi$
$564$	−0.427425	−0.0179979
$565$	0	0
$566$	25.5901	1.07563
$567$	−3.87455	−0.162716
$568$	20.0322	0.840534
$569$	−34.1611	−1.43211	−0.716055	−	0.698044i	$-0.754054\pi$
$569$	−34.1611	−1.43211	−0.716055	+	0.698044i	$0.754054\pi$
$570$	0	0
$571$	0.457455	0.0191439	0.00957195	−	0.999954i	$-0.496953\pi$
$571$	0.457455	0.0191439	0.00957195	+	0.999954i	$0.496953\pi$
$572$	1.51760	0.0634541
$573$	7.84659	0.327796
$574$	−68.3941	−2.85472
$575$	0	0
$576$	5.63762	0.234901
$577$	−33.5583	−1.39705	−0.698525	−	0.715586i	$-0.746160\pi$
$577$	−33.5583	−1.39705	−0.698525	+	0.715586i	$0.746160\pi$
$578$	−17.5860	−0.731482
$579$	11.2626	0.468058
$580$	0	0
$581$	−21.6002	−0.896127
$582$	−21.2579	−0.881170
$583$	4.37086	0.181022
$584$	34.7247	1.43692
$585$	0	0
$586$	39.9759	1.65139
$587$	32.1260	1.32598	0.662990	−	0.748628i	$-0.269287\pi$
$587$	32.1260	1.32598	0.662990	+	0.748628i	$0.269287\pi$
$588$	3.42458	0.141227
$589$	23.8971	0.984663
$590$	0	0
$591$	5.49967	0.226226
$592$	1.85971	0.0764337
$593$	−13.4105	−0.550704	−0.275352	−	0.961343i	$-0.588794\pi$
$593$	−13.4105	−0.550704	−0.275352	+	0.961343i	$0.588794\pi$
$594$	−2.60785	−0.107001
$595$	0	0
$596$	−5.43817	−0.222756
$597$	14.9707	0.612711
$598$	2.21253	0.0904772
$599$	20.9045	0.854133	0.427067	−	0.904220i	$-0.359547\pi$
$599$	20.9045	0.854133	0.427067	+	0.904220i	$0.359547\pi$
$600$	0	0
$601$	21.0432	0.858368	0.429184	−	0.903217i	$-0.358801\pi$
$601$	21.0432	0.858368	0.429184	+	0.903217i	$0.358801\pi$
$602$	−11.0028	−0.448441
$603$	−0.720799	−0.0293532
$604$	−8.14405	−0.331377
$605$	0	0
$606$	7.10571	0.288650
$607$	14.3823	0.583759	0.291879	−	0.956455i	$-0.405719\pi$
$607$	14.3823	0.583759	0.291879	+	0.956455i	$0.405719\pi$
$608$	−19.8356	−0.804441
$609$	−12.2379	−0.495907
$610$	0	0
$611$	−2.12123	−0.0858159
$612$	2.27330	0.0918928
$613$	29.5540	1.19367	0.596836	−	0.802363i	$-0.296424\pi$
$613$	29.5540	1.19367	0.596836	+	0.802363i	$0.296424\pi$
$614$	12.1945	0.492131
$615$	0	0
$616$	−15.8897	−0.640212
$617$	−19.5620	−0.787537	−0.393769	−	0.919210i	$-0.628829\pi$
$617$	−19.5620	−0.787537	−0.393769	+	0.919210i	$0.628829\pi$
$618$	−7.65862	−0.308075
$619$	4.55802	0.183202	0.0916011	−	0.995796i	$-0.470802\pi$
$619$	4.55802	0.183202	0.0916011	+	0.995796i	$0.470802\pi$
$620$	0	0
$621$	−0.669466	−0.0268648
$622$	2.63578	0.105685
$623$	14.4857	0.580357
$624$	−9.91073	−0.396747
$625$	0	0
$626$	−8.46123	−0.338179
$627$	−13.9554	−0.557323
$628$	3.35432	0.133852
$629$	−2.11702	−0.0844111
$630$	0	0
$631$	0.619092	0.0246457	0.0123228	−	0.999924i	$-0.496077\pi$
$631$	0.619092	0.0246457	0.0123228	+	0.999924i	$0.496077\pi$
$632$	−38.7134	−1.53994
$633$	−2.58347	−0.102684
$634$	7.93827	0.315269
$635$	0	0
$636$	1.11614	0.0442577
$637$	16.9955	0.673388
$638$	−8.23702	−0.326107
$639$	8.17608	0.323441
$640$	0	0
$641$	42.0848	1.66225	0.831125	−	0.556086i	$-0.187698\pi$
$641$	42.0848	1.66225	0.831125	+	0.556086i	$0.187698\pi$
$642$	−3.80372	−0.150121
$643$	32.2615	1.27227	0.636135	−	0.771578i	$-0.280532\pi$
$643$	32.2615	1.27227	0.636135	+	0.771578i	$0.280532\pi$
$644$	1.10869	0.0436885
$645$	0	0
$646$	69.0878	2.71822
$647$	3.25289	0.127884	0.0639422	−	0.997954i	$-0.479633\pi$
$647$	3.25289	0.127884	0.0639422	+	0.997954i	$0.479633\pi$
$648$	2.45010	0.0962491
$649$	−4.11065	−0.161357
$650$	0	0
$651$	11.1054	0.435255
$652$	−10.2258	−0.400475
$653$	17.8165	0.697215	0.348607	−	0.937269i	$-0.386655\pi$
$653$	17.8165	0.697215	0.348607	+	0.937269i	$0.386655\pi$
$654$	12.8751	0.503455
$655$	0	0
$656$	52.9350	2.06676
$657$	14.1727	0.552931
$658$	−6.03662	−0.235332
$659$	−35.3504	−1.37706	−0.688529	−	0.725209i	$-0.741743\pi$
$659$	−35.3504	−1.37706	−0.688529	+	0.725209i	$0.741743\pi$
$660$	0	0
$661$	−34.5543	−1.34401	−0.672003	−	0.740548i	$-0.734566\pi$
$661$	−34.5543	−1.34401	−0.672003	+	0.740548i	$0.734566\pi$
$662$	13.4820	0.523994
$663$	11.2820	0.438155
$664$	13.6591	0.530075
$665$	0	0
$666$	0.620156	0.0240306
$667$	−2.11454	−0.0818754
$668$	−3.36509	−0.130199
$669$	−0.956824	−0.0369929
$670$	0	0
$671$	20.8267	0.804005
$672$	−9.21797	−0.355591
$673$	−22.6275	−0.872226	−0.436113	−	0.899892i	$-0.643645\pi$
$673$	−22.6275	−0.872226	−0.436113	+	0.899892i	$0.643645\pi$
$674$	37.2689	1.43554
$675$	0	0
$676$	−3.63328	−0.139741
$677$	−0.741784	−0.0285091	−0.0142545	−	0.999898i	$-0.504538\pi$
$677$	−0.741784	−0.0285091	−0.0142545	+	0.999898i	$0.504538\pi$
$678$	26.2731	1.00901
$679$	−52.8651	−2.02878
$680$	0	0
$681$	−2.45535	−0.0940892
$682$	7.47474	0.286222
$683$	−21.4927	−0.822396	−0.411198	−	0.911546i	$-0.634890\pi$
$683$	−21.4927	−0.822396	−0.411198	+	0.911546i	$0.634890\pi$
$684$	−3.56362	−0.136259
$685$	0	0
$686$	6.10969	0.233269
$687$	−4.34066	−0.165606
$688$	8.51584	0.324663
$689$	5.53918	0.211026
$690$	0	0
$691$	−13.8003	−0.524987	−0.262493	−	0.964934i	$-0.584545\pi$
$691$	−13.8003	−0.524987	−0.262493	+	0.964934i	$0.584545\pi$
$692$	9.22655	0.350741
$693$	−6.48530	−0.246356
$694$	6.10120	0.231599
$695$	0	0
$696$	7.73877	0.293337
$697$	−60.2590	−2.28247
$698$	39.9518	1.51220
$699$	−5.97881	−0.226139
$700$	0	0
$701$	−31.2632	−1.18079	−0.590397	−	0.807113i	$-0.701029\pi$
$701$	−31.2632	−1.18079	−0.590397	+	0.807113i	$0.701029\pi$
$702$	−3.30492	−0.124736
$703$	3.31864	0.125165
$704$	9.43637	0.355646
$705$	0	0
$706$	16.0730	0.604915
$707$	17.6708	0.664577
$708$	−1.04969	−0.0394498
$709$	−47.2201	−1.77339	−0.886694	−	0.462358i	$-0.847004\pi$
$709$	−47.2201	−1.77339	−0.886694	+	0.462358i	$0.847004\pi$
$710$	0	0
$711$	−15.8007	−0.592574
$712$	−9.16015	−0.343291
$713$	1.91886	0.0718617
$714$	32.1063	1.20155
$715$	0	0
$716$	−2.63609	−0.0985154
$717$	−22.8096	−0.851841
$718$	55.0098	2.05295
$719$	−26.4455	−0.986252	−0.493126	−	0.869958i	$-0.664146\pi$
$719$	−26.4455	−0.986252	−0.493126	+	0.869958i	$0.664146\pi$
$720$	0	0
$721$	−19.0458	−0.709301
$722$	−78.6995	−2.92889
$723$	5.79509	0.215522
$724$	−8.72689	−0.324332
$725$	0	0
$726$	12.7731	0.474056
$727$	−14.9274	−0.553627	−0.276813	−	0.960924i	$-0.589278\pi$
$727$	−14.9274	−0.553627	−0.276813	+	0.960924i	$0.589278\pi$
$728$	−20.1369	−0.746324
$729$	1.00000	0.0370370
$730$	0	0
$731$	−9.69408	−0.358549
$732$	5.31828	0.196569
$733$	−11.4251	−0.421996	−0.210998	−	0.977487i	$-0.567671\pi$
$733$	−11.4251	−0.421996	−0.210998	+	0.977487i	$0.567671\pi$
$734$	−48.4172	−1.78711
$735$	0	0
$736$	−1.59273	−0.0587090
$737$	−1.20649	−0.0444416
$738$	17.6522	0.649785
$739$	−40.5220	−1.49063	−0.745313	−	0.666714i	$-0.767700\pi$
$739$	−40.5220	−1.49063	−0.745313	+	0.666714i	$0.767700\pi$
$740$	0	0
$741$	−17.6856	−0.649697
$742$	15.7634	0.578694
$743$	3.79926	0.139381	0.0696907	−	0.997569i	$-0.477799\pi$
$743$	3.79926	0.139381	0.0696907	+	0.997569i	$0.477799\pi$
$744$	−7.02260	−0.257461
$745$	0	0
$746$	19.0471	0.697365
$747$	5.57490	0.203975
$748$	3.80510	0.139128
$749$	−9.45924	−0.345633
$750$	0	0
$751$	31.5811	1.15241	0.576204	−	0.817306i	$-0.304533\pi$
$751$	31.5811	1.15241	0.576204	+	0.817306i	$0.304533\pi$
$752$	4.67216	0.170376
$753$	−12.4869	−0.455046
$754$	−10.4388	−0.380157
$755$	0	0
$756$	−1.65608	−0.0602310
$757$	37.1673	1.35087	0.675434	−	0.737421i	$-0.263957\pi$
$757$	37.1673	1.35087	0.675434	+	0.737421i	$0.263957\pi$
$758$	−21.4101	−0.777651
$759$	−1.12057	−0.0406740
$760$	0	0
$761$	3.90594	0.141590	0.0707951	−	0.997491i	$-0.477446\pi$
$761$	3.90594	0.141590	0.0707951	+	0.997491i	$0.477446\pi$
$762$	29.9981	1.08672
$763$	32.0182	1.15914
$764$	3.35383	0.121337
$765$	0	0
$766$	48.7288	1.76064
$767$	−5.20942	−0.188101
$768$	9.82306	0.354459
$769$	−7.68220	−0.277027	−0.138514	−	0.990361i	$-0.544232\pi$
$769$	−7.68220	−0.277027	−0.138514	+	0.990361i	$0.544232\pi$
$770$	0	0
$771$	−16.0155	−0.576784
$772$	4.81393	0.173257
$773$	43.8076	1.57565	0.787824	−	0.615900i	$-0.211208\pi$
$773$	43.8076	1.57565	0.787824	+	0.615900i	$0.211208\pi$
$774$	2.83977	0.102073
$775$	0	0
$776$	33.4297	1.20006
$777$	1.54223	0.0553272
$778$	43.9131	1.57436
$779$	94.4619	3.38445
$780$	0	0
$781$	13.6853	0.489699
$782$	5.54751	0.198379
$783$	3.15855	0.112877
$784$	−37.4338	−1.33692
$785$	0	0
$786$	12.0304	0.429109
$787$	39.6332	1.41277	0.706385	−	0.707828i	$-0.250325\pi$
$787$	39.6332	1.41277	0.706385	+	0.707828i	$0.250325\pi$
$788$	2.35070	0.0837401
$789$	−5.41400	−0.192743
$790$	0	0
$791$	65.3370	2.32312
$792$	4.10104	0.145724
$793$	26.3936	0.937265
$794$	11.5832	0.411072
$795$	0	0
$796$	6.39887	0.226802
$797$	6.03035	0.213606	0.106803	−	0.994280i	$-0.465939\pi$
$797$	6.03035	0.213606	0.106803	+	0.994280i	$0.465939\pi$
$798$	−50.3298	−1.78166
$799$	−5.31859	−0.188158
$800$	0	0
$801$	−3.73868	−0.132100
$802$	18.1210	0.639876
$803$	23.7227	0.837154
$804$	−0.308088	−0.0108654
$805$	0	0
$806$	9.47272	0.333662
$807$	29.6868	1.04503
$808$	−11.1743	−0.393109
$809$	29.2133	1.02708	0.513542	−	0.858064i	$-0.328333\pi$
$809$	29.2133	1.02708	0.513542	+	0.858064i	$0.328333\pi$
$810$	0	0
$811$	−53.5235	−1.87946	−0.939732	−	0.341912i	$-0.888926\pi$
$811$	−53.5235	−1.87946	−0.939732	+	0.341912i	$0.888926\pi$
$812$	−5.23081	−0.183565
$813$	−4.27710	−0.150004
$814$	1.03803	0.0363830
$815$	0	0
$816$	−24.8493	−0.869900
$817$	15.1964	0.531656
$818$	29.3076	1.02472
$819$	−8.21881	−0.287189
$820$	0	0
$821$	−38.2003	−1.33320	−0.666600	−	0.745415i	$-0.732251\pi$
$821$	−38.2003	−1.33320	−0.666600	+	0.745415i	$0.732251\pi$
$822$	31.1077	1.08501
$823$	−23.1959	−0.808557	−0.404279	−	0.914636i	$-0.632477\pi$
$823$	−23.1959	−0.808557	−0.404279	+	0.914636i	$0.632477\pi$
$824$	12.0437	0.419564
$825$	0	0
$826$	−14.8250	−0.515828
$827$	38.6986	1.34568	0.672841	−	0.739787i	$-0.265074\pi$
$827$	38.6986	1.34568	0.672841	+	0.739787i	$0.265074\pi$
$828$	−0.286147	−0.00994429
$829$	30.9717	1.07569	0.537846	−	0.843043i	$-0.319238\pi$
$829$	30.9717	1.07569	0.537846	+	0.843043i	$0.319238\pi$
$830$	0	0
$831$	10.0695	0.349308
$832$	11.9587	0.414593
$833$	42.6131	1.47646
$834$	−4.52752	−0.156775
$835$	0	0
$836$	−5.96487	−0.206299
$837$	−2.86625	−0.0990720
$838$	−8.98233	−0.310290
$839$	27.4310	0.947023	0.473511	−	0.880788i	$-0.342986\pi$
$839$	27.4310	0.947023	0.473511	+	0.880788i	$0.342986\pi$
$840$	0	0
$841$	−19.0236	−0.655985
$842$	13.1561	0.453389
$843$	18.4511	0.635491
$844$	−1.10424	−0.0380095
$845$	0	0
$846$	1.55802	0.0535658
$847$	31.7648	1.09145
$848$	−12.2004	−0.418964
$849$	−16.4247	−0.563695
$850$	0	0
$851$	0.266475	0.00913465
$852$	3.49466	0.119725
$853$	−29.5779	−1.01273	−0.506364	−	0.862320i	$-0.669011\pi$
$853$	−29.5779	−1.01273	−0.506364	+	0.862320i	$0.669011\pi$
$854$	75.1112	2.57025
$855$	0	0
$856$	5.98163	0.204448
$857$	−49.1607	−1.67930	−0.839650	−	0.543129i	$-0.817240\pi$
$857$	−49.1607	−1.67930	−0.839650	+	0.543129i	$0.817240\pi$
$858$	−5.53185	−0.188854
$859$	−24.9344	−0.850751	−0.425376	−	0.905017i	$-0.639858\pi$
$859$	−24.9344	−0.850751	−0.425376	+	0.905017i	$0.639858\pi$
$860$	0	0
$861$	43.8981	1.49604
$862$	−34.3348	−1.16945
$863$	41.8600	1.42493	0.712466	−	0.701707i	$-0.247578\pi$
$863$	41.8600	1.42493	0.712466	+	0.701707i	$0.247578\pi$
$864$	2.37911	0.0809390
$865$	0	0
$866$	55.3117	1.87957
$867$	11.2874	0.383341
$868$	4.74673	0.161115
$869$	−26.4476	−0.897174
$870$	0	0
$871$	−1.52898	−0.0518076
$872$	−20.2470	−0.685650
$873$	13.6442	0.461786
$874$	−8.69627	−0.294156
$875$	0	0
$876$	6.05779	0.204674
$877$	20.4505	0.690564	0.345282	−	0.938499i	$-0.387783\pi$
$877$	20.4505	0.690564	0.345282	+	0.938499i	$0.387783\pi$
$878$	−50.0126	−1.68784
$879$	−25.6582	−0.865429
$880$	0	0
$881$	36.9756	1.24574	0.622870	−	0.782325i	$-0.285967\pi$
$881$	36.9756	1.24574	0.622870	+	0.782325i	$0.285967\pi$
$882$	−12.4830	−0.420325
$883$	−16.0136	−0.538901	−0.269451	−	0.963014i	$-0.586842\pi$
$883$	−16.0136	−0.538901	−0.269451	+	0.963014i	$0.586842\pi$
$884$	4.82220	0.162188
$885$	0	0
$886$	−20.1272	−0.676185
$887$	−15.1502	−0.508694	−0.254347	−	0.967113i	$-0.581861\pi$
$887$	−15.1502	−0.508694	−0.254347	+	0.967113i	$0.581861\pi$
$888$	−0.975242	−0.0327270
$889$	74.6004	2.50202
$890$	0	0
$891$	1.67382	0.0560752
$892$	−0.408971	−0.0136934
$893$	8.33742	0.279001
$894$	19.8228	0.662974
$895$	0	0
$896$	52.4681	1.75284
$897$	−1.42009	−0.0474155
$898$	−26.2609	−0.876338
$899$	−9.05318	−0.301941
$900$	0	0
$901$	13.8885	0.462692
$902$	29.5466	0.983794
$903$	7.06205	0.235010
$904$	−41.3164	−1.37416
$905$	0	0
$906$	29.6861	0.986255
$907$	−2.85565	−0.0948204	−0.0474102	−	0.998876i	$-0.515097\pi$
$907$	−2.85565	−0.0948204	−0.0474102	+	0.998876i	$0.515097\pi$
$908$	−1.04948	−0.0348282
$909$	−4.56073	−0.151270
$910$	0	0
$911$	53.1257	1.76013	0.880067	−	0.474849i	$-0.157497\pi$
$911$	53.1257	1.76013	0.880067	+	0.474849i	$0.157497\pi$
$912$	38.9537	1.28989
$913$	9.33139	0.308824
$914$	−18.1956	−0.601856
$915$	0	0
$916$	−1.85531	−0.0613011
$917$	29.9176	0.987966
$918$	−8.28647	−0.273494
$919$	52.4797	1.73115	0.865573	−	0.500783i	$-0.166955\pi$
$919$	52.4797	1.73115	0.865573	+	0.500783i	$0.166955\pi$
$920$	0	0
$921$	−7.82693	−0.257906
$922$	−21.9468	−0.722780
$923$	17.3434	0.570864
$924$	−2.77198	−0.0911915
$925$	0	0
$926$	−11.1114	−0.365145
$927$	4.91561	0.161450
$928$	7.51454	0.246677
$929$	−14.0294	−0.460289	−0.230144	−	0.973156i	$-0.573920\pi$
$929$	−14.0294	−0.460289	−0.230144	+	0.973156i	$0.573920\pi$
$930$	0	0
$931$	−66.8003	−2.18929
$932$	−2.55550	−0.0837081
$933$	−1.69175	−0.0553854
$934$	24.3206	0.795795
$935$	0	0
$936$	5.19724	0.169877
$937$	18.7408	0.612235	0.306117	−	0.951994i	$-0.400970\pi$
$937$	18.7408	0.612235	0.306117	+	0.951994i	$0.400970\pi$
$938$	−4.35119	−0.142071
$939$	5.43076	0.177226
$940$	0	0
$941$	31.7009	1.03342	0.516710	−	0.856160i	$-0.327156\pi$
$941$	31.7009	1.03342	0.516710	+	0.856160i	$0.327156\pi$
$942$	−12.2269	−0.398375
$943$	7.58497	0.247001
$944$	11.4741	0.373450
$945$	0	0
$946$	4.75327	0.154542
$947$	58.4999	1.90099	0.950496	−	0.310738i	$-0.100576\pi$
$947$	58.4999	1.90099	0.950496	+	0.310738i	$0.100576\pi$
$948$	−6.75364	−0.219348
$949$	30.0637	0.975909
$950$	0	0
$951$	−5.09510	−0.165220
$952$	−50.4896	−1.63638
$953$	24.5978	0.796801	0.398401	−	0.917211i	$-0.369565\pi$
$953$	24.5978	0.796801	0.398401	+	0.917211i	$0.369565\pi$
$954$	−4.06846	−0.131721
$955$	0	0
$956$	−9.74942	−0.315319
$957$	5.28685	0.170900
$958$	−2.44055	−0.0788505
$959$	77.3599	2.49808
$960$	0	0
$961$	−22.7846	−0.734988
$962$	1.31550	0.0424133
$963$	2.44138	0.0786724
$964$	2.47697	0.0797778
$965$	0	0
$966$	−4.04131	−0.130027
$967$	35.6914	1.14776	0.573879	−	0.818940i	$-0.305438\pi$
$967$	35.6914	1.14776	0.573879	+	0.818940i	$0.305438\pi$
$968$	−20.0867	−0.645612
$969$	−44.3433	−1.42451
$970$	0	0
$971$	−12.5154	−0.401639	−0.200820	−	0.979628i	$-0.564360\pi$
$971$	−12.5154	−0.401639	−0.200820	+	0.979628i	$0.564360\pi$
$972$	0.427425	0.0137097
$973$	−11.2592	−0.360954
$974$	10.5383	0.337668
$975$	0	0
$976$	−58.1338	−1.86082
$977$	−38.3289	−1.22625	−0.613126	−	0.789985i	$-0.710088\pi$
$977$	−38.3289	−1.22625	−0.613126	+	0.789985i	$0.710088\pi$
$978$	37.2745	1.19191
$979$	−6.25788	−0.200003
$980$	0	0
$981$	−8.26373	−0.263841
$982$	−2.01680	−0.0643587
$983$	−6.54478	−0.208746	−0.104373	−	0.994538i	$-0.533284\pi$
$983$	−6.54478	−0.208746	−0.104373	+	0.994538i	$0.533284\pi$
$984$	−27.7593	−0.884936
$985$	0	0
$986$	−26.1732	−0.833526
$987$	3.87455	0.123328
$988$	−7.55927	−0.240493
$989$	1.22022	0.0388008
$990$	0	0
$991$	33.4437	1.06238	0.531188	−	0.847254i	$-0.321746\pi$
$991$	33.4437	1.06238	0.531188	+	0.847254i	$0.321746\pi$
$992$	−6.81912	−0.216507
$993$	−8.65332	−0.274605
$994$	49.3559	1.56547
$995$	0	0
$996$	2.38285	0.0755036
$997$	−20.0965	−0.636461	−0.318231	−	0.948013i	$-0.603089\pi$
$997$	−20.0965	−0.636461	−0.318231	+	0.948013i	$0.603089\pi$
$998$	−8.33738	−0.263915
$999$	−0.398041	−0.0125935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bf.1.3		10
5.2	odd	4		705.2.c.b.424.5	✓	20
5.3	odd	4		705.2.c.b.424.16	yes	20
5.4	even	2		3525.2.a.bg.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.5	✓	20	5.2	odd	4
705.2.c.b.424.16	yes	20	5.3	odd	4
3525.2.a.bf.1.3		10	1.1	even	1	trivial
3525.2.a.bg.1.8		10	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.55802 q^{2} +1.00000 q^{3} +0.427425 q^{4} -1.55802 q^{6} -3.87455 q^{7} +2.45010 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.55802 q^{2} +1.00000 q^{3} +0.427425 q^{4} -1.55802 q^{6} -3.87455 q^{7} +2.45010 q^{8} +1.00000 q^{9} +1.67382 q^{11} +0.427425 q^{12} +2.12123 q^{13} +6.03662 q^{14} -4.67216 q^{16} +5.31859 q^{17} -1.55802 q^{18} -8.33742 q^{19} -3.87455 q^{21} -2.60785 q^{22} -0.669466 q^{23} +2.45010 q^{24} -3.30492 q^{26} +1.00000 q^{27} -1.65608 q^{28} +3.15855 q^{29} -2.86625 q^{31} +2.37911 q^{32} +1.67382 q^{33} -8.28647 q^{34} +0.427425 q^{36} -0.398041 q^{37} +12.9899 q^{38} +2.12123 q^{39} -11.3299 q^{41} +6.03662 q^{42} -1.82268 q^{43} +0.715434 q^{44} +1.04304 q^{46} -1.00000 q^{47} -4.67216 q^{48} +8.01211 q^{49} +5.31859 q^{51} +0.906669 q^{52} +2.61130 q^{53} -1.55802 q^{54} -9.49303 q^{56} -8.33742 q^{57} -4.92108 q^{58} -2.45585 q^{59} +12.4426 q^{61} +4.46567 q^{62} -3.87455 q^{63} +5.63762 q^{64} -2.60785 q^{66} -0.720799 q^{67} +2.27330 q^{68} -0.669466 q^{69} +8.17608 q^{71} +2.45010 q^{72} +14.1727 q^{73} +0.620156 q^{74} -3.56362 q^{76} -6.48530 q^{77} -3.30492 q^{78} -15.8007 q^{79} +1.00000 q^{81} +17.6522 q^{82} +5.57490 q^{83} -1.65608 q^{84} +2.83977 q^{86} +3.15855 q^{87} +4.10104 q^{88} -3.73868 q^{89} -8.21881 q^{91} -0.286147 q^{92} -2.86625 q^{93} +1.55802 q^{94} +2.37911 q^{96} +13.6442 q^{97} -12.4830 q^{98} +1.67382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 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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