LMFDB - Embedded newform 4025.2.a.bd.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.157646 q^{2} -0.829461 q^{3} -1.97515 q^{4} -0.130761 q^{6} -1.00000 q^{7} -0.626665 q^{8} -2.31200 q^{9} +O(q^{10})$	\(q+0.157646 q^{2} -0.829461 q^{3} -1.97515 q^{4} -0.130761 q^{6} -1.00000 q^{7} -0.626665 q^{8} -2.31200 q^{9} -3.37541 q^{11} +1.63831 q^{12} +5.51947 q^{13} -0.157646 q^{14} +3.85150 q^{16} -3.82753 q^{17} -0.364476 q^{18} -8.00372 q^{19} +0.829461 q^{21} -0.532119 q^{22} -1.00000 q^{23} +0.519794 q^{24} +0.870121 q^{26} +4.40609 q^{27} +1.97515 q^{28} -1.05770 q^{29} +0.791022 q^{31} +1.86050 q^{32} +2.79977 q^{33} -0.603395 q^{34} +4.56653 q^{36} -8.93176 q^{37} -1.26175 q^{38} -4.57818 q^{39} -1.78194 q^{41} +0.130761 q^{42} -7.33768 q^{43} +6.66693 q^{44} -0.157646 q^{46} -7.90278 q^{47} -3.19467 q^{48} +1.00000 q^{49} +3.17479 q^{51} -10.9018 q^{52} -1.75075 q^{53} +0.694602 q^{54} +0.626665 q^{56} +6.63877 q^{57} -0.166742 q^{58} -1.61366 q^{59} -4.58037 q^{61} +0.124701 q^{62} +2.31200 q^{63} -7.40971 q^{64} +0.441372 q^{66} +5.76964 q^{67} +7.55995 q^{68} +0.829461 q^{69} +16.3589 q^{71} +1.44885 q^{72} -3.89278 q^{73} -1.40806 q^{74} +15.8085 q^{76} +3.37541 q^{77} -0.721731 q^{78} +13.4135 q^{79} +3.28131 q^{81} -0.280916 q^{82} -2.22082 q^{83} -1.63831 q^{84} -1.15676 q^{86} +0.877323 q^{87} +2.11525 q^{88} -1.02347 q^{89} -5.51947 q^{91} +1.97515 q^{92} -0.656122 q^{93} -1.24584 q^{94} -1.54322 q^{96} +0.149389 q^{97} +0.157646 q^{98} +7.80393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * 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 $

$2$	0.157646	0.111472	0.0557362	−	0.998446i	$-0.482249\pi$
$2$	0.157646	0.111472	0.0557362	+	0.998446i	$0.482249\pi$
$3$	−0.829461	−0.478889	−0.239445	−	0.970910i	$-0.576965\pi$
$3$	−0.829461	−0.478889	−0.239445	+	0.970910i	$0.576965\pi$
$4$	−1.97515	−0.987574
$5$	0	0
$5$	0	0
$6$	−0.130761	−0.0533830
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.626665	−0.221560
$9$	−2.31200	−0.770665
$10$	0	0
$11$	−3.37541	−1.01772	−0.508862	−	0.860848i	$-0.669934\pi$
$11$	−3.37541	−1.01772	−0.508862	+	0.860848i	$0.669934\pi$
$12$	1.63831	0.472939
$13$	5.51947	1.53082	0.765412	−	0.643540i	$-0.222535\pi$
$13$	5.51947	1.53082	0.765412	+	0.643540i	$0.222535\pi$
$14$	−0.157646	−0.0421326
$15$	0	0
$16$	3.85150	0.962876
$17$	−3.82753	−0.928313	−0.464157	−	0.885753i	$-0.653643\pi$
$17$	−3.82753	−0.928313	−0.464157	+	0.885753i	$0.653643\pi$
$18$	−0.364476	−0.0859079
$19$	−8.00372	−1.83618	−0.918089	−	0.396373i	$-0.870269\pi$
$19$	−8.00372	−1.83618	−0.918089	+	0.396373i	$0.870269\pi$
$20$	0	0
$21$	0.829461	0.181003
$22$	−0.532119	−0.113448
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.519794	0.106103
$25$	0	0
$26$	0.870121	0.170645
$27$	4.40609	0.847953
$28$	1.97515	0.373268
$29$	−1.05770	−0.196410	−0.0982052	−	0.995166i	$-0.531310\pi$
$29$	−1.05770	−0.196410	−0.0982052	+	0.995166i	$0.531310\pi$
$30$	0	0
$31$	0.791022	0.142072	0.0710359	−	0.997474i	$-0.477370\pi$
$31$	0.791022	0.142072	0.0710359	+	0.997474i	$0.477370\pi$
$32$	1.86050	0.328894
$33$	2.79977	0.487377
$34$	−0.603395	−0.103481
$35$	0	0
$36$	4.56653	0.761089
$37$	−8.93176	−1.46837	−0.734186	−	0.678948i	$-0.762436\pi$
$37$	−8.93176	−1.46837	−0.734186	+	0.678948i	$0.762436\pi$
$38$	−1.26175	−0.204683
$39$	−4.57818	−0.733096
$40$	0	0
$41$	−1.78194	−0.278293	−0.139146	−	0.990272i	$-0.544436\pi$
$41$	−1.78194	−0.278293	−0.139146	+	0.990272i	$0.544436\pi$
$42$	0.130761	0.0201769
$43$	−7.33768	−1.11899	−0.559493	−	0.828835i	$-0.689004\pi$
$43$	−7.33768	−1.11899	−0.559493	+	0.828835i	$0.689004\pi$
$44$	6.66693	1.00508
$45$	0	0
$46$	−0.157646	−0.0232436
$47$	−7.90278	−1.15274	−0.576369	−	0.817189i	$-0.695531\pi$
$47$	−7.90278	−1.15274	−0.576369	+	0.817189i	$0.695531\pi$
$48$	−3.19467	−0.461111
$49$	1.00000	0.142857
$50$	0	0
$51$	3.17479	0.444559
$52$	−10.9018	−1.51180
$53$	−1.75075	−0.240483	−0.120242	−	0.992745i	$-0.538367\pi$
$53$	−1.75075	−0.240483	−0.120242	+	0.992745i	$0.538367\pi$
$54$	0.694602	0.0945233
$55$	0	0
$56$	0.626665	0.0837417
$57$	6.63877	0.879326
$58$	−0.166742	−0.0218944
$59$	−1.61366	−0.210080	−0.105040	−	0.994468i	$-0.533497\pi$
$59$	−1.61366	−0.210080	−0.105040	+	0.994468i	$0.533497\pi$
$60$	0	0
$61$	−4.58037	−0.586457	−0.293228	−	0.956042i	$-0.594730\pi$
$61$	−4.58037	−0.586457	−0.293228	+	0.956042i	$0.594730\pi$
$62$	0.124701	0.0158371
$63$	2.31200	0.291284
$64$	−7.40971	−0.926214
$65$	0	0
$66$	0.441372	0.0543291
$67$	5.76964	0.704874	0.352437	−	0.935836i	$-0.385353\pi$
$67$	5.76964	0.704874	0.352437	+	0.935836i	$0.385353\pi$
$68$	7.55995	0.916778
$69$	0.829461	0.0998553
$70$	0	0
$71$	16.3589	1.94144	0.970720	−	0.240214i	$-0.0772175\pi$
$71$	16.3589	1.94144	0.970720	+	0.240214i	$0.0772175\pi$
$72$	1.44885	0.170748
$73$	−3.89278	−0.455616	−0.227808	−	0.973706i	$-0.573156\pi$
$73$	−3.89278	−0.455616	−0.227808	+	0.973706i	$0.573156\pi$
$74$	−1.40806	−0.163683
$75$	0	0
$76$	15.8085	1.81336
$77$	3.37541	0.384663
$78$	−0.721731	−0.0817200
$79$	13.4135	1.50913	0.754567	−	0.656223i	$-0.227847\pi$
$79$	13.4135	1.50913	0.754567	+	0.656223i	$0.227847\pi$
$80$	0	0
$81$	3.28131	0.364590
$82$	−0.280916	−0.0310220
$83$	−2.22082	−0.243767	−0.121883	−	0.992544i	$-0.538893\pi$
$83$	−2.22082	−0.243767	−0.121883	+	0.992544i	$0.538893\pi$
$84$	−1.63831	−0.178754
$85$	0	0
$86$	−1.15676	−0.124736
$87$	0.877323	0.0940589
$88$	2.11525	0.225487
$89$	−1.02347	−0.108487	−0.0542437	−	0.998528i	$-0.517275\pi$
$89$	−1.02347	−0.108487	−0.0542437	+	0.998528i	$0.517275\pi$
$90$	0	0
$91$	−5.51947	−0.578597
$92$	1.97515	0.205923
$93$	−0.656122	−0.0680367
$94$	−1.24584	−0.128499
$95$	0	0
$96$	−1.54322	−0.157504
$97$	0.149389	0.0151681	0.00758406	−	0.999971i	$-0.497586\pi$
$97$	0.149389	0.0151681	0.00758406	+	0.999971i	$0.497586\pi$
$98$	0.157646	0.0159246
$99$	7.80393	0.784324
$100$	0	0
$101$	−2.96702	−0.295230	−0.147615	−	0.989045i	$-0.547160\pi$
$101$	−2.96702	−0.295230	−0.147615	+	0.989045i	$0.547160\pi$
$102$	0.500492	0.0495561
$103$	17.7225	1.74625	0.873123	−	0.487500i	$-0.162091\pi$
$103$	17.7225	1.74625	0.873123	+	0.487500i	$0.162091\pi$
$104$	−3.45886	−0.339169
$105$	0	0
$106$	−0.275998	−0.0268073
$107$	−0.0672476	−0.00650107	−0.00325054	−	0.999995i	$-0.501035\pi$
$107$	−0.0672476	−0.00650107	−0.00325054	+	0.999995i	$0.501035\pi$
$108$	−8.70268	−0.837416
$109$	−0.161749	−0.0154927	−0.00774637	−	0.999970i	$-0.502466\pi$
$109$	−0.161749	−0.0154927	−0.00774637	+	0.999970i	$0.502466\pi$
$110$	0	0
$111$	7.40855	0.703188
$112$	−3.85150	−0.363933
$113$	−14.1548	−1.33157	−0.665786	−	0.746143i	$-0.731904\pi$
$113$	−14.1548	−1.33157	−0.665786	+	0.746143i	$0.731904\pi$
$114$	1.04657	0.0980206
$115$	0	0
$116$	2.08912	0.193970
$117$	−12.7610	−1.17975
$118$	−0.254386	−0.0234181
$119$	3.82753	0.350870
$120$	0	0
$121$	0.393378	0.0357616
$122$	−0.722077	−0.0653738
$123$	1.47805	0.133271
$124$	−1.56239	−0.140306
$125$	0	0
$126$	0.364476	0.0324701
$127$	16.7400	1.48543	0.742717	−	0.669606i	$-0.233537\pi$
$127$	16.7400	1.48543	0.742717	+	0.669606i	$0.233537\pi$
$128$	−4.88912	−0.432141
$129$	6.08632	0.535871
$130$	0	0
$131$	−0.0130485	−0.00114005	−0.000570025	−	1.00000i	$-0.500181\pi$
$131$	−0.0130485	−0.00114005	−0.000570025		1.00000i	$0.500181\pi$
$132$	−5.52996	−0.481321
$133$	8.00372	0.694010
$134$	0.909560	0.0785740
$135$	0	0
$136$	2.39858	0.205677
$137$	−18.1221	−1.54828	−0.774138	−	0.633017i	$-0.781816\pi$
$137$	−18.1221	−1.54828	−0.774138	+	0.633017i	$0.781816\pi$
$138$	0.130761	0.0111311
$139$	19.2780	1.63514	0.817571	−	0.575828i	$-0.195320\pi$
$139$	19.2780	1.63514	0.817571	+	0.575828i	$0.195320\pi$
$140$	0	0
$141$	6.55504	0.552034
$142$	2.57891	0.216417
$143$	−18.6305	−1.55796
$144$	−8.90466	−0.742055
$145$	0	0
$146$	−0.613681	−0.0507886
$147$	−0.829461	−0.0684128
$148$	17.6416	1.45013
$149$	−1.53816	−0.126011	−0.0630055	−	0.998013i	$-0.520069\pi$
$149$	−1.53816	−0.126011	−0.0630055	+	0.998013i	$0.520069\pi$
$150$	0	0
$151$	12.1492	0.988685	0.494343	−	0.869267i	$-0.335409\pi$
$151$	12.1492	0.988685	0.494343	+	0.869267i	$0.335409\pi$
$152$	5.01565	0.406823
$153$	8.84924	0.715419
$154$	0.532119	0.0428794
$155$	0	0
$156$	9.04258	0.723986
$157$	−1.19256	−0.0951770	−0.0475885	−	0.998867i	$-0.515154\pi$
$157$	−1.19256	−0.0951770	−0.0475885	+	0.998867i	$0.515154\pi$
$158$	2.11458	0.168227
$159$	1.45217	0.115165
$160$	0	0
$161$	1.00000	0.0788110
$162$	0.517284	0.0406417
$163$	3.49286	0.273582	0.136791	−	0.990600i	$-0.456321\pi$
$163$	3.49286	0.273582	0.136791	+	0.990600i	$0.456321\pi$
$164$	3.51960	0.274835
$165$	0	0
$166$	−0.350103	−0.0271733
$167$	13.1991	1.02138	0.510689	−	0.859766i	$-0.329390\pi$
$167$	13.1991	1.02138	0.510689	+	0.859766i	$0.329390\pi$
$168$	−0.519794	−0.0401030
$169$	17.4645	1.34343
$170$	0	0
$171$	18.5046	1.41508
$172$	14.4930	1.10508
$173$	−15.4444	−1.17422	−0.587110	−	0.809507i	$-0.699734\pi$
$173$	−15.4444	−1.17422	−0.587110	+	0.809507i	$0.699734\pi$
$174$	0.138306	0.0104850
$175$	0	0
$176$	−13.0004	−0.979942
$177$	1.33846	0.100605
$178$	−0.161346	−0.0120934
$179$	25.8032	1.92862	0.964311	−	0.264773i	$-0.0852969\pi$
$179$	25.8032	1.92862	0.964311	+	0.264773i	$0.0852969\pi$
$180$	0	0
$181$	−20.4654	−1.52118	−0.760590	−	0.649232i	$-0.775090\pi$
$181$	−20.4654	−1.52118	−0.760590	+	0.649232i	$0.775090\pi$
$182$	−0.870121	−0.0644977
$183$	3.79924	0.280848
$184$	0.626665	0.0461984
$185$	0	0
$186$	−0.103435	−0.00758421
$187$	12.9195	0.944767
$188$	15.6092	1.13841
$189$	−4.40609	−0.320496
$190$	0	0
$191$	−17.8473	−1.29138	−0.645691	−	0.763599i	$-0.723431\pi$
$191$	−17.8473	−1.29138	−0.645691	+	0.763599i	$0.723431\pi$
$192$	6.14606	0.443554
$193$	3.15959	0.227432	0.113716	−	0.993513i	$-0.463725\pi$
$193$	3.15959	0.227432	0.113716	+	0.993513i	$0.463725\pi$
$194$	0.0235505	0.00169083
$195$	0	0
$196$	−1.97515	−0.141082
$197$	24.9539	1.77789	0.888944	−	0.458015i	$-0.151439\pi$
$197$	24.9539	1.77789	0.888944	+	0.458015i	$0.151439\pi$
$198$	1.23026	0.0874305
$199$	−0.722581	−0.0512224	−0.0256112	−	0.999672i	$-0.508153\pi$
$199$	−0.722581	−0.0512224	−0.0256112	+	0.999672i	$0.508153\pi$
$200$	0	0
$201$	−4.78569	−0.337557
$202$	−0.467739	−0.0329100
$203$	1.05770	0.0742362
$204$	−6.27068	−0.439035
$205$	0	0
$206$	2.79387	0.194658
$207$	2.31200	0.160695
$208$	21.2583	1.47399
$209$	27.0158	1.86872
$210$	0	0
$211$	6.70905	0.461870	0.230935	−	0.972969i	$-0.425822\pi$
$211$	6.70905	0.461870	0.230935	+	0.972969i	$0.425822\pi$
$212$	3.45798	0.237495
$213$	−13.5690	−0.929735
$214$	−0.0106013	−0.000724691 0
$215$	0	0
$216$	−2.76114	−0.187872
$217$	−0.791022	−0.0536981
$218$	−0.0254991	−0.00172701
$219$	3.22891	0.218190
$220$	0	0
$221$	−21.1260	−1.42109
$222$	1.16793	0.0783861
$223$	−11.9110	−0.797622	−0.398811	−	0.917033i	$-0.630577\pi$
$223$	−11.9110	−0.797622	−0.398811	+	0.917033i	$0.630577\pi$
$224$	−1.86050	−0.124310
$225$	0	0
$226$	−2.23145	−0.148434
$227$	10.7876	0.715999	0.358000	−	0.933722i	$-0.383459\pi$
$227$	10.7876	0.715999	0.358000	+	0.933722i	$0.383459\pi$
$228$	−13.1125	−0.868400
$229$	11.7536	0.776701	0.388350	−	0.921512i	$-0.373045\pi$
$229$	11.7536	0.776701	0.388350	+	0.921512i	$0.373045\pi$
$230$	0	0
$231$	−2.79977	−0.184211
$232$	0.662826	0.0435166
$233$	19.3317	1.26646	0.633231	−	0.773963i	$-0.281728\pi$
$233$	19.3317	1.26646	0.633231	+	0.773963i	$0.281728\pi$
$234$	−2.01172	−0.131510
$235$	0	0
$236$	3.18721	0.207470
$237$	−11.1260	−0.722708
$238$	0.603395	0.0391123
$239$	−1.54822	−0.100146	−0.0500729	−	0.998746i	$-0.515945\pi$
$239$	−1.54822	−0.100146	−0.0500729	+	0.998746i	$0.515945\pi$
$240$	0	0
$241$	6.35250	0.409201	0.204600	−	0.978846i	$-0.434411\pi$
$241$	6.35250	0.409201	0.204600	+	0.978846i	$0.434411\pi$
$242$	0.0620144	0.00398643
$243$	−15.9400	−1.02255
$244$	9.04692	0.579170
$245$	0	0
$246$	0.233009	0.0148561
$247$	−44.1763	−2.81087
$248$	−0.495706	−0.0314774
$249$	1.84208	0.116737
$250$	0	0
$251$	18.4257	1.16302	0.581511	−	0.813538i	$-0.302462\pi$
$251$	18.4257	1.16302	0.581511	+	0.813538i	$0.302462\pi$
$252$	−4.56653	−0.287664
$253$	3.37541	0.212210
$254$	2.63899	0.165585
$255$	0	0
$256$	14.0487	0.878042
$257$	4.64854	0.289968	0.144984	−	0.989434i	$-0.453687\pi$
$257$	4.64854	0.289968	0.144984	+	0.989434i	$0.453687\pi$
$258$	0.959483	0.0597348
$259$	8.93176	0.554993
$260$	0	0
$261$	2.44540	0.151367
$262$	−0.00205704	−0.000127084 0
$263$	−8.85885	−0.546260	−0.273130	−	0.961977i	$-0.588059\pi$
$263$	−8.85885	−0.546260	−0.273130	+	0.961977i	$0.588059\pi$
$264$	−1.75452	−0.107983
$265$	0	0
$266$	1.26175	0.0773630
$267$	0.848927	0.0519535
$268$	−11.3959	−0.696115
$269$	11.3725	0.693396	0.346698	−	0.937977i	$-0.387303\pi$
$269$	11.3725	0.693396	0.346698	+	0.937977i	$0.387303\pi$
$270$	0	0
$271$	22.5537	1.37004	0.685020	−	0.728524i	$-0.259793\pi$
$271$	22.5537	1.37004	0.685020	+	0.728524i	$0.259793\pi$
$272$	−14.7418	−0.893851
$273$	4.57818	0.277084
$274$	−2.85687	−0.172590
$275$	0	0
$276$	−1.63831	−0.0986145
$277$	11.6428	0.699546	0.349773	−	0.936834i	$-0.386259\pi$
$277$	11.6428	0.699546	0.349773	+	0.936834i	$0.386259\pi$
$278$	3.03910	0.182273
$279$	−1.82884	−0.109490
$280$	0	0
$281$	12.1603	0.725421	0.362711	−	0.931902i	$-0.381851\pi$
$281$	12.1603	0.725421	0.362711	+	0.931902i	$0.381851\pi$
$282$	1.03338	0.0615366
$283$	−21.8067	−1.29628	−0.648138	−	0.761523i	$-0.724452\pi$
$283$	−21.8067	−1.29628	−0.648138	+	0.761523i	$0.724452\pi$
$284$	−32.3112	−1.91732
$285$	0	0
$286$	−2.93701	−0.173669
$287$	1.78194	0.105185
$288$	−4.30148	−0.253467
$289$	−2.34998	−0.138234
$290$	0	0
$291$	−0.123912	−0.00726385
$292$	7.68882	0.449954
$293$	7.36115	0.430043	0.215022	−	0.976609i	$-0.431018\pi$
$293$	7.36115	0.430043	0.215022	+	0.976609i	$0.431018\pi$
$294$	−0.130761	−0.00762614
$295$	0	0
$296$	5.59723	0.325332
$297$	−14.8724	−0.862981
$298$	−0.242485	−0.0140468
$299$	−5.51947	−0.319199
$300$	0	0
$301$	7.33768	0.422937
$302$	1.91527	0.110211
$303$	2.46103	0.141382
$304$	−30.8264	−1.76801
$305$	0	0
$306$	1.39505	0.0797495
$307$	−4.26166	−0.243226	−0.121613	−	0.992578i	$-0.538807\pi$
$307$	−4.26166	−0.243226	−0.121613	+	0.992578i	$0.538807\pi$
$308$	−6.66693	−0.379884
$309$	−14.7001	−0.836258
$310$	0	0
$311$	23.0988	1.30981	0.654907	−	0.755709i	$-0.272708\pi$
$311$	23.0988	1.30981	0.654907	+	0.755709i	$0.272708\pi$
$312$	2.86899	0.162424
$313$	−30.2712	−1.71103	−0.855515	−	0.517777i	$-0.826760\pi$
$313$	−30.2712	−1.71103	−0.855515	+	0.517777i	$0.826760\pi$
$314$	−0.188003	−0.0106096
$315$	0	0
$316$	−26.4936	−1.49038
$317$	−25.1647	−1.41339	−0.706695	−	0.707518i	$-0.749815\pi$
$317$	−25.1647	−1.41339	−0.706695	+	0.707518i	$0.749815\pi$
$318$	0.228929	0.0128377
$319$	3.57018	0.199892
$320$	0	0
$321$	0.0557793	0.00311329
$322$	0.157646	0.00878526
$323$	30.6345	1.70455
$324$	−6.48107	−0.360059
$325$	0	0
$326$	0.550634	0.0304968
$327$	0.134164	0.00741931
$328$	1.11668	0.0616584
$329$	7.90278	0.435694
$330$	0	0
$331$	−10.2482	−0.563293	−0.281646	−	0.959518i	$-0.590881\pi$
$331$	−10.2482	−0.563293	−0.281646	+	0.959518i	$0.590881\pi$
$332$	4.38645	0.240738
$333$	20.6502	1.13162
$334$	2.08078	0.113855
$335$	0	0
$336$	3.19467	0.174284
$337$	16.1390	0.879149	0.439574	−	0.898206i	$-0.355129\pi$
$337$	16.1390	0.879149	0.439574	+	0.898206i	$0.355129\pi$
$338$	2.75321	0.149755
$339$	11.7409	0.637676
$340$	0	0
$341$	−2.67002	−0.144590
$342$	2.91717	0.157742
$343$	−1.00000	−0.0539949
$344$	4.59827	0.247922
$345$	0	0
$346$	−2.43475	−0.130893
$347$	−27.3122	−1.46620	−0.733098	−	0.680123i	$-0.761926\pi$
$347$	−27.3122	−1.46620	−0.733098	+	0.680123i	$0.761926\pi$
$348$	−1.73284	−0.0928901
$349$	−27.5873	−1.47671	−0.738357	−	0.674410i	$-0.764398\pi$
$349$	−27.5873	−1.47671	−0.738357	+	0.674410i	$0.764398\pi$
$350$	0	0
$351$	24.3193	1.29807
$352$	−6.27996	−0.334723
$353$	−24.1342	−1.28453	−0.642266	−	0.766482i	$-0.722006\pi$
$353$	−24.1342	−1.28453	−0.642266	+	0.766482i	$0.722006\pi$
$354$	0.211003	0.0112147
$355$	0	0
$356$	2.02150	0.107139
$357$	−3.17479	−0.168028
$358$	4.06777	0.214988
$359$	−23.1952	−1.22420	−0.612099	−	0.790781i	$-0.709675\pi$
$359$	−23.1952	−1.22420	−0.612099	+	0.790781i	$0.709675\pi$
$360$	0	0
$361$	45.0595	2.37155
$362$	−3.22628	−0.169570
$363$	−0.326291	−0.0171259
$364$	10.9018	0.571408
$365$	0	0
$366$	0.598934	0.0313068
$367$	12.2234	0.638055	0.319027	−	0.947745i	$-0.396644\pi$
$367$	12.2234	0.638055	0.319027	+	0.947745i	$0.396644\pi$
$368$	−3.85150	−0.200774
$369$	4.11984	0.214470
$370$	0	0
$371$	1.75075	0.0908942
$372$	1.29594	0.0671913
$373$	−28.5189	−1.47665	−0.738326	−	0.674444i	$-0.764384\pi$
$373$	−28.5189	−1.47665	−0.738326	+	0.674444i	$0.764384\pi$
$374$	2.03670	0.105315
$375$	0	0
$376$	4.95240	0.255400
$377$	−5.83796	−0.300670
$378$	−0.694602	−0.0357265
$379$	1.50851	0.0774871	0.0387435	−	0.999249i	$-0.487664\pi$
$379$	1.50851	0.0774871	0.0387435	+	0.999249i	$0.487664\pi$
$380$	0	0
$381$	−13.8852	−0.711358
$382$	−2.81355	−0.143953
$383$	29.8483	1.52517	0.762587	−	0.646885i	$-0.223929\pi$
$383$	29.8483	1.52517	0.762587	+	0.646885i	$0.223929\pi$
$384$	4.05533	0.206948
$385$	0	0
$386$	0.498096	0.0253524
$387$	16.9647	0.862364
$388$	−0.295065	−0.0149796
$389$	13.6785	0.693527	0.346763	−	0.937953i	$-0.387281\pi$
$389$	13.6785	0.693527	0.346763	+	0.937953i	$0.387281\pi$
$390$	0	0
$391$	3.82753	0.193567
$392$	−0.626665	−0.0316514
$393$	0.0108232	0.000545957 0
$394$	3.93387	0.198186
$395$	0	0
$396$	−15.4139	−0.774578
$397$	11.2481	0.564526	0.282263	−	0.959337i	$-0.408915\pi$
$397$	11.2481	0.564526	0.282263	+	0.959337i	$0.408915\pi$
$398$	−0.113912	−0.00570988
$399$	−6.63877	−0.332354
$400$	0	0
$401$	25.9025	1.29351	0.646753	−	0.762699i	$-0.276126\pi$
$401$	25.9025	1.29351	0.646753	+	0.762699i	$0.276126\pi$
$402$	−0.754444	−0.0376282
$403$	4.36602	0.217487
$404$	5.86031	0.291561
$405$	0	0
$406$	0.166742	0.00827529
$407$	30.1483	1.49440
$408$	−1.98953	−0.0984964
$409$	35.1679	1.73894	0.869469	−	0.493987i	$-0.164461\pi$
$409$	35.1679	1.73894	0.869469	+	0.493987i	$0.164461\pi$
$410$	0	0
$411$	15.0316	0.741453
$412$	−35.0045	−1.72455
$413$	1.61366	0.0794028
$414$	0.364476	0.0179130
$415$	0	0
$416$	10.2690	0.503479
$417$	−15.9904	−0.783052
$418$	4.25893	0.208311
$419$	−6.44748	−0.314980	−0.157490	−	0.987521i	$-0.550340\pi$
$419$	−6.44748	−0.314980	−0.157490	+	0.987521i	$0.550340\pi$
$420$	0	0
$421$	0.634712	0.0309340	0.0154670	−	0.999880i	$-0.495077\pi$
$421$	0.634712	0.0309340	0.0154670	+	0.999880i	$0.495077\pi$
$422$	1.05765	0.0514858
$423$	18.2712	0.888375
$424$	1.09713	0.0532814
$425$	0	0
$426$	−2.13910	−0.103640
$427$	4.58037	0.221660
$428$	0.132824	0.00642029
$429$	15.4532	0.746089
$430$	0	0
$431$	4.51735	0.217593	0.108797	−	0.994064i	$-0.465300\pi$
$431$	4.51735	0.217593	0.108797	+	0.994064i	$0.465300\pi$
$432$	16.9701	0.816473
$433$	25.1748	1.20982	0.604911	−	0.796293i	$-0.293209\pi$
$433$	25.1748	1.20982	0.604911	+	0.796293i	$0.293209\pi$
$434$	−0.124701	−0.00598586
$435$	0	0
$436$	0.319478	0.0153002
$437$	8.00372	0.382870
$438$	0.509024	0.0243221
$439$	−3.92619	−0.187387	−0.0936933	−	0.995601i	$-0.529867\pi$
$439$	−3.92619	−0.187387	−0.0936933	+	0.995601i	$0.529867\pi$
$440$	0	0
$441$	−2.31200	−0.110095
$442$	−3.33042	−0.158412
$443$	−1.26716	−0.0602046	−0.0301023	−	0.999547i	$-0.509583\pi$
$443$	−1.26716	−0.0602046	−0.0301023	+	0.999547i	$0.509583\pi$
$444$	−14.6330	−0.694450
$445$	0	0
$446$	−1.87772	−0.0889128
$447$	1.27584	0.0603453
$448$	7.40971	0.350076
$449$	−22.3964	−1.05695	−0.528477	−	0.848948i	$-0.677237\pi$
$449$	−22.3964	−1.05695	−0.528477	+	0.848948i	$0.677237\pi$
$450$	0	0
$451$	6.01478	0.283225
$452$	27.9578	1.31503
$453$	−10.0773	−0.473471
$454$	1.70062	0.0798142
$455$	0	0
$456$	−4.16029	−0.194823
$457$	2.94710	0.137859	0.0689296	−	0.997622i	$-0.478042\pi$
$457$	2.94710	0.137859	0.0689296	+	0.997622i	$0.478042\pi$
$458$	1.85291	0.0865807
$459$	−16.8645	−0.787166
$460$	0	0
$461$	−33.2147	−1.54696	−0.773480	−	0.633820i	$-0.781486\pi$
$461$	−33.2147	−1.54696	−0.773480	+	0.633820i	$0.781486\pi$
$462$	−0.441372	−0.0205345
$463$	1.98102	0.0920660	0.0460330	−	0.998940i	$-0.485342\pi$
$463$	1.98102	0.0920660	0.0460330	+	0.998940i	$0.485342\pi$
$464$	−4.07375	−0.189119
$465$	0	0
$466$	3.04756	0.141176
$467$	32.3057	1.49493	0.747464	−	0.664302i	$-0.231271\pi$
$467$	32.3057	1.49493	0.747464	+	0.664302i	$0.231271\pi$
$468$	25.2048	1.16509
$469$	−5.76964	−0.266417
$470$	0	0
$471$	0.989185	0.0455793
$472$	1.01122	0.0465453
$473$	24.7677	1.13882
$474$	−1.75396	−0.0805620
$475$	0	0
$476$	−7.55995	−0.346510
$477$	4.04771	0.185332
$478$	−0.244070	−0.0111635
$479$	−8.41075	−0.384297	−0.192148	−	0.981366i	$-0.561546\pi$
$479$	−8.41075	−0.384297	−0.192148	+	0.981366i	$0.561546\pi$
$480$	0	0
$481$	−49.2986	−2.24782
$482$	1.00145	0.0456146
$483$	−0.829461	−0.0377418
$484$	−0.776979	−0.0353172
$485$	0	0
$486$	−2.51287	−0.113986
$487$	−27.7672	−1.25825	−0.629126	−	0.777303i	$-0.716587\pi$
$487$	−27.7672	−1.25825	−0.629126	+	0.777303i	$0.716587\pi$
$488$	2.87036	0.129935
$489$	−2.89719	−0.131015
$490$	0	0
$491$	−15.5783	−0.703037	−0.351519	−	0.936181i	$-0.614335\pi$
$491$	−15.5783	−0.703037	−0.351519	+	0.936181i	$0.614335\pi$
$492$	−2.91937	−0.131615
$493$	4.04839	0.182330
$494$	−6.96420	−0.313334
$495$	0	0
$496$	3.04663	0.136798
$497$	−16.3589	−0.733795
$498$	0.290397	0.0130130
$499$	−20.8986	−0.935552	−0.467776	−	0.883847i	$-0.654945\pi$
$499$	−20.8986	−0.935552	−0.467776	+	0.883847i	$0.654945\pi$
$500$	0	0
$501$	−10.9481	−0.489127
$502$	2.90474	0.129645
$503$	−28.1873	−1.25681	−0.628405	−	0.777886i	$-0.716292\pi$
$503$	−28.1873	−1.25681	−0.628405	+	0.777886i	$0.716292\pi$
$504$	−1.44885	−0.0645368
$505$	0	0
$506$	0.532119	0.0236556
$507$	−14.4861	−0.643352
$508$	−33.0639	−1.46698
$509$	34.2647	1.51876	0.759378	−	0.650649i	$-0.225503\pi$
$509$	34.2647	1.51876	0.759378	+	0.650649i	$0.225503\pi$
$510$	0	0
$511$	3.89278	0.172207
$512$	11.9930	0.530019
$513$	−35.2651	−1.55699
$514$	0.732822	0.0323234
$515$	0	0
$516$	−12.0214	−0.529212
$517$	26.6751	1.17317
$518$	1.40806	0.0618664
$519$	12.8106	0.562321
$520$	0	0
$521$	8.74203	0.382995	0.191498	−	0.981493i	$-0.438666\pi$
$521$	8.74203	0.382995	0.191498	+	0.981493i	$0.438666\pi$
$522$	0.385508	0.0168732
$523$	37.7017	1.64858	0.824291	−	0.566167i	$-0.191574\pi$
$523$	37.7017	1.64858	0.824291	+	0.566167i	$0.191574\pi$
$524$	0.0257726	0.00112588
$525$	0	0
$526$	−1.39656	−0.0608930
$527$	−3.02767	−0.131887
$528$	10.7833	0.469284
$529$	1.00000	0.0434783
$530$	0	0
$531$	3.73077	0.161901
$532$	−15.8085	−0.685386
$533$	−9.83537	−0.426017
$534$	0.133830	0.00579138
$535$	0	0
$536$	−3.61563	−0.156172
$537$	−21.4027	−0.923596
$538$	1.79283	0.0772945
$539$	−3.37541	−0.145389
$540$	0	0
$541$	−11.2435	−0.483394	−0.241697	−	0.970352i	$-0.577704\pi$
$541$	−11.2435	−0.483394	−0.241697	+	0.970352i	$0.577704\pi$
$542$	3.55550	0.152722
$543$	16.9752	0.728477
$544$	−7.12115	−0.305317
$545$	0	0
$546$	0.721731	0.0308872
$547$	5.74937	0.245825	0.122913	−	0.992417i	$-0.460777\pi$
$547$	5.74937	0.245825	0.122913	+	0.992417i	$0.460777\pi$
$548$	35.7938	1.52904
$549$	10.5898	0.451962
$550$	0	0
$551$	8.46555	0.360645
$552$	−0.519794	−0.0221239
$553$	−13.4135	−0.570399
$554$	1.83543	0.0779801
$555$	0	0
$556$	−38.0770	−1.61482
$557$	0.758243	0.0321278	0.0160639	−	0.999871i	$-0.494886\pi$
$557$	0.758243	0.0321278	0.0160639	+	0.999871i	$0.494886\pi$
$558$	−0.288309	−0.0122051
$559$	−40.5001	−1.71297
$560$	0	0
$561$	−10.7162	−0.452439
$562$	1.91702	0.0808645
$563$	−12.1600	−0.512484	−0.256242	−	0.966613i	$-0.582484\pi$
$563$	−12.1600	−0.512484	−0.256242	+	0.966613i	$0.582484\pi$
$564$	−12.9472	−0.545175
$565$	0	0
$566$	−3.43774	−0.144499
$567$	−3.28131	−0.137802
$568$	−10.2515	−0.430145
$569$	−24.7666	−1.03827	−0.519135	−	0.854692i	$-0.673746\pi$
$569$	−24.7666	−1.03827	−0.519135	+	0.854692i	$0.673746\pi$
$570$	0	0
$571$	23.8088	0.996369	0.498184	−	0.867071i	$-0.334000\pi$
$571$	23.8088	0.996369	0.498184	+	0.867071i	$0.334000\pi$
$572$	36.7979	1.53860
$573$	14.8036	0.618429
$574$	0.280916	0.0117252
$575$	0	0
$576$	17.1312	0.713800
$577$	−14.9609	−0.622829	−0.311415	−	0.950274i	$-0.600803\pi$
$577$	−14.9609	−0.622829	−0.311415	+	0.950274i	$0.600803\pi$
$578$	−0.370464	−0.0154093
$579$	−2.62075	−0.108915
$580$	0	0
$581$	2.22082	0.0921352
$582$	−0.0195342	−0.000809719 0
$583$	5.90948	0.244746
$584$	2.43947	0.100946
$585$	0	0
$586$	1.16045	0.0479379
$587$	22.2839	0.919755	0.459878	−	0.887982i	$-0.347893\pi$
$587$	22.2839	0.919755	0.459878	+	0.887982i	$0.347893\pi$
$588$	1.63831	0.0675627
$589$	−6.33112	−0.260869
$590$	0	0
$591$	−20.6982	−0.851412
$592$	−34.4007	−1.41386
$593$	−17.7298	−0.728077	−0.364039	−	0.931384i	$-0.618602\pi$
$593$	−17.7298	−0.728077	−0.364039	+	0.931384i	$0.618602\pi$
$594$	−2.34456	−0.0961986
$595$	0	0
$596$	3.03810	0.124445
$597$	0.599352	0.0245299
$598$	−0.870121	−0.0355819
$599$	−45.5070	−1.85937	−0.929683	−	0.368361i	$-0.879919\pi$
$599$	−45.5070	−1.85937	−0.929683	+	0.368361i	$0.879919\pi$
$600$	0	0
$601$	12.9268	0.527297	0.263649	−	0.964619i	$-0.415074\pi$
$601$	12.9268	0.527297	0.263649	+	0.964619i	$0.415074\pi$
$602$	1.15676	0.0471458
$603$	−13.3394	−0.543222
$604$	−23.9964	−0.976400
$605$	0	0
$606$	0.387971	0.0157602
$607$	−8.58071	−0.348280	−0.174140	−	0.984721i	$-0.555715\pi$
$607$	−8.58071	−0.348280	−0.174140	+	0.984721i	$0.555715\pi$
$608$	−14.8910	−0.603908
$609$	−0.877323	−0.0355509
$610$	0	0
$611$	−43.6191	−1.76464
$612$	−17.4786	−0.706529
$613$	−34.9904	−1.41325	−0.706624	−	0.707589i	$-0.749783\pi$
$613$	−34.9904	−1.41325	−0.706624	+	0.707589i	$0.749783\pi$
$614$	−0.671833	−0.0271130
$615$	0	0
$616$	−2.11525	−0.0852259
$617$	2.18137	0.0878186	0.0439093	−	0.999036i	$-0.486019\pi$
$617$	2.18137	0.0878186	0.0439093	+	0.999036i	$0.486019\pi$
$618$	−2.31741	−0.0932198
$619$	−6.97143	−0.280206	−0.140103	−	0.990137i	$-0.544743\pi$
$619$	−6.97143	−0.280206	−0.140103	+	0.990137i	$0.544743\pi$
$620$	0	0
$621$	−4.40609	−0.176810
$622$	3.64143	0.146008
$623$	1.02347	0.0410044
$624$	−17.6329	−0.705880
$625$	0	0
$626$	−4.77213	−0.190733
$627$	−22.4086	−0.894911
$628$	2.35549	0.0939943
$629$	34.1866	1.36311
$630$	0	0
$631$	21.5643	0.858463	0.429231	−	0.903195i	$-0.358785\pi$
$631$	21.5643	0.858463	0.429231	+	0.903195i	$0.358785\pi$
$632$	−8.40576	−0.334363
$633$	−5.56489	−0.221185
$634$	−3.96711	−0.157554
$635$	0	0
$636$	−2.86826	−0.113734
$637$	5.51947	0.218689
$638$	0.562824	0.0222824
$639$	−37.8216	−1.49620
$640$	0	0
$641$	−24.9216	−0.984343	−0.492172	−	0.870498i	$-0.663797\pi$
$641$	−24.9216	−0.984343	−0.492172	+	0.870498i	$0.663797\pi$
$642$	0.00879337	0.000347047 0
$643$	−4.42277	−0.174417	−0.0872085	−	0.996190i	$-0.527795\pi$
$643$	−4.42277	−0.174417	−0.0872085	+	0.996190i	$0.527795\pi$
$644$	−1.97515	−0.0778317
$645$	0	0
$646$	4.82940	0.190010
$647$	−38.0337	−1.49526	−0.747630	−	0.664116i	$-0.768808\pi$
$647$	−38.0337	−1.49526	−0.747630	+	0.664116i	$0.768808\pi$
$648$	−2.05628	−0.0807784
$649$	5.44675	0.213804
$650$	0	0
$651$	0.656122	0.0257154
$652$	−6.89891	−0.270182
$653$	28.0808	1.09889	0.549443	−	0.835531i	$-0.314840\pi$
$653$	28.0808	1.09889	0.549443	+	0.835531i	$0.314840\pi$
$654$	0.0211505	0.000827048 0
$655$	0	0
$656$	−6.86316	−0.267961
$657$	9.00010	0.351127
$658$	1.24584	0.0485679
$659$	−9.48296	−0.369404	−0.184702	−	0.982795i	$-0.559132\pi$
$659$	−9.48296	−0.369404	−0.184702	+	0.982795i	$0.559132\pi$
$660$	0	0
$661$	−17.5357	−0.682059	−0.341029	−	0.940053i	$-0.610776\pi$
$661$	−17.5357	−0.682059	−0.341029	+	0.940053i	$0.610776\pi$
$662$	−1.61559	−0.0627916
$663$	17.5231	0.680543
$664$	1.39171	0.0540089
$665$	0	0
$666$	3.25542	0.126145
$667$	1.05770	0.0409544
$668$	−26.0702	−1.00869
$669$	9.87973	0.381972
$670$	0	0
$671$	15.4606	0.596851
$672$	1.54322	0.0595308
$673$	−40.4512	−1.55928	−0.779639	−	0.626229i	$-0.784597\pi$
$673$	−40.4512	−1.55928	−0.779639	+	0.626229i	$0.784597\pi$
$674$	2.54425	0.0980009
$675$	0	0
$676$	−34.4950	−1.32673
$677$	−17.5560	−0.674733	−0.337366	−	0.941373i	$-0.609536\pi$
$677$	−17.5560	−0.674733	−0.337366	+	0.941373i	$0.609536\pi$
$678$	1.85090	0.0710833
$679$	−0.149389	−0.00573301
$680$	0	0
$681$	−8.94790	−0.342884
$682$	−0.420918	−0.0161178
$683$	34.0183	1.30168	0.650838	−	0.759217i	$-0.274418\pi$
$683$	34.0183	1.30168	0.650838	+	0.759217i	$0.274418\pi$
$684$	−36.5492	−1.39749
$685$	0	0
$686$	−0.157646	−0.00601895
$687$	−9.74916	−0.371954
$688$	−28.2611	−1.07745
$689$	−9.66318	−0.368138
$690$	0	0
$691$	18.0373	0.686170	0.343085	−	0.939304i	$-0.388528\pi$
$691$	18.0373	0.686170	0.343085	+	0.939304i	$0.388528\pi$
$692$	30.5051	1.15963
$693$	−7.80393	−0.296447
$694$	−4.30566	−0.163440
$695$	0	0
$696$	−0.549788	−0.0208397
$697$	6.82045	0.258343
$698$	−4.34902	−0.164613
$699$	−16.0349	−0.606495
$700$	0	0
$701$	−32.9207	−1.24340	−0.621700	−	0.783256i	$-0.713558\pi$
$701$	−32.9207	−1.24340	−0.621700	+	0.783256i	$0.713558\pi$
$702$	3.83383	0.144699
$703$	71.4873	2.69620
$704$	25.0108	0.942629
$705$	0	0
$706$	−3.80465	−0.143190
$707$	2.96702	0.111586
$708$	−2.64366	−0.0993550
$709$	37.9849	1.42655	0.713276	−	0.700883i	$-0.247211\pi$
$709$	37.9849	1.42655	0.713276	+	0.700883i	$0.247211\pi$
$710$	0	0
$711$	−31.0119	−1.16304
$712$	0.641372	0.0240364
$713$	−0.791022	−0.0296240
$714$	−0.500492	−0.0187305
$715$	0	0
$716$	−50.9651	−1.90466
$717$	1.28419	0.0479588
$718$	−3.65663	−0.136464
$719$	13.0338	0.486078	0.243039	−	0.970017i	$-0.421856\pi$
$719$	13.0338	0.486078	0.243039	+	0.970017i	$0.421856\pi$
$720$	0	0
$721$	−17.7225	−0.660019
$722$	7.10344	0.264363
$723$	−5.26915	−0.195962
$724$	40.4222	1.50228
$725$	0	0
$726$	−0.0514385	−0.00190906
$727$	−11.2295	−0.416478	−0.208239	−	0.978078i	$-0.566773\pi$
$727$	−11.2295	−0.416478	−0.208239	+	0.978078i	$0.566773\pi$
$728$	3.45886	0.128194
$729$	3.37767	0.125099
$730$	0	0
$731$	28.0852	1.03877
$732$	−7.50406	−0.277358
$733$	31.6833	1.17025	0.585125	−	0.810943i	$-0.301046\pi$
$733$	31.6833	1.17025	0.585125	+	0.810943i	$0.301046\pi$
$734$	1.92696	0.0711255
$735$	0	0
$736$	−1.86050	−0.0685791
$737$	−19.4749	−0.717367
$738$	0.649476	0.0239075
$739$	32.4644	1.19422	0.597111	−	0.802159i	$-0.296315\pi$
$739$	32.4644	1.19422	0.597111	+	0.802159i	$0.296315\pi$
$740$	0	0
$741$	36.6425	1.34609
$742$	0.275998	0.0101322
$743$	−4.78238	−0.175449	−0.0877243	−	0.996145i	$-0.527959\pi$
$743$	−4.78238	−0.175449	−0.0877243	+	0.996145i	$0.527959\pi$
$744$	0.411169	0.0150742
$745$	0	0
$746$	−4.49589	−0.164606
$747$	5.13453	0.187863
$748$	−25.5179	−0.933027
$749$	0.0672476	0.00245718
$750$	0	0
$751$	15.4824	0.564959	0.282480	−	0.959273i	$-0.408843\pi$
$751$	15.4824	0.564959	0.282480	+	0.959273i	$0.408843\pi$
$752$	−30.4376	−1.10994
$753$	−15.2834	−0.556959
$754$	−0.920329	−0.0335164
$755$	0	0
$756$	8.70268	0.316513
$757$	−52.3854	−1.90398	−0.951989	−	0.306131i	$-0.900965\pi$
$757$	−52.3854	−1.90398	−0.951989	+	0.306131i	$0.900965\pi$
$758$	0.237811	0.00863767
$759$	−2.79977	−0.101625
$760$	0	0
$761$	−30.0924	−1.09085	−0.545425	−	0.838160i	$-0.683632\pi$
$761$	−30.0924	−1.09085	−0.545425	+	0.838160i	$0.683632\pi$
$762$	−2.18894	−0.0792968
$763$	0.161749	0.00585571
$764$	35.2510	1.27534
$765$	0	0
$766$	4.70545	0.170015
$767$	−8.90652	−0.321596
$768$	−11.6528	−0.420485
$769$	19.5165	0.703783	0.351891	−	0.936041i	$-0.385539\pi$
$769$	19.5165	0.703783	0.351891	+	0.936041i	$0.385539\pi$
$770$	0	0
$771$	−3.85578	−0.138862
$772$	−6.24066	−0.224606
$773$	−25.1441	−0.904370	−0.452185	−	0.891924i	$-0.649355\pi$
$773$	−25.1441	−0.904370	−0.452185	+	0.891924i	$0.649355\pi$
$774$	2.67441	0.0961298
$775$	0	0
$776$	−0.0936167	−0.00336065
$777$	−7.40855	−0.265780
$778$	2.15636	0.0773091
$779$	14.2622	0.510995
$780$	0	0
$781$	−55.2178	−1.97585
$782$	0.603395	0.0215774
$783$	−4.66033	−0.166547
$784$	3.85150	0.137554
$785$	0	0
$786$	0.00170623	6.08592e−5 0
$787$	51.8128	1.84693	0.923463	−	0.383687i	$-0.125346\pi$
$787$	51.8128	1.84693	0.923463	+	0.383687i	$0.125346\pi$
$788$	−49.2876	−1.75580
$789$	7.34807	0.261598
$790$	0	0
$791$	14.1548	0.503287
$792$	−4.89045	−0.173775
$793$	−25.2812	−0.897763
$794$	1.77322	0.0629291
$795$	0	0
$796$	1.42720	0.0505859
$797$	47.3867	1.67852	0.839262	−	0.543727i	$-0.182987\pi$
$797$	47.3867	1.67852	0.839262	+	0.543727i	$0.182987\pi$
$798$	−1.04657	−0.0370483
$799$	30.2482	1.07010
$800$	0	0
$801$	2.36625	0.0836075
$802$	4.08341	0.144190
$803$	13.1397	0.463691
$804$	9.45245	0.333362
$805$	0	0
$806$	0.688285	0.0242438
$807$	−9.43307	−0.332060
$808$	1.85933	0.0654110
$809$	14.5896	0.512943	0.256472	−	0.966552i	$-0.417440\pi$
$809$	14.5896	0.512943	0.256472	+	0.966552i	$0.417440\pi$
$810$	0	0
$811$	−26.7032	−0.937675	−0.468837	−	0.883285i	$-0.655327\pi$
$811$	−26.7032	−0.937675	−0.468837	+	0.883285i	$0.655327\pi$
$812$	−2.08912	−0.0733137
$813$	−18.7074	−0.656097
$814$	4.75276	0.166584
$815$	0	0
$816$	12.2277	0.428056
$817$	58.7288	2.05466
$818$	5.54407	0.193844
$819$	12.7610	0.445905
$820$	0	0
$821$	18.9119	0.660032	0.330016	−	0.943975i	$-0.392946\pi$
$821$	18.9119	0.660032	0.330016	+	0.943975i	$0.392946\pi$
$822$	2.36966	0.0826515
$823$	−9.56159	−0.333296	−0.166648	−	0.986016i	$-0.553294\pi$
$823$	−9.56159	−0.333296	−0.166648	+	0.986016i	$0.553294\pi$
$824$	−11.1061	−0.386898
$825$	0	0
$826$	0.254386	0.00885123
$827$	−18.5104	−0.643668	−0.321834	−	0.946796i	$-0.604299\pi$
$827$	−18.5104	−0.643668	−0.321834	+	0.946796i	$0.604299\pi$
$828$	−4.56653	−0.158698
$829$	−7.62220	−0.264730	−0.132365	−	0.991201i	$-0.542257\pi$
$829$	−7.62220	−0.264730	−0.132365	+	0.991201i	$0.542257\pi$
$830$	0	0
$831$	−9.65722	−0.335005
$832$	−40.8976	−1.41787
$833$	−3.82753	−0.132616
$834$	−2.52082	−0.0872887
$835$	0	0
$836$	−53.3602	−1.84550
$837$	3.48532	0.120470
$838$	−1.01642	−0.0351116
$839$	37.6363	1.29935	0.649674	−	0.760213i	$-0.274905\pi$
$839$	37.6363	1.29935	0.649674	+	0.760213i	$0.274905\pi$
$840$	0	0
$841$	−27.8813	−0.961423
$842$	0.100060	0.00344828
$843$	−10.0865	−0.347397
$844$	−13.2514	−0.456131
$845$	0	0
$846$	2.88038	0.0990294
$847$	−0.393378	−0.0135166
$848$	−6.74300	−0.231556
$849$	18.0878	0.620773
$850$	0	0
$851$	8.93176	0.306177
$852$	26.8008	0.918182
$853$	22.9691	0.786446	0.393223	−	0.919443i	$-0.371360\pi$
$853$	22.9691	0.786446	0.393223	+	0.919443i	$0.371360\pi$
$854$	0.722077	0.0247090
$855$	0	0
$856$	0.0421418	0.00144038
$857$	34.5165	1.17906	0.589531	−	0.807746i	$-0.299313\pi$
$857$	34.5165	1.17906	0.589531	+	0.807746i	$0.299313\pi$
$858$	2.43614	0.0831683
$859$	9.87849	0.337050	0.168525	−	0.985697i	$-0.446100\pi$
$859$	9.87849	0.337050	0.168525	+	0.985697i	$0.446100\pi$
$860$	0	0
$861$	−1.47805	−0.0503718
$862$	0.712142	0.0242556
$863$	−38.5664	−1.31282	−0.656408	−	0.754407i	$-0.727925\pi$
$863$	−38.5664	−1.31282	−0.656408	+	0.754407i	$0.727925\pi$
$864$	8.19755	0.278886
$865$	0	0
$866$	3.96869	0.134862
$867$	1.94922	0.0661988
$868$	1.56239	0.0530308
$869$	−45.2760	−1.53588
$870$	0	0
$871$	31.8453	1.07904
$872$	0.101363	0.00343257
$873$	−0.345386	−0.0116895
$874$	1.26175	0.0426794
$875$	0	0
$876$	−6.37758	−0.215478
$877$	23.7187	0.800925	0.400463	−	0.916313i	$-0.368849\pi$
$877$	23.7187	0.800925	0.400463	+	0.916313i	$0.368849\pi$
$878$	−0.618947	−0.0208884
$879$	−6.10579	−0.205943
$880$	0	0
$881$	29.7544	1.00245	0.501226	−	0.865317i	$-0.332883\pi$
$881$	29.7544	1.00245	0.501226	+	0.865317i	$0.332883\pi$
$882$	−0.364476	−0.0122726
$883$	13.1231	0.441628	0.220814	−	0.975316i	$-0.429129\pi$
$883$	13.1231	0.441628	0.220814	+	0.975316i	$0.429129\pi$
$884$	41.7269	1.40343
$885$	0	0
$886$	−0.199762	−0.00671115
$887$	11.4014	0.382823	0.191411	−	0.981510i	$-0.438694\pi$
$887$	11.4014	0.382823	0.191411	+	0.981510i	$0.438694\pi$
$888$	−4.64268	−0.155798
$889$	−16.7400	−0.561441
$890$	0	0
$891$	−11.0757	−0.371052
$892$	23.5260	0.787710
$893$	63.2516	2.11663
$894$	0.201131	0.00672684
$895$	0	0
$896$	4.88912	0.163334
$897$	4.57818	0.152861
$898$	−3.53070	−0.117821
$899$	−0.836667	−0.0279044
$900$	0	0
$901$	6.70104	0.223244
$902$	0.948205	0.0315718
$903$	−6.08632	−0.202540
$904$	8.87033	0.295023
$905$	0	0
$906$	−1.58864	−0.0527789
$907$	−8.93752	−0.296765	−0.148383	−	0.988930i	$-0.547407\pi$
$907$	−8.93752	−0.296765	−0.148383	+	0.988930i	$0.547407\pi$
$908$	−21.3071	−0.707102
$909$	6.85974	0.227523
$910$	0	0
$911$	2.69061	0.0891440	0.0445720	−	0.999006i	$-0.485808\pi$
$911$	2.69061	0.0891440	0.0445720	+	0.999006i	$0.485808\pi$
$912$	25.5692	0.846682
$913$	7.49618	0.248087
$914$	0.464597	0.0153675
$915$	0	0
$916$	−23.2151	−0.767049
$917$	0.0130485	0.000430898 0
$918$	−2.65861	−0.0877473
$919$	−46.6833	−1.53994	−0.769971	−	0.638079i	$-0.779729\pi$
$919$	−46.6833	−1.53994	−0.769971	+	0.638079i	$0.779729\pi$
$920$	0	0
$921$	3.53488	0.116478
$922$	−5.23615	−0.172443
$923$	90.2922	2.97200
$924$	5.52996	0.181922
$925$	0	0
$926$	0.312300	0.0102628
$927$	−40.9742	−1.34577
$928$	−1.96786	−0.0645982
$929$	13.2823	0.435777	0.217889	−	0.975974i	$-0.430083\pi$
$929$	13.2823	0.435777	0.217889	+	0.975974i	$0.430083\pi$
$930$	0	0
$931$	−8.00372	−0.262311
$932$	−38.1829	−1.25072
$933$	−19.1596	−0.627256
$934$	5.09285	0.166643
$935$	0	0
$936$	7.99687	0.261386
$937$	51.7299	1.68994	0.844970	−	0.534813i	$-0.179618\pi$
$937$	51.7299	1.68994	0.844970	+	0.534813i	$0.179618\pi$
$938$	−0.909560	−0.0296982
$939$	25.1088	0.819394
$940$	0	0
$941$	17.9866	0.586346	0.293173	−	0.956059i	$-0.405289\pi$
$941$	17.9866	0.586346	0.293173	+	0.956059i	$0.405289\pi$
$942$	0.155941	0.00508083
$943$	1.78194	0.0580280
$944$	−6.21500	−0.202281
$945$	0	0
$946$	3.90452	0.126947
$947$	−55.0802	−1.78987	−0.894933	−	0.446201i	$-0.852777\pi$
$947$	−55.0802	−1.78987	−0.894933	+	0.446201i	$0.852777\pi$
$948$	21.9754	0.713728
$949$	−21.4861	−0.697468
$950$	0	0
$951$	20.8731	0.676857
$952$	−2.39858	−0.0777385
$953$	32.7886	1.06213	0.531063	−	0.847332i	$-0.321793\pi$
$953$	32.7886	1.06213	0.531063	+	0.847332i	$0.321793\pi$
$954$	0.638105	0.0206594
$955$	0	0
$956$	3.05796	0.0989015
$957$	−2.96132	−0.0957259
$958$	−1.32592	−0.0428385
$959$	18.1221	0.585193
$960$	0	0
$961$	−30.3743	−0.979816
$962$	−7.77172	−0.250570
$963$	0.155476	0.00501015
$964$	−12.5471	−0.404116
$965$	0	0
$966$	−0.130761	−0.00420717
$967$	4.88683	0.157150	0.0785749	−	0.996908i	$-0.474963\pi$
$967$	4.88683	0.157150	0.0785749	+	0.996908i	$0.474963\pi$
$968$	−0.246516	−0.00792333
$969$	−25.4101	−0.816291
$970$	0	0
$971$	−30.7346	−0.986319	−0.493159	−	0.869939i	$-0.664158\pi$
$971$	−30.7346	−0.986319	−0.493159	+	0.869939i	$0.664158\pi$
$972$	31.4838	1.00984
$973$	−19.2780	−0.618026
$974$	−4.37738	−0.140260
$975$	0	0
$976$	−17.6413	−0.564685
$977$	−26.4177	−0.845178	−0.422589	−	0.906321i	$-0.638879\pi$
$977$	−26.4177	−0.845178	−0.422589	+	0.906321i	$0.638879\pi$
$978$	−0.456730	−0.0146046
$979$	3.45462	0.110410
$980$	0	0
$981$	0.373963	0.0119397
$982$	−2.45585	−0.0783693
$983$	−39.3804	−1.25604	−0.628020	−	0.778198i	$-0.716134\pi$
$983$	−39.3804	−1.25604	−0.628020	+	0.778198i	$0.716134\pi$
$984$	−0.926243	−0.0295276
$985$	0	0
$986$	0.638212	0.0203248
$987$	−6.55504	−0.208649
$988$	87.2546	2.77594
$989$	7.33768	0.233325
$990$	0	0
$991$	16.3733	0.520114	0.260057	−	0.965593i	$-0.416259\pi$
$991$	16.3733	0.520114	0.260057	+	0.965593i	$0.416259\pi$
$992$	1.47170	0.0467265
$993$	8.50049	0.269755
$994$	−2.57891	−0.0817980
$995$	0	0
$996$	−3.63839	−0.115287
$997$	−55.9700	−1.77259	−0.886295	−	0.463122i	$-0.846729\pi$
$997$	−55.9700	−1.77259	−0.886295	+	0.463122i	$0.846729\pi$
$998$	−3.29458	−0.104288
$999$	−39.3542	−1.24511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bd.1.11		21
5.2	odd	4		805.2.c.c.484.22	yes	42
5.3	odd	4		805.2.c.c.484.21	✓	42
5.4	even	2		4025.2.a.be.1.11		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.21	✓	42	5.3	odd	4
805.2.c.c.484.22	yes	42	5.2	odd	4
4025.2.a.bd.1.11		21	1.1	even	1	trivial
4025.2.a.be.1.11		21	5.4	even	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.157646 q^{2} -0.829461 q^{3} -1.97515 q^{4} -0.130761 q^{6} -1.00000 q^{7} -0.626665 q^{8} -2.31200 q^{9} +O(q^{10})\)	\(q+0.157646 q^{2} -0.829461 q^{3} -1.97515 q^{4} -0.130761 q^{6} -1.00000 q^{7} -0.626665 q^{8} -2.31200 q^{9} -3.37541 q^{11} +1.63831 q^{12} +5.51947 q^{13} -0.157646 q^{14} +3.85150 q^{16} -3.82753 q^{17} -0.364476 q^{18} -8.00372 q^{19} +0.829461 q^{21} -0.532119 q^{22} -1.00000 q^{23} +0.519794 q^{24} +0.870121 q^{26} +4.40609 q^{27} +1.97515 q^{28} -1.05770 q^{29} +0.791022 q^{31} +1.86050 q^{32} +2.79977 q^{33} -0.603395 q^{34} +4.56653 q^{36} -8.93176 q^{37} -1.26175 q^{38} -4.57818 q^{39} -1.78194 q^{41} +0.130761 q^{42} -7.33768 q^{43} +6.66693 q^{44} -0.157646 q^{46} -7.90278 q^{47} -3.19467 q^{48} +1.00000 q^{49} +3.17479 q^{51} -10.9018 q^{52} -1.75075 q^{53} +0.694602 q^{54} +0.626665 q^{56} +6.63877 q^{57} -0.166742 q^{58} -1.61366 q^{59} -4.58037 q^{61} +0.124701 q^{62} +2.31200 q^{63} -7.40971 q^{64} +0.441372 q^{66} +5.76964 q^{67} +7.55995 q^{68} +0.829461 q^{69} +16.3589 q^{71} +1.44885 q^{72} -3.89278 q^{73} -1.40806 q^{74} +15.8085 q^{76} +3.37541 q^{77} -0.721731 q^{78} +13.4135 q^{79} +3.28131 q^{81} -0.280916 q^{82} -2.22082 q^{83} -1.63831 q^{84} -1.15676 q^{86} +0.877323 q^{87} +2.11525 q^{88} -1.02347 q^{89} -5.51947 q^{91} +1.97515 q^{92} -0.656122 q^{93} -1.24584 q^{94} -1.54322 q^{96} +0.149389 q^{97} +0.157646 q^{98} +7.80393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * q^99

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