LMFDB - Embedded newform 1925.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, 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("1925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.53919 q^{2} -1.17009 q^{3} +0.369102 q^{4} -1.80098 q^{6} +1.00000 q^{7} -2.51026 q^{8} -1.63090 q^{9} +O(q^{10})$	\(q+1.53919 q^{2} -1.17009 q^{3} +0.369102 q^{4} -1.80098 q^{6} +1.00000 q^{7} -2.51026 q^{8} -1.63090 q^{9} -1.00000 q^{11} -0.431882 q^{12} +0.0917087 q^{13} +1.53919 q^{14} -4.60197 q^{16} +5.51026 q^{17} -2.51026 q^{18} +0.921622 q^{19} -1.17009 q^{21} -1.53919 q^{22} +5.70928 q^{23} +2.93722 q^{24} +0.141157 q^{26} +5.41855 q^{27} +0.369102 q^{28} +1.41855 q^{29} +0.879362 q^{31} -2.06278 q^{32} +1.17009 q^{33} +8.48133 q^{34} -0.601968 q^{36} +8.78765 q^{37} +1.41855 q^{38} -0.107307 q^{39} -1.61757 q^{41} -1.80098 q^{42} -3.86603 q^{43} -0.369102 q^{44} +8.78765 q^{46} +5.90829 q^{47} +5.38470 q^{48} +1.00000 q^{49} -6.44748 q^{51} +0.0338499 q^{52} +10.0494 q^{53} +8.34017 q^{54} -2.51026 q^{56} -1.07838 q^{57} +2.18342 q^{58} -2.14116 q^{59} -3.03612 q^{61} +1.35350 q^{62} -1.63090 q^{63} +6.02893 q^{64} +1.80098 q^{66} +1.52586 q^{67} +2.03385 q^{68} -6.68035 q^{69} +4.09890 q^{71} +4.09398 q^{72} -14.1906 q^{73} +13.5259 q^{74} +0.340173 q^{76} -1.00000 q^{77} -0.165166 q^{78} +14.5464 q^{79} -1.44748 q^{81} -2.48974 q^{82} +8.52359 q^{83} -0.431882 q^{84} -5.95055 q^{86} -1.65983 q^{87} +2.51026 q^{88} -2.83710 q^{89} +0.0917087 q^{91} +2.10731 q^{92} -1.02893 q^{93} +9.09398 q^{94} +2.41363 q^{96} -14.2557 q^{97} +1.53919 q^{98} +1.63090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 5 q^{4} + 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 + 4 * q^6 + 3 * q^7 + 9 * q^8 - q^9	$ 3 q + 3 q^{2} + 2 q^{3} + 5 q^{4} + 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9} - 3 q^{11} + 12 q^{12} - 2 q^{13} + 3 q^{14} + 5 q^{16} + 9 q^{18} + 6 q^{19} + 2 q^{21} - 3 q^{22} + 10 q^{23} + 26 q^{24} - 20 q^{26} + 2 q^{27} + 5 q^{28} - 10 q^{29} - 10 q^{31} + 11 q^{32} - 2 q^{33} - 6 q^{34} + 17 q^{36} + 16 q^{37} - 10 q^{38} - 12 q^{39} + 4 q^{42} + 2 q^{43} - 5 q^{44} + 16 q^{46} + 20 q^{47} + 34 q^{48} + 3 q^{49} - 20 q^{51} - 32 q^{52} + 12 q^{53} + 14 q^{54} + 9 q^{56} + 2 q^{58} + 14 q^{59} + 10 q^{61} - 6 q^{62} - q^{63} + 33 q^{64} - 4 q^{66} + 2 q^{67} - 26 q^{68} + 2 q^{69} - 24 q^{71} + 23 q^{72} - 4 q^{73} + 38 q^{74} - 10 q^{76} - 3 q^{77} - 42 q^{78} + 8 q^{79} - 5 q^{81} - 24 q^{82} + 10 q^{83} + 12 q^{84} - 36 q^{86} - 16 q^{87} - 9 q^{88} + 20 q^{89} - 2 q^{91} + 18 q^{92} - 18 q^{93} + 38 q^{94} + 40 q^{96} + 3 q^{98} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 + 4 * q^6 + 3 * q^7 + 9 * q^8 - q^9 - 3 * q^11 + 12 * q^12 - 2 * q^13 + 3 * q^14 + 5 * q^16 + 9 * q^18 + 6 * q^19 + 2 * q^21 - 3 * q^22 + 10 * q^23 + 26 * q^24 - 20 * q^26 + 2 * q^27 + 5 * q^28 - 10 * q^29 - 10 * q^31 + 11 * q^32 - 2 * q^33 - 6 * q^34 + 17 * q^36 + 16 * q^37 - 10 * q^38 - 12 * q^39 + 4 * q^42 + 2 * q^43 - 5 * q^44 + 16 * q^46 + 20 * q^47 + 34 * q^48 + 3 * q^49 - 20 * q^51 - 32 * q^52 + 12 * q^53 + 14 * q^54 + 9 * q^56 + 2 * q^58 + 14 * q^59 + 10 * q^61 - 6 * q^62 - q^63 + 33 * q^64 - 4 * q^66 + 2 * q^67 - 26 * q^68 + 2 * q^69 - 24 * q^71 + 23 * q^72 - 4 * q^73 + 38 * q^74 - 10 * q^76 - 3 * q^77 - 42 * q^78 + 8 * q^79 - 5 * q^81 - 24 * q^82 + 10 * q^83 + 12 * q^84 - 36 * q^86 - 16 * q^87 - 9 * q^88 + 20 * q^89 - 2 * q^91 + 18 * q^92 - 18 * q^93 + 38 * q^94 + 40 * q^96 + 3 * q^98 + 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 $

$2$	1.53919	1.08837	0.544185	−	0.838965i	$-0.316839\pi$
$2$	1.53919	1.08837	0.544185	+	0.838965i	$0.316839\pi$
$3$	−1.17009	−0.675550	−0.337775	−	0.941227i	$-0.609674\pi$
$3$	−1.17009	−0.675550	−0.337775	+	0.941227i	$0.609674\pi$
$4$	0.369102	0.184551
$5$	0	0
$5$	0	0
$6$	−1.80098	−0.735249
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.51026	−0.887511
$9$	−1.63090	−0.543633
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.431882	−0.124674
$13$	0.0917087	0.0254354	0.0127177	−	0.999919i	$-0.495952\pi$
$13$	0.0917087	0.0254354	0.0127177	+	0.999919i	$0.495952\pi$
$14$	1.53919	0.411366
$15$	0	0
$16$	−4.60197	−1.15049
$17$	5.51026	1.33643	0.668217	−	0.743966i	$-0.267058\pi$
$17$	5.51026	1.33643	0.668217	+	0.743966i	$0.267058\pi$
$18$	−2.51026	−0.591674
$19$	0.921622	0.211435	0.105717	−	0.994396i	$-0.466286\pi$
$19$	0.921622	0.211435	0.105717	+	0.994396i	$0.466286\pi$
$20$	0	0
$21$	−1.17009	−0.255334
$22$	−1.53919	−0.328156
$23$	5.70928	1.19047	0.595233	−	0.803553i	$-0.297060\pi$
$23$	5.70928	1.19047	0.595233	+	0.803553i	$0.297060\pi$
$24$	2.93722	0.599558
$25$	0	0
$26$	0.141157	0.0276832
$27$	5.41855	1.04280
$28$	0.369102	0.0697538
$29$	1.41855	0.263418	0.131709	−	0.991288i	$-0.457954\pi$
$29$	1.41855	0.263418	0.131709	+	0.991288i	$0.457954\pi$
$30$	0	0
$31$	0.879362	0.157938	0.0789690	−	0.996877i	$-0.474837\pi$
$31$	0.879362	0.157938	0.0789690	+	0.996877i	$0.474837\pi$
$32$	−2.06278	−0.364651
$33$	1.17009	0.203686
$34$	8.48133	1.45454
$35$	0	0
$36$	−0.601968	−0.100328
$37$	8.78765	1.44468	0.722341	−	0.691537i	$-0.243066\pi$
$37$	8.78765	1.44468	0.722341	+	0.691537i	$0.243066\pi$
$38$	1.41855	0.230119
$39$	−0.107307	−0.0171829
$40$	0	0
$41$	−1.61757	−0.252621	−0.126311	−	0.991991i	$-0.540314\pi$
$41$	−1.61757	−0.252621	−0.126311	+	0.991991i	$0.540314\pi$
$42$	−1.80098	−0.277898
$43$	−3.86603	−0.589564	−0.294782	−	0.955565i	$-0.595247\pi$
$43$	−3.86603	−0.589564	−0.294782	+	0.955565i	$0.595247\pi$
$44$	−0.369102	−0.0556443
$45$	0	0
$46$	8.78765	1.29567
$47$	5.90829	0.861813	0.430906	−	0.902397i	$-0.358194\pi$
$47$	5.90829	0.861813	0.430906	+	0.902397i	$0.358194\pi$
$48$	5.38470	0.777215
$49$	1.00000	0.142857
$50$	0	0
$51$	−6.44748	−0.902828
$52$	0.0338499	0.00469414
$53$	10.0494	1.38040	0.690199	−	0.723620i	$-0.257523\pi$
$53$	10.0494	1.38040	0.690199	+	0.723620i	$0.257523\pi$
$54$	8.34017	1.13495
$55$	0	0
$56$	−2.51026	−0.335448
$57$	−1.07838	−0.142835
$58$	2.18342	0.286697
$59$	−2.14116	−0.278755	−0.139377	−	0.990239i	$-0.544510\pi$
$59$	−2.14116	−0.278755	−0.139377	+	0.990239i	$0.544510\pi$
$60$	0	0
$61$	−3.03612	−0.388735	−0.194367	−	0.980929i	$-0.562265\pi$
$61$	−3.03612	−0.388735	−0.194367	+	0.980929i	$0.562265\pi$
$62$	1.35350	0.171895
$63$	−1.63090	−0.205474
$64$	6.02893	0.753616
$65$	0	0
$66$	1.80098	0.221686
$67$	1.52586	0.186413	0.0932066	−	0.995647i	$-0.470288\pi$
$67$	1.52586	0.186413	0.0932066	+	0.995647i	$0.470288\pi$
$68$	2.03385	0.246641
$69$	−6.68035	−0.804219
$70$	0	0
$71$	4.09890	0.486450	0.243225	−	0.969970i	$-0.421795\pi$
$71$	4.09890	0.486450	0.243225	+	0.969970i	$0.421795\pi$
$72$	4.09398	0.482480
$73$	−14.1906	−1.66088	−0.830442	−	0.557105i	$-0.811912\pi$
$73$	−14.1906	−1.66088	−0.830442	+	0.557105i	$0.811912\pi$
$74$	13.5259	1.57235
$75$	0	0
$76$	0.340173	0.0390205
$77$	−1.00000	−0.113961
$78$	−0.165166	−0.0187014
$79$	14.5464	1.63660	0.818298	−	0.574795i	$-0.194918\pi$
$79$	14.5464	1.63660	0.818298	+	0.574795i	$0.194918\pi$
$80$	0	0
$81$	−1.44748	−0.160831
$82$	−2.48974	−0.274946
$83$	8.52359	0.935586	0.467793	−	0.883838i	$-0.345049\pi$
$83$	8.52359	0.935586	0.467793	+	0.883838i	$0.345049\pi$
$84$	−0.431882	−0.0471222
$85$	0	0
$86$	−5.95055	−0.641664
$87$	−1.65983	−0.177952
$88$	2.51026	0.267595
$89$	−2.83710	−0.300732	−0.150366	−	0.988630i	$-0.548045\pi$
$89$	−2.83710	−0.300732	−0.150366	+	0.988630i	$0.548045\pi$
$90$	0	0
$91$	0.0917087	0.00961369
$92$	2.10731	0.219702
$93$	−1.02893	−0.106695
$94$	9.09398	0.937972
$95$	0	0
$96$	2.41363	0.246340
$97$	−14.2557	−1.44744	−0.723721	−	0.690093i	$-0.757570\pi$
$97$	−14.2557	−1.44744	−0.723721	+	0.690093i	$0.757570\pi$
$98$	1.53919	0.155482
$99$	1.63090	0.163911
$100$	0	0
$101$	9.03612	0.899127	0.449564	−	0.893248i	$-0.351579\pi$
$101$	9.03612	0.899127	0.449564	+	0.893248i	$0.351579\pi$
$102$	−9.92389	−0.982611
$103$	−3.32684	−0.327803	−0.163902	−	0.986477i	$-0.552408\pi$
$103$	−3.32684	−0.327803	−0.163902	+	0.986477i	$0.552408\pi$
$104$	−0.230213	−0.0225742
$105$	0	0
$106$	15.4680	1.50238
$107$	−8.09890	−0.782950	−0.391475	−	0.920189i	$-0.628035\pi$
$107$	−8.09890	−0.782950	−0.391475	+	0.920189i	$0.628035\pi$
$108$	2.00000	0.192450
$109$	15.1773	1.45372	0.726860	−	0.686786i	$-0.240979\pi$
$109$	15.1773	1.45372	0.726860	+	0.686786i	$0.240979\pi$
$110$	0	0
$111$	−10.2823	−0.975954
$112$	−4.60197	−0.434845
$113$	7.07838	0.665878	0.332939	−	0.942948i	$-0.391960\pi$
$113$	7.07838	0.665878	0.332939	+	0.942948i	$0.391960\pi$
$114$	−1.65983	−0.155457
$115$	0	0
$116$	0.523590	0.0486142
$117$	−0.149568	−0.0138275
$118$	−3.29565	−0.303389
$119$	5.51026	0.505125
$120$	0	0
$121$	1.00000	0.0909091
$122$	−4.67316	−0.423088
$123$	1.89269	0.170658
$124$	0.324575	0.0291477
$125$	0	0
$126$	−2.51026	−0.223632
$127$	9.65983	0.857171	0.428586	−	0.903501i	$-0.359012\pi$
$127$	9.65983	0.857171	0.428586	+	0.903501i	$0.359012\pi$
$128$	13.4052	1.18487
$129$	4.52359	0.398280
$130$	0	0
$131$	4.68035	0.408924	0.204462	−	0.978875i	$-0.434456\pi$
$131$	4.68035	0.408924	0.204462	+	0.978875i	$0.434456\pi$
$132$	0.431882	0.0375905
$133$	0.921622	0.0799148
$134$	2.34858	0.202887
$135$	0	0
$136$	−13.8322	−1.18610
$137$	−8.88655	−0.759229	−0.379615	−	0.925145i	$-0.623943\pi$
$137$	−8.88655	−0.759229	−0.379615	+	0.925145i	$0.623943\pi$
$138$	−10.2823	−0.875289
$139$	−15.0205	−1.27402	−0.637012	−	0.770854i	$-0.719830\pi$
$139$	−15.0205	−1.27402	−0.637012	+	0.770854i	$0.719830\pi$
$140$	0	0
$141$	−6.91321	−0.582197
$142$	6.30898	0.529438
$143$	−0.0917087	−0.00766907
$144$	7.50534	0.625445
$145$	0	0
$146$	−21.8420	−1.80766
$147$	−1.17009	−0.0965071
$148$	3.24354	0.266618
$149$	−13.7009	−1.12242	−0.561209	−	0.827674i	$-0.689664\pi$
$149$	−13.7009	−1.12242	−0.561209	+	0.827674i	$0.689664\pi$
$150$	0	0
$151$	1.05559	0.0859028	0.0429514	−	0.999077i	$-0.486324\pi$
$151$	1.05559	0.0859028	0.0429514	+	0.999077i	$0.486324\pi$
$152$	−2.31351	−0.187651
$153$	−8.98667	−0.726529
$154$	−1.53919	−0.124031
$155$	0	0
$156$	−0.0396073	−0.00317112
$157$	17.7587	1.41730	0.708650	−	0.705560i	$-0.249304\pi$
$157$	17.7587	1.41730	0.708650	+	0.705560i	$0.249304\pi$
$158$	22.3896	1.78122
$159$	−11.7587	−0.932527
$160$	0	0
$161$	5.70928	0.449954
$162$	−2.22795	−0.175044
$163$	11.4680	0.898243	0.449122	−	0.893471i	$-0.351737\pi$
$163$	11.4680	0.898243	0.449122	+	0.893471i	$0.351737\pi$
$164$	−0.597048	−0.0466216
$165$	0	0
$166$	13.1194	1.01826
$167$	5.60197	0.433493	0.216747	−	0.976228i	$-0.430455\pi$
$167$	5.60197	0.433493	0.216747	+	0.976228i	$0.430455\pi$
$168$	2.93722	0.226611
$169$	−12.9916	−0.999353
$170$	0	0
$171$	−1.50307	−0.114943
$172$	−1.42696	−0.108805
$173$	−21.6092	−1.64291	−0.821457	−	0.570271i	$-0.806838\pi$
$173$	−21.6092	−1.64291	−0.821457	+	0.570271i	$0.806838\pi$
$174$	−2.55479	−0.193678
$175$	0	0
$176$	4.60197	0.346886
$177$	2.50534	0.188313
$178$	−4.36683	−0.327308
$179$	−2.05786	−0.153812	−0.0769058	−	0.997038i	$-0.524504\pi$
$179$	−2.05786	−0.153812	−0.0769058	+	0.997038i	$0.524504\pi$
$180$	0	0
$181$	20.2823	1.50757	0.753786	−	0.657120i	$-0.228225\pi$
$181$	20.2823	1.50757	0.753786	+	0.657120i	$0.228225\pi$
$182$	0.141157	0.0104633
$183$	3.55252	0.262610
$184$	−14.3318	−1.05655
$185$	0	0
$186$	−1.58372	−0.116124
$187$	−5.51026	−0.402950
$188$	2.18076	0.159049
$189$	5.41855	0.394142
$190$	0	0
$191$	−20.2823	−1.46758	−0.733788	−	0.679378i	$-0.762250\pi$
$191$	−20.2823	−1.46758	−0.733788	+	0.679378i	$0.762250\pi$
$192$	−7.05437	−0.509105
$193$	24.3051	1.74952	0.874760	−	0.484557i	$-0.161019\pi$
$193$	24.3051	1.74952	0.874760	+	0.484557i	$0.161019\pi$
$194$	−21.9421	−1.57535
$195$	0	0
$196$	0.369102	0.0263645
$197$	14.1483	1.00803	0.504014	−	0.863696i	$-0.331856\pi$
$197$	14.1483	1.00803	0.504014	+	0.863696i	$0.331856\pi$
$198$	2.51026	0.178396
$199$	10.4813	0.743002	0.371501	−	0.928433i	$-0.378843\pi$
$199$	10.4813	0.743002	0.371501	+	0.928433i	$0.378843\pi$
$200$	0	0
$201$	−1.78539	−0.125931
$202$	13.9083	0.978584
$203$	1.41855	0.0995627
$204$	−2.37978	−0.166618
$205$	0	0
$206$	−5.12064	−0.356772
$207$	−9.31124	−0.647176
$208$	−0.422041	−0.0292633
$209$	−0.921622	−0.0637499
$210$	0	0
$211$	−2.65368	−0.182687	−0.0913436	−	0.995819i	$-0.529116\pi$
$211$	−2.65368	−0.182687	−0.0913436	+	0.995819i	$0.529116\pi$
$212$	3.70928	0.254754
$213$	−4.79606	−0.328621
$214$	−12.4657	−0.852140
$215$	0	0
$216$	−13.6020	−0.925497
$217$	0.879362	0.0596950
$218$	23.3607	1.58219
$219$	16.6042	1.12201
$220$	0	0
$221$	0.505339	0.0339928
$222$	−15.8264	−1.06220
$223$	8.67316	0.580798	0.290399	−	0.956906i	$-0.406212\pi$
$223$	8.67316	0.580798	0.290399	+	0.956906i	$0.406212\pi$
$224$	−2.06278	−0.137825
$225$	0	0
$226$	10.8950	0.724722
$227$	−9.67420	−0.642099	−0.321050	−	0.947062i	$-0.604036\pi$
$227$	−9.67420	−0.642099	−0.321050	+	0.947062i	$0.604036\pi$
$228$	−0.398032	−0.0263603
$229$	−13.5486	−0.895320	−0.447660	−	0.894204i	$-0.647742\pi$
$229$	−13.5486	−0.895320	−0.447660	+	0.894204i	$0.647742\pi$
$230$	0	0
$231$	1.17009	0.0769860
$232$	−3.56093	−0.233787
$233$	−8.38962	−0.549622	−0.274811	−	0.961498i	$-0.588615\pi$
$233$	−8.38962	−0.549622	−0.274811	+	0.961498i	$0.588615\pi$
$234$	−0.230213	−0.0150495
$235$	0	0
$236$	−0.790306	−0.0514446
$237$	−17.0205	−1.10560
$238$	8.48133	0.549763
$239$	−29.4908	−1.90760	−0.953800	−	0.300442i	$-0.902866\pi$
$239$	−29.4908	−1.90760	−0.953800	+	0.300442i	$0.902866\pi$
$240$	0	0
$241$	3.64423	0.234745	0.117373	−	0.993088i	$-0.462553\pi$
$241$	3.64423	0.234745	0.117373	+	0.993088i	$0.462553\pi$
$242$	1.53919	0.0989428
$243$	−14.5620	−0.934151
$244$	−1.12064	−0.0717415
$245$	0	0
$246$	2.91321	0.185740
$247$	0.0845208	0.00537793
$248$	−2.20743	−0.140172
$249$	−9.97334	−0.632035
$250$	0	0
$251$	23.1350	1.46027	0.730135	−	0.683303i	$-0.239457\pi$
$251$	23.1350	1.46027	0.730135	+	0.683303i	$0.239457\pi$
$252$	−0.601968	−0.0379204
$253$	−5.70928	−0.358939
$254$	14.8683	0.932920
$255$	0	0
$256$	8.57531	0.535957
$257$	−20.8104	−1.29812	−0.649060	−	0.760737i	$-0.724838\pi$
$257$	−20.8104	−1.29812	−0.649060	+	0.760737i	$0.724838\pi$
$258$	6.96266	0.433476
$259$	8.78765	0.546038
$260$	0	0
$261$	−2.31351	−0.143203
$262$	7.20394	0.445061
$263$	23.7009	1.46146	0.730729	−	0.682668i	$-0.239180\pi$
$263$	23.7009	1.46146	0.730729	+	0.682668i	$0.239180\pi$
$264$	−2.93722	−0.180773
$265$	0	0
$266$	1.41855	0.0869769
$267$	3.31965	0.203160
$268$	0.563198	0.0344028
$269$	−3.50307	−0.213586	−0.106793	−	0.994281i	$-0.534058\pi$
$269$	−3.50307	−0.213586	−0.106793	+	0.994281i	$0.534058\pi$
$270$	0	0
$271$	−8.49693	−0.516152	−0.258076	−	0.966125i	$-0.583088\pi$
$271$	−8.49693	−0.516152	−0.258076	+	0.966125i	$0.583088\pi$
$272$	−25.3580	−1.53756
$273$	−0.107307	−0.00649452
$274$	−13.6781	−0.826323
$275$	0	0
$276$	−2.46573	−0.148420
$277$	25.9649	1.56008	0.780041	−	0.625729i	$-0.215198\pi$
$277$	25.9649	1.56008	0.780041	+	0.625729i	$0.215198\pi$
$278$	−23.1194	−1.38661
$279$	−1.43415	−0.0858603
$280$	0	0
$281$	11.6742	0.696425	0.348212	−	0.937416i	$-0.386789\pi$
$281$	11.6742	0.696425	0.348212	+	0.937416i	$0.386789\pi$
$282$	−10.6407	−0.633647
$283$	14.2557	0.847411	0.423705	−	0.905800i	$-0.360729\pi$
$283$	14.2557	0.847411	0.423705	+	0.905800i	$0.360729\pi$
$284$	1.51291	0.0897748
$285$	0	0
$286$	−0.141157	−0.00834679
$287$	−1.61757	−0.0954819
$288$	3.36418	0.198236
$289$	13.3630	0.786056
$290$	0	0
$291$	16.6803	0.977819
$292$	−5.23779	−0.306518
$293$	−25.1122	−1.46707	−0.733536	−	0.679651i	$-0.762131\pi$
$293$	−25.1122	−1.46707	−0.733536	+	0.679651i	$0.762131\pi$
$294$	−1.80098	−0.105036
$295$	0	0
$296$	−22.0593	−1.28217
$297$	−5.41855	−0.314416
$298$	−21.0882	−1.22161
$299$	0.523590	0.0302800
$300$	0	0
$301$	−3.86603	−0.222834
$302$	1.62475	0.0934941
$303$	−10.5730	−0.607405
$304$	−4.24128	−0.243254
$305$	0	0
$306$	−13.8322	−0.790733
$307$	−8.02666	−0.458106	−0.229053	−	0.973414i	$-0.573563\pi$
$307$	−8.02666	−0.458106	−0.229053	+	0.973414i	$0.573563\pi$
$308$	−0.369102	−0.0210316
$309$	3.89269	0.221448
$310$	0	0
$311$	−26.3968	−1.49683	−0.748413	−	0.663233i	$-0.769184\pi$
$311$	−26.3968	−1.49683	−0.748413	+	0.663233i	$0.769184\pi$
$312$	0.269369	0.0152500
$313$	−25.7321	−1.45446	−0.727231	−	0.686393i	$-0.759193\pi$
$313$	−25.7321	−1.45446	−0.727231	+	0.686393i	$0.759193\pi$
$314$	27.3340	1.54255
$315$	0	0
$316$	5.36910	0.302036
$317$	−6.31351	−0.354602	−0.177301	−	0.984157i	$-0.556737\pi$
$317$	−6.31351	−0.354602	−0.177301	+	0.984157i	$0.556737\pi$
$318$	−18.0989	−1.01494
$319$	−1.41855	−0.0794236
$320$	0	0
$321$	9.47641	0.528922
$322$	8.78765	0.489717
$323$	5.07838	0.282568
$324$	−0.534268	−0.0296816
$325$	0	0
$326$	17.6514	0.977622
$327$	−17.7587	−0.982060
$328$	4.06051	0.224204
$329$	5.90829	0.325735
$330$	0	0
$331$	3.50307	0.192546	0.0962731	−	0.995355i	$-0.469308\pi$
$331$	3.50307	0.192546	0.0962731	+	0.995355i	$0.469308\pi$
$332$	3.14608	0.172663
$333$	−14.3318	−0.785376
$334$	8.62249	0.471802
$335$	0	0
$336$	5.38470	0.293760
$337$	−7.57918	−0.412864	−0.206432	−	0.978461i	$-0.566185\pi$
$337$	−7.57918	−0.412864	−0.206432	+	0.978461i	$0.566185\pi$
$338$	−19.9965	−1.08767
$339$	−8.28231	−0.449834
$340$	0	0
$341$	−0.879362	−0.0476201
$342$	−2.31351	−0.125100
$343$	1.00000	0.0539949
$344$	9.70474	0.523245
$345$	0	0
$346$	−33.2606	−1.78810
$347$	35.4824	1.90479	0.952397	−	0.304861i	$-0.0986100\pi$
$347$	35.4824	1.90479	0.952397	+	0.304861i	$0.0986100\pi$
$348$	−0.612646	−0.0328413
$349$	−13.6586	−0.731128	−0.365564	−	0.930786i	$-0.619124\pi$
$349$	−13.6586	−0.731128	−0.365564	+	0.930786i	$0.619124\pi$
$350$	0	0
$351$	0.496928	0.0265241
$352$	2.06278	0.109947
$353$	−26.4657	−1.40863	−0.704314	−	0.709888i	$-0.748745\pi$
$353$	−26.4657	−1.40863	−0.704314	+	0.709888i	$0.748745\pi$
$354$	3.85619	0.204954
$355$	0	0
$356$	−1.04718	−0.0555005
$357$	−6.44748	−0.341237
$358$	−3.16743	−0.167404
$359$	−15.3958	−0.812557	−0.406279	−	0.913749i	$-0.633174\pi$
$359$	−15.3958	−0.812557	−0.406279	+	0.913749i	$0.633174\pi$
$360$	0	0
$361$	−18.1506	−0.955295
$362$	31.2183	1.64080
$363$	−1.17009	−0.0614136
$364$	0.0338499	0.00177422
$365$	0	0
$366$	5.46800	0.285817
$367$	34.6875	1.81067	0.905337	−	0.424693i	$-0.139618\pi$
$367$	34.6875	1.81067	0.905337	+	0.424693i	$0.139618\pi$
$368$	−26.2739	−1.36962
$369$	2.63809	0.137333
$370$	0	0
$371$	10.0494	0.521741
$372$	−0.379780	−0.0196907
$373$	−36.3584	−1.88257	−0.941284	−	0.337616i	$-0.890379\pi$
$373$	−36.3584	−1.88257	−0.941284	+	0.337616i	$0.890379\pi$
$374$	−8.48133	−0.438559
$375$	0	0
$376$	−14.8313	−0.764868
$377$	0.130094	0.00670016
$378$	8.34017	0.428972
$379$	−33.1461	−1.70260	−0.851300	−	0.524680i	$-0.824185\pi$
$379$	−33.1461	−1.70260	−0.851300	+	0.524680i	$0.824185\pi$
$380$	0	0
$381$	−11.3028	−0.579062
$382$	−31.2183	−1.59727
$383$	34.2628	1.75075	0.875375	−	0.483445i	$-0.160615\pi$
$383$	34.2628	1.75075	0.875375	+	0.483445i	$0.160615\pi$
$384$	−15.6853	−0.800435
$385$	0	0
$386$	37.4101	1.90413
$387$	6.30510	0.320506
$388$	−5.26180	−0.267127
$389$	23.2762	1.18015	0.590074	−	0.807349i	$-0.299098\pi$
$389$	23.2762	1.18015	0.590074	+	0.807349i	$0.299098\pi$
$390$	0	0
$391$	31.4596	1.59098
$392$	−2.51026	−0.126787
$393$	−5.47641	−0.276248
$394$	21.7770	1.09711
$395$	0	0
$396$	0.601968	0.0302500
$397$	29.8576	1.49851	0.749256	−	0.662281i	$-0.230412\pi$
$397$	29.8576	1.49851	0.749256	+	0.662281i	$0.230412\pi$
$398$	16.1327	0.808662
$399$	−1.07838	−0.0539864
$400$	0	0
$401$	−5.51745	−0.275528	−0.137764	−	0.990465i	$-0.543992\pi$
$401$	−5.51745	−0.275528	−0.137764	+	0.990465i	$0.543992\pi$
$402$	−2.74805	−0.137060
$403$	0.0806452	0.00401722
$404$	3.33525	0.165935
$405$	0	0
$406$	2.18342	0.108361
$407$	−8.78765	−0.435588
$408$	16.1848	0.801269
$409$	−3.43415	−0.169808	−0.0849039	−	0.996389i	$-0.527058\pi$
$409$	−3.43415	−0.169808	−0.0849039	+	0.996389i	$0.527058\pi$
$410$	0	0
$411$	10.3980	0.512897
$412$	−1.22795	−0.0604965
$413$	−2.14116	−0.105359
$414$	−14.3318	−0.704368
$415$	0	0
$416$	−0.189175	−0.00927506
$417$	17.5753	0.860666
$418$	−1.41855	−0.0693836
$419$	18.2134	0.889782	0.444891	−	0.895585i	$-0.353242\pi$
$419$	18.2134	0.889782	0.444891	+	0.895585i	$0.353242\pi$
$420$	0	0
$421$	10.6576	0.519418	0.259709	−	0.965687i	$-0.416373\pi$
$421$	10.6576	0.519418	0.259709	+	0.965687i	$0.416373\pi$
$422$	−4.08452	−0.198831
$423$	−9.63582	−0.468510
$424$	−25.2267	−1.22512
$425$	0	0
$426$	−7.38205	−0.357661
$427$	−3.03612	−0.146928
$428$	−2.98932	−0.144494
$429$	0.107307	0.00518084
$430$	0	0
$431$	−7.61038	−0.366579	−0.183290	−	0.983059i	$-0.558675\pi$
$431$	−7.61038	−0.366579	−0.183290	+	0.983059i	$0.558675\pi$
$432$	−24.9360	−1.19973
$433$	−33.5318	−1.61144	−0.805718	−	0.592299i	$-0.798220\pi$
$433$	−33.5318	−1.61144	−0.805718	+	0.592299i	$0.798220\pi$
$434$	1.35350	0.0649703
$435$	0	0
$436$	5.60197	0.268286
$437$	5.26180	0.251706
$438$	25.5571	1.22116
$439$	−13.7587	−0.656668	−0.328334	−	0.944562i	$-0.606487\pi$
$439$	−13.7587	−0.656668	−0.328334	+	0.944562i	$0.606487\pi$
$440$	0	0
$441$	−1.63090	−0.0776618
$442$	0.777812	0.0369967
$443$	11.1689	0.530649	0.265324	−	0.964159i	$-0.414521\pi$
$443$	11.1689	0.530649	0.265324	+	0.964159i	$0.414521\pi$
$444$	−3.79523	−0.180113
$445$	0	0
$446$	13.3496	0.632123
$447$	16.0312	0.758250
$448$	6.02893	0.284840
$449$	−19.0700	−0.899967	−0.449984	−	0.893037i	$-0.648570\pi$
$449$	−19.0700	−0.899967	−0.449984	+	0.893037i	$0.648570\pi$
$450$	0	0
$451$	1.61757	0.0761682
$452$	2.61265	0.122889
$453$	−1.23513	−0.0580316
$454$	−14.8904	−0.698842
$455$	0	0
$456$	2.70701	0.126767
$457$	0.787653	0.0368449	0.0184224	−	0.999830i	$-0.494136\pi$
$457$	0.787653	0.0368449	0.0184224	+	0.999830i	$0.494136\pi$
$458$	−20.8539	−0.974440
$459$	29.8576	1.39363
$460$	0	0
$461$	25.5864	1.19168	0.595838	−	0.803105i	$-0.296820\pi$
$461$	25.5864	1.19168	0.595838	+	0.803105i	$0.296820\pi$
$462$	1.80098	0.0837894
$463$	14.2595	0.662696	0.331348	−	0.943509i	$-0.392497\pi$
$463$	14.2595	0.662696	0.331348	+	0.943509i	$0.392497\pi$
$464$	−6.52813	−0.303061
$465$	0	0
$466$	−12.9132	−0.598193
$467$	−18.3474	−0.849015	−0.424507	−	0.905425i	$-0.639553\pi$
$467$	−18.3474	−0.849015	−0.424507	+	0.905425i	$0.639553\pi$
$468$	−0.0552057	−0.00255189
$469$	1.52586	0.0704576
$470$	0	0
$471$	−20.7792	−0.957457
$472$	5.37486	0.247398
$473$	3.86603	0.177760
$474$	−26.1978	−1.20330
$475$	0	0
$476$	2.03385	0.0932214
$477$	−16.3896	−0.750429
$478$	−45.3919	−2.07618
$479$	12.1711	0.556113	0.278057	−	0.960565i	$-0.410310\pi$
$479$	12.1711	0.556113	0.278057	+	0.960565i	$0.410310\pi$
$480$	0	0
$481$	0.805905	0.0367461
$482$	5.60916	0.255490
$483$	−6.68035	−0.303966
$484$	0.369102	0.0167774
$485$	0	0
$486$	−22.4136	−1.01670
$487$	4.23287	0.191809	0.0959047	−	0.995391i	$-0.469426\pi$
$487$	4.23287	0.191809	0.0959047	+	0.995391i	$0.469426\pi$
$488$	7.62144	0.345006
$489$	−13.4186	−0.606808
$490$	0	0
$491$	22.0183	0.993670	0.496835	−	0.867845i	$-0.334495\pi$
$491$	22.0183	0.993670	0.496835	+	0.867845i	$0.334495\pi$
$492$	0.698597	0.0314952
$493$	7.81658	0.352041
$494$	0.130094	0.00585318
$495$	0	0
$496$	−4.04680	−0.181706
$497$	4.09890	0.183861
$498$	−15.3509	−0.687888
$499$	32.9939	1.47701	0.738504	−	0.674249i	$-0.235533\pi$
$499$	32.9939	1.47701	0.738504	+	0.674249i	$0.235533\pi$
$500$	0	0
$501$	−6.55479	−0.292846
$502$	35.6092	1.58931
$503$	29.0349	1.29460	0.647301	−	0.762235i	$-0.275898\pi$
$503$	29.0349	1.29460	0.647301	+	0.762235i	$0.275898\pi$
$504$	4.09398	0.182360
$505$	0	0
$506$	−8.78765	−0.390659
$507$	15.2013	0.675113
$508$	3.56547	0.158192
$509$	−21.5031	−0.953107	−0.476553	−	0.879146i	$-0.658114\pi$
$509$	−21.5031	−0.953107	−0.476553	+	0.879146i	$0.658114\pi$
$510$	0	0
$511$	−14.1906	−0.627755
$512$	−13.6114	−0.601546
$513$	4.99386	0.220484
$514$	−32.0312	−1.41284
$515$	0	0
$516$	1.66967	0.0735030
$517$	−5.90829	−0.259846
$518$	13.5259	0.594292
$519$	25.2846	1.10987
$520$	0	0
$521$	24.5958	1.07756	0.538781	−	0.842446i	$-0.318885\pi$
$521$	24.5958	1.07756	0.538781	+	0.842446i	$0.318885\pi$
$522$	−3.56093	−0.155858
$523$	−38.0677	−1.66458	−0.832292	−	0.554337i	$-0.812972\pi$
$523$	−38.0677	−1.66458	−0.832292	+	0.554337i	$0.812972\pi$
$524$	1.72753	0.0754674
$525$	0	0
$526$	36.4801	1.59061
$527$	4.84551	0.211074
$528$	−5.38470	−0.234339
$529$	9.59583	0.417210
$530$	0	0
$531$	3.49201	0.151540
$532$	0.340173	0.0147484
$533$	−0.148345	−0.00642554
$534$	5.10957	0.221113
$535$	0	0
$536$	−3.83030	−0.165444
$537$	2.40787	0.103907
$538$	−5.39189	−0.232461
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	2.13009	0.0915799	0.0457899	−	0.998951i	$-0.485420\pi$
$541$	2.13009	0.0915799	0.0457899	+	0.998951i	$0.485420\pi$
$542$	−13.0784	−0.561764
$543$	−23.7321	−1.01844
$544$	−11.3664	−0.487332
$545$	0	0
$546$	−0.165166	−0.00706845
$547$	9.13170	0.390443	0.195222	−	0.980759i	$-0.437457\pi$
$547$	9.13170	0.390443	0.195222	+	0.980759i	$0.437457\pi$
$548$	−3.28005	−0.140117
$549$	4.95160	0.211329
$550$	0	0
$551$	1.30737	0.0556957
$552$	16.7694	0.713753
$553$	14.5464	0.618575
$554$	39.9649	1.69795
$555$	0	0
$556$	−5.54411	−0.235123
$557$	11.7093	0.496138	0.248069	−	0.968742i	$-0.420204\pi$
$557$	11.7093	0.496138	0.248069	+	0.968742i	$0.420204\pi$
$558$	−2.20743	−0.0934478
$559$	−0.354549	−0.0149958
$560$	0	0
$561$	6.44748	0.272213
$562$	17.9688	0.757968
$563$	−12.5958	−0.530851	−0.265425	−	0.964131i	$-0.585512\pi$
$563$	−12.5958	−0.530851	−0.265425	+	0.964131i	$0.585512\pi$
$564$	−2.55168	−0.107445
$565$	0	0
$566$	21.9421	0.922297
$567$	−1.44748	−0.0607885
$568$	−10.2893	−0.431729
$569$	7.54411	0.316266	0.158133	−	0.987418i	$-0.449453\pi$
$569$	7.54411	0.316266	0.158133	+	0.987418i	$0.449453\pi$
$570$	0	0
$571$	36.8104	1.54047	0.770234	−	0.637761i	$-0.220139\pi$
$571$	36.8104	1.54047	0.770234	+	0.637761i	$0.220139\pi$
$572$	−0.0338499	−0.00141534
$573$	23.7321	0.991421
$574$	−2.48974	−0.103920
$575$	0	0
$576$	−9.83257	−0.409690
$577$	39.5174	1.64513	0.822566	−	0.568669i	$-0.192541\pi$
$577$	39.5174	1.64513	0.822566	+	0.568669i	$0.192541\pi$
$578$	20.5681	0.855521
$579$	−28.4391	−1.18189
$580$	0	0
$581$	8.52359	0.353618
$582$	25.6742	1.06423
$583$	−10.0494	−0.416206
$584$	35.6221	1.47405
$585$	0	0
$586$	−38.6525	−1.59672
$587$	−1.56812	−0.0647232	−0.0323616	−	0.999476i	$-0.510303\pi$
$587$	−1.56812	−0.0647232	−0.0323616	+	0.999476i	$0.510303\pi$
$588$	−0.431882	−0.0178105
$589$	0.810439	0.0333936
$590$	0	0
$591$	−16.5548	−0.680973
$592$	−40.4405	−1.66209
$593$	−4.95547	−0.203497	−0.101748	−	0.994810i	$-0.532444\pi$
$593$	−4.95547	−0.203497	−0.101748	+	0.994810i	$0.532444\pi$
$594$	−8.34017	−0.342201
$595$	0	0
$596$	−5.05702	−0.207144
$597$	−12.2641	−0.501935
$598$	0.805905	0.0329559
$599$	−12.3668	−0.505295	−0.252648	−	0.967558i	$-0.581301\pi$
$599$	−12.3668	−0.505295	−0.252648	+	0.967558i	$0.581301\pi$
$600$	0	0
$601$	24.9516	1.01780	0.508898	−	0.860827i	$-0.330053\pi$
$601$	24.9516	1.01780	0.508898	+	0.860827i	$0.330053\pi$
$602$	−5.95055	−0.242526
$603$	−2.48852	−0.101340
$604$	0.389621	0.0158535
$605$	0	0
$606$	−16.2739	−0.661082
$607$	19.2762	0.782396	0.391198	−	0.920307i	$-0.372061\pi$
$607$	19.2762	0.782396	0.391198	+	0.920307i	$0.372061\pi$
$608$	−1.90110	−0.0770999
$609$	−1.65983	−0.0672596
$610$	0	0
$611$	0.541842	0.0219206
$612$	−3.31700	−0.134082
$613$	42.6986	1.72458	0.862290	−	0.506415i	$-0.169029\pi$
$613$	42.6986	1.72458	0.862290	+	0.506415i	$0.169029\pi$
$614$	−12.3545	−0.498589
$615$	0	0
$616$	2.51026	0.101141
$617$	−31.7770	−1.27929	−0.639646	−	0.768669i	$-0.720919\pi$
$617$	−31.7770	−1.27929	−0.639646	+	0.768669i	$0.720919\pi$
$618$	5.99159	0.241017
$619$	−19.8420	−0.797518	−0.398759	−	0.917056i	$-0.630559\pi$
$619$	−19.8420	−0.797518	−0.398759	+	0.917056i	$0.630559\pi$
$620$	0	0
$621$	30.9360	1.24142
$622$	−40.6297	−1.62910
$623$	−2.83710	−0.113666
$624$	0.493824	0.0197688
$625$	0	0
$626$	−39.6065	−1.58299
$627$	1.07838	0.0430663
$628$	6.55479	0.261564
$629$	48.4222	1.93072
$630$	0	0
$631$	−3.63317	−0.144634	−0.0723170	−	0.997382i	$-0.523039\pi$
$631$	−3.63317	−0.144634	−0.0723170	+	0.997382i	$0.523039\pi$
$632$	−36.5152	−1.45250
$633$	3.10504	0.123414
$634$	−9.71769	−0.385939
$635$	0	0
$636$	−4.34017	−0.172099
$637$	0.0917087	0.00363363
$638$	−2.18342	−0.0864423
$639$	−6.68488	−0.264450
$640$	0	0
$641$	37.5402	1.48275	0.741375	−	0.671091i	$-0.234174\pi$
$641$	37.5402	1.48275	0.741375	+	0.671091i	$0.234174\pi$
$642$	14.5860	0.575663
$643$	34.8710	1.37518	0.687588	−	0.726101i	$-0.258670\pi$
$643$	34.8710	1.37518	0.687588	+	0.726101i	$0.258670\pi$
$644$	2.10731	0.0830395
$645$	0	0
$646$	7.81658	0.307539
$647$	−30.6342	−1.20436	−0.602178	−	0.798362i	$-0.705700\pi$
$647$	−30.6342	−1.20436	−0.602178	+	0.798362i	$0.705700\pi$
$648$	3.63355	0.142739
$649$	2.14116	0.0840478
$650$	0	0
$651$	−1.02893	−0.0403269
$652$	4.23287	0.165772
$653$	−5.40417	−0.211482	−0.105741	−	0.994394i	$-0.533721\pi$
$653$	−5.40417	−0.211482	−0.105741	+	0.994394i	$0.533721\pi$
$654$	−27.3340	−1.06885
$655$	0	0
$656$	7.44399	0.290639
$657$	23.1434	0.902911
$658$	9.09398	0.354520
$659$	−19.4101	−0.756112	−0.378056	−	0.925783i	$-0.623407\pi$
$659$	−19.4101	−0.756112	−0.378056	+	0.925783i	$0.623407\pi$
$660$	0	0
$661$	−26.3090	−1.02330	−0.511650	−	0.859194i	$-0.670966\pi$
$661$	−26.3090	−1.02330	−0.511650	+	0.859194i	$0.670966\pi$
$662$	5.39189	0.209562
$663$	−0.591290	−0.0229638
$664$	−21.3964	−0.830342
$665$	0	0
$666$	−22.0593	−0.854780
$667$	8.09890	0.313591
$668$	2.06770	0.0800017
$669$	−10.1483	−0.392358
$670$	0	0
$671$	3.03612	0.117208
$672$	2.41363	0.0931078
$673$	15.7938	0.608806	0.304403	−	0.952543i	$-0.401543\pi$
$673$	15.7938	0.608806	0.304403	+	0.952543i	$0.401543\pi$
$674$	−11.6658	−0.449350
$675$	0	0
$676$	−4.79523	−0.184432
$677$	15.7081	0.603710	0.301855	−	0.953354i	$-0.402394\pi$
$677$	15.7081	0.603710	0.301855	+	0.953354i	$0.402394\pi$
$678$	−12.7480	−0.489586
$679$	−14.2557	−0.547082
$680$	0	0
$681$	11.3197	0.433770
$682$	−1.35350	−0.0518283
$683$	44.0326	1.68486	0.842431	−	0.538805i	$-0.181124\pi$
$683$	44.0326	1.68486	0.842431	+	0.538805i	$0.181124\pi$
$684$	−0.554787	−0.0212128
$685$	0	0
$686$	1.53919	0.0587665
$687$	15.8531	0.604833
$688$	17.7914	0.678289
$689$	0.921622	0.0351110
$690$	0	0
$691$	4.63809	0.176441	0.0882205	−	0.996101i	$-0.471882\pi$
$691$	4.63809	0.176441	0.0882205	+	0.996101i	$0.471882\pi$
$692$	−7.97599	−0.303202
$693$	1.63090	0.0619527
$694$	54.6141	2.07312
$695$	0	0
$696$	4.16660	0.157934
$697$	−8.91321	−0.337612
$698$	−21.0232	−0.795739
$699$	9.81658	0.371297
$700$	0	0
$701$	−14.6491	−0.553291	−0.276645	−	0.960972i	$-0.589223\pi$
$701$	−14.6491	−0.553291	−0.276645	+	0.960972i	$0.589223\pi$
$702$	0.764867	0.0288680
$703$	8.09890	0.305456
$704$	−6.02893	−0.227224
$705$	0	0
$706$	−40.7358	−1.53311
$707$	9.03612	0.339838
$708$	0.924727	0.0347534
$709$	−25.5174	−0.958328	−0.479164	−	0.877725i	$-0.659060\pi$
$709$	−25.5174	−0.958328	−0.479164	+	0.877725i	$0.659060\pi$
$710$	0	0
$711$	−23.7237	−0.889706
$712$	7.12186	0.266903
$713$	5.02052	0.188020
$714$	−9.92389	−0.371392
$715$	0	0
$716$	−0.759561	−0.0283861
$717$	34.5068	1.28868
$718$	−23.6970	−0.884364
$719$	39.2918	1.46534	0.732668	−	0.680586i	$-0.238275\pi$
$719$	39.2918	1.46534	0.732668	+	0.680586i	$0.238275\pi$
$720$	0	0
$721$	−3.32684	−0.123898
$722$	−27.9372	−1.03972
$723$	−4.26406	−0.158582
$724$	7.48625	0.278224
$725$	0	0
$726$	−1.80098	−0.0668408
$727$	37.7081	1.39851	0.699257	−	0.714870i	$-0.253514\pi$
$727$	37.7081	1.39851	0.699257	+	0.714870i	$0.253514\pi$
$728$	−0.230213	−0.00853225
$729$	21.3812	0.791897
$730$	0	0
$731$	−21.3028	−0.787914
$732$	1.31124	0.0484650
$733$	4.34736	0.160573	0.0802867	−	0.996772i	$-0.474416\pi$
$733$	4.34736	0.160573	0.0802867	+	0.996772i	$0.474416\pi$
$734$	53.3907	1.97069
$735$	0	0
$736$	−11.7770	−0.434105
$737$	−1.52586	−0.0562057
$738$	4.06051	0.149470
$739$	38.1568	1.40362	0.701809	−	0.712365i	$-0.252376\pi$
$739$	38.1568	1.40362	0.701809	+	0.712365i	$0.252376\pi$
$740$	0	0
$741$	−0.0988967	−0.00363306
$742$	15.4680	0.567848
$743$	29.2618	1.07351	0.536756	−	0.843738i	$-0.319650\pi$
$743$	29.2618	1.07351	0.536756	+	0.843738i	$0.319650\pi$
$744$	2.58288	0.0946930
$745$	0	0
$746$	−55.9625	−2.04893
$747$	−13.9011	−0.508615
$748$	−2.03385	−0.0743649
$749$	−8.09890	−0.295927
$750$	0	0
$751$	41.6886	1.52124	0.760619	−	0.649199i	$-0.224896\pi$
$751$	41.6886	1.52124	0.760619	+	0.649199i	$0.224896\pi$
$752$	−27.1898	−0.991509
$753$	−27.0700	−0.986484
$754$	0.200238	0.00729225
$755$	0	0
$756$	2.00000	0.0727393
$757$	−39.7419	−1.44444	−0.722222	−	0.691661i	$-0.756879\pi$
$757$	−39.7419	−1.44444	−0.722222	+	0.691661i	$0.756879\pi$
$758$	−51.0181	−1.85306
$759$	6.68035	0.242481
$760$	0	0
$761$	−36.4112	−1.31990	−0.659952	−	0.751308i	$-0.729423\pi$
$761$	−36.4112	−1.31990	−0.659952	+	0.751308i	$0.729423\pi$
$762$	−17.3972	−0.630234
$763$	15.1773	0.549454
$764$	−7.48625	−0.270843
$765$	0	0
$766$	52.7370	1.90546
$767$	−0.196363	−0.00709025
$768$	−10.0338	−0.362065
$769$	−10.5347	−0.379889	−0.189945	−	0.981795i	$-0.560831\pi$
$769$	−10.5347	−0.379889	−0.189945	+	0.981795i	$0.560831\pi$
$770$	0	0
$771$	24.3500	0.876944
$772$	8.97107	0.322876
$773$	1.52198	0.0547419	0.0273709	−	0.999625i	$-0.491286\pi$
$773$	1.52198	0.0547419	0.0273709	+	0.999625i	$0.491286\pi$
$774$	9.70474	0.348830
$775$	0	0
$776$	35.7854	1.28462
$777$	−10.2823	−0.368876
$778$	35.8264	1.28444
$779$	−1.49079	−0.0534129
$780$	0	0
$781$	−4.09890	−0.146670
$782$	48.4222	1.73158
$783$	7.68649	0.274693
$784$	−4.60197	−0.164356
$785$	0	0
$786$	−8.42923	−0.300661
$787$	15.6020	0.556150	0.278075	−	0.960559i	$-0.410304\pi$
$787$	15.6020	0.556150	0.278075	+	0.960559i	$0.410304\pi$
$788$	5.22219	0.186033
$789$	−27.7321	−0.987288
$790$	0	0
$791$	7.07838	0.251678
$792$	−4.09398	−0.145473
$793$	−0.278438	−0.00988764
$794$	45.9565	1.63094
$795$	0	0
$796$	3.86868	0.137122
$797$	−12.6491	−0.448056	−0.224028	−	0.974583i	$-0.571921\pi$
$797$	−12.6491	−0.448056	−0.224028	+	0.974583i	$0.571921\pi$
$798$	−1.65983	−0.0587572
$799$	32.5562	1.15176
$800$	0	0
$801$	4.62702	0.163488
$802$	−8.49239	−0.299877
$803$	14.1906	0.500776
$804$	−0.658990	−0.0232408
$805$	0	0
$806$	0.124128	0.00437223
$807$	4.09890	0.144288
$808$	−22.6830	−0.797985
$809$	−49.9299	−1.75544	−0.877720	−	0.479174i	$-0.840936\pi$
$809$	−49.9299	−1.75544	−0.877720	+	0.479174i	$0.840936\pi$
$810$	0	0
$811$	7.95896	0.279477	0.139738	−	0.990188i	$-0.455374\pi$
$811$	7.95896	0.279477	0.139738	+	0.990188i	$0.455374\pi$
$812$	0.523590	0.0183744
$813$	9.94214	0.348686
$814$	−13.5259	−0.474081
$815$	0	0
$816$	29.6711	1.03870
$817$	−3.56302	−0.124654
$818$	−5.28580	−0.184814
$819$	−0.149568	−0.00522631
$820$	0	0
$821$	4.92162	0.171766	0.0858829	−	0.996305i	$-0.472629\pi$
$821$	4.92162	0.171766	0.0858829	+	0.996305i	$0.472629\pi$
$822$	16.0045	0.558222
$823$	4.04945	0.141155	0.0705774	−	0.997506i	$-0.477516\pi$
$823$	4.04945	0.141155	0.0705774	+	0.997506i	$0.477516\pi$
$824$	8.35124	0.290929
$825$	0	0
$826$	−3.29565	−0.114670
$827$	−33.3256	−1.15885	−0.579423	−	0.815027i	$-0.696722\pi$
$827$	−33.3256	−1.15885	−0.579423	+	0.815027i	$0.696722\pi$
$828$	−3.43680	−0.119437
$829$	−0.156755	−0.00544434	−0.00272217	−	0.999996i	$-0.500866\pi$
$829$	−0.156755	−0.00544434	−0.00272217	+	0.999996i	$0.500866\pi$
$830$	0	0
$831$	−30.3812	−1.05391
$832$	0.552906	0.0191686
$833$	5.51026	0.190919
$834$	27.0517	0.936724
$835$	0	0
$836$	−0.340173	−0.0117651
$837$	4.76487	0.164698
$838$	28.0338	0.968413
$839$	−49.6775	−1.71506	−0.857529	−	0.514435i	$-0.828002\pi$
$839$	−49.6775	−1.71506	−0.857529	+	0.514435i	$0.828002\pi$
$840$	0	0
$841$	−26.9877	−0.930611
$842$	16.4040	0.565319
$843$	−13.6598	−0.470469
$844$	−0.979481	−0.0337151
$845$	0	0
$846$	−14.8313	−0.509912
$847$	1.00000	0.0343604
$848$	−46.2472	−1.58814
$849$	−16.6803	−0.572468
$850$	0	0
$851$	50.1711	1.71984
$852$	−1.77024	−0.0606474
$853$	−39.4257	−1.34991	−0.674956	−	0.737858i	$-0.735837\pi$
$853$	−39.4257	−1.34991	−0.674956	+	0.737858i	$0.735837\pi$
$854$	−4.67316	−0.159912
$855$	0	0
$856$	20.3303	0.694876
$857$	−33.2423	−1.13554	−0.567768	−	0.823189i	$-0.692193\pi$
$857$	−33.2423	−1.13554	−0.567768	+	0.823189i	$0.692193\pi$
$858$	0.165166	0.00563867
$859$	7.71646	0.263282	0.131641	−	0.991297i	$-0.457975\pi$
$859$	7.71646	0.263282	0.131641	+	0.991297i	$0.457975\pi$
$860$	0	0
$861$	1.89269	0.0645028
$862$	−11.7138	−0.398974
$863$	24.6453	0.838935	0.419467	−	0.907770i	$-0.362217\pi$
$863$	24.6453	0.838935	0.419467	+	0.907770i	$0.362217\pi$
$864$	−11.1773	−0.380259
$865$	0	0
$866$	−51.6118	−1.75384
$867$	−15.6358	−0.531020
$868$	0.324575	0.0110168
$869$	−14.5464	−0.493452
$870$	0	0
$871$	0.139935	0.00474150
$872$	−38.0989	−1.29019
$873$	23.2495	0.786877
$874$	8.09890	0.273949
$875$	0	0
$876$	6.12866	0.207068
$877$	−6.17954	−0.208668	−0.104334	−	0.994542i	$-0.533271\pi$
$877$	−6.17954	−0.208668	−0.104334	+	0.994542i	$0.533271\pi$
$878$	−21.1773	−0.714698
$879$	29.3835	0.991080
$880$	0	0
$881$	−49.3295	−1.66195	−0.830976	−	0.556308i	$-0.812218\pi$
$881$	−49.3295	−1.66195	−0.830976	+	0.556308i	$0.812218\pi$
$882$	−2.51026	−0.0845248
$883$	22.1529	0.745504	0.372752	−	0.927931i	$-0.378414\pi$
$883$	22.1529	0.745504	0.372752	+	0.927931i	$0.378414\pi$
$884$	0.186522	0.00627341
$885$	0	0
$886$	17.1910	0.577543
$887$	−38.7358	−1.30062	−0.650310	−	0.759669i	$-0.725361\pi$
$887$	−38.7358	−1.30062	−0.650310	+	0.759669i	$0.725361\pi$
$888$	25.8113	0.866170
$889$	9.65983	0.323980
$890$	0	0
$891$	1.44748	0.0484924
$892$	3.20128	0.107187
$893$	5.44521	0.182217
$894$	24.6750	0.825257
$895$	0	0
$896$	13.4052	0.447837
$897$	−0.612646	−0.0204557
$898$	−29.3523	−0.979498
$899$	1.24742	0.0416038
$900$	0	0
$901$	55.3751	1.84481
$902$	2.48974	0.0828993
$903$	4.52359	0.150536
$904$	−17.7686	−0.590974
$905$	0	0
$906$	−1.90110	−0.0631599
$907$	−18.4352	−0.612131	−0.306065	−	0.952011i	$-0.599013\pi$
$907$	−18.4352	−0.612131	−0.306065	+	0.952011i	$0.599013\pi$
$908$	−3.57077	−0.118500
$909$	−14.7370	−0.488795
$910$	0	0
$911$	−11.9011	−0.394301	−0.197151	−	0.980373i	$-0.563169\pi$
$911$	−11.9011	−0.394301	−0.197151	+	0.980373i	$0.563169\pi$
$912$	4.96266	0.164330
$913$	−8.52359	−0.282090
$914$	1.21235	0.0401009
$915$	0	0
$916$	−5.00084	−0.165232
$917$	4.68035	0.154559
$918$	45.9565	1.51679
$919$	56.3812	1.85984	0.929922	−	0.367756i	$-0.119874\pi$
$919$	56.3812	1.85984	0.929922	+	0.367756i	$0.119874\pi$
$920$	0	0
$921$	9.39189	0.309473
$922$	39.3823	1.29699
$923$	0.375905	0.0123731
$924$	0.431882	0.0142079
$925$	0	0
$926$	21.9481	0.721260
$927$	5.42574	0.178205
$928$	−2.92616	−0.0960558
$929$	19.2351	0.631084	0.315542	−	0.948912i	$-0.397814\pi$
$929$	19.2351	0.631084	0.315542	+	0.948912i	$0.397814\pi$
$930$	0	0
$931$	0.921622	0.0302049
$932$	−3.09663	−0.101433
$933$	30.8865	1.01118
$934$	−28.2401	−0.924043
$935$	0	0
$936$	0.375453	0.0122721
$937$	−17.6358	−0.576137	−0.288069	−	0.957610i	$-0.593013\pi$
$937$	−17.6358	−0.576137	−0.288069	+	0.957610i	$0.593013\pi$
$938$	2.34858	0.0766840
$939$	30.1087	0.982562
$940$	0	0
$941$	−20.1990	−0.658469	−0.329235	−	0.944248i	$-0.606791\pi$
$941$	−20.1990	−0.658469	−0.329235	+	0.944248i	$0.606791\pi$
$942$	−31.9832	−1.04207
$943$	−9.23513	−0.300737
$944$	9.85354	0.320705
$945$	0	0
$946$	5.95055	0.193469
$947$	−17.6925	−0.574928	−0.287464	−	0.957792i	$-0.592812\pi$
$947$	−17.6925	−0.574928	−0.287464	+	0.957792i	$0.592812\pi$
$948$	−6.28231	−0.204040
$949$	−1.30140	−0.0422453
$950$	0	0
$951$	7.38735	0.239551
$952$	−13.8322	−0.448304
$953$	−39.7093	−1.28631	−0.643155	−	0.765736i	$-0.722375\pi$
$953$	−39.7093	−1.28631	−0.643155	+	0.765736i	$0.722375\pi$
$954$	−25.2267	−0.816745
$955$	0	0
$956$	−10.8851	−0.352050
$957$	1.65983	0.0536546
$958$	18.7337	0.605257
$959$	−8.88655	−0.286962
$960$	0	0
$961$	−30.2267	−0.975056
$962$	1.24044	0.0399934
$963$	13.2085	0.425637
$964$	1.34509	0.0433225
$965$	0	0
$966$	−10.2823	−0.330828
$967$	−3.01664	−0.0970087	−0.0485044	−	0.998823i	$-0.515445\pi$
$967$	−3.01664	−0.0970087	−0.0485044	+	0.998823i	$0.515445\pi$
$968$	−2.51026	−0.0806828
$969$	−5.94214	−0.190889
$970$	0	0
$971$	−18.2134	−0.584496	−0.292248	−	0.956343i	$-0.594403\pi$
$971$	−18.2134	−0.584496	−0.292248	+	0.956343i	$0.594403\pi$
$972$	−5.37486	−0.172399
$973$	−15.0205	−0.481536
$974$	6.51518	0.208760
$975$	0	0
$976$	13.9721	0.447237
$977$	30.0845	0.962489	0.481245	−	0.876586i	$-0.340185\pi$
$977$	30.0845	0.962489	0.481245	+	0.876586i	$0.340185\pi$
$978$	−20.6537	−0.660432
$979$	2.83710	0.0906742
$980$	0	0
$981$	−24.7526	−0.790289
$982$	33.8902	1.08148
$983$	−5.92267	−0.188904	−0.0944519	−	0.995529i	$-0.530110\pi$
$983$	−5.92267	−0.188904	−0.0944519	+	0.995529i	$0.530110\pi$
$984$	−4.75115	−0.151461
$985$	0	0
$986$	12.0312	0.383151
$987$	−6.91321	−0.220050
$988$	0.0311968	0.000992504 0
$989$	−22.0722	−0.701856
$990$	0	0
$991$	9.24742	0.293754	0.146877	−	0.989155i	$-0.453078\pi$
$991$	9.24742	0.293754	0.146877	+	0.989155i	$0.453078\pi$
$992$	−1.81393	−0.0575923
$993$	−4.09890	−0.130075
$994$	6.30898	0.200109
$995$	0	0
$996$	−3.68118	−0.116643
$997$	−32.1496	−1.01819	−0.509094	−	0.860711i	$-0.670019\pi$
$997$	−32.1496	−1.01819	−0.509094	+	0.860711i	$0.670019\pi$
$998$	50.7838	1.60753
$999$	47.6163	1.50651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.v.1.2		3
5.2	odd	4		1925.2.b.n.1849.5		6
5.3	odd	4		1925.2.b.n.1849.2		6
5.4	even	2		385.2.a.f.1.2	✓	3
15.14	odd	2		3465.2.a.bh.1.2		3
20.19	odd	2		6160.2.a.bn.1.1		3
35.34	odd	2		2695.2.a.g.1.2		3
55.54	odd	2		4235.2.a.q.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.f.1.2	✓	3	5.4	even	2
1925.2.a.v.1.2		3	1.1	even	1	trivial
1925.2.b.n.1849.2		6	5.3	odd	4
1925.2.b.n.1849.5		6	5.2	odd	4
2695.2.a.g.1.2		3	35.34	odd	2
3465.2.a.bh.1.2		3	15.14	odd	2
4235.2.a.q.1.2		3	55.54	odd	2
6160.2.a.bn.1.1		3	20.19	odd	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:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

\(f(q)\)	\(=\)	\(q+1.53919 q^{2} -1.17009 q^{3} +0.369102 q^{4} -1.80098 q^{6} +1.00000 q^{7} -2.51026 q^{8} -1.63090 q^{9} +O(q^{10})\)	\(q+1.53919 q^{2} -1.17009 q^{3} +0.369102 q^{4} -1.80098 q^{6} +1.00000 q^{7} -2.51026 q^{8} -1.63090 q^{9} -1.00000 q^{11} -0.431882 q^{12} +0.0917087 q^{13} +1.53919 q^{14} -4.60197 q^{16} +5.51026 q^{17} -2.51026 q^{18} +0.921622 q^{19} -1.17009 q^{21} -1.53919 q^{22} +5.70928 q^{23} +2.93722 q^{24} +0.141157 q^{26} +5.41855 q^{27} +0.369102 q^{28} +1.41855 q^{29} +0.879362 q^{31} -2.06278 q^{32} +1.17009 q^{33} +8.48133 q^{34} -0.601968 q^{36} +8.78765 q^{37} +1.41855 q^{38} -0.107307 q^{39} -1.61757 q^{41} -1.80098 q^{42} -3.86603 q^{43} -0.369102 q^{44} +8.78765 q^{46} +5.90829 q^{47} +5.38470 q^{48} +1.00000 q^{49} -6.44748 q^{51} +0.0338499 q^{52} +10.0494 q^{53} +8.34017 q^{54} -2.51026 q^{56} -1.07838 q^{57} +2.18342 q^{58} -2.14116 q^{59} -3.03612 q^{61} +1.35350 q^{62} -1.63090 q^{63} +6.02893 q^{64} +1.80098 q^{66} +1.52586 q^{67} +2.03385 q^{68} -6.68035 q^{69} +4.09890 q^{71} +4.09398 q^{72} -14.1906 q^{73} +13.5259 q^{74} +0.340173 q^{76} -1.00000 q^{77} -0.165166 q^{78} +14.5464 q^{79} -1.44748 q^{81} -2.48974 q^{82} +8.52359 q^{83} -0.431882 q^{84} -5.95055 q^{86} -1.65983 q^{87} +2.51026 q^{88} -2.83710 q^{89} +0.0917087 q^{91} +2.10731 q^{92} -1.02893 q^{93} +9.09398 q^{94} +2.41363 q^{96} -14.2557 q^{97} +1.53919 q^{98} +1.63090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 5 q^{4} + 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 + 4 * q^6 + 3 * q^7 + 9 * q^8 - q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 5 q^{4} + 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9} - 3 q^{11} + 12 q^{12} - 2 q^{13} + 3 q^{14} + 5 q^{16} + 9 q^{18} + 6 q^{19} + 2 q^{21} - 3 q^{22} + 10 q^{23} + 26 q^{24} - 20 q^{26} + 2 q^{27} + 5 q^{28} - 10 q^{29} - 10 q^{31} + 11 q^{32} - 2 q^{33} - 6 q^{34} + 17 q^{36} + 16 q^{37} - 10 q^{38} - 12 q^{39} + 4 q^{42} + 2 q^{43} - 5 q^{44} + 16 q^{46} + 20 q^{47} + 34 q^{48} + 3 q^{49} - 20 q^{51} - 32 q^{52} + 12 q^{53} + 14 q^{54} + 9 q^{56} + 2 q^{58} + 14 q^{59} + 10 q^{61} - 6 q^{62} - q^{63} + 33 q^{64} - 4 q^{66} + 2 q^{67} - 26 q^{68} + 2 q^{69} - 24 q^{71} + 23 q^{72} - 4 q^{73} + 38 q^{74} - 10 q^{76} - 3 q^{77} - 42 q^{78} + 8 q^{79} - 5 q^{81} - 24 q^{82} + 10 q^{83} + 12 q^{84} - 36 q^{86} - 16 q^{87} - 9 q^{88} + 20 q^{89} - 2 q^{91} + 18 q^{92} - 18 q^{93} + 38 q^{94} + 40 q^{96} + 3 q^{98} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 + 4 * q^6 + 3 * q^7 + 9 * q^8 - q^9 - 3 * q^11 + 12 * q^12 - 2 * q^13 + 3 * q^14 + 5 * q^16 + 9 * q^18 + 6 * q^19 + 2 * q^21 - 3 * q^22 + 10 * q^23 + 26 * q^24 - 20 * q^26 + 2 * q^27 + 5 * q^28 - 10 * q^29 - 10 * q^31 + 11 * q^32 - 2 * q^33 - 6 * q^34 + 17 * q^36 + 16 * q^37 - 10 * q^38 - 12 * q^39 + 4 * q^42 + 2 * q^43 - 5 * q^44 + 16 * q^46 + 20 * q^47 + 34 * q^48 + 3 * q^49 - 20 * q^51 - 32 * q^52 + 12 * q^53 + 14 * q^54 + 9 * q^56 + 2 * q^58 + 14 * q^59 + 10 * q^61 - 6 * q^62 - q^63 + 33 * q^64 - 4 * q^66 + 2 * q^67 - 26 * q^68 + 2 * q^69 - 24 * q^71 + 23 * q^72 - 4 * q^73 + 38 * q^74 - 10 * q^76 - 3 * q^77 - 42 * q^78 + 8 * q^79 - 5 * q^81 - 24 * q^82 + 10 * q^83 + 12 * q^84 - 36 * q^86 - 16 * q^87 - 9 * q^88 + 20 * q^89 - 2 * q^91 + 18 * q^92 - 18 * q^93 + 38 * q^94 + 40 * q^96 + 3 * q^98 + q^99

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