LMFDB - Embedded newform 1875.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{15})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + 4x + 1 $ x^4 - x^3 - 4x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.209057$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.33826 q^{2} -1.00000 q^{3} -0.209057 q^{4} -1.33826 q^{6} +1.27977 q^{7} -2.95630 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.33826 q^{2} -1.00000 q^{3} -0.209057 q^{4} -1.33826 q^{6} +1.27977 q^{7} -2.95630 q^{8} +1.00000 q^{9} +1.16535 q^{11} +0.209057 q^{12} -3.61048 q^{13} +1.71267 q^{14} -3.53818 q^{16} +5.35772 q^{17} +1.33826 q^{18} -7.61048 q^{19} -1.27977 q^{21} +1.55955 q^{22} +3.41811 q^{23} +2.95630 q^{24} -4.83176 q^{26} -1.00000 q^{27} -0.267545 q^{28} -3.21661 q^{29} -1.09306 q^{31} +1.17758 q^{32} -1.16535 q^{33} +7.17002 q^{34} -0.209057 q^{36} -7.80126 q^{37} -10.1848 q^{38} +3.61048 q^{39} -3.00565 q^{41} -1.71267 q^{42} -3.42278 q^{43} -0.243625 q^{44} +4.57433 q^{46} -9.41462 q^{47} +3.53818 q^{48} -5.36218 q^{49} -5.35772 q^{51} +0.754795 q^{52} -7.64760 q^{53} -1.33826 q^{54} -3.78339 q^{56} +7.61048 q^{57} -4.30467 q^{58} +12.7500 q^{59} -10.1506 q^{61} -1.46280 q^{62} +1.27977 q^{63} +8.65227 q^{64} -1.55955 q^{66} +8.78903 q^{67} -1.12007 q^{68} -3.41811 q^{69} -15.0647 q^{71} -2.95630 q^{72} +13.1533 q^{73} -10.4401 q^{74} +1.59102 q^{76} +1.49139 q^{77} +4.83176 q^{78} -11.5155 q^{79} +1.00000 q^{81} -4.02234 q^{82} -10.7189 q^{83} +0.267545 q^{84} -4.58058 q^{86} +3.21661 q^{87} -3.44512 q^{88} -4.51584 q^{89} -4.62059 q^{91} -0.714580 q^{92} +1.09306 q^{93} -12.5992 q^{94} -1.17758 q^{96} +18.0135 q^{97} -7.17600 q^{98} +1.16535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9	$ 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9} - 6 q^{11} - q^{12} + 7 q^{13} - 10 q^{14} - 9 q^{16} - 7 q^{17} + q^{18} - 9 q^{19} - 5 q^{21} + 6 q^{22} + 10 q^{23} + 3 q^{24} - 2 q^{26} - 4 q^{27} + 5 q^{28} - 28 q^{29} - 10 q^{31} + 6 q^{33} + 7 q^{34} + q^{36} - 10 q^{37} - 6 q^{38} - 7 q^{39} + 10 q^{42} + q^{43} - 9 q^{44} + 5 q^{46} - 23 q^{47} + 9 q^{48} - 3 q^{49} + 7 q^{51} + 13 q^{52} - q^{54} + 9 q^{57} - 2 q^{58} + 4 q^{59} - 43 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} - 6 q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 27 q^{71} - 3 q^{72} + 15 q^{73} + 5 q^{74} + 9 q^{76} - 15 q^{77} + 2 q^{78} + 10 q^{79} + 4 q^{81} - 20 q^{82} + 3 q^{83} - 5 q^{84} + 24 q^{86} + 28 q^{87} - 3 q^{88} - 9 q^{89} + 5 q^{91} - 15 q^{92} + 10 q^{93} - 22 q^{94} + 13 q^{97} - 42 q^{98} - 6 q^{99}+O(q^{100}) $ 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9 - 6 * q^11 - q^12 + 7 * q^13 - 10 * q^14 - 9 * q^16 - 7 * q^17 + q^18 - 9 * q^19 - 5 * q^21 + 6 * q^22 + 10 * q^23 + 3 * q^24 - 2 * q^26 - 4 * q^27 + 5 * q^28 - 28 * q^29 - 10 * q^31 + 6 * q^33 + 7 * q^34 + q^36 - 10 * q^37 - 6 * q^38 - 7 * q^39 + 10 * q^42 + q^43 - 9 * q^44 + 5 * q^46 - 23 * q^47 + 9 * q^48 - 3 * q^49 + 7 * q^51 + 13 * q^52 - q^54 + 9 * q^57 - 2 * q^58 + 4 * q^59 - 43 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 - 6 * q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 27 * q^71 - 3 * q^72 + 15 * q^73 + 5 * q^74 + 9 * q^76 - 15 * q^77 + 2 * q^78 + 10 * q^79 + 4 * q^81 - 20 * q^82 + 3 * q^83 - 5 * q^84 + 24 * q^86 + 28 * q^87 - 3 * q^88 - 9 * q^89 + 5 * q^91 - 15 * q^92 + 10 * q^93 - 22 * q^94 + 13 * q^97 - 42 * q^98 - 6 * 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 $

$2$	1.33826	0.946294	0.473147	−	0.880984i	$-0.343118\pi$
$2$	1.33826	0.946294	0.473147	+	0.880984i	$0.343118\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.209057	−0.104528
$5$	0	0
$5$	0	0
$6$	−1.33826	−0.546343
$7$	1.27977	0.483709	0.241854	−	0.970313i	$-0.422244\pi$
$7$	1.27977	0.483709	0.241854	+	0.970313i	$0.422244\pi$
$8$	−2.95630	−1.04521
$9$	1.00000	0.333333
$10$	0	0
$11$	1.16535	0.351367	0.175683	−	0.984447i	$-0.443786\pi$
$11$	1.16535	0.351367	0.175683	+	0.984447i	$0.443786\pi$
$12$	0.209057	0.0603495
$13$	−3.61048	−1.00137	−0.500683	−	0.865631i	$-0.666918\pi$
$13$	−3.61048	−1.00137	−0.500683	+	0.865631i	$0.666918\pi$
$14$	1.71267	0.457730
$15$	0	0
$16$	−3.53818	−0.884545
$17$	5.35772	1.29944	0.649718	−	0.760175i	$-0.274887\pi$
$17$	5.35772	1.29944	0.649718	+	0.760175i	$0.274887\pi$
$18$	1.33826	0.315431
$19$	−7.61048	−1.74596	−0.872982	−	0.487753i	$-0.837817\pi$
$19$	−7.61048	−1.74596	−0.872982	+	0.487753i	$0.837817\pi$
$20$	0	0
$21$	−1.27977	−0.279269
$22$	1.55955	0.332496
$23$	3.41811	0.712726	0.356363	−	0.934348i	$-0.384017\pi$
$23$	3.41811	0.712726	0.356363	+	0.934348i	$0.384017\pi$
$24$	2.95630	0.603451
$25$	0	0
$26$	−4.83176	−0.947586
$27$	−1.00000	−0.192450
$28$	−0.267545	−0.0505613
$29$	−3.21661	−0.597310	−0.298655	−	0.954361i	$-0.596538\pi$
$29$	−3.21661	−0.597310	−0.298655	+	0.954361i	$0.596538\pi$
$30$	0	0
$31$	−1.09306	−0.196319	−0.0981594	−	0.995171i	$-0.531295\pi$
$31$	−1.09306	−0.196319	−0.0981594	+	0.995171i	$0.531295\pi$
$32$	1.17758	0.208169
$33$	−1.16535	−0.202862
$34$	7.17002	1.22965
$35$	0	0
$36$	−0.209057	−0.0348428
$37$	−7.80126	−1.28252	−0.641260	−	0.767324i	$-0.721588\pi$
$37$	−7.80126	−1.28252	−0.641260	+	0.767324i	$0.721588\pi$
$38$	−10.1848	−1.65219
$39$	3.61048	0.578139
$40$	0	0
$41$	−3.00565	−0.469403	−0.234702	−	0.972067i	$-0.575411\pi$
$41$	−3.00565	−0.469403	−0.234702	+	0.972067i	$0.575411\pi$
$42$	−1.71267	−0.264271
$43$	−3.42278	−0.521970	−0.260985	−	0.965343i	$-0.584047\pi$
$43$	−3.42278	−0.521970	−0.260985	+	0.965343i	$0.584047\pi$
$44$	−0.243625	−0.0367278
$45$	0	0
$46$	4.57433	0.674448
$47$	−9.41462	−1.37326	−0.686632	−	0.727005i	$-0.740912\pi$
$47$	−9.41462	−1.37326	−0.686632	+	0.727005i	$0.740912\pi$
$48$	3.53818	0.510692
$49$	−5.36218	−0.766026
$50$	0	0
$51$	−5.35772	−0.750230
$52$	0.754795	0.104671
$53$	−7.64760	−1.05048	−0.525239	−	0.850954i	$-0.676024\pi$
$53$	−7.64760	−1.05048	−0.525239	+	0.850954i	$0.676024\pi$
$54$	−1.33826	−0.182114
$55$	0	0
$56$	−3.78339	−0.505576
$57$	7.61048	1.00803
$58$	−4.30467	−0.565231
$59$	12.7500	1.65991	0.829954	−	0.557832i	$-0.188366\pi$
$59$	12.7500	1.65991	0.829954	+	0.557832i	$0.188366\pi$
$60$	0	0
$61$	−10.1506	−1.29965	−0.649824	−	0.760085i	$-0.725157\pi$
$61$	−10.1506	−1.29965	−0.649824	+	0.760085i	$0.725157\pi$
$62$	−1.46280	−0.185775
$63$	1.27977	0.161236
$64$	8.65227	1.08153
$65$	0	0
$66$	−1.55955	−0.191967
$67$	8.78903	1.07375	0.536876	−	0.843661i	$-0.319604\pi$
$67$	8.78903	1.07375	0.536876	+	0.843661i	$0.319604\pi$
$68$	−1.12007	−0.135828
$69$	−3.41811	−0.411493
$70$	0	0
$71$	−15.0647	−1.78786	−0.893928	−	0.448211i	$-0.852061\pi$
$71$	−15.0647	−1.78786	−0.893928	+	0.448211i	$0.852061\pi$
$72$	−2.95630	−0.348403
$73$	13.1533	1.53948	0.769740	−	0.638357i	$-0.220386\pi$
$73$	13.1533	1.53948	0.769740	+	0.638357i	$0.220386\pi$
$74$	−10.4401	−1.21364
$75$	0	0
$76$	1.59102	0.182503
$77$	1.49139	0.169959
$78$	4.83176	0.547089
$79$	−11.5155	−1.29560	−0.647798	−	0.761812i	$-0.724310\pi$
$79$	−11.5155	−1.29560	−0.647798	+	0.761812i	$0.724310\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−4.02234	−0.444193
$83$	−10.7189	−1.17655	−0.588277	−	0.808659i	$-0.700194\pi$
$83$	−10.7189	−1.17655	−0.588277	+	0.808659i	$0.700194\pi$
$84$	0.267545	0.0291916
$85$	0	0
$86$	−4.58058	−0.493937
$87$	3.21661	0.344857
$88$	−3.44512	−0.367252
$89$	−4.51584	−0.478678	−0.239339	−	0.970936i	$-0.576931\pi$
$89$	−4.51584	−0.478678	−0.239339	+	0.970936i	$0.576931\pi$
$90$	0	0
$91$	−4.62059	−0.484369
$92$	−0.714580	−0.0745002
$93$	1.09306	0.113345
$94$	−12.5992	−1.29951
$95$	0	0
$96$	−1.17758	−0.120186
$97$	18.0135	1.82899	0.914496	−	0.404596i	$-0.132588\pi$
$97$	18.0135	1.82899	0.914496	+	0.404596i	$0.132588\pi$
$98$	−7.17600	−0.724885
$99$	1.16535	0.117122
$100$	0	0
$101$	−6.54634	−0.651385	−0.325693	−	0.945476i	$-0.605597\pi$
$101$	−6.54634	−0.651385	−0.325693	+	0.945476i	$0.605597\pi$
$102$	−7.17002	−0.709938
$103$	11.1588	1.09951	0.549753	−	0.835327i	$-0.314722\pi$
$103$	11.1588	1.09951	0.549753	+	0.835327i	$0.314722\pi$
$104$	10.6736	1.04664
$105$	0	0
$106$	−10.2345	−0.994061
$107$	−3.72681	−0.360284	−0.180142	−	0.983641i	$-0.557656\pi$
$107$	−3.72681	−0.360284	−0.180142	+	0.983641i	$0.557656\pi$
$108$	0.209057	0.0201165
$109$	−6.99533	−0.670031	−0.335016	−	0.942213i	$-0.608742\pi$
$109$	−6.99533	−0.670031	−0.335016	+	0.942213i	$0.608742\pi$
$110$	0	0
$111$	7.80126	0.740463
$112$	−4.52807	−0.427862
$113$	−5.59858	−0.526670	−0.263335	−	0.964704i	$-0.584822\pi$
$113$	−5.59858	−0.526670	−0.263335	+	0.964704i	$0.584822\pi$
$114$	10.1848	0.953895
$115$	0	0
$116$	0.672455	0.0624359
$117$	−3.61048	−0.333789
$118$	17.0628	1.57076
$119$	6.85666	0.628549
$120$	0	0
$121$	−9.64195	−0.876541
$122$	−13.5841	−1.22985
$123$	3.00565	0.271010
$124$	0.228511	0.0205209
$125$	0	0
$126$	1.71267	0.152577
$127$	−4.38919	−0.389478	−0.194739	−	0.980855i	$-0.562386\pi$
$127$	−4.38919	−0.389478	−0.194739	+	0.980855i	$0.562386\pi$
$128$	9.22384	0.815280
$129$	3.42278	0.301359
$130$	0	0
$131$	−4.99244	−0.436192	−0.218096	−	0.975927i	$-0.569985\pi$
$131$	−4.99244	−0.436192	−0.218096	+	0.975927i	$0.569985\pi$
$132$	0.243625	0.0212048
$133$	−9.73968	−0.844537
$134$	11.7620	1.01608
$135$	0	0
$136$	−15.8390	−1.35818
$137$	12.2056	1.04279	0.521396	−	0.853315i	$-0.325411\pi$
$137$	12.2056	1.04279	0.521396	+	0.853315i	$0.325411\pi$
$138$	−4.57433	−0.389393
$139$	−5.20617	−0.441582	−0.220791	−	0.975321i	$-0.570864\pi$
$139$	−5.20617	−0.441582	−0.220791	+	0.975321i	$0.570864\pi$
$140$	0	0
$141$	9.41462	0.792854
$142$	−20.1606	−1.69184
$143$	−4.20748	−0.351847
$144$	−3.53818	−0.294848
$145$	0	0
$146$	17.6026	1.45680
$147$	5.36218	0.442265
$148$	1.63091	0.134060
$149$	−21.6208	−1.77124	−0.885622	−	0.464406i	$-0.846268\pi$
$149$	−21.6208	−1.77124	−0.885622	+	0.464406i	$0.846268\pi$
$150$	0	0
$151$	11.8918	0.967743	0.483872	−	0.875139i	$-0.339230\pi$
$151$	11.8918	0.967743	0.483872	+	0.875139i	$0.339230\pi$
$152$	22.4988	1.82490
$153$	5.35772	0.433146
$154$	1.99586	0.160831
$155$	0	0
$156$	−0.754795	−0.0604320
$157$	−12.1112	−0.966579	−0.483290	−	0.875461i	$-0.660558\pi$
$157$	−12.1112	−0.966579	−0.483290	+	0.875461i	$0.660558\pi$
$158$	−15.4108	−1.22601
$159$	7.64760	0.606494
$160$	0	0
$161$	4.37441	0.344752
$162$	1.33826	0.105144
$163$	8.26913	0.647688	0.323844	−	0.946111i	$-0.395025\pi$
$163$	8.26913	0.647688	0.323844	+	0.946111i	$0.395025\pi$
$164$	0.628351	0.0490660
$165$	0	0
$166$	−14.3447	−1.11337
$167$	6.26564	0.484849	0.242425	−	0.970170i	$-0.422057\pi$
$167$	6.26564	0.484849	0.242425	+	0.970170i	$0.422057\pi$
$168$	3.78339	0.291895
$169$	0.0355444	0.00273418
$170$	0	0
$171$	−7.61048	−0.581988
$172$	0.715557	0.0545607
$173$	6.65609	0.506053	0.253027	−	0.967459i	$-0.418574\pi$
$173$	6.65609	0.506053	0.253027	+	0.967459i	$0.418574\pi$
$174$	4.30467	0.326336
$175$	0	0
$176$	−4.12323	−0.310800
$177$	−12.7500	−0.958349
$178$	−6.04337	−0.452970
$179$	21.7154	1.62309	0.811544	−	0.584292i	$-0.198628\pi$
$179$	21.7154	1.62309	0.811544	+	0.584292i	$0.198628\pi$
$180$	0	0
$181$	12.9474	0.962375	0.481188	−	0.876618i	$-0.340206\pi$
$181$	12.9474	0.962375	0.481188	+	0.876618i	$0.340206\pi$
$182$	−6.18356	−0.458356
$183$	10.1506	0.750352
$184$	−10.1050	−0.744947
$185$	0	0
$186$	1.46280	0.107257
$187$	6.24362	0.456579
$188$	1.96819	0.143545
$189$	−1.27977	−0.0930898
$190$	0	0
$191$	15.7683	1.14095	0.570476	−	0.821314i	$-0.306759\pi$
$191$	15.7683	1.14095	0.570476	+	0.821314i	$0.306759\pi$
$192$	−8.65227	−0.624424
$193$	6.93514	0.499202	0.249601	−	0.968349i	$-0.419701\pi$
$193$	6.93514	0.499202	0.249601	+	0.968349i	$0.419701\pi$
$194$	24.1067	1.73076
$195$	0	0
$196$	1.12100	0.0800715
$197$	−7.43948	−0.530041	−0.265020	−	0.964243i	$-0.585379\pi$
$197$	−7.43948	−0.530041	−0.265020	+	0.964243i	$0.585379\pi$
$198$	1.55955	0.110832
$199$	−14.2398	−1.00943	−0.504716	−	0.863285i	$-0.668403\pi$
$199$	−14.2398	−1.00943	−0.504716	+	0.863285i	$0.668403\pi$
$200$	0	0
$201$	−8.78903	−0.619931
$202$	−8.76072	−0.616402
$203$	−4.11653	−0.288924
$204$	1.12007	0.0784204
$205$	0	0
$206$	14.9334	1.04046
$207$	3.41811	0.237575
$208$	12.7745	0.885754
$209$	−8.86889	−0.613474
$210$	0	0
$211$	6.89569	0.474719	0.237360	−	0.971422i	$-0.423718\pi$
$211$	6.89569	0.474719	0.237360	+	0.971422i	$0.423718\pi$
$212$	1.59878	0.109805
$213$	15.0647	1.03222
$214$	−4.98744	−0.340935
$215$	0	0
$216$	2.95630	0.201150
$217$	−1.39886	−0.0949611
$218$	−9.36158	−0.634046
$219$	−13.1533	−0.888820
$220$	0	0
$221$	−19.3439	−1.30121
$222$	10.4401	0.700695
$223$	13.3983	0.897219	0.448609	−	0.893728i	$-0.351920\pi$
$223$	13.3983	0.897219	0.448609	+	0.893728i	$0.351920\pi$
$224$	1.50703	0.100693
$225$	0	0
$226$	−7.49236	−0.498385
$227$	−0.849831	−0.0564053	−0.0282026	−	0.999602i	$-0.508978\pi$
$227$	−0.849831	−0.0564053	−0.0282026	+	0.999602i	$0.508978\pi$
$228$	−1.59102	−0.105368
$229$	−8.79561	−0.581231	−0.290615	−	0.956840i	$-0.593860\pi$
$229$	−8.79561	−0.581231	−0.290615	+	0.956840i	$0.593860\pi$
$230$	0	0
$231$	−1.49139	−0.0981260
$232$	9.50926	0.624314
$233$	21.2093	1.38947	0.694734	−	0.719267i	$-0.255522\pi$
$233$	21.2093	1.38947	0.694734	+	0.719267i	$0.255522\pi$
$234$	−4.83176	−0.315862
$235$	0	0
$236$	−2.66548	−0.173508
$237$	11.5155	0.748013
$238$	9.17600	0.594792
$239$	−16.7972	−1.08652	−0.543261	−	0.839564i	$-0.682811\pi$
$239$	−16.7972	−1.08652	−0.543261	+	0.839564i	$0.682811\pi$
$240$	0	0
$241$	9.51860	0.613147	0.306573	−	0.951847i	$-0.400817\pi$
$241$	9.51860	0.613147	0.306573	+	0.951847i	$0.400817\pi$
$242$	−12.9035	−0.829465
$243$	−1.00000	−0.0641500
$244$	2.12205	0.135850
$245$	0	0
$246$	4.02234	0.256455
$247$	27.4775	1.74835
$248$	3.23140	0.205194
$249$	10.7189	0.679284
$250$	0	0
$251$	12.9486	0.817309	0.408655	−	0.912689i	$-0.365998\pi$
$251$	12.9486	0.817309	0.408655	+	0.912689i	$0.365998\pi$
$252$	−0.267545	−0.0168538
$253$	3.98331	0.250428
$254$	−5.87389	−0.368560
$255$	0	0
$256$	−4.96064	−0.310040
$257$	−16.6837	−1.04070	−0.520352	−	0.853952i	$-0.674199\pi$
$257$	−16.6837	−1.04070	−0.520352	+	0.853952i	$0.674199\pi$
$258$	4.58058	0.285174
$259$	−9.98384	−0.620366
$260$	0	0
$261$	−3.21661	−0.199103
$262$	−6.68119	−0.412765
$263$	−9.45426	−0.582975	−0.291487	−	0.956575i	$-0.594150\pi$
$263$	−9.45426	−0.582975	−0.291487	+	0.956575i	$0.594150\pi$
$264$	3.44512	0.212033
$265$	0	0
$266$	−13.0342	−0.799180
$267$	4.51584	0.276365
$268$	−1.83741	−0.112238
$269$	31.7384	1.93513	0.967563	−	0.252631i	$-0.0812958\pi$
$269$	31.7384	1.93513	0.967563	+	0.252631i	$0.0812958\pi$
$270$	0	0
$271$	19.0556	1.15755	0.578773	−	0.815489i	$-0.303532\pi$
$271$	19.0556	1.15755	0.578773	+	0.815489i	$0.303532\pi$
$272$	−18.9566	−1.14941
$273$	4.62059	0.279651
$274$	16.3342	0.986787
$275$	0	0
$276$	0.714580	0.0430127
$277$	−2.71929	−0.163387	−0.0816933	−	0.996658i	$-0.526033\pi$
$277$	−2.71929	−0.163387	−0.0816933	+	0.996658i	$0.526033\pi$
$278$	−6.96722	−0.417866
$279$	−1.09306	−0.0654396
$280$	0	0
$281$	−14.6076	−0.871416	−0.435708	−	0.900088i	$-0.643502\pi$
$281$	−14.6076	−0.871416	−0.435708	+	0.900088i	$0.643502\pi$
$282$	12.5992	0.750273
$283$	18.0890	1.07528	0.537639	−	0.843175i	$-0.319316\pi$
$283$	18.0890	1.07528	0.537639	+	0.843175i	$0.319316\pi$
$284$	3.14939	0.186882
$285$	0	0
$286$	−5.63070	−0.332950
$287$	−3.84655	−0.227054
$288$	1.17758	0.0693895
$289$	11.7051	0.688536
$290$	0	0
$291$	−18.0135	−1.05597
$292$	−2.74979	−0.160920
$293$	−0.293910	−0.0171704	−0.00858521	−	0.999963i	$-0.502733\pi$
$293$	−0.293910	−0.0171704	−0.00858521	+	0.999963i	$0.502733\pi$
$294$	7.17600	0.418513
$295$	0	0
$296$	23.0628	1.34050
$297$	−1.16535	−0.0676206
$298$	−28.9343	−1.67612
$299$	−12.3410	−0.713700
$300$	0	0
$301$	−4.38039	−0.252481
$302$	15.9144	0.915769
$303$	6.54634	0.376078
$304$	26.9272	1.54438
$305$	0	0
$306$	7.17002	0.409883
$307$	−1.34411	−0.0767125	−0.0383563	−	0.999264i	$-0.512212\pi$
$307$	−1.34411	−0.0767125	−0.0383563	+	0.999264i	$0.512212\pi$
$308$	−0.311785	−0.0177656
$309$	−11.1588	−0.634800
$310$	0	0
$311$	19.9569	1.13165	0.565826	−	0.824525i	$-0.308557\pi$
$311$	19.9569	1.13165	0.565826	+	0.824525i	$0.308557\pi$
$312$	−10.6736	−0.604276
$313$	14.1446	0.799500	0.399750	−	0.916624i	$-0.369097\pi$
$313$	14.1446	0.799500	0.399750	+	0.916624i	$0.369097\pi$
$314$	−16.2080	−0.914668
$315$	0	0
$316$	2.40740	0.135427
$317$	17.5897	0.987937	0.493968	−	0.869480i	$-0.335546\pi$
$317$	17.5897	0.987937	0.493968	+	0.869480i	$0.335546\pi$
$318$	10.2345	0.573922
$319$	−3.74849	−0.209875
$320$	0	0
$321$	3.72681	0.208010
$322$	5.85410	0.326236
$323$	−40.7748	−2.26877
$324$	−0.209057	−0.0116143
$325$	0	0
$326$	11.0662	0.612903
$327$	6.99533	0.386843
$328$	8.88558	0.490624
$329$	−12.0486	−0.664260
$330$	0	0
$331$	8.00683	0.440095	0.220048	−	0.975489i	$-0.429379\pi$
$331$	8.00683	0.440095	0.220048	+	0.975489i	$0.429379\pi$
$332$	2.24086	0.122983
$333$	−7.80126	−0.427506
$334$	8.38506	0.458810
$335$	0	0
$336$	4.52807	0.247026
$337$	10.8474	0.590895	0.295448	−	0.955359i	$-0.404531\pi$
$337$	10.8474	0.590895	0.295448	+	0.955359i	$0.404531\pi$
$338$	0.0475677	0.00258734
$339$	5.59858	0.304073
$340$	0	0
$341$	−1.27380	−0.0689799
$342$	−10.1848	−0.550731
$343$	−15.8208	−0.854242
$344$	10.1188	0.545567
$345$	0	0
$346$	8.90759	0.478875
$347$	1.86153	0.0999323	0.0499662	−	0.998751i	$-0.484089\pi$
$347$	1.86153	0.0999323	0.0499662	+	0.998751i	$0.484089\pi$
$348$	−0.672455	−0.0360474
$349$	24.4623	1.30944	0.654719	−	0.755872i	$-0.272787\pi$
$349$	24.4623	1.30944	0.654719	+	0.755872i	$0.272787\pi$
$350$	0	0
$351$	3.61048	0.192713
$352$	1.37229	0.0731436
$353$	−37.3621	−1.98858	−0.994291	−	0.106704i	$-0.965970\pi$
$353$	−37.3621	−1.98858	−0.994291	+	0.106704i	$0.965970\pi$
$354$	−17.0628	−0.906879
$355$	0	0
$356$	0.944068	0.0500355
$357$	−6.85666	−0.362893
$358$	29.0609	1.53592
$359$	−25.3360	−1.33718	−0.668592	−	0.743629i	$-0.733103\pi$
$359$	−25.3360	−1.33718	−0.668592	+	0.743629i	$0.733103\pi$
$360$	0	0
$361$	38.9194	2.04839
$362$	17.3270	0.910689
$363$	9.64195	0.506071
$364$	0.965966	0.0506304
$365$	0	0
$366$	13.5841	0.710053
$367$	23.7057	1.23743	0.618714	−	0.785616i	$-0.287654\pi$
$367$	23.7057	1.23743	0.618714	+	0.785616i	$0.287654\pi$
$368$	−12.0939	−0.630438
$369$	−3.00565	−0.156468
$370$	0	0
$371$	−9.78719	−0.508126
$372$	−0.228511	−0.0118477
$373$	−2.93244	−0.151836	−0.0759181	−	0.997114i	$-0.524189\pi$
$373$	−2.93244	−0.151836	−0.0759181	+	0.997114i	$0.524189\pi$
$374$	8.35560	0.432058
$375$	0	0
$376$	27.8324	1.43535
$377$	11.6135	0.598126
$378$	−1.71267	−0.0880903
$379$	−17.7349	−0.910980	−0.455490	−	0.890241i	$-0.650536\pi$
$379$	−17.7349	−0.910980	−0.455490	+	0.890241i	$0.650536\pi$
$380$	0	0
$381$	4.38919	0.224865
$382$	21.1021	1.07968
$383$	−4.40524	−0.225097	−0.112549	−	0.993646i	$-0.535901\pi$
$383$	−4.40524	−0.225097	−0.112549	+	0.993646i	$0.535901\pi$
$384$	−9.22384	−0.470702
$385$	0	0
$386$	9.28102	0.472392
$387$	−3.42278	−0.173990
$388$	−3.76584	−0.191182
$389$	−31.3215	−1.58806	−0.794031	−	0.607877i	$-0.792021\pi$
$389$	−31.3215	−1.58806	−0.794031	+	0.607877i	$0.792021\pi$
$390$	0	0
$391$	18.3133	0.926142
$392$	15.8522	0.800657
$393$	4.99244	0.251835
$394$	−9.95596	−0.501574
$395$	0	0
$396$	−0.243625	−0.0122426
$397$	−16.4281	−0.824501	−0.412250	−	0.911071i	$-0.635257\pi$
$397$	−16.4281	−0.824501	−0.412250	+	0.911071i	$0.635257\pi$
$398$	−19.0566	−0.955220
$399$	9.73968	0.487594
$400$	0	0
$401$	−15.1813	−0.758120	−0.379060	−	0.925372i	$-0.623753\pi$
$401$	−15.1813	−0.758120	−0.379060	+	0.925372i	$0.623753\pi$
$402$	−11.7620	−0.586636
$403$	3.94646	0.196587
$404$	1.36856	0.0680883
$405$	0	0
$406$	−5.50900	−0.273407
$407$	−9.09122	−0.450635
$408$	15.8390	0.784147
$409$	−14.8421	−0.733897	−0.366948	−	0.930241i	$-0.619597\pi$
$409$	−14.8421	−0.733897	−0.366948	+	0.930241i	$0.619597\pi$
$410$	0	0
$411$	−12.2056	−0.602056
$412$	−2.33282	−0.114930
$413$	16.3171	0.802912
$414$	4.57433	0.224816
$415$	0	0
$416$	−4.25162	−0.208453
$417$	5.20617	0.254947
$418$	−11.8689	−0.580526
$419$	−35.2636	−1.72274	−0.861370	−	0.507978i	$-0.830393\pi$
$419$	−35.2636	−1.72274	−0.861370	+	0.507978i	$0.830393\pi$
$420$	0	0
$421$	−11.2827	−0.549887	−0.274943	−	0.961460i	$-0.588659\pi$
$421$	−11.2827	−0.549887	−0.274943	+	0.961460i	$0.588659\pi$
$422$	9.22824	0.449224
$423$	−9.41462	−0.457755
$424$	22.6086	1.09797
$425$	0	0
$426$	20.1606	0.976782
$427$	−12.9904	−0.628651
$428$	0.779115	0.0376599
$429$	4.20748	0.203139
$430$	0	0
$431$	25.8249	1.24394	0.621971	−	0.783041i	$-0.286332\pi$
$431$	25.8249	1.24394	0.621971	+	0.783041i	$0.286332\pi$
$432$	3.53818	0.170231
$433$	−9.99902	−0.480522	−0.240261	−	0.970708i	$-0.577233\pi$
$433$	−9.99902	−0.480522	−0.240261	+	0.970708i	$0.577233\pi$
$434$	−1.87205	−0.0898610
$435$	0	0
$436$	1.46242	0.0700373
$437$	−26.0135	−1.24439
$438$	−17.6026	−0.841084
$439$	9.20385	0.439276	0.219638	−	0.975581i	$-0.429512\pi$
$439$	9.20385	0.439276	0.219638	+	0.975581i	$0.429512\pi$
$440$	0	0
$441$	−5.36218	−0.255342
$442$	−25.8872	−1.23133
$443$	−9.12790	−0.433680	−0.216840	−	0.976207i	$-0.569575\pi$
$443$	−9.12790	−0.433680	−0.216840	+	0.976207i	$0.569575\pi$
$444$	−1.63091	−0.0773994
$445$	0	0
$446$	17.9305	0.849032
$447$	21.6208	1.02263
$448$	11.0729	0.523147
$449$	35.4831	1.67455	0.837275	−	0.546781i	$-0.184147\pi$
$449$	35.4831	1.67455	0.837275	+	0.546781i	$0.184147\pi$
$450$	0	0
$451$	−3.50264	−0.164933
$452$	1.17042	0.0550520
$453$	−11.8918	−0.558727
$454$	−1.13730	−0.0533759
$455$	0	0
$456$	−22.4988	−1.05360
$457$	18.7516	0.877162	0.438581	−	0.898692i	$-0.355481\pi$
$457$	18.7516	0.877162	0.438581	+	0.898692i	$0.355481\pi$
$458$	−11.7708	−0.550015
$459$	−5.35772	−0.250077
$460$	0	0
$461$	−16.0877	−0.749280	−0.374640	−	0.927170i	$-0.622234\pi$
$461$	−16.0877	−0.749280	−0.374640	+	0.927170i	$0.622234\pi$
$462$	−1.99586	−0.0928560
$463$	−21.1040	−0.980787	−0.490393	−	0.871501i	$-0.663147\pi$
$463$	−21.1040	−0.980787	−0.490393	+	0.871501i	$0.663147\pi$
$464$	11.3810	0.528348
$465$	0	0
$466$	28.3836	1.31484
$467$	18.0122	0.833504	0.416752	−	0.909020i	$-0.363168\pi$
$467$	18.0122	0.833504	0.416752	+	0.909020i	$0.363168\pi$
$468$	0.754795	0.0348904
$469$	11.2480	0.519383
$470$	0	0
$471$	12.1112	0.558055
$472$	−37.6928	−1.73495
$473$	−3.98875	−0.183403
$474$	15.4108	0.707840
$475$	0	0
$476$	−1.43343	−0.0657012
$477$	−7.64760	−0.350160
$478$	−22.4791	−1.02817
$479$	7.31414	0.334191	0.167096	−	0.985941i	$-0.446561\pi$
$479$	7.31414	0.334191	0.167096	+	0.985941i	$0.446561\pi$
$480$	0	0
$481$	28.1663	1.28427
$482$	12.7384	0.580217
$483$	−4.37441	−0.199043
$484$	2.01572	0.0916235
$485$	0	0
$486$	−1.33826	−0.0607048
$487$	11.9433	0.541202	0.270601	−	0.962692i	$-0.412778\pi$
$487$	11.9433	0.541202	0.270601	+	0.962692i	$0.412778\pi$
$488$	30.0081	1.35840
$489$	−8.26913	−0.373943
$490$	0	0
$491$	11.1658	0.503904	0.251952	−	0.967740i	$-0.418928\pi$
$491$	11.1658	0.503904	0.251952	+	0.967740i	$0.418928\pi$
$492$	−0.628351	−0.0283283
$493$	−17.2337	−0.776167
$494$	36.7720	1.65445
$495$	0	0
$496$	3.86743	0.173653
$497$	−19.2794	−0.864801
$498$	14.3447	0.642802
$499$	30.6045	1.37005	0.685023	−	0.728522i	$-0.259792\pi$
$499$	30.6045	1.37005	0.685023	+	0.728522i	$0.259792\pi$
$500$	0	0
$501$	−6.26564	−0.279928
$502$	17.3286	0.773414
$503$	−1.90950	−0.0851404	−0.0425702	−	0.999093i	$-0.513555\pi$
$503$	−1.90950	−0.0851404	−0.0425702	+	0.999093i	$0.513555\pi$
$504$	−3.78339	−0.168525
$505$	0	0
$506$	5.33070	0.236979
$507$	−0.0355444	−0.00157858
$508$	0.917591	0.0407115
$509$	2.52518	0.111927	0.0559634	−	0.998433i	$-0.482177\pi$
$509$	2.52518	0.111927	0.0559634	+	0.998433i	$0.482177\pi$
$510$	0	0
$511$	16.8333	0.744660
$512$	−25.0863	−1.10867
$513$	7.61048	0.336011
$514$	−22.3272	−0.984811
$515$	0	0
$516$	−0.715557	−0.0315006
$517$	−10.9714	−0.482520
$518$	−13.3610	−0.587048
$519$	−6.65609	−0.292170
$520$	0	0
$521$	3.65479	0.160119	0.0800595	−	0.996790i	$-0.474489\pi$
$521$	3.65479	0.160119	0.0800595	+	0.996790i	$0.474489\pi$
$522$	−4.30467	−0.188410
$523$	−36.3215	−1.58823	−0.794114	−	0.607768i	$-0.792065\pi$
$523$	−36.3215	−1.58823	−0.794114	+	0.607768i	$0.792065\pi$
$524$	1.04370	0.0455945
$525$	0	0
$526$	−12.6523	−0.551665
$527$	−5.85629	−0.255104
$528$	4.12323	0.179440
$529$	−11.3165	−0.492022
$530$	0	0
$531$	12.7500	0.553303
$532$	2.03615	0.0882782
$533$	10.8518	0.470044
$534$	6.04337	0.261522
$535$	0	0
$536$	−25.9830	−1.12229
$537$	−21.7154	−0.937090
$538$	42.4743	1.83120
$539$	−6.24883	−0.269156
$540$	0	0
$541$	−13.3159	−0.572496	−0.286248	−	0.958156i	$-0.592408\pi$
$541$	−13.3159	−0.572496	−0.286248	+	0.958156i	$0.592408\pi$
$542$	25.5014	1.09538
$543$	−12.9474	−0.555627
$544$	6.30914	0.270502
$545$	0	0
$546$	6.18356	0.264632
$547$	−29.6657	−1.26841	−0.634207	−	0.773163i	$-0.718673\pi$
$547$	−29.6657	−1.26841	−0.634207	+	0.773163i	$0.718673\pi$
$548$	−2.55166	−0.109001
$549$	−10.1506	−0.433216
$550$	0	0
$551$	24.4800	1.04288
$552$	10.1050	0.430095
$553$	−14.7372	−0.626691
$554$	−3.63913	−0.154612
$555$	0	0
$556$	1.08839	0.0461578
$557$	−42.4585	−1.79902	−0.899512	−	0.436897i	$-0.856078\pi$
$557$	−42.4585	−1.79902	−0.899512	+	0.436897i	$0.856078\pi$
$558$	−1.46280	−0.0619251
$559$	12.3579	0.522683
$560$	0	0
$561$	−6.24362	−0.263606
$562$	−19.5488	−0.824615
$563$	−41.0132	−1.72850	−0.864250	−	0.503063i	$-0.832206\pi$
$563$	−41.0132	−1.72850	−0.864250	+	0.503063i	$0.832206\pi$
$564$	−1.96819	−0.0828758
$565$	0	0
$566$	24.2078	1.01753
$567$	1.27977	0.0537454
$568$	44.5358	1.86868
$569$	−29.0619	−1.21834	−0.609169	−	0.793040i	$-0.708497\pi$
$569$	−29.0619	−1.21834	−0.609169	+	0.793040i	$0.708497\pi$
$570$	0	0
$571$	−0.230751	−0.00965665	−0.00482832	−	0.999988i	$-0.501537\pi$
$571$	−0.230751	−0.00965665	−0.00482832	+	0.999988i	$0.501537\pi$
$572$	0.879602	0.0367780
$573$	−15.7683	−0.658729
$574$	−5.14768	−0.214860
$575$	0	0
$576$	8.65227	0.360511
$577$	−37.4944	−1.56091	−0.780456	−	0.625211i	$-0.785013\pi$
$577$	−37.4944	−1.56091	−0.780456	+	0.625211i	$0.785013\pi$
$578$	15.6645	0.651557
$579$	−6.93514	−0.288214
$580$	0	0
$581$	−13.7178	−0.569110
$582$	−24.1067	−0.999256
$583$	−8.91215	−0.369103
$584$	−38.8851	−1.60908
$585$	0	0
$586$	−0.393329	−0.0162483
$587$	−15.3719	−0.634464	−0.317232	−	0.948348i	$-0.602753\pi$
$587$	−15.3719	−0.634464	−0.317232	+	0.948348i	$0.602753\pi$
$588$	−1.12100	−0.0462293
$589$	8.31868	0.342765
$590$	0	0
$591$	7.43948	0.306019
$592$	27.6023	1.13445
$593$	8.30710	0.341132	0.170566	−	0.985346i	$-0.445440\pi$
$593$	8.30710	0.341132	0.170566	+	0.985346i	$0.445440\pi$
$594$	−1.55955	−0.0639889
$595$	0	0
$596$	4.51998	0.185145
$597$	14.2398	0.582796
$598$	−16.5155	−0.675369
$599$	−29.0293	−1.18610	−0.593052	−	0.805164i	$-0.702077\pi$
$599$	−29.0293	−1.18610	−0.593052	+	0.805164i	$0.702077\pi$
$600$	0	0
$601$	−43.2988	−1.76620	−0.883098	−	0.469188i	$-0.844547\pi$
$601$	−43.2988	−1.76620	−0.883098	+	0.469188i	$0.844547\pi$
$602$	−5.86210	−0.238921
$603$	8.78903	0.357917
$604$	−2.48607	−0.101157
$605$	0	0
$606$	8.76072	0.355880
$607$	14.4484	0.586443	0.293222	−	0.956044i	$-0.405273\pi$
$607$	14.4484	0.586443	0.293222	+	0.956044i	$0.405273\pi$
$608$	−8.96194	−0.363455
$609$	4.11653	0.166810
$610$	0	0
$611$	33.9913	1.37514
$612$	−1.12007	−0.0452760
$613$	−8.63973	−0.348955	−0.174478	−	0.984661i	$-0.555824\pi$
$613$	−8.63973	−0.348955	−0.174478	+	0.984661i	$0.555824\pi$
$614$	−1.79877	−0.0725926
$615$	0	0
$616$	−4.40898	−0.177643
$617$	−32.9268	−1.32559	−0.662793	−	0.748803i	$-0.730629\pi$
$617$	−32.9268	−1.32559	−0.662793	+	0.748803i	$0.730629\pi$
$618$	−14.9334	−0.600707
$619$	9.82425	0.394870	0.197435	−	0.980316i	$-0.436739\pi$
$619$	9.82425	0.394870	0.197435	+	0.980316i	$0.436739\pi$
$620$	0	0
$621$	−3.41811	−0.137164
$622$	26.7075	1.07087
$623$	−5.77925	−0.231541
$624$	−12.7745	−0.511390
$625$	0	0
$626$	18.9292	0.756561
$627$	8.86889	0.354189
$628$	2.53193	0.101035
$629$	−41.7969	−1.66655
$630$	0	0
$631$	2.88051	0.114671	0.0573356	−	0.998355i	$-0.481739\pi$
$631$	2.88051	0.114671	0.0573356	+	0.998355i	$0.481739\pi$
$632$	34.0432	1.35417
$633$	−6.89569	−0.274079
$634$	23.5396	0.934878
$635$	0	0
$636$	−1.59878	−0.0633959
$637$	19.3600	0.767072
$638$	−5.01646	−0.198603
$639$	−15.0647	−0.595952
$640$	0	0
$641$	−18.6464	−0.736490	−0.368245	−	0.929729i	$-0.620041\pi$
$641$	−18.6464	−0.736490	−0.368245	+	0.929729i	$0.620041\pi$
$642$	4.98744	0.196839
$643$	1.96215	0.0773795	0.0386897	−	0.999251i	$-0.487682\pi$
$643$	1.96215	0.0773795	0.0386897	+	0.999251i	$0.487682\pi$
$644$	−0.914501	−0.0360364
$645$	0	0
$646$	−54.5673	−2.14692
$647$	−1.72726	−0.0679055	−0.0339528	−	0.999423i	$-0.510810\pi$
$647$	−1.72726	−0.0679055	−0.0339528	+	0.999423i	$0.510810\pi$
$648$	−2.95630	−0.116134
$649$	14.8582	0.583237
$650$	0	0
$651$	1.39886	0.0548258
$652$	−1.72872	−0.0677018
$653$	8.37928	0.327907	0.163953	−	0.986468i	$-0.447575\pi$
$653$	8.37928	0.327907	0.163953	+	0.986468i	$0.447575\pi$
$654$	9.36158	0.366067
$655$	0	0
$656$	10.6345	0.415208
$657$	13.1533	0.513160
$658$	−16.1241	−0.628585
$659$	31.2624	1.21781	0.608905	−	0.793243i	$-0.291609\pi$
$659$	31.2624	1.21781	0.608905	+	0.793243i	$0.291609\pi$
$660$	0	0
$661$	−10.8798	−0.423175	−0.211588	−	0.977359i	$-0.567863\pi$
$661$	−10.8798	−0.423175	−0.211588	+	0.977359i	$0.567863\pi$
$662$	10.7152	0.416459
$663$	19.3439	0.751255
$664$	31.6883	1.22974
$665$	0	0
$666$	−10.4401	−0.404547
$667$	−10.9948	−0.425719
$668$	−1.30987	−0.0506806
$669$	−13.3983	−0.518009
$670$	0	0
$671$	−11.8290	−0.456653
$672$	−1.50703	−0.0581351
$673$	28.9803	1.11711	0.558554	−	0.829468i	$-0.311356\pi$
$673$	28.9803	1.11711	0.558554	+	0.829468i	$0.311356\pi$
$674$	14.5166	0.559160
$675$	0	0
$676$	−0.00743080	−0.000285800 0
$677$	−5.89919	−0.226724	−0.113362	−	0.993554i	$-0.536162\pi$
$677$	−5.89919	−0.226724	−0.113362	+	0.993554i	$0.536162\pi$
$678$	7.49236	0.287742
$679$	23.0532	0.884699
$680$	0	0
$681$	0.849831	0.0325656
$682$	−1.70467	−0.0652752
$683$	45.9083	1.75663	0.878316	−	0.478081i	$-0.158668\pi$
$683$	45.9083	1.75663	0.878316	+	0.478081i	$0.158668\pi$
$684$	1.59102	0.0608343
$685$	0	0
$686$	−21.1723	−0.808364
$687$	8.79561	0.335574
$688$	12.1104	0.461706
$689$	27.6115	1.05191
$690$	0	0
$691$	20.9475	0.796880	0.398440	−	0.917194i	$-0.369552\pi$
$691$	20.9475	0.796880	0.398440	+	0.917194i	$0.369552\pi$
$692$	−1.39150	−0.0528970
$693$	1.49139	0.0566531
$694$	2.49122	0.0945653
$695$	0	0
$696$	−9.50926	−0.360448
$697$	−16.1034	−0.609960
$698$	32.7370	1.23911
$699$	−21.2093	−0.802210
$700$	0	0
$701$	52.2223	1.97241	0.986204	−	0.165533i	$-0.0529346\pi$
$701$	52.2223	1.97241	0.986204	+	0.165533i	$0.0529346\pi$
$702$	4.83176	0.182363
$703$	59.3713	2.23923
$704$	10.0829	0.380015
$705$	0	0
$706$	−50.0002	−1.88178
$707$	−8.37783	−0.315081
$708$	2.66548	0.100175
$709$	−46.9974	−1.76503	−0.882513	−	0.470288i	$-0.844150\pi$
$709$	−46.9974	−1.76503	−0.882513	+	0.470288i	$0.844150\pi$
$710$	0	0
$711$	−11.5155	−0.431865
$712$	13.3502	0.500318
$713$	−3.73619	−0.139921
$714$	−9.17600	−0.343403
$715$	0	0
$716$	−4.53976	−0.169659
$717$	16.7972	0.627304
$718$	−33.9062	−1.26537
$719$	−4.69037	−0.174921	−0.0874607	−	0.996168i	$-0.527875\pi$
$719$	−4.69037	−0.174921	−0.0874607	+	0.996168i	$0.527875\pi$
$720$	0	0
$721$	14.2807	0.531841
$722$	52.0843	1.93838
$723$	−9.51860	−0.354001
$724$	−2.70675	−0.100596
$725$	0	0
$726$	12.9035	0.478892
$727$	27.7594	1.02954	0.514769	−	0.857329i	$-0.327878\pi$
$727$	27.7594	1.02954	0.514769	+	0.857329i	$0.327878\pi$
$728$	13.6598	0.506267
$729$	1.00000	0.0370370
$730$	0	0
$731$	−18.3383	−0.678267
$732$	−2.12205	−0.0784331
$733$	−30.6040	−1.13038	−0.565192	−	0.824960i	$-0.691198\pi$
$733$	−30.6040	−1.13038	−0.565192	+	0.824960i	$0.691198\pi$
$734$	31.7244	1.17097
$735$	0	0
$736$	4.02510	0.148367
$737$	10.2423	0.377281
$738$	−4.02234	−0.148064
$739$	4.93383	0.181494	0.0907469	−	0.995874i	$-0.471075\pi$
$739$	4.93383	0.181494	0.0907469	+	0.995874i	$0.471075\pi$
$740$	0	0
$741$	−27.4775	−1.00941
$742$	−13.0978	−0.480836
$743$	21.7109	0.796496	0.398248	−	0.917278i	$-0.369618\pi$
$743$	21.7109	0.796496	0.398248	+	0.917278i	$0.369618\pi$
$744$	−3.23140	−0.118469
$745$	0	0
$746$	−3.92438	−0.143682
$747$	−10.7189	−0.392185
$748$	−1.30527	−0.0477255
$749$	−4.76947	−0.174273
$750$	0	0
$751$	−33.6080	−1.22637	−0.613186	−	0.789939i	$-0.710112\pi$
$751$	−33.6080	−1.22637	−0.613186	+	0.789939i	$0.710112\pi$
$752$	33.3106	1.21471
$753$	−12.9486	−0.471874
$754$	15.5419	0.566003
$755$	0	0
$756$	0.267545	0.00973053
$757$	−4.88834	−0.177670	−0.0888349	−	0.996046i	$-0.528314\pi$
$757$	−4.88834	−0.177670	−0.0888349	+	0.996046i	$0.528314\pi$
$758$	−23.7339	−0.862054
$759$	−3.98331	−0.144585
$760$	0	0
$761$	−30.2366	−1.09608	−0.548038	−	0.836453i	$-0.684625\pi$
$761$	−30.2366	−1.09608	−0.548038	+	0.836453i	$0.684625\pi$
$762$	5.87389	0.212788
$763$	−8.95243	−0.324100
$764$	−3.29647	−0.119262
$765$	0	0
$766$	−5.89536	−0.213008
$767$	−46.0336	−1.66218
$768$	4.96064	0.179002
$769$	51.0523	1.84099	0.920497	−	0.390751i	$-0.127785\pi$
$769$	51.0523	1.84099	0.920497	+	0.390751i	$0.127785\pi$
$770$	0	0
$771$	16.6837	0.600851
$772$	−1.44984	−0.0521808
$773$	−6.54233	−0.235311	−0.117656	−	0.993054i	$-0.537538\pi$
$773$	−6.54233	−0.235311	−0.117656	+	0.993054i	$0.537538\pi$
$774$	−4.58058	−0.164646
$775$	0	0
$776$	−53.2532	−1.91168
$777$	9.98384	0.358168
$778$	−41.9163	−1.50277
$779$	22.8744	0.819561
$780$	0	0
$781$	−17.5557	−0.628193
$782$	24.5080	0.876403
$783$	3.21661	0.114952
$784$	18.9724	0.677585
$785$	0	0
$786$	6.68119	0.238310
$787$	10.9765	0.391269	0.195635	−	0.980677i	$-0.437323\pi$
$787$	10.9765	0.391269	0.195635	+	0.980677i	$0.437323\pi$
$788$	1.55527	0.0554044
$789$	9.45426	0.336581
$790$	0	0
$791$	−7.16491	−0.254755
$792$	−3.44512	−0.122417
$793$	36.6484	1.30142
$794$	−21.9850	−0.780220
$795$	0	0
$796$	2.97693	0.105514
$797$	12.6891	0.449473	0.224736	−	0.974420i	$-0.427848\pi$
$797$	12.6891	0.449473	0.224736	+	0.974420i	$0.427848\pi$
$798$	13.0342	0.461407
$799$	−50.4409	−1.78447
$800$	0	0
$801$	−4.51584	−0.159559
$802$	−20.3166	−0.717404
$803$	15.3283	0.540923
$804$	1.83741	0.0648004
$805$	0	0
$806$	5.28139	0.186029
$807$	−31.7384	−1.11725
$808$	19.3529	0.680833
$809$	−17.7818	−0.625174	−0.312587	−	0.949889i	$-0.601195\pi$
$809$	−17.7818	−0.625174	−0.312587	+	0.949889i	$0.601195\pi$
$810$	0	0
$811$	37.0811	1.30210	0.651048	−	0.759037i	$-0.274330\pi$
$811$	37.0811	1.30210	0.651048	+	0.759037i	$0.274330\pi$
$812$	0.860590	0.0302008
$813$	−19.0556	−0.668309
$814$	−12.1664	−0.426433
$815$	0	0
$816$	18.9566	0.663613
$817$	26.0490	0.911340
$818$	−19.8627	−0.694482
$819$	−4.62059	−0.161456
$820$	0	0
$821$	−0.337853	−0.0117911	−0.00589557	−	0.999983i	$-0.501877\pi$
$821$	−0.337853	−0.0117911	−0.00589557	+	0.999983i	$0.501877\pi$
$822$	−16.3342	−0.569722
$823$	26.6629	0.929409	0.464704	−	0.885466i	$-0.346161\pi$
$823$	26.6629	0.929409	0.464704	+	0.885466i	$0.346161\pi$
$824$	−32.9886	−1.14921
$825$	0	0
$826$	21.8365	0.759791
$827$	−43.4655	−1.51144	−0.755722	−	0.654893i	$-0.772714\pi$
$827$	−43.4655	−1.51144	−0.755722	+	0.654893i	$0.772714\pi$
$828$	−0.714580	−0.0248334
$829$	18.9493	0.658137	0.329068	−	0.944306i	$-0.393265\pi$
$829$	18.9493	0.658137	0.329068	+	0.944306i	$0.393265\pi$
$830$	0	0
$831$	2.71929	0.0943312
$832$	−31.2388	−1.08301
$833$	−28.7290	−0.995402
$834$	6.96722	0.241255
$835$	0	0
$836$	1.85410	0.0641255
$837$	1.09306	0.0377816
$838$	−47.1919	−1.63022
$839$	22.7357	0.784922	0.392461	−	0.919769i	$-0.371624\pi$
$839$	22.7357	0.784922	0.392461	+	0.919769i	$0.371624\pi$
$840$	0	0
$841$	−18.6534	−0.643221
$842$	−15.0992	−0.520355
$843$	14.6076	0.503112
$844$	−1.44159	−0.0496217
$845$	0	0
$846$	−12.5992	−0.433170
$847$	−12.3395	−0.423991
$848$	27.0586	0.929196
$849$	−18.0890	−0.620813
$850$	0	0
$851$	−26.6656	−0.914085
$852$	−3.14939	−0.107896
$853$	−35.9922	−1.23235	−0.616175	−	0.787610i	$-0.711318\pi$
$853$	−35.9922	−1.23235	−0.616175	+	0.787610i	$0.711318\pi$
$854$	−17.3846	−0.594888
$855$	0	0
$856$	11.0175	0.376572
$857$	−20.1724	−0.689076	−0.344538	−	0.938772i	$-0.611964\pi$
$857$	−20.1724	−0.689076	−0.344538	+	0.938772i	$0.611964\pi$
$858$	5.63070	0.192229
$859$	39.0077	1.33093	0.665464	−	0.746430i	$-0.268234\pi$
$859$	39.0077	1.33093	0.665464	+	0.746430i	$0.268234\pi$
$860$	0	0
$861$	3.84655	0.131090
$862$	34.5605	1.17713
$863$	24.4962	0.833861	0.416930	−	0.908938i	$-0.363106\pi$
$863$	24.4962	0.833861	0.416930	+	0.908938i	$0.363106\pi$
$864$	−1.17758	−0.0400621
$865$	0	0
$866$	−13.3813	−0.454715
$867$	−11.7051	−0.397526
$868$	0.292442	0.00992613
$869$	−13.4196	−0.455230
$870$	0	0
$871$	−31.7326	−1.07522
$872$	20.6803	0.700322
$873$	18.0135	0.609664
$874$	−34.8128	−1.17756
$875$	0	0
$876$	2.74979	0.0929069
$877$	29.2278	0.986952	0.493476	−	0.869759i	$-0.335726\pi$
$877$	29.2278	0.986952	0.493476	+	0.869759i	$0.335726\pi$
$878$	12.3172	0.415684
$879$	0.293910	0.00991335
$880$	0	0
$881$	−3.72194	−0.125395	−0.0626977	−	0.998033i	$-0.519970\pi$
$881$	−3.72194	−0.125395	−0.0626977	+	0.998033i	$0.519970\pi$
$882$	−7.17600	−0.241628
$883$	−7.01518	−0.236080	−0.118040	−	0.993009i	$-0.537661\pi$
$883$	−7.01518	−0.236080	−0.118040	+	0.993009i	$0.537661\pi$
$884$	4.04398	0.136014
$885$	0	0
$886$	−12.2155	−0.410388
$887$	27.4537	0.921806	0.460903	−	0.887451i	$-0.347526\pi$
$887$	27.4537	0.921806	0.460903	+	0.887451i	$0.347526\pi$
$888$	−23.0628	−0.773938
$889$	−5.61717	−0.188394
$890$	0	0
$891$	1.16535	0.0390408
$892$	−2.80101	−0.0937849
$893$	71.6498	2.39767
$894$	28.9343	0.967707
$895$	0	0
$896$	11.8044	0.394358
$897$	12.3410	0.412055
$898$	47.4857	1.58462
$899$	3.51594	0.117263
$900$	0	0
$901$	−40.9737	−1.36503
$902$	−4.68744	−0.156075
$903$	4.38039	0.145770
$904$	16.5511	0.550480
$905$	0	0
$906$	−15.9144	−0.528720
$907$	−6.09167	−0.202271	−0.101135	−	0.994873i	$-0.532248\pi$
$907$	−6.09167	−0.202271	−0.101135	+	0.994873i	$0.532248\pi$
$908$	0.177663	0.00589595
$909$	−6.54634	−0.217128
$910$	0	0
$911$	−2.77586	−0.0919682	−0.0459841	−	0.998942i	$-0.514642\pi$
$911$	−2.77586	−0.0919682	−0.0459841	+	0.998942i	$0.514642\pi$
$912$	−26.9272	−0.891650
$913$	−12.4913	−0.413402
$914$	25.0945	0.830053
$915$	0	0
$916$	1.83878	0.0607551
$917$	−6.38919	−0.210990
$918$	−7.17002	−0.236646
$919$	−23.7566	−0.783659	−0.391829	−	0.920038i	$-0.628158\pi$
$919$	−23.7566	−0.783659	−0.391829	+	0.920038i	$0.628158\pi$
$920$	0	0
$921$	1.34411	0.0442900
$922$	−21.5296	−0.709039
$923$	54.3909	1.79030
$924$	0.311785	0.0102570
$925$	0	0
$926$	−28.2427	−0.928112
$927$	11.1588	0.366502
$928$	−3.78782	−0.124341
$929$	28.7158	0.942136	0.471068	−	0.882097i	$-0.343869\pi$
$929$	28.7158	0.942136	0.471068	+	0.882097i	$0.343869\pi$
$930$	0	0
$931$	40.8088	1.33745
$932$	−4.43395	−0.145239
$933$	−19.9569	−0.653360
$934$	24.1050	0.788739
$935$	0	0
$936$	10.6736	0.348879
$937$	−13.1368	−0.429161	−0.214580	−	0.976706i	$-0.568838\pi$
$937$	−13.1368	−0.429161	−0.214580	+	0.976706i	$0.568838\pi$
$938$	15.0527	0.491489
$939$	−14.1446	−0.461591
$940$	0	0
$941$	−39.4446	−1.28586	−0.642929	−	0.765926i	$-0.722281\pi$
$941$	−39.4446	−1.28586	−0.642929	+	0.765926i	$0.722281\pi$
$942$	16.2080	0.528084
$943$	−10.2736	−0.334556
$944$	−45.1118	−1.46826
$945$	0	0
$946$	−5.33799	−0.173553
$947$	25.1266	0.816504	0.408252	−	0.912869i	$-0.366138\pi$
$947$	25.1266	0.816504	0.408252	+	0.912869i	$0.366138\pi$
$948$	−2.40740	−0.0781886
$949$	−47.4898	−1.54158
$950$	0	0
$951$	−17.5897	−0.570386
$952$	−20.2703	−0.656964
$953$	−6.14850	−0.199169	−0.0995847	−	0.995029i	$-0.531751\pi$
$953$	−6.14850	−0.199169	−0.0995847	+	0.995029i	$0.531751\pi$
$954$	−10.2345	−0.331354
$955$	0	0
$956$	3.51158	0.113573
$957$	3.74849	0.121171
$958$	9.78823	0.316243
$959$	15.6204	0.504407
$960$	0	0
$961$	−29.8052	−0.961459
$962$	37.6938	1.21530
$963$	−3.72681	−0.120095
$964$	−1.98993	−0.0640913
$965$	0	0
$966$	−5.85410	−0.188353
$967$	−49.4461	−1.59008	−0.795040	−	0.606557i	$-0.792550\pi$
$967$	−49.4461	−1.59008	−0.795040	+	0.606557i	$0.792550\pi$
$968$	28.5045	0.916168
$969$	40.7748	1.30987
$970$	0	0
$971$	51.7332	1.66020	0.830099	−	0.557616i	$-0.188284\pi$
$971$	51.7332	1.66020	0.830099	+	0.557616i	$0.188284\pi$
$972$	0.209057	0.00670550
$973$	−6.66272	−0.213597
$974$	15.9832	0.512136
$975$	0	0
$976$	35.9146	1.14960
$977$	−36.3167	−1.16187	−0.580937	−	0.813948i	$-0.697314\pi$
$977$	−36.3167	−1.16187	−0.580937	+	0.813948i	$0.697314\pi$
$978$	−11.0662	−0.353860
$979$	−5.26254	−0.168192
$980$	0	0
$981$	−6.99533	−0.223344
$982$	14.9427	0.476841
$983$	52.0481	1.66008	0.830039	−	0.557706i	$-0.188318\pi$
$983$	52.0481	1.66008	0.830039	+	0.557706i	$0.188318\pi$
$984$	−8.88558	−0.283262
$985$	0	0
$986$	−23.0632	−0.734482
$987$	12.0486	0.383511
$988$	−5.74435	−0.182752
$989$	−11.6995	−0.372021
$990$	0	0
$991$	−29.4843	−0.936599	−0.468300	−	0.883570i	$-0.655133\pi$
$991$	−29.4843	−0.936599	−0.468300	+	0.883570i	$0.655133\pi$
$992$	−1.28716	−0.0408674
$993$	−8.00683	−0.254089
$994$	−25.8009	−0.818356
$995$	0	0
$996$	−2.24086	−0.0710045
$997$	42.4390	1.34406	0.672029	−	0.740525i	$-0.265423\pi$
$997$	42.4390	1.34406	0.672029	+	0.740525i	$0.265423\pi$
$998$	40.9568	1.29647
$999$	7.80126	0.246821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.g.1.3	yes	4
3.2	odd	2		5625.2.a.j.1.2		4
5.2	odd	4		1875.2.b.d.1249.6		8
5.3	odd	4		1875.2.b.d.1249.3		8
5.4	even	2		1875.2.a.f.1.2	✓	4
15.14	odd	2		5625.2.a.m.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.f.1.2	✓	4	5.4	even	2
1875.2.a.g.1.3	yes	4	1.1	even	1	trivial
1875.2.b.d.1249.3		8	5.3	odd	4
1875.2.b.d.1249.6		8	5.2	odd	4
5625.2.a.j.1.2		4	3.2	odd	2
5625.2.a.m.1.3		4	15.14	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+1.33826 q^{2} -1.00000 q^{3} -0.209057 q^{4} -1.33826 q^{6} +1.27977 q^{7} -2.95630 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.33826 q^{2} -1.00000 q^{3} -0.209057 q^{4} -1.33826 q^{6} +1.27977 q^{7} -2.95630 q^{8} +1.00000 q^{9} +1.16535 q^{11} +0.209057 q^{12} -3.61048 q^{13} +1.71267 q^{14} -3.53818 q^{16} +5.35772 q^{17} +1.33826 q^{18} -7.61048 q^{19} -1.27977 q^{21} +1.55955 q^{22} +3.41811 q^{23} +2.95630 q^{24} -4.83176 q^{26} -1.00000 q^{27} -0.267545 q^{28} -3.21661 q^{29} -1.09306 q^{31} +1.17758 q^{32} -1.16535 q^{33} +7.17002 q^{34} -0.209057 q^{36} -7.80126 q^{37} -10.1848 q^{38} +3.61048 q^{39} -3.00565 q^{41} -1.71267 q^{42} -3.42278 q^{43} -0.243625 q^{44} +4.57433 q^{46} -9.41462 q^{47} +3.53818 q^{48} -5.36218 q^{49} -5.35772 q^{51} +0.754795 q^{52} -7.64760 q^{53} -1.33826 q^{54} -3.78339 q^{56} +7.61048 q^{57} -4.30467 q^{58} +12.7500 q^{59} -10.1506 q^{61} -1.46280 q^{62} +1.27977 q^{63} +8.65227 q^{64} -1.55955 q^{66} +8.78903 q^{67} -1.12007 q^{68} -3.41811 q^{69} -15.0647 q^{71} -2.95630 q^{72} +13.1533 q^{73} -10.4401 q^{74} +1.59102 q^{76} +1.49139 q^{77} +4.83176 q^{78} -11.5155 q^{79} +1.00000 q^{81} -4.02234 q^{82} -10.7189 q^{83} +0.267545 q^{84} -4.58058 q^{86} +3.21661 q^{87} -3.44512 q^{88} -4.51584 q^{89} -4.62059 q^{91} -0.714580 q^{92} +1.09306 q^{93} -12.5992 q^{94} -1.17758 q^{96} +18.0135 q^{97} -7.17600 q^{98} +1.16535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9	\( 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9} - 6 q^{11} - q^{12} + 7 q^{13} - 10 q^{14} - 9 q^{16} - 7 q^{17} + q^{18} - 9 q^{19} - 5 q^{21} + 6 q^{22} + 10 q^{23} + 3 q^{24} - 2 q^{26} - 4 q^{27} + 5 q^{28} - 28 q^{29} - 10 q^{31} + 6 q^{33} + 7 q^{34} + q^{36} - 10 q^{37} - 6 q^{38} - 7 q^{39} + 10 q^{42} + q^{43} - 9 q^{44} + 5 q^{46} - 23 q^{47} + 9 q^{48} - 3 q^{49} + 7 q^{51} + 13 q^{52} - q^{54} + 9 q^{57} - 2 q^{58} + 4 q^{59} - 43 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} - 6 q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 27 q^{71} - 3 q^{72} + 15 q^{73} + 5 q^{74} + 9 q^{76} - 15 q^{77} + 2 q^{78} + 10 q^{79} + 4 q^{81} - 20 q^{82} + 3 q^{83} - 5 q^{84} + 24 q^{86} + 28 q^{87} - 3 q^{88} - 9 q^{89} + 5 q^{91} - 15 q^{92} + 10 q^{93} - 22 q^{94} + 13 q^{97} - 42 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9 - 6 * q^11 - q^12 + 7 * q^13 - 10 * q^14 - 9 * q^16 - 7 * q^17 + q^18 - 9 * q^19 - 5 * q^21 + 6 * q^22 + 10 * q^23 + 3 * q^24 - 2 * q^26 - 4 * q^27 + 5 * q^28 - 28 * q^29 - 10 * q^31 + 6 * q^33 + 7 * q^34 + q^36 - 10 * q^37 - 6 * q^38 - 7 * q^39 + 10 * q^42 + q^43 - 9 * q^44 + 5 * q^46 - 23 * q^47 + 9 * q^48 - 3 * q^49 + 7 * q^51 + 13 * q^52 - q^54 + 9 * q^57 - 2 * q^58 + 4 * q^59 - 43 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 - 6 * q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 27 * q^71 - 3 * q^72 + 15 * q^73 + 5 * q^74 + 9 * q^76 - 15 * q^77 + 2 * q^78 + 10 * q^79 + 4 * q^81 - 20 * q^82 + 3 * q^83 - 5 * q^84 + 24 * q^86 + 28 * q^87 - 3 * q^88 - 9 * q^89 + 5 * q^91 - 15 * q^92 + 10 * q^93 - 22 * q^94 + 13 * q^97 - 42 * q^98 - 6 * q^99

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