LMFDB - Embedded newform 1925.2.a.z.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:	$6$
Coefficient field:	6.6.9921856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 7x^{4} + 11x^{2} - 2x - 1 $ x^6 - 7x^4 + 11x^2 - 2*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			$-1.68955$ 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)

$f(q)$	$=$	$q-1.68955 q^{2} +2.93524 q^{3} +0.854580 q^{4} -4.95924 q^{6} -1.00000 q^{7} +1.93524 q^{8} +5.61566 q^{9} +O(q^{10})$	\(q-1.68955 q^{2} +2.93524 q^{3} +0.854580 q^{4} -4.95924 q^{6} -1.00000 q^{7} +1.93524 q^{8} +5.61566 q^{9} -1.00000 q^{11} +2.50840 q^{12} -3.59605 q^{13} +1.68955 q^{14} -4.97885 q^{16} -1.75150 q^{17} -9.48794 q^{18} -1.84285 q^{19} -2.93524 q^{21} +1.68955 q^{22} +8.49424 q^{23} +5.68042 q^{24} +6.07571 q^{26} +7.67761 q^{27} -0.854580 q^{28} +4.43102 q^{29} +6.61939 q^{31} +4.54153 q^{32} -2.93524 q^{33} +2.95924 q^{34} +4.79903 q^{36} +4.91497 q^{37} +3.11359 q^{38} -10.5553 q^{39} +5.49965 q^{41} +4.95924 q^{42} +9.93310 q^{43} -0.854580 q^{44} -14.3514 q^{46} +4.65189 q^{47} -14.6142 q^{48} +1.00000 q^{49} -5.14108 q^{51} -3.07311 q^{52} +4.76762 q^{53} -12.9717 q^{54} -1.93524 q^{56} -5.40921 q^{57} -7.48644 q^{58} -8.72384 q^{59} -7.08196 q^{61} -11.1838 q^{62} -5.61566 q^{63} +2.28456 q^{64} +4.95924 q^{66} +7.30384 q^{67} -1.49679 q^{68} +24.9327 q^{69} -7.93402 q^{71} +10.8677 q^{72} +16.7363 q^{73} -8.30409 q^{74} -1.57486 q^{76} +1.00000 q^{77} +17.8337 q^{78} -6.47350 q^{79} +5.68868 q^{81} -9.29193 q^{82} +7.82170 q^{83} -2.50840 q^{84} -16.7825 q^{86} +13.0061 q^{87} -1.93524 q^{88} +9.03302 q^{89} +3.59605 q^{91} +7.25901 q^{92} +19.4295 q^{93} -7.85959 q^{94} +13.3305 q^{96} +10.8948 q^{97} -1.68955 q^{98} -5.61566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 2 q^{4} - 2 q^{6} - 6 q^{7} + 10 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 + 2 * q^4 - 2 * q^6 - 6 * q^7 + 10 * q^9	$ 6 q + 6 q^{3} + 2 q^{4} - 2 q^{6} - 6 q^{7} + 10 q^{9} - 6 q^{11} + 12 q^{12} + 6 q^{13} - 6 q^{16} - 2 q^{17} + 14 q^{18} - 2 q^{19} - 6 q^{21} + 8 q^{23} + 22 q^{24} + 24 q^{27} - 2 q^{28} - 8 q^{29} + 4 q^{31} + 10 q^{32} - 6 q^{33} - 10 q^{34} + 26 q^{36} + 22 q^{37} - 10 q^{38} - 8 q^{39} + 4 q^{41} + 2 q^{42} + 30 q^{43} - 2 q^{44} - 8 q^{46} + 16 q^{47} - 8 q^{48} + 6 q^{49} - 4 q^{51} + 22 q^{52} + 6 q^{53} + 38 q^{54} + 18 q^{57} - 14 q^{58} + 14 q^{59} + 12 q^{61} - 14 q^{62} - 10 q^{63} - 22 q^{64} + 2 q^{66} + 46 q^{67} - 20 q^{68} + 12 q^{69} + 4 q^{71} + 32 q^{72} - 4 q^{73} - 8 q^{74} - 8 q^{76} + 6 q^{77} + 24 q^{78} - 8 q^{79} + 26 q^{81} - 10 q^{82} + 14 q^{83} - 12 q^{84} + 12 q^{86} - 2 q^{87} + 8 q^{89} - 6 q^{91} + 18 q^{92} + 12 q^{93} - 10 q^{94} - 16 q^{96} + 42 q^{97} - 10 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 + 2 * q^4 - 2 * q^6 - 6 * q^7 + 10 * q^9 - 6 * q^11 + 12 * q^12 + 6 * q^13 - 6 * q^16 - 2 * q^17 + 14 * q^18 - 2 * q^19 - 6 * q^21 + 8 * q^23 + 22 * q^24 + 24 * q^27 - 2 * q^28 - 8 * q^29 + 4 * q^31 + 10 * q^32 - 6 * q^33 - 10 * q^34 + 26 * q^36 + 22 * q^37 - 10 * q^38 - 8 * q^39 + 4 * q^41 + 2 * q^42 + 30 * q^43 - 2 * q^44 - 8 * q^46 + 16 * q^47 - 8 * q^48 + 6 * q^49 - 4 * q^51 + 22 * q^52 + 6 * q^53 + 38 * q^54 + 18 * q^57 - 14 * q^58 + 14 * q^59 + 12 * q^61 - 14 * q^62 - 10 * q^63 - 22 * q^64 + 2 * q^66 + 46 * q^67 - 20 * q^68 + 12 * q^69 + 4 * q^71 + 32 * q^72 - 4 * q^73 - 8 * q^74 - 8 * q^76 + 6 * q^77 + 24 * q^78 - 8 * q^79 + 26 * q^81 - 10 * q^82 + 14 * q^83 - 12 * q^84 + 12 * q^86 - 2 * q^87 + 8 * q^89 - 6 * q^91 + 18 * q^92 + 12 * q^93 - 10 * q^94 - 16 * q^96 + 42 * q^97 - 10 * 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 $

$2$	−1.68955	−1.19469	−0.597346	−	0.801983i	$-0.703778\pi$
$2$	−1.68955	−1.19469	−0.597346	+	0.801983i	$0.703778\pi$
$3$	2.93524	1.69466	0.847332	−	0.531063i	$-0.178207\pi$
$3$	2.93524	1.69466	0.847332	+	0.531063i	$0.178207\pi$
$4$	0.854580	0.427290
$5$	0	0
$5$	0	0
$6$	−4.95924	−2.02460
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.93524	0.684212
$9$	5.61566	1.87189
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.50840	0.724113
$13$	−3.59605	−0.997366	−0.498683	−	0.866785i	$-0.666183\pi$
$13$	−3.59605	−0.997366	−0.498683	+	0.866785i	$0.666183\pi$
$14$	1.68955	0.451551
$15$	0	0
$16$	−4.97885	−1.24471
$17$	−1.75150	−0.424801	−0.212400	−	0.977183i	$-0.568128\pi$
$17$	−1.75150	−0.424801	−0.212400	+	0.977183i	$0.568128\pi$
$18$	−9.48794	−2.23633
$19$	−1.84285	−0.422779	−0.211389	−	0.977402i	$-0.567799\pi$
$19$	−1.84285	−0.422779	−0.211389	+	0.977402i	$0.567799\pi$
$20$	0	0
$21$	−2.93524	−0.640523
$22$	1.68955	0.360213
$23$	8.49424	1.77117	0.885586	−	0.464476i	$-0.153757\pi$
$23$	8.49424	1.77117	0.885586	+	0.464476i	$0.153757\pi$
$24$	5.68042	1.15951
$25$	0	0
$26$	6.07571	1.19155
$27$	7.67761	1.47756
$28$	−0.854580	−0.161500
$29$	4.43102	0.822820	0.411410	−	0.911450i	$-0.365036\pi$
$29$	4.43102	0.822820	0.411410	+	0.911450i	$0.365036\pi$
$30$	0	0
$31$	6.61939	1.18888	0.594439	−	0.804141i	$-0.297374\pi$
$31$	6.61939	1.18888	0.594439	+	0.804141i	$0.297374\pi$
$32$	4.54153	0.802837
$33$	−2.93524	−0.510961
$34$	2.95924	0.507506
$35$	0	0
$36$	4.79903	0.799839
$37$	4.91497	0.808017	0.404008	−	0.914755i	$-0.367617\pi$
$37$	4.91497	0.808017	0.404008	+	0.914755i	$0.367617\pi$
$38$	3.11359	0.505090
$39$	−10.5553	−1.69020
$40$	0	0
$41$	5.49965	0.858900	0.429450	−	0.903091i	$-0.358707\pi$
$41$	5.49965	0.858900	0.429450	+	0.903091i	$0.358707\pi$
$42$	4.95924	0.765228
$43$	9.93310	1.51478	0.757392	−	0.652961i	$-0.226473\pi$
$43$	9.93310	1.51478	0.757392	+	0.652961i	$0.226473\pi$
$44$	−0.854580	−0.128833
$45$	0	0
$46$	−14.3514	−2.11601
$47$	4.65189	0.678547	0.339274	−	0.940688i	$-0.389819\pi$
$47$	4.65189	0.678547	0.339274	+	0.940688i	$0.389819\pi$
$48$	−14.6142	−2.10937
$49$	1.00000	0.142857
$50$	0	0
$51$	−5.14108	−0.719895
$52$	−3.07311	−0.426164
$53$	4.76762	0.654883	0.327441	−	0.944872i	$-0.393814\pi$
$53$	4.76762	0.654883	0.327441	+	0.944872i	$0.393814\pi$
$54$	−12.9717	−1.76523
$55$	0	0
$56$	−1.93524	−0.258608
$57$	−5.40921	−0.716468
$58$	−7.48644	−0.983017
$59$	−8.72384	−1.13575	−0.567874	−	0.823116i	$-0.692234\pi$
$59$	−8.72384	−1.13575	−0.567874	+	0.823116i	$0.692234\pi$
$60$	0	0
$61$	−7.08196	−0.906752	−0.453376	−	0.891319i	$-0.649781\pi$
$61$	−7.08196	−0.906752	−0.453376	+	0.891319i	$0.649781\pi$
$62$	−11.1838	−1.42034
$63$	−5.61566	−0.707507
$64$	2.28456	0.285570
$65$	0	0
$66$	4.95924	0.610441
$67$	7.30384	0.892306	0.446153	−	0.894957i	$-0.352794\pi$
$67$	7.30384	0.892306	0.446153	+	0.894957i	$0.352794\pi$
$68$	−1.49679	−0.181513
$69$	24.9327	3.00154
$70$	0	0
$71$	−7.93402	−0.941595	−0.470797	−	0.882241i	$-0.656034\pi$
$71$	−7.93402	−0.941595	−0.470797	+	0.882241i	$0.656034\pi$
$72$	10.8677	1.28077
$73$	16.7363	1.95883	0.979416	−	0.201853i	$-0.0646964\pi$
$73$	16.7363	1.95883	0.979416	+	0.201853i	$0.0646964\pi$
$74$	−8.30409	−0.965331
$75$	0	0
$76$	−1.57486	−0.180649
$77$	1.00000	0.113961
$78$	17.8337	2.01927
$79$	−6.47350	−0.728326	−0.364163	−	0.931335i	$-0.618645\pi$
$79$	−6.47350	−0.728326	−0.364163	+	0.931335i	$0.618645\pi$
$80$	0	0
$81$	5.68868	0.632075
$82$	−9.29193	−1.02612
$83$	7.82170	0.858543	0.429272	−	0.903175i	$-0.358770\pi$
$83$	7.82170	0.858543	0.429272	+	0.903175i	$0.358770\pi$
$84$	−2.50840	−0.273689
$85$	0	0
$86$	−16.7825	−1.80970
$87$	13.0061	1.39440
$88$	−1.93524	−0.206298
$89$	9.03302	0.957499	0.478749	−	0.877952i	$-0.341090\pi$
$89$	9.03302	0.957499	0.478749	+	0.877952i	$0.341090\pi$
$90$	0	0
$91$	3.59605	0.376969
$92$	7.25901	0.756804
$93$	19.4295	2.01475
$94$	−7.85959	−0.810655
$95$	0	0
$96$	13.3305	1.36054
$97$	10.8948	1.10620	0.553098	−	0.833116i	$-0.313445\pi$
$97$	10.8948	1.10620	0.553098	+	0.833116i	$0.313445\pi$
$98$	−1.68955	−0.170670
$99$	−5.61566	−0.564395
$100$	0	0
$101$	5.53367	0.550621	0.275310	−	0.961355i	$-0.411219\pi$
$101$	5.53367	0.550621	0.275310	+	0.961355i	$0.411219\pi$
$102$	8.68610	0.860053
$103$	−11.2110	−1.10465	−0.552327	−	0.833627i	$-0.686260\pi$
$103$	−11.2110	−1.10465	−0.552327	+	0.833627i	$0.686260\pi$
$104$	−6.95924	−0.682410
$105$	0	0
$106$	−8.05513	−0.782383
$107$	−6.44910	−0.623458	−0.311729	−	0.950171i	$-0.600908\pi$
$107$	−6.44910	−0.623458	−0.311729	+	0.950171i	$0.600908\pi$
$108$	6.56113	0.631345
$109$	−18.9353	−1.81367	−0.906836	−	0.421484i	$-0.861509\pi$
$109$	−18.9353	−1.81367	−0.906836	+	0.421484i	$0.861509\pi$
$110$	0	0
$111$	14.4267	1.36932
$112$	4.97885	0.470457
$113$	−0.0174640	−0.00164288	−0.000821438	−	1.00000i	$-0.500261\pi$
$113$	−0.0174640	−0.00164288	−0.000821438		1.00000i	$0.500261\pi$
$114$	9.13914	0.855959
$115$	0	0
$116$	3.78666	0.351583
$117$	−20.1942	−1.86696
$118$	14.7394	1.35687
$119$	1.75150	0.160560
$120$	0	0
$121$	1.00000	0.0909091
$122$	11.9653	1.08329
$123$	16.1428	1.45555
$124$	5.65680	0.507995
$125$	0	0
$126$	9.48794	0.845253
$127$	3.81559	0.338579	0.169289	−	0.985566i	$-0.445853\pi$
$127$	3.81559	0.338579	0.169289	+	0.985566i	$0.445853\pi$
$128$	−12.9429	−1.14401
$129$	29.1561	2.56705
$130$	0	0
$131$	2.39529	0.209278	0.104639	−	0.994510i	$-0.466631\pi$
$131$	2.39529	0.209278	0.104639	+	0.994510i	$0.466631\pi$
$132$	−2.50840	−0.218328
$133$	1.84285	0.159795
$134$	−12.3402	−1.06603
$135$	0	0
$136$	−3.38958	−0.290654
$137$	−19.4393	−1.66081	−0.830404	−	0.557162i	$-0.811890\pi$
$137$	−19.4393	−1.66081	−0.830404	+	0.557162i	$0.811890\pi$
$138$	−42.1250	−3.58592
$139$	5.68824	0.482470	0.241235	−	0.970467i	$-0.422448\pi$
$139$	5.68824	0.482470	0.241235	+	0.970467i	$0.422448\pi$
$140$	0	0
$141$	13.6544	1.14991
$142$	13.4049	1.12492
$143$	3.59605	0.300717
$144$	−27.9596	−2.32996
$145$	0	0
$146$	−28.2768	−2.34020
$147$	2.93524	0.242095
$148$	4.20024	0.345257
$149$	−17.3898	−1.42463	−0.712313	−	0.701862i	$-0.752352\pi$
$149$	−17.3898	−1.42463	−0.712313	+	0.701862i	$0.752352\pi$
$150$	0	0
$151$	6.54075	0.532279	0.266140	−	0.963935i	$-0.414252\pi$
$151$	6.54075	0.532279	0.266140	+	0.963935i	$0.414252\pi$
$152$	−3.56637	−0.289270
$153$	−9.83582	−0.795179
$154$	−1.68955	−0.136148
$155$	0	0
$156$	−9.02034	−0.722205
$157$	23.2280	1.85380	0.926899	−	0.375310i	$-0.122464\pi$
$157$	23.2280	1.85380	0.926899	+	0.375310i	$0.122464\pi$
$158$	10.9373	0.870125
$159$	13.9941	1.10981
$160$	0	0
$161$	−8.49424	−0.669440
$162$	−9.61131	−0.755136
$163$	−14.7123	−1.15236	−0.576179	−	0.817324i	$-0.695457\pi$
$163$	−14.7123	−1.15236	−0.576179	+	0.817324i	$0.695457\pi$
$164$	4.69989	0.366999
$165$	0	0
$166$	−13.2152	−1.02570
$167$	−21.4503	−1.65987	−0.829935	−	0.557860i	$-0.811623\pi$
$167$	−21.4503	−1.65987	−0.829935	+	0.557860i	$0.811623\pi$
$168$	−5.68042	−0.438254
$169$	−0.0684016	−0.00526166
$170$	0	0
$171$	−10.3488	−0.791394
$172$	8.48863	0.647252
$173$	−10.3341	−0.785689	−0.392844	−	0.919605i	$-0.628509\pi$
$173$	−10.3341	−0.785689	−0.392844	+	0.919605i	$0.628509\pi$
$174$	−21.9745	−1.66588
$175$	0	0
$176$	4.97885	0.375295
$177$	−25.6066	−1.92471
$178$	−15.2617	−1.14392
$179$	−5.67740	−0.424348	−0.212174	−	0.977232i	$-0.568054\pi$
$179$	−5.67740	−0.424348	−0.212174	+	0.977232i	$0.568054\pi$
$180$	0	0
$181$	21.2115	1.57664	0.788318	−	0.615268i	$-0.210952\pi$
$181$	21.2115	1.57664	0.788318	+	0.615268i	$0.210952\pi$
$182$	−6.07571	−0.450362
$183$	−20.7873	−1.53664
$184$	16.4384	1.21186
$185$	0	0
$186$	−32.8272	−2.40700
$187$	1.75150	0.128082
$188$	3.97541	0.289936
$189$	−7.67761	−0.558464
$190$	0	0
$191$	6.83000	0.494202	0.247101	−	0.968990i	$-0.420522\pi$
$191$	6.83000	0.494202	0.247101	+	0.968990i	$0.420522\pi$
$192$	6.70574	0.483945
$193$	13.4586	0.968772	0.484386	−	0.874854i	$-0.339043\pi$
$193$	13.4586	0.968772	0.484386	+	0.874854i	$0.339043\pi$
$194$	−18.4073	−1.32156
$195$	0	0
$196$	0.854580	0.0610414
$197$	−13.2385	−0.943202	−0.471601	−	0.881812i	$-0.656324\pi$
$197$	−13.2385	−0.943202	−0.471601	+	0.881812i	$0.656324\pi$
$198$	9.48794	0.674279
$199$	−6.98738	−0.495322	−0.247661	−	0.968847i	$-0.579662\pi$
$199$	−6.98738	−0.495322	−0.247661	+	0.968847i	$0.579662\pi$
$200$	0	0
$201$	21.4386	1.51216
$202$	−9.34941	−0.657822
$203$	−4.43102	−0.310997
$204$	−4.39346	−0.307604
$205$	0	0
$206$	18.9416	1.31972
$207$	47.7008	3.31543
$208$	17.9042	1.24143
$209$	1.84285	0.127473
$210$	0	0
$211$	14.0484	0.967134	0.483567	−	0.875307i	$-0.339341\pi$
$211$	14.0484	0.967134	0.483567	+	0.875307i	$0.339341\pi$
$212$	4.07431	0.279825
$213$	−23.2883	−1.59569
$214$	10.8961	0.744840
$215$	0	0
$216$	14.8581	1.01096
$217$	−6.61939	−0.449353
$218$	31.9921	2.16678
$219$	49.1250	3.31956
$220$	0	0
$221$	6.29848	0.423682
$222$	−24.3746	−1.63591
$223$	7.68300	0.514492	0.257246	−	0.966346i	$-0.417185\pi$
$223$	7.68300	0.514492	0.257246	+	0.966346i	$0.417185\pi$
$224$	−4.54153	−0.303444
$225$	0	0
$226$	0.0295063	0.00196273
$227$	16.2711	1.07995	0.539974	−	0.841681i	$-0.318434\pi$
$227$	16.2711	1.07995	0.539974	+	0.841681i	$0.318434\pi$
$228$	−4.62261	−0.306140
$229$	−13.9687	−0.923079	−0.461540	−	0.887120i	$-0.652703\pi$
$229$	−13.9687	−0.923079	−0.461540	+	0.887120i	$0.652703\pi$
$230$	0	0
$231$	2.93524	0.193125
$232$	8.57512	0.562984
$233$	−20.3722	−1.33463	−0.667313	−	0.744777i	$-0.732556\pi$
$233$	−20.3722	−1.33463	−0.667313	+	0.744777i	$0.732556\pi$
$234$	34.1192	2.23044
$235$	0	0
$236$	−7.45522	−0.485294
$237$	−19.0013	−1.23427
$238$	−2.95924	−0.191819
$239$	0.813371	0.0526126	0.0263063	−	0.999654i	$-0.491625\pi$
$239$	0.813371	0.0526126	0.0263063	+	0.999654i	$0.491625\pi$
$240$	0	0
$241$	1.94243	0.125123	0.0625615	−	0.998041i	$-0.480073\pi$
$241$	1.94243	0.125123	0.0625615	+	0.998041i	$0.480073\pi$
$242$	−1.68955	−0.108608
$243$	−6.33517	−0.406401
$244$	−6.05210	−0.387446
$245$	0	0
$246$	−27.2741	−1.73893
$247$	6.62698	0.421665
$248$	12.8101	0.813445
$249$	22.9586	1.45494
$250$	0	0
$251$	6.56563	0.414419	0.207209	−	0.978297i	$-0.433562\pi$
$251$	6.56563	0.414419	0.207209	+	0.978297i	$0.433562\pi$
$252$	−4.79903	−0.302311
$253$	−8.49424	−0.534028
$254$	−6.44663	−0.404498
$255$	0	0
$256$	17.2986	1.08116
$257$	24.0198	1.49831	0.749157	−	0.662392i	$-0.230459\pi$
$257$	24.0198	1.49831	0.749157	+	0.662392i	$0.230459\pi$
$258$	−49.2607	−3.06683
$259$	−4.91497	−0.305402
$260$	0	0
$261$	24.8831	1.54023
$262$	−4.04697	−0.250023
$263$	8.99713	0.554787	0.277394	−	0.960756i	$-0.410529\pi$
$263$	8.99713	0.554787	0.277394	+	0.960756i	$0.410529\pi$
$264$	−5.68042	−0.349606
$265$	0	0
$266$	−3.11359	−0.190906
$267$	26.5141	1.62264
$268$	6.24171	0.381273
$269$	22.1504	1.35053	0.675266	−	0.737575i	$-0.264029\pi$
$269$	22.1504	1.35053	0.675266	+	0.737575i	$0.264029\pi$
$270$	0	0
$271$	−15.2076	−0.923795	−0.461898	−	0.886933i	$-0.652831\pi$
$271$	−15.2076	−0.923795	−0.461898	+	0.886933i	$0.652831\pi$
$272$	8.72045	0.528755
$273$	10.5553	0.638836
$274$	32.8436	1.98415
$275$	0	0
$276$	21.3070	1.28253
$277$	11.9060	0.715360	0.357680	−	0.933844i	$-0.383568\pi$
$277$	11.9060	0.715360	0.357680	+	0.933844i	$0.383568\pi$
$278$	−9.61056	−0.576403
$279$	37.1723	2.22544
$280$	0	0
$281$	−14.8195	−0.884059	−0.442029	−	0.897001i	$-0.645741\pi$
$281$	−14.8195	−0.884059	−0.442029	+	0.897001i	$0.645741\pi$
$282$	−23.0698	−1.37379
$283$	25.1541	1.49526	0.747628	−	0.664118i	$-0.231193\pi$
$283$	25.1541	1.49526	0.747628	+	0.664118i	$0.231193\pi$
$284$	−6.78025	−0.402334
$285$	0	0
$286$	−6.07571	−0.359264
$287$	−5.49965	−0.324634
$288$	25.5037	1.50282
$289$	−13.9323	−0.819544
$290$	0	0
$291$	31.9788	1.87463
$292$	14.3025	0.836989
$293$	−12.2872	−0.717824	−0.358912	−	0.933371i	$-0.616852\pi$
$293$	−12.2872	−0.717824	−0.358912	+	0.933371i	$0.616852\pi$
$294$	−4.95924	−0.289229
$295$	0	0
$296$	9.51168	0.552855
$297$	−7.67761	−0.445500
$298$	29.3809	1.70199
$299$	−30.5457	−1.76651
$300$	0	0
$301$	−9.93310	−0.572534
$302$	−11.0509	−0.635910
$303$	16.2427	0.933117
$304$	9.17528	0.526238
$305$	0	0
$306$	16.6181	0.949994
$307$	−6.34340	−0.362037	−0.181018	−	0.983480i	$-0.557939\pi$
$307$	−6.34340	−0.362037	−0.181018	+	0.983480i	$0.557939\pi$
$308$	0.854580	0.0486942
$309$	−32.9071	−1.87202
$310$	0	0
$311$	−11.8700	−0.673086	−0.336543	−	0.941668i	$-0.609258\pi$
$311$	−11.8700	−0.673086	−0.336543	+	0.941668i	$0.609258\pi$
$312$	−20.4271	−1.15646
$313$	22.5619	1.27527	0.637637	−	0.770337i	$-0.279912\pi$
$313$	22.5619	1.27527	0.637637	+	0.770337i	$0.279912\pi$
$314$	−39.2449	−2.21472
$315$	0	0
$316$	−5.53212	−0.311206
$317$	5.26577	0.295755	0.147877	−	0.989006i	$-0.452756\pi$
$317$	5.26577	0.295755	0.147877	+	0.989006i	$0.452756\pi$
$318$	−23.6438	−1.32588
$319$	−4.43102	−0.248090
$320$	0	0
$321$	−18.9297	−1.05655
$322$	14.3514	0.799775
$323$	3.22775	0.179597
$324$	4.86143	0.270079
$325$	0	0
$326$	24.8572	1.37671
$327$	−55.5797	−3.07357
$328$	10.6432	0.587670
$329$	−4.65189	−0.256467
$330$	0	0
$331$	−32.1189	−1.76541	−0.882707	−	0.469923i	$-0.844282\pi$
$331$	−32.1189	−1.76541	−0.882707	+	0.469923i	$0.844282\pi$
$332$	6.68427	0.366847
$333$	27.6008	1.51252
$334$	36.2413	1.98303
$335$	0	0
$336$	14.6142	0.797267
$337$	−27.8757	−1.51848	−0.759242	−	0.650808i	$-0.774430\pi$
$337$	−27.8757	−1.51848	−0.759242	+	0.650808i	$0.774430\pi$
$338$	0.115568	0.00628607
$339$	−0.0512612	−0.00278413
$340$	0	0
$341$	−6.61939	−0.358460
$342$	17.4849	0.945473
$343$	−1.00000	−0.0539949
$344$	19.2230	1.03643
$345$	0	0
$346$	17.4600	0.938656
$347$	20.0682	1.07732	0.538659	−	0.842524i	$-0.318931\pi$
$347$	20.0682	1.07732	0.538659	+	0.842524i	$0.318931\pi$
$348$	11.1148	0.595815
$349$	17.8094	0.953316	0.476658	−	0.879089i	$-0.341848\pi$
$349$	17.8094	0.953316	0.476658	+	0.879089i	$0.341848\pi$
$350$	0	0
$351$	−27.6091	−1.47366
$352$	−4.54153	−0.242064
$353$	−27.0142	−1.43782	−0.718911	−	0.695102i	$-0.755359\pi$
$353$	−27.0142	−1.43782	−0.718911	+	0.695102i	$0.755359\pi$
$354$	43.2637	2.29944
$355$	0	0
$356$	7.71944	0.409129
$357$	5.14108	0.272095
$358$	9.59224	0.506966
$359$	−11.6176	−0.613154	−0.306577	−	0.951846i	$-0.599184\pi$
$359$	−11.6176	−0.613154	−0.306577	+	0.951846i	$0.599184\pi$
$360$	0	0
$361$	−15.6039	−0.821258
$362$	−35.8379	−1.88360
$363$	2.93524	0.154060
$364$	3.07311	0.161075
$365$	0	0
$366$	35.1212	1.83581
$367$	0.143655	0.00749874	0.00374937	−	0.999993i	$-0.498807\pi$
$367$	0.143655	0.00749874	0.00374937	+	0.999993i	$0.498807\pi$
$368$	−42.2916	−2.20460
$369$	30.8842	1.60777
$370$	0	0
$371$	−4.76762	−0.247522
$372$	16.6041	0.860882
$373$	6.97831	0.361323	0.180662	−	0.983545i	$-0.442176\pi$
$373$	6.97831	0.361323	0.180662	+	0.983545i	$0.442176\pi$
$374$	−2.95924	−0.153019
$375$	0	0
$376$	9.00254	0.464270
$377$	−15.9342	−0.820653
$378$	12.9717	0.667193
$379$	11.7983	0.606039	0.303020	−	0.952984i	$-0.402005\pi$
$379$	11.7983	0.606039	0.303020	+	0.952984i	$0.402005\pi$
$380$	0	0
$381$	11.1997	0.573778
$382$	−11.5396	−0.590419
$383$	−16.2417	−0.829913	−0.414956	−	0.909841i	$-0.636203\pi$
$383$	−16.2417	−0.829913	−0.414956	+	0.909841i	$0.636203\pi$
$384$	−37.9907	−1.93871
$385$	0	0
$386$	−22.7390	−1.15738
$387$	55.7809	2.83550
$388$	9.31045	0.472667
$389$	1.46174	0.0741134	0.0370567	−	0.999313i	$-0.488202\pi$
$389$	1.46174	0.0741134	0.0370567	+	0.999313i	$0.488202\pi$
$390$	0	0
$391$	−14.8776	−0.752395
$392$	1.93524	0.0977446
$393$	7.03078	0.354656
$394$	22.3671	1.12684
$395$	0	0
$396$	−4.79903	−0.241160
$397$	−15.4702	−0.776425	−0.388212	−	0.921570i	$-0.626907\pi$
$397$	−15.4702	−0.776425	−0.388212	+	0.921570i	$0.626907\pi$
$398$	11.8055	0.591758
$399$	5.40921	0.270799
$400$	0	0
$401$	21.8408	1.09068	0.545340	−	0.838215i	$-0.316401\pi$
$401$	21.8408	1.09068	0.545340	+	0.838215i	$0.316401\pi$
$402$	−36.2215	−1.80657
$403$	−23.8037	−1.18575
$404$	4.72896	0.235275
$405$	0	0
$406$	7.48644	0.371546
$407$	−4.91497	−0.243626
$408$	−9.94924	−0.492561
$409$	20.2574	1.00166	0.500832	−	0.865545i	$-0.333027\pi$
$409$	20.2574	1.00166	0.500832	+	0.865545i	$0.333027\pi$
$410$	0	0
$411$	−57.0590	−2.81451
$412$	−9.58071	−0.472008
$413$	8.72384	0.429272
$414$	−80.5929	−3.96092
$415$	0	0
$416$	−16.3316	−0.800722
$417$	16.6964	0.817625
$418$	−3.11359	−0.152291
$419$	−0.590485	−0.0288471	−0.0144235	−	0.999896i	$-0.504591\pi$
$419$	−0.590485	−0.0288471	−0.0144235	+	0.999896i	$0.504591\pi$
$420$	0	0
$421$	28.0174	1.36549	0.682743	−	0.730659i	$-0.260787\pi$
$421$	28.0174	1.36549	0.682743	+	0.730659i	$0.260787\pi$
$422$	−23.7355	−1.15543
$423$	26.1234	1.27016
$424$	9.22651	0.448079
$425$	0	0
$426$	39.3467	1.90636
$427$	7.08196	0.342720
$428$	−5.51127	−0.266397
$429$	10.5553	0.509615
$430$	0	0
$431$	−7.56856	−0.364565	−0.182282	−	0.983246i	$-0.558348\pi$
$431$	−7.56856	−0.364565	−0.182282	+	0.983246i	$0.558348\pi$
$432$	−38.2257	−1.83913
$433$	−10.4631	−0.502823	−0.251412	−	0.967880i	$-0.580895\pi$
$433$	−10.4631	−0.502823	−0.251412	+	0.967880i	$0.580895\pi$
$434$	11.1838	0.536839
$435$	0	0
$436$	−16.1817	−0.774964
$437$	−15.6536	−0.748814
$438$	−82.9992	−3.96586
$439$	−14.2208	−0.678722	−0.339361	−	0.940656i	$-0.610211\pi$
$439$	−14.2208	−0.678722	−0.339361	+	0.940656i	$0.610211\pi$
$440$	0	0
$441$	5.61566	0.267413
$442$	−10.6416	−0.506169
$443$	−0.985249	−0.0468106	−0.0234053	−	0.999726i	$-0.507451\pi$
$443$	−0.985249	−0.0468106	−0.0234053	+	0.999726i	$0.507451\pi$
$444$	12.3287	0.585095
$445$	0	0
$446$	−12.9808	−0.614659
$447$	−51.0432	−2.41426
$448$	−2.28456	−0.107935
$449$	−18.3006	−0.863657	−0.431829	−	0.901956i	$-0.642131\pi$
$449$	−18.3006	−0.863657	−0.431829	+	0.901956i	$0.642131\pi$
$450$	0	0
$451$	−5.49965	−0.258968
$452$	−0.0149244	−0.000701985 0
$453$	19.1987	0.902034
$454$	−27.4908	−1.29021
$455$	0	0
$456$	−10.4682	−0.490216
$457$	2.97818	0.139313	0.0696566	−	0.997571i	$-0.477810\pi$
$457$	2.97818	0.139313	0.0696566	+	0.997571i	$0.477810\pi$
$458$	23.6009	1.10280
$459$	−13.4473	−0.627667
$460$	0	0
$461$	−35.6463	−1.66021	−0.830106	−	0.557606i	$-0.811720\pi$
$461$	−35.6463	−1.66021	−0.830106	+	0.557606i	$0.811720\pi$
$462$	−4.95924	−0.230725
$463$	−28.7121	−1.33437	−0.667183	−	0.744894i	$-0.732500\pi$
$463$	−28.7121	−1.33437	−0.667183	+	0.744894i	$0.732500\pi$
$464$	−22.0614	−1.02418
$465$	0	0
$466$	34.4198	1.59447
$467$	6.70656	0.310343	0.155171	−	0.987888i	$-0.450407\pi$
$467$	6.70656	0.310343	0.155171	+	0.987888i	$0.450407\pi$
$468$	−17.2576	−0.797732
$469$	−7.30384	−0.337260
$470$	0	0
$471$	68.1800	3.14157
$472$	−16.8828	−0.777093
$473$	−9.93310	−0.456724
$474$	32.1037	1.47457
$475$	0	0
$476$	1.49679	0.0686055
$477$	26.7733	1.22587
$478$	−1.37423	−0.0628559
$479$	−8.26047	−0.377430	−0.188715	−	0.982032i	$-0.560432\pi$
$479$	−8.26047	−0.377430	−0.188715	+	0.982032i	$0.560432\pi$
$480$	0	0
$481$	−17.6745	−0.805888
$482$	−3.28183	−0.149483
$483$	−24.9327	−1.13448
$484$	0.854580	0.0388445
$485$	0	0
$486$	10.7036	0.485524
$487$	−35.3962	−1.60396	−0.801978	−	0.597354i	$-0.796219\pi$
$487$	−35.3962	−1.60396	−0.801978	+	0.597354i	$0.796219\pi$
$488$	−13.7053	−0.620411
$489$	−43.1842	−1.95286
$490$	0	0
$491$	−0.647846	−0.0292369	−0.0146184	−	0.999893i	$-0.504653\pi$
$491$	−0.647846	−0.0292369	−0.0146184	+	0.999893i	$0.504653\pi$
$492$	13.7953	0.621941
$493$	−7.76093	−0.349535
$494$	−11.1966	−0.503760
$495$	0	0
$496$	−32.9570	−1.47981
$497$	7.93402	0.355889
$498$	−38.7897	−1.73821
$499$	32.0408	1.43434	0.717172	−	0.696896i	$-0.245436\pi$
$499$	32.0408	1.43434	0.717172	+	0.696896i	$0.245436\pi$
$500$	0	0
$501$	−62.9617	−2.81292
$502$	−11.0930	−0.495103
$503$	8.97336	0.400103	0.200051	−	0.979785i	$-0.435889\pi$
$503$	8.97336	0.400103	0.200051	+	0.979785i	$0.435889\pi$
$504$	−10.8677	−0.484085
$505$	0	0
$506$	14.3514	0.638000
$507$	−0.200776	−0.00891675
$508$	3.26073	0.144671
$509$	4.79958	0.212738	0.106369	−	0.994327i	$-0.466078\pi$
$509$	4.79958	0.212738	0.106369	+	0.994327i	$0.466078\pi$
$510$	0	0
$511$	−16.7363	−0.740369
$512$	−3.34102	−0.147654
$513$	−14.1487	−0.624679
$514$	−40.5827	−1.79002
$515$	0	0
$516$	24.9162	1.09687
$517$	−4.65189	−0.204590
$518$	8.30409	0.364861
$519$	−30.3332	−1.33148
$520$	0	0
$521$	0.615141	0.0269498	0.0134749	−	0.999909i	$-0.495711\pi$
$521$	0.615141	0.0269498	0.0134749	+	0.999909i	$0.495711\pi$
$522$	−42.0413	−1.84010
$523$	2.31342	0.101159	0.0505795	−	0.998720i	$-0.483893\pi$
$523$	2.31342	0.101159	0.0505795	+	0.998720i	$0.483893\pi$
$524$	2.04697	0.0894223
$525$	0	0
$526$	−15.2011	−0.662800
$527$	−11.5938	−0.505036
$528$	14.6142	0.635999
$529$	49.1521	2.13705
$530$	0	0
$531$	−48.9902	−2.12599
$532$	1.57486	0.0682789
$533$	−19.7770	−0.856638
$534$	−44.7970	−1.93855
$535$	0	0
$536$	14.1347	0.610527
$537$	−16.6645	−0.719128
$538$	−37.4241	−1.61347
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−33.4865	−1.43970	−0.719849	−	0.694130i	$-0.755789\pi$
$541$	−33.4865	−1.43970	−0.719849	+	0.694130i	$0.755789\pi$
$542$	25.6940	1.10365
$543$	62.2609	2.67187
$544$	−7.95448	−0.341046
$545$	0	0
$546$	−17.8337	−0.763212
$547$	38.4969	1.64601	0.823005	−	0.568035i	$-0.192296\pi$
$547$	38.4969	1.64601	0.823005	+	0.568035i	$0.192296\pi$
$548$	−16.6124	−0.709646
$549$	−39.7699	−1.69734
$550$	0	0
$551$	−8.16571	−0.347871
$552$	48.2508	2.05369
$553$	6.47350	0.275281
$554$	−20.1157	−0.854635
$555$	0	0
$556$	4.86105	0.206155
$557$	29.3070	1.24178	0.620889	−	0.783899i	$-0.286772\pi$
$557$	29.3070	1.24178	0.620889	+	0.783899i	$0.286772\pi$
$558$	−62.8044	−2.65872
$559$	−35.7200	−1.51079
$560$	0	0
$561$	5.14108	0.217056
$562$	25.0383	1.05618
$563$	−27.7170	−1.16813	−0.584066	−	0.811706i	$-0.698539\pi$
$563$	−27.7170	−1.16813	−0.584066	+	0.811706i	$0.698539\pi$
$564$	11.6688	0.491345
$565$	0	0
$566$	−42.4991	−1.78637
$567$	−5.68868	−0.238902
$568$	−15.3543	−0.644251
$569$	14.2301	0.596556	0.298278	−	0.954479i	$-0.403588\pi$
$569$	14.2301	0.596556	0.298278	+	0.954479i	$0.403588\pi$
$570$	0	0
$571$	−10.6231	−0.444563	−0.222281	−	0.974983i	$-0.571350\pi$
$571$	−10.6231	−0.444563	−0.222281	+	0.974983i	$0.571350\pi$
$572$	3.07311	0.128493
$573$	20.0477	0.837506
$574$	9.29193	0.387838
$575$	0	0
$576$	12.8293	0.534555
$577$	−35.1789	−1.46452	−0.732259	−	0.681027i	$-0.761534\pi$
$577$	−35.1789	−1.46452	−0.732259	+	0.681027i	$0.761534\pi$
$578$	23.5392	0.979103
$579$	39.5043	1.64174
$580$	0	0
$581$	−7.82170	−0.324499
$582$	−54.0298	−2.23961
$583$	−4.76762	−0.197455
$584$	32.3888	1.34026
$585$	0	0
$586$	20.7598	0.857579
$587$	18.6001	0.767710	0.383855	−	0.923393i	$-0.374596\pi$
$587$	18.6001	0.767710	0.383855	+	0.923393i	$0.374596\pi$
$588$	2.50840	0.103445
$589$	−12.1985	−0.502632
$590$	0	0
$591$	−38.8581	−1.59841
$592$	−24.4709	−1.00575
$593$	−16.7486	−0.687784	−0.343892	−	0.939009i	$-0.611745\pi$
$593$	−16.7486	−0.687784	−0.343892	+	0.939009i	$0.611745\pi$
$594$	12.9717	0.532236
$595$	0	0
$596$	−14.8609	−0.608728
$597$	−20.5097	−0.839405
$598$	51.6086	2.11043
$599$	−6.12489	−0.250256	−0.125128	−	0.992141i	$-0.539934\pi$
$599$	−6.12489	−0.250256	−0.125128	+	0.992141i	$0.539934\pi$
$600$	0	0
$601$	32.8690	1.34075	0.670377	−	0.742021i	$-0.266132\pi$
$601$	32.8690	1.34075	0.670377	+	0.742021i	$0.266132\pi$
$602$	16.7825	0.684002
$603$	41.0159	1.67030
$604$	5.58960	0.227437
$605$	0	0
$606$	−27.4428	−1.11479
$607$	2.51883	0.102236	0.0511181	−	0.998693i	$-0.483722\pi$
$607$	2.51883	0.102236	0.0511181	+	0.998693i	$0.483722\pi$
$608$	−8.36936	−0.339422
$609$	−13.0061	−0.527035
$610$	0	0
$611$	−16.7284	−0.676760
$612$	−8.40549	−0.339772
$613$	29.4405	1.18909	0.594546	−	0.804062i	$-0.297332\pi$
$613$	29.4405	1.18909	0.594546	+	0.804062i	$0.297332\pi$
$614$	10.7175	0.432523
$615$	0	0
$616$	1.93524	0.0779732
$617$	−14.2375	−0.573181	−0.286590	−	0.958053i	$-0.592522\pi$
$617$	−14.2375	−0.573181	−0.286590	+	0.958053i	$0.592522\pi$
$618$	55.5982	2.23649
$619$	14.5186	0.583550	0.291775	−	0.956487i	$-0.405754\pi$
$619$	14.5186	0.583550	0.291775	+	0.956487i	$0.405754\pi$
$620$	0	0
$621$	65.2155	2.61701
$622$	20.0550	0.804130
$623$	−9.03302	−0.361900
$624$	52.5533	2.10381
$625$	0	0
$626$	−38.1195	−1.52356
$627$	5.40921	0.216023
$628$	19.8502	0.792110
$629$	−8.60857	−0.343246
$630$	0	0
$631$	11.7388	0.467313	0.233657	−	0.972319i	$-0.424931\pi$
$631$	11.7388	0.467313	0.233657	+	0.972319i	$0.424931\pi$
$632$	−12.5278	−0.498330
$633$	41.2356	1.63897
$634$	−8.89678	−0.353336
$635$	0	0
$636$	11.9591	0.474209
$637$	−3.59605	−0.142481
$638$	7.48644	0.296391
$639$	−44.5548	−1.76256
$640$	0	0
$641$	−35.5107	−1.40259	−0.701293	−	0.712873i	$-0.747394\pi$
$641$	−35.5107	−1.40259	−0.701293	+	0.712873i	$0.747394\pi$
$642$	31.9826	1.26225
$643$	27.4051	1.08075	0.540377	−	0.841423i	$-0.318282\pi$
$643$	27.4051	1.08075	0.540377	+	0.841423i	$0.318282\pi$
$644$	−7.25901	−0.286045
$645$	0	0
$646$	−5.45344	−0.214563
$647$	−21.9689	−0.863687	−0.431844	−	0.901948i	$-0.642137\pi$
$647$	−21.9689	−0.863687	−0.431844	+	0.901948i	$0.642137\pi$
$648$	11.0090	0.432474
$649$	8.72384	0.342441
$650$	0	0
$651$	−19.4295	−0.761503
$652$	−12.5728	−0.492391
$653$	−24.4212	−0.955676	−0.477838	−	0.878448i	$-0.658579\pi$
$653$	−24.4212	−0.955676	−0.477838	+	0.878448i	$0.658579\pi$
$654$	93.9047	3.67196
$655$	0	0
$656$	−27.3819	−1.06908
$657$	93.9852	3.66671
$658$	7.85959	0.306399
$659$	−11.1612	−0.434779	−0.217389	−	0.976085i	$-0.569754\pi$
$659$	−11.1612	−0.434779	−0.217389	+	0.976085i	$0.569754\pi$
$660$	0	0
$661$	−10.0360	−0.390355	−0.195177	−	0.980768i	$-0.562528\pi$
$661$	−10.0360	−0.390355	−0.195177	+	0.980768i	$0.562528\pi$
$662$	54.2665	2.10913
$663$	18.4876	0.717998
$664$	15.1369	0.587426
$665$	0	0
$666$	−46.6330	−1.80699
$667$	37.6382	1.45736
$668$	−18.3310	−0.709246
$669$	22.5515	0.871891
$670$	0	0
$671$	7.08196	0.273396
$672$	−13.3305	−0.514236
$673$	1.63730	0.0631131	0.0315565	−	0.999502i	$-0.489954\pi$
$673$	1.63730	0.0631131	0.0315565	+	0.999502i	$0.489954\pi$
$674$	47.0973	1.81412
$675$	0	0
$676$	−0.0584546	−0.00224826
$677$	9.24088	0.355156	0.177578	−	0.984107i	$-0.443174\pi$
$677$	9.24088	0.355156	0.177578	+	0.984107i	$0.443174\pi$
$678$	0.0866083	0.00332617
$679$	−10.8948	−0.418103
$680$	0	0
$681$	47.7596	1.83015
$682$	11.1838	0.428249
$683$	−8.12240	−0.310795	−0.155398	−	0.987852i	$-0.549666\pi$
$683$	−8.12240	−0.310795	−0.155398	+	0.987852i	$0.549666\pi$
$684$	−8.84389	−0.338155
$685$	0	0
$686$	1.68955	0.0645073
$687$	−41.0016	−1.56431
$688$	−49.4554	−1.88547
$689$	−17.1446	−0.653157
$690$	0	0
$691$	40.5364	1.54208	0.771038	−	0.636789i	$-0.219738\pi$
$691$	40.5364	1.54208	0.771038	+	0.636789i	$0.219738\pi$
$692$	−8.83133	−0.335717
$693$	5.61566	0.213321
$694$	−33.9062	−1.28706
$695$	0	0
$696$	25.1701	0.954069
$697$	−9.63262	−0.364861
$698$	−30.0899	−1.13892
$699$	−59.7974	−2.26174
$700$	0	0
$701$	39.3047	1.48452	0.742259	−	0.670114i	$-0.233755\pi$
$701$	39.3047	1.48452	0.742259	+	0.670114i	$0.233755\pi$
$702$	46.6470	1.76058
$703$	−9.05756	−0.341612
$704$	−2.28456	−0.0861026
$705$	0	0
$706$	45.6419	1.71776
$707$	−5.53367	−0.208115
$708$	−21.8829	−0.822410
$709$	−48.6858	−1.82843	−0.914217	−	0.405224i	$-0.867194\pi$
$709$	−48.6858	−1.82843	−0.914217	+	0.405224i	$0.867194\pi$
$710$	0	0
$711$	−36.3530	−1.36334
$712$	17.4811	0.655132
$713$	56.2267	2.10571
$714$	−8.68610	−0.325069
$715$	0	0
$716$	−4.85179	−0.181320
$717$	2.38744	0.0891607
$718$	19.6285	0.732531
$719$	−35.6720	−1.33034	−0.665171	−	0.746691i	$-0.731641\pi$
$719$	−35.6720	−1.33034	−0.665171	+	0.746691i	$0.731641\pi$
$720$	0	0
$721$	11.2110	0.417520
$722$	26.3636	0.981151
$723$	5.70151	0.212041
$724$	18.1269	0.673681
$725$	0	0
$726$	−4.95924	−0.184055
$727$	2.10788	0.0781769	0.0390884	−	0.999236i	$-0.487555\pi$
$727$	2.10788	0.0781769	0.0390884	+	0.999236i	$0.487555\pi$
$728$	6.95924	0.257927
$729$	−35.6613	−1.32079
$730$	0	0
$731$	−17.3978	−0.643481
$732$	−17.7644	−0.656591
$733$	29.5903	1.09294	0.546472	−	0.837478i	$-0.315971\pi$
$733$	29.5903	1.09294	0.546472	+	0.837478i	$0.315971\pi$
$734$	−0.242713	−0.00895869
$735$	0	0
$736$	38.5769	1.42196
$737$	−7.30384	−0.269040
$738$	−52.1803	−1.92078
$739$	−45.2134	−1.66320	−0.831601	−	0.555374i	$-0.812575\pi$
$739$	−45.2134	−1.66320	−0.831601	+	0.555374i	$0.812575\pi$
$740$	0	0
$741$	19.4518	0.714581
$742$	8.05513	0.295713
$743$	−15.6873	−0.575512	−0.287756	−	0.957704i	$-0.592909\pi$
$743$	−15.6873	−0.575512	−0.287756	+	0.957704i	$0.592909\pi$
$744$	37.6009	1.37852
$745$	0	0
$746$	−11.7902	−0.431670
$747$	43.9240	1.60710
$748$	1.49679	0.0547282
$749$	6.44910	0.235645
$750$	0	0
$751$	−43.5568	−1.58941	−0.794705	−	0.606996i	$-0.792374\pi$
$751$	−43.5568	−1.58941	−0.794705	+	0.606996i	$0.792374\pi$
$752$	−23.1611	−0.844597
$753$	19.2717	0.702301
$754$	26.9216	0.980428
$755$	0	0
$756$	−6.56113	−0.238626
$757$	3.70349	0.134606	0.0673029	−	0.997733i	$-0.478561\pi$
$757$	3.70349	0.134606	0.0673029	+	0.997733i	$0.478561\pi$
$758$	−19.9339	−0.724031
$759$	−24.9327	−0.904999
$760$	0	0
$761$	−13.9814	−0.506825	−0.253412	−	0.967358i	$-0.581553\pi$
$761$	−13.9814	−0.506825	−0.253412	+	0.967358i	$0.581553\pi$
$762$	−18.9224	−0.685488
$763$	18.9353	0.685503
$764$	5.83678	0.211167
$765$	0	0
$766$	27.4412	0.991490
$767$	31.3714	1.13276
$768$	50.7757	1.83221
$769$	19.0164	0.685750	0.342875	−	0.939381i	$-0.388599\pi$
$769$	19.0164	0.685750	0.342875	+	0.939381i	$0.388599\pi$
$770$	0	0
$771$	70.5040	2.53914
$772$	11.5015	0.413946
$773$	−3.76217	−0.135316	−0.0676579	−	0.997709i	$-0.521553\pi$
$773$	−3.76217	−0.135316	−0.0676579	+	0.997709i	$0.521553\pi$
$774$	−94.2447	−3.38756
$775$	0	0
$776$	21.0841	0.756873
$777$	−14.4267	−0.517553
$778$	−2.46969	−0.0885427
$779$	−10.1350	−0.363125
$780$	0	0
$781$	7.93402	0.283902
$782$	25.1365	0.898880
$783$	34.0197	1.21576
$784$	−4.97885	−0.177816
$785$	0	0
$786$	−11.8788	−0.423705
$787$	17.5146	0.624330	0.312165	−	0.950028i	$-0.398946\pi$
$787$	17.5146	0.624330	0.312165	+	0.950028i	$0.398946\pi$
$788$	−11.3133	−0.403021
$789$	26.4088	0.940178
$790$	0	0
$791$	0.0174640	0.000620949 0
$792$	−10.8677	−0.386166
$793$	25.4671	0.904364
$794$	26.1376	0.927589
$795$	0	0
$796$	−5.97127	−0.211646
$797$	4.71730	0.167095	0.0835477	−	0.996504i	$-0.473375\pi$
$797$	4.71730	0.167095	0.0835477	+	0.996504i	$0.473375\pi$
$798$	−9.13914	−0.323522
$799$	−8.14777	−0.288247
$800$	0	0
$801$	50.7264	1.79233
$802$	−36.9012	−1.30303
$803$	−16.7363	−0.590610
$804$	18.3210	0.646130
$805$	0	0
$806$	40.2175	1.41660
$807$	65.0167	2.28870
$808$	10.7090	0.376742
$809$	3.28974	0.115661	0.0578306	−	0.998326i	$-0.481582\pi$
$809$	3.28974	0.115661	0.0578306	+	0.998326i	$0.481582\pi$
$810$	0	0
$811$	37.5502	1.31857	0.659283	−	0.751895i	$-0.270860\pi$
$811$	37.5502	1.31857	0.659283	+	0.751895i	$0.270860\pi$
$812$	−3.78666	−0.132886
$813$	−44.6380	−1.56552
$814$	8.30409	0.291058
$815$	0	0
$816$	25.5967	0.896062
$817$	−18.3052	−0.640418
$818$	−34.2259	−1.19668
$819$	20.1942	0.705643
$820$	0	0
$821$	−19.7528	−0.689379	−0.344690	−	0.938717i	$-0.612016\pi$
$821$	−19.7528	−0.689379	−0.344690	+	0.938717i	$0.612016\pi$
$822$	96.4040	3.36248
$823$	−45.8579	−1.59851	−0.799253	−	0.600995i	$-0.794771\pi$
$823$	−45.8579	−1.59851	−0.799253	+	0.600995i	$0.794771\pi$
$824$	−21.6961	−0.755819
$825$	0	0
$826$	−14.7394	−0.512848
$827$	−23.9374	−0.832385	−0.416192	−	0.909277i	$-0.636636\pi$
$827$	−23.9374	−0.832385	−0.416192	+	0.909277i	$0.636636\pi$
$828$	40.7641	1.41665
$829$	−22.8596	−0.793947	−0.396974	−	0.917830i	$-0.629940\pi$
$829$	−22.8596	−0.793947	−0.396974	+	0.917830i	$0.629940\pi$
$830$	0	0
$831$	34.9469	1.21230
$832$	−8.21540	−0.284818
$833$	−1.75150	−0.0606858
$834$	−28.2094	−0.976810
$835$	0	0
$836$	1.57486	0.0544677
$837$	50.8211	1.75663
$838$	0.997654	0.0344634
$839$	−29.2730	−1.01062	−0.505308	−	0.862939i	$-0.668621\pi$
$839$	−29.2730	−1.01062	−0.505308	+	0.862939i	$0.668621\pi$
$840$	0	0
$841$	−9.36603	−0.322967
$842$	−47.3368	−1.63133
$843$	−43.4989	−1.49818
$844$	12.0055	0.413246
$845$	0	0
$846$	−44.1368	−1.51746
$847$	−1.00000	−0.0343604
$848$	−23.7373	−0.815141
$849$	73.8335	2.53396
$850$	0	0
$851$	41.7490	1.43114
$852$	−19.9017	−0.681821
$853$	−10.3181	−0.353286	−0.176643	−	0.984275i	$-0.556524\pi$
$853$	−10.3181	−0.353286	−0.176643	+	0.984275i	$0.556524\pi$
$854$	−11.9653	−0.409445
$855$	0	0
$856$	−12.4806	−0.426577
$857$	−15.5992	−0.532858	−0.266429	−	0.963855i	$-0.585844\pi$
$857$	−15.5992	−0.532858	−0.266429	+	0.963855i	$0.585844\pi$
$858$	−17.8337	−0.608833
$859$	14.6335	0.499289	0.249645	−	0.968338i	$-0.419686\pi$
$859$	14.6335	0.499289	0.249645	+	0.968338i	$0.419686\pi$
$860$	0	0
$861$	−16.1428	−0.550145
$862$	12.7875	0.435543
$863$	−29.5000	−1.00419	−0.502096	−	0.864812i	$-0.667438\pi$
$863$	−29.5000	−1.00419	−0.502096	+	0.864812i	$0.667438\pi$
$864$	34.8681	1.18624
$865$	0	0
$866$	17.6779	0.600719
$867$	−40.8946	−1.38885
$868$	−5.65680	−0.192004
$869$	6.47350	0.219599
$870$	0	0
$871$	−26.2650	−0.889956
$872$	−36.6444	−1.24094
$873$	61.1814	2.07068
$874$	26.4476	0.894602
$875$	0	0
$876$	41.9813	1.41842
$877$	−36.1858	−1.22191	−0.610954	−	0.791666i	$-0.709214\pi$
$877$	−36.1858	−1.22191	−0.610954	+	0.791666i	$0.709214\pi$
$878$	24.0268	0.810864
$879$	−36.0658	−1.21647
$880$	0	0
$881$	−35.9099	−1.20983	−0.604917	−	0.796289i	$-0.706794\pi$
$881$	−35.9099	−1.20983	−0.604917	+	0.796289i	$0.706794\pi$
$882$	−9.48794	−0.319476
$883$	11.7886	0.396720	0.198360	−	0.980129i	$-0.436439\pi$
$883$	11.7886	0.396720	0.198360	+	0.980129i	$0.436439\pi$
$884$	5.38255	0.181035
$885$	0	0
$886$	1.66463	0.0559242
$887$	−17.6251	−0.591793	−0.295896	−	0.955220i	$-0.595618\pi$
$887$	−17.6251	−0.591793	−0.295896	+	0.955220i	$0.595618\pi$
$888$	27.9191	0.936904
$889$	−3.81559	−0.127971
$890$	0	0
$891$	−5.68868	−0.190578
$892$	6.56574	0.219837
$893$	−8.57272	−0.286875
$894$	86.2401	2.88430
$895$	0	0
$896$	12.9429	0.432393
$897$	−89.6592	−2.99363
$898$	30.9197	1.03180
$899$	29.3307	0.978233
$900$	0	0
$901$	−8.35047	−0.278195
$902$	9.29193	0.309387
$903$	−29.1561	−0.970254
$904$	−0.0337972	−0.00112408
$905$	0	0
$906$	−32.4372	−1.07765
$907$	−4.28322	−0.142222	−0.0711110	−	0.997468i	$-0.522654\pi$
$907$	−4.28322	−0.142222	−0.0711110	+	0.997468i	$0.522654\pi$
$908$	13.9049	0.461451
$909$	31.0752	1.03070
$910$	0	0
$911$	53.6814	1.77854	0.889272	−	0.457379i	$-0.151212\pi$
$911$	53.6814	1.77854	0.889272	+	0.457379i	$0.151212\pi$
$912$	26.9317	0.891797
$913$	−7.82170	−0.258861
$914$	−5.03178	−0.166436
$915$	0	0
$916$	−11.9374	−0.394422
$917$	−2.39529	−0.0790996
$918$	22.7199	0.749869
$919$	23.0274	0.759602	0.379801	−	0.925068i	$-0.375992\pi$
$919$	23.0274	0.759602	0.379801	+	0.925068i	$0.375992\pi$
$920$	0	0
$921$	−18.6194	−0.613531
$922$	60.2261	1.98344
$923$	28.5312	0.939114
$924$	2.50840	0.0825203
$925$	0	0
$926$	48.5106	1.59416
$927$	−62.9573	−2.06779
$928$	20.1236	0.660591
$929$	35.6526	1.16972	0.584861	−	0.811133i	$-0.301149\pi$
$929$	35.6526	1.16972	0.584861	+	0.811133i	$0.301149\pi$
$930$	0	0
$931$	−1.84285	−0.0603970
$932$	−17.4097	−0.570272
$933$	−34.8413	−1.14065
$934$	−11.3311	−0.370764
$935$	0	0
$936$	−39.0808	−1.27739
$937$	14.6147	0.477442	0.238721	−	0.971088i	$-0.423272\pi$
$937$	14.6147	0.477442	0.238721	+	0.971088i	$0.423272\pi$
$938$	12.3402	0.402922
$939$	66.2247	2.16116
$940$	0	0
$941$	31.7910	1.03636	0.518178	−	0.855273i	$-0.326610\pi$
$941$	31.7910	1.03636	0.518178	+	0.855273i	$0.326610\pi$
$942$	−115.193	−3.75321
$943$	46.7153	1.52126
$944$	43.4347	1.41368
$945$	0	0
$946$	16.7825	0.545645
$947$	−26.1700	−0.850412	−0.425206	−	0.905097i	$-0.639798\pi$
$947$	−26.1700	−0.850412	−0.425206	+	0.905097i	$0.639798\pi$
$948$	−16.2381	−0.527390
$949$	−60.1845	−1.95367
$950$	0	0
$951$	15.4563	0.501205
$952$	3.38958	0.109857
$953$	34.9843	1.13325	0.566626	−	0.823975i	$-0.308248\pi$
$953$	34.9843	1.13325	0.566626	+	0.823975i	$0.308248\pi$
$954$	−45.2349	−1.46453
$955$	0	0
$956$	0.695090	0.0224808
$957$	−13.0061	−0.420429
$958$	13.9565	0.450913
$959$	19.4393	0.627726
$960$	0	0
$961$	12.8163	0.413430
$962$	29.8620	0.962788
$963$	−36.2159	−1.16704
$964$	1.65996	0.0534638
$965$	0	0
$966$	42.1250	1.35535
$967$	3.60712	0.115997	0.0579985	−	0.998317i	$-0.481528\pi$
$967$	3.60712	0.115997	0.0579985	+	0.998317i	$0.481528\pi$
$968$	1.93524	0.0622011
$969$	9.47423	0.304356
$970$	0	0
$971$	11.0925	0.355974	0.177987	−	0.984033i	$-0.443041\pi$
$971$	11.0925	0.355974	0.177987	+	0.984033i	$0.443041\pi$
$972$	−5.41390	−0.173651
$973$	−5.68824	−0.182357
$974$	59.8037	1.91623
$975$	0	0
$976$	35.2601	1.12865
$977$	−3.14654	−0.100667	−0.0503334	−	0.998732i	$-0.516028\pi$
$977$	−3.14654	−0.100667	−0.0503334	+	0.998732i	$0.516028\pi$
$978$	72.9619	2.33307
$979$	−9.03302	−0.288697
$980$	0	0
$981$	−106.334	−3.39499
$982$	1.09457	0.0349291
$983$	−28.0142	−0.893515	−0.446758	−	0.894655i	$-0.647421\pi$
$983$	−28.0142	−0.893515	−0.446758	+	0.894655i	$0.647421\pi$
$984$	31.2403	0.995904
$985$	0	0
$986$	13.1125	0.417586
$987$	−13.6544	−0.434625
$988$	5.66329	0.180173
$989$	84.3741	2.68294
$990$	0	0
$991$	21.1389	0.671501	0.335750	−	0.941951i	$-0.391010\pi$
$991$	21.1389	0.671501	0.335750	+	0.941951i	$0.391010\pi$
$992$	30.0622	0.954475
$993$	−94.2768	−2.99178
$994$	−13.4049	−0.425178
$995$	0	0
$996$	19.6200	0.621682
$997$	−20.7522	−0.657228	−0.328614	−	0.944464i	$-0.606582\pi$
$997$	−20.7522	−0.657228	−0.328614	+	0.944464i	$0.606582\pi$
$998$	−54.1346	−1.71360
$999$	37.7353	1.19389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.z.1.2		6
5.2	odd	4		385.2.b.c.309.3	✓	12
5.3	odd	4		385.2.b.c.309.10	yes	12
5.4	even	2		1925.2.a.y.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.b.c.309.3	✓	12	5.2	odd	4
385.2.b.c.309.10	yes	12	5.3	odd	4
1925.2.a.y.1.5		6	5.4	even	2
1925.2.a.z.1.2		6	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-1.68955 q^{2} +2.93524 q^{3} +0.854580 q^{4} -4.95924 q^{6} -1.00000 q^{7} +1.93524 q^{8} +5.61566 q^{9} +O(q^{10})\)	\(q-1.68955 q^{2} +2.93524 q^{3} +0.854580 q^{4} -4.95924 q^{6} -1.00000 q^{7} +1.93524 q^{8} +5.61566 q^{9} -1.00000 q^{11} +2.50840 q^{12} -3.59605 q^{13} +1.68955 q^{14} -4.97885 q^{16} -1.75150 q^{17} -9.48794 q^{18} -1.84285 q^{19} -2.93524 q^{21} +1.68955 q^{22} +8.49424 q^{23} +5.68042 q^{24} +6.07571 q^{26} +7.67761 q^{27} -0.854580 q^{28} +4.43102 q^{29} +6.61939 q^{31} +4.54153 q^{32} -2.93524 q^{33} +2.95924 q^{34} +4.79903 q^{36} +4.91497 q^{37} +3.11359 q^{38} -10.5553 q^{39} +5.49965 q^{41} +4.95924 q^{42} +9.93310 q^{43} -0.854580 q^{44} -14.3514 q^{46} +4.65189 q^{47} -14.6142 q^{48} +1.00000 q^{49} -5.14108 q^{51} -3.07311 q^{52} +4.76762 q^{53} -12.9717 q^{54} -1.93524 q^{56} -5.40921 q^{57} -7.48644 q^{58} -8.72384 q^{59} -7.08196 q^{61} -11.1838 q^{62} -5.61566 q^{63} +2.28456 q^{64} +4.95924 q^{66} +7.30384 q^{67} -1.49679 q^{68} +24.9327 q^{69} -7.93402 q^{71} +10.8677 q^{72} +16.7363 q^{73} -8.30409 q^{74} -1.57486 q^{76} +1.00000 q^{77} +17.8337 q^{78} -6.47350 q^{79} +5.68868 q^{81} -9.29193 q^{82} +7.82170 q^{83} -2.50840 q^{84} -16.7825 q^{86} +13.0061 q^{87} -1.93524 q^{88} +9.03302 q^{89} +3.59605 q^{91} +7.25901 q^{92} +19.4295 q^{93} -7.85959 q^{94} +13.3305 q^{96} +10.8948 q^{97} -1.68955 q^{98} -5.61566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 2 q^{4} - 2 q^{6} - 6 q^{7} + 10 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 + 2 * q^4 - 2 * q^6 - 6 * q^7 + 10 * q^9	\( 6 q + 6 q^{3} + 2 q^{4} - 2 q^{6} - 6 q^{7} + 10 q^{9} - 6 q^{11} + 12 q^{12} + 6 q^{13} - 6 q^{16} - 2 q^{17} + 14 q^{18} - 2 q^{19} - 6 q^{21} + 8 q^{23} + 22 q^{24} + 24 q^{27} - 2 q^{28} - 8 q^{29} + 4 q^{31} + 10 q^{32} - 6 q^{33} - 10 q^{34} + 26 q^{36} + 22 q^{37} - 10 q^{38} - 8 q^{39} + 4 q^{41} + 2 q^{42} + 30 q^{43} - 2 q^{44} - 8 q^{46} + 16 q^{47} - 8 q^{48} + 6 q^{49} - 4 q^{51} + 22 q^{52} + 6 q^{53} + 38 q^{54} + 18 q^{57} - 14 q^{58} + 14 q^{59} + 12 q^{61} - 14 q^{62} - 10 q^{63} - 22 q^{64} + 2 q^{66} + 46 q^{67} - 20 q^{68} + 12 q^{69} + 4 q^{71} + 32 q^{72} - 4 q^{73} - 8 q^{74} - 8 q^{76} + 6 q^{77} + 24 q^{78} - 8 q^{79} + 26 q^{81} - 10 q^{82} + 14 q^{83} - 12 q^{84} + 12 q^{86} - 2 q^{87} + 8 q^{89} - 6 q^{91} + 18 q^{92} + 12 q^{93} - 10 q^{94} - 16 q^{96} + 42 q^{97} - 10 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 + 2 * q^4 - 2 * q^6 - 6 * q^7 + 10 * q^9 - 6 * q^11 + 12 * q^12 + 6 * q^13 - 6 * q^16 - 2 * q^17 + 14 * q^18 - 2 * q^19 - 6 * q^21 + 8 * q^23 + 22 * q^24 + 24 * q^27 - 2 * q^28 - 8 * q^29 + 4 * q^31 + 10 * q^32 - 6 * q^33 - 10 * q^34 + 26 * q^36 + 22 * q^37 - 10 * q^38 - 8 * q^39 + 4 * q^41 + 2 * q^42 + 30 * q^43 - 2 * q^44 - 8 * q^46 + 16 * q^47 - 8 * q^48 + 6 * q^49 - 4 * q^51 + 22 * q^52 + 6 * q^53 + 38 * q^54 + 18 * q^57 - 14 * q^58 + 14 * q^59 + 12 * q^61 - 14 * q^62 - 10 * q^63 - 22 * q^64 + 2 * q^66 + 46 * q^67 - 20 * q^68 + 12 * q^69 + 4 * q^71 + 32 * q^72 - 4 * q^73 - 8 * q^74 - 8 * q^76 + 6 * q^77 + 24 * q^78 - 8 * q^79 + 26 * q^81 - 10 * q^82 + 14 * q^83 - 12 * q^84 + 12 * q^86 - 2 * q^87 + 8 * q^89 - 6 * q^91 + 18 * q^92 + 12 * q^93 - 10 * q^94 - 16 * q^96 + 42 * q^97 - 10 * q^99

Introduction

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