LMFDB - Embedded newform 6025.2.a.l.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.60847 q^{2} -3.19065 q^{3} +0.587161 q^{4} +5.13204 q^{6} -4.87921 q^{7} +2.27250 q^{8} +7.18022 q^{9} +O(q^{10})$	\(q-1.60847 q^{2} -3.19065 q^{3} +0.587161 q^{4} +5.13204 q^{6} -4.87921 q^{7} +2.27250 q^{8} +7.18022 q^{9} -1.54559 q^{11} -1.87342 q^{12} +6.58861 q^{13} +7.84804 q^{14} -4.82956 q^{16} -3.07006 q^{17} -11.5491 q^{18} +2.72015 q^{19} +15.5678 q^{21} +2.48602 q^{22} -7.62835 q^{23} -7.25075 q^{24} -10.5976 q^{26} -13.3376 q^{27} -2.86488 q^{28} -4.16544 q^{29} +9.93936 q^{31} +3.22318 q^{32} +4.93142 q^{33} +4.93809 q^{34} +4.21595 q^{36} +7.67570 q^{37} -4.37527 q^{38} -21.0219 q^{39} -9.17775 q^{41} -25.0403 q^{42} -7.76666 q^{43} -0.907508 q^{44} +12.2699 q^{46} -12.4928 q^{47} +15.4094 q^{48} +16.8067 q^{49} +9.79548 q^{51} +3.86858 q^{52} +2.25429 q^{53} +21.4531 q^{54} -11.0880 q^{56} -8.67905 q^{57} +6.69996 q^{58} -3.80303 q^{59} -9.88453 q^{61} -15.9871 q^{62} -35.0338 q^{63} +4.47475 q^{64} -7.93201 q^{66} +0.537837 q^{67} -1.80262 q^{68} +24.3394 q^{69} +5.63516 q^{71} +16.3171 q^{72} +2.21313 q^{73} -12.3461 q^{74} +1.59717 q^{76} +7.54124 q^{77} +33.8131 q^{78} +0.751176 q^{79} +21.0149 q^{81} +14.7621 q^{82} +9.33088 q^{83} +9.14083 q^{84} +12.4924 q^{86} +13.2904 q^{87} -3.51235 q^{88} +7.48911 q^{89} -32.1472 q^{91} -4.47907 q^{92} -31.7130 q^{93} +20.0942 q^{94} -10.2840 q^{96} +3.72891 q^{97} -27.0330 q^{98} -11.0976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.60847	−1.13736	−0.568678	−	0.822560i	$-0.692545\pi$
$2$	−1.60847	−1.13736	−0.568678	+	0.822560i	$0.692545\pi$
$3$	−3.19065	−1.84212	−0.921060	−	0.389420i	$-0.872675\pi$
$3$	−3.19065	−1.84212	−0.921060	+	0.389420i	$0.872675\pi$
$4$	0.587161	0.293581
$5$	0	0
$5$	0	0
$6$	5.13204	2.09515
$7$	−4.87921	−1.84417	−0.922084	−	0.386990i	$-0.873515\pi$
$7$	−4.87921	−1.84417	−0.922084	+	0.386990i	$0.873515\pi$
$8$	2.27250	0.803451
$9$	7.18022	2.39341
$10$	0	0
$11$	−1.54559	−0.466011	−0.233006	−	0.972475i	$-0.574856\pi$
$11$	−1.54559	−0.466011	−0.233006	+	0.972475i	$0.574856\pi$
$12$	−1.87342	−0.540811
$13$	6.58861	1.82735	0.913676	−	0.406443i	$-0.133231\pi$
$13$	6.58861	1.82735	0.913676	+	0.406443i	$0.133231\pi$
$14$	7.84804	2.09748
$15$	0	0
$16$	−4.82956	−1.20739
$17$	−3.07006	−0.744599	−0.372300	−	0.928113i	$-0.621431\pi$
$17$	−3.07006	−0.744599	−0.372300	+	0.928113i	$0.621431\pi$
$18$	−11.5491	−2.72216
$19$	2.72015	0.624046	0.312023	−	0.950075i	$-0.398993\pi$
$19$	2.72015	0.624046	0.312023	+	0.950075i	$0.398993\pi$
$20$	0	0
$21$	15.5678	3.39718
$22$	2.48602	0.530021
$23$	−7.62835	−1.59062	−0.795310	−	0.606202i	$-0.792692\pi$
$23$	−7.62835	−1.59062	−0.795310	+	0.606202i	$0.792692\pi$
$24$	−7.25075	−1.48005
$25$	0	0
$26$	−10.5976	−2.07835
$27$	−13.3376	−2.56682
$28$	−2.86488	−0.541412
$29$	−4.16544	−0.773503	−0.386751	−	0.922184i	$-0.626403\pi$
$29$	−4.16544	−0.773503	−0.386751	+	0.922184i	$0.626403\pi$
$30$	0	0
$31$	9.93936	1.78516	0.892581	−	0.450887i	$-0.148892\pi$
$31$	9.93936	1.78516	0.892581	+	0.450887i	$0.148892\pi$
$32$	3.22318	0.569784
$33$	4.93142	0.858449
$34$	4.93809	0.846875
$35$	0	0
$36$	4.21595	0.702658
$37$	7.67570	1.26188	0.630939	−	0.775833i	$-0.282670\pi$
$37$	7.67570	1.26188	0.630939	+	0.775833i	$0.282670\pi$
$38$	−4.37527	−0.709763
$39$	−21.0219	−3.36620
$40$	0	0
$41$	−9.17775	−1.43332	−0.716662	−	0.697421i	$-0.754331\pi$
$41$	−9.17775	−1.43332	−0.716662	+	0.697421i	$0.754331\pi$
$42$	−25.0403	−3.86381
$43$	−7.76666	−1.18440	−0.592202	−	0.805790i	$-0.701741\pi$
$43$	−7.76666	−1.18440	−0.592202	+	0.805790i	$0.701741\pi$
$44$	−0.907508	−0.136812
$45$	0	0
$46$	12.2699	1.80910
$47$	−12.4928	−1.82226	−0.911132	−	0.412116i	$-0.864790\pi$
$47$	−12.4928	−1.82226	−0.911132	+	0.412116i	$0.864790\pi$
$48$	15.4094	2.22416
$49$	16.8067	2.40096
$50$	0	0
$51$	9.79548	1.37164
$52$	3.86858	0.536475
$53$	2.25429	0.309650	0.154825	−	0.987942i	$-0.450519\pi$
$53$	2.25429	0.309650	0.154825	+	0.987942i	$0.450519\pi$
$54$	21.4531	2.91939
$55$	0	0
$56$	−11.0880	−1.48170
$57$	−8.67905	−1.14957
$58$	6.69996	0.879748
$59$	−3.80303	−0.495113	−0.247556	−	0.968873i	$-0.579628\pi$
$59$	−3.80303	−0.495113	−0.247556	+	0.968873i	$0.579628\pi$
$60$	0	0
$61$	−9.88453	−1.26558	−0.632792	−	0.774322i	$-0.718091\pi$
$61$	−9.88453	−1.26558	−0.632792	+	0.774322i	$0.718091\pi$
$62$	−15.9871	−2.03037
$63$	−35.0338	−4.41384
$64$	4.47475	0.559344
$65$	0	0
$66$	−7.93201	−0.976363
$67$	0.537837	0.0657072	0.0328536	−	0.999460i	$-0.489540\pi$
$67$	0.537837	0.0657072	0.0328536	+	0.999460i	$0.489540\pi$
$68$	−1.80262	−0.218600
$69$	24.3394	2.93011
$70$	0	0
$71$	5.63516	0.668771	0.334385	−	0.942436i	$-0.391471\pi$
$71$	5.63516	0.668771	0.334385	+	0.942436i	$0.391471\pi$
$72$	16.3171	1.92298
$73$	2.21313	0.259028	0.129514	−	0.991578i	$-0.458658\pi$
$73$	2.21313	0.259028	0.129514	+	0.991578i	$0.458658\pi$
$74$	−12.3461	−1.43521
$75$	0	0
$76$	1.59717	0.183208
$77$	7.54124	0.859403
$78$	33.8131	3.82857
$79$	0.751176	0.0845139	0.0422569	−	0.999107i	$-0.486545\pi$
$79$	0.751176	0.0845139	0.0422569	+	0.999107i	$0.486545\pi$
$80$	0	0
$81$	21.0149	2.33499
$82$	14.7621	1.63020
$83$	9.33088	1.02420	0.512099	−	0.858927i	$-0.328868\pi$
$83$	9.33088	1.02420	0.512099	+	0.858927i	$0.328868\pi$
$84$	9.14083	0.997346
$85$	0	0
$86$	12.4924	1.34709
$87$	13.2904	1.42488
$88$	−3.51235	−0.374417
$89$	7.48911	0.793844	0.396922	−	0.917852i	$-0.370078\pi$
$89$	7.48911	0.793844	0.396922	+	0.917852i	$0.370078\pi$
$90$	0	0
$91$	−32.1472	−3.36994
$92$	−4.47907	−0.466976
$93$	−31.7130	−3.28848
$94$	20.0942	2.07256
$95$	0	0
$96$	−10.2840	−1.04961
$97$	3.72891	0.378614	0.189307	−	0.981918i	$-0.439376\pi$
$97$	3.72891	0.378614	0.189307	+	0.981918i	$0.439376\pi$
$98$	−27.0330	−2.73074
$99$	−11.0976	−1.11536
$100$	0	0
$101$	9.17104	0.912552	0.456276	−	0.889838i	$-0.349183\pi$
$101$	9.17104	0.912552	0.456276	+	0.889838i	$0.349183\pi$
$102$	−15.7557	−1.56005
$103$	1.10926	0.109298	0.0546492	−	0.998506i	$-0.482596\pi$
$103$	1.10926	0.109298	0.0546492	+	0.998506i	$0.482596\pi$
$104$	14.9726	1.46819
$105$	0	0
$106$	−3.62594	−0.352183
$107$	−5.30500	−0.512854	−0.256427	−	0.966564i	$-0.582545\pi$
$107$	−5.30500	−0.512854	−0.256427	+	0.966564i	$0.582545\pi$
$108$	−7.83133	−0.753570
$109$	−1.00707	−0.0964598	−0.0482299	−	0.998836i	$-0.515358\pi$
$109$	−1.00707	−0.0964598	−0.0482299	+	0.998836i	$0.515358\pi$
$110$	0	0
$111$	−24.4905	−2.32453
$112$	23.5645	2.22663
$113$	2.65076	0.249363	0.124681	−	0.992197i	$-0.460209\pi$
$113$	2.65076	0.249363	0.124681	+	0.992197i	$0.460209\pi$
$114$	13.9599	1.30747
$115$	0	0
$116$	−2.44579	−0.227085
$117$	47.3077	4.37360
$118$	6.11705	0.563120
$119$	14.9795	1.37317
$120$	0	0
$121$	−8.61117	−0.782833
$122$	15.8989	1.43942
$123$	29.2830	2.64036
$124$	5.83601	0.524089
$125$	0	0
$126$	56.3507	5.02012
$127$	18.8663	1.67411	0.837055	−	0.547119i	$-0.184276\pi$
$127$	18.8663	1.67411	0.837055	+	0.547119i	$0.184276\pi$
$128$	−13.6438	−1.20596
$129$	24.7806	2.18181
$130$	0	0
$131$	−16.9051	−1.47700	−0.738502	−	0.674251i	$-0.764467\pi$
$131$	−16.9051	−1.47700	−0.738502	+	0.674251i	$0.764467\pi$
$132$	2.89554	0.252024
$133$	−13.2722	−1.15085
$134$	−0.865092	−0.0747326
$135$	0	0
$136$	−6.97672	−0.598249
$137$	13.8318	1.18173	0.590865	−	0.806770i	$-0.298787\pi$
$137$	13.8318	1.18173	0.590865	+	0.806770i	$0.298787\pi$
$138$	−39.1490	−3.33259
$139$	8.17546	0.693434	0.346717	−	0.937970i	$-0.387296\pi$
$139$	8.17546	0.693434	0.346717	+	0.937970i	$0.387296\pi$
$140$	0	0
$141$	39.8601	3.35683
$142$	−9.06396	−0.760631
$143$	−10.1833	−0.851567
$144$	−34.6773	−2.88978
$145$	0	0
$146$	−3.55975	−0.294607
$147$	−53.6242	−4.42285
$148$	4.50688	0.370463
$149$	−6.87133	−0.562922	−0.281461	−	0.959573i	$-0.590819\pi$
$149$	−6.87133	−0.562922	−0.281461	+	0.959573i	$0.590819\pi$
$150$	0	0
$151$	4.23040	0.344265	0.172132	−	0.985074i	$-0.444934\pi$
$151$	4.23040	0.344265	0.172132	+	0.985074i	$0.444934\pi$
$152$	6.18155	0.501390
$153$	−22.0437	−1.78213
$154$	−12.1298	−0.977448
$155$	0	0
$156$	−12.3433	−0.988252
$157$	7.57999	0.604949	0.302474	−	0.953157i	$-0.402187\pi$
$157$	7.57999	0.604949	0.302474	+	0.953157i	$0.402187\pi$
$158$	−1.20824	−0.0961225
$159$	−7.19263	−0.570412
$160$	0	0
$161$	37.2203	2.93337
$162$	−33.8018	−2.65572
$163$	8.78233	0.687885	0.343943	−	0.938991i	$-0.388237\pi$
$163$	8.78233	0.687885	0.343943	+	0.938991i	$0.388237\pi$
$164$	−5.38882	−0.420796
$165$	0	0
$166$	−15.0084	−1.16488
$167$	11.2813	0.872971	0.436485	−	0.899711i	$-0.356223\pi$
$167$	11.2813	0.872971	0.436485	+	0.899711i	$0.356223\pi$
$168$	35.3779	2.72947
$169$	30.4098	2.33922
$170$	0	0
$171$	19.5313	1.49360
$172$	−4.56028	−0.347718
$173$	−11.5629	−0.879111	−0.439556	−	0.898215i	$-0.644864\pi$
$173$	−11.5629	−0.879111	−0.439556	+	0.898215i	$0.644864\pi$
$174$	−21.3772	−1.62060
$175$	0	0
$176$	7.46450	0.562658
$177$	12.1341	0.912057
$178$	−12.0460	−0.902884
$179$	12.6264	0.943745	0.471872	−	0.881667i	$-0.343578\pi$
$179$	12.6264	0.943745	0.471872	+	0.881667i	$0.343578\pi$
$180$	0	0
$181$	−20.7444	−1.54192	−0.770958	−	0.636886i	$-0.780222\pi$
$181$	−20.7444	−1.54192	−0.770958	+	0.636886i	$0.780222\pi$
$182$	51.7077	3.83283
$183$	31.5380	2.33136
$184$	−17.3354	−1.27799
$185$	0	0
$186$	51.0093	3.74018
$187$	4.74504	0.346992
$188$	−7.33529	−0.534981
$189$	65.0770	4.73365
$190$	0	0
$191$	−5.27724	−0.381847	−0.190924	−	0.981605i	$-0.561148\pi$
$191$	−5.27724	−0.381847	−0.190924	+	0.981605i	$0.561148\pi$
$192$	−14.2773	−1.03038
$193$	−2.16516	−0.155851	−0.0779257	−	0.996959i	$-0.524830\pi$
$193$	−2.16516	−0.155851	−0.0779257	+	0.996959i	$0.524830\pi$
$194$	−5.99783	−0.430619
$195$	0	0
$196$	9.86824	0.704874
$197$	6.64480	0.473423	0.236711	−	0.971580i	$-0.423930\pi$
$197$	6.64480	0.473423	0.236711	+	0.971580i	$0.423930\pi$
$198$	17.8502	1.26856
$199$	1.61234	0.114296	0.0571479	−	0.998366i	$-0.481799\pi$
$199$	1.61234	0.114296	0.0571479	+	0.998366i	$0.481799\pi$
$200$	0	0
$201$	−1.71605	−0.121041
$202$	−14.7513	−1.03790
$203$	20.3241	1.42647
$204$	5.75153	0.402687
$205$	0	0
$206$	−1.78420	−0.124311
$207$	−54.7732	−3.80700
$208$	−31.8201	−2.20633
$209$	−4.20423	−0.290813
$210$	0	0
$211$	−10.3641	−0.713495	−0.356747	−	0.934201i	$-0.616114\pi$
$211$	−10.3641	−0.713495	−0.356747	+	0.934201i	$0.616114\pi$
$212$	1.32363	0.0909073
$213$	−17.9798	−1.23196
$214$	8.53291	0.583298
$215$	0	0
$216$	−30.3097	−2.06232
$217$	−48.4962	−3.29214
$218$	1.61984	0.109709
$219$	−7.06133	−0.477160
$220$	0	0
$221$	−20.2274	−1.36065
$222$	39.3920	2.64382
$223$	17.0726	1.14327	0.571634	−	0.820509i	$-0.306310\pi$
$223$	17.0726	1.14327	0.571634	+	0.820509i	$0.306310\pi$
$224$	−15.7266	−1.05078
$225$	0	0
$226$	−4.26366	−0.283614
$227$	16.2917	1.08132	0.540658	−	0.841243i	$-0.318175\pi$
$227$	16.2917	1.08132	0.540658	+	0.841243i	$0.318175\pi$
$228$	−5.09600	−0.337491
$229$	23.5153	1.55393	0.776966	−	0.629542i	$-0.216758\pi$
$229$	23.5153	1.55393	0.776966	+	0.629542i	$0.216758\pi$
$230$	0	0
$231$	−24.0614	−1.58312
$232$	−9.46597	−0.621471
$233$	25.3487	1.66065	0.830324	−	0.557281i	$-0.188156\pi$
$233$	25.3487	1.66065	0.830324	+	0.557281i	$0.188156\pi$
$234$	−76.0928	−4.97434
$235$	0	0
$236$	−2.23300	−0.145356
$237$	−2.39674	−0.155685
$238$	−24.0940	−1.56178
$239$	−6.68216	−0.432233	−0.216117	−	0.976368i	$-0.569339\pi$
$239$	−6.68216	−0.432233	−0.216117	+	0.976368i	$0.569339\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	13.8508	0.890361
$243$	−27.0383	−1.73451
$244$	−5.80381	−0.371551
$245$	0	0
$246$	−47.1006	−3.00303
$247$	17.9220	1.14035
$248$	22.5872	1.43429
$249$	−29.7715	−1.88669
$250$	0	0
$251$	−12.7158	−0.802616	−0.401308	−	0.915943i	$-0.631444\pi$
$251$	−12.7158	−0.802616	−0.401308	+	0.915943i	$0.631444\pi$
$252$	−20.5705	−1.29582
$253$	11.7903	0.741248
$254$	−30.3457	−1.90406
$255$	0	0
$256$	12.9962	0.812260
$257$	−22.4179	−1.39839	−0.699196	−	0.714930i	$-0.746458\pi$
$257$	−22.4179	−1.39839	−0.699196	+	0.714930i	$0.746458\pi$
$258$	−39.8588	−2.48150
$259$	−37.4514	−2.32711
$260$	0	0
$261$	−29.9088	−1.85131
$262$	27.1913	1.67988
$263$	9.41164	0.580347	0.290173	−	0.956974i	$-0.406287\pi$
$263$	9.41164	0.580347	0.290173	+	0.956974i	$0.406287\pi$
$264$	11.2067	0.689722
$265$	0	0
$266$	21.3479	1.30892
$267$	−23.8951	−1.46236
$268$	0.315797	0.0192904
$269$	−11.2364	−0.685093	−0.342547	−	0.939501i	$-0.611289\pi$
$269$	−11.2364	−0.685093	−0.342547	+	0.939501i	$0.611289\pi$
$270$	0	0
$271$	−3.00322	−0.182432	−0.0912162	−	0.995831i	$-0.529075\pi$
$271$	−3.00322	−0.182432	−0.0912162	+	0.995831i	$0.529075\pi$
$272$	14.8271	0.899022
$273$	102.570	6.20784
$274$	−22.2480	−1.34405
$275$	0	0
$276$	14.2911	0.860225
$277$	10.1535	0.610065	0.305032	−	0.952342i	$-0.401333\pi$
$277$	10.1535	0.610065	0.305032	+	0.952342i	$0.401333\pi$
$278$	−13.1500	−0.788682
$279$	71.3668	4.27262
$280$	0	0
$281$	4.13211	0.246501	0.123251	−	0.992376i	$-0.460668\pi$
$281$	4.13211	0.246501	0.123251	+	0.992376i	$0.460668\pi$
$282$	−64.1136	−3.81791
$283$	13.7412	0.816829	0.408414	−	0.912797i	$-0.366082\pi$
$283$	13.7412	0.816829	0.408414	+	0.912797i	$0.366082\pi$
$284$	3.30875	0.196338
$285$	0	0
$286$	16.3794	0.968536
$287$	44.7802	2.64329
$288$	23.1432	1.36372
$289$	−7.57473	−0.445572
$290$	0	0
$291$	−11.8976	−0.697452
$292$	1.29947	0.0760456
$293$	19.7386	1.15314	0.576569	−	0.817048i	$-0.304391\pi$
$293$	19.7386	1.15314	0.576569	+	0.817048i	$0.304391\pi$
$294$	86.2527	5.03036
$295$	0	0
$296$	17.4431	1.01386
$297$	20.6144	1.19617
$298$	11.0523	0.640243
$299$	−50.2602	−2.90662
$300$	0	0
$301$	37.8951	2.18424
$302$	−6.80445	−0.391552
$303$	−29.2615	−1.68103
$304$	−13.1372	−0.753468
$305$	0	0
$306$	35.4566	2.02692
$307$	−2.13607	−0.121912	−0.0609559	−	0.998140i	$-0.519415\pi$
$307$	−2.13607	−0.121912	−0.0609559	+	0.998140i	$0.519415\pi$
$308$	4.42792	0.252304
$309$	−3.53925	−0.201341
$310$	0	0
$311$	12.2416	0.694155	0.347078	−	0.937836i	$-0.387174\pi$
$311$	12.2416	0.694155	0.347078	+	0.937836i	$0.387174\pi$
$312$	−47.7724	−2.70458
$313$	5.06141	0.286088	0.143044	−	0.989716i	$-0.454311\pi$
$313$	5.06141	0.286088	0.143044	+	0.989716i	$0.454311\pi$
$314$	−12.1922	−0.688043
$315$	0	0
$316$	0.441062	0.0248117
$317$	−21.8137	−1.22518	−0.612590	−	0.790401i	$-0.709872\pi$
$317$	−21.8137	−1.22518	−0.612590	+	0.790401i	$0.709872\pi$
$318$	11.5691	0.648763
$319$	6.43804	0.360461
$320$	0	0
$321$	16.9264	0.944739
$322$	−59.8676	−3.33629
$323$	−8.35104	−0.464664
$324$	12.3391	0.685508
$325$	0	0
$326$	−14.1261	−0.782371
$327$	3.21320	0.177691
$328$	−20.8565	−1.15161
$329$	60.9550	3.36056
$330$	0	0
$331$	10.6015	0.582714	0.291357	−	0.956614i	$-0.405893\pi$
$331$	10.6015	0.582714	0.291357	+	0.956614i	$0.405893\pi$
$332$	5.47874	0.300685
$333$	55.1132	3.02019
$334$	−18.1455	−0.992879
$335$	0	0
$336$	−75.1858	−4.10172
$337$	32.4169	1.76586	0.882932	−	0.469501i	$-0.155566\pi$
$337$	32.4169	1.76586	0.882932	+	0.469501i	$0.155566\pi$
$338$	−48.9131	−2.66052
$339$	−8.45764	−0.459356
$340$	0	0
$341$	−15.3621	−0.831906
$342$	−31.4154	−1.69875
$343$	−47.8489	−2.58360
$344$	−17.6497	−0.951610
$345$	0	0
$346$	18.5985	0.999863
$347$	5.57545	0.299306	0.149653	−	0.988739i	$-0.452184\pi$
$347$	5.57545	0.299306	0.149653	+	0.988739i	$0.452184\pi$
$348$	7.80363	0.418319
$349$	−27.3705	−1.46511	−0.732556	−	0.680707i	$-0.761673\pi$
$349$	−27.3705	−1.46511	−0.732556	+	0.680707i	$0.761673\pi$
$350$	0	0
$351$	−87.8763	−4.69049
$352$	−4.98171	−0.265526
$353$	−7.33274	−0.390283	−0.195141	−	0.980775i	$-0.562517\pi$
$353$	−7.33274	−0.390283	−0.195141	+	0.980775i	$0.562517\pi$
$354$	−19.5173	−1.03733
$355$	0	0
$356$	4.39732	0.233057
$357$	−47.7942	−2.52954
$358$	−20.3092	−1.07337
$359$	25.8875	1.36629	0.683144	−	0.730284i	$-0.260612\pi$
$359$	25.8875	1.36629	0.683144	+	0.730284i	$0.260612\pi$
$360$	0	0
$361$	−11.6008	−0.610567
$362$	33.3666	1.75371
$363$	27.4752	1.44207
$364$	−18.8756	−0.989351
$365$	0	0
$366$	−50.7278	−2.65159
$367$	−29.6628	−1.54839	−0.774194	−	0.632948i	$-0.781845\pi$
$367$	−29.6628	−1.54839	−0.774194	+	0.632948i	$0.781845\pi$
$368$	36.8416	1.92050
$369$	−65.8983	−3.43053
$370$	0	0
$371$	−10.9991	−0.571047
$372$	−18.6206	−0.965436
$373$	−26.2265	−1.35796	−0.678978	−	0.734159i	$-0.737577\pi$
$373$	−26.2265	−1.35796	−0.678978	+	0.734159i	$0.737577\pi$
$374$	−7.63224	−0.394653
$375$	0	0
$376$	−28.3899	−1.46410
$377$	−27.4445	−1.41346
$378$	−104.674	−5.38385
$379$	−4.21015	−0.216261	−0.108130	−	0.994137i	$-0.534486\pi$
$379$	−4.21015	−0.216261	−0.108130	+	0.994137i	$0.534486\pi$
$380$	0	0
$381$	−60.1955	−3.08391
$382$	8.48825	0.434297
$383$	2.68629	0.137263	0.0686316	−	0.997642i	$-0.478137\pi$
$383$	2.68629	0.137263	0.0686316	+	0.997642i	$0.478137\pi$
$384$	43.5327	2.22152
$385$	0	0
$386$	3.48258	0.177259
$387$	−55.7663	−2.83476
$388$	2.18947	0.111154
$389$	−4.75744	−0.241212	−0.120606	−	0.992700i	$-0.538484\pi$
$389$	−4.75744	−0.241212	−0.120606	+	0.992700i	$0.538484\pi$
$390$	0	0
$391$	23.4195	1.18437
$392$	38.1932	1.92905
$393$	53.9382	2.72082
$394$	−10.6879	−0.538450
$395$	0	0
$396$	−6.51611	−0.327447
$397$	−14.4711	−0.726284	−0.363142	−	0.931734i	$-0.618296\pi$
$397$	−14.4711	−0.726284	−0.363142	+	0.931734i	$0.618296\pi$
$398$	−2.59339	−0.129995
$399$	42.3469	2.12000
$400$	0	0
$401$	−1.65035	−0.0824143	−0.0412072	−	0.999151i	$-0.513120\pi$
$401$	−1.65035	−0.0824143	−0.0412072	+	0.999151i	$0.513120\pi$
$402$	2.76020	0.137666
$403$	65.4866	3.26212
$404$	5.38488	0.267908
$405$	0	0
$406$	−32.6905	−1.62240
$407$	−11.8635	−0.588050
$408$	22.2602	1.10205
$409$	14.3555	0.709833	0.354916	−	0.934898i	$-0.384509\pi$
$409$	14.3555	0.709833	0.354916	+	0.934898i	$0.384509\pi$
$410$	0	0
$411$	−44.1324	−2.17689
$412$	0.651313	0.0320879
$413$	18.5558	0.913071
$414$	88.1009	4.32992
$415$	0	0
$416$	21.2363	1.04120
$417$	−26.0850	−1.27739
$418$	6.76236	0.330758
$419$	23.1046	1.12873	0.564367	−	0.825524i	$-0.309120\pi$
$419$	23.1046	1.12873	0.564367	+	0.825524i	$0.309120\pi$
$420$	0	0
$421$	13.1040	0.638651	0.319326	−	0.947645i	$-0.396544\pi$
$421$	13.1040	0.638651	0.319326	+	0.947645i	$0.396544\pi$
$422$	16.6703	0.811498
$423$	−89.7011	−4.36142
$424$	5.12287	0.248789
$425$	0	0
$426$	28.9199	1.40117
$427$	48.2287	2.33395
$428$	−3.11489	−0.150564
$429$	32.4912	1.56869
$430$	0	0
$431$	5.00951	0.241300	0.120650	−	0.992695i	$-0.461502\pi$
$431$	5.00951	0.241300	0.120650	+	0.992695i	$0.461502\pi$
$432$	64.4148	3.09916
$433$	−24.6826	−1.18617	−0.593084	−	0.805140i	$-0.702090\pi$
$433$	−24.6826	−1.18617	−0.593084	+	0.805140i	$0.702090\pi$
$434$	78.0045	3.74434
$435$	0	0
$436$	−0.591313	−0.0283187
$437$	−20.7503	−0.992621
$438$	11.3579	0.542702
$439$	14.7801	0.705416	0.352708	−	0.935733i	$-0.385261\pi$
$439$	14.7801	0.705416	0.352708	+	0.935733i	$0.385261\pi$
$440$	0	0
$441$	120.676	5.74646
$442$	32.5351	1.54754
$443$	−38.3422	−1.82169	−0.910846	−	0.412747i	$-0.864570\pi$
$443$	−38.3422	−1.82169	−0.910846	+	0.412747i	$0.864570\pi$
$444$	−14.3799	−0.682437
$445$	0	0
$446$	−27.4607	−1.30030
$447$	21.9240	1.03697
$448$	−21.8332	−1.03152
$449$	−10.8947	−0.514151	−0.257076	−	0.966391i	$-0.582759\pi$
$449$	−10.8947	−0.514151	−0.257076	+	0.966391i	$0.582759\pi$
$450$	0	0
$451$	14.1850	0.667946
$452$	1.55643	0.0732081
$453$	−13.4977	−0.634177
$454$	−26.2046	−1.22984
$455$	0	0
$456$	−19.7232	−0.923621
$457$	11.7412	0.549232	0.274616	−	0.961554i	$-0.411449\pi$
$457$	11.7412	0.549232	0.274616	+	0.961554i	$0.411449\pi$
$458$	−37.8235	−1.76738
$459$	40.9473	1.91125
$460$	0	0
$461$	36.4150	1.69602	0.848008	−	0.529983i	$-0.177802\pi$
$461$	36.4150	1.69602	0.848008	+	0.529983i	$0.177802\pi$
$462$	38.7020	1.80058
$463$	2.29506	0.106661	0.0533303	−	0.998577i	$-0.483016\pi$
$463$	2.29506	0.106661	0.0533303	+	0.998577i	$0.483016\pi$
$464$	20.1173	0.933920
$465$	0	0
$466$	−40.7725	−1.88875
$467$	5.73563	0.265413	0.132707	−	0.991155i	$-0.457633\pi$
$467$	5.73563	0.265413	0.132707	+	0.991155i	$0.457633\pi$
$468$	27.7773	1.28400
$469$	−2.62422	−0.121175
$470$	0	0
$471$	−24.1851	−1.11439
$472$	−8.64240	−0.397799
$473$	12.0040	0.551946
$474$	3.85507	0.177069
$475$	0	0
$476$	8.79537	0.403135
$477$	16.1863	0.741118
$478$	10.7480	0.491603
$479$	−20.5632	−0.939556	−0.469778	−	0.882785i	$-0.655666\pi$
$479$	−20.5632	−0.939556	−0.469778	+	0.882785i	$0.655666\pi$
$480$	0	0
$481$	50.5722	2.30590
$482$	1.60847	0.0732636
$483$	−118.757	−5.40362
$484$	−5.05615	−0.229825
$485$	0	0
$486$	43.4902	1.97276
$487$	−20.3438	−0.921867	−0.460934	−	0.887435i	$-0.652485\pi$
$487$	−20.3438	−0.921867	−0.460934	+	0.887435i	$0.652485\pi$
$488$	−22.4626	−1.01683
$489$	−28.0213	−1.26717
$490$	0	0
$491$	30.0142	1.35452	0.677261	−	0.735743i	$-0.263167\pi$
$491$	30.0142	1.35452	0.677261	+	0.735743i	$0.263167\pi$
$492$	17.1938	0.775158
$493$	12.7882	0.575949
$494$	−28.8270	−1.29699
$495$	0	0
$496$	−48.0028	−2.15539
$497$	−27.4951	−1.23333
$498$	47.8865	2.14585
$499$	−23.9106	−1.07039	−0.535193	−	0.844730i	$-0.679761\pi$
$499$	−23.9106	−1.07039	−0.535193	+	0.844730i	$0.679761\pi$
$500$	0	0
$501$	−35.9945	−1.60812
$502$	20.4530	0.912861
$503$	−15.1690	−0.676351	−0.338176	−	0.941083i	$-0.609810\pi$
$503$	−15.1690	−0.676351	−0.338176	+	0.941083i	$0.609810\pi$
$504$	−79.6144	−3.54631
$505$	0	0
$506$	−18.9642	−0.843063
$507$	−97.0270	−4.30912
$508$	11.0775	0.491486
$509$	1.84003	0.0815581	0.0407791	−	0.999168i	$-0.487016\pi$
$509$	1.84003	0.0815581	0.0407791	+	0.999168i	$0.487016\pi$
$510$	0	0
$511$	−10.7983	−0.477691
$512$	6.38382	0.282127
$513$	−36.2803	−1.60182
$514$	36.0585	1.59047
$515$	0	0
$516$	14.5502	0.640539
$517$	19.3087	0.849196
$518$	60.2392	2.64676
$519$	36.8931	1.61943
$520$	0	0
$521$	−3.20670	−0.140488	−0.0702441	−	0.997530i	$-0.522378\pi$
$521$	−3.20670	−0.140488	−0.0702441	+	0.997530i	$0.522378\pi$
$522$	48.1072	2.10560
$523$	−24.0831	−1.05308	−0.526539	−	0.850151i	$-0.676511\pi$
$523$	−24.0831	−1.05308	−0.526539	+	0.850151i	$0.676511\pi$
$524$	−9.92602	−0.433620
$525$	0	0
$526$	−15.1383	−0.660061
$527$	−30.5145	−1.32923
$528$	−23.8166	−1.03648
$529$	35.1917	1.53007
$530$	0	0
$531$	−27.3066	−1.18501
$532$	−7.79293	−0.337866
$533$	−60.4687	−2.61919
$534$	38.4344	1.66322
$535$	0	0
$536$	1.22224	0.0527925
$537$	−40.2865	−1.73849
$538$	18.0733	0.779195
$539$	−25.9762	−1.11887
$540$	0	0
$541$	7.40237	0.318253	0.159126	−	0.987258i	$-0.449132\pi$
$541$	7.40237	0.318253	0.159126	+	0.987258i	$0.449132\pi$
$542$	4.83057	0.207491
$543$	66.1879	2.84040
$544$	−9.89537	−0.424261
$545$	0	0
$546$	−164.981	−7.06053
$547$	−4.37542	−0.187080	−0.0935398	−	0.995616i	$-0.529818\pi$
$547$	−4.37542	−0.187080	−0.0935398	+	0.995616i	$0.529818\pi$
$548$	8.12150	0.346933
$549$	−70.9731	−3.02906
$550$	0	0
$551$	−11.3306	−0.482701
$552$	55.3112	2.35420
$553$	−3.66515	−0.155858
$554$	−16.3316	−0.693862
$555$	0	0
$556$	4.80032	0.203579
$557$	1.63556	0.0693010	0.0346505	−	0.999399i	$-0.488968\pi$
$557$	1.63556	0.0693010	0.0346505	+	0.999399i	$0.488968\pi$
$558$	−114.791	−4.85949
$559$	−51.1715	−2.16432
$560$	0	0
$561$	−15.1397	−0.639201
$562$	−6.64636	−0.280360
$563$	16.2932	0.686675	0.343338	−	0.939212i	$-0.388442\pi$
$563$	16.2932	0.686675	0.343338	+	0.939212i	$0.388442\pi$
$564$	23.4043	0.985500
$565$	0	0
$566$	−22.1022	−0.929026
$567$	−102.536	−4.30611
$568$	12.8059	0.537324
$569$	−19.5093	−0.817873	−0.408936	−	0.912563i	$-0.634100\pi$
$569$	−19.5093	−0.817873	−0.408936	+	0.912563i	$0.634100\pi$
$570$	0	0
$571$	−7.92309	−0.331571	−0.165786	−	0.986162i	$-0.553016\pi$
$571$	−7.92309	−0.331571	−0.165786	+	0.986162i	$0.553016\pi$
$572$	−5.97922	−0.250004
$573$	16.8378	0.703409
$574$	−72.0274	−3.00636
$575$	0	0
$576$	32.1297	1.33874
$577$	23.0143	0.958098	0.479049	−	0.877788i	$-0.340982\pi$
$577$	23.0143	0.958098	0.479049	+	0.877788i	$0.340982\pi$
$578$	12.1837	0.506774
$579$	6.90825	0.287097
$580$	0	0
$581$	−45.5273	−1.88879
$582$	19.1370	0.793252
$583$	−3.48419	−0.144300
$584$	5.02935	0.208116
$585$	0	0
$586$	−31.7488	−1.31153
$587$	−33.4974	−1.38259	−0.691293	−	0.722574i	$-0.742959\pi$
$587$	−33.4974	−1.38259	−0.691293	+	0.722574i	$0.742959\pi$
$588$	−31.4861	−1.29846
$589$	27.0366	1.11402
$590$	0	0
$591$	−21.2012	−0.872101
$592$	−37.0703	−1.52358
$593$	−0.644693	−0.0264744	−0.0132372	−	0.999912i	$-0.504214\pi$
$593$	−0.644693	−0.0264744	−0.0132372	+	0.999912i	$0.504214\pi$
$594$	−33.1576	−1.36047
$595$	0	0
$596$	−4.03458	−0.165263
$597$	−5.14440	−0.210546
$598$	80.8419	3.30587
$599$	−14.9943	−0.612649	−0.306324	−	0.951927i	$-0.599099\pi$
$599$	−14.9943	−0.612649	−0.306324	+	0.951927i	$0.599099\pi$
$600$	0	0
$601$	−10.4488	−0.426215	−0.213108	−	0.977029i	$-0.568359\pi$
$601$	−10.4488	−0.426215	−0.213108	+	0.977029i	$0.568359\pi$
$602$	−60.9530	−2.48426
$603$	3.86179	0.157264
$604$	2.48393	0.101070
$605$	0	0
$606$	47.0662	1.91193
$607$	45.0799	1.82974	0.914868	−	0.403752i	$-0.132294\pi$
$607$	45.0799	1.82974	0.914868	+	0.403752i	$0.132294\pi$
$608$	8.76756	0.355571
$609$	−64.8469	−2.62773
$610$	0	0
$611$	−82.3103	−3.32992
$612$	−12.9432	−0.523199
$613$	−45.3825	−1.83298	−0.916492	−	0.400054i	$-0.868992\pi$
$613$	−45.3825	−1.83298	−0.916492	+	0.400054i	$0.868992\pi$
$614$	3.43579	0.138657
$615$	0	0
$616$	17.1375	0.690488
$617$	−24.2876	−0.977782	−0.488891	−	0.872345i	$-0.662598\pi$
$617$	−24.2876	−0.977782	−0.488891	+	0.872345i	$0.662598\pi$
$618$	5.69276	0.228996
$619$	35.0791	1.40995	0.704974	−	0.709233i	$-0.250959\pi$
$619$	35.0791	1.40995	0.704974	+	0.709233i	$0.250959\pi$
$620$	0	0
$621$	101.744	4.08284
$622$	−19.6901	−0.789503
$623$	−36.5409	−1.46398
$624$	101.527	4.06432
$625$	0	0
$626$	−8.14111	−0.325384
$627$	13.4142	0.535712
$628$	4.45068	0.177601
$629$	−23.5649	−0.939593
$630$	0	0
$631$	9.87717	0.393204	0.196602	−	0.980483i	$-0.437009\pi$
$631$	9.87717	0.393204	0.196602	+	0.980483i	$0.437009\pi$
$632$	1.70705	0.0679028
$633$	33.0682	1.31434
$634$	35.0866	1.39347
$635$	0	0
$636$	−4.22323	−0.167462
$637$	110.733	4.38739
$638$	−10.3554	−0.409973
$639$	40.4617	1.60064
$640$	0	0
$641$	−26.6214	−1.05148	−0.525741	−	0.850645i	$-0.676212\pi$
$641$	−26.6214	−1.05148	−0.525741	+	0.850645i	$0.676212\pi$
$642$	−27.2255	−1.07451
$643$	39.2102	1.54630	0.773149	−	0.634224i	$-0.218680\pi$
$643$	39.2102	1.54630	0.773149	+	0.634224i	$0.218680\pi$
$644$	21.8543	0.861182
$645$	0	0
$646$	13.4324	0.528489
$647$	−37.0577	−1.45689	−0.728443	−	0.685106i	$-0.759756\pi$
$647$	−37.0577	−1.45689	−0.728443	+	0.685106i	$0.759756\pi$
$648$	47.7564	1.87605
$649$	5.87791	0.230728
$650$	0	0
$651$	154.734	6.06452
$652$	5.15665	0.201950
$653$	26.2186	1.02601	0.513006	−	0.858385i	$-0.328532\pi$
$653$	26.2186	1.02601	0.513006	+	0.858385i	$0.328532\pi$
$654$	−5.16833	−0.202098
$655$	0	0
$656$	44.3245	1.73058
$657$	15.8908	0.619959
$658$	−98.0441	−3.82216
$659$	8.81860	0.343524	0.171762	−	0.985138i	$-0.445054\pi$
$659$	8.81860	0.343524	0.171762	+	0.985138i	$0.445054\pi$
$660$	0	0
$661$	−23.7912	−0.925369	−0.462684	−	0.886523i	$-0.653114\pi$
$661$	−23.7912	−0.925369	−0.462684	+	0.886523i	$0.653114\pi$
$662$	−17.0522	−0.662753
$663$	64.5386	2.50647
$664$	21.2045	0.822892
$665$	0	0
$666$	−88.6478	−3.43503
$667$	31.7754	1.23035
$668$	6.62393	0.256287
$669$	−54.4727	−2.10604
$670$	0	0
$671$	15.2774	0.589777
$672$	50.1780	1.93566
$673$	−12.8341	−0.494718	−0.247359	−	0.968924i	$-0.579563\pi$
$673$	−12.8341	−0.494718	−0.247359	+	0.968924i	$0.579563\pi$
$674$	−52.1415	−2.00842
$675$	0	0
$676$	17.8555	0.686749
$677$	−38.3536	−1.47405	−0.737025	−	0.675865i	$-0.763770\pi$
$677$	−38.3536	−1.47405	−0.737025	+	0.675865i	$0.763770\pi$
$678$	13.6038	0.522452
$679$	−18.1942	−0.698228
$680$	0	0
$681$	−51.9809	−1.99191
$682$	24.7095	0.946174
$683$	19.1853	0.734106	0.367053	−	0.930200i	$-0.380367\pi$
$683$	19.1853	0.734106	0.367053	+	0.930200i	$0.380367\pi$
$684$	11.4680	0.438491
$685$	0	0
$686$	76.9633	2.93847
$687$	−75.0289	−2.86253
$688$	37.5096	1.43004
$689$	14.8526	0.565840
$690$	0	0
$691$	−18.1040	−0.688708	−0.344354	−	0.938840i	$-0.611902\pi$
$691$	−18.1040	−0.688708	−0.344354	+	0.938840i	$0.611902\pi$
$692$	−6.78929	−0.258090
$693$	54.1477	2.05690
$694$	−8.96792	−0.340418
$695$	0	0
$696$	30.2026	1.14482
$697$	28.1763	1.06725
$698$	44.0246	1.66635
$699$	−80.8787	−3.05911
$700$	0	0
$701$	41.8422	1.58036	0.790179	−	0.612876i	$-0.209988\pi$
$701$	41.8422	1.58036	0.790179	+	0.612876i	$0.209988\pi$
$702$	141.346	5.33476
$703$	20.8791	0.787470
$704$	−6.91611	−0.260661
$705$	0	0
$706$	11.7945	0.443891
$707$	−44.7474	−1.68290
$708$	7.12470	0.267762
$709$	−2.17472	−0.0816733	−0.0408366	−	0.999166i	$-0.513002\pi$
$709$	−2.17472	−0.0816733	−0.0408366	+	0.999166i	$0.513002\pi$
$710$	0	0
$711$	5.39361	0.202276
$712$	17.0190	0.637815
$713$	−75.8209	−2.83952
$714$	76.8753	2.87699
$715$	0	0
$716$	7.41376	0.277065
$717$	21.3204	0.796225
$718$	−41.6391	−1.55396
$719$	−19.3755	−0.722585	−0.361292	−	0.932453i	$-0.617664\pi$
$719$	−19.3755	−0.722585	−0.361292	+	0.932453i	$0.617664\pi$
$720$	0	0
$721$	−5.41230	−0.201564
$722$	18.6594	0.694432
$723$	3.19065	0.118661
$724$	−12.1803	−0.452677
$725$	0	0
$726$	−44.1929	−1.64015
$727$	15.5495	0.576697	0.288349	−	0.957525i	$-0.406894\pi$
$727$	15.5495	0.576697	0.288349	+	0.957525i	$0.406894\pi$
$728$	−73.0546	−2.70759
$729$	23.2250	0.860185
$730$	0	0
$731$	23.8441	0.881906
$732$	18.5179	0.684442
$733$	45.9211	1.69613	0.848067	−	0.529888i	$-0.177766\pi$
$733$	45.9211	1.69613	0.848067	+	0.529888i	$0.177766\pi$
$734$	47.7117	1.76107
$735$	0	0
$736$	−24.5876	−0.906310
$737$	−0.831273	−0.0306203
$738$	105.995	3.90173
$739$	−30.1693	−1.10980	−0.554898	−	0.831918i	$-0.687243\pi$
$739$	−30.1693	−1.10980	−0.554898	+	0.831918i	$0.687243\pi$
$740$	0	0
$741$	−57.1829	−2.10067
$742$	17.6917	0.649484
$743$	13.8850	0.509390	0.254695	−	0.967021i	$-0.418025\pi$
$743$	13.8850	0.509390	0.254695	+	0.967021i	$0.418025\pi$
$744$	−72.0678	−2.64214
$745$	0	0
$746$	42.1844	1.54448
$747$	66.9978	2.45132
$748$	2.78611	0.101870
$749$	25.8842	0.945789
$750$	0	0
$751$	−40.1682	−1.46576	−0.732879	−	0.680359i	$-0.761824\pi$
$751$	−40.1682	−1.46576	−0.732879	+	0.680359i	$0.761824\pi$
$752$	60.3348	2.20018
$753$	40.5717	1.47851
$754$	44.1435	1.60761
$755$	0	0
$756$	38.2107	1.38971
$757$	−44.3388	−1.61152	−0.805761	−	0.592242i	$-0.798243\pi$
$757$	−44.3388	−1.61152	−0.805761	+	0.592242i	$0.798243\pi$
$758$	6.77187	0.245966
$759$	−37.6186	−1.36547
$760$	0	0
$761$	−30.1359	−1.09243	−0.546213	−	0.837646i	$-0.683931\pi$
$761$	−30.1359	−1.09243	−0.546213	+	0.837646i	$0.683931\pi$
$762$	96.8224	3.50751
$763$	4.91371	0.177888
$764$	−3.09859	−0.112103
$765$	0	0
$766$	−4.32081	−0.156117
$767$	−25.0567	−0.904746
$768$	−41.4661	−1.49628
$769$	−18.5628	−0.669391	−0.334696	−	0.942326i	$-0.608633\pi$
$769$	−18.5628	−0.669391	−0.334696	+	0.942326i	$0.608633\pi$
$770$	0	0
$771$	71.5276	2.57601
$772$	−1.27130	−0.0457550
$773$	13.0851	0.470637	0.235318	−	0.971918i	$-0.424387\pi$
$773$	13.0851	0.470637	0.235318	+	0.971918i	$0.424387\pi$
$774$	89.6982	3.22413
$775$	0	0
$776$	8.47397	0.304198
$777$	119.494	4.28683
$778$	7.65218	0.274344
$779$	−24.9649	−0.894460
$780$	0	0
$781$	−8.70962	−0.311655
$782$	−37.6695	−1.34706
$783$	55.5570	1.98544
$784$	−81.1690	−2.89889
$785$	0	0
$786$	−86.7577	−3.09454
$787$	−40.9986	−1.46144	−0.730721	−	0.682676i	$-0.760816\pi$
$787$	−40.9986	−1.46144	−0.730721	+	0.682676i	$0.760816\pi$
$788$	3.90157	0.138988
$789$	−30.0292	−1.06907
$790$	0	0
$791$	−12.9336	−0.459867
$792$	−25.2194	−0.896133
$793$	−65.1253	−2.31267
$794$	23.2763	0.826044
$795$	0	0
$796$	0.946704	0.0335550
$797$	−14.9494	−0.529534	−0.264767	−	0.964312i	$-0.585295\pi$
$797$	−14.9494	−0.529534	−0.264767	+	0.964312i	$0.585295\pi$
$798$	−68.1135	−2.41119
$799$	38.3537	1.35686
$800$	0	0
$801$	53.7735	1.89999
$802$	2.65452	0.0937345
$803$	−3.42059	−0.120710
$804$	−1.00760	−0.0355352
$805$	0	0
$806$	−105.333	−3.71020
$807$	35.8513	1.26202
$808$	20.8412	0.733191
$809$	28.8259	1.01346	0.506732	−	0.862104i	$-0.330853\pi$
$809$	28.8259	1.01346	0.506732	+	0.862104i	$0.330853\pi$
$810$	0	0
$811$	52.4342	1.84122	0.920608	−	0.390489i	$-0.127694\pi$
$811$	52.4342	1.84122	0.920608	+	0.390489i	$0.127694\pi$
$812$	11.9335	0.418784
$813$	9.58220	0.336062
$814$	19.0820	0.668822
$815$	0	0
$816$	−47.3079	−1.65611
$817$	−21.1265	−0.739123
$818$	−23.0903	−0.807333
$819$	−230.824	−8.06565
$820$	0	0
$821$	33.3290	1.16319	0.581596	−	0.813478i	$-0.302429\pi$
$821$	33.3290	1.16319	0.581596	+	0.813478i	$0.302429\pi$
$822$	70.9854	2.47590
$823$	−32.3847	−1.12886	−0.564430	−	0.825481i	$-0.690904\pi$
$823$	−32.3847	−1.12886	−0.564430	+	0.825481i	$0.690904\pi$
$824$	2.52079	0.0878158
$825$	0	0
$826$	−29.8464	−1.03849
$827$	−20.7771	−0.722489	−0.361245	−	0.932471i	$-0.617648\pi$
$827$	−20.7771	−0.722489	−0.361245	+	0.932471i	$0.617648\pi$
$828$	−32.1607	−1.11766
$829$	21.3970	0.743149	0.371575	−	0.928403i	$-0.378818\pi$
$829$	21.3970	0.743149	0.371575	+	0.928403i	$0.378818\pi$
$830$	0	0
$831$	−32.3962	−1.12381
$832$	29.4824	1.02212
$833$	−51.5976	−1.78775
$834$	41.9568	1.45285
$835$	0	0
$836$	−2.46856	−0.0853770
$837$	−132.567	−4.58220
$838$	−37.1629	−1.28377
$839$	48.6343	1.67904	0.839521	−	0.543327i	$-0.182835\pi$
$839$	48.6343	1.67904	0.839521	+	0.543327i	$0.182835\pi$
$840$	0	0
$841$	−11.6491	−0.401694
$842$	−21.0774	−0.726375
$843$	−13.1841	−0.454085
$844$	−6.08541	−0.209468
$845$	0	0
$846$	144.281	4.96049
$847$	42.0157	1.44368
$848$	−10.8872	−0.373869
$849$	−43.8432	−1.50470
$850$	0	0
$851$	−58.5529	−2.00717
$852$	−10.5571	−0.361679
$853$	−10.6254	−0.363807	−0.181903	−	0.983316i	$-0.558226\pi$
$853$	−10.6254	−0.363807	−0.181903	+	0.983316i	$0.558226\pi$
$854$	−77.5742	−2.65453
$855$	0	0
$856$	−12.0556	−0.412053
$857$	−7.00136	−0.239162	−0.119581	−	0.992824i	$-0.538155\pi$
$857$	−7.00136	−0.239162	−0.119581	+	0.992824i	$0.538155\pi$
$858$	−52.2610	−1.78416
$859$	−11.0294	−0.376319	−0.188160	−	0.982138i	$-0.560252\pi$
$859$	−11.0294	−0.376319	−0.188160	+	0.982138i	$0.560252\pi$
$860$	0	0
$861$	−142.878	−4.86926
$862$	−8.05763	−0.274444
$863$	7.23497	0.246281	0.123141	−	0.992389i	$-0.460703\pi$
$863$	7.23497	0.246281	0.123141	+	0.992389i	$0.460703\pi$
$864$	−42.9896	−1.46253
$865$	0	0
$866$	39.7011	1.34910
$867$	24.1683	0.820797
$868$	−28.4751	−0.966509
$869$	−1.16101	−0.0393844
$870$	0	0
$871$	3.54360	0.120070
$872$	−2.28857	−0.0775007
$873$	26.7744	0.906177
$874$	33.3761	1.12896
$875$	0	0
$876$	−4.14614	−0.140085
$877$	25.0651	0.846388	0.423194	−	0.906039i	$-0.360909\pi$
$877$	25.0651	0.846388	0.423194	+	0.906039i	$0.360909\pi$
$878$	−23.7733	−0.802310
$879$	−62.9787	−2.12422
$880$	0	0
$881$	−21.3132	−0.718059	−0.359030	−	0.933326i	$-0.616892\pi$
$881$	−21.3132	−0.718059	−0.359030	+	0.933326i	$0.616892\pi$
$882$	−194.103	−6.53578
$883$	17.9689	0.604703	0.302352	−	0.953196i	$-0.402228\pi$
$883$	17.9689	0.604703	0.302352	+	0.953196i	$0.402228\pi$
$884$	−11.8768	−0.399459
$885$	0	0
$886$	61.6721	2.07191
$887$	20.6299	0.692685	0.346342	−	0.938108i	$-0.387424\pi$
$887$	20.6299	0.692685	0.346342	+	0.938108i	$0.387424\pi$
$888$	−55.6546	−1.86765
$889$	−92.0524	−3.08734
$890$	0	0
$891$	−32.4803	−1.08813
$892$	10.0244	0.335642
$893$	−33.9824	−1.13718
$894$	−35.2640	−1.17940
$895$	0	0
$896$	66.5712	2.22399
$897$	160.363	5.35435
$898$	17.5237	0.584773
$899$	−41.4018	−1.38083
$900$	0	0
$901$	−6.92079	−0.230565
$902$	−22.8161	−0.759692
$903$	−120.910	−4.02363
$904$	6.02386	0.200351
$905$	0	0
$906$	21.7106	0.721286
$907$	−32.1116	−1.06625	−0.533124	−	0.846037i	$-0.678982\pi$
$907$	−32.1116	−1.06625	−0.533124	+	0.846037i	$0.678982\pi$
$908$	9.56584	0.317454
$909$	65.8501	2.18411
$910$	0	0
$911$	2.18660	0.0724452	0.0362226	−	0.999344i	$-0.488467\pi$
$911$	2.18660	0.0724452	0.0362226	+	0.999344i	$0.488467\pi$
$912$	41.9160	1.38798
$913$	−14.4217	−0.477288
$914$	−18.8854	−0.624673
$915$	0	0
$916$	13.8073	0.456205
$917$	82.4835	2.72384
$918$	−65.8623	−2.17378
$919$	24.9679	0.823613	0.411807	−	0.911271i	$-0.364898\pi$
$919$	24.9679	0.823613	0.411807	+	0.911271i	$0.364898\pi$
$920$	0	0
$921$	6.81544	0.224576
$922$	−58.5723	−1.92898
$923$	37.1279	1.22208
$924$	−14.1279	−0.464775
$925$	0	0
$926$	−3.69153	−0.121311
$927$	7.96471	0.261595
$928$	−13.4260	−0.440729
$929$	1.70629	0.0559817	0.0279908	−	0.999608i	$-0.491089\pi$
$929$	1.70629	0.0559817	0.0279908	+	0.999608i	$0.491089\pi$
$930$	0	0
$931$	45.7168	1.49831
$932$	14.8838	0.487534
$933$	−39.0585	−1.27872
$934$	−9.22556	−0.301870
$935$	0	0
$936$	107.507	3.51397
$937$	44.2739	1.44637	0.723183	−	0.690656i	$-0.242678\pi$
$937$	44.2739	1.44637	0.723183	+	0.690656i	$0.242678\pi$
$938$	4.22097	0.137819
$939$	−16.1492	−0.527008
$940$	0	0
$941$	31.9043	1.04005	0.520025	−	0.854151i	$-0.325923\pi$
$941$	31.9043	1.04005	0.520025	+	0.854151i	$0.325923\pi$
$942$	38.9008	1.26746
$943$	70.0111	2.27988
$944$	18.3670	0.597795
$945$	0	0
$946$	−19.3081	−0.627759
$947$	−29.8307	−0.969367	−0.484684	−	0.874690i	$-0.661065\pi$
$947$	−29.8307	−0.969367	−0.484684	+	0.874690i	$0.661065\pi$
$948$	−1.40727	−0.0457061
$949$	14.5815	0.473335
$950$	0	0
$951$	69.5998	2.25693
$952$	34.0409	1.10327
$953$	5.12326	0.165959	0.0829794	−	0.996551i	$-0.473556\pi$
$953$	5.12326	0.165959	0.0829794	+	0.996551i	$0.473556\pi$
$954$	−26.0351	−0.842916
$955$	0	0
$956$	−3.92351	−0.126895
$957$	−20.5415	−0.664013
$958$	33.0752	1.06861
$959$	−67.4882	−2.17931
$960$	0	0
$961$	67.7910	2.18680
$962$	−81.3437	−2.62263
$963$	−38.0911	−1.22747
$964$	−0.587161	−0.0189112
$965$	0	0
$966$	191.016	6.14585
$967$	41.6766	1.34023	0.670114	−	0.742258i	$-0.266245\pi$
$967$	41.6766	1.34023	0.670114	+	0.742258i	$0.266245\pi$
$968$	−19.5689	−0.628968
$969$	26.6452	0.855967
$970$	0	0
$971$	−39.7498	−1.27563	−0.637817	−	0.770188i	$-0.720162\pi$
$971$	−39.7498	−1.27563	−0.637817	+	0.770188i	$0.720162\pi$
$972$	−15.8759	−0.509219
$973$	−39.8898	−1.27881
$974$	32.7224	1.04849
$975$	0	0
$976$	47.7380	1.52805
$977$	11.1877	0.357927	0.178963	−	0.983856i	$-0.442726\pi$
$977$	11.1877	0.357927	0.178963	+	0.983856i	$0.442726\pi$
$978$	45.0713	1.44122
$979$	−11.5751	−0.369940
$980$	0	0
$981$	−7.23098	−0.230868
$982$	−48.2768	−1.54057
$983$	−17.3012	−0.551824	−0.275912	−	0.961183i	$-0.588980\pi$
$983$	−17.3012	−0.551824	−0.275912	+	0.961183i	$0.588980\pi$
$984$	66.5456	2.12140
$985$	0	0
$986$	−20.5693	−0.655060
$987$	−194.486	−6.19055
$988$	10.5231	0.334785
$989$	59.2468	1.88394
$990$	0	0
$991$	−29.9246	−0.950585	−0.475293	−	0.879828i	$-0.657658\pi$
$991$	−29.9246	−0.950585	−0.475293	+	0.879828i	$0.657658\pi$
$992$	32.0364	1.01716
$993$	−33.8258	−1.07343
$994$	44.2250	1.40273
$995$	0	0
$996$	−17.4807	−0.553897
$997$	−46.9435	−1.48672	−0.743358	−	0.668894i	$-0.766768\pi$
$997$	−46.9435	−1.48672	−0.743358	+	0.668894i	$0.766768\pi$
$998$	38.4594	1.21741
$999$	−102.376	−3.23902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.l.1.11	✓	40
5.4	even	2		6025.2.a.o.1.30	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.11	✓	40	1.1	even	1	trivial
6025.2.a.o.1.30	yes	40	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.60847 q^{2} -3.19065 q^{3} +0.587161 q^{4} +5.13204 q^{6} -4.87921 q^{7} +2.27250 q^{8} +7.18022 q^{9} +O(q^{10})\)	\(q-1.60847 q^{2} -3.19065 q^{3} +0.587161 q^{4} +5.13204 q^{6} -4.87921 q^{7} +2.27250 q^{8} +7.18022 q^{9} -1.54559 q^{11} -1.87342 q^{12} +6.58861 q^{13} +7.84804 q^{14} -4.82956 q^{16} -3.07006 q^{17} -11.5491 q^{18} +2.72015 q^{19} +15.5678 q^{21} +2.48602 q^{22} -7.62835 q^{23} -7.25075 q^{24} -10.5976 q^{26} -13.3376 q^{27} -2.86488 q^{28} -4.16544 q^{29} +9.93936 q^{31} +3.22318 q^{32} +4.93142 q^{33} +4.93809 q^{34} +4.21595 q^{36} +7.67570 q^{37} -4.37527 q^{38} -21.0219 q^{39} -9.17775 q^{41} -25.0403 q^{42} -7.76666 q^{43} -0.907508 q^{44} +12.2699 q^{46} -12.4928 q^{47} +15.4094 q^{48} +16.8067 q^{49} +9.79548 q^{51} +3.86858 q^{52} +2.25429 q^{53} +21.4531 q^{54} -11.0880 q^{56} -8.67905 q^{57} +6.69996 q^{58} -3.80303 q^{59} -9.88453 q^{61} -15.9871 q^{62} -35.0338 q^{63} +4.47475 q^{64} -7.93201 q^{66} +0.537837 q^{67} -1.80262 q^{68} +24.3394 q^{69} +5.63516 q^{71} +16.3171 q^{72} +2.21313 q^{73} -12.3461 q^{74} +1.59717 q^{76} +7.54124 q^{77} +33.8131 q^{78} +0.751176 q^{79} +21.0149 q^{81} +14.7621 q^{82} +9.33088 q^{83} +9.14083 q^{84} +12.4924 q^{86} +13.2904 q^{87} -3.51235 q^{88} +7.48911 q^{89} -32.1472 q^{91} -4.47907 q^{92} -31.7130 q^{93} +20.0942 q^{94} -10.2840 q^{96} +3.72891 q^{97} -27.0330 q^{98} -11.0976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Introduction

L-functions

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