LMFDB - Embedded newform 6025.2.a.o.1.12

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:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-0.859912 q^{2} +1.32501 q^{3} -1.26055 q^{4} -1.13939 q^{6} +0.529848 q^{7} +2.80379 q^{8} -1.24436 q^{9} +O(q^{10})$	\(q-0.859912 q^{2} +1.32501 q^{3} -1.26055 q^{4} -1.13939 q^{6} +0.529848 q^{7} +2.80379 q^{8} -1.24436 q^{9} +5.79943 q^{11} -1.67024 q^{12} +6.67680 q^{13} -0.455622 q^{14} +0.110090 q^{16} -4.32134 q^{17} +1.07004 q^{18} +3.78869 q^{19} +0.702052 q^{21} -4.98700 q^{22} +5.89377 q^{23} +3.71504 q^{24} -5.74146 q^{26} -5.62380 q^{27} -0.667900 q^{28} -1.38212 q^{29} +2.87836 q^{31} -5.70224 q^{32} +7.68429 q^{33} +3.71597 q^{34} +1.56857 q^{36} +4.89139 q^{37} -3.25795 q^{38} +8.84681 q^{39} +6.31922 q^{41} -0.603703 q^{42} -3.37117 q^{43} -7.31048 q^{44} -5.06813 q^{46} +10.5171 q^{47} +0.145870 q^{48} -6.71926 q^{49} -5.72580 q^{51} -8.41644 q^{52} -7.63063 q^{53} +4.83598 q^{54} +1.48558 q^{56} +5.02005 q^{57} +1.18850 q^{58} +15.1388 q^{59} +1.41782 q^{61} -2.47514 q^{62} -0.659319 q^{63} +4.68325 q^{64} -6.60782 q^{66} +1.62244 q^{67} +5.44726 q^{68} +7.80929 q^{69} +0.160238 q^{71} -3.48891 q^{72} -1.85086 q^{73} -4.20617 q^{74} -4.77584 q^{76} +3.07282 q^{77} -7.60748 q^{78} -4.62995 q^{79} -3.71851 q^{81} -5.43397 q^{82} -10.8002 q^{83} -0.884972 q^{84} +2.89891 q^{86} -1.83132 q^{87} +16.2604 q^{88} +6.27933 q^{89} +3.53769 q^{91} -7.42940 q^{92} +3.81385 q^{93} -9.04376 q^{94} -7.55551 q^{96} +16.7487 q^{97} +5.77798 q^{98} -7.21656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.859912	−0.608050	−0.304025	−	0.952664i	$-0.598331\pi$
$2$	−0.859912	−0.608050	−0.304025	+	0.952664i	$0.598331\pi$
$3$	1.32501	0.764993	0.382497	−	0.923957i	$-0.375064\pi$
$3$	1.32501	0.764993	0.382497	+	0.923957i	$0.375064\pi$
$4$	−1.26055	−0.630275
$5$	0	0
$5$	0	0
$6$	−1.13939	−0.465154
$7$	0.529848	0.200264	0.100132	−	0.994974i	$-0.468074\pi$
$7$	0.529848	0.200264	0.100132	+	0.994974i	$0.468074\pi$
$8$	2.80379	0.991289
$9$	−1.24436	−0.414785
$10$	0	0
$11$	5.79943	1.74859	0.874297	−	0.485391i	$-0.161323\pi$
$11$	5.79943	1.74859	0.874297	+	0.485391i	$0.161323\pi$
$12$	−1.67024	−0.482156
$13$	6.67680	1.85181	0.925905	−	0.377755i	$-0.123304\pi$
$13$	6.67680	1.85181	0.925905	+	0.377755i	$0.123304\pi$
$14$	−0.455622	−0.121770
$15$	0	0
$16$	0.110090	0.0275224
$17$	−4.32134	−1.04808	−0.524039	−	0.851694i	$-0.675575\pi$
$17$	−4.32134	−1.04808	−0.524039	+	0.851694i	$0.675575\pi$
$18$	1.07004	0.252210
$19$	3.78869	0.869186	0.434593	−	0.900627i	$-0.356892\pi$
$19$	3.78869	0.869186	0.434593	+	0.900627i	$0.356892\pi$
$20$	0	0
$21$	0.702052	0.153200
$22$	−4.98700	−1.06323
$23$	5.89377	1.22894	0.614468	−	0.788942i	$-0.289371\pi$
$23$	5.89377	1.22894	0.614468	+	0.788942i	$0.289371\pi$
$24$	3.71504	0.758329
$25$	0	0
$26$	−5.74146	−1.12599
$27$	−5.62380	−1.08230
$28$	−0.667900	−0.126221
$29$	−1.38212	−0.256654	−0.128327	−	0.991732i	$-0.540961\pi$
$29$	−1.38212	−0.256654	−0.128327	+	0.991732i	$0.540961\pi$
$30$	0	0
$31$	2.87836	0.516969	0.258484	−	0.966015i	$-0.416777\pi$
$31$	2.87836	0.516969	0.258484	+	0.966015i	$0.416777\pi$
$32$	−5.70224	−1.00802
$33$	7.68429	1.33766
$34$	3.71597	0.637284
$35$	0	0
$36$	1.56857	0.261429
$37$	4.89139	0.804140	0.402070	−	0.915609i	$-0.368291\pi$
$37$	4.89139	0.804140	0.402070	+	0.915609i	$0.368291\pi$
$38$	−3.25795	−0.528508
$39$	8.84681	1.41662
$40$	0	0
$41$	6.31922	0.986896	0.493448	−	0.869775i	$-0.335736\pi$
$41$	6.31922	0.986896	0.493448	+	0.869775i	$0.335736\pi$
$42$	−0.603703	−0.0931534
$43$	−3.37117	−0.514099	−0.257049	−	0.966398i	$-0.582750\pi$
$43$	−3.37117	−0.514099	−0.257049	+	0.966398i	$0.582750\pi$
$44$	−7.31048	−1.10210
$45$	0	0
$46$	−5.06813	−0.747254
$47$	10.5171	1.53407	0.767036	−	0.641604i	$-0.221731\pi$
$47$	10.5171	1.53407	0.767036	+	0.641604i	$0.221731\pi$
$48$	0.145870	0.0210545
$49$	−6.71926	−0.959895
$50$	0	0
$51$	−5.72580	−0.801772
$52$	−8.41644	−1.16715
$53$	−7.63063	−1.04815	−0.524074	−	0.851673i	$-0.675588\pi$
$53$	−7.63063	−1.04815	−0.524074	+	0.851673i	$0.675588\pi$
$54$	4.83598	0.658093
$55$	0	0
$56$	1.48558	0.198519
$57$	5.02005	0.664921
$58$	1.18850	0.156058
$59$	15.1388	1.97091	0.985453	−	0.169948i	$-0.0543600\pi$
$59$	15.1388	1.97091	0.985453	+	0.169948i	$0.0543600\pi$
$60$	0	0
$61$	1.41782	0.181533	0.0907666	−	0.995872i	$-0.471068\pi$
$61$	1.41782	0.181533	0.0907666	+	0.995872i	$0.471068\pi$
$62$	−2.47514	−0.314343
$63$	−0.659319	−0.0830664
$64$	4.68325	0.585406
$65$	0	0
$66$	−6.60782	−0.813366
$67$	1.62244	0.198213	0.0991066	−	0.995077i	$-0.468402\pi$
$67$	1.62244	0.198213	0.0991066	+	0.995077i	$0.468402\pi$
$68$	5.44726	0.660578
$69$	7.80929	0.940128
$70$	0	0
$71$	0.160238	0.0190167	0.00950837	−	0.999955i	$-0.496973\pi$
$71$	0.160238	0.0190167	0.00950837	+	0.999955i	$0.496973\pi$
$72$	−3.48891	−0.411172
$73$	−1.85086	−0.216627	−0.108314	−	0.994117i	$-0.534545\pi$
$73$	−1.85086	−0.216627	−0.108314	+	0.994117i	$0.534545\pi$
$74$	−4.20617	−0.488957
$75$	0	0
$76$	−4.77584	−0.547827
$77$	3.07282	0.350180
$78$	−7.60748	−0.861377
$79$	−4.62995	−0.520910	−0.260455	−	0.965486i	$-0.583873\pi$
$79$	−4.62995	−0.520910	−0.260455	+	0.965486i	$0.583873\pi$
$80$	0	0
$81$	−3.71851	−0.413168
$82$	−5.43397	−0.600082
$83$	−10.8002	−1.18547	−0.592737	−	0.805396i	$-0.701953\pi$
$83$	−10.8002	−1.18547	−0.592737	+	0.805396i	$0.701953\pi$
$84$	−0.884972	−0.0965584
$85$	0	0
$86$	2.89891	0.312598
$87$	−1.83132	−0.196338
$88$	16.2604	1.73336
$89$	6.27933	0.665608	0.332804	−	0.942996i	$-0.392005\pi$
$89$	6.27933	0.665608	0.332804	+	0.942996i	$0.392005\pi$
$90$	0	0
$91$	3.53769	0.370850
$92$	−7.42940	−0.774568
$93$	3.81385	0.395478
$94$	−9.04376	−0.932793
$95$	0	0
$96$	−7.55551	−0.771131
$97$	16.7487	1.70057	0.850285	−	0.526323i	$-0.176430\pi$
$97$	16.7487	1.70057	0.850285	+	0.526323i	$0.176430\pi$
$98$	5.77798	0.583664
$99$	−7.21656	−0.725292
$100$	0	0
$101$	−13.3802	−1.33138	−0.665692	−	0.746227i	$-0.731864\pi$
$101$	−13.3802	−1.33138	−0.665692	+	0.746227i	$0.731864\pi$
$102$	4.92369	0.487518
$103$	−3.75505	−0.369996	−0.184998	−	0.982739i	$-0.559228\pi$
$103$	−3.75505	−0.369996	−0.184998	+	0.982739i	$0.559228\pi$
$104$	18.7203	1.83568
$105$	0	0
$106$	6.56167	0.637326
$107$	−9.17667	−0.887142	−0.443571	−	0.896239i	$-0.646289\pi$
$107$	−9.17667	−0.887142	−0.443571	+	0.896239i	$0.646289\pi$
$108$	7.08909	0.682148
$109$	−17.2987	−1.65692	−0.828458	−	0.560051i	$-0.810782\pi$
$109$	−17.2987	−1.65692	−0.828458	+	0.560051i	$0.810782\pi$
$110$	0	0
$111$	6.48113	0.615161
$112$	0.0583307	0.00551173
$113$	−5.77167	−0.542953	−0.271477	−	0.962445i	$-0.587512\pi$
$113$	−5.77167	−0.542953	−0.271477	+	0.962445i	$0.587512\pi$
$114$	−4.31680	−0.404305
$115$	0	0
$116$	1.74223	0.161762
$117$	−8.30832	−0.768104
$118$	−13.0181	−1.19841
$119$	−2.28965	−0.209892
$120$	0	0
$121$	22.6334	2.05758
$122$	−1.21920	−0.110381
$123$	8.37301	0.754969
$124$	−3.62832	−0.325833
$125$	0	0
$126$	0.566957	0.0505085
$127$	−6.49226	−0.576095	−0.288047	−	0.957616i	$-0.593006\pi$
$127$	−6.49226	−0.576095	−0.288047	+	0.957616i	$0.593006\pi$
$128$	7.37730	0.652068
$129$	−4.46682	−0.393282
$130$	0	0
$131$	−19.0530	−1.66467	−0.832334	−	0.554274i	$-0.812996\pi$
$131$	−19.0530	−1.66467	−0.832334	+	0.554274i	$0.812996\pi$
$132$	−9.68644	−0.843096
$133$	2.00743	0.174066
$134$	−1.39516	−0.120523
$135$	0	0
$136$	−12.1161	−1.03895
$137$	14.6360	1.25044	0.625218	−	0.780450i	$-0.285010\pi$
$137$	14.6360	1.25044	0.625218	+	0.780450i	$0.285010\pi$
$138$	−6.71530	−0.571645
$139$	−15.6318	−1.32588	−0.662938	−	0.748675i	$-0.730691\pi$
$139$	−15.6318	−1.32588	−0.662938	+	0.748675i	$0.730691\pi$
$140$	0	0
$141$	13.9352	1.17355
$142$	−0.137791	−0.0115631
$143$	38.7216	3.23807
$144$	−0.136991	−0.0114159
$145$	0	0
$146$	1.59158	0.131720
$147$	−8.90307	−0.734313
$148$	−6.16585	−0.506830
$149$	−16.0209	−1.31248	−0.656242	−	0.754550i	$-0.727855\pi$
$149$	−16.0209	−1.31248	−0.656242	+	0.754550i	$0.727855\pi$
$150$	0	0
$151$	−10.2287	−0.832398	−0.416199	−	0.909273i	$-0.636638\pi$
$151$	−10.2287	−0.832398	−0.416199	+	0.909273i	$0.636638\pi$
$152$	10.6227	0.861614
$153$	5.37728	0.434727
$154$	−2.64235	−0.212927
$155$	0	0
$156$	−11.1518	−0.892862
$157$	21.3081	1.70057	0.850287	−	0.526319i	$-0.176428\pi$
$157$	21.3081	1.70057	0.850287	+	0.526319i	$0.176428\pi$
$158$	3.98135	0.316740
$159$	−10.1106	−0.801826
$160$	0	0
$161$	3.12280	0.246111
$162$	3.19759	0.251227
$163$	−15.8551	−1.24186	−0.620932	−	0.783864i	$-0.713246\pi$
$163$	−15.8551	−1.24186	−0.620932	+	0.783864i	$0.713246\pi$
$164$	−7.96570	−0.622016
$165$	0	0
$166$	9.28721	0.720827
$167$	−16.2566	−1.25797	−0.628986	−	0.777417i	$-0.716530\pi$
$167$	−16.2566	−1.25797	−0.628986	+	0.777417i	$0.716530\pi$
$168$	1.96840	0.151866
$169$	31.5796	2.42920
$170$	0	0
$171$	−4.71449	−0.360526
$172$	4.24953	0.324024
$173$	23.9666	1.82215	0.911073	−	0.412244i	$-0.135255\pi$
$173$	23.9666	1.82215	0.911073	+	0.412244i	$0.135255\pi$
$174$	1.57478	0.119383
$175$	0	0
$176$	0.638457	0.0481255
$177$	20.0590	1.50773
$178$	−5.39967	−0.404723
$179$	−1.58278	−0.118302	−0.0591512	−	0.998249i	$-0.518839\pi$
$179$	−1.58278	−0.118302	−0.0591512	+	0.998249i	$0.518839\pi$
$180$	0	0
$181$	−24.9297	−1.85301	−0.926506	−	0.376280i	$-0.877203\pi$
$181$	−24.9297	−1.85301	−0.926506	+	0.376280i	$0.877203\pi$
$182$	−3.04210	−0.225495
$183$	1.87862	0.138872
$184$	16.5249	1.21823
$185$	0	0
$186$	−3.27958	−0.240470
$187$	−25.0613	−1.83266
$188$	−13.2573	−0.966888
$189$	−2.97976	−0.216745
$190$	0	0
$191$	19.0090	1.37544	0.687722	−	0.725974i	$-0.258611\pi$
$191$	19.0090	1.37544	0.687722	+	0.725974i	$0.258611\pi$
$192$	6.20534	0.447832
$193$	4.72254	0.339936	0.169968	−	0.985450i	$-0.445634\pi$
$193$	4.72254	0.339936	0.169968	+	0.985450i	$0.445634\pi$
$194$	−14.4024	−1.03403
$195$	0	0
$196$	8.46997	0.604998
$197$	−8.54257	−0.608633	−0.304316	−	0.952571i	$-0.598428\pi$
$197$	−8.54257	−0.608633	−0.304316	+	0.952571i	$0.598428\pi$
$198$	6.20561	0.441013
$199$	9.81059	0.695455	0.347727	−	0.937596i	$-0.386954\pi$
$199$	9.81059	0.695455	0.347727	+	0.937596i	$0.386954\pi$
$200$	0	0
$201$	2.14975	0.151632
$202$	11.5058	0.809548
$203$	−0.732314	−0.0513984
$204$	7.21766	0.505337
$205$	0	0
$206$	3.22901	0.224976
$207$	−7.33395	−0.509745
$208$	0.735046	0.0509663
$209$	21.9723	1.51985
$210$	0	0
$211$	−12.6816	−0.873040	−0.436520	−	0.899695i	$-0.643789\pi$
$211$	−12.6816	−0.873040	−0.436520	+	0.899695i	$0.643789\pi$
$212$	9.61879	0.660622
$213$	0.212316	0.0145477
$214$	7.89113	0.539426
$215$	0	0
$216$	−15.7679	−1.07287
$217$	1.52509	0.103530
$218$	14.8754	1.00749
$219$	−2.45241	−0.165718
$220$	0	0
$221$	−28.8527	−1.94084
$222$	−5.57320	−0.374049
$223$	23.3734	1.56520	0.782601	−	0.622524i	$-0.213893\pi$
$223$	23.3734	1.56520	0.782601	+	0.622524i	$0.213893\pi$
$224$	−3.02132	−0.201870
$225$	0	0
$226$	4.96313	0.330143
$227$	14.0321	0.931346	0.465673	−	0.884957i	$-0.345812\pi$
$227$	14.0321	0.931346	0.465673	+	0.884957i	$0.345812\pi$
$228$	−6.32802	−0.419084
$229$	3.45016	0.227993	0.113996	−	0.993481i	$-0.463635\pi$
$229$	3.45016	0.227993	0.113996	+	0.993481i	$0.463635\pi$
$230$	0	0
$231$	4.07150	0.267885
$232$	−3.87518	−0.254418
$233$	10.2917	0.674234	0.337117	−	0.941463i	$-0.390548\pi$
$233$	10.2917	0.674234	0.337117	+	0.941463i	$0.390548\pi$
$234$	7.14442	0.467046
$235$	0	0
$236$	−19.0832	−1.24221
$237$	−6.13472	−0.398493
$238$	1.96890	0.127625
$239$	10.5183	0.680374	0.340187	−	0.940358i	$-0.389510\pi$
$239$	10.5183	0.680374	0.340187	+	0.940358i	$0.389510\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−19.4628	−1.25111
$243$	11.9444	0.766231
$244$	−1.78723	−0.114416
$245$	0	0
$246$	−7.20005	−0.459059
$247$	25.2964	1.60957
$248$	8.07031	0.512465
$249$	−14.3103	−0.906879
$250$	0	0
$251$	19.9953	1.26209	0.631047	−	0.775744i	$-0.282625\pi$
$251$	19.9953	1.26209	0.631047	+	0.775744i	$0.282625\pi$
$252$	0.831105	0.0523547
$253$	34.1805	2.14891
$254$	5.58278	0.350294
$255$	0	0
$256$	−15.7103	−0.981896
$257$	18.4924	1.15353	0.576763	−	0.816911i	$-0.304315\pi$
$257$	18.4924	1.15353	0.576763	+	0.816911i	$0.304315\pi$
$258$	3.84108	0.239135
$259$	2.59169	0.161040
$260$	0	0
$261$	1.71985	0.106456
$262$	16.3839	1.01220
$263$	−5.10678	−0.314898	−0.157449	−	0.987527i	$-0.550327\pi$
$263$	−5.10678	−0.314898	−0.157449	+	0.987527i	$0.550327\pi$
$264$	21.5451	1.32601
$265$	0	0
$266$	−1.72621	−0.105841
$267$	8.32016	0.509185
$268$	−2.04517	−0.124929
$269$	−4.40015	−0.268282	−0.134141	−	0.990962i	$-0.542828\pi$
$269$	−4.40015	−0.268282	−0.134141	+	0.990962i	$0.542828\pi$
$270$	0	0
$271$	0.312081	0.0189576	0.00947880	−	0.999955i	$-0.496983\pi$
$271$	0.312081	0.0189576	0.00947880	+	0.999955i	$0.496983\pi$
$272$	−0.475734	−0.0288456
$273$	4.68746	0.283698
$274$	−12.5857	−0.760328
$275$	0	0
$276$	−9.84400	−0.592539
$277$	13.2341	0.795163	0.397581	−	0.917567i	$-0.369850\pi$
$277$	13.2341	0.795163	0.397581	+	0.917567i	$0.369850\pi$
$278$	13.4420	0.806198
$279$	−3.58171	−0.214431
$280$	0	0
$281$	24.1977	1.44351	0.721757	−	0.692147i	$-0.243335\pi$
$281$	24.1977	1.44351	0.721757	+	0.692147i	$0.243335\pi$
$282$	−11.9830	−0.713580
$283$	20.1084	1.19532	0.597661	−	0.801749i	$-0.296097\pi$
$283$	20.1084	1.19532	0.597661	+	0.801749i	$0.296097\pi$
$284$	−0.201988	−0.0119858
$285$	0	0
$286$	−33.2972	−1.96891
$287$	3.34822	0.197639
$288$	7.09562	0.418114
$289$	1.67394	0.0984673
$290$	0	0
$291$	22.1921	1.30092
$292$	2.33311	0.136535
$293$	−11.8518	−0.692388	−0.346194	−	0.938163i	$-0.612526\pi$
$293$	−11.8518	−0.692388	−0.346194	+	0.938163i	$0.612526\pi$
$294$	7.65586	0.446499
$295$	0	0
$296$	13.7144	0.797135
$297$	−32.6149	−1.89251
$298$	13.7766	0.798056
$299$	39.3515	2.27576
$300$	0	0
$301$	−1.78621	−0.102955
$302$	8.79577	0.506140
$303$	−17.7289	−1.01850
$304$	0.417096	0.0239221
$305$	0	0
$306$	−4.62399	−0.264336
$307$	11.5990	0.661991	0.330996	−	0.943632i	$-0.392615\pi$
$307$	11.5990	0.661991	0.330996	+	0.943632i	$0.392615\pi$
$308$	−3.87344	−0.220710
$309$	−4.97546	−0.283044
$310$	0	0
$311$	29.9354	1.69748	0.848740	−	0.528811i	$-0.177362\pi$
$311$	29.9354	1.69748	0.848740	+	0.528811i	$0.177362\pi$
$312$	24.8046	1.40428
$313$	28.1006	1.58834	0.794169	−	0.607696i	$-0.207906\pi$
$313$	28.1006	1.58834	0.794169	+	0.607696i	$0.207906\pi$
$314$	−18.3231	−1.03403
$315$	0	0
$316$	5.83629	0.328317
$317$	−16.4916	−0.926258	−0.463129	−	0.886291i	$-0.653273\pi$
$317$	−16.4916	−0.926258	−0.463129	+	0.886291i	$0.653273\pi$
$318$	8.69426	0.487550
$319$	−8.01552	−0.448783
$320$	0	0
$321$	−12.1591	−0.678657
$322$	−2.68533	−0.149648
$323$	−16.3722	−0.910975
$324$	4.68737	0.260409
$325$	0	0
$326$	13.6340	0.755115
$327$	−22.9209	−1.26753
$328$	17.7177	0.978299
$329$	5.57244	0.307219
$330$	0	0
$331$	−28.0666	−1.54268	−0.771339	−	0.636424i	$-0.780413\pi$
$331$	−28.0666	−1.54268	−0.771339	+	0.636424i	$0.780413\pi$
$332$	13.6142	0.747175
$333$	−6.08663	−0.333545
$334$	13.9792	0.764910
$335$	0	0
$336$	0.0772886	0.00421644
$337$	−7.53031	−0.410202	−0.205101	−	0.978741i	$-0.565752\pi$
$337$	−7.53031	−0.410202	−0.205101	+	0.978741i	$0.565752\pi$
$338$	−27.1557	−1.47708
$339$	−7.64750	−0.415355
$340$	0	0
$341$	16.6929	0.903969
$342$	4.05404	0.219218
$343$	−7.26912	−0.392495
$344$	−9.45205	−0.509620
$345$	0	0
$346$	−20.6092	−1.10796
$347$	3.89646	0.209173	0.104587	−	0.994516i	$-0.466648\pi$
$347$	3.89646	0.209173	0.104587	+	0.994516i	$0.466648\pi$
$348$	2.30847	0.123747
$349$	16.9878	0.909335	0.454668	−	0.890661i	$-0.349758\pi$
$349$	16.9878	0.909335	0.454668	+	0.890661i	$0.349758\pi$
$350$	0	0
$351$	−37.5490	−2.00422
$352$	−33.0698	−1.76262
$353$	15.0416	0.800584	0.400292	−	0.916388i	$-0.368909\pi$
$353$	15.0416	0.800584	0.400292	+	0.916388i	$0.368909\pi$
$354$	−17.2490	−0.916775
$355$	0	0
$356$	−7.91541	−0.419516
$357$	−3.03380	−0.160566
$358$	1.36105	0.0719338
$359$	−6.60197	−0.348439	−0.174219	−	0.984707i	$-0.555740\pi$
$359$	−6.60197	−0.348439	−0.174219	+	0.984707i	$0.555740\pi$
$360$	0	0
$361$	−4.64579	−0.244515
$362$	21.4374	1.12672
$363$	29.9894	1.57404
$364$	−4.45943	−0.233738
$365$	0	0
$366$	−1.61545	−0.0844409
$367$	29.4321	1.53634	0.768172	−	0.640244i	$-0.221167\pi$
$367$	29.4321	1.53634	0.768172	+	0.640244i	$0.221167\pi$
$368$	0.648843	0.0338233
$369$	−7.86336	−0.409350
$370$	0	0
$371$	−4.04307	−0.209906
$372$	−4.80755	−0.249260
$373$	−22.8760	−1.18447	−0.592236	−	0.805764i	$-0.701755\pi$
$373$	−22.8760	−1.18447	−0.592236	+	0.805764i	$0.701755\pi$
$374$	21.5505	1.11435
$375$	0	0
$376$	29.4876	1.52071
$377$	−9.22815	−0.475274
$378$	2.56233	0.131792
$379$	−8.87254	−0.455752	−0.227876	−	0.973690i	$-0.573178\pi$
$379$	−8.87254	−0.455752	−0.227876	+	0.973690i	$0.573178\pi$
$380$	0	0
$381$	−8.60229	−0.440709
$382$	−16.3461	−0.836339
$383$	−26.2573	−1.34169	−0.670843	−	0.741599i	$-0.734068\pi$
$383$	−26.2573	−1.34169	−0.670843	+	0.741599i	$0.734068\pi$
$384$	9.77498	0.498827
$385$	0	0
$386$	−4.06097	−0.206698
$387$	4.19494	0.213241
$388$	−21.1125	−1.07183
$389$	−28.3044	−1.43509	−0.717545	−	0.696512i	$-0.754734\pi$
$389$	−28.3044	−1.43509	−0.717545	+	0.696512i	$0.754734\pi$
$390$	0	0
$391$	−25.4690	−1.28802
$392$	−18.8394	−0.951533
$393$	−25.2454	−1.27346
$394$	7.34586	0.370079
$395$	0	0
$396$	9.09684	0.457133
$397$	38.8932	1.95199	0.975996	−	0.217787i	$-0.0698838\pi$
$397$	38.8932	1.95199	0.975996	+	0.217787i	$0.0698838\pi$
$398$	−8.43625	−0.422871
$399$	2.65986	0.133160
$400$	0	0
$401$	−24.9026	−1.24358	−0.621789	−	0.783185i	$-0.713594\pi$
$401$	−24.9026	−1.24358	−0.621789	+	0.783185i	$0.713594\pi$
$402$	−1.84860	−0.0921996
$403$	19.2182	0.957329
$404$	16.8665	0.839139
$405$	0	0
$406$	0.629726	0.0312528
$407$	28.3673	1.40611
$408$	−16.0539	−0.794788
$409$	10.5175	0.520059	0.260029	−	0.965601i	$-0.416268\pi$
$409$	10.5175	0.520059	0.260029	+	0.965601i	$0.416268\pi$
$410$	0	0
$411$	19.3928	0.956575
$412$	4.73343	0.233199
$413$	8.02127	0.394701
$414$	6.30655	0.309950
$415$	0	0
$416$	−38.0727	−1.86667
$417$	−20.7123	−1.01429
$418$	−18.8942	−0.924147
$419$	15.8047	0.772111	0.386056	−	0.922475i	$-0.373837\pi$
$419$	15.8047	0.772111	0.386056	+	0.922475i	$0.373837\pi$
$420$	0	0
$421$	4.37889	0.213414	0.106707	−	0.994291i	$-0.465969\pi$
$421$	4.37889	0.213414	0.106707	+	0.994291i	$0.465969\pi$
$422$	10.9051	0.530852
$423$	−13.0870	−0.636311
$424$	−21.3947	−1.03902
$425$	0	0
$426$	−0.182573	−0.00884571
$427$	0.751228	0.0363545
$428$	11.5677	0.559144
$429$	51.3065	2.47710
$430$	0	0
$431$	−4.82987	−0.232647	−0.116323	−	0.993211i	$-0.537111\pi$
$431$	−4.82987	−0.232647	−0.116323	+	0.993211i	$0.537111\pi$
$432$	−0.619122	−0.0297875
$433$	4.85827	0.233473	0.116737	−	0.993163i	$-0.462757\pi$
$433$	4.85827	0.233473	0.116737	+	0.993163i	$0.462757\pi$
$434$	−1.31145	−0.0629514
$435$	0	0
$436$	21.8059	1.04431
$437$	22.3297	1.06817
$438$	2.10886	0.100765
$439$	−22.3149	−1.06503	−0.532516	−	0.846420i	$-0.678753\pi$
$439$	−22.3149	−1.06503	−0.532516	+	0.846420i	$0.678753\pi$
$440$	0	0
$441$	8.36116	0.398150
$442$	24.8108	1.18013
$443$	22.9506	1.09042	0.545209	−	0.838300i	$-0.316450\pi$
$443$	22.9506	1.09042	0.545209	+	0.838300i	$0.316450\pi$
$444$	−8.16979	−0.387721
$445$	0	0
$446$	−20.0991	−0.951720
$447$	−21.2278	−1.00404
$448$	2.48141	0.117236
$449$	−9.43674	−0.445347	−0.222674	−	0.974893i	$-0.571478\pi$
$449$	−9.43674	−0.445347	−0.222674	+	0.974893i	$0.571478\pi$
$450$	0	0
$451$	36.6479	1.72568
$452$	7.27548	0.342210
$453$	−13.5531	−0.636779
$454$	−12.0664	−0.566305
$455$	0	0
$456$	14.0751	0.659129
$457$	−4.03835	−0.188906	−0.0944529	−	0.995529i	$-0.530110\pi$
$457$	−4.03835	−0.188906	−0.0944529	+	0.995529i	$0.530110\pi$
$458$	−2.96683	−0.138631
$459$	24.3023	1.13434
$460$	0	0
$461$	28.0020	1.30418	0.652092	−	0.758139i	$-0.273891\pi$
$461$	28.0020	1.30418	0.652092	+	0.758139i	$0.273891\pi$
$462$	−3.50114	−0.162888
$463$	−4.43399	−0.206065	−0.103032	−	0.994678i	$-0.532855\pi$
$463$	−4.43399	−0.206065	−0.103032	+	0.994678i	$0.532855\pi$
$464$	−0.152157	−0.00706372
$465$	0	0
$466$	−8.84999	−0.409968
$467$	−5.90702	−0.273344	−0.136672	−	0.990616i	$-0.543641\pi$
$467$	−5.90702	−0.273344	−0.136672	+	0.990616i	$0.543641\pi$
$468$	10.4731	0.484117
$469$	0.859648	0.0396949
$470$	0	0
$471$	28.2334	1.30093
$472$	42.4460	1.95374
$473$	−19.5509	−0.898950
$474$	5.27532	0.242304
$475$	0	0
$476$	2.88622	0.132290
$477$	9.49522	0.434756
$478$	−9.04484	−0.413701
$479$	−21.6294	−0.988272	−0.494136	−	0.869385i	$-0.664516\pi$
$479$	−21.6294	−0.988272	−0.494136	+	0.869385i	$0.664516\pi$
$480$	0	0
$481$	32.6588	1.48911
$482$	0.859912	0.0391679
$483$	4.13773	0.188273
$484$	−28.5306	−1.29684
$485$	0	0
$486$	−10.2711	−0.465907
$487$	19.8610	0.899989	0.449994	−	0.893031i	$-0.351426\pi$
$487$	19.8610	0.899989	0.449994	+	0.893031i	$0.351426\pi$
$488$	3.97527	0.179952
$489$	−21.0081	−0.950018
$490$	0	0
$491$	11.0797	0.500019	0.250009	−	0.968243i	$-0.419566\pi$
$491$	11.0797	0.500019	0.250009	+	0.968243i	$0.419566\pi$
$492$	−10.5546	−0.475838
$493$	5.97261	0.268993
$494$	−21.7526	−0.978698
$495$	0	0
$496$	0.316878	0.0142282
$497$	0.0849017	0.00380836
$498$	12.3056	0.551428
$499$	6.19713	0.277421	0.138711	−	0.990333i	$-0.455704\pi$
$499$	6.19713	0.277421	0.138711	+	0.990333i	$0.455704\pi$
$500$	0	0
$501$	−21.5401	−0.962340
$502$	−17.1942	−0.767417
$503$	−20.6917	−0.922599	−0.461300	−	0.887244i	$-0.652617\pi$
$503$	−20.6917	−0.922599	−0.461300	+	0.887244i	$0.652617\pi$
$504$	−1.84859	−0.0823428
$505$	0	0
$506$	−29.3923	−1.30665
$507$	41.8432	1.85832
$508$	8.18382	0.363098
$509$	29.1481	1.29197	0.645984	−	0.763351i	$-0.276447\pi$
$509$	29.1481	1.29197	0.645984	+	0.763351i	$0.276447\pi$
$510$	0	0
$511$	−0.980676	−0.0433826
$512$	−1.24509	−0.0550259
$513$	−21.3069	−0.940721
$514$	−15.9019	−0.701402
$515$	0	0
$516$	5.63066	0.247876
$517$	60.9930	2.68247
$518$	−2.22863	−0.0979203
$519$	31.7559	1.39393
$520$	0	0
$521$	−11.5138	−0.504430	−0.252215	−	0.967671i	$-0.581159\pi$
$521$	−11.5138	−0.504430	−0.252215	+	0.967671i	$0.581159\pi$
$522$	−1.47892	−0.0647307
$523$	40.8166	1.78478	0.892392	−	0.451261i	$-0.149025\pi$
$523$	40.8166	1.78478	0.892392	+	0.451261i	$0.149025\pi$
$524$	24.0173	1.04920
$525$	0	0
$526$	4.39139	0.191474
$527$	−12.4384	−0.541824
$528$	0.845960	0.0368157
$529$	11.7365	0.510284
$530$	0	0
$531$	−18.8381	−0.817503
$532$	−2.53047	−0.109710
$533$	42.1922	1.82754
$534$	−7.15460	−0.309610
$535$	0	0
$536$	4.54899	0.196486
$537$	−2.09719	−0.0905006
$538$	3.78375	0.163129
$539$	−38.9679	−1.67847
$540$	0	0
$541$	−8.58566	−0.369126	−0.184563	−	0.982821i	$-0.559087\pi$
$541$	−8.58566	−0.369126	−0.184563	+	0.982821i	$0.559087\pi$
$542$	−0.268363	−0.0115272
$543$	−33.0321	−1.41754
$544$	24.6413	1.05649
$545$	0	0
$546$	−4.03080	−0.172502
$547$	−36.8989	−1.57768	−0.788841	−	0.614597i	$-0.789318\pi$
$547$	−36.8989	−1.57768	−0.788841	+	0.614597i	$0.789318\pi$
$548$	−18.4494	−0.788119
$549$	−1.76427	−0.0752973
$550$	0	0
$551$	−5.23644	−0.223080
$552$	21.8956	0.931938
$553$	−2.45317	−0.104319
$554$	−11.3802	−0.483499
$555$	0	0
$556$	19.7047	0.835667
$557$	15.8389	0.671117	0.335558	−	0.942019i	$-0.391075\pi$
$557$	15.8389	0.671117	0.335558	+	0.942019i	$0.391075\pi$
$558$	3.07995	0.130385
$559$	−22.5086	−0.952013
$560$	0	0
$561$	−33.2064	−1.40198
$562$	−20.8079	−0.877728
$563$	−35.4503	−1.49405	−0.747025	−	0.664796i	$-0.768519\pi$
$563$	−35.4503	−1.49405	−0.747025	+	0.664796i	$0.768519\pi$
$564$	−17.5660	−0.739663
$565$	0	0
$566$	−17.2915	−0.726816
$567$	−1.97024	−0.0827424
$568$	0.449273	0.0188511
$569$	12.7094	0.532805	0.266402	−	0.963862i	$-0.414165\pi$
$569$	12.7094	0.532805	0.266402	+	0.963862i	$0.414165\pi$
$570$	0	0
$571$	−33.2355	−1.39086	−0.695432	−	0.718592i	$-0.744787\pi$
$571$	−33.2355	−1.39086	−0.695432	+	0.718592i	$0.744787\pi$
$572$	−48.8106	−2.04087
$573$	25.1871	1.05221
$574$	−2.87918	−0.120175
$575$	0	0
$576$	−5.82763	−0.242818
$577$	−4.49251	−0.187026	−0.0935129	−	0.995618i	$-0.529810\pi$
$577$	−4.49251	−0.187026	−0.0935129	+	0.995618i	$0.529810\pi$
$578$	−1.43944	−0.0598730
$579$	6.25740	0.260049
$580$	0	0
$581$	−5.72245	−0.237407
$582$	−19.0833	−0.791027
$583$	−44.2533	−1.83279
$584$	−5.18943	−0.214740
$585$	0	0
$586$	10.1915	0.421006
$587$	−15.0948	−0.623029	−0.311514	−	0.950241i	$-0.600836\pi$
$587$	−15.0948	−0.623029	−0.311514	+	0.950241i	$0.600836\pi$
$588$	11.2228	0.462819
$589$	10.9052	0.449342
$590$	0	0
$591$	−11.3190	−0.465600
$592$	0.538491	0.0221319
$593$	−27.4532	−1.12737	−0.563683	−	0.825991i	$-0.690616\pi$
$593$	−27.4532	−1.12737	−0.563683	+	0.825991i	$0.690616\pi$
$594$	28.0459	1.15074
$595$	0	0
$596$	20.1952	0.827227
$597$	12.9991	0.532018
$598$	−33.8389	−1.38377
$599$	−34.0023	−1.38930	−0.694648	−	0.719350i	$-0.744440\pi$
$599$	−34.0023	−1.38930	−0.694648	+	0.719350i	$0.744440\pi$
$600$	0	0
$601$	2.29578	0.0936467	0.0468234	−	0.998903i	$-0.485090\pi$
$601$	2.29578	0.0936467	0.0468234	+	0.998903i	$0.485090\pi$
$602$	1.53598	0.0626019
$603$	−2.01890	−0.0822159
$604$	12.8938	0.524640
$605$	0	0
$606$	15.2453	0.619299
$607$	−2.26854	−0.0920772	−0.0460386	−	0.998940i	$-0.514660\pi$
$607$	−2.26854	−0.0920772	−0.0460386	+	0.998940i	$0.514660\pi$
$608$	−21.6041	−0.876160
$609$	−0.970321	−0.0393194
$610$	0	0
$611$	70.2204	2.84081
$612$	−6.77834	−0.273998
$613$	−15.3931	−0.621721	−0.310861	−	0.950456i	$-0.600617\pi$
$613$	−15.3931	−0.621721	−0.310861	+	0.950456i	$0.600617\pi$
$614$	−9.97414	−0.402524
$615$	0	0
$616$	8.61552	0.347129
$617$	−15.3523	−0.618062	−0.309031	−	0.951052i	$-0.600005\pi$
$617$	−15.3523	−0.618062	−0.309031	+	0.951052i	$0.600005\pi$
$618$	4.27846	0.172105
$619$	10.2172	0.410662	0.205331	−	0.978693i	$-0.434173\pi$
$619$	10.2172	0.410662	0.205331	+	0.978693i	$0.434173\pi$
$620$	0	0
$621$	−33.1454	−1.33008
$622$	−25.7418	−1.03215
$623$	3.32709	0.133297
$624$	0.973941	0.0389889
$625$	0	0
$626$	−24.1640	−0.965789
$627$	29.1134	1.16268
$628$	−26.8600	−1.07183
$629$	−21.1373	−0.842801
$630$	0	0
$631$	0.129224	0.00514433	0.00257216	−	0.999997i	$-0.499181\pi$
$631$	0.129224	0.00514433	0.00257216	+	0.999997i	$0.499181\pi$
$632$	−12.9814	−0.516373
$633$	−16.8033	−0.667870
$634$	14.1813	0.563211
$635$	0	0
$636$	12.7450	0.505371
$637$	−44.8632	−1.77754
$638$	6.89265	0.272883
$639$	−0.199393	−0.00788787
$640$	0	0
$641$	40.8265	1.61255	0.806274	−	0.591542i	$-0.201481\pi$
$641$	40.8265	1.61255	0.806274	+	0.591542i	$0.201481\pi$
$642$	10.4558	0.412658
$643$	1.99077	0.0785085	0.0392542	−	0.999229i	$-0.487502\pi$
$643$	1.99077	0.0785085	0.0392542	+	0.999229i	$0.487502\pi$
$644$	−3.93645	−0.155118
$645$	0	0
$646$	14.0787	0.553918
$647$	−26.5951	−1.04556	−0.522781	−	0.852467i	$-0.675105\pi$
$647$	−26.5951	−1.04556	−0.522781	+	0.852467i	$0.675105\pi$
$648$	−10.4259	−0.409568
$649$	87.7965	3.44632
$650$	0	0
$651$	2.02076	0.0791998
$652$	19.9861	0.782716
$653$	−16.8733	−0.660302	−0.330151	−	0.943928i	$-0.607100\pi$
$653$	−16.8733	−0.660302	−0.330151	+	0.943928i	$0.607100\pi$
$654$	19.7100	0.770721
$655$	0	0
$656$	0.695680	0.0271618
$657$	2.30314	0.0898539
$658$	−4.79181	−0.186804
$659$	−38.3378	−1.49343	−0.746713	−	0.665146i	$-0.768369\pi$
$659$	−38.3378	−1.49343	−0.746713	+	0.665146i	$0.768369\pi$
$660$	0	0
$661$	−9.34951	−0.363654	−0.181827	−	0.983331i	$-0.558201\pi$
$661$	−9.34951	−0.363654	−0.181827	+	0.983331i	$0.558201\pi$
$662$	24.1348	0.938025
$663$	−38.2300	−1.48473
$664$	−30.2814	−1.17515
$665$	0	0
$666$	5.23397	0.202812
$667$	−8.14591	−0.315411
$668$	20.4922	0.792869
$669$	30.9700	1.19737
$670$	0	0
$671$	8.22255	0.317428
$672$	−4.00327	−0.154429
$673$	47.5282	1.83208	0.916039	−	0.401089i	$-0.131368\pi$
$673$	47.5282	1.83208	0.916039	+	0.401089i	$0.131368\pi$
$674$	6.47541	0.249423
$675$	0	0
$676$	−39.8077	−1.53107
$677$	20.2888	0.779760	0.389880	−	0.920866i	$-0.372516\pi$
$677$	20.2888	0.779760	0.389880	+	0.920866i	$0.372516\pi$
$678$	6.57618	0.252557
$679$	8.87424	0.340562
$680$	0	0
$681$	18.5927	0.712474
$682$	−14.3544	−0.549658
$683$	39.0317	1.49351	0.746753	−	0.665102i	$-0.231612\pi$
$683$	39.0317	1.49351	0.746753	+	0.665102i	$0.231612\pi$
$684$	5.94285	0.227230
$685$	0	0
$686$	6.25080	0.238657
$687$	4.57148	0.174413
$688$	−0.371131	−0.0141492
$689$	−50.9482	−1.94097
$690$	0	0
$691$	−39.2421	−1.49284	−0.746420	−	0.665476i	$-0.768229\pi$
$691$	−39.2421	−1.49284	−0.746420	+	0.665476i	$0.768229\pi$
$692$	−30.2111	−1.14845
$693$	−3.82368	−0.145249
$694$	−3.35062	−0.127188
$695$	0	0
$696$	−5.13464	−0.194628
$697$	−27.3075	−1.03434
$698$	−14.6080	−0.552921
$699$	13.6366	0.515784
$700$	0	0
$701$	0.0987773	0.00373077	0.00186538	−	0.999998i	$-0.499406\pi$
$701$	0.0987773	0.00373077	0.00186538	+	0.999998i	$0.499406\pi$
$702$	32.2888	1.21866
$703$	18.5320	0.698947
$704$	27.1602	1.02364
$705$	0	0
$706$	−12.9345	−0.486795
$707$	−7.08949	−0.266628
$708$	−25.2854	−0.950285
$709$	−8.64032	−0.324494	−0.162247	−	0.986750i	$-0.551874\pi$
$709$	−8.64032	−0.324494	−0.162247	+	0.986750i	$0.551874\pi$
$710$	0	0
$711$	5.76131	0.216066
$712$	17.6059	0.659809
$713$	16.9644	0.635322
$714$	2.60880	0.0976320
$715$	0	0
$716$	1.99517	0.0745631
$717$	13.9369	0.520482
$718$	5.67712	0.211868
$719$	−1.81865	−0.0678243	−0.0339121	−	0.999425i	$-0.510797\pi$
$719$	−1.81865	−0.0678243	−0.0339121	+	0.999425i	$0.510797\pi$
$720$	0	0
$721$	−1.98960	−0.0740967
$722$	3.99498	0.148678
$723$	−1.32501	−0.0492775
$724$	31.4252	1.16791
$725$	0	0
$726$	−25.7883	−0.957093
$727$	−47.5038	−1.76182	−0.880909	−	0.473286i	$-0.843068\pi$
$727$	−47.5038	−1.76182	−0.880909	+	0.473286i	$0.843068\pi$
$728$	9.91892	0.367620
$729$	26.9819	0.999329
$730$	0	0
$731$	14.5680	0.538815
$732$	−2.36810	−0.0875274
$733$	−22.7276	−0.839464	−0.419732	−	0.907648i	$-0.637876\pi$
$733$	−22.7276	−0.839464	−0.419732	+	0.907648i	$0.637876\pi$
$734$	−25.3090	−0.934174
$735$	0	0
$736$	−33.6077	−1.23880
$737$	9.40926	0.346594
$738$	6.76180	0.248905
$739$	−16.4176	−0.603930	−0.301965	−	0.953319i	$-0.597643\pi$
$739$	−16.4176	−0.603930	−0.301965	+	0.953319i	$0.597643\pi$
$740$	0	0
$741$	33.5178	1.23131
$742$	3.47669	0.127633
$743$	14.7395	0.540741	0.270370	−	0.962756i	$-0.412854\pi$
$743$	14.7395	0.540741	0.270370	+	0.962756i	$0.412854\pi$
$744$	10.6932	0.392033
$745$	0	0
$746$	19.6713	0.720219
$747$	13.4393	0.491717
$748$	31.5910	1.15508
$749$	−4.86223	−0.177662
$750$	0	0
$751$	−0.542400	−0.0197925	−0.00989624	−	0.999951i	$-0.503150\pi$
$751$	−0.542400	−0.0197925	−0.00989624	+	0.999951i	$0.503150\pi$
$752$	1.15782	0.0422214
$753$	26.4940	0.965494
$754$	7.93540	0.288990
$755$	0	0
$756$	3.75614	0.136609
$757$	−31.0859	−1.12984	−0.564918	−	0.825147i	$-0.691092\pi$
$757$	−31.0859	−1.12984	−0.564918	+	0.825147i	$0.691092\pi$
$758$	7.62960	0.277120
$759$	45.2894	1.64390
$760$	0	0
$761$	−27.6276	−1.00150	−0.500751	−	0.865592i	$-0.666943\pi$
$761$	−27.6276	−1.00150	−0.500751	+	0.865592i	$0.666943\pi$
$762$	7.39722	0.267973
$763$	−9.16568	−0.331820
$764$	−23.9618	−0.866909
$765$	0	0
$766$	22.5790	0.815812
$767$	101.079	3.64975
$768$	−20.8163	−0.751144
$769$	−1.83448	−0.0661530	−0.0330765	−	0.999453i	$-0.510530\pi$
$769$	−1.83448	−0.0661530	−0.0330765	+	0.999453i	$0.510530\pi$
$770$	0	0
$771$	24.5026	0.882440
$772$	−5.95300	−0.214253
$773$	−18.3436	−0.659772	−0.329886	−	0.944021i	$-0.607010\pi$
$773$	−18.3436	−0.659772	−0.329886	+	0.944021i	$0.607010\pi$
$774$	−3.60728	−0.129661
$775$	0	0
$776$	46.9597	1.68576
$777$	3.43401	0.123194
$778$	24.3393	0.872606
$779$	23.9416	0.857796
$780$	0	0
$781$	0.929289	0.0332526
$782$	21.9011	0.783181
$783$	7.77278	0.277777
$784$	−0.739721	−0.0264186
$785$	0	0
$786$	21.7088	0.774327
$787$	25.9956	0.926642	0.463321	−	0.886191i	$-0.346658\pi$
$787$	25.9956	0.926642	0.463321	+	0.886191i	$0.346658\pi$
$788$	10.7683	0.383606
$789$	−6.76653	−0.240895
$790$	0	0
$791$	−3.05811	−0.108734
$792$	−20.2337	−0.718973
$793$	9.46650	0.336165
$794$	−33.4447	−1.18691
$795$	0	0
$796$	−12.3668	−0.438328
$797$	16.4380	0.582265	0.291133	−	0.956683i	$-0.405968\pi$
$797$	16.4380	0.582265	0.291133	+	0.956683i	$0.405968\pi$
$798$	−2.28725	−0.0809676
$799$	−45.4478	−1.60783
$800$	0	0
$801$	−7.81372	−0.276084
$802$	21.4141	0.756157
$803$	−10.7340	−0.378793
$804$	−2.70987	−0.0955697
$805$	0	0
$806$	−16.5260	−0.582103
$807$	−5.83024	−0.205234
$808$	−37.5154	−1.31979
$809$	22.6680	0.796964	0.398482	−	0.917176i	$-0.369537\pi$
$809$	22.6680	0.796964	0.398482	+	0.917176i	$0.369537\pi$
$810$	0	0
$811$	−18.8126	−0.660600	−0.330300	−	0.943876i	$-0.607150\pi$
$811$	−18.8126	−0.660600	−0.330300	+	0.943876i	$0.607150\pi$
$812$	0.923119	0.0323951
$813$	0.413510	0.0145024
$814$	−24.3934	−0.854988
$815$	0	0
$816$	−0.630351	−0.0220667
$817$	−12.7723	−0.446847
$818$	−9.04416	−0.316222
$819$	−4.40214	−0.153823
$820$	0	0
$821$	−2.81049	−0.0980869	−0.0490435	−	0.998797i	$-0.515617\pi$
$821$	−2.81049	−0.0980869	−0.0490435	+	0.998797i	$0.515617\pi$
$822$	−16.6761	−0.581645
$823$	34.5542	1.20449	0.602243	−	0.798313i	$-0.294274\pi$
$823$	34.5542	1.20449	0.602243	+	0.798313i	$0.294274\pi$
$824$	−10.5284	−0.366773
$825$	0	0
$826$	−6.89759	−0.239998
$827$	−31.0173	−1.07858	−0.539288	−	0.842121i	$-0.681307\pi$
$827$	−31.0173	−1.07858	−0.539288	+	0.842121i	$0.681307\pi$
$828$	9.24482	0.321280
$829$	−12.7763	−0.443738	−0.221869	−	0.975076i	$-0.571216\pi$
$829$	−12.7763	−0.443738	−0.221869	+	0.975076i	$0.571216\pi$
$830$	0	0
$831$	17.5353	0.608294
$832$	31.2691	1.08406
$833$	29.0362	1.00604
$834$	17.8108	0.616736
$835$	0	0
$836$	−27.6972	−0.957927
$837$	−16.1873	−0.559516
$838$	−13.5907	−0.469482
$839$	53.5310	1.84810	0.924048	−	0.382276i	$-0.124860\pi$
$839$	53.5310	1.84810	0.924048	+	0.382276i	$0.124860\pi$
$840$	0	0
$841$	−27.0897	−0.934129
$842$	−3.76546	−0.129766
$843$	32.0621	1.10428
$844$	15.9858	0.550256
$845$	0	0
$846$	11.2537	0.386909
$847$	11.9923	0.412059
$848$	−0.840053	−0.0288475
$849$	26.6438	0.914414
$850$	0	0
$851$	28.8287	0.988236
$852$	−0.267636	−0.00916904
$853$	−44.4609	−1.52231	−0.761156	−	0.648569i	$-0.775368\pi$
$853$	−44.4609	−1.52231	−0.761156	+	0.648569i	$0.775368\pi$
$854$	−0.645991	−0.0221053
$855$	0	0
$856$	−25.7294	−0.879414
$857$	−30.9367	−1.05678	−0.528389	−	0.849003i	$-0.677204\pi$
$857$	−30.9367	−1.05678	−0.528389	+	0.849003i	$0.677204\pi$
$858$	−44.1191	−1.50620
$859$	9.48878	0.323753	0.161876	−	0.986811i	$-0.448245\pi$
$859$	9.48878	0.323753	0.161876	+	0.986811i	$0.448245\pi$
$860$	0	0
$861$	4.43642	0.151193
$862$	4.15326	0.141461
$863$	21.9437	0.746974	0.373487	−	0.927635i	$-0.378162\pi$
$863$	21.9437	0.746974	0.373487	+	0.927635i	$0.378162\pi$
$864$	32.0683	1.09099
$865$	0	0
$866$	−4.17768	−0.141964
$867$	2.21799	0.0753268
$868$	−1.92246	−0.0652524
$869$	−26.8511	−0.910861
$870$	0	0
$871$	10.8327	0.367053
$872$	−48.5019	−1.64248
$873$	−20.8413	−0.705371
$874$	−19.2016	−0.649503
$875$	0	0
$876$	3.09139	0.104448
$877$	14.8274	0.500686	0.250343	−	0.968157i	$-0.419457\pi$
$877$	14.8274	0.500686	0.250343	+	0.968157i	$0.419457\pi$
$878$	19.1889	0.647592
$879$	−15.7037	−0.529672
$880$	0	0
$881$	56.7878	1.91323	0.956615	−	0.291353i	$-0.0941055\pi$
$881$	56.7878	1.91323	0.956615	+	0.291353i	$0.0941055\pi$
$882$	−7.18986	−0.242095
$883$	−6.95695	−0.234120	−0.117060	−	0.993125i	$-0.537347\pi$
$883$	−6.95695	−0.234120	−0.117060	+	0.993125i	$0.537347\pi$
$884$	36.3703	1.22326
$885$	0	0
$886$	−19.7355	−0.663028
$887$	35.5014	1.19202	0.596011	−	0.802976i	$-0.296751\pi$
$887$	35.5014	1.19202	0.596011	+	0.802976i	$0.296751\pi$
$888$	18.1717	0.609803
$889$	−3.43991	−0.115371
$890$	0	0
$891$	−21.5652	−0.722463
$892$	−29.4634	−0.986508
$893$	39.8460	1.33339
$894$	18.2541	0.610507
$895$	0	0
$896$	3.90885	0.130585
$897$	52.1410	1.74094
$898$	8.11477	0.270793
$899$	−3.97825	−0.132682
$900$	0	0
$901$	32.9745	1.09854
$902$	−31.5140	−1.04930
$903$	−2.36674	−0.0787600
$904$	−16.1825	−0.538223
$905$	0	0
$906$	11.6545	0.387193
$907$	−41.1888	−1.36765	−0.683826	−	0.729645i	$-0.739685\pi$
$907$	−41.1888	−1.36765	−0.683826	+	0.729645i	$0.739685\pi$
$908$	−17.6882	−0.587005
$909$	16.6498	0.552239
$910$	0	0
$911$	−6.41896	−0.212670	−0.106335	−	0.994330i	$-0.533912\pi$
$911$	−6.41896	−0.212670	−0.106335	+	0.994330i	$0.533912\pi$
$912$	0.552655	0.0183002
$913$	−62.6349	−2.07291
$914$	3.47262	0.114864
$915$	0	0
$916$	−4.34910	−0.143698
$917$	−10.0952	−0.333373
$918$	−20.8979	−0.689733
$919$	18.3387	0.604937	0.302469	−	0.953159i	$-0.402189\pi$
$919$	18.3387	0.604937	0.302469	+	0.953159i	$0.402189\pi$
$920$	0	0
$921$	15.3688	0.506419
$922$	−24.0793	−0.793009
$923$	1.06988	0.0352154
$924$	−5.13234	−0.168841
$925$	0	0
$926$	3.81284	0.125298
$927$	4.67262	0.153469
$928$	7.88120	0.258713
$929$	−37.6451	−1.23510	−0.617548	−	0.786534i	$-0.711874\pi$
$929$	−37.6451	−1.23510	−0.617548	+	0.786534i	$0.711874\pi$
$930$	0	0
$931$	−25.4572	−0.834327
$932$	−12.9732	−0.424953
$933$	39.6646	1.29856
$934$	5.07952	0.166207
$935$	0	0
$936$	−23.2948	−0.761413
$937$	−23.2053	−0.758083	−0.379041	−	0.925380i	$-0.623746\pi$
$937$	−23.2053	−0.758083	−0.379041	+	0.925380i	$0.623746\pi$
$938$	−0.739222	−0.0241365
$939$	37.2335	1.21507
$940$	0	0
$941$	37.6707	1.22803	0.614016	−	0.789294i	$-0.289553\pi$
$941$	37.6707	1.22803	0.614016	+	0.789294i	$0.289553\pi$
$942$	−24.2783	−0.791029
$943$	37.2440	1.21283
$944$	1.66663	0.0542441
$945$	0	0
$946$	16.8120	0.546607
$947$	−3.14992	−0.102359	−0.0511794	−	0.998689i	$-0.516298\pi$
$947$	−3.14992	−0.102359	−0.0511794	+	0.998689i	$0.516298\pi$
$948$	7.73313	0.251160
$949$	−12.3579	−0.401153
$950$	0	0
$951$	−21.8514	−0.708581
$952$	−6.41969	−0.208063
$953$	−18.0318	−0.584107	−0.292054	−	0.956402i	$-0.594339\pi$
$953$	−18.0318	−0.584107	−0.292054	+	0.956402i	$0.594339\pi$
$954$	−8.16506	−0.264353
$955$	0	0
$956$	−13.2589	−0.428823
$957$	−10.6206	−0.343316
$958$	18.5994	0.600919
$959$	7.75484	0.250417
$960$	0	0
$961$	−22.7150	−0.732743
$962$	−28.0837	−0.905456
$963$	11.4190	0.367973
$964$	1.26055	0.0405996
$965$	0	0
$966$	−3.55809	−0.114480
$967$	59.0317	1.89833	0.949165	−	0.314778i	$-0.101930\pi$
$967$	59.0317	1.89833	0.949165	+	0.314778i	$0.101930\pi$
$968$	63.4593	2.03966
$969$	−21.6933	−0.696889
$970$	0	0
$971$	10.9718	0.352102	0.176051	−	0.984381i	$-0.443668\pi$
$971$	10.9718	0.352102	0.176051	+	0.984381i	$0.443668\pi$
$972$	−15.0565	−0.482936
$973$	−8.28249	−0.265525
$974$	−17.0787	−0.547238
$975$	0	0
$976$	0.156087	0.00499623
$977$	59.4174	1.90093	0.950465	−	0.310831i	$-0.100607\pi$
$977$	59.4174	1.90093	0.950465	+	0.310831i	$0.100607\pi$
$978$	18.0651	0.577658
$979$	36.4165	1.16388
$980$	0	0
$981$	21.5258	0.687265
$982$	−9.52755	−0.304036
$983$	5.99551	0.191227	0.0956135	−	0.995419i	$-0.469519\pi$
$983$	5.99551	0.191227	0.0956135	+	0.995419i	$0.469519\pi$
$984$	23.4761	0.748392
$985$	0	0
$986$	−5.13592	−0.163561
$987$	7.38353	0.235020
$988$	−31.8873	−1.01447
$989$	−19.8689	−0.631794
$990$	0	0
$991$	−36.5152	−1.15994	−0.579972	−	0.814636i	$-0.696937\pi$
$991$	−36.5152	−1.15994	−0.579972	+	0.814636i	$0.696937\pi$
$992$	−16.4131	−0.521117
$993$	−37.1884	−1.18014
$994$	−0.0730080	−0.00231567
$995$	0	0
$996$	18.0389	0.571584
$997$	−14.1576	−0.448375	−0.224188	−	0.974546i	$-0.571973\pi$
$997$	−14.1576	−0.448375	−0.224188	+	0.974546i	$0.571973\pi$
$998$	−5.32898	−0.168686
$999$	−27.5082	−0.870321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.o.1.12	yes	40
5.4	even	2		6025.2.a.l.1.29	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.29	✓	40	5.4	even	2
6025.2.a.o.1.12	yes	40	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.859912 q^{2} +1.32501 q^{3} -1.26055 q^{4} -1.13939 q^{6} +0.529848 q^{7} +2.80379 q^{8} -1.24436 q^{9} +O(q^{10})\)	\(q-0.859912 q^{2} +1.32501 q^{3} -1.26055 q^{4} -1.13939 q^{6} +0.529848 q^{7} +2.80379 q^{8} -1.24436 q^{9} +5.79943 q^{11} -1.67024 q^{12} +6.67680 q^{13} -0.455622 q^{14} +0.110090 q^{16} -4.32134 q^{17} +1.07004 q^{18} +3.78869 q^{19} +0.702052 q^{21} -4.98700 q^{22} +5.89377 q^{23} +3.71504 q^{24} -5.74146 q^{26} -5.62380 q^{27} -0.667900 q^{28} -1.38212 q^{29} +2.87836 q^{31} -5.70224 q^{32} +7.68429 q^{33} +3.71597 q^{34} +1.56857 q^{36} +4.89139 q^{37} -3.25795 q^{38} +8.84681 q^{39} +6.31922 q^{41} -0.603703 q^{42} -3.37117 q^{43} -7.31048 q^{44} -5.06813 q^{46} +10.5171 q^{47} +0.145870 q^{48} -6.71926 q^{49} -5.72580 q^{51} -8.41644 q^{52} -7.63063 q^{53} +4.83598 q^{54} +1.48558 q^{56} +5.02005 q^{57} +1.18850 q^{58} +15.1388 q^{59} +1.41782 q^{61} -2.47514 q^{62} -0.659319 q^{63} +4.68325 q^{64} -6.60782 q^{66} +1.62244 q^{67} +5.44726 q^{68} +7.80929 q^{69} +0.160238 q^{71} -3.48891 q^{72} -1.85086 q^{73} -4.20617 q^{74} -4.77584 q^{76} +3.07282 q^{77} -7.60748 q^{78} -4.62995 q^{79} -3.71851 q^{81} -5.43397 q^{82} -10.8002 q^{83} -0.884972 q^{84} +2.89891 q^{86} -1.83132 q^{87} +16.2604 q^{88} +6.27933 q^{89} +3.53769 q^{91} -7.42940 q^{92} +3.81385 q^{93} -9.04376 q^{94} -7.55551 q^{96} +16.7487 q^{97} +5.77798 q^{98} -7.21656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9}+O(q^{10}) \) 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

Modular forms

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