LMFDB - Embedded newform 8925.2.a.cu.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8925,2,Mod(1,8925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8925, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$8925 = 3 \cdot 5^{2} \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	8925.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:	$71.2664838040$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{14} - 3 x^{13} - 18 x^{12} + 54 x^{11} + 124 x^{10} - 366 x^{9} - 416 x^{8} + 1164 x^{7} + 727 x^{6} + \cdots - 40$ x^14 - 3x^13 - 18x^12 + 54x^11 + 124x^10 - 366x^9 - 416x^8 + 1164x^7 + 727x^6 - 1783x^5 - 662x^4 + 1242x^3 + 284x^2 - 300*x - 40
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$2^{6}$
Twist minimal:	no (minimal twist has level 1785)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.10180$ of defining polynomial
Character	$\chi$	$=$	8925.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.10180 q^{2} -1.00000 q^{3} -0.786043 q^{4} +1.10180 q^{6} -1.00000 q^{7} +3.06965 q^{8} +1.00000 q^{9} -3.04644 q^{11} +0.786043 q^{12} -0.439346 q^{13} +1.10180 q^{14} -1.81005 q^{16} +1.00000 q^{17} -1.10180 q^{18} -5.90487 q^{19} +1.00000 q^{21} +3.35656 q^{22} +7.65430 q^{23} -3.06965 q^{24} +0.484071 q^{26} -1.00000 q^{27} +0.786043 q^{28} -8.16879 q^{29} +9.73478 q^{31} -4.14500 q^{32} +3.04644 q^{33} -1.10180 q^{34} -0.786043 q^{36} +3.68208 q^{37} +6.50597 q^{38} +0.439346 q^{39} +8.19605 q^{41} -1.10180 q^{42} -10.3591 q^{43} +2.39463 q^{44} -8.43348 q^{46} -9.33290 q^{47} +1.81005 q^{48} +1.00000 q^{49} -1.00000 q^{51} +0.345345 q^{52} -12.4473 q^{53} +1.10180 q^{54} -3.06965 q^{56} +5.90487 q^{57} +9.00035 q^{58} +10.5293 q^{59} +12.1407 q^{61} -10.7257 q^{62} -1.00000 q^{63} +8.18705 q^{64} -3.35656 q^{66} +2.39025 q^{67} -0.786043 q^{68} -7.65430 q^{69} +2.34874 q^{71} +3.06965 q^{72} +3.03284 q^{73} -4.05690 q^{74} +4.64148 q^{76} +3.04644 q^{77} -0.484071 q^{78} -11.3895 q^{79} +1.00000 q^{81} -9.03039 q^{82} -10.1906 q^{83} -0.786043 q^{84} +11.4136 q^{86} +8.16879 q^{87} -9.35152 q^{88} +8.78928 q^{89} +0.439346 q^{91} -6.01661 q^{92} -9.73478 q^{93} +10.2830 q^{94} +4.14500 q^{96} +3.56287 q^{97} -1.10180 q^{98} -3.04644 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$14 q - 3 q^{2} - 14 q^{3} + 17 q^{4} + 3 q^{6} - 14 q^{7} - 15 q^{8} + 14 q^{9} + 4 q^{11} - 17 q^{12} + q^{13} + 3 q^{14} + 19 q^{16} + 14 q^{17} - 3 q^{18} - 6 q^{19} + 14 q^{21} - 12 q^{22} - 7 q^{23}+ \cdots + 4 q^{99}+O(q^{100})$ 14 * q - 3 * q^2 - 14 * q^3 + 17 * q^4 + 3 * q^6 - 14 * q^7 - 15 * q^8 + 14 * q^9 + 4 * q^11 - 17 * q^12 + q^13 + 3 * q^14 + 19 * q^16 + 14 * q^17 - 3 * q^18 - 6 * q^19 + 14 * q^21 - 12 * q^22 - 7 * q^23 + 15 * q^24 - 2 * q^26 - 14 * q^27 - 17 * q^28 + 20 * q^29 - 7 * q^31 - 33 * q^32 - 4 * q^33 - 3 * q^34 + 17 * q^36 - 9 * q^37 - 18 * q^38 - q^39 + 25 * q^41 - 3 * q^42 - 28 * q^43 + 24 * q^44 - 10 * q^46 - 29 * q^47 - 19 * q^48 + 14 * q^49 - 14 * q^51 - 4 * q^52 - 26 * q^53 + 3 * q^54 + 15 * q^56 + 6 * q^57 - 2 * q^58 + 14 * q^59 - 9 * q^61 - 28 * q^62 - 14 * q^63 + 27 * q^64 + 12 * q^66 - 32 * q^67 + 17 * q^68 + 7 * q^69 + 2 * q^71 - 15 * q^72 - 18 * q^73 + 64 * q^74 - 42 * q^76 - 4 * q^77 + 2 * q^78 - 4 * q^79 + 14 * q^81 - 42 * q^82 - 51 * q^83 + 17 * q^84 + 44 * q^86 - 20 * q^87 - 32 * q^88 + 38 * q^89 - q^91 + 16 * q^92 + 7 * q^93 + 8 * q^94 + 33 * q^96 - 14 * q^97 - 3 * q^98 + 4 * q^99

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

)

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

$2$	−1.10180	−0.779088	−0.389544	−	0.921008i	$-0.627367\pi$
$2$	−1.10180	−0.779088	−0.389544	+	0.921008i	$0.627367\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.786043	−0.393022
$5$	0	0
$5$	0	0
$6$	1.10180	0.449807
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.06965	1.08529
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.04644	−0.918536	−0.459268	−	0.888298i	$-0.651888\pi$
$11$	−3.04644	−0.918536	−0.459268	+	0.888298i	$0.651888\pi$
$12$	0.786043	0.226911
$13$	−0.439346	−0.121853	−0.0609264	−	0.998142i	$-0.519405\pi$
$13$	−0.439346	−0.121853	−0.0609264	+	0.998142i	$0.519405\pi$
$14$	1.10180	0.294468
$15$	0	0
$16$	−1.81005	−0.452512
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.10180	−0.259696
$19$	−5.90487	−1.35467	−0.677335	−	0.735675i	$-0.736865\pi$
$19$	−5.90487	−1.35467	−0.677335	+	0.735675i	$0.736865\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	3.35656	0.715621
$23$	7.65430	1.59603	0.798016	−	0.602637i	$-0.205883\pi$
$23$	7.65430	1.59603	0.798016	+	0.602637i	$0.205883\pi$
$24$	−3.06965	−0.626591
$25$	0	0
$26$	0.484071	0.0949341
$27$	−1.00000	−0.192450
$28$	0.786043	0.148548
$29$	−8.16879	−1.51691	−0.758453	−	0.651728i	$-0.774044\pi$
$29$	−8.16879	−1.51691	−0.758453	+	0.651728i	$0.774044\pi$
$30$	0	0
$31$	9.73478	1.74842	0.874209	−	0.485551i	$-0.161381\pi$
$31$	9.73478	1.74842	0.874209	+	0.485551i	$0.161381\pi$
$32$	−4.14500	−0.732740
$33$	3.04644	0.530317
$34$	−1.10180	−0.188957
$35$	0	0
$36$	−0.786043	−0.131007
$37$	3.68208	0.605330	0.302665	−	0.953097i	$-0.402124\pi$
$37$	3.68208	0.605330	0.302665	+	0.953097i	$0.402124\pi$
$38$	6.50597	1.05541
$39$	0.439346	0.0703517
$40$	0	0
$41$	8.19605	1.28001	0.640004	−	0.768371i	$-0.278933\pi$
$41$	8.19605	1.28001	0.640004	+	0.768371i	$0.278933\pi$
$42$	−1.10180	−0.170011
$43$	−10.3591	−1.57975	−0.789876	−	0.613267i	$-0.789855\pi$
$43$	−10.3591	−1.57975	−0.789876	+	0.613267i	$0.789855\pi$
$44$	2.39463	0.361005
$45$	0	0
$46$	−8.43348	−1.24345
$47$	−9.33290	−1.36134	−0.680672	−	0.732589i	$-0.738312\pi$
$47$	−9.33290	−1.36134	−0.680672	+	0.732589i	$0.738312\pi$
$48$	1.81005	0.261258
$49$	1.00000	0.142857
$50$	0	0
$51$	−1.00000	−0.140028
$52$	0.345345	0.0478908
$53$	−12.4473	−1.70976	−0.854881	−	0.518824i	$-0.826370\pi$
$53$	−12.4473	−1.70976	−0.854881	+	0.518824i	$0.826370\pi$
$54$	1.10180	0.149936
$55$	0	0
$56$	−3.06965	−0.410200
$57$	5.90487	0.782119
$58$	9.00035	1.18180
$59$	10.5293	1.37080	0.685402	−	0.728165i	$-0.259627\pi$
$59$	10.5293	1.37080	0.685402	+	0.728165i	$0.259627\pi$
$60$	0	0
$61$	12.1407	1.55446	0.777229	−	0.629218i	$-0.216625\pi$
$61$	12.1407	1.55446	0.777229	+	0.629218i	$0.216625\pi$
$62$	−10.7257	−1.36217
$63$	−1.00000	−0.125988
$64$	8.18705	1.02338
$65$	0	0
$66$	−3.35656	−0.413164
$67$	2.39025	0.292016	0.146008	−	0.989283i	$-0.453357\pi$
$67$	2.39025	0.292016	0.146008	+	0.989283i	$0.453357\pi$
$68$	−0.786043	−0.0953218
$69$	−7.65430	−0.921469
$70$	0	0
$71$	2.34874	0.278744	0.139372	−	0.990240i	$-0.455492\pi$
$71$	2.34874	0.278744	0.139372	+	0.990240i	$0.455492\pi$
$72$	3.06965	0.361762
$73$	3.03284	0.354967	0.177484	−	0.984124i	$-0.443204\pi$
$73$	3.03284	0.354967	0.177484	+	0.984124i	$0.443204\pi$
$74$	−4.05690	−0.471605
$75$	0	0
$76$	4.64148	0.532415
$77$	3.04644	0.347174
$78$	−0.484071	−0.0548102
$79$	−11.3895	−1.28142	−0.640708	−	0.767784i	$-0.721359\pi$
$79$	−11.3895	−1.28142	−0.640708	+	0.767784i	$0.721359\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−9.03039	−0.997239
$83$	−10.1906	−1.11856	−0.559281	−	0.828978i	$-0.688923\pi$
$83$	−10.1906	−1.11856	−0.559281	+	0.828978i	$0.688923\pi$
$84$	−0.786043	−0.0857644
$85$	0	0
$86$	11.4136	1.23077
$87$	8.16879	0.875786
$88$	−9.35152	−0.996875
$89$	8.78928	0.931662	0.465831	−	0.884874i	$-0.345755\pi$
$89$	8.78928	0.931662	0.465831	+	0.884874i	$0.345755\pi$
$90$	0	0
$91$	0.439346	0.0460560
$92$	−6.01661	−0.627275
$93$	−9.73478	−1.00945
$94$	10.2830	1.06061
$95$	0	0
$96$	4.14500	0.423047
$97$	3.56287	0.361755	0.180877	−	0.983506i	$-0.442106\pi$
$97$	3.56287	0.361755	0.180877	+	0.983506i	$0.442106\pi$
$98$	−1.10180	−0.111298
$99$	−3.04644	−0.306179
$100$	0	0
$101$	15.9788	1.58995	0.794975	−	0.606642i	$-0.207484\pi$
$101$	15.9788	1.58995	0.794975	+	0.606642i	$0.207484\pi$
$102$	1.10180	0.109094
$103$	7.30742	0.720021	0.360011	−	0.932948i	$-0.382773\pi$
$103$	7.30742	0.720021	0.360011	+	0.932948i	$0.382773\pi$
$104$	−1.34864	−0.132245
$105$	0	0
$106$	13.7144	1.33206
$107$	−8.43009	−0.814967	−0.407484	−	0.913213i	$-0.633594\pi$
$107$	−8.43009	−0.814967	−0.407484	+	0.913213i	$0.633594\pi$
$108$	0.786043	0.0756371
$109$	4.50550	0.431549	0.215774	−	0.976443i	$-0.430772\pi$
$109$	4.50550	0.431549	0.215774	+	0.976443i	$0.430772\pi$
$110$	0	0
$111$	−3.68208	−0.349487
$112$	1.81005	0.171034
$113$	6.16464	0.579920	0.289960	−	0.957039i	$-0.406358\pi$
$113$	6.16464	0.579920	0.289960	+	0.957039i	$0.406358\pi$
$114$	−6.50597	−0.609340
$115$	0	0
$116$	6.42102	0.596177
$117$	−0.439346	−0.0406176
$118$	−11.6012	−1.06798
$119$	−1.00000	−0.0916698
$120$	0	0
$121$	−1.71920	−0.156291
$122$	−13.3766	−1.21106
$123$	−8.19605	−0.739013
$124$	−7.65196	−0.687166
$125$	0	0
$126$	1.10180	0.0981559
$127$	−10.2969	−0.913703	−0.456851	−	0.889543i	$-0.651023\pi$
$127$	−10.2969	−0.913703	−0.456851	+	0.889543i	$0.651023\pi$
$128$	−0.730462	−0.0645643
$129$	10.3591	0.912070
$130$	0	0
$131$	−4.92183	−0.430022	−0.215011	−	0.976612i	$-0.568979\pi$
$131$	−4.92183	−0.430022	−0.215011	+	0.976612i	$0.568979\pi$
$132$	−2.39463	−0.208426
$133$	5.90487	0.512017
$134$	−2.63358	−0.227506
$135$	0	0
$136$	3.06965	0.263221
$137$	−1.94023	−0.165765	−0.0828825	−	0.996559i	$-0.526413\pi$
$137$	−1.94023	−0.165765	−0.0828825	+	0.996559i	$0.526413\pi$
$138$	8.43348	0.717906
$139$	3.81408	0.323506	0.161753	−	0.986831i	$-0.448285\pi$
$139$	3.81408	0.323506	0.161753	+	0.986831i	$0.448285\pi$
$140$	0	0
$141$	9.33290	0.785972
$142$	−2.58784	−0.217166
$143$	1.33844	0.111926
$144$	−1.81005	−0.150837
$145$	0	0
$146$	−3.34158	−0.276551
$147$	−1.00000	−0.0824786
$148$	−2.89427	−0.237908
$149$	2.84752	0.233278	0.116639	−	0.993174i	$-0.462788\pi$
$149$	2.84752	0.233278	0.116639	+	0.993174i	$0.462788\pi$
$150$	0	0
$151$	1.87286	0.152411	0.0762054	−	0.997092i	$-0.475720\pi$
$151$	1.87286	0.152411	0.0762054	+	0.997092i	$0.475720\pi$
$152$	−18.1259	−1.47021
$153$	1.00000	0.0808452
$154$	−3.35656	−0.270479
$155$	0	0
$156$	−0.345345	−0.0276498
$157$	−8.58171	−0.684895	−0.342447	−	0.939537i	$-0.611256\pi$
$157$	−8.58171	−0.684895	−0.342447	+	0.939537i	$0.611256\pi$
$158$	12.5489	0.998336
$159$	12.4473	0.987132
$160$	0	0
$161$	−7.65430	−0.603243
$162$	−1.10180	−0.0865653
$163$	23.0878	1.80837	0.904187	−	0.427137i	$-0.140478\pi$
$163$	23.0878	1.80837	0.904187	+	0.427137i	$0.140478\pi$
$164$	−6.44245	−0.503071
$165$	0	0
$166$	11.2280	0.871459
$167$	−3.39386	−0.262625	−0.131312	−	0.991341i	$-0.541919\pi$
$167$	−3.39386	−0.262625	−0.131312	+	0.991341i	$0.541919\pi$
$168$	3.06965	0.236829
$169$	−12.8070	−0.985152
$170$	0	0
$171$	−5.90487	−0.451557
$172$	8.14272	0.620876
$173$	−2.55812	−0.194491	−0.0972453	−	0.995260i	$-0.531003\pi$
$173$	−2.55812	−0.194491	−0.0972453	+	0.995260i	$0.531003\pi$
$174$	−9.00035	−0.682314
$175$	0	0
$176$	5.51421	0.415649
$177$	−10.5293	−0.791434
$178$	−9.68401	−0.725847
$179$	7.83699	0.585764	0.292882	−	0.956149i	$-0.405386\pi$
$179$	7.83699	0.585764	0.292882	+	0.956149i	$0.405386\pi$
$180$	0	0
$181$	−22.8457	−1.69811	−0.849054	−	0.528307i	$-0.822827\pi$
$181$	−22.8457	−1.69811	−0.849054	+	0.528307i	$0.822827\pi$
$182$	−0.484071	−0.0358817
$183$	−12.1407	−0.897466
$184$	23.4960	1.73215
$185$	0	0
$186$	10.7257	0.786450
$187$	−3.04644	−0.222778
$188$	7.33606	0.535037
$189$	1.00000	0.0727393
$190$	0	0
$191$	−9.30557	−0.673327	−0.336664	−	0.941625i	$-0.609298\pi$
$191$	−9.30557	−0.673327	−0.336664	+	0.941625i	$0.609298\pi$
$192$	−8.18705	−0.590849
$193$	19.4366	1.39908	0.699540	−	0.714594i	$-0.253388\pi$
$193$	19.4366	1.39908	0.699540	+	0.714594i	$0.253388\pi$
$194$	−3.92556	−0.281839
$195$	0	0
$196$	−0.786043	−0.0561460
$197$	19.1313	1.36305	0.681525	−	0.731795i	$-0.261317\pi$
$197$	19.1313	1.36305	0.681525	+	0.731795i	$0.261317\pi$
$198$	3.35656	0.238540
$199$	−7.83165	−0.555171	−0.277586	−	0.960701i	$-0.589534\pi$
$199$	−7.83165	−0.555171	−0.277586	+	0.960701i	$0.589534\pi$
$200$	0	0
$201$	−2.39025	−0.168596
$202$	−17.6054	−1.23871
$203$	8.16879	0.573336
$204$	0.786043	0.0550340
$205$	0	0
$206$	−8.05129	−0.560960
$207$	7.65430	0.532010
$208$	0.795239	0.0551399
$209$	17.9888	1.24431
$210$	0	0
$211$	9.76289	0.672105	0.336053	−	0.941843i	$-0.390908\pi$
$211$	9.76289	0.672105	0.336053	+	0.941843i	$0.390908\pi$
$212$	9.78409	0.671974
$213$	−2.34874	−0.160933
$214$	9.28824	0.634931
$215$	0	0
$216$	−3.06965	−0.208864
$217$	−9.73478	−0.660840
$218$	−4.96415	−0.336215
$219$	−3.03284	−0.204940
$220$	0	0
$221$	−0.439346	−0.0295536
$222$	4.05690	0.272282
$223$	6.18501	0.414179	0.207090	−	0.978322i	$-0.433601\pi$
$223$	6.18501	0.414179	0.207090	+	0.978322i	$0.433601\pi$
$224$	4.14500	0.276950
$225$	0	0
$226$	−6.79218	−0.451809
$227$	−10.2016	−0.677101	−0.338551	−	0.940948i	$-0.609937\pi$
$227$	−10.2016	−0.677101	−0.338551	+	0.940948i	$0.609937\pi$
$228$	−4.64148	−0.307390
$229$	0.173014	0.0114331	0.00571655	−	0.999984i	$-0.498180\pi$
$229$	0.173014	0.0114331	0.00571655	+	0.999984i	$0.498180\pi$
$230$	0	0
$231$	−3.04644	−0.200441
$232$	−25.0754	−1.64628
$233$	−9.68797	−0.634680	−0.317340	−	0.948312i	$-0.602790\pi$
$233$	−9.68797	−0.634680	−0.317340	+	0.948312i	$0.602790\pi$
$234$	0.484071	0.0316447
$235$	0	0
$236$	−8.27652	−0.538755
$237$	11.3895	0.739826
$238$	1.10180	0.0714189
$239$	13.7928	0.892183	0.446091	−	0.894987i	$-0.352816\pi$
$239$	13.7928	0.892183	0.446091	+	0.894987i	$0.352816\pi$
$240$	0	0
$241$	14.8482	0.956458	0.478229	−	0.878235i	$-0.341279\pi$
$241$	14.8482	0.956458	0.478229	+	0.878235i	$0.341279\pi$
$242$	1.89421	0.121765
$243$	−1.00000	−0.0641500
$244$	−9.54312	−0.610935
$245$	0	0
$246$	9.03039	0.575756
$247$	2.59428	0.165070
$248$	29.8824	1.89753
$249$	10.1906	0.645803
$250$	0	0
$251$	5.41270	0.341646	0.170823	−	0.985302i	$-0.445357\pi$
$251$	5.41270	0.341646	0.170823	+	0.985302i	$0.445357\pi$
$252$	0.786043	0.0495161
$253$	−23.3184	−1.46601
$254$	11.3451	0.711855
$255$	0	0
$256$	−15.5693	−0.973080
$257$	−9.73884	−0.607492	−0.303746	−	0.952753i	$-0.598237\pi$
$257$	−9.73884	−0.607492	−0.303746	+	0.952753i	$0.598237\pi$
$258$	−11.4136	−0.710583
$259$	−3.68208	−0.228793
$260$	0	0
$261$	−8.16879	−0.505635
$262$	5.42285	0.335025
$263$	20.0693	1.23753	0.618763	−	0.785578i	$-0.287634\pi$
$263$	20.0693	1.23753	0.618763	+	0.785578i	$0.287634\pi$
$264$	9.35152	0.575546
$265$	0	0
$266$	−6.50597	−0.398907
$267$	−8.78928	−0.537895
$268$	−1.87884	−0.114769
$269$	13.3115	0.811617	0.405808	−	0.913958i	$-0.366990\pi$
$269$	13.3115	0.811617	0.405808	+	0.913958i	$0.366990\pi$
$270$	0	0
$271$	−7.51453	−0.456475	−0.228238	−	0.973605i	$-0.573296\pi$
$271$	−7.51453	−0.456475	−0.228238	+	0.973605i	$0.573296\pi$
$272$	−1.81005	−0.109750
$273$	−0.439346	−0.0265905
$274$	2.13774	0.129146
$275$	0	0
$276$	6.01661	0.362157
$277$	15.6195	0.938484	0.469242	−	0.883070i	$-0.344527\pi$
$277$	15.6195	0.938484	0.469242	+	0.883070i	$0.344527\pi$
$278$	−4.20234	−0.252040
$279$	9.73478	0.582806
$280$	0	0
$281$	9.60615	0.573055	0.286527	−	0.958072i	$-0.407499\pi$
$281$	9.60615	0.573055	0.286527	+	0.958072i	$0.407499\pi$
$282$	−10.2830	−0.612341
$283$	−11.4373	−0.679877	−0.339938	−	0.940448i	$-0.610406\pi$
$283$	−11.4373	−0.679877	−0.339938	+	0.940448i	$0.610406\pi$
$284$	−1.84621	−0.109553
$285$	0	0
$286$	−1.47469	−0.0872004
$287$	−8.19605	−0.483798
$288$	−4.14500	−0.244247
$289$	1.00000	0.0588235
$290$	0	0
$291$	−3.56287	−0.208859
$292$	−2.38394	−0.139510
$293$	12.2750	0.717111	0.358555	−	0.933508i	$-0.383269\pi$
$293$	12.2750	0.717111	0.358555	+	0.933508i	$0.383269\pi$
$294$	1.10180	0.0642581
$295$	0	0
$296$	11.3027	0.656957
$297$	3.04644	0.176772
$298$	−3.13739	−0.181744
$299$	−3.36289	−0.194481
$300$	0	0
$301$	10.3591	0.597090
$302$	−2.06351	−0.118741
$303$	−15.9788	−0.917958
$304$	10.6881	0.613005
$305$	0	0
$306$	−1.10180	−0.0629855
$307$	5.40443	0.308447	0.154224	−	0.988036i	$-0.450712\pi$
$307$	5.40443	0.308447	0.154224	+	0.988036i	$0.450712\pi$
$308$	−2.39463	−0.136447
$309$	−7.30742	−0.415704
$310$	0	0
$311$	32.2620	1.82941	0.914706	−	0.404120i	$-0.132422\pi$
$311$	32.2620	1.82941	0.914706	+	0.404120i	$0.132422\pi$
$312$	1.34864	0.0763518
$313$	−21.0758	−1.19128	−0.595638	−	0.803253i	$-0.703101\pi$
$313$	−21.0758	−1.19128	−0.595638	+	0.803253i	$0.703101\pi$
$314$	9.45530	0.533593
$315$	0	0
$316$	8.95262	0.503624
$317$	3.98509	0.223825	0.111912	−	0.993718i	$-0.464302\pi$
$317$	3.98509	0.223825	0.111912	+	0.993718i	$0.464302\pi$
$318$	−13.7144	−0.769063
$319$	24.8857	1.39333
$320$	0	0
$321$	8.43009	0.470522
$322$	8.43348	0.469980
$323$	−5.90487	−0.328556
$324$	−0.786043	−0.0436691
$325$	0	0
$326$	−25.4380	−1.40888
$327$	−4.50550	−0.249155
$328$	25.1590	1.38918
$329$	9.33290	0.514539
$330$	0	0
$331$	−8.35495	−0.459230	−0.229615	−	0.973282i	$-0.573747\pi$
$331$	−8.35495	−0.459230	−0.229615	+	0.973282i	$0.573747\pi$
$332$	8.01025	0.439619
$333$	3.68208	0.201777
$334$	3.73934	0.204608
$335$	0	0
$336$	−1.81005	−0.0987463
$337$	−14.9303	−0.813306	−0.406653	−	0.913583i	$-0.633304\pi$
$337$	−14.9303	−0.813306	−0.406653	+	0.913583i	$0.633304\pi$
$338$	14.1107	0.767520
$339$	−6.16464	−0.334817
$340$	0	0
$341$	−29.6564	−1.60598
$342$	6.50597	0.351803
$343$	−1.00000	−0.0539949
$344$	−31.7989	−1.71448
$345$	0	0
$346$	2.81853	0.151525
$347$	3.39494	0.182250	0.0911249	−	0.995839i	$-0.470954\pi$
$347$	3.39494	0.182250	0.0911249	+	0.995839i	$0.470954\pi$
$348$	−6.42102	−0.344203
$349$	−15.7574	−0.843475	−0.421737	−	0.906718i	$-0.638580\pi$
$349$	−15.7574	−0.843475	−0.421737	+	0.906718i	$0.638580\pi$
$350$	0	0
$351$	0.439346	0.0234506
$352$	12.6275	0.673048
$353$	−23.7404	−1.26358	−0.631788	−	0.775141i	$-0.717679\pi$
$353$	−23.7404	−1.26358	−0.631788	+	0.775141i	$0.717679\pi$
$354$	11.6012	0.616597
$355$	0	0
$356$	−6.90876	−0.366163
$357$	1.00000	0.0529256
$358$	−8.63477	−0.456362
$359$	31.2687	1.65030	0.825148	−	0.564916i	$-0.191092\pi$
$359$	31.2687	1.65030	0.825148	+	0.564916i	$0.191092\pi$
$360$	0	0
$361$	15.8675	0.835132
$362$	25.1713	1.32298
$363$	1.71920	0.0902349
$364$	−0.345345	−0.0181010
$365$	0	0
$366$	13.3766	0.699205
$367$	22.1182	1.15456	0.577279	−	0.816547i	$-0.304114\pi$
$367$	22.1182	1.15456	0.577279	+	0.816547i	$0.304114\pi$
$368$	−13.8547	−0.722224
$369$	8.19605	0.426669
$370$	0	0
$371$	12.4473	0.646229
$372$	7.65196	0.396735
$373$	−17.9326	−0.928514	−0.464257	−	0.885701i	$-0.653679\pi$
$373$	−17.9326	−0.928514	−0.464257	+	0.885701i	$0.653679\pi$
$374$	3.35656	0.173563
$375$	0	0
$376$	−28.6488	−1.47745
$377$	3.58893	0.184839
$378$	−1.10180	−0.0566703
$379$	−24.4538	−1.25611	−0.628053	−	0.778171i	$-0.716148\pi$
$379$	−24.4538	−1.25611	−0.628053	+	0.778171i	$0.716148\pi$
$380$	0	0
$381$	10.2969	0.527527
$382$	10.2528	0.524581
$383$	−33.0565	−1.68911	−0.844555	−	0.535469i	$-0.820135\pi$
$383$	−33.0565	−1.68911	−0.844555	+	0.535469i	$0.820135\pi$
$384$	0.730462	0.0372762
$385$	0	0
$386$	−21.4152	−1.09001
$387$	−10.3591	−0.526584
$388$	−2.80057	−0.142178
$389$	24.9851	1.26679	0.633397	−	0.773827i	$-0.281660\pi$
$389$	24.9851	1.26679	0.633397	+	0.773827i	$0.281660\pi$
$390$	0	0
$391$	7.65430	0.387094
$392$	3.06965	0.155041
$393$	4.92183	0.248273
$394$	−21.0788	−1.06194
$395$	0	0
$396$	2.39463	0.120335
$397$	−19.9555	−1.00154	−0.500768	−	0.865582i	$-0.666949\pi$
$397$	−19.9555	−1.00154	−0.500768	+	0.865582i	$0.666949\pi$
$398$	8.62889	0.432527
$399$	−5.90487	−0.295613
$400$	0	0
$401$	16.3095	0.814458	0.407229	−	0.913326i	$-0.366495\pi$
$401$	16.3095	0.814458	0.407229	+	0.913326i	$0.366495\pi$
$402$	2.63358	0.131351
$403$	−4.27694	−0.213050
$404$	−12.5600	−0.624885
$405$	0	0
$406$	−9.00035	−0.446680
$407$	−11.2172	−0.556017
$408$	−3.06965	−0.151971
$409$	−0.397490	−0.0196546	−0.00982730	−	0.999952i	$-0.503128\pi$
$409$	−0.397490	−0.0196546	−0.00982730	+	0.999952i	$0.503128\pi$
$410$	0	0
$411$	1.94023	0.0957045
$412$	−5.74395	−0.282984
$413$	−10.5293	−0.518115
$414$	−8.43348	−0.414483
$415$	0	0
$416$	1.82109	0.0892864
$417$	−3.81408	−0.186776
$418$	−19.8200	−0.969430
$419$	−20.3671	−0.995000	−0.497500	−	0.867464i	$-0.665748\pi$
$419$	−20.3671	−0.995000	−0.497500	+	0.867464i	$0.665748\pi$
$420$	0	0
$421$	−26.6356	−1.29814	−0.649071	−	0.760728i	$-0.724842\pi$
$421$	−26.6356	−1.29814	−0.649071	+	0.760728i	$0.724842\pi$
$422$	−10.7567	−0.523629
$423$	−9.33290	−0.453781
$424$	−38.2088	−1.85558
$425$	0	0
$426$	2.58784	0.125381
$427$	−12.1407	−0.587530
$428$	6.62641	0.320300
$429$	−1.33844	−0.0646206
$430$	0	0
$431$	11.5505	0.556368	0.278184	−	0.960528i	$-0.410268\pi$
$431$	11.5505	0.556368	0.278184	+	0.960528i	$0.410268\pi$
$432$	1.81005	0.0870860
$433$	2.95930	0.142215	0.0711074	−	0.997469i	$-0.477347\pi$
$433$	2.95930	0.142215	0.0711074	+	0.997469i	$0.477347\pi$
$434$	10.7257	0.514852
$435$	0	0
$436$	−3.54152	−0.169608
$437$	−45.1976	−2.16210
$438$	3.34158	0.159667
$439$	15.5747	0.743338	0.371669	−	0.928365i	$-0.378786\pi$
$439$	15.5747	0.743338	0.371669	+	0.928365i	$0.378786\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0.484071	0.0230249
$443$	6.36488	0.302405	0.151202	−	0.988503i	$-0.451685\pi$
$443$	6.36488	0.302405	0.151202	+	0.988503i	$0.451685\pi$
$444$	2.89427	0.137356
$445$	0	0
$446$	−6.81463	−0.322682
$447$	−2.84752	−0.134683
$448$	−8.18705	−0.386802
$449$	−3.81045	−0.179826	−0.0899131	−	0.995950i	$-0.528659\pi$
$449$	−3.81045	−0.179826	−0.0899131	+	0.995950i	$0.528659\pi$
$450$	0	0
$451$	−24.9688	−1.17573
$452$	−4.84567	−0.227921
$453$	−1.87286	−0.0879944
$454$	11.2400	0.527522
$455$	0	0
$456$	18.1259	0.848824
$457$	−15.3587	−0.718452	−0.359226	−	0.933251i	$-0.616959\pi$
$457$	−15.3587	−0.718452	−0.359226	+	0.933251i	$0.616959\pi$
$458$	−0.190626	−0.00890739
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	−22.0311	−1.02609	−0.513045	−	0.858361i	$-0.671483\pi$
$461$	−22.0311	−1.02609	−0.513045	+	0.858361i	$0.671483\pi$
$462$	3.35656	0.156161
$463$	−36.3054	−1.68725	−0.843627	−	0.536930i	$-0.819584\pi$
$463$	−36.3054	−1.68725	−0.843627	+	0.536930i	$0.819584\pi$
$464$	14.7859	0.686418
$465$	0	0
$466$	10.6742	0.494472
$467$	−30.3145	−1.40279	−0.701393	−	0.712775i	$-0.747438\pi$
$467$	−30.3145	−1.40279	−0.701393	+	0.712775i	$0.747438\pi$
$468$	0.345345	0.0159636
$469$	−2.39025	−0.110372
$470$	0	0
$471$	8.58171	0.395424
$472$	32.3214	1.48771
$473$	31.5584	1.45106
$474$	−12.5489	−0.576390
$475$	0	0
$476$	0.786043	0.0360282
$477$	−12.4473	−0.569921
$478$	−15.1969	−0.695089
$479$	−42.1665	−1.92664	−0.963318	−	0.268361i	$-0.913518\pi$
$479$	−42.1665	−1.92664	−0.963318	+	0.268361i	$0.913518\pi$
$480$	0	0
$481$	−1.61771	−0.0737611
$482$	−16.3597	−0.745165
$483$	7.65430	0.348283
$484$	1.35137	0.0614259
$485$	0	0
$486$	1.10180	0.0499785
$487$	−13.3369	−0.604351	−0.302176	−	0.953252i	$-0.597713\pi$
$487$	−13.3369	−0.604351	−0.302176	+	0.953252i	$0.597713\pi$
$488$	37.2678	1.68703
$489$	−23.0878	−1.04407
$490$	0	0
$491$	−23.8826	−1.07781	−0.538904	−	0.842367i	$-0.681162\pi$
$491$	−23.8826	−1.07781	−0.538904	+	0.842367i	$0.681162\pi$
$492$	6.44245	0.290448
$493$	−8.16879	−0.367904
$494$	−2.85837	−0.128604
$495$	0	0
$496$	−17.6204	−0.791180
$497$	−2.34874	−0.105356
$498$	−11.2280	−0.503137
$499$	40.4328	1.81002	0.905011	−	0.425388i	$-0.139862\pi$
$499$	40.4328	1.81002	0.905011	+	0.425388i	$0.139862\pi$
$500$	0	0
$501$	3.39386	0.151626
$502$	−5.96369	−0.266173
$503$	−41.7195	−1.86018	−0.930091	−	0.367329i	$-0.880272\pi$
$503$	−41.7195	−1.86018	−0.930091	+	0.367329i	$0.880272\pi$
$504$	−3.06965	−0.136733
$505$	0	0
$506$	25.6921	1.14215
$507$	12.8070	0.568778
$508$	8.09382	0.359105
$509$	28.0323	1.24251	0.621256	−	0.783608i	$-0.286623\pi$
$509$	28.0323	1.24251	0.621256	+	0.783608i	$0.286623\pi$
$510$	0	0
$511$	−3.03284	−0.134165
$512$	18.6151	0.822679
$513$	5.90487	0.260706
$514$	10.7302	0.473290
$515$	0	0
$516$	−8.14272	−0.358463
$517$	28.4321	1.25044
$518$	4.05690	0.178250
$519$	2.55812	0.112289
$520$	0	0
$521$	14.2991	0.626455	0.313227	−	0.949678i	$-0.398590\pi$
$521$	14.2991	0.626455	0.313227	+	0.949678i	$0.398590\pi$
$522$	9.00035	0.393934
$523$	−36.8839	−1.61282	−0.806409	−	0.591358i	$-0.798592\pi$
$523$	−36.8839	−1.61282	−0.806409	+	0.591358i	$0.798592\pi$
$524$	3.86877	0.169008
$525$	0	0
$526$	−22.1123	−0.964142
$527$	9.73478	0.424053
$528$	−5.51421	−0.239975
$529$	35.5883	1.54732
$530$	0	0
$531$	10.5293	0.456934
$532$	−4.64148	−0.201234
$533$	−3.60091	−0.155973
$534$	9.68401	0.419068
$535$	0	0
$536$	7.33726	0.316921
$537$	−7.83699	−0.338191
$538$	−14.6666	−0.632321
$539$	−3.04644	−0.131219
$540$	0	0
$541$	−42.2184	−1.81511	−0.907555	−	0.419933i	$-0.862054\pi$
$541$	−42.2184	−1.81511	−0.907555	+	0.419933i	$0.862054\pi$
$542$	8.27949	0.355635
$543$	22.8457	0.980403
$544$	−4.14500	−0.177715
$545$	0	0
$546$	0.484071	0.0207163
$547$	25.9995	1.11166	0.555829	−	0.831296i	$-0.312401\pi$
$547$	25.9995	1.11166	0.555829	+	0.831296i	$0.312401\pi$
$548$	1.52510	0.0651492
$549$	12.1407	0.518152
$550$	0	0
$551$	48.2356	2.05491
$552$	−23.4960	−1.00006
$553$	11.3895	0.484330
$554$	−17.2095	−0.731162
$555$	0	0
$556$	−2.99803	−0.127145
$557$	35.3873	1.49941	0.749704	−	0.661773i	$-0.230196\pi$
$557$	35.3873	1.49941	0.749704	+	0.661773i	$0.230196\pi$
$558$	−10.7257	−0.454057
$559$	4.55124	0.192497
$560$	0	0
$561$	3.04644	0.128621
$562$	−10.5840	−0.446460
$563$	−16.3680	−0.689831	−0.344915	−	0.938634i	$-0.612092\pi$
$563$	−16.3680	−0.689831	−0.344915	+	0.938634i	$0.612092\pi$
$564$	−7.33606	−0.308904
$565$	0	0
$566$	12.6016	0.529684
$567$	−1.00000	−0.0419961
$568$	7.20983	0.302518
$569$	−30.6319	−1.28416	−0.642079	−	0.766638i	$-0.721928\pi$
$569$	−30.6319	−1.28416	−0.642079	+	0.766638i	$0.721928\pi$
$570$	0	0
$571$	−41.5486	−1.73875	−0.869376	−	0.494150i	$-0.835479\pi$
$571$	−41.5486	−1.73875	−0.869376	+	0.494150i	$0.835479\pi$
$572$	−1.05207	−0.0439894
$573$	9.30557	0.388746
$574$	9.03039	0.376921
$575$	0	0
$576$	8.18705	0.341127
$577$	−12.6099	−0.524955	−0.262478	−	0.964938i	$-0.584540\pi$
$577$	−12.6099	−0.524955	−0.262478	+	0.964938i	$0.584540\pi$
$578$	−1.10180	−0.0458287
$579$	−19.4366	−0.807759
$580$	0	0
$581$	10.1906	0.422777
$582$	3.92556	0.162720
$583$	37.9198	1.57048
$584$	9.30977	0.385241
$585$	0	0
$586$	−13.5245	−0.558692
$587$	10.9579	0.452282	0.226141	−	0.974095i	$-0.427389\pi$
$587$	10.9579	0.452282	0.226141	+	0.974095i	$0.427389\pi$
$588$	0.786043	0.0324159
$589$	−57.4826	−2.36853
$590$	0	0
$591$	−19.1313	−0.786957
$592$	−6.66474	−0.273919
$593$	43.7442	1.79636	0.898180	−	0.439627i	$-0.144889\pi$
$593$	43.7442	1.79636	0.898180	+	0.439627i	$0.144889\pi$
$594$	−3.35656	−0.137721
$595$	0	0
$596$	−2.23828	−0.0916833
$597$	7.83165	0.320528
$598$	3.70522	0.151518
$599$	−13.8647	−0.566498	−0.283249	−	0.959046i	$-0.591412\pi$
$599$	−13.8647	−0.566498	−0.283249	+	0.959046i	$0.591412\pi$
$600$	0	0
$601$	−27.8746	−1.13703	−0.568514	−	0.822673i	$-0.692482\pi$
$601$	−27.8746	−1.13703	−0.568514	+	0.822673i	$0.692482\pi$
$602$	−11.4136	−0.465186
$603$	2.39025	0.0973387
$604$	−1.47215	−0.0599008
$605$	0	0
$606$	17.6054	0.715170
$607$	2.81833	0.114392	0.0571962	−	0.998363i	$-0.481784\pi$
$607$	2.81833	0.114392	0.0571962	+	0.998363i	$0.481784\pi$
$608$	24.4757	0.992621
$609$	−8.16879	−0.331016
$610$	0	0
$611$	4.10038	0.165883
$612$	−0.786043	−0.0317739
$613$	−12.5272	−0.505970	−0.252985	−	0.967470i	$-0.581412\pi$
$613$	−12.5272	−0.505970	−0.252985	+	0.967470i	$0.581412\pi$
$614$	−5.95458	−0.240307
$615$	0	0
$616$	9.35152	0.376783
$617$	48.3928	1.94822	0.974111	−	0.226069i	$-0.0725876\pi$
$617$	48.3928	1.94822	0.974111	+	0.226069i	$0.0725876\pi$
$618$	8.05129	0.323870
$619$	−19.4428	−0.781471	−0.390735	−	0.920503i	$-0.627779\pi$
$619$	−19.4428	−0.781471	−0.390735	+	0.920503i	$0.627779\pi$
$620$	0	0
$621$	−7.65430	−0.307156
$622$	−35.5462	−1.42527
$623$	−8.78928	−0.352135
$624$	−0.795239	−0.0318350
$625$	0	0
$626$	23.2213	0.928108
$627$	−17.9888	−0.718405
$628$	6.74559	0.269179
$629$	3.68208	0.146814
$630$	0	0
$631$	4.93929	0.196630	0.0983149	−	0.995155i	$-0.468655\pi$
$631$	4.93929	0.196630	0.0983149	+	0.995155i	$0.468655\pi$
$632$	−34.9618	−1.39070
$633$	−9.76289	−0.388040
$634$	−4.39076	−0.174379
$635$	0	0
$636$	−9.78409	−0.387964
$637$	−0.439346	−0.0174075
$638$	−27.4190	−1.08553
$639$	2.34874	0.0929148
$640$	0	0
$641$	−32.2483	−1.27373	−0.636865	−	0.770976i	$-0.719769\pi$
$641$	−32.2483	−1.27373	−0.636865	+	0.770976i	$0.719769\pi$
$642$	−9.28824	−0.366578
$643$	−27.7433	−1.09409	−0.547045	−	0.837103i	$-0.684247\pi$
$643$	−27.7433	−1.09409	−0.547045	+	0.837103i	$0.684247\pi$
$644$	6.01661	0.237088
$645$	0	0
$646$	6.50597	0.255974
$647$	1.02524	0.0403063	0.0201531	−	0.999797i	$-0.493585\pi$
$647$	1.02524	0.0403063	0.0201531	+	0.999797i	$0.493585\pi$
$648$	3.06965	0.120587
$649$	−32.0770	−1.25913
$650$	0	0
$651$	9.73478	0.381536
$652$	−18.1480	−0.710730
$653$	−50.1760	−1.96354	−0.981769	−	0.190080i	$-0.939125\pi$
$653$	−50.1760	−1.96354	−0.981769	+	0.190080i	$0.939125\pi$
$654$	4.96415	0.194114
$655$	0	0
$656$	−14.8353	−0.579219
$657$	3.03284	0.118322
$658$	−10.2830	−0.400872
$659$	−43.9669	−1.71271	−0.856355	−	0.516388i	$-0.827276\pi$
$659$	−43.9669	−1.71271	−0.856355	+	0.516388i	$0.827276\pi$
$660$	0	0
$661$	−15.5771	−0.605879	−0.302939	−	0.953010i	$-0.597968\pi$
$661$	−15.5771	−0.605879	−0.302939	+	0.953010i	$0.597968\pi$
$662$	9.20546	0.357780
$663$	0.439346	0.0170628
$664$	−31.2816	−1.21396
$665$	0	0
$666$	−4.05690	−0.157202
$667$	−62.5263	−2.42103
$668$	2.66772	0.103217
$669$	−6.18501	−0.239126
$670$	0	0
$671$	−36.9859	−1.42783
$672$	−4.14500	−0.159897
$673$	−38.4772	−1.48319	−0.741594	−	0.670848i	$-0.765930\pi$
$673$	−38.4772	−1.48319	−0.741594	+	0.670848i	$0.765930\pi$
$674$	16.4502	0.633637
$675$	0	0
$676$	10.0668	0.387186
$677$	−19.3144	−0.742312	−0.371156	−	0.928570i	$-0.621039\pi$
$677$	−19.3144	−0.742312	−0.371156	+	0.928570i	$0.621039\pi$
$678$	6.79218	0.260852
$679$	−3.56287	−0.136730
$680$	0	0
$681$	10.2016	0.390925
$682$	32.6753	1.25120
$683$	0.181089	0.00692916	0.00346458	−	0.999994i	$-0.498897\pi$
$683$	0.181089	0.00692916	0.00346458	+	0.999994i	$0.498897\pi$
$684$	4.64148	0.177472
$685$	0	0
$686$	1.10180	0.0420668
$687$	−0.173014	−0.00660090
$688$	18.7505	0.714857
$689$	5.46866	0.208339
$690$	0	0
$691$	7.55113	0.287259	0.143629	−	0.989632i	$-0.454123\pi$
$691$	7.55113	0.287259	0.143629	+	0.989632i	$0.454123\pi$
$692$	2.01080	0.0764390
$693$	3.04644	0.115725
$694$	−3.74053	−0.141989
$695$	0	0
$696$	25.0754	0.950479
$697$	8.19605	0.310448
$698$	17.3615	0.657141
$699$	9.68797	0.366433
$700$	0	0
$701$	13.7957	0.521058	0.260529	−	0.965466i	$-0.416103\pi$
$701$	13.7957	0.521058	0.260529	+	0.965466i	$0.416103\pi$
$702$	−0.484071	−0.0182701
$703$	−21.7422	−0.820023
$704$	−24.9414	−0.940013
$705$	0	0
$706$	26.1571	0.984437
$707$	−15.9788	−0.600945
$708$	8.27652	0.311051
$709$	25.3542	0.952196	0.476098	−	0.879392i	$-0.342051\pi$
$709$	25.3542	0.952196	0.476098	+	0.879392i	$0.342051\pi$
$710$	0	0
$711$	−11.3895	−0.427139
$712$	26.9801	1.01112
$713$	74.5129	2.79053
$714$	−1.10180	−0.0412337
$715$	0	0
$716$	−6.16021	−0.230218
$717$	−13.7928	−0.515102
$718$	−34.4517	−1.28573
$719$	−14.1092	−0.526186	−0.263093	−	0.964770i	$-0.584743\pi$
$719$	−14.1092	−0.526186	−0.263093	+	0.964770i	$0.584743\pi$
$720$	0	0
$721$	−7.30742	−0.272142
$722$	−17.4828	−0.650641
$723$	−14.8482	−0.552211
$724$	17.9577	0.667393
$725$	0	0
$726$	−1.89421	−0.0703009
$727$	−17.6802	−0.655721	−0.327860	−	0.944726i	$-0.606328\pi$
$727$	−17.6802	−0.655721	−0.327860	+	0.944726i	$0.606328\pi$
$728$	1.34864	0.0499840
$729$	1.00000	0.0370370
$730$	0	0
$731$	−10.3591	−0.383146
$732$	9.54312	0.352724
$733$	−35.4352	−1.30883	−0.654414	−	0.756136i	$-0.727085\pi$
$733$	−35.4352	−1.30883	−0.654414	+	0.756136i	$0.727085\pi$
$734$	−24.3697	−0.899503
$735$	0	0
$736$	−31.7271	−1.16948
$737$	−7.28177	−0.268227
$738$	−9.03039	−0.332413
$739$	17.4636	0.642408	0.321204	−	0.947010i	$-0.395912\pi$
$739$	17.4636	0.642408	0.321204	+	0.947010i	$0.395912\pi$
$740$	0	0
$741$	−2.59428	−0.0953034
$742$	−13.7144	−0.503470
$743$	−10.6247	−0.389784	−0.194892	−	0.980825i	$-0.562436\pi$
$743$	−10.6247	−0.389784	−0.194892	+	0.980825i	$0.562436\pi$
$744$	−29.8824	−1.09554
$745$	0	0
$746$	19.7581	0.723394
$747$	−10.1906	−0.372854
$748$	2.39463	0.0875565
$749$	8.43009	0.308029
$750$	0	0
$751$	−18.2518	−0.666018	−0.333009	−	0.942924i	$-0.608064\pi$
$751$	−18.2518	−0.666018	−0.333009	+	0.942924i	$0.608064\pi$
$752$	16.8930	0.616025
$753$	−5.41270	−0.197250
$754$	−3.95427	−0.144006
$755$	0	0
$756$	−0.786043	−0.0285881
$757$	−5.39572	−0.196111	−0.0980554	−	0.995181i	$-0.531262\pi$
$757$	−5.39572	−0.196111	−0.0980554	+	0.995181i	$0.531262\pi$
$758$	26.9431	0.978617
$759$	23.3184	0.846403
$760$	0	0
$761$	0.498875	0.0180842	0.00904210	−	0.999959i	$-0.497122\pi$
$761$	0.498875	0.0180842	0.00904210	+	0.999959i	$0.497122\pi$
$762$	−11.3451	−0.410990
$763$	−4.50550	−0.163110
$764$	7.31458	0.264632
$765$	0	0
$766$	36.4216	1.31597
$767$	−4.62603	−0.167036
$768$	15.5693	0.561808
$769$	−18.3495	−0.661698	−0.330849	−	0.943684i	$-0.607335\pi$
$769$	−18.3495	−0.661698	−0.330849	+	0.943684i	$0.607335\pi$
$770$	0	0
$771$	9.73884	0.350736
$772$	−15.2780	−0.549869
$773$	19.7746	0.711242	0.355621	−	0.934630i	$-0.384269\pi$
$773$	19.7746	0.711242	0.355621	+	0.934630i	$0.384269\pi$
$774$	11.4136	0.410255
$775$	0	0
$776$	10.9368	0.392608
$777$	3.68208	0.132094
$778$	−27.5285	−0.986944
$779$	−48.3966	−1.73399
$780$	0	0
$781$	−7.15530	−0.256037
$782$	−8.43348	−0.301581
$783$	8.16879	0.291929
$784$	−1.81005	−0.0646446
$785$	0	0
$786$	−5.42285	−0.193427
$787$	−54.9074	−1.95724	−0.978620	−	0.205679i	$-0.934060\pi$
$787$	−54.9074	−1.95724	−0.978620	+	0.205679i	$0.934060\pi$
$788$	−15.0380	−0.535708
$789$	−20.0693	−0.714486
$790$	0	0
$791$	−6.16464	−0.219189
$792$	−9.35152	−0.332292
$793$	−5.33397	−0.189415
$794$	21.9869	0.780284
$795$	0	0
$796$	6.15602	0.218194
$797$	1.68210	0.0595829	0.0297915	−	0.999556i	$-0.490516\pi$
$797$	1.68210	0.0595829	0.0297915	+	0.999556i	$0.490516\pi$
$798$	6.50597	0.230309
$799$	−9.33290	−0.330174
$800$	0	0
$801$	8.78928	0.310554
$802$	−17.9698	−0.634534
$803$	−9.23937	−0.326050
$804$	1.87884	0.0662617
$805$	0	0
$806$	4.71232	0.165984
$807$	−13.3115	−0.468587
$808$	49.0494	1.72555
$809$	−23.3025	−0.819271	−0.409635	−	0.912249i	$-0.634344\pi$
$809$	−23.3025	−0.819271	−0.409635	+	0.912249i	$0.634344\pi$
$810$	0	0
$811$	34.6479	1.21665	0.608326	−	0.793687i	$-0.291841\pi$
$811$	34.6479	1.21665	0.608326	+	0.793687i	$0.291841\pi$
$812$	−6.42102	−0.225334
$813$	7.51453	0.263546
$814$	12.3591	0.433187
$815$	0	0
$816$	1.81005	0.0633644
$817$	61.1693	2.14004
$818$	0.437953	0.0153127
$819$	0.439346	0.0153520
$820$	0	0
$821$	−49.0570	−1.71210	−0.856050	−	0.516893i	$-0.827089\pi$
$821$	−49.0570	−1.71210	−0.856050	+	0.516893i	$0.827089\pi$
$822$	−2.13774	−0.0745622
$823$	36.0235	1.25570	0.627850	−	0.778335i	$-0.283935\pi$
$823$	36.0235	1.25570	0.627850	+	0.778335i	$0.283935\pi$
$824$	22.4312	0.781429
$825$	0	0
$826$	11.6012	0.403657
$827$	−20.2569	−0.704400	−0.352200	−	0.935925i	$-0.614566\pi$
$827$	−20.2569	−0.704400	−0.352200	+	0.935925i	$0.614566\pi$
$828$	−6.01661	−0.209092
$829$	−8.08234	−0.280711	−0.140356	−	0.990101i	$-0.544825\pi$
$829$	−8.08234	−0.280711	−0.140356	+	0.990101i	$0.544825\pi$
$830$	0	0
$831$	−15.6195	−0.541834
$832$	−3.59695	−0.124702
$833$	1.00000	0.0346479
$834$	4.20234	0.145515
$835$	0	0
$836$	−14.1400	−0.489042
$837$	−9.73478	−0.336483
$838$	22.4404	0.775192
$839$	7.77593	0.268455	0.134227	−	0.990951i	$-0.457145\pi$
$839$	7.77593	0.268455	0.134227	+	0.990951i	$0.457145\pi$
$840$	0	0
$841$	37.7291	1.30100
$842$	29.3471	1.01137
$843$	−9.60615	−0.330853
$844$	−7.67406	−0.264152
$845$	0	0
$846$	10.2830	0.353535
$847$	1.71920	0.0590726
$848$	22.5301	0.773688
$849$	11.4373	0.392527
$850$	0	0
$851$	28.1837	0.966126
$852$	1.84621	0.0632502
$853$	16.3466	0.559697	0.279848	−	0.960044i	$-0.409716\pi$
$853$	16.3466	0.559697	0.279848	+	0.960044i	$0.409716\pi$
$854$	13.3766	0.457737
$855$	0	0
$856$	−25.8774	−0.884473
$857$	39.7324	1.35723	0.678617	−	0.734493i	$-0.262580\pi$
$857$	39.7324	1.35723	0.678617	+	0.734493i	$0.262580\pi$
$858$	1.47469	0.0503452
$859$	−21.9711	−0.749646	−0.374823	−	0.927096i	$-0.622296\pi$
$859$	−21.9711	−0.749646	−0.374823	+	0.927096i	$0.622296\pi$
$860$	0	0
$861$	8.19605	0.279321
$862$	−12.7263	−0.433459
$863$	28.2334	0.961077	0.480538	−	0.876974i	$-0.340441\pi$
$863$	28.2334	0.961077	0.480538	+	0.876974i	$0.340441\pi$
$864$	4.14500	0.141016
$865$	0	0
$866$	−3.26054	−0.110798
$867$	−1.00000	−0.0339618
$868$	7.65196	0.259724
$869$	34.6974	1.17703
$870$	0	0
$871$	−1.05015	−0.0355830
$872$	13.8303	0.468354
$873$	3.56287	0.120585
$874$	49.7986	1.68446
$875$	0	0
$876$	2.38394	0.0805460
$877$	−41.0884	−1.38746	−0.693729	−	0.720237i	$-0.744033\pi$
$877$	−41.0884	−1.38746	−0.693729	+	0.720237i	$0.744033\pi$
$878$	−17.1601	−0.579126
$879$	−12.2750	−0.414024
$880$	0	0
$881$	−45.6061	−1.53651	−0.768255	−	0.640144i	$-0.778875\pi$
$881$	−45.6061	−1.53651	−0.768255	+	0.640144i	$0.778875\pi$
$882$	−1.10180	−0.0370994
$883$	−13.5143	−0.454794	−0.227397	−	0.973802i	$-0.573021\pi$
$883$	−13.5143	−0.454794	−0.227397	+	0.973802i	$0.573021\pi$
$884$	0.345345	0.0116152
$885$	0	0
$886$	−7.01281	−0.235600
$887$	−45.8729	−1.54026	−0.770130	−	0.637886i	$-0.779809\pi$
$887$	−45.8729	−1.54026	−0.770130	+	0.637886i	$0.779809\pi$
$888$	−11.3027	−0.379294
$889$	10.2969	0.345347
$890$	0	0
$891$	−3.04644	−0.102060
$892$	−4.86169	−0.162781
$893$	55.1096	1.84417
$894$	3.13739	0.104930
$895$	0	0
$896$	0.730462	0.0244030
$897$	3.36289	0.112284
$898$	4.19834	0.140100
$899$	−79.5213	−2.65218
$900$	0	0
$901$	−12.4473	−0.414678
$902$	27.5105	0.916000
$903$	−10.3591	−0.344730
$904$	18.9233	0.629380
$905$	0	0
$906$	2.06351	0.0685554
$907$	−33.6478	−1.11726	−0.558629	−	0.829418i	$-0.688672\pi$
$907$	−33.6478	−1.11726	−0.558629	+	0.829418i	$0.688672\pi$
$908$	8.01887	0.266116
$909$	15.9788	0.529983
$910$	0	0
$911$	−9.72408	−0.322173	−0.161087	−	0.986940i	$-0.551500\pi$
$911$	−9.72408	−0.322173	−0.161087	+	0.986940i	$0.551500\pi$
$912$	−10.6881	−0.353919
$913$	31.0450	1.02744
$914$	16.9222	0.559737
$915$	0	0
$916$	−0.135997	−0.00449345
$917$	4.92183	0.162533
$918$	1.10180	0.0363647
$919$	9.65047	0.318340	0.159170	−	0.987251i	$-0.449118\pi$
$919$	9.65047	0.318340	0.159170	+	0.987251i	$0.449118\pi$
$920$	0	0
$921$	−5.40443	−0.178082
$922$	24.2738	0.799415
$923$	−1.03191	−0.0339658
$924$	2.39463	0.0787777
$925$	0	0
$926$	40.0012	1.31452
$927$	7.30742	0.240007
$928$	33.8596	1.11150
$929$	28.8272	0.945790	0.472895	−	0.881119i	$-0.343209\pi$
$929$	28.8272	0.945790	0.472895	+	0.881119i	$0.343209\pi$
$930$	0	0
$931$	−5.90487	−0.193524
$932$	7.61517	0.249443
$933$	−32.2620	−1.05621
$934$	33.4004	1.09289
$935$	0	0
$936$	−1.34864	−0.0440817
$937$	−3.70199	−0.120939	−0.0604694	−	0.998170i	$-0.519260\pi$
$937$	−3.70199	−0.120939	−0.0604694	+	0.998170i	$0.519260\pi$
$938$	2.63358	0.0859893
$939$	21.0758	0.687783
$940$	0	0
$941$	−2.27664	−0.0742163	−0.0371081	−	0.999311i	$-0.511815\pi$
$941$	−2.27664	−0.0742163	−0.0371081	+	0.999311i	$0.511815\pi$
$942$	−9.45530	−0.308070
$943$	62.7350	2.04293
$944$	−19.0586	−0.620305
$945$	0	0
$946$	−34.7710	−1.13050
$947$	−35.7225	−1.16083	−0.580413	−	0.814322i	$-0.697109\pi$
$947$	−35.7225	−1.16083	−0.580413	+	0.814322i	$0.697109\pi$
$948$	−8.95262	−0.290768
$949$	−1.33247	−0.0432537
$950$	0	0
$951$	−3.98509	−0.129225
$952$	−3.06965	−0.0994881
$953$	2.30568	0.0746884	0.0373442	−	0.999302i	$-0.488110\pi$
$953$	2.30568	0.0746884	0.0373442	+	0.999302i	$0.488110\pi$
$954$	13.7144	0.444019
$955$	0	0
$956$	−10.8417	−0.350647
$957$	−24.8857	−0.804441
$958$	46.4589	1.50102
$959$	1.94023	0.0626533
$960$	0	0
$961$	63.7658	2.05696
$962$	1.78239	0.0574664
$963$	−8.43009	−0.271656
$964$	−11.6713	−0.375909
$965$	0	0
$966$	−8.43348	−0.271343
$967$	−34.1970	−1.09970	−0.549850	−	0.835263i	$-0.685315\pi$
$967$	−34.1970	−1.09970	−0.549850	+	0.835263i	$0.685315\pi$
$968$	−5.27736	−0.169621
$969$	5.90487	0.189692
$970$	0	0
$971$	27.4706	0.881572	0.440786	−	0.897612i	$-0.354700\pi$
$971$	27.4706	0.881572	0.440786	+	0.897612i	$0.354700\pi$
$972$	0.786043	0.0252124
$973$	−3.81408	−0.122274
$974$	14.6945	0.470843
$975$	0	0
$976$	−21.9753	−0.703411
$977$	6.27388	0.200719	0.100360	−	0.994951i	$-0.468001\pi$
$977$	6.27388	0.200719	0.100360	+	0.994951i	$0.468001\pi$
$978$	25.4380	0.813419
$979$	−26.7760	−0.855765
$980$	0	0
$981$	4.50550	0.143850
$982$	26.3138	0.839708
$983$	−53.7390	−1.71401	−0.857004	−	0.515310i	$-0.827677\pi$
$983$	−53.7390	−1.71401	−0.857004	+	0.515310i	$0.827677\pi$
$984$	−25.1590	−0.802041
$985$	0	0
$986$	9.00035	0.286629
$987$	−9.33290	−0.297069
$988$	−2.03922	−0.0648762
$989$	−79.2918	−2.52133
$990$	0	0
$991$	0.161791	0.00513947	0.00256973	−	0.999997i	$-0.499182\pi$
$991$	0.161791	0.00513947	0.00256973	+	0.999997i	$0.499182\pi$
$992$	−40.3507	−1.28113
$993$	8.35495	0.265136
$994$	2.58784	0.0820812
$995$	0	0
$996$	−8.01025	−0.253814
$997$	18.7831	0.594867	0.297433	−	0.954743i	$-0.403869\pi$
$997$	18.7831	0.594867	0.297433	+	0.954743i	$0.403869\pi$
$998$	−44.5488	−1.41017
$999$	−3.68208	−0.116496

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8925.2.a.cu.1.6		14
5.2	odd	4		1785.2.g.g.1429.11	✓	28
5.3	odd	4		1785.2.g.g.1429.18	yes	28
5.4	even	2		8925.2.a.cx.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1785.2.g.g.1429.11	✓	28	5.2	odd	4
1785.2.g.g.1429.18	yes	28	5.3	odd	4
8925.2.a.cu.1.6		14	1.1	even	1	trivial
8925.2.a.cx.1.9		14	5.4	even	2

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	8925.2.a.cu.1.6

Level	$8925$
Weight	$2$
Character	8925.1
Self dual	yes
Analytic conductor	$71.266$
Analytic rank	$1$
Dimension	$14$
CM	no
Inner twists	$1$