LMFDB - Embedded newform 1759.2.a.b.1.74

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1759,2,Mod(1,1759)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1759, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1759.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1759$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1759.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$14.0456857155$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.74
Character	$\chi$	$=$	1759.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.24492 q^{2} +3.21397 q^{3} +3.03965 q^{4} -2.36190 q^{5} +7.21508 q^{6} -1.03422 q^{7} +2.33393 q^{8} +7.32957 q^{9} -5.30226 q^{10} +6.14143 q^{11} +9.76933 q^{12} -0.596023 q^{13} -2.32173 q^{14} -7.59105 q^{15} -0.839825 q^{16} +0.0577882 q^{17} +16.4543 q^{18} +0.132713 q^{19} -7.17934 q^{20} -3.32393 q^{21} +13.7870 q^{22} -3.29501 q^{23} +7.50117 q^{24} +0.578557 q^{25} -1.33802 q^{26} +13.9151 q^{27} -3.14366 q^{28} -5.83126 q^{29} -17.0413 q^{30} +9.74636 q^{31} -6.55320 q^{32} +19.7384 q^{33} +0.129730 q^{34} +2.44271 q^{35} +22.2793 q^{36} +1.48049 q^{37} +0.297929 q^{38} -1.91560 q^{39} -5.51250 q^{40} +6.35485 q^{41} -7.46196 q^{42} -4.15748 q^{43} +18.6678 q^{44} -17.3117 q^{45} -7.39702 q^{46} -7.70719 q^{47} -2.69917 q^{48} -5.93040 q^{49} +1.29881 q^{50} +0.185729 q^{51} -1.81170 q^{52} -6.27948 q^{53} +31.2382 q^{54} -14.5054 q^{55} -2.41379 q^{56} +0.426533 q^{57} -13.0907 q^{58} +2.43438 q^{59} -23.0742 q^{60} -3.51326 q^{61} +21.8798 q^{62} -7.58036 q^{63} -13.0317 q^{64} +1.40774 q^{65} +44.3110 q^{66} -9.47401 q^{67} +0.175656 q^{68} -10.5900 q^{69} +5.48368 q^{70} +10.3934 q^{71} +17.1067 q^{72} -12.6814 q^{73} +3.32357 q^{74} +1.85946 q^{75} +0.403400 q^{76} -6.35157 q^{77} -4.30035 q^{78} +15.2086 q^{79} +1.98358 q^{80} +22.7339 q^{81} +14.2661 q^{82} +2.29076 q^{83} -10.1036 q^{84} -0.136490 q^{85} -9.33320 q^{86} -18.7415 q^{87} +14.3337 q^{88} -9.43605 q^{89} -38.8633 q^{90} +0.616416 q^{91} -10.0157 q^{92} +31.3244 q^{93} -17.3020 q^{94} -0.313453 q^{95} -21.0617 q^{96} +11.2272 q^{97} -13.3132 q^{98} +45.0141 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$86 q + 10 q^{2} + 11 q^{3} + 94 q^{4} + 30 q^{5} + 13 q^{6} + 30 q^{8} + 135 q^{9} + 9 q^{10} + 22 q^{11} + 26 q^{12} + 16 q^{13} + 52 q^{14} + 9 q^{15} + 102 q^{16} + 72 q^{17} + 21 q^{18} + 10 q^{19}+ \cdots - 17 q^{99}+O(q^{100})$ 86 * q + 10 * q^2 + 11 * q^3 + 94 * q^4 + 30 * q^5 + 13 * q^6 + 30 * q^8 + 135 * q^9 + 9 * q^10 + 22 * q^11 + 26 * q^12 + 16 * q^13 + 52 * q^14 + 9 * q^15 + 102 * q^16 + 72 * q^17 + 21 * q^18 + 10 * q^19 + 64 * q^20 + 30 * q^21 - 4 * q^22 + 15 * q^23 + 30 * q^24 + 124 * q^25 + 59 * q^26 + 35 * q^27 - 15 * q^28 + 62 * q^29 - 19 * q^30 + 27 * q^31 + 50 * q^32 + 42 * q^33 + 19 * q^34 + 39 * q^35 + 151 * q^36 + 7 * q^37 + 49 * q^38 + 3 * q^39 - 4 * q^40 + 159 * q^41 - 15 * q^42 - 4 * q^43 + 27 * q^44 + 73 * q^45 - 18 * q^46 + 61 * q^47 + 36 * q^48 + 158 * q^49 + 30 * q^50 + 23 * q^51 + 17 * q^52 + 80 * q^53 + 8 * q^54 - 9 * q^55 + 140 * q^56 + 24 * q^57 - 4 * q^58 + 130 * q^59 - 22 * q^60 + 41 * q^61 + 25 * q^62 - 25 * q^63 + 96 * q^64 + 56 * q^65 + 37 * q^66 - 10 * q^67 + 85 * q^68 + 125 * q^69 - 25 * q^70 + 69 * q^71 + 9 * q^72 + 18 * q^73 + 27 * q^74 + 37 * q^75 - 10 * q^76 + 66 * q^77 - 40 * q^78 - 21 * q^79 + 103 * q^80 + 258 * q^81 - 18 * q^82 + 18 * q^83 - 20 * q^84 - 14 * q^85 - 7 * q^86 + 21 * q^87 - 44 * q^88 + 297 * q^89 + q^90 - 2 * q^91 - 14 * q^92 + 19 * q^93 - 19 * q^94 + 19 * q^95 - 4 * q^96 + 53 * q^97 + 40 * q^98 - 17 * 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

)

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

$2$	2.24492	1.58740	0.793698	−	0.608312i	$-0.208153\pi$
$2$	2.24492	1.58740	0.793698	+	0.608312i	$0.208153\pi$
$3$	3.21397	1.85558	0.927792	−	0.373098i	$-0.121705\pi$
$3$	3.21397	1.85558	0.927792	+	0.373098i	$0.121705\pi$
$4$	3.03965	1.51983
$5$	−2.36190	−1.05627	−0.528136	−	0.849160i	$-0.677109\pi$
$5$	−2.36190	−1.05627	−0.528136	+	0.849160i	$0.677109\pi$
$6$	7.21508	2.94555
$7$	−1.03422	−0.390897	−0.195448	−	0.980714i	$-0.562616\pi$
$7$	−1.03422	−0.390897	−0.195448	+	0.980714i	$0.562616\pi$
$8$	2.33393	0.825169
$9$	7.32957	2.44319
$10$	−5.30226	−1.67672
$11$	6.14143	1.85171	0.925856	−	0.377876i	$-0.123346\pi$
$11$	6.14143	1.85171	0.925856	+	0.377876i	$0.123346\pi$
$12$	9.76933	2.82016
$13$	−0.596023	−0.165307	−0.0826535	−	0.996578i	$-0.526339\pi$
$13$	−0.596023	−0.165307	−0.0826535	+	0.996578i	$0.526339\pi$
$14$	−2.32173	−0.620508
$15$	−7.59105	−1.96000
$16$	−0.839825	−0.209956
$17$	0.0577882	0.0140157	0.00700785	−	0.999975i	$-0.497769\pi$
$17$	0.0577882	0.0140157	0.00700785	+	0.999975i	$0.497769\pi$
$18$	16.4543	3.87831
$19$	0.132713	0.0304463	0.0152232	−	0.999884i	$-0.495154\pi$
$19$	0.132713	0.0304463	0.0152232	+	0.999884i	$0.495154\pi$
$20$	−7.17934	−1.60535
$21$	−3.32393	−0.725342
$22$	13.7870	2.93940
$23$	−3.29501	−0.687057	−0.343528	−	0.939142i	$-0.611622\pi$
$23$	−3.29501	−0.687057	−0.343528	+	0.939142i	$0.611622\pi$
$24$	7.50117	1.53117
$25$	0.578557	0.115711
$26$	−1.33802	−0.262408
$27$	13.9151	2.67796
$28$	−3.14366	−0.594095
$29$	−5.83126	−1.08284	−0.541418	−	0.840753i	$-0.682113\pi$
$29$	−5.83126	−1.08284	−0.541418	+	0.840753i	$0.682113\pi$
$30$	−17.0413	−3.11130
$31$	9.74636	1.75050	0.875249	−	0.483673i	$-0.160698\pi$
$31$	9.74636	1.75050	0.875249	+	0.483673i	$0.160698\pi$
$32$	−6.55320	−1.15845
$33$	19.7384	3.43601
$34$	0.129730	0.0222485
$35$	2.44271	0.412894
$36$	22.2793	3.71322
$37$	1.48049	0.243391	0.121695	−	0.992567i	$-0.461167\pi$
$37$	1.48049	0.243391	0.121695	+	0.992567i	$0.461167\pi$
$38$	0.297929	0.0483304
$39$	−1.91560	−0.306741
$40$	−5.51250	−0.871603
$41$	6.35485	0.992461	0.496231	−	0.868191i	$-0.334717\pi$
$41$	6.35485	0.992461	0.496231	+	0.868191i	$0.334717\pi$
$42$	−7.46196	−1.15140
$43$	−4.15748	−0.634010	−0.317005	−	0.948424i	$-0.602677\pi$
$43$	−4.15748	−0.634010	−0.317005	+	0.948424i	$0.602677\pi$
$44$	18.6678	2.81428
$45$	−17.3117	−2.58067
$46$	−7.39702	−1.09063
$47$	−7.70719	−1.12421	−0.562105	−	0.827066i	$-0.690008\pi$
$47$	−7.70719	−1.12421	−0.562105	+	0.827066i	$0.690008\pi$
$48$	−2.69917	−0.389591
$49$	−5.93040	−0.847200
$50$	1.29881	0.183680
$51$	0.185729	0.0260073
$52$	−1.81170	−0.251238
$53$	−6.27948	−0.862553	−0.431276	−	0.902220i	$-0.641937\pi$
$53$	−6.27948	−0.862553	−0.431276	+	0.902220i	$0.641937\pi$
$54$	31.2382	4.25098
$55$	−14.5054	−1.95591
$56$	−2.41379	−0.322556
$57$	0.426533	0.0564957
$58$	−13.0907	−1.71889
$59$	2.43438	0.316929	0.158465	−	0.987365i	$-0.449346\pi$
$59$	2.43438	0.316929	0.158465	+	0.987365i	$0.449346\pi$
$60$	−23.0742	−2.97886
$61$	−3.51326	−0.449827	−0.224914	−	0.974379i	$-0.572210\pi$
$61$	−3.51326	−0.449827	−0.224914	+	0.974379i	$0.572210\pi$
$62$	21.8798	2.77873
$63$	−7.58036	−0.955036
$64$	−13.0317	−1.62897
$65$	1.40774	0.174609
$66$	44.3110	5.45430
$67$	−9.47401	−1.15743	−0.578717	−	0.815528i	$-0.696447\pi$
$67$	−9.47401	−1.15743	−0.578717	+	0.815528i	$0.696447\pi$
$68$	0.175656	0.0213014
$69$	−10.5900	−1.27489
$70$	5.48368	0.655426
$71$	10.3934	1.23347	0.616735	−	0.787171i	$-0.288455\pi$
$71$	10.3934	1.23347	0.616735	+	0.787171i	$0.288455\pi$
$72$	17.1067	2.01604
$73$	−12.6814	−1.48425	−0.742123	−	0.670264i	$-0.766181\pi$
$73$	−12.6814	−1.48425	−0.742123	+	0.670264i	$0.766181\pi$
$74$	3.32357	0.386357
$75$	1.85946	0.214712
$76$	0.403400	0.0462731
$77$	−6.35157	−0.723829
$78$	−4.30035	−0.486919
$79$	15.2086	1.71110	0.855551	−	0.517719i	$-0.173219\pi$
$79$	15.2086	1.71110	0.855551	+	0.517719i	$0.173219\pi$
$80$	1.98358	0.221771
$81$	22.7339	2.52599
$82$	14.2661	1.57543
$83$	2.29076	0.251444	0.125722	−	0.992066i	$-0.459875\pi$
$83$	2.29076	0.251444	0.125722	+	0.992066i	$0.459875\pi$
$84$	−10.1036	−1.10239
$85$	−0.136490	−0.0148044
$86$	−9.33320	−1.00642
$87$	−18.7415	−2.00929
$88$	14.3337	1.52797
$89$	−9.43605	−1.00022	−0.500110	−	0.865962i	$-0.666707\pi$
$89$	−9.43605	−1.00022	−0.500110	+	0.865962i	$0.666707\pi$
$90$	−38.8633	−4.09655
$91$	0.616416	0.0646180
$92$	−10.0157	−1.04421
$93$	31.3244	3.24819
$94$	−17.3020	−1.78457
$95$	−0.313453	−0.0321596
$96$	−21.0617	−2.14960
$97$	11.2272	1.13995	0.569974	−	0.821663i	$-0.306953\pi$
$97$	11.2272	1.13995	0.569974	+	0.821663i	$0.306953\pi$
$98$	−13.3132	−1.34484
$99$	45.0141	4.52409
$100$	1.75861	0.175861
$101$	−6.32392	−0.629253	−0.314627	−	0.949215i	$-0.601879\pi$
$101$	−6.32392	−0.629253	−0.314627	+	0.949215i	$0.601879\pi$
$102$	0.416947	0.0412839
$103$	−16.3231	−1.60836	−0.804182	−	0.594384i	$-0.797396\pi$
$103$	−16.3231	−1.60836	−0.804182	+	0.594384i	$0.797396\pi$
$104$	−1.39107	−0.136406
$105$	7.85079	0.766159
$106$	−14.0969	−1.36921
$107$	0.514140	0.0497038	0.0248519	−	0.999691i	$-0.492089\pi$
$107$	0.514140	0.0497038	0.0248519	+	0.999691i	$0.492089\pi$
$108$	42.2970	4.07003
$109$	−15.9742	−1.53005	−0.765027	−	0.643999i	$-0.777274\pi$
$109$	−15.9742	−1.53005	−0.765027	+	0.643999i	$0.777274\pi$
$110$	−32.5635	−3.10481
$111$	4.75824	0.451632
$112$	0.868561	0.0820713
$113$	4.54716	0.427760	0.213880	−	0.976860i	$-0.431390\pi$
$113$	4.54716	0.427760	0.213880	+	0.976860i	$0.431390\pi$
$114$	0.957532	0.0896811
$115$	7.78247	0.725719
$116$	−17.7250	−1.64572
$117$	−4.36859	−0.403876
$118$	5.46498	0.503092
$119$	−0.0597655	−0.00547870
$120$	−17.7170	−1.61733
$121$	26.7172	2.42884
$122$	−7.88698	−0.714054
$123$	20.4243	1.84159
$124$	29.6255	2.66045
$125$	10.4430	0.934050
$126$	−17.0173	−1.51602
$127$	2.24350	0.199078	0.0995390	−	0.995034i	$-0.468263\pi$
$127$	2.24350	0.199078	0.0995390	+	0.995034i	$0.468263\pi$
$128$	−16.1488	−1.42736
$129$	−13.3620	−1.17646
$130$	3.16027	0.277174
$131$	−10.2853	−0.898630	−0.449315	−	0.893373i	$-0.648332\pi$
$131$	−10.2853	−0.898630	−0.449315	+	0.893373i	$0.648332\pi$
$132$	59.9977	5.22213
$133$	−0.137253	−0.0119014
$134$	−21.2684	−1.83731
$135$	−32.8660	−2.82866
$136$	0.134874	0.0115653
$137$	11.0363	0.942894	0.471447	−	0.881894i	$-0.343732\pi$
$137$	11.0363	0.942894	0.471447	+	0.881894i	$0.343732\pi$
$138$	−23.7738	−2.02376
$139$	14.5931	1.23777	0.618887	−	0.785480i	$-0.287584\pi$
$139$	14.5931	1.23777	0.618887	+	0.785480i	$0.287584\pi$
$140$	7.42499	0.627526
$141$	−24.7706	−2.08606
$142$	23.3323	1.95800
$143$	−3.66043	−0.306101
$144$	−6.15556	−0.512963
$145$	13.7728	1.14377
$146$	−28.4687	−2.35608
$147$	−19.0601	−1.57205
$148$	4.50017	0.369911
$149$	−4.46627	−0.365891	−0.182945	−	0.983123i	$-0.558563\pi$
$149$	−4.46627	−0.365891	−0.182945	+	0.983123i	$0.558563\pi$
$150$	4.17434	0.340833
$151$	3.03934	0.247338	0.123669	−	0.992324i	$-0.460534\pi$
$151$	3.03934	0.247338	0.123669	+	0.992324i	$0.460534\pi$
$152$	0.309742	0.0251234
$153$	0.423563	0.0342430
$154$	−14.2587	−1.14900
$155$	−23.0199	−1.84900
$156$	−5.82274	−0.466193
$157$	−1.69889	−0.135587	−0.0677933	−	0.997699i	$-0.521596\pi$
$157$	−1.69889	−0.135587	−0.0677933	+	0.997699i	$0.521596\pi$
$158$	34.1420	2.71619
$159$	−20.1820	−1.60054
$160$	15.4780	1.22364
$161$	3.40775	0.268568
$162$	51.0357	4.00974
$163$	6.64571	0.520532	0.260266	−	0.965537i	$-0.416190\pi$
$163$	6.64571	0.520532	0.260266	+	0.965537i	$0.416190\pi$
$164$	19.3165	1.50837
$165$	−46.6200	−3.62936
$166$	5.14257	0.399141
$167$	−3.78297	−0.292735	−0.146368	−	0.989230i	$-0.546758\pi$
$167$	−3.78297	−0.292735	−0.146368	+	0.989230i	$0.546758\pi$
$168$	−7.75783	−0.598529
$169$	−12.6448	−0.972674
$170$	−0.306408	−0.0235005
$171$	0.972726	0.0743862
$172$	−12.6373	−0.963585
$173$	−4.31613	−0.328149	−0.164075	−	0.986448i	$-0.552464\pi$
$173$	−4.31613	−0.328149	−0.164075	+	0.986448i	$0.552464\pi$
$174$	−42.0730	−3.18955
$175$	−0.598353	−0.0452312
$176$	−5.15773	−0.388779
$177$	7.82401	0.588089
$178$	−21.1831	−1.58774
$179$	2.96561	0.221660	0.110830	−	0.993839i	$-0.464649\pi$
$179$	2.96561	0.221660	0.110830	+	0.993839i	$0.464649\pi$
$180$	−52.6215	−3.92217
$181$	−1.08727	−0.0808162	−0.0404081	−	0.999183i	$-0.512866\pi$
$181$	−1.08727	−0.0808162	−0.0404081	+	0.999183i	$0.512866\pi$
$182$	1.38380	0.102574
$183$	−11.2915	−0.834692
$184$	−7.69031	−0.566937
$185$	−3.49676	−0.257087
$186$	70.3208	5.15617
$187$	0.354903	0.0259531
$188$	−23.4272	−1.70860
$189$	−14.3912	−1.04681
$190$	−0.703676	−0.0510501
$191$	−3.59544	−0.260157	−0.130079	−	0.991504i	$-0.541523\pi$
$191$	−3.59544	−0.260157	−0.130079	+	0.991504i	$0.541523\pi$
$192$	−41.8835	−3.02268
$193$	−11.3825	−0.819327	−0.409664	−	0.912237i	$-0.634354\pi$
$193$	−11.3825	−0.819327	−0.409664	+	0.912237i	$0.634354\pi$
$194$	25.2041	1.80955
$195$	4.52444	0.324002
$196$	−18.0263	−1.28760
$197$	−6.96506	−0.496240	−0.248120	−	0.968729i	$-0.579813\pi$
$197$	−6.96506	−0.496240	−0.248120	+	0.968729i	$0.579813\pi$
$198$	101.053	7.18151
$199$	24.0059	1.70173	0.850866	−	0.525383i	$-0.176078\pi$
$199$	24.0059	1.70173	0.850866	+	0.525383i	$0.176078\pi$
$200$	1.35031	0.0954814
$201$	−30.4491	−2.14772
$202$	−14.1967	−0.998874
$203$	6.03078	0.423278
$204$	0.564553	0.0395266
$205$	−15.0095	−1.04831
$206$	−36.6440	−2.55311
$207$	−24.1510	−1.67861
$208$	0.500555	0.0347072
$209$	0.815045	0.0563779
$210$	17.6244	1.21620
$211$	−9.65234	−0.664495	−0.332247	−	0.943192i	$-0.607807\pi$
$211$	−9.65234	−0.664495	−0.332247	+	0.943192i	$0.607807\pi$
$212$	−19.0874	−1.31093
$213$	33.4040	2.28881
$214$	1.15420	0.0788997
$215$	9.81954	0.669687
$216$	32.4768	2.20977
$217$	−10.0798	−0.684264
$218$	−35.8608	−2.42880
$219$	−40.7576	−2.75414
$220$	−44.0915	−2.97265
$221$	−0.0344431	−0.00231689
$222$	10.6818	0.716919
$223$	21.6959	1.45286	0.726432	−	0.687238i	$-0.241177\pi$
$223$	21.6959	1.45286	0.726432	+	0.687238i	$0.241177\pi$
$224$	6.77742	0.452835
$225$	4.24057	0.282705
$226$	10.2080	0.679025
$227$	8.77090	0.582145	0.291073	−	0.956701i	$-0.405988\pi$
$227$	8.77090	0.582145	0.291073	+	0.956701i	$0.405988\pi$
$228$	1.29651	0.0858636
$229$	−18.4561	−1.21961	−0.609805	−	0.792551i	$-0.708752\pi$
$229$	−18.4561	−1.21961	−0.609805	+	0.792551i	$0.708752\pi$
$230$	17.4710	1.15200
$231$	−20.4137	−1.34312
$232$	−13.6097	−0.893523
$233$	18.5105	1.21267	0.606333	−	0.795211i	$-0.292640\pi$
$233$	18.5105	1.21267	0.606333	+	0.795211i	$0.292640\pi$
$234$	−9.80712	−0.641112
$235$	18.2036	1.18747
$236$	7.39966	0.481677
$237$	48.8799	3.17509
$238$	−0.134169	−0.00869686
$239$	28.6743	1.85479	0.927393	−	0.374088i	$-0.122044\pi$
$239$	28.6743	1.85479	0.927393	+	0.374088i	$0.122044\pi$
$240$	6.37516	0.411515
$241$	16.1850	1.04257	0.521283	−	0.853384i	$-0.325453\pi$
$241$	16.1850	1.04257	0.521283	+	0.853384i	$0.325453\pi$
$242$	59.9779	3.85553
$243$	31.3207	2.00922
$244$	−10.6791	−0.683659
$245$	14.0070	0.894873
$246$	45.8508	2.92334
$247$	−0.0790997	−0.00503299
$248$	22.7473	1.44446
$249$	7.36243	0.466575
$250$	23.4436	1.48271
$251$	−0.465551	−0.0293853	−0.0146927	−	0.999892i	$-0.504677\pi$
$251$	−0.465551	−0.0293853	−0.0146927	+	0.999892i	$0.504677\pi$
$252$	−23.0417	−1.45149
$253$	−20.2361	−1.27223
$254$	5.03646	0.316016
$255$	−0.438674	−0.0274708
$256$	−10.1891	−0.636822
$257$	3.35139	0.209054	0.104527	−	0.994522i	$-0.466667\pi$
$257$	3.35139	0.209054	0.104527	+	0.994522i	$0.466667\pi$
$258$	−29.9966	−1.86751
$259$	−1.53114	−0.0951407
$260$	4.27905	0.265375
$261$	−42.7406	−2.64558
$262$	−23.0896	−1.42648
$263$	−27.4877	−1.69496	−0.847482	−	0.530823i	$-0.821883\pi$
$263$	−27.4877	−1.69496	−0.847482	+	0.530823i	$0.821883\pi$
$264$	46.0679	2.83528
$265$	14.8315	0.911091
$266$	−0.308123	−0.0188922
$267$	−30.3271	−1.85599
$268$	−28.7977	−1.75910
$269$	22.0040	1.34161	0.670804	−	0.741634i	$-0.265949\pi$
$269$	22.0040	1.34161	0.670804	+	0.741634i	$0.265949\pi$
$270$	−73.7815	−4.49020
$271$	10.5123	0.638578	0.319289	−	0.947657i	$-0.396556\pi$
$271$	10.5123	0.638578	0.319289	+	0.947657i	$0.396556\pi$
$272$	−0.0485320	−0.00294269
$273$	1.98114	0.119904
$274$	24.7756	1.49675
$275$	3.55317	0.214264
$276$	−32.1900	−1.93761
$277$	27.7017	1.66444	0.832218	−	0.554449i	$-0.187071\pi$
$277$	27.7017	1.66444	0.832218	+	0.554449i	$0.187071\pi$
$278$	32.7604	1.96484
$279$	71.4366	4.27680
$280$	5.70112	0.340707
$281$	−18.5417	−1.10610	−0.553052	−	0.833147i	$-0.686537\pi$
$281$	−18.5417	−1.10610	−0.553052	+	0.833147i	$0.686537\pi$
$282$	−55.6080	−3.31141
$283$	−19.6738	−1.16949	−0.584744	−	0.811218i	$-0.698805\pi$
$283$	−19.6738	−1.16949	−0.584744	+	0.811218i	$0.698805\pi$
$284$	31.5923	1.87466
$285$	−1.00743	−0.0596749
$286$	−8.21737	−0.485903
$287$	−6.57229	−0.387950
$288$	−48.0321	−2.83032
$289$	−16.9967	−0.999804
$290$	30.9188	1.81562
$291$	36.0838	2.11527
$292$	−38.5470	−2.25579
$293$	−33.5644	−1.96085	−0.980426	−	0.196889i	$-0.936916\pi$
$293$	−33.5644	−1.96085	−0.980426	+	0.196889i	$0.936916\pi$
$294$	−42.7883	−2.49546
$295$	−5.74975	−0.334764
$296$	3.45535	0.200838
$297$	85.4586	4.95881
$298$	−10.0264	−0.580813
$299$	1.96390	0.113575
$300$	5.65211	0.326325
$301$	4.29974	0.247833
$302$	6.82306	0.392623
$303$	−20.3249	−1.16763
$304$	−0.111455	−0.00639240
$305$	8.29796	0.475140
$306$	0.950864	0.0543573
$307$	29.1840	1.66562	0.832811	−	0.553558i	$-0.186730\pi$
$307$	29.1840	1.66562	0.832811	+	0.553558i	$0.186730\pi$
$308$	−19.3066	−1.10009
$309$	−52.4619	−2.98445
$310$	−51.6777	−2.93510
$311$	31.4112	1.78116	0.890582	−	0.454823i	$-0.150298\pi$
$311$	31.4112	1.78116	0.890582	+	0.454823i	$0.150298\pi$
$312$	−4.47087	−0.253113
$313$	−13.6420	−0.771089	−0.385544	−	0.922689i	$-0.625986\pi$
$313$	−13.6420	−0.771089	−0.385544	+	0.922689i	$0.625986\pi$
$314$	−3.81388	−0.215229
$315$	17.9040	1.00878
$316$	46.2288	2.60057
$317$	−4.59025	−0.257814	−0.128907	−	0.991657i	$-0.541147\pi$
$317$	−4.59025	−0.257814	−0.128907	+	0.991657i	$0.541147\pi$
$318$	−45.3070	−2.54069
$319$	−35.8123	−2.00510
$320$	30.7796	1.72063
$321$	1.65243	0.0922296
$322$	7.65011	0.426324
$323$	0.00766922	0.000426727 0
$324$	69.1031	3.83906
$325$	−0.344833	−0.0191279
$326$	14.9191	0.826291
$327$	−51.3406	−2.83914
$328$	14.8318	0.818948
$329$	7.97090	0.439450
$330$	−104.658	−5.76123
$331$	13.6657	0.751134	0.375567	−	0.926795i	$-0.377448\pi$
$331$	13.6657	0.751134	0.375567	+	0.926795i	$0.377448\pi$
$332$	6.96312	0.382151
$333$	10.8513	0.594650
$334$	−8.49246	−0.464687
$335$	22.3766	1.22257
$336$	2.79152	0.152290
$337$	0.832706	0.0453604	0.0226802	−	0.999743i	$-0.492780\pi$
$337$	0.832706	0.0453604	0.0226802	+	0.999743i	$0.492780\pi$
$338$	−28.3864	−1.54402
$339$	14.6144	0.793745
$340$	−0.414882	−0.0225001
$341$	59.8566	3.24142
$342$	2.18369	0.118080
$343$	13.3728	0.722065
$344$	−9.70327	−0.523165
$345$	25.0126	1.34663
$346$	−9.68935	−0.520903
$347$	34.3654	1.84483	0.922416	−	0.386197i	$-0.126212\pi$
$347$	34.3654	1.84483	0.922416	+	0.386197i	$0.126212\pi$
$348$	−56.9675	−3.05378
$349$	12.3871	0.663068	0.331534	−	0.943443i	$-0.392434\pi$
$349$	12.3871	0.663068	0.331534	+	0.943443i	$0.392434\pi$
$350$	−1.34325	−0.0717998
$351$	−8.29371	−0.442686
$352$	−40.2460	−2.14512
$353$	29.2487	1.55675	0.778377	−	0.627798i	$-0.216043\pi$
$353$	29.2487	1.55675	0.778377	+	0.627798i	$0.216043\pi$
$354$	17.5643	0.933529
$355$	−24.5481	−1.30288
$356$	−28.6823	−1.52016
$357$	−0.192084	−0.0101662
$358$	6.65755	0.351862
$359$	−18.8749	−0.996178	−0.498089	−	0.867126i	$-0.665965\pi$
$359$	−18.8749	−0.996178	−0.498089	+	0.867126i	$0.665965\pi$
$360$	−40.4043	−2.12949
$361$	−18.9824	−0.999073
$362$	−2.44083	−0.128287
$363$	85.8682	4.50691
$364$	1.87369	0.0982081
$365$	29.9521	1.56777
$366$	−25.3485	−1.32499
$367$	14.1738	0.739868	0.369934	−	0.929058i	$-0.379380\pi$
$367$	14.1738	0.739868	0.369934	+	0.929058i	$0.379380\pi$
$368$	2.76723	0.144252
$369$	46.5783	2.42477
$370$	−7.84994	−0.408099
$371$	6.49434	0.337169
$372$	95.2154	4.93669
$373$	−24.4583	−1.26640	−0.633202	−	0.773987i	$-0.718260\pi$
$373$	−24.4583	−1.26640	−0.633202	+	0.773987i	$0.718260\pi$
$374$	0.796727	0.0411978
$375$	33.5634	1.73321
$376$	−17.9880	−0.927662
$377$	3.47556	0.179000
$378$	−32.3071	−1.66170
$379$	25.4898	1.30932	0.654660	−	0.755923i	$-0.272812\pi$
$379$	25.4898	1.30932	0.654660	+	0.755923i	$0.272812\pi$
$380$	−0.952788	−0.0488770
$381$	7.21052	0.369406
$382$	−8.07147	−0.412972
$383$	−5.20428	−0.265926	−0.132963	−	0.991121i	$-0.542449\pi$
$383$	−5.20428	−0.265926	−0.132963	+	0.991121i	$0.542449\pi$
$384$	−51.9015	−2.64859
$385$	15.0018	0.764560
$386$	−25.5527	−1.30060
$387$	−30.4726	−1.54901
$388$	34.1267	1.73252
$389$	20.5243	1.04062	0.520311	−	0.853977i	$-0.325816\pi$
$389$	20.5243	1.04062	0.520311	+	0.853977i	$0.325816\pi$
$390$	10.1570	0.514319
$391$	−0.190413	−0.00962958
$392$	−13.8411	−0.699082
$393$	−33.0566	−1.66748
$394$	−15.6360	−0.787729
$395$	−35.9211	−1.80739
$396$	136.827	6.87582
$397$	−7.86087	−0.394526	−0.197263	−	0.980351i	$-0.563205\pi$
$397$	−7.86087	−0.394526	−0.197263	+	0.980351i	$0.563205\pi$
$398$	53.8912	2.70132
$399$	−0.441128	−0.0220840
$400$	−0.485886	−0.0242943
$401$	−6.21341	−0.310283	−0.155141	−	0.987892i	$-0.549583\pi$
$401$	−6.21341	−0.310283	−0.155141	+	0.987892i	$0.549583\pi$
$402$	−68.3558	−3.40928
$403$	−5.80905	−0.289369
$404$	−19.2225	−0.956355
$405$	−53.6951	−2.66813
$406$	13.5386	0.671909
$407$	9.09232	0.450690
$408$	0.433479	0.0214604
$409$	24.1897	1.19610	0.598051	−	0.801458i	$-0.295942\pi$
$409$	24.1897	1.19610	0.598051	+	0.801458i	$0.295942\pi$
$410$	−33.6951	−1.66408
$411$	35.4703	1.74962
$412$	−49.6165	−2.44443
$413$	−2.51767	−0.123887
$414$	−54.2170	−2.66462
$415$	−5.41054	−0.265593
$416$	3.90585	0.191500
$417$	46.9019	2.29679
$418$	1.82971	0.0894940
$419$	2.21763	0.108338	0.0541692	−	0.998532i	$-0.482749\pi$
$419$	2.21763	0.108338	0.0541692	+	0.998532i	$0.482749\pi$
$420$	23.8637	1.16443
$421$	−9.47358	−0.461714	−0.230857	−	0.972988i	$-0.574153\pi$
$421$	−9.47358	−0.461714	−0.230857	+	0.972988i	$0.574153\pi$
$422$	−21.6687	−1.05482
$423$	−56.4904	−2.74666
$424$	−14.6559	−0.711752
$425$	0.0334338	0.00162178
$426$	74.9892	3.63324
$427$	3.63347	0.175836
$428$	1.56281	0.0755412
$429$	−11.7645	−0.567996
$430$	22.0441	1.06306
$431$	23.2815	1.12143	0.560715	−	0.828009i	$-0.310526\pi$
$431$	23.2815	1.12143	0.560715	+	0.828009i	$0.310526\pi$
$432$	−11.6862	−0.562255
$433$	−11.5779	−0.556397	−0.278199	−	0.960524i	$-0.589737\pi$
$433$	−11.5779	−0.556397	−0.278199	+	0.960524i	$0.589737\pi$
$434$	−22.6284	−1.08620
$435$	44.2654	2.12236
$436$	−48.5561	−2.32541
$437$	−0.437289	−0.0209184
$438$	−91.4973	−4.37191
$439$	20.9587	1.00030	0.500151	−	0.865938i	$-0.333278\pi$
$439$	20.9587	1.00030	0.500151	+	0.865938i	$0.333278\pi$
$440$	−33.8547	−1.61396
$441$	−43.4673	−2.06987
$442$	−0.0773219	−0.00367783
$443$	14.8965	0.707756	0.353878	−	0.935292i	$-0.384863\pi$
$443$	14.8965	0.707756	0.353878	+	0.935292i	$0.384863\pi$
$444$	14.4634	0.686402
$445$	22.2870	1.05650
$446$	48.7055	2.30627
$447$	−14.3544	−0.678941
$448$	13.4776	0.636758
$449$	−22.1131	−1.04358	−0.521790	−	0.853074i	$-0.674736\pi$
$449$	−22.1131	−1.04358	−0.521790	+	0.853074i	$0.674736\pi$
$450$	9.51973	0.448765
$451$	39.0279	1.83775
$452$	13.8218	0.650121
$453$	9.76832	0.458956
$454$	19.6899	0.924095
$455$	−1.45591	−0.0682542
$456$	0.995499	0.0466185
$457$	−20.4898	−0.958472	−0.479236	−	0.877686i	$-0.659086\pi$
$457$	−20.4898	−0.958472	−0.479236	+	0.877686i	$0.659086\pi$
$458$	−41.4323	−1.93600
$459$	0.804129	0.0375335
$460$	23.6560	1.10297
$461$	−12.0820	−0.562713	−0.281357	−	0.959603i	$-0.590784\pi$
$461$	−12.0820	−0.562713	−0.281357	+	0.959603i	$0.590784\pi$
$462$	−45.8271	−2.13207
$463$	−20.4560	−0.950671	−0.475336	−	0.879805i	$-0.657673\pi$
$463$	−20.4560	−0.950671	−0.475336	+	0.879805i	$0.657673\pi$
$464$	4.89723	0.227348
$465$	−73.9851	−3.43098
$466$	41.5546	1.92498
$467$	8.53872	0.395125	0.197562	−	0.980290i	$-0.436697\pi$
$467$	8.53872	0.395125	0.197562	+	0.980290i	$0.436697\pi$
$468$	−13.2790	−0.613822
$469$	9.79818	0.452438
$470$	40.8655	1.88499
$471$	−5.46019	−0.251592
$472$	5.68167	0.261520
$473$	−25.5329	−1.17400
$474$	109.731	5.04013
$475$	0.0767817	0.00352299
$476$	−0.181666	−0.00832666
$477$	−46.0259	−2.10738
$478$	64.3714	2.94428
$479$	0.737828	0.0337122	0.0168561	−	0.999858i	$-0.494634\pi$
$479$	0.737828	0.0337122	0.0168561	+	0.999858i	$0.494634\pi$
$480$	49.7457	2.27057
$481$	−0.882405	−0.0402342
$482$	36.3340	1.65497
$483$	10.9524	0.498351
$484$	81.2110	3.69141
$485$	−26.5175	−1.20410
$486$	70.3124	3.18943
$487$	−25.0984	−1.13732	−0.568659	−	0.822573i	$-0.692538\pi$
$487$	−25.0984	−1.13732	−0.568659	+	0.822573i	$0.692538\pi$
$488$	−8.19970	−0.371183
$489$	21.3591	0.965891
$490$	31.4445	1.42052
$491$	14.2534	0.643249	0.321624	−	0.946867i	$-0.395771\pi$
$491$	14.2534	0.643249	0.321624	+	0.946867i	$0.395771\pi$
$492$	62.0827	2.79890
$493$	−0.336978	−0.0151767
$494$	−0.177572	−0.00798935
$495$	−106.319	−4.77867
$496$	−8.18523	−0.367528
$497$	−10.7490	−0.482160
$498$	16.5280	0.740639
$499$	3.45457	0.154648	0.0773240	−	0.997006i	$-0.475362\pi$
$499$	3.45457	0.154648	0.0773240	+	0.997006i	$0.475362\pi$
$500$	31.7431	1.41959
$501$	−12.1583	−0.543195
$502$	−1.04512	−0.0466462
$503$	20.4044	0.909786	0.454893	−	0.890546i	$-0.349678\pi$
$503$	20.4044	0.909786	0.454893	+	0.890546i	$0.349678\pi$
$504$	−17.6920	−0.788065
$505$	14.9364	0.664663
$506$	−45.4283	−2.01953
$507$	−40.6398	−1.80488
$508$	6.81944	0.302564
$509$	−6.58722	−0.291973	−0.145987	−	0.989287i	$-0.546636\pi$
$509$	−6.58722	−0.291973	−0.145987	+	0.989287i	$0.546636\pi$
$510$	−0.984786	−0.0436071
$511$	13.1153	0.580187
$512$	9.42372	0.416474
$513$	1.84671	0.0815341
$514$	7.52359	0.331851
$515$	38.5535	1.69887
$516$	−40.6158	−1.78801
$517$	−47.3332	−2.08171
$518$	−3.43729	−0.151026
$519$	−13.8719	−0.608908
$520$	3.28558	0.144082
$521$	35.2478	1.54424	0.772118	−	0.635479i	$-0.219197\pi$
$521$	35.2478	1.54424	0.772118	+	0.635479i	$0.219197\pi$
$522$	−95.9491	−4.19958
$523$	14.8176	0.647930	0.323965	−	0.946069i	$-0.394984\pi$
$523$	14.8176	0.647930	0.323965	+	0.946069i	$0.394984\pi$
$524$	−31.2637	−1.36576
$525$	−1.92309	−0.0839303
$526$	−61.7076	−2.69058
$527$	0.563225	0.0245345
$528$	−16.5768	−0.721411
$529$	−12.1429	−0.527953
$530$	33.2954	1.44626
$531$	17.8430	0.774318
$532$	−0.417203	−0.0180880
$533$	−3.78764	−0.164061
$534$	−68.0819	−2.94619
$535$	−1.21435	−0.0525008
$536$	−22.1117	−0.955079
$537$	9.53137	0.411309
$538$	49.3972	2.12966
$539$	−36.4211	−1.56877
$540$	−99.9012	−4.29906
$541$	14.4561	0.621516	0.310758	−	0.950489i	$-0.399417\pi$
$541$	14.4561	0.621516	0.310758	+	0.950489i	$0.399417\pi$
$542$	23.5993	1.01368
$543$	−3.49445	−0.149961
$544$	−0.378698	−0.0162365
$545$	37.7295	1.61615
$546$	4.44750	0.190335
$547$	38.3084	1.63795	0.818975	−	0.573830i	$-0.194543\pi$
$547$	38.3084	1.63795	0.818975	+	0.573830i	$0.194543\pi$
$548$	33.5465	1.43303
$549$	−25.7507	−1.09901
$550$	7.97657	0.340122
$551$	−0.773881	−0.0329684
$552$	−24.7164	−1.05200
$553$	−15.7290	−0.668864
$554$	62.1881	2.64212
$555$	−11.2385	−0.477046
$556$	44.3581	1.88120
$557$	−32.7639	−1.38825	−0.694126	−	0.719854i	$-0.744209\pi$
$557$	−32.7639	−1.38825	−0.694126	+	0.719854i	$0.744209\pi$
$558$	160.369	6.78897
$559$	2.47795	0.104806
$560$	−2.05145	−0.0866896
$561$	1.14064	0.0481581
$562$	−41.6245	−1.75582
$563$	−9.88871	−0.416759	−0.208380	−	0.978048i	$-0.566819\pi$
$563$	−9.88871	−0.416759	−0.208380	+	0.978048i	$0.566819\pi$
$564$	−75.2941	−3.17045
$565$	−10.7399	−0.451832
$566$	−44.1661	−1.85644
$567$	−23.5118	−0.987402
$568$	24.2575	1.01782
$569$	45.8001	1.92004	0.960019	−	0.279934i	$-0.0903125\pi$
$569$	45.8001	1.92004	0.960019	+	0.279934i	$0.0903125\pi$
$570$	−2.26159	−0.0947277
$571$	−12.5093	−0.523497	−0.261748	−	0.965136i	$-0.584299\pi$
$571$	−12.5093	−0.523497	−0.261748	+	0.965136i	$0.584299\pi$
$572$	−11.1264	−0.465220
$573$	−11.5556	−0.482743
$574$	−14.7542	−0.615830
$575$	−1.90635	−0.0795002
$576$	−95.5170	−3.97987
$577$	−24.3421	−1.01337	−0.506687	−	0.862130i	$-0.669130\pi$
$577$	−24.3421	−1.01337	−0.506687	+	0.862130i	$0.669130\pi$
$578$	−38.1561	−1.58708
$579$	−36.5828	−1.52033
$580$	41.8646	1.73833
$581$	−2.36914	−0.0982886
$582$	81.0051	3.35777
$583$	−38.5650	−1.59720
$584$	−29.5975	−1.22475
$585$	10.3182	0.426603
$586$	−75.3492	−3.11265
$587$	44.0426	1.81783	0.908917	−	0.416977i	$-0.136910\pi$
$587$	44.0426	1.81783	0.908917	+	0.416977i	$0.136910\pi$
$588$	−57.9360	−2.38924
$589$	1.29346	0.0532962
$590$	−12.9077	−0.531402
$591$	−22.3855	−0.920815
$592$	−1.24335	−0.0511014
$593$	−13.6802	−0.561777	−0.280888	−	0.959740i	$-0.590629\pi$
$593$	−13.6802	−0.561777	−0.280888	+	0.959740i	$0.590629\pi$
$594$	191.847	7.87160
$595$	0.141160	0.00578700
$596$	−13.5759	−0.556090
$597$	77.1541	3.15771
$598$	4.40879	0.180289
$599$	31.3267	1.27998	0.639988	−	0.768385i	$-0.278939\pi$
$599$	31.3267	1.27998	0.639988	+	0.768385i	$0.278939\pi$
$600$	4.33985	0.177174
$601$	−29.4453	−1.20110	−0.600550	−	0.799587i	$-0.705052\pi$
$601$	−29.4453	−1.20110	−0.600550	+	0.799587i	$0.705052\pi$
$602$	9.65255	0.393408
$603$	−69.4404	−2.82783
$604$	9.23852	0.375910
$605$	−63.1033	−2.56551
$606$	−45.6276	−1.85349
$607$	2.52821	0.102617	0.0513084	−	0.998683i	$-0.483661\pi$
$607$	2.52821	0.102617	0.0513084	+	0.998683i	$0.483661\pi$
$608$	−0.869691	−0.0352706
$609$	19.3827	0.785427
$610$	18.6282	0.754235
$611$	4.59366	0.185840
$612$	1.28748	0.0520434
$613$	−42.6658	−1.72326	−0.861628	−	0.507541i	$-0.830555\pi$
$613$	−42.6658	−1.72326	−0.861628	+	0.507541i	$0.830555\pi$
$614$	65.5157	2.64400
$615$	−48.2400	−1.94523
$616$	−14.8241	−0.597281
$617$	−11.0656	−0.445485	−0.222742	−	0.974877i	$-0.571501\pi$
$617$	−11.0656	−0.445485	−0.222742	+	0.974877i	$0.571501\pi$
$618$	−117.773	−4.73751
$619$	−14.9668	−0.601568	−0.300784	−	0.953692i	$-0.597248\pi$
$619$	−14.9668	−0.601568	−0.300784	+	0.953692i	$0.597248\pi$
$620$	−69.9724	−2.81016
$621$	−45.8503	−1.83991
$622$	70.5154	2.82741
$623$	9.75892	0.390983
$624$	1.60877	0.0644022
$625$	−27.5581	−1.10232
$626$	−30.6250	−1.22402
$627$	2.61953	0.104614
$628$	−5.16405	−0.206068
$629$	0.0855548	0.00341129
$630$	40.1931	1.60133
$631$	−39.4824	−1.57177	−0.785886	−	0.618372i	$-0.787793\pi$
$631$	−39.4824	−1.57177	−0.785886	+	0.618372i	$0.787793\pi$
$632$	35.4958	1.41195
$633$	−31.0223	−1.23303
$634$	−10.3047	−0.409253
$635$	−5.29891	−0.210281
$636$	−61.3463	−2.43254
$637$	3.53465	0.140048
$638$	−80.3956	−3.18289
$639$	76.1792	3.01360
$640$	38.1417	1.50768
$641$	−30.5297	−1.20585	−0.602924	−	0.797798i	$-0.705998\pi$
$641$	−30.5297	−1.20585	−0.602924	+	0.797798i	$0.705998\pi$
$642$	3.70957	0.146405
$643$	30.0564	1.18531	0.592654	−	0.805457i	$-0.298080\pi$
$643$	30.0564	1.18531	0.592654	+	0.805457i	$0.298080\pi$
$644$	10.3584	0.408177
$645$	31.5597	1.24266
$646$	0.0172168	0.000677385 0
$647$	7.73364	0.304041	0.152020	−	0.988377i	$-0.451422\pi$
$647$	7.73364	0.304041	0.152020	+	0.988377i	$0.451422\pi$
$648$	53.0593	2.08437
$649$	14.9506	0.586862
$650$	−0.774121	−0.0303635
$651$	−32.3963	−1.26971
$652$	20.2006	0.791118
$653$	−29.8860	−1.16953	−0.584764	−	0.811204i	$-0.698813\pi$
$653$	−29.8860	−1.16953	−0.584764	+	0.811204i	$0.698813\pi$
$654$	−115.255	−4.50684
$655$	24.2928	0.949199
$656$	−5.33696	−0.208373
$657$	−92.9492	−3.62629
$658$	17.8940	0.697581
$659$	−26.2518	−1.02262	−0.511312	−	0.859395i	$-0.670840\pi$
$659$	−26.2518	−1.02262	−0.511312	+	0.859395i	$0.670840\pi$
$660$	−141.708	−5.51599
$661$	45.9335	1.78661	0.893304	−	0.449454i	$-0.148381\pi$
$661$	45.9335	1.78661	0.893304	+	0.449454i	$0.148381\pi$
$662$	30.6783	1.19235
$663$	−0.110699	−0.00429919
$664$	5.34648	0.207484
$665$	0.324178	0.0125711
$666$	24.3604	0.943945
$667$	19.2140	0.743970
$668$	−11.4989	−0.444907
$669$	69.7298	2.69591
$670$	50.2337	1.94070
$671$	−21.5765	−0.832950
$672$	21.7824	0.840274
$673$	−15.5366	−0.598893	−0.299447	−	0.954113i	$-0.596802\pi$
$673$	−15.5366	−0.598893	−0.299447	+	0.954113i	$0.596802\pi$
$674$	1.86936	0.0720049
$675$	8.05067	0.309870
$676$	−38.4356	−1.47829
$677$	21.0071	0.807370	0.403685	−	0.914898i	$-0.367729\pi$
$677$	21.0071	0.807370	0.403685	+	0.914898i	$0.367729\pi$
$678$	32.8081	1.25999
$679$	−11.6113	−0.445602
$680$	−0.318558	−0.0122161
$681$	28.1894	1.08022
$682$	134.373	5.14541
$683$	20.4044	0.780754	0.390377	−	0.920655i	$-0.372345\pi$
$683$	20.4044	0.780754	0.390377	+	0.920655i	$0.372345\pi$
$684$	2.95675	0.113054
$685$	−26.0666	−0.995953
$686$	30.0209	1.14620
$687$	−59.3171	−2.26309
$688$	3.49156	0.133114
$689$	3.74271	0.142586
$690$	56.1512	2.13764
$691$	35.5763	1.35339	0.676693	−	0.736265i	$-0.263412\pi$
$691$	35.5763	1.35339	0.676693	+	0.736265i	$0.263412\pi$
$692$	−13.1195	−0.498729
$693$	−46.5543	−1.76845
$694$	77.1475	2.92848
$695$	−34.4675	−1.30743
$696$	−43.7412	−1.65801
$697$	0.367236	0.0139100
$698$	27.8081	1.05255
$699$	59.4922	2.25020
$700$	−1.81878	−0.0687436
$701$	35.1534	1.32772	0.663862	−	0.747855i	$-0.268916\pi$
$701$	35.1534	1.32772	0.663862	+	0.747855i	$0.268916\pi$
$702$	−18.6187	−0.702717
$703$	0.196479	0.00741036
$704$	−80.0335	−3.01638
$705$	58.5057	2.20345
$706$	65.6610	2.47118
$707$	6.54030	0.245973
$708$	23.7823	0.893792
$709$	−37.9452	−1.42506	−0.712531	−	0.701640i	$-0.752451\pi$
$709$	−37.9452	−1.42506	−0.712531	+	0.701640i	$0.752451\pi$
$710$	−55.1085	−2.06819
$711$	111.473	4.18055
$712$	−22.0231	−0.825350
$713$	−32.1143	−1.20269
$714$	−0.431213	−0.0161378
$715$	8.64557	0.323326
$716$	9.01442	0.336885
$717$	92.1582	3.44171
$718$	−42.3725	−1.58133
$719$	48.3250	1.80222	0.901109	−	0.433592i	$-0.142754\pi$
$719$	48.3250	1.80222	0.901109	+	0.433592i	$0.142754\pi$
$720$	14.5388	0.541829
$721$	16.8816	0.628704
$722$	−42.6139	−1.58592
$723$	52.0180	1.93457
$724$	−3.30492	−0.122826
$725$	−3.37371	−0.125297
$726$	192.767	7.15425
$727$	2.75644	0.102231	0.0511154	−	0.998693i	$-0.483722\pi$
$727$	2.75644	0.102231	0.0511154	+	0.998693i	$0.483722\pi$
$728$	1.43867	0.0533207
$729$	32.4619	1.20229
$730$	67.2401	2.48867
$731$	−0.240254	−0.00888610
$732$	−34.3222	−1.26859
$733$	2.48193	0.0916722	0.0458361	−	0.998949i	$-0.485405\pi$
$733$	2.48193	0.0916722	0.0458361	+	0.998949i	$0.485405\pi$
$734$	31.8191	1.17446
$735$	45.0180	1.66051
$736$	21.5928	0.795922
$737$	−58.1840	−2.14324
$738$	104.564	3.84907
$739$	−34.4121	−1.26587	−0.632935	−	0.774205i	$-0.718150\pi$
$739$	−34.4121	−1.26587	−0.632935	+	0.774205i	$0.718150\pi$
$740$	−10.6289	−0.390727
$741$	−0.254224	−0.00933914
$742$	14.5793	0.535221
$743$	−24.8231	−0.910672	−0.455336	−	0.890320i	$-0.650481\pi$
$743$	−24.8231	−0.910672	−0.455336	+	0.890320i	$0.650481\pi$
$744$	73.1090	2.68031
$745$	10.5489	0.386480
$746$	−54.9069	−2.01028
$747$	16.7903	0.614325
$748$	1.07878	0.0394441
$749$	−0.531732	−0.0194291
$750$	75.3471	2.75129
$751$	4.68815	0.171073	0.0855365	−	0.996335i	$-0.472740\pi$
$751$	4.68815	0.171073	0.0855365	+	0.996335i	$0.472740\pi$
$752$	6.47269	0.236035
$753$	−1.49627	−0.0545269
$754$	7.80234	0.284145
$755$	−7.17860	−0.261256
$756$	−43.7443	−1.59096
$757$	−33.1228	−1.20387	−0.601934	−	0.798546i	$-0.705603\pi$
$757$	−33.1228	−1.20387	−0.601934	+	0.798546i	$0.705603\pi$
$758$	57.2224	2.07841
$759$	−65.0380	−2.36073
$760$	−0.731578	−0.0265371
$761$	−6.31858	−0.229048	−0.114524	−	0.993420i	$-0.536534\pi$
$761$	−6.31858	−0.229048	−0.114524	+	0.993420i	$0.536534\pi$
$762$	16.1870	0.586394
$763$	16.5208	0.598093
$764$	−10.9289	−0.395393
$765$	−1.00041	−0.0361700
$766$	−11.6832	−0.422130
$767$	−1.45095	−0.0523906
$768$	−32.7476	−1.18168
$769$	0.702154	0.0253203	0.0126602	−	0.999920i	$-0.495970\pi$
$769$	0.702154	0.0253203	0.0126602	+	0.999920i	$0.495970\pi$
$770$	33.6777	1.21366
$771$	10.7713	0.387917
$772$	−34.5987	−1.24523
$773$	24.4052	0.877796	0.438898	−	0.898537i	$-0.355369\pi$
$773$	24.4052	0.877796	0.438898	+	0.898537i	$0.355369\pi$
$774$	−68.4084	−2.45889
$775$	5.63882	0.202552
$776$	26.2035	0.940649
$777$	−4.92105	−0.176542
$778$	46.0753	1.65188
$779$	0.843368	0.0302168
$780$	13.7527	0.492426
$781$	63.8304	2.28403
$782$	−0.427461	−0.0152860
$783$	−81.1425	−2.89979
$784$	4.98050	0.177875
$785$	4.01261	0.143216
$786$	−74.2093	−2.64696
$787$	−30.6886	−1.09393	−0.546966	−	0.837155i	$-0.684217\pi$
$787$	−30.6886	−1.09393	−0.546966	+	0.837155i	$0.684217\pi$
$788$	−21.1713	−0.754198
$789$	−88.3445	−3.14515
$790$	−80.6400	−2.86904
$791$	−4.70274	−0.167210
$792$	105.060	3.73313
$793$	2.09398	0.0743595
$794$	−17.6470	−0.626269
$795$	47.6679	1.69061
$796$	72.9695	2.58634
$797$	4.18327	0.148179	0.0740895	−	0.997252i	$-0.476395\pi$
$797$	4.18327	0.148179	0.0740895	+	0.997252i	$0.476395\pi$
$798$	−0.990295	−0.0350561
$799$	−0.445385	−0.0157566
$800$	−3.79140	−0.134046
$801$	−69.1622	−2.44373
$802$	−13.9486	−0.492542
$803$	−77.8820	−2.74839
$804$	−92.5547	−3.26415
$805$	−8.04875	−0.283681
$806$	−13.0408	−0.459344
$807$	70.7202	2.48947
$808$	−14.7596	−0.519240
$809$	35.5012	1.24815	0.624077	−	0.781363i	$-0.285475\pi$
$809$	35.5012	1.24815	0.624077	+	0.781363i	$0.285475\pi$
$810$	−120.541	−4.23538
$811$	−43.6179	−1.53163	−0.765815	−	0.643061i	$-0.777664\pi$
$811$	−43.6179	−1.53163	−0.765815	+	0.643061i	$0.777664\pi$
$812$	18.3315	0.643308
$813$	33.7862	1.18493
$814$	20.4115	0.715423
$815$	−15.6965	−0.549824
$816$	−0.155980	−0.00546040
$817$	−0.551750	−0.0193033
$818$	54.3038	1.89869
$819$	4.51807	0.157874
$820$	−45.6237	−1.59325
$821$	−49.4272	−1.72502	−0.862511	−	0.506038i	$-0.831109\pi$
$821$	−49.4272	−1.72502	−0.862511	+	0.506038i	$0.831109\pi$
$822$	79.6278	2.77734
$823$	36.8287	1.28377	0.641884	−	0.766801i	$-0.278153\pi$
$823$	36.8287	1.28377	0.641884	+	0.766801i	$0.278153\pi$
$824$	−38.0970	−1.32717
$825$	11.4198	0.397585
$826$	−5.65197	−0.196657
$827$	5.91133	0.205557	0.102779	−	0.994704i	$-0.467227\pi$
$827$	5.91133	0.205557	0.102779	+	0.994704i	$0.467227\pi$
$828$	−73.4106	−2.55119
$829$	−1.13503	−0.0394214	−0.0197107	−	0.999806i	$-0.506275\pi$
$829$	−1.13503	−0.0394214	−0.0197107	+	0.999806i	$0.506275\pi$
$830$	−12.1462	−0.421601
$831$	89.0324	3.08850
$832$	7.76721	0.269279
$833$	−0.342707	−0.0118741
$834$	105.291	3.64592
$835$	8.93499	0.309208
$836$	2.47745	0.0856845
$837$	135.621	4.68776
$838$	4.97840	0.171976
$839$	−4.01466	−0.138602	−0.0693008	−	0.997596i	$-0.522077\pi$
$839$	−4.01466	−0.138602	−0.0693008	+	0.997596i	$0.522077\pi$
$840$	18.3232	0.632210
$841$	5.00354	0.172536
$842$	−21.2674	−0.732923
$843$	−59.5923	−2.05247
$844$	−29.3397	−1.00992
$845$	29.8656	1.02741
$846$	−126.816	−4.36003
$847$	−27.6314	−0.949425
$848$	5.27366	0.181098
$849$	−63.2310	−2.17008
$850$	0.0750561	0.00257440
$851$	−4.87822	−0.167223
$852$	101.537	3.47859
$853$	−17.9650	−0.615111	−0.307555	−	0.951530i	$-0.599511\pi$
$853$	−17.9650	−0.615111	−0.307555	+	0.951530i	$0.599511\pi$
$854$	8.15684	0.279121
$855$	−2.29748	−0.0785721
$856$	1.19997	0.0410140
$857$	−45.8035	−1.56462	−0.782308	−	0.622892i	$-0.785958\pi$
$857$	−45.8035	−1.56462	−0.782308	+	0.622892i	$0.785958\pi$
$858$	−26.4103	−0.901634
$859$	−31.5308	−1.07582	−0.537908	−	0.843003i	$-0.680785\pi$
$859$	−31.5308	−1.07582	−0.537908	+	0.843003i	$0.680785\pi$
$860$	29.8480	1.01781
$861$	−21.1231	−0.719874
$862$	52.2650	1.78015
$863$	−1.69411	−0.0576683	−0.0288341	−	0.999584i	$-0.509179\pi$
$863$	−1.69411	−0.0576683	−0.0288341	+	0.999584i	$0.509179\pi$
$864$	−91.1883	−3.10229
$865$	10.1943	0.346615
$866$	−25.9914	−0.883223
$867$	−54.6267	−1.85522
$868$	−30.6392	−1.03996
$869$	93.4026	3.16847
$870$	99.3721	3.36903
$871$	5.64673	0.191332
$872$	−37.2827	−1.26255
$873$	82.2905	2.78511
$874$	−0.981677	−0.0332057
$875$	−10.8003	−0.365117
$876$	−123.889	−4.18581
$877$	−25.7896	−0.870852	−0.435426	−	0.900225i	$-0.643402\pi$
$877$	−25.7896	−0.870852	−0.435426	+	0.900225i	$0.643402\pi$
$878$	47.0505	1.58788
$879$	−107.875	−3.63852
$880$	12.1820	0.410656
$881$	−28.7157	−0.967456	−0.483728	−	0.875218i	$-0.660718\pi$
$881$	−28.7157	−0.967456	−0.483728	+	0.875218i	$0.660718\pi$
$882$	−97.5804	−3.28570
$883$	−56.0227	−1.88532	−0.942658	−	0.333761i	$-0.891682\pi$
$883$	−56.0227	−1.88532	−0.942658	+	0.333761i	$0.891682\pi$
$884$	−0.104695	−0.00352127
$885$	−18.4795	−0.621182
$886$	33.4415	1.12349
$887$	7.16363	0.240531	0.120266	−	0.992742i	$-0.461625\pi$
$887$	7.16363	0.240531	0.120266	+	0.992742i	$0.461625\pi$
$888$	11.1054	0.372672
$889$	−2.32026	−0.0778190
$890$	50.0324	1.67709
$891$	139.619	4.67741
$892$	65.9479	2.20810
$893$	−1.02284	−0.0342281
$894$	−32.2245	−1.07775
$895$	−7.00447	−0.234133
$896$	16.7013	0.557951
$897$	6.31190	0.210748
$898$	−49.6420	−1.65658
$899$	−56.8335	−1.89550
$900$	12.8899	0.429662
$901$	−0.362880	−0.0120893
$902$	87.6144	2.91724
$903$	13.8192	0.459874
$904$	10.6127	0.352974
$905$	2.56802	0.0853639
$906$	21.9291	0.728545
$907$	20.8611	0.692681	0.346340	−	0.938109i	$-0.387424\pi$
$907$	20.8611	0.692681	0.346340	+	0.938109i	$0.387424\pi$
$908$	26.6605	0.884759
$909$	−46.3516	−1.53739
$910$	−3.26840	−0.108346
$911$	53.1969	1.76249	0.881247	−	0.472657i	$-0.156705\pi$
$911$	53.1969	1.76249	0.881247	+	0.472657i	$0.156705\pi$
$912$	−0.358213	−0.0118616
$913$	14.0686	0.465602
$914$	−45.9979	−1.52148
$915$	26.6694	0.881662
$916$	−56.1000	−1.85359
$917$	10.6372	0.351272
$918$	1.80520	0.0595805
$919$	24.1820	0.797692	0.398846	−	0.917018i	$-0.369411\pi$
$919$	24.1820	0.797692	0.398846	+	0.917018i	$0.369411\pi$
$920$	18.1637	0.598840
$921$	93.7965	3.09070
$922$	−27.1230	−0.893248
$923$	−6.19470	−0.203901
$924$	−62.0506	−2.04131
$925$	0.856546	0.0281631
$926$	−45.9220	−1.50909
$927$	−119.641	−3.92954
$928$	38.2134	1.25441
$929$	−24.7183	−0.810982	−0.405491	−	0.914099i	$-0.632899\pi$
$929$	−24.7183	−0.810982	−0.405491	+	0.914099i	$0.632899\pi$
$930$	−166.090	−5.44632
$931$	−0.787038	−0.0257941
$932$	56.2655	1.84304
$933$	100.954	3.30510
$934$	19.1687	0.627219
$935$	−0.838244	−0.0274135
$936$	−10.1960	−0.333266
$937$	12.9847	0.424191	0.212095	−	0.977249i	$-0.431971\pi$
$937$	12.9847	0.424191	0.212095	+	0.977249i	$0.431971\pi$
$938$	21.9961	0.718198
$939$	−43.8448	−1.43082
$940$	55.3326	1.80475
$941$	40.1728	1.30960	0.654798	−	0.755804i	$-0.272754\pi$
$941$	40.1728	1.30960	0.654798	+	0.755804i	$0.272754\pi$
$942$	−12.2577	−0.399376
$943$	−20.9393	−0.681877
$944$	−2.04445	−0.0665413
$945$	33.9906	1.10571
$946$	−57.3192	−1.86361
$947$	17.1892	0.558574	0.279287	−	0.960208i	$-0.409902\pi$
$947$	17.1892	0.558574	0.279287	+	0.960208i	$0.409902\pi$
$948$	148.578	4.82558
$949$	7.55840	0.245356
$950$	0.172369	0.00559238
$951$	−14.7529	−0.478396
$952$	−0.139489	−0.00452085
$953$	−5.91681	−0.191664	−0.0958322	−	0.995398i	$-0.530551\pi$
$953$	−5.91681	−0.191664	−0.0958322	+	0.995398i	$0.530551\pi$
$954$	−103.324	−3.34525
$955$	8.49207	0.274797
$956$	87.1599	2.81895
$957$	−115.099	−3.72064
$958$	1.65636	0.0535146
$959$	−11.4139	−0.368575
$960$	98.9245	3.19278
$961$	63.9915	2.06424
$962$	−1.98092	−0.0638676
$963$	3.76843	0.121436
$964$	49.1967	1.58452
$965$	26.8842	0.865433
$966$	24.5872	0.791080
$967$	33.5827	1.07995	0.539974	−	0.841682i	$-0.318434\pi$
$967$	33.5827	1.07995	0.539974	+	0.841682i	$0.318434\pi$
$968$	62.3561	2.00420
$969$	0.0246486	0.000791828 0
$970$	−59.5295	−1.91138
$971$	−19.1921	−0.615903	−0.307951	−	0.951402i	$-0.599643\pi$
$971$	−19.1921	−0.615903	−0.307951	+	0.951402i	$0.599643\pi$
$972$	95.2040	3.05367
$973$	−15.0925	−0.483842
$974$	−56.3438	−1.80537
$975$	−1.10828	−0.0354934
$976$	2.95052	0.0944440
$977$	−18.8689	−0.603671	−0.301835	−	0.953360i	$-0.597599\pi$
$977$	−18.8689	−0.603671	−0.301835	+	0.953360i	$0.597599\pi$
$978$	47.9494	1.53325
$979$	−57.9509	−1.85212
$980$	42.5763	1.36005
$981$	−117.084	−3.73821
$982$	31.9978	1.02109
$983$	−58.9832	−1.88127	−0.940637	−	0.339415i	$-0.889771\pi$
$983$	−58.9832	−1.88127	−0.940637	+	0.339415i	$0.889771\pi$
$984$	47.6688	1.51963
$985$	16.4508	0.524164
$986$	−0.756488	−0.0240915
$987$	25.6182	0.815436
$988$	−0.240435	−0.00764927
$989$	13.6989	0.435601
$990$	−238.676	−7.58564
$991$	−34.3162	−1.09009	−0.545046	−	0.838406i	$-0.683488\pi$
$991$	−34.3162	−1.09009	−0.545046	+	0.838406i	$0.683488\pi$
$992$	−63.8698	−2.02787
$993$	43.9210	1.39379
$994$	−24.1307	−0.765378
$995$	−56.6994	−1.79749
$996$	22.3792	0.709112
$997$	−29.9366	−0.948102	−0.474051	−	0.880497i	$-0.657209\pi$
$997$	−29.9366	−0.948102	−0.474051	+	0.880497i	$0.657209\pi$
$998$	7.75523	0.245488
$999$	20.6011	0.651791

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1759.2.a.b.1.74	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1759.2.a.b.1.74	✓	86	1.1	even	1	trivial

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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

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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	1759.2.a.b.1.74

Level	$1759$
Weight	$2$
Character	1759.1
Self dual	yes
Analytic conductor	$14.046$
Analytic rank	$0$
Dimension	$86$
CM	no
Inner twists	$1$