LMFDB - Embedded newform 1759.2.a.b.1.63

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			1.63
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)

$f(q)$	$=$	$q+1.65306 q^{2} +3.39411 q^{3} +0.732607 q^{4} -0.248020 q^{5} +5.61067 q^{6} +5.21873 q^{7} -2.09508 q^{8} +8.51998 q^{9} -0.409991 q^{10} -5.09191 q^{11} +2.48655 q^{12} +0.389321 q^{13} +8.62687 q^{14} -0.841806 q^{15} -4.92850 q^{16} +3.46293 q^{17} +14.0840 q^{18} -7.69977 q^{19} -0.181701 q^{20} +17.7129 q^{21} -8.41723 q^{22} +3.40101 q^{23} -7.11092 q^{24} -4.93849 q^{25} +0.643572 q^{26} +18.7354 q^{27} +3.82328 q^{28} -4.21520 q^{29} -1.39156 q^{30} +1.42317 q^{31} -3.95696 q^{32} -17.2825 q^{33} +5.72443 q^{34} -1.29435 q^{35} +6.24180 q^{36} -2.30128 q^{37} -12.7282 q^{38} +1.32140 q^{39} +0.519620 q^{40} +4.16525 q^{41} +29.2806 q^{42} -5.78619 q^{43} -3.73037 q^{44} -2.11312 q^{45} +5.62207 q^{46} -3.01265 q^{47} -16.7279 q^{48} +20.2351 q^{49} -8.16361 q^{50} +11.7536 q^{51} +0.285220 q^{52} +7.48420 q^{53} +30.9708 q^{54} +1.26289 q^{55} -10.9336 q^{56} -26.1339 q^{57} -6.96799 q^{58} -11.0147 q^{59} -0.616713 q^{60} +0.822430 q^{61} +2.35259 q^{62} +44.4635 q^{63} +3.31592 q^{64} -0.0965594 q^{65} -28.5690 q^{66} -10.6782 q^{67} +2.53697 q^{68} +11.5434 q^{69} -2.13963 q^{70} +8.75733 q^{71} -17.8500 q^{72} -8.20031 q^{73} -3.80415 q^{74} -16.7618 q^{75} -5.64091 q^{76} -26.5733 q^{77} +2.18435 q^{78} -13.5726 q^{79} +1.22236 q^{80} +38.0302 q^{81} +6.88540 q^{82} -10.0693 q^{83} +12.9766 q^{84} -0.858875 q^{85} -9.56493 q^{86} -14.3069 q^{87} +10.6679 q^{88} +6.56982 q^{89} -3.49312 q^{90} +2.03176 q^{91} +2.49160 q^{92} +4.83041 q^{93} -4.98010 q^{94} +1.90969 q^{95} -13.4303 q^{96} +5.91197 q^{97} +33.4499 q^{98} -43.3830 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$86 q + 10 q^{2} + 11 q^{3} + 94 q^{4} + 30 q^{5} + 13 q^{6} + 30 q^{8} + 135 q^{9} + 9 q^{10} + 22 q^{11} + 26 q^{12} + 16 q^{13} + 52 q^{14} + 9 q^{15} + 102 q^{16} + 72 q^{17} + 21 q^{18} + 10 q^{19}+ \cdots - 17 q^{99}+O(q^{100})$ 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

)

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

$2$	1.65306	1.16889	0.584445	−	0.811433i	$-0.301312\pi$
$2$	1.65306	1.16889	0.584445	+	0.811433i	$0.301312\pi$
$3$	3.39411	1.95959	0.979795	−	0.200004i	$-0.0640954\pi$
$3$	3.39411	1.95959	0.979795	+	0.200004i	$0.0640954\pi$
$4$	0.732607	0.366304
$5$	−0.248020	−0.110918	−0.0554589	−	0.998461i	$-0.517662\pi$
$5$	−0.248020	−0.110918	−0.0554589	+	0.998461i	$0.517662\pi$
$6$	5.61067	2.29055
$7$	5.21873	1.97249	0.986247	−	0.165276i	$-0.0528515\pi$
$7$	5.21873	1.97249	0.986247	+	0.165276i	$0.0528515\pi$
$8$	−2.09508	−0.740721
$9$	8.51998	2.83999
$10$	−0.409991	−0.129651
$11$	−5.09191	−1.53527	−0.767634	−	0.640889i	$-0.778566\pi$
$11$	−5.09191	−1.53527	−0.767634	+	0.640889i	$0.778566\pi$
$12$	2.48655	0.717805
$13$	0.389321	0.107978	0.0539892	−	0.998542i	$-0.482806\pi$
$13$	0.389321	0.107978	0.0539892	+	0.998542i	$0.482806\pi$
$14$	8.62687	2.30563
$15$	−0.841806	−0.217353
$16$	−4.92850	−1.23213
$17$	3.46293	0.839884	0.419942	−	0.907551i	$-0.362050\pi$
$17$	3.46293	0.839884	0.419942	+	0.907551i	$0.362050\pi$
$18$	14.0840	3.31964
$19$	−7.69977	−1.76645	−0.883225	−	0.468950i	$-0.844632\pi$
$19$	−7.69977	−1.76645	−0.883225	+	0.468950i	$0.844632\pi$
$20$	−0.181701	−0.0406296
$21$	17.7129	3.86528
$22$	−8.41723	−1.79456
$23$	3.40101	0.709159	0.354580	−	0.935026i	$-0.384624\pi$
$23$	3.40101	0.709159	0.354580	+	0.935026i	$0.384624\pi$
$24$	−7.11092	−1.45151
$25$	−4.93849	−0.987697
$26$	0.643572	0.126215
$27$	18.7354	3.60563
$28$	3.82328	0.722532
$29$	−4.21520	−0.782744	−0.391372	−	0.920233i	$-0.627999\pi$
$29$	−4.21520	−0.782744	−0.391372	+	0.920233i	$0.627999\pi$
$30$	−1.39156	−0.254062
$31$	1.42317	0.255609	0.127805	−	0.991799i	$-0.459207\pi$
$31$	1.42317	0.255609	0.127805	+	0.991799i	$0.459207\pi$
$32$	−3.95696	−0.699498
$33$	−17.2825	−3.00850
$34$	5.72443	0.981732
$35$	−1.29435	−0.218785
$36$	6.24180	1.04030
$37$	−2.30128	−0.378328	−0.189164	−	0.981946i	$-0.560578\pi$
$37$	−2.30128	−0.378328	−0.189164	+	0.981946i	$0.560578\pi$
$38$	−12.7282	−2.06478
$39$	1.32140	0.211593
$40$	0.519620	0.0821591
$41$	4.16525	0.650502	0.325251	−	0.945628i	$-0.394551\pi$
$41$	4.16525	0.650502	0.325251	+	0.945628i	$0.394551\pi$
$42$	29.2806	4.51809
$43$	−5.78619	−0.882386	−0.441193	−	0.897412i	$-0.645445\pi$
$43$	−5.78619	−0.882386	−0.441193	+	0.897412i	$0.645445\pi$
$44$	−3.73037	−0.562374
$45$	−2.11312	−0.315006
$46$	5.62207	0.828929
$47$	−3.01265	−0.439441	−0.219720	−	0.975563i	$-0.570514\pi$
$47$	−3.01265	−0.439441	−0.219720	+	0.975563i	$0.570514\pi$
$48$	−16.7279	−2.41446
$49$	20.2351	2.89074
$50$	−8.16361	−1.15451
$51$	11.7536	1.64583
$52$	0.285220	0.0395529
$53$	7.48420	1.02803	0.514017	−	0.857780i	$-0.328157\pi$
$53$	7.48420	1.02803	0.514017	+	0.857780i	$0.328157\pi$
$54$	30.9708	4.21459
$55$	1.26289	0.170288
$56$	−10.9336	−1.46107
$57$	−26.1339	−3.46152
$58$	−6.96799	−0.914941
$59$	−11.0147	−1.43399	−0.716993	−	0.697081i	$-0.754482\pi$
$59$	−11.0147	−1.43399	−0.716993	+	0.697081i	$0.754482\pi$
$60$	−0.616713	−0.0796173
$61$	0.822430	0.105301	0.0526507	−	0.998613i	$-0.483233\pi$
$61$	0.822430	0.105301	0.0526507	+	0.998613i	$0.483233\pi$
$62$	2.35259	0.298779
$63$	44.4635	5.60187
$64$	3.31592	0.414490
$65$	−0.0965594	−0.0119767
$66$	−28.5690	−3.51660
$67$	−10.6782	−1.30455	−0.652275	−	0.757982i	$-0.726185\pi$
$67$	−10.6782	−1.30455	−0.652275	+	0.757982i	$0.726185\pi$
$68$	2.53697	0.307653
$69$	11.5434	1.38966
$70$	−2.13963	−0.255735
$71$	8.75733	1.03930	0.519652	−	0.854378i	$-0.326062\pi$
$71$	8.75733	1.03930	0.519652	+	0.854378i	$0.326062\pi$
$72$	−17.8500	−2.10364
$73$	−8.20031	−0.959773	−0.479887	−	0.877331i	$-0.659322\pi$
$73$	−8.20031	−0.959773	−0.479887	+	0.877331i	$0.659322\pi$
$74$	−3.80415	−0.442224
$75$	−16.7618	−1.93548
$76$	−5.64091	−0.647057
$77$	−26.5733	−3.02831
$78$	2.18435	0.247329
$79$	−13.5726	−1.52703	−0.763516	−	0.645789i	$-0.776529\pi$
$79$	−13.5726	−1.52703	−0.763516	+	0.645789i	$0.776529\pi$
$80$	1.22236	0.136665
$81$	38.0302	4.22557
$82$	6.88540	0.760366
$83$	−10.0693	−1.10525	−0.552623	−	0.833431i	$-0.686373\pi$
$83$	−10.0693	−1.10525	−0.552623	+	0.833431i	$0.686373\pi$
$84$	12.9766	1.41587
$85$	−0.858875	−0.0931580
$86$	−9.56493	−1.03141
$87$	−14.3069	−1.53386
$88$	10.6679	1.13721
$89$	6.56982	0.696400	0.348200	−	0.937420i	$-0.386793\pi$
$89$	6.56982	0.696400	0.348200	+	0.937420i	$0.386793\pi$
$90$	−3.49312	−0.368207
$91$	2.03176	0.212987
$92$	2.49160	0.259768
$93$	4.83041	0.500890
$94$	−4.98010	−0.513658
$95$	1.90969	0.195931
$96$	−13.4303	−1.37073
$97$	5.91197	0.600270	0.300135	−	0.953897i	$-0.402968\pi$
$97$	5.91197	0.600270	0.300135	+	0.953897i	$0.402968\pi$
$98$	33.4499	3.37895
$99$	−43.3830	−4.36015
$100$	−3.61797	−0.361797
$101$	8.10465	0.806443	0.403222	−	0.915102i	$-0.367890\pi$
$101$	8.10465	0.806443	0.403222	+	0.915102i	$0.367890\pi$
$102$	19.4294	1.92379
$103$	13.0124	1.28215	0.641076	−	0.767478i	$-0.278488\pi$
$103$	13.0124	1.28215	0.641076	+	0.767478i	$0.278488\pi$
$104$	−0.815658	−0.0799819
$105$	−4.39316	−0.428728
$106$	12.3718	1.20166
$107$	−7.16473	−0.692641	−0.346321	−	0.938116i	$-0.612569\pi$
$107$	−7.16473	−0.692641	−0.346321	+	0.938116i	$0.612569\pi$
$108$	13.7257	1.32076
$109$	7.06538	0.676740	0.338370	−	0.941013i	$-0.390124\pi$
$109$	7.06538	0.676740	0.338370	+	0.941013i	$0.390124\pi$
$110$	2.08764	0.199048
$111$	−7.81079	−0.741368
$112$	−25.7205	−2.43036
$113$	16.4406	1.54660	0.773301	−	0.634039i	$-0.218604\pi$
$113$	16.4406	1.54660	0.773301	+	0.634039i	$0.218604\pi$
$114$	−43.2009	−4.04613
$115$	−0.843517	−0.0786584
$116$	−3.08809	−0.286722
$117$	3.31701	0.306658
$118$	−18.2079	−1.67617
$119$	18.0721	1.65667
$120$	1.76365	0.160998
$121$	14.9275	1.35705
$122$	1.35953	0.123086
$123$	14.1373	1.27472
$124$	1.04263	0.0936307
$125$	2.46494	0.220471
$126$	73.5008	6.54797
$127$	−4.14007	−0.367372	−0.183686	−	0.982985i	$-0.558803\pi$
$127$	−4.14007	−0.367372	−0.183686	+	0.982985i	$0.558803\pi$
$128$	13.3953	1.18399
$129$	−19.6390	−1.72912
$130$	−0.159618	−0.0139995
$131$	8.02893	0.701491	0.350745	−	0.936471i	$-0.385928\pi$
$131$	8.02893	0.701491	0.350745	+	0.936471i	$0.385928\pi$
$132$	−12.6613	−1.10202
$133$	−40.1830	−3.48431
$134$	−17.6517	−1.52488
$135$	−4.64675	−0.399929
$136$	−7.25510	−0.622120
$137$	−5.14949	−0.439951	−0.219976	−	0.975505i	$-0.570598\pi$
$137$	−5.14949	−0.439951	−0.219976	+	0.975505i	$0.570598\pi$
$138$	19.0819	1.62436
$139$	−6.11477	−0.518648	−0.259324	−	0.965790i	$-0.583500\pi$
$139$	−6.11477	−0.518648	−0.259324	+	0.965790i	$0.583500\pi$
$140$	−0.948248	−0.0801416
$141$	−10.2253	−0.861124
$142$	14.4764	1.21483
$143$	−1.98239	−0.165776
$144$	−41.9907	−3.49923
$145$	1.04545	0.0868202
$146$	−13.5556	−1.12187
$147$	68.6803	5.66466
$148$	−1.68593	−0.138583
$149$	16.5652	1.35707	0.678536	−	0.734567i	$-0.262615\pi$
$149$	16.5652	1.35707	0.678536	+	0.734567i	$0.262615\pi$
$150$	−27.7082	−2.26237
$151$	0.151371	0.0123184	0.00615920	−	0.999981i	$-0.498039\pi$
$151$	0.151371	0.0123184	0.00615920	+	0.999981i	$0.498039\pi$
$152$	16.1316	1.30845
$153$	29.5041	2.38527
$154$	−43.9272	−3.53976
$155$	−0.352975	−0.0283516
$156$	0.968067	0.0775074
$157$	13.4004	1.06947	0.534736	−	0.845019i	$-0.320411\pi$
$157$	13.4004	1.06947	0.534736	+	0.845019i	$0.320411\pi$
$158$	−22.4363	−1.78493
$159$	25.4022	2.01453
$160$	0.981403	0.0775867
$161$	17.7489	1.39881
$162$	62.8661	4.93923
$163$	2.55654	0.200243	0.100122	−	0.994975i	$-0.468077\pi$
$163$	2.55654	0.200243	0.100122	+	0.994975i	$0.468077\pi$
$164$	3.05149	0.238281
$165$	4.28640	0.333696
$166$	−16.6451	−1.29191
$167$	−11.7546	−0.909601	−0.454801	−	0.890593i	$-0.650289\pi$
$167$	−11.7546	−0.909601	−0.454801	+	0.890593i	$0.650289\pi$
$168$	−37.1100	−2.86310
$169$	−12.8484	−0.988341
$170$	−1.41977	−0.108891
$171$	−65.6019	−5.01671
$172$	−4.23901	−0.323221
$173$	−0.888137	−0.0675238	−0.0337619	−	0.999430i	$-0.510749\pi$
$173$	−0.888137	−0.0675238	−0.0337619	+	0.999430i	$0.510749\pi$
$174$	−23.6501	−1.79291
$175$	−25.7726	−1.94823
$176$	25.0955	1.89164
$177$	−37.3849	−2.81002
$178$	10.8603	0.814015
$179$	10.2434	0.765627	0.382813	−	0.923826i	$-0.374955\pi$
$179$	10.2434	0.765627	0.382813	+	0.923826i	$0.374955\pi$
$180$	−1.54809	−0.115388
$181$	−2.31415	−0.172009	−0.0860047	−	0.996295i	$-0.527410\pi$
$181$	−2.31415	−0.172009	−0.0860047	+	0.996295i	$0.527410\pi$
$182$	3.35863	0.248958
$183$	2.79142	0.206348
$184$	−7.12537	−0.525289
$185$	0.570762	0.0419633
$186$	7.98495	0.585485
$187$	−17.6329	−1.28945
$188$	−2.20709	−0.160969
$189$	97.7751	7.11210
$190$	3.15684	0.229021
$191$	−8.39367	−0.607345	−0.303672	−	0.952776i	$-0.598213\pi$
$191$	−8.39367	−0.607345	−0.303672	+	0.952776i	$0.598213\pi$
$192$	11.2546	0.812230
$193$	10.3645	0.746056	0.373028	−	0.927820i	$-0.378319\pi$
$193$	10.3645	0.746056	0.373028	+	0.927820i	$0.378319\pi$
$194$	9.77284	0.701649
$195$	−0.327733	−0.0234695
$196$	14.8244	1.05889
$197$	2.26266	0.161208	0.0806040	−	0.996746i	$-0.474315\pi$
$197$	2.26266	0.161208	0.0806040	+	0.996746i	$0.474315\pi$
$198$	−71.7146	−5.09654
$199$	−9.73185	−0.689873	−0.344936	−	0.938626i	$-0.612100\pi$
$199$	−9.73185	−0.689873	−0.344936	+	0.938626i	$0.612100\pi$
$200$	10.3465	0.731608
$201$	−36.2430	−2.55639
$202$	13.3975	0.942643
$203$	−21.9980	−1.54396
$204$	8.61075	0.602873
$205$	−1.03306	−0.0721523
$206$	21.5103	1.49869
$207$	28.9765	2.01401
$208$	−1.91877	−0.133043
$209$	39.2065	2.71197
$210$	−7.26215	−0.501136
$211$	−5.21241	−0.358837	−0.179419	−	0.983773i	$-0.557422\pi$
$211$	−5.21241	−0.358837	−0.179419	+	0.983773i	$0.557422\pi$
$212$	5.48298	0.376573
$213$	29.7233	2.03661
$214$	−11.8437	−0.809621
$215$	1.43509	0.0978723
$216$	−39.2521	−2.67077
$217$	7.42716	0.504188
$218$	11.6795	0.791035
$219$	−27.8327	−1.88076
$220$	0.925204	0.0623773
$221$	1.34819	0.0906893
$222$	−12.9117	−0.866577
$223$	−29.1870	−1.95451	−0.977253	−	0.212079i	$-0.931977\pi$
$223$	−29.1870	−1.95451	−0.977253	+	0.212079i	$0.931977\pi$
$224$	−20.6503	−1.37976
$225$	−42.0758	−2.80505
$226$	27.1773	1.80781
$227$	5.07623	0.336921	0.168461	−	0.985708i	$-0.446120\pi$
$227$	5.07623	0.336921	0.168461	+	0.985708i	$0.446120\pi$
$228$	−19.1459	−1.26797
$229$	−14.2475	−0.941502	−0.470751	−	0.882266i	$-0.656017\pi$
$229$	−14.2475	−0.941502	−0.470751	+	0.882266i	$0.656017\pi$
$230$	−1.39438	−0.0919430
$231$	−90.1927	−5.93424
$232$	8.83117	0.579795
$233$	14.5402	0.952560	0.476280	−	0.879294i	$-0.341985\pi$
$233$	14.5402	0.952560	0.476280	+	0.879294i	$0.341985\pi$
$234$	5.48322	0.358449
$235$	0.747197	0.0487418
$236$	−8.06941	−0.525274
$237$	−46.0668	−2.99236
$238$	29.8743	1.93646
$239$	−2.76005	−0.178533	−0.0892664	−	0.996008i	$-0.528452\pi$
$239$	−2.76005	−0.178533	−0.0892664	+	0.996008i	$0.528452\pi$
$240$	4.14884	0.267807
$241$	−28.5876	−1.84149	−0.920743	−	0.390169i	$-0.872417\pi$
$241$	−28.5876	−1.84149	−0.920743	+	0.390169i	$0.872417\pi$
$242$	24.6761	1.58624
$243$	72.8722	4.67476
$244$	0.602519	0.0385723
$245$	−5.01871	−0.320634
$246$	23.3698	1.49001
$247$	−2.99769	−0.190738
$248$	−2.98166	−0.189335
$249$	−34.1762	−2.16583
$250$	4.07469	0.257706
$251$	9.79772	0.618427	0.309213	−	0.950993i	$-0.399934\pi$
$251$	9.79772	0.618427	0.309213	+	0.950993i	$0.399934\pi$
$252$	32.5743	2.05199
$253$	−17.3176	−1.08875
$254$	−6.84379	−0.429418
$255$	−2.91512	−0.182552
$256$	15.5114	0.969465
$257$	−4.78846	−0.298696	−0.149348	−	0.988785i	$-0.547717\pi$
$257$	−4.78846	−0.298696	−0.149348	+	0.988785i	$0.547717\pi$
$258$	−32.4644	−2.02115
$259$	−12.0098	−0.746250
$260$	−0.0707401	−0.00438711
$261$	−35.9135	−2.22299
$262$	13.2723	0.819966
$263$	5.34367	0.329505	0.164752	−	0.986335i	$-0.447318\pi$
$263$	5.34367	0.329505	0.164752	+	0.986335i	$0.447318\pi$
$264$	36.2081	2.22846
$265$	−1.85623	−0.114027
$266$	−66.4250	−4.07278
$267$	22.2987	1.36466
$268$	−7.82293	−0.477862
$269$	2.93720	0.179084	0.0895421	−	0.995983i	$-0.471460\pi$
$269$	2.93720	0.179084	0.0895421	+	0.995983i	$0.471460\pi$
$270$	−7.68136	−0.467473
$271$	15.3690	0.933601	0.466801	−	0.884363i	$-0.345407\pi$
$271$	15.3690	0.933601	0.466801	+	0.884363i	$0.345407\pi$
$272$	−17.0671	−1.03484
$273$	6.89603	0.417367
$274$	−8.51242	−0.514254
$275$	25.1463	1.51638
$276$	8.45678	0.509038
$277$	−19.7095	−1.18423	−0.592113	−	0.805855i	$-0.701706\pi$
$277$	−19.7095	−1.18423	−0.592113	+	0.805855i	$0.701706\pi$
$278$	−10.1081	−0.606243
$279$	12.1254	0.725929
$280$	2.71176	0.162058
$281$	0.697310	0.0415981	0.0207990	−	0.999784i	$-0.493379\pi$
$281$	0.697310	0.0415981	0.0207990	+	0.999784i	$0.493379\pi$
$282$	−16.9030	−1.00656
$283$	10.9282	0.649616	0.324808	−	0.945780i	$-0.394700\pi$
$283$	10.9282	0.649616	0.324808	+	0.945780i	$0.394700\pi$
$284$	6.41568	0.380701
$285$	6.48171	0.383944
$286$	−3.27701	−0.193774
$287$	21.7373	1.28311
$288$	−33.7132	−1.98657
$289$	−5.00811	−0.294595
$290$	1.72820	0.101483
$291$	20.0659	1.17628
$292$	−6.00760	−0.351568
$293$	−29.3063	−1.71209	−0.856046	−	0.516900i	$-0.827086\pi$
$293$	−29.3063	−1.71209	−0.856046	+	0.516900i	$0.827086\pi$
$294$	113.533	6.62136
$295$	2.73185	0.159054
$296$	4.82135	0.280235
$297$	−95.3991	−5.53561
$298$	27.3832	1.58627
$299$	1.32409	0.0765739
$300$	−12.2798	−0.708974
$301$	−30.1966	−1.74050
$302$	0.250225	0.0143989
$303$	27.5081	1.58030
$304$	37.9483	2.17649
$305$	−0.203979	−0.0116798
$306$	48.7721	2.78811
$307$	−12.5836	−0.718186	−0.359093	−	0.933302i	$-0.616914\pi$
$307$	−12.5836	−0.718186	−0.359093	+	0.933302i	$0.616914\pi$
$308$	−19.4678	−1.10928
$309$	44.1656	2.51249
$310$	−0.583489	−0.0331399
$311$	7.91347	0.448731	0.224366	−	0.974505i	$-0.427969\pi$
$311$	7.91347	0.448731	0.224366	+	0.974505i	$0.427969\pi$
$312$	−2.76843	−0.156732
$313$	12.8422	0.725884	0.362942	−	0.931812i	$-0.381772\pi$
$313$	12.8422	0.725884	0.362942	+	0.931812i	$0.381772\pi$
$314$	22.1517	1.25010
$315$	−11.0278	−0.621347
$316$	−9.94336	−0.559358
$317$	27.2960	1.53310	0.766549	−	0.642186i	$-0.221972\pi$
$317$	27.2960	1.53310	0.766549	+	0.642186i	$0.221972\pi$
$318$	41.9914	2.35476
$319$	21.4634	1.20172
$320$	−0.822412	−0.0459743
$321$	−24.3179	−1.35729
$322$	29.3401	1.63506
$323$	−26.6638	−1.48361
$324$	27.8612	1.54784
$325$	−1.92266	−0.106650
$326$	4.22611	0.234062
$327$	23.9807	1.32613
$328$	−8.72651	−0.481841
$329$	−15.7222	−0.866794
$330$	7.08567	0.390053
$331$	14.5444	0.799433	0.399716	−	0.916639i	$-0.369109\pi$
$331$	14.5444	0.799433	0.399716	+	0.916639i	$0.369109\pi$
$332$	−7.37682	−0.404856
$333$	−19.6069	−1.07445
$334$	−19.4311	−1.06322
$335$	2.64841	0.144698
$336$	−87.2983	−4.76251
$337$	−27.4734	−1.49657	−0.748285	−	0.663378i	$-0.769122\pi$
$337$	−27.4734	−1.49657	−0.748285	+	0.663378i	$0.769122\pi$
$338$	−21.2392	−1.15526
$339$	55.8012	3.03071
$340$	−0.629218	−0.0341241
$341$	−7.24666	−0.392429
$342$	−108.444	−5.86398
$343$	69.0707	3.72947
$344$	12.1225	0.653602
$345$	−2.86299	−0.154138
$346$	−1.46814	−0.0789279
$347$	7.39807	0.397149	0.198575	−	0.980086i	$-0.436369\pi$
$347$	7.39807	0.397149	0.198575	+	0.980086i	$0.436369\pi$
$348$	−10.4813	−0.561858
$349$	4.96950	0.266011	0.133006	−	0.991115i	$-0.457537\pi$
$349$	4.96950	0.266011	0.133006	+	0.991115i	$0.457537\pi$
$350$	−42.6037	−2.27726
$351$	7.29410	0.389331
$352$	20.1484	1.07392
$353$	−9.80863	−0.522061	−0.261030	−	0.965331i	$-0.584062\pi$
$353$	−9.80863	−0.522061	−0.261030	+	0.965331i	$0.584062\pi$
$354$	−61.7995	−3.28461
$355$	−2.17199	−0.115277
$356$	4.81310	0.255094
$357$	61.3387	3.24639
$358$	16.9329	0.894934
$359$	−27.4048	−1.44637	−0.723184	−	0.690655i	$-0.757322\pi$
$359$	−27.4048	−1.44637	−0.723184	+	0.690655i	$0.757322\pi$
$360$	4.42715	0.233331
$361$	40.2865	2.12034
$362$	−3.82543	−0.201060
$363$	50.6656	2.65926
$364$	1.48849	0.0780178
$365$	2.03384	0.106456
$366$	4.61438	0.241198
$367$	−2.86167	−0.149378	−0.0746890	−	0.997207i	$-0.523796\pi$
$367$	−2.86167	−0.149378	−0.0746890	+	0.997207i	$0.523796\pi$
$368$	−16.7619	−0.873773
$369$	35.4878	1.84742
$370$	0.943504	0.0490504
$371$	39.0580	2.02779
$372$	3.53879	0.183478
$373$	−5.46183	−0.282803	−0.141401	−	0.989952i	$-0.545161\pi$
$373$	−5.46183	−0.282803	−0.141401	+	0.989952i	$0.545161\pi$
$374$	−29.1483	−1.50722
$375$	8.36628	0.432033
$376$	6.31174	0.325503
$377$	−1.64107	−0.0845194
$378$	161.628	8.31326
$379$	−4.72712	−0.242816	−0.121408	−	0.992603i	$-0.538741\pi$
$379$	−4.72712	−0.242816	−0.121408	+	0.992603i	$0.538741\pi$
$380$	1.39906	0.0717701
$381$	−14.0519	−0.719899
$382$	−13.8752	−0.709919
$383$	5.83789	0.298302	0.149151	−	0.988814i	$-0.452346\pi$
$383$	5.83789	0.298302	0.149151	+	0.988814i	$0.452346\pi$
$384$	45.4652	2.32014
$385$	6.59070	0.335893
$386$	17.1332	0.872058
$387$	−49.2983	−2.50597
$388$	4.33115	0.219881
$389$	−18.8576	−0.956116	−0.478058	−	0.878328i	$-0.658659\pi$
$389$	−18.8576	−0.956116	−0.478058	+	0.878328i	$0.658659\pi$
$390$	−0.541762	−0.0274332
$391$	11.7775	0.595612
$392$	−42.3942	−2.14123
$393$	27.2511	1.37463
$394$	3.74032	0.188434
$395$	3.36626	0.169375
$396$	−31.7827	−1.59714
$397$	−3.81702	−0.191571	−0.0957853	−	0.995402i	$-0.530536\pi$
$397$	−3.81702	−0.191571	−0.0957853	+	0.995402i	$0.530536\pi$
$398$	−16.0873	−0.806385
$399$	−136.386	−6.82782
$400$	24.3393	1.21697
$401$	−19.0411	−0.950865	−0.475432	−	0.879752i	$-0.657708\pi$
$401$	−19.0411	−0.950865	−0.475432	+	0.879752i	$0.657708\pi$
$402$	−59.9119	−2.98813
$403$	0.554072	0.0276003
$404$	5.93753	0.295403
$405$	−9.43222	−0.468691
$406$	−36.3640	−1.80472
$407$	11.7179	0.580835
$408$	−24.6246	−1.21910
$409$	35.6584	1.76319	0.881597	−	0.472003i	$-0.156469\pi$
$409$	35.6584	1.76319	0.881597	+	0.472003i	$0.156469\pi$
$410$	−1.70772	−0.0843380
$411$	−17.4780	−0.862124
$412$	9.53299	0.469657
$413$	−57.4825	−2.82853
$414$	47.9000	2.35415
$415$	2.49738	0.122591
$416$	−1.54053	−0.0755306
$417$	−20.7542	−1.01634
$418$	64.8107	3.17000
$419$	29.4082	1.43668	0.718341	−	0.695691i	$-0.244902\pi$
$419$	29.4082	1.43668	0.718341	+	0.695691i	$0.244902\pi$
$420$	−3.21846	−0.157045
$421$	10.3743	0.505613	0.252807	−	0.967517i	$-0.418646\pi$
$421$	10.3743	0.505613	0.252807	+	0.967517i	$0.418646\pi$
$422$	−8.61643	−0.419441
$423$	−25.6678	−1.24801
$424$	−15.6800	−0.761487
$425$	−17.1016	−0.829551
$426$	49.1345	2.38057
$427$	4.29204	0.207707
$428$	−5.24894	−0.253717
$429$	−6.72845	−0.324852
$430$	2.37229	0.114402
$431$	11.8838	0.572423	0.286212	−	0.958166i	$-0.407604\pi$
$431$	11.8838	0.572423	0.286212	+	0.958166i	$0.407604\pi$
$432$	−92.3376	−4.44259
$433$	6.97315	0.335108	0.167554	−	0.985863i	$-0.446413\pi$
$433$	6.97315	0.335108	0.167554	+	0.985863i	$0.446413\pi$
$434$	12.2775	0.589341
$435$	3.54838	0.170132
$436$	5.17615	0.247893
$437$	−26.1870	−1.25269
$438$	−46.0092	−2.19840
$439$	−2.40033	−0.114561	−0.0572806	−	0.998358i	$-0.518243\pi$
$439$	−2.40033	−0.114561	−0.0572806	+	0.998358i	$0.518243\pi$
$440$	−2.64586	−0.126136
$441$	172.403	8.20967
$442$	2.22864	0.106006
$443$	13.3945	0.636390	0.318195	−	0.948025i	$-0.396923\pi$
$443$	13.3945	0.636390	0.318195	+	0.948025i	$0.396923\pi$
$444$	−5.72224	−0.271566
$445$	−1.62944	−0.0772431
$446$	−48.2478	−2.28460
$447$	56.2240	2.65930
$448$	17.3049	0.817579
$449$	34.3897	1.62295	0.811475	−	0.584388i	$-0.198665\pi$
$449$	34.3897	1.62295	0.811475	+	0.584388i	$0.198665\pi$
$450$	−69.5538	−3.27880
$451$	−21.2091	−0.998695
$452$	12.0445	0.566526
$453$	0.513770	0.0241390
$454$	8.39131	0.393824
$455$	−0.503917	−0.0236240
$456$	54.7525	2.56402
$457$	35.5425	1.66261	0.831304	−	0.555818i	$-0.187595\pi$
$457$	35.5425	1.66261	0.831304	+	0.555818i	$0.187595\pi$
$458$	−23.5520	−1.10051
$459$	64.8795	3.02832
$460$	−0.617967	−0.0288128
$461$	36.7383	1.71107	0.855536	−	0.517743i	$-0.173227\pi$
$461$	36.7383	1.71107	0.855536	+	0.517743i	$0.173227\pi$
$462$	−149.094	−6.93648
$463$	−16.0358	−0.745246	−0.372623	−	0.927983i	$-0.621541\pi$
$463$	−16.0358	−0.745246	−0.372623	+	0.927983i	$0.621541\pi$
$464$	20.7746	0.964439
$465$	−1.19804	−0.0555576
$466$	24.0358	1.11344
$467$	14.2901	0.661265	0.330633	−	0.943760i	$-0.392738\pi$
$467$	14.2901	0.661265	0.330633	+	0.943760i	$0.392738\pi$
$468$	2.43007	0.112330
$469$	−55.7267	−2.57322
$470$	1.23516	0.0569738
$471$	45.4826	2.09573
$472$	23.0765	1.06218
$473$	29.4628	1.35470
$474$	−76.1511	−3.49774
$475$	38.0252	1.74472
$476$	13.2398	0.606843
$477$	63.7652	2.91961
$478$	−4.56253	−0.208685
$479$	−28.7148	−1.31201	−0.656007	−	0.754755i	$-0.727756\pi$
$479$	−28.7148	−1.31201	−0.656007	+	0.754755i	$0.727756\pi$
$480$	3.33099	0.152038
$481$	−0.895937	−0.0408512
$482$	−47.2570	−2.15250
$483$	60.2419	2.74110
$484$	10.9360	0.497091
$485$	−1.46628	−0.0665806
$486$	120.462	5.46428
$487$	42.6361	1.93203	0.966014	−	0.258491i	$-0.0832253\pi$
$487$	42.6361	1.93203	0.966014	+	0.258491i	$0.0832253\pi$
$488$	−1.72305	−0.0779990
$489$	8.67716	0.392395
$490$	−8.29623	−0.374786
$491$	−2.12331	−0.0958235	−0.0479118	−	0.998852i	$-0.515257\pi$
$491$	−2.12331	−0.0958235	−0.0479118	+	0.998852i	$0.515257\pi$
$492$	10.3571	0.466934
$493$	−14.5970	−0.657414
$494$	−4.95536	−0.222952
$495$	10.7598	0.483618
$496$	−7.01411	−0.314943
$497$	45.7021	2.05002
$498$	−56.4953	−2.53162
$499$	16.8343	0.753605	0.376803	−	0.926294i	$-0.377023\pi$
$499$	16.8343	0.753605	0.376803	+	0.926294i	$0.377023\pi$
$500$	1.80583	0.0807593
$501$	−39.8965	−1.78245
$502$	16.1962	0.722873
$503$	24.3694	1.08658	0.543290	−	0.839545i	$-0.317178\pi$
$503$	24.3694	1.08658	0.543290	+	0.839545i	$0.317178\pi$
$504$	−93.1544	−4.14943
$505$	−2.01011	−0.0894488
$506$	−28.6271	−1.27263
$507$	−43.6090	−1.93674
$508$	−3.03305	−0.134570
$509$	−34.0372	−1.50867	−0.754336	−	0.656488i	$-0.772041\pi$
$509$	−34.0372	−1.50867	−0.754336	+	0.656488i	$0.772041\pi$
$510$	−4.81886	−0.213383
$511$	−42.7952	−1.89315
$512$	−1.14931	−0.0507928
$513$	−144.259	−6.36917
$514$	−7.91560	−0.349142
$515$	−3.22733	−0.142213
$516$	−14.3877	−0.633381
$517$	15.3402	0.674659
$518$	−19.8528	−0.872284
$519$	−3.01443	−0.132319
$520$	0.202299	0.00887141
$521$	−3.05217	−0.133718	−0.0668590	−	0.997762i	$-0.521298\pi$
$521$	−3.05217	−0.133718	−0.0668590	+	0.997762i	$0.521298\pi$
$522$	−59.3671	−2.59843
$523$	−44.1264	−1.92951	−0.964757	−	0.263143i	$-0.915241\pi$
$523$	−44.1264	−1.92951	−0.964757	+	0.263143i	$0.915241\pi$
$524$	5.88205	0.256959
$525$	−87.4751	−3.81773
$526$	8.83340	0.385155
$527$	4.92835	0.214682
$528$	85.1768	3.70684
$529$	−11.4331	−0.497093
$530$	−3.06846	−0.133285
$531$	−93.8446	−4.07251
$532$	−29.4384	−1.27632
$533$	1.62162	0.0702402
$534$	36.8611	1.59514
$535$	1.77699	0.0768262
$536$	22.3717	0.966309
$537$	34.7672	1.50031
$538$	4.85537	0.209330
$539$	−103.035	−4.43805
$540$	−3.40425	−0.146495
$541$	12.7563	0.548435	0.274218	−	0.961668i	$-0.411581\pi$
$541$	12.7563	0.548435	0.274218	+	0.961668i	$0.411581\pi$
$542$	25.4059	1.09128
$543$	−7.85448	−0.337068
$544$	−13.7027	−0.587497
$545$	−1.75235	−0.0750625
$546$	11.3996	0.487856
$547$	24.9606	1.06724	0.533620	−	0.845725i	$-0.320831\pi$
$547$	24.9606	1.06724	0.533620	+	0.845725i	$0.320831\pi$
$548$	−3.77256	−0.161156
$549$	7.00709	0.299055
$550$	41.5684	1.77248
$551$	32.4561	1.38268
$552$	−24.1843	−1.02935
$553$	−70.8315	−3.01206
$554$	−32.5809	−1.38423
$555$	1.93723	0.0822308
$556$	−4.47973	−0.189983
$557$	−13.7776	−0.583776	−0.291888	−	0.956453i	$-0.594283\pi$
$557$	−13.7776	−0.583776	−0.291888	+	0.956453i	$0.594283\pi$
$558$	20.0440	0.848531
$559$	−2.25269	−0.0952786
$560$	6.37919	0.269570
$561$	−59.8481	−2.52679
$562$	1.15270	0.0486235
$563$	24.1004	1.01571	0.507855	−	0.861442i	$-0.330438\pi$
$563$	24.1004	1.01571	0.507855	+	0.861442i	$0.330438\pi$
$564$	−7.49111	−0.315433
$565$	−4.07759	−0.171546
$566$	18.0650	0.759330
$567$	198.469	8.33492
$568$	−18.3473	−0.769835
$569$	−29.7332	−1.24648	−0.623241	−	0.782030i	$-0.714184\pi$
$569$	−29.7332	−1.24648	−0.623241	+	0.782030i	$0.714184\pi$
$570$	10.7147	0.448788
$571$	−3.01461	−0.126158	−0.0630788	−	0.998009i	$-0.520092\pi$
$571$	−3.01461	−0.126158	−0.0630788	+	0.998009i	$0.520092\pi$
$572$	−1.45231	−0.0607242
$573$	−28.4891	−1.19015
$574$	35.9331	1.49982
$575$	−16.7958	−0.700435
$576$	28.2516	1.17715
$577$	−16.4062	−0.682998	−0.341499	−	0.939882i	$-0.610935\pi$
$577$	−16.4062	−0.682998	−0.341499	+	0.939882i	$0.610935\pi$
$578$	−8.27871	−0.344349
$579$	35.1784	1.46196
$580$	0.765907	0.0318026
$581$	−52.5488	−2.18009
$582$	33.1701	1.37495
$583$	−38.1088	−1.57831
$584$	17.1803	0.710924
$585$	−0.822684	−0.0340138
$586$	−48.4451	−2.00125
$587$	20.2534	0.835945	0.417973	−	0.908460i	$-0.362741\pi$
$587$	20.2534	0.835945	0.417973	+	0.908460i	$0.362741\pi$
$588$	50.3157	2.07498
$589$	−10.9581	−0.451521
$590$	4.51591	0.185917
$591$	7.67972	0.315902
$592$	11.3419	0.466147
$593$	33.3880	1.37108	0.685539	−	0.728035i	$-0.259566\pi$
$593$	33.3880	1.37108	0.685539	+	0.728035i	$0.259566\pi$
$594$	−157.700	−6.47052
$595$	−4.48224	−0.183754
$596$	12.1358	0.497100
$597$	−33.0310	−1.35187
$598$	2.18879	0.0895064
$599$	−0.653102	−0.0266850	−0.0133425	−	0.999911i	$-0.504247\pi$
$599$	−0.653102	−0.0266850	−0.0133425	+	0.999911i	$0.504247\pi$
$600$	35.1172	1.43365
$601$	35.7275	1.45735	0.728677	−	0.684857i	$-0.240135\pi$
$601$	35.7275	1.45735	0.728677	+	0.684857i	$0.240135\pi$
$602$	−49.9168	−2.03446
$603$	−90.9782	−3.70492
$604$	0.110896	0.00451228
$605$	−3.70232	−0.150521
$606$	45.4725	1.84719
$607$	−30.2534	−1.22795	−0.613973	−	0.789327i	$-0.710430\pi$
$607$	−30.2534	−1.22795	−0.613973	+	0.789327i	$0.710430\pi$
$608$	30.4677	1.23563
$609$	−74.6637	−3.02553
$610$	−0.337189	−0.0136524
$611$	−1.17289	−0.0474501
$612$	21.6149	0.873732
$613$	−18.2433	−0.736838	−0.368419	−	0.929660i	$-0.620101\pi$
$613$	−18.2433	−0.736838	−0.368419	+	0.929660i	$0.620101\pi$
$614$	−20.8015	−0.839480
$615$	−3.50633	−0.141389
$616$	55.6731	2.24313
$617$	−37.2194	−1.49840	−0.749198	−	0.662346i	$-0.769561\pi$
$617$	−37.2194	−1.49840	−0.749198	+	0.662346i	$0.769561\pi$
$618$	73.0083	2.93683
$619$	−46.2028	−1.85705	−0.928523	−	0.371274i	$-0.878921\pi$
$619$	−46.2028	−1.85705	−0.928523	+	0.371274i	$0.878921\pi$
$620$	−0.258592	−0.0103853
$621$	63.7194	2.55697
$622$	13.0814	0.524518
$623$	34.2861	1.37365
$624$	−6.51252	−0.260709
$625$	24.0811	0.963243
$626$	21.2289	0.848478
$627$	133.071	5.31436
$628$	9.81727	0.391752
$629$	−7.96917	−0.317752
$630$	−18.2296	−0.726286
$631$	20.1051	0.800373	0.400187	−	0.916434i	$-0.368945\pi$
$631$	20.1051	0.800373	0.400187	+	0.916434i	$0.368945\pi$
$632$	28.4356	1.13111
$633$	−17.6915	−0.703174
$634$	45.1220	1.79202
$635$	1.02682	0.0407481
$636$	18.6098	0.737928
$637$	7.87798	0.312137
$638$	35.4803	1.40468
$639$	74.6123	2.95162
$640$	−3.32230	−0.131326
$641$	39.9385	1.57748	0.788738	−	0.614729i	$-0.210735\pi$
$641$	39.9385	1.57748	0.788738	+	0.614729i	$0.210735\pi$
$642$	−40.1989	−1.58653
$643$	−11.2149	−0.442272	−0.221136	−	0.975243i	$-0.570977\pi$
$643$	−11.2149	−0.442272	−0.221136	+	0.975243i	$0.570977\pi$
$644$	13.0030	0.512390
$645$	4.87085	0.191790
$646$	−44.0768	−1.73418
$647$	−22.4270	−0.881696	−0.440848	−	0.897582i	$-0.645322\pi$
$647$	−22.4270	−0.881696	−0.440848	+	0.897582i	$0.645322\pi$
$648$	−79.6761	−3.12997
$649$	56.0856	2.20155
$650$	−3.17827	−0.124662
$651$	25.2086	0.988002
$652$	1.87294	0.0733498
$653$	23.0516	0.902079	0.451039	−	0.892504i	$-0.351053\pi$
$653$	23.0516	0.902079	0.451039	+	0.892504i	$0.351053\pi$
$654$	39.6415	1.55010
$655$	−1.99133	−0.0778078
$656$	−20.5284	−0.801500
$657$	−69.8665	−2.72575
$658$	−25.9898	−1.01319
$659$	−28.0890	−1.09419	−0.547097	−	0.837069i	$-0.684267\pi$
$659$	−28.0890	−1.09419	−0.547097	+	0.837069i	$0.684267\pi$
$660$	3.14025	0.122234
$661$	22.6080	0.879349	0.439675	−	0.898157i	$-0.355094\pi$
$661$	22.6080	0.879349	0.439675	+	0.898157i	$0.355094\pi$
$662$	24.0428	0.934449
$663$	4.57592	0.177714
$664$	21.0959	0.818679
$665$	9.96618	0.386472
$666$	−32.4113	−1.25591
$667$	−14.3359	−0.555090
$668$	−8.61153	−0.333190
$669$	−99.0638	−3.83003
$670$	4.37797	0.169136
$671$	−4.18774	−0.161666
$672$	−70.0893	−2.70376
$673$	13.6455	0.525997	0.262998	−	0.964796i	$-0.415289\pi$
$673$	13.6455	0.525997	0.262998	+	0.964796i	$0.415289\pi$
$674$	−45.4151	−1.74932
$675$	−92.5247	−3.56128
$676$	−9.41285	−0.362033
$677$	−2.09832	−0.0806450	−0.0403225	−	0.999187i	$-0.512839\pi$
$677$	−2.09832	−0.0806450	−0.0403225	+	0.999187i	$0.512839\pi$
$678$	92.2428	3.54256
$679$	30.8530	1.18403
$680$	1.79941	0.0690041
$681$	17.2293	0.660228
$682$	−11.9792	−0.458706
$683$	36.7274	1.40533	0.702667	−	0.711519i	$-0.251992\pi$
$683$	36.7274	1.40533	0.702667	+	0.711519i	$0.251992\pi$
$684$	−48.0605	−1.83764
$685$	1.27718	0.0487984
$686$	114.178	4.35933
$687$	−48.3576	−1.84496
$688$	28.5173	1.08721
$689$	2.91376	0.111005
$690$	−4.73269	−0.180171
$691$	−19.4020	−0.738087	−0.369044	−	0.929412i	$-0.620315\pi$
$691$	−19.4020	−0.738087	−0.369044	+	0.929412i	$0.620315\pi$
$692$	−0.650655	−0.0247342
$693$	−226.404	−8.60038
$694$	12.2295	0.464224
$695$	1.51658	0.0575273
$696$	29.9740	1.13616
$697$	14.4240	0.546347
$698$	8.21488	0.310938
$699$	49.3510	1.86663
$700$	−18.8812	−0.713643
$701$	10.5531	0.398586	0.199293	−	0.979940i	$-0.436136\pi$
$701$	10.5531	0.398586	0.199293	+	0.979940i	$0.436136\pi$
$702$	12.0576	0.455085
$703$	17.7193	0.668297
$704$	−16.8843	−0.636353
$705$	2.53607	0.0955139
$706$	−16.2143	−0.610232
$707$	42.2960	1.59070
$708$	−27.3885	−1.02932
$709$	28.3172	1.06347	0.531737	−	0.846910i	$-0.321540\pi$
$709$	28.3172	1.06347	0.531737	+	0.846910i	$0.321540\pi$
$710$	−3.59043	−0.134746
$711$	−115.638	−4.33676
$712$	−13.7643	−0.515838
$713$	4.84022	0.181268
$714$	101.397	3.79467
$715$	0.491671	0.0183875
$716$	7.50438	0.280452
$717$	−9.36791	−0.349851
$718$	−45.3017	−1.69064
$719$	−24.7641	−0.923544	−0.461772	−	0.886999i	$-0.652786\pi$
$719$	−24.7641	−0.923544	−0.461772	+	0.886999i	$0.652786\pi$
$720$	10.4145	0.388127
$721$	67.9083	2.52904
$722$	66.5960	2.47845
$723$	−97.0293	−3.60856
$724$	−1.69536	−0.0630077
$725$	20.8167	0.773114
$726$	83.7533	3.10838
$727$	5.73960	0.212870	0.106435	−	0.994320i	$-0.466056\pi$
$727$	5.73960	0.212870	0.106435	+	0.994320i	$0.466056\pi$
$728$	−4.25670	−0.157764
$729$	133.246	4.93503
$730$	3.36205	0.124435
$731$	−20.0372	−0.741102
$732$	2.04501	0.0755859
$733$	19.2172	0.709802	0.354901	−	0.934904i	$-0.384515\pi$
$733$	19.2172	0.709802	0.354901	+	0.934904i	$0.384515\pi$
$734$	−4.73051	−0.174606
$735$	−17.0341	−0.628311
$736$	−13.4576	−0.496055
$737$	54.3724	2.00283
$738$	58.6635	2.15943
$739$	18.5922	0.683924	0.341962	−	0.939714i	$-0.388909\pi$
$739$	18.5922	0.683924	0.341962	+	0.939714i	$0.388909\pi$
$740$	0.418145	0.0153713
$741$	−10.1745	−0.373769
$742$	64.5652	2.37026
$743$	27.4092	1.00554	0.502772	−	0.864419i	$-0.332313\pi$
$743$	27.4092	1.00554	0.502772	+	0.864419i	$0.332313\pi$
$744$	−10.1201	−0.371020
$745$	−4.10849	−0.150523
$746$	−9.02873	−0.330565
$747$	−85.7900	−3.13889
$748$	−12.9180	−0.472329
$749$	−37.3908	−1.36623
$750$	13.8300	0.504999
$751$	12.7262	0.464387	0.232193	−	0.972670i	$-0.425410\pi$
$751$	12.7262	0.464387	0.232193	+	0.972670i	$0.425410\pi$
$752$	14.8479	0.541446
$753$	33.2545	1.21186
$754$	−2.71279	−0.0987939
$755$	−0.0375430	−0.00136633
$756$	71.6308	2.60519
$757$	−5.99274	−0.217810	−0.108905	−	0.994052i	$-0.534734\pi$
$757$	−5.99274	−0.217810	−0.108905	+	0.994052i	$0.534734\pi$
$758$	−7.81421	−0.283825
$759$	−58.7779	−2.13350
$760$	−4.00096	−0.145130
$761$	−24.5812	−0.891067	−0.445534	−	0.895265i	$-0.646986\pi$
$761$	−24.5812	−0.891067	−0.445534	+	0.895265i	$0.646986\pi$
$762$	−23.2286	−0.841483
$763$	36.8723	1.33487
$764$	−6.14927	−0.222473
$765$	−7.31760	−0.264568
$766$	9.65039	0.348683
$767$	−4.28824	−0.154839
$768$	52.6475	1.89975
$769$	16.0952	0.580408	0.290204	−	0.956965i	$-0.406277\pi$
$769$	16.0952	0.580408	0.290204	+	0.956965i	$0.406277\pi$
$770$	10.8948	0.392622
$771$	−16.2525	−0.585321
$772$	7.59314	0.273283
$773$	−38.1304	−1.37146	−0.685728	−	0.727858i	$-0.740516\pi$
$773$	−38.1304	−1.37146	−0.685728	+	0.727858i	$0.740516\pi$
$774$	−81.4930	−2.92921
$775$	−7.02832	−0.252465
$776$	−12.3860	−0.444633
$777$	−40.7624	−1.46234
$778$	−31.1727	−1.11759
$779$	−32.0715	−1.14908
$780$	−0.240100	−0.00859695
$781$	−44.5915	−1.59561
$782$	19.4688	0.696204
$783$	−78.9737	−2.82229
$784$	−99.7289	−3.56175
$785$	−3.32357	−0.118623
$786$	45.0477	1.60680
$787$	15.5846	0.555531	0.277766	−	0.960649i	$-0.410406\pi$
$787$	15.5846	0.555531	0.277766	+	0.960649i	$0.410406\pi$
$788$	1.65764	0.0590511
$789$	18.1370	0.645694
$790$	5.56463	0.197981
$791$	85.7991	3.05066
$792$	90.8906	3.22966
$793$	0.320190	0.0113703
$794$	−6.30976	−0.223925
$795$	−6.30024	−0.223447
$796$	−7.12963	−0.252703
$797$	47.1325	1.66952	0.834759	−	0.550616i	$-0.185607\pi$
$797$	47.1325	1.66952	0.834759	+	0.550616i	$0.185607\pi$
$798$	−225.454	−7.98097
$799$	−10.4326	−0.369079
$800$	19.5414	0.690892
$801$	55.9748	1.97777
$802$	−31.4760	−1.11146
$803$	41.7552	1.47351
$804$	−26.5519	−0.936413
$805$	−4.40209	−0.155153
$806$	0.915914	0.0322617
$807$	9.96918	0.350932
$808$	−16.9799	−0.597349
$809$	6.04880	0.212664	0.106332	−	0.994331i	$-0.466089\pi$
$809$	6.04880	0.212664	0.106332	+	0.994331i	$0.466089\pi$
$810$	−15.5920	−0.547848
$811$	−52.3118	−1.83692	−0.918458	−	0.395519i	$-0.870565\pi$
$811$	−52.3118	−1.83692	−0.918458	+	0.395519i	$0.870565\pi$
$812$	−16.1159	−0.565558
$813$	52.1641	1.82948
$814$	19.3704	0.678932
$815$	−0.634071	−0.0222105
$816$	−57.9275	−2.02787
$817$	44.5524	1.55869
$818$	58.9455	2.06098
$819$	17.3106	0.604881
$820$	−0.756830	−0.0264296
$821$	−6.17498	−0.215508	−0.107754	−	0.994178i	$-0.534366\pi$
$821$	−6.17498	−0.215508	−0.107754	+	0.994178i	$0.534366\pi$
$822$	−28.8921	−1.00773
$823$	−43.5482	−1.51799	−0.758997	−	0.651094i	$-0.774310\pi$
$823$	−43.5482	−1.51799	−0.758997	+	0.651094i	$0.774310\pi$
$824$	−27.2620	−0.949717
$825$	85.3493	2.97148
$826$	−95.0220	−3.30624
$827$	27.4102	0.953147	0.476574	−	0.879135i	$-0.341879\pi$
$827$	27.4102	0.953147	0.476574	+	0.879135i	$0.341879\pi$
$828$	21.2284	0.737739
$829$	−52.5074	−1.82366	−0.911829	−	0.410569i	$-0.865330\pi$
$829$	−52.5074	−1.82366	−0.911829	+	0.410569i	$0.865330\pi$
$830$	4.12831	0.143296
$831$	−66.8961	−2.32060
$832$	1.29096	0.0447559
$833$	70.0729	2.42788
$834$	−34.3080	−1.18799
$835$	2.91538	0.100891
$836$	28.7230	0.993405
$837$	26.6638	0.921634
$838$	48.6135	1.67932
$839$	33.7729	1.16597	0.582985	−	0.812483i	$-0.301885\pi$
$839$	33.7729	1.16597	0.582985	+	0.812483i	$0.301885\pi$
$840$	9.20400	0.317568
$841$	−11.2320	−0.387312
$842$	17.1494	0.591006
$843$	2.36675	0.0815151
$844$	−3.81865	−0.131443
$845$	3.18666	0.109625
$846$	−42.4303	−1.45879
$847$	77.9027	2.67677
$848$	−36.8859	−1.26667
$849$	37.0916	1.27298
$850$	−28.2700	−0.969654
$851$	−7.82667	−0.268295
$852$	21.7755	0.746018
$853$	2.43672	0.0834318	0.0417159	−	0.999130i	$-0.486718\pi$
$853$	2.43672	0.0834318	0.0417159	+	0.999130i	$0.486718\pi$
$854$	7.09500	0.242786
$855$	16.2706	0.556442
$856$	15.0107	0.513054
$857$	−17.0904	−0.583797	−0.291899	−	0.956449i	$-0.594287\pi$
$857$	−17.0904	−0.583797	−0.291899	+	0.956449i	$0.594287\pi$
$858$	−11.1225	−0.379717
$859$	−11.1590	−0.380741	−0.190371	−	0.981712i	$-0.560969\pi$
$859$	−11.1590	−0.380741	−0.190371	+	0.981712i	$0.560969\pi$
$860$	1.05136	0.0358510
$861$	73.7788	2.51437
$862$	19.6447	0.669100
$863$	38.0440	1.29503	0.647517	−	0.762051i	$-0.275808\pi$
$863$	38.0440	1.29503	0.647517	+	0.762051i	$0.275808\pi$
$864$	−74.1353	−2.52213
$865$	0.220275	0.00748959
$866$	11.5270	0.391704
$867$	−16.9981	−0.577285
$868$	5.44119	0.184686
$869$	69.1102	2.34440
$870$	5.86569	0.198866
$871$	−4.15726	−0.140863
$872$	−14.8025	−0.501276
$873$	50.3699	1.70476
$874$	−43.2887	−1.46426
$875$	12.8639	0.434878
$876$	−20.3905	−0.688930
$877$	11.1319	0.375898	0.187949	−	0.982179i	$-0.439816\pi$
$877$	11.1319	0.375898	0.187949	+	0.982179i	$0.439816\pi$
$878$	−3.96788	−0.133910
$879$	−99.4688	−3.35500
$880$	−6.22417	−0.209817
$881$	−29.1896	−0.983424	−0.491712	−	0.870758i	$-0.663629\pi$
$881$	−29.1896	−0.983424	−0.491712	+	0.870758i	$0.663629\pi$
$882$	284.993	9.59620
$883$	−2.66828	−0.0897948	−0.0448974	−	0.998992i	$-0.514296\pi$
$883$	−2.66828	−0.0897948	−0.0448974	+	0.998992i	$0.514296\pi$
$884$	0.987696	0.0332198
$885$	9.27220	0.311681
$886$	22.1418	0.743870
$887$	46.8168	1.57195	0.785977	−	0.618255i	$-0.212160\pi$
$887$	46.8168	1.57195	0.785977	+	0.618255i	$0.212160\pi$
$888$	16.3642	0.549147
$889$	−21.6059	−0.724640
$890$	−2.69357	−0.0902887
$891$	−193.646	−6.48739
$892$	−21.3826	−0.715942
$893$	23.1968	0.776250
$894$	92.9416	3.10843
$895$	−2.54056	−0.0849216
$896$	69.9066	2.33541
$897$	4.49409	0.150053
$898$	56.8482	1.89705
$899$	−5.99897	−0.200077
$900$	−30.8251	−1.02750
$901$	25.9173	0.863429
$902$	−35.0598	−1.16736
$903$	−102.491	−3.41067
$904$	−34.4443	−1.14560
$905$	0.573954	0.0190789
$906$	0.849293	0.0282159
$907$	50.4344	1.67465	0.837323	−	0.546709i	$-0.184120\pi$
$907$	50.4344	1.67465	0.837323	+	0.546709i	$0.184120\pi$
$908$	3.71888	0.123416
$909$	69.0515	2.29029
$910$	−0.833006	−0.0276139
$911$	13.8276	0.458130	0.229065	−	0.973411i	$-0.426433\pi$
$911$	13.8276	0.458130	0.229065	+	0.973411i	$0.426433\pi$
$912$	128.801	4.26502
$913$	51.2718	1.69685
$914$	58.7539	1.94341
$915$	−0.692327	−0.0228876
$916$	−10.4378	−0.344876
$917$	41.9008	1.38369
$918$	107.250	3.53977
$919$	−7.78823	−0.256910	−0.128455	−	0.991715i	$-0.541002\pi$
$919$	−7.78823	−0.256910	−0.128455	+	0.991715i	$0.541002\pi$
$920$	1.76723	0.0582639
$921$	−42.7102	−1.40735
$922$	60.7306	2.00006
$923$	3.40942	0.112222
$924$	−66.0758	−2.17373
$925$	11.3648	0.373673
$926$	−26.5081	−0.871110
$927$	110.866	3.64130
$928$	16.6794	0.547527
$929$	−6.09855	−0.200087	−0.100044	−	0.994983i	$-0.531898\pi$
$929$	−6.09855	−0.200087	−0.100044	+	0.994983i	$0.531898\pi$
$930$	−1.98042	−0.0649407
$931$	−155.806	−5.10634
$932$	10.6523	0.348926
$933$	26.8592	0.879330
$934$	23.6223	0.772946
$935$	4.37331	0.143023
$936$	−6.94939	−0.227148
$937$	5.26357	0.171953	0.0859767	−	0.996297i	$-0.472599\pi$
$937$	5.26357	0.171953	0.0859767	+	0.996297i	$0.472599\pi$
$938$	−92.1196	−3.00781
$939$	43.5878	1.42243
$940$	0.547402	0.0178543
$941$	39.7008	1.29421	0.647104	−	0.762402i	$-0.275980\pi$
$941$	39.7008	1.29421	0.647104	+	0.762402i	$0.275980\pi$
$942$	75.1855	2.44967
$943$	14.1660	0.461310
$944$	54.2857	1.76685
$945$	−24.2502	−0.788858
$946$	48.7037	1.58349
$947$	38.0367	1.23603	0.618013	−	0.786168i	$-0.287938\pi$
$947$	38.0367	1.23603	0.618013	+	0.786168i	$0.287938\pi$
$948$	−33.7489	−1.09611
$949$	−3.19256	−0.103635
$950$	62.8580	2.03938
$951$	92.6458	3.00424
$952$	−37.8624	−1.22713
$953$	−24.5430	−0.795027	−0.397513	−	0.917596i	$-0.630127\pi$
$953$	−24.5430	−0.795027	−0.397513	+	0.917596i	$0.630127\pi$
$954$	105.408	3.41270
$955$	2.08180	0.0673653
$956$	−2.02203	−0.0653972
$957$	72.8492	2.35488
$958$	−47.4674	−1.53360
$959$	−26.8738	−0.867801
$960$	−2.79136	−0.0900907
$961$	−28.9746	−0.934664
$962$	−1.48104	−0.0477506
$963$	−61.0434	−1.96710
$964$	−20.9435	−0.674543
$965$	−2.57061	−0.0827509
$966$	99.5834	3.20404
$967$	−24.9644	−0.802800	−0.401400	−	0.915903i	$-0.631476\pi$
$967$	−24.9644	−0.802800	−0.401400	+	0.915903i	$0.631476\pi$
$968$	−31.2743	−1.00519
$969$	−90.4998	−2.90727
$970$	−2.42386	−0.0778253
$971$	−19.3300	−0.620330	−0.310165	−	0.950683i	$-0.600384\pi$
$971$	−19.3300	−0.620330	−0.310165	+	0.950683i	$0.600384\pi$
$972$	53.3867	1.71238
$973$	−31.9114	−1.02303
$974$	70.4801	2.25833
$975$	−6.52572	−0.208990
$976$	−4.05335	−0.129745
$977$	12.6311	0.404105	0.202052	−	0.979375i	$-0.435239\pi$
$977$	12.6311	0.404105	0.202052	+	0.979375i	$0.435239\pi$
$978$	14.3439	0.458666
$979$	−33.4529	−1.06916
$980$	−3.67675	−0.117449
$981$	60.1969	1.92194
$982$	−3.50996	−0.112007
$983$	−53.3946	−1.70302	−0.851512	−	0.524335i	$-0.824314\pi$
$983$	−53.3946	−1.70302	−0.851512	+	0.524335i	$0.824314\pi$
$984$	−29.6187	−0.944211
$985$	−0.561185	−0.0178808
$986$	−24.1297	−0.768445
$987$	−53.3630	−1.69856
$988$	−2.19613	−0.0698681
$989$	−19.6789	−0.625753
$990$	17.7866	0.565296
$991$	47.5165	1.50941	0.754705	−	0.656064i	$-0.227780\pi$
$991$	47.5165	1.50941	0.754705	+	0.656064i	$0.227780\pi$
$992$	−5.63143	−0.178798
$993$	49.3653	1.56656
$994$	75.5484	2.39625
$995$	2.41369	0.0765191
$996$	−25.0377	−0.793351
$997$	35.2936	1.11776	0.558880	−	0.829248i	$-0.311231\pi$
$997$	35.2936	1.11776	0.558880	+	0.829248i	$0.311231\pi$
$998$	27.8281	0.880882
$999$	−43.1154	−1.36411

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1759.2.a.b.1.63	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1759.2.a.b.1.63	✓	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.1.63

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