LMFDB - Embedded newform 1859.4.a.j.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$1859 = 11 \cdot 13^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{18} - 2 x^{17} - 108 x^{16} + 212 x^{15} + 4721 x^{14} - 8963 x^{13} - 107626 x^{12} + 194656 x^{11} + \cdots + 9847296$ x^18 - 2x^17 - 108x^16 + 212x^15 + 4721x^14 - 8963x^13 - 107626x^12 + 194656x^11 + 1375700x^10 - 2336289x^9 - 9875440x^8 + 15599166x^7 + 37652624x^6 - 55787484x^5 - 64147728x^4 + 92949968x^3 + 22620800x^2 - 43697856*x + 9847296
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$2^{5}\cdot 3^{2}$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$-4.98751$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.98751 q^{2} -4.47034 q^{3} +16.8752 q^{4} +20.1605 q^{5} -22.2959 q^{6} -23.8481 q^{7} +44.2654 q^{8} -7.01607 q^{9} +100.551 q^{10} -11.0000 q^{11} -75.4381 q^{12} -118.943 q^{14} -90.1244 q^{15} +85.7719 q^{16} -111.997 q^{17} -34.9927 q^{18} +3.85957 q^{19} +340.214 q^{20} +106.609 q^{21} -54.8626 q^{22} -76.9220 q^{23} -197.881 q^{24} +281.447 q^{25} +152.063 q^{27} -402.443 q^{28} -85.3018 q^{29} -449.496 q^{30} +244.686 q^{31} +73.6653 q^{32} +49.1737 q^{33} -558.588 q^{34} -480.790 q^{35} -118.398 q^{36} -180.288 q^{37} +19.2496 q^{38} +892.413 q^{40} -470.715 q^{41} +531.714 q^{42} -194.463 q^{43} -185.628 q^{44} -141.448 q^{45} -383.649 q^{46} -287.601 q^{47} -383.430 q^{48} +225.732 q^{49} +1403.72 q^{50} +500.666 q^{51} -564.081 q^{53} +758.417 q^{54} -221.766 q^{55} -1055.65 q^{56} -17.2536 q^{57} -425.444 q^{58} +50.4331 q^{59} -1520.87 q^{60} +334.404 q^{61} +1220.37 q^{62} +167.320 q^{63} -318.769 q^{64} +245.254 q^{66} -199.275 q^{67} -1889.98 q^{68} +343.868 q^{69} -2397.95 q^{70} +152.078 q^{71} -310.569 q^{72} +245.095 q^{73} -899.188 q^{74} -1258.16 q^{75} +65.1311 q^{76} +262.329 q^{77} -281.145 q^{79} +1729.21 q^{80} -490.341 q^{81} -2347.69 q^{82} +434.099 q^{83} +1799.06 q^{84} -2257.92 q^{85} -969.884 q^{86} +381.328 q^{87} -486.919 q^{88} +1032.68 q^{89} -705.472 q^{90} -1298.08 q^{92} -1093.83 q^{93} -1434.41 q^{94} +77.8109 q^{95} -329.309 q^{96} +802.898 q^{97} +1125.84 q^{98} +77.1768 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$18 q - 2 q^{2} + 76 q^{4} - 20 q^{5} - 49 q^{6} - 28 q^{7} + 12 q^{8} + 180 q^{9} + 56 q^{10} - 198 q^{11} + 54 q^{12} + 4 q^{14} - 60 q^{15} + 364 q^{16} - 138 q^{17} - 298 q^{18} - 24 q^{19} - 160 q^{20}+ \cdots - 1980 q^{99}+O(q^{100})$ 18 * q - 2 * q^2 + 76 * q^4 - 20 * q^5 - 49 * q^6 - 28 * q^7 + 12 * q^8 + 180 * q^9 + 56 * q^10 - 198 * q^11 + 54 * q^12 + 4 * q^14 - 60 * q^15 + 364 * q^16 - 138 * q^17 - 298 * q^18 - 24 * q^19 - 160 * q^20 - 352 * q^21 + 22 * q^22 + 236 * q^23 - 124 * q^24 + 586 * q^25 - 6 * q^27 - 691 * q^28 - 286 * q^29 - 356 * q^30 - 642 * q^31 + 379 * q^32 - 2068 * q^34 + 34 * q^35 + 215 * q^36 - 530 * q^37 + 25 * q^38 - 108 * q^40 - 608 * q^41 + 563 * q^42 - 460 * q^43 - 836 * q^44 - 452 * q^45 + 580 * q^46 - 986 * q^47 + 837 * q^48 + 1082 * q^49 + 2578 * q^50 + 170 * q^51 + 1216 * q^53 - 1539 * q^54 + 220 * q^55 + 1137 * q^56 - 1282 * q^57 - 90 * q^58 - 1366 * q^59 - 5104 * q^60 - 922 * q^61 - 1398 * q^62 + 3236 * q^63 + 1296 * q^64 + 539 * q^66 - 1118 * q^67 - 2274 * q^68 + 1644 * q^69 - 416 * q^70 - 1118 * q^71 - 3295 * q^72 - 2444 * q^73 - 2018 * q^74 - 410 * q^75 + 1326 * q^76 + 308 * q^77 + 180 * q^79 - 5446 * q^80 + 426 * q^81 - 974 * q^82 + 696 * q^83 - 1061 * q^84 - 4580 * q^85 - 4652 * q^86 - 1240 * q^87 - 132 * q^88 + 3664 * q^89 + 248 * q^90 + 227 * q^92 - 3696 * q^93 - 244 * q^94 - 476 * q^95 + 5426 * q^96 - 2660 * q^97 - 6003 * q^98 - 1980 * 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

)

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

$2$	4.98751	1.76335	0.881675	−	0.471857i	$-0.156416\pi$
$2$	4.98751	1.76335	0.881675	+	0.471857i	$0.156416\pi$
$3$	−4.47034	−0.860317	−0.430159	−	0.902753i	$-0.641542\pi$
$3$	−4.47034	−0.860317	−0.430159	+	0.902753i	$0.641542\pi$
$4$	16.8752	2.10941
$5$	20.1605	1.80321	0.901606	−	0.432558i	$-0.142389\pi$
$5$	20.1605	1.80321	0.901606	+	0.432558i	$0.142389\pi$
$6$	−22.2959	−1.51704
$7$	−23.8481	−1.28768	−0.643839	−	0.765161i	$-0.722659\pi$
$7$	−23.8481	−1.28768	−0.643839	+	0.765161i	$0.722659\pi$
$8$	44.2654	1.95627
$9$	−7.01607	−0.259855
$10$	100.551	3.17969
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−75.4381	−1.81476
$13$	0	0
$13$	0	0
$14$	−118.943	−2.27063
$15$	−90.1244	−1.55133
$16$	85.7719	1.34019
$17$	−111.997	−1.59784	−0.798922	−	0.601435i	$-0.794596\pi$
$17$	−111.997	−1.59784	−0.798922	+	0.601435i	$0.794596\pi$
$18$	−34.9927	−0.458215
$19$	3.85957	0.0466024	0.0233012	−	0.999728i	$-0.492582\pi$
$19$	3.85957	0.0466024	0.0233012	+	0.999728i	$0.492582\pi$
$20$	340.214	3.80371
$21$	106.609	1.10781
$22$	−54.8626	−0.531670
$23$	−76.9220	−0.697363	−0.348682	−	0.937241i	$-0.613371\pi$
$23$	−76.9220	−0.697363	−0.348682	+	0.937241i	$0.613371\pi$
$24$	−197.881	−1.68301
$25$	281.447	2.25157
$26$	0	0
$27$	152.063	1.08387
$28$	−402.443	−2.71623
$29$	−85.3018	−0.546212	−0.273106	−	0.961984i	$-0.588051\pi$
$29$	−85.3018	−0.546212	−0.273106	+	0.961984i	$0.588051\pi$
$30$	−449.496	−2.73555
$31$	244.686	1.41764	0.708821	−	0.705388i	$-0.249227\pi$
$31$	244.686	1.41764	0.708821	+	0.705388i	$0.249227\pi$
$32$	73.6653	0.406947
$33$	49.1737	0.259395
$34$	−558.588	−2.81756
$35$	−480.790	−2.32195
$36$	−118.398	−0.548139
$37$	−180.288	−0.801058	−0.400529	−	0.916284i	$-0.631174\pi$
$37$	−180.288	−0.801058	−0.400529	+	0.916284i	$0.631174\pi$
$38$	19.2496	0.0821763
$39$	0	0
$40$	892.413	3.52757
$41$	−470.715	−1.79301	−0.896503	−	0.443037i	$-0.853901\pi$
$41$	−470.715	−1.79301	−0.896503	+	0.443037i	$0.853901\pi$
$42$	531.714	1.95346
$43$	−194.463	−0.689658	−0.344829	−	0.938666i	$-0.612063\pi$
$43$	−194.463	−0.689658	−0.344829	+	0.938666i	$0.612063\pi$
$44$	−185.628	−0.636010
$45$	−141.448	−0.468573
$46$	−383.649	−1.22970
$47$	−287.601	−0.892572	−0.446286	−	0.894890i	$-0.647254\pi$
$47$	−287.601	−0.892572	−0.446286	+	0.894890i	$0.647254\pi$
$48$	−383.430	−1.15299
$49$	225.732	0.658112
$50$	1403.72	3.97031
$51$	500.666	1.37465
$52$	0	0
$53$	−564.081	−1.46193	−0.730966	−	0.682414i	$-0.760930\pi$
$53$	−564.081	−1.46193	−0.730966	+	0.682414i	$0.760930\pi$
$54$	758.417	1.91125
$55$	−221.766	−0.543689
$56$	−1055.65	−2.51905
$57$	−17.2536	−0.0400928
$58$	−425.444	−0.963164
$59$	50.4331	0.111285	0.0556426	−	0.998451i	$-0.482279\pi$
$59$	50.4331	0.111285	0.0556426	+	0.998451i	$0.482279\pi$
$60$	−1520.87	−3.27239
$61$	334.404	0.701902	0.350951	−	0.936394i	$-0.385858\pi$
$61$	334.404	0.701902	0.350951	+	0.936394i	$0.385858\pi$
$62$	1220.37	2.49980
$63$	167.320	0.334609
$64$	−318.769	−0.622595
$65$	0	0
$66$	245.254	0.457405
$67$	−199.275	−0.363363	−0.181681	−	0.983357i	$-0.558154\pi$
$67$	−199.275	−0.363363	−0.181681	+	0.983357i	$0.558154\pi$
$68$	−1889.98	−3.37050
$69$	343.868	0.599954
$70$	−2397.95	−4.09442
$71$	152.078	0.254202	0.127101	−	0.991890i	$-0.459433\pi$
$71$	152.078	0.254202	0.127101	+	0.991890i	$0.459433\pi$
$72$	−310.569	−0.508346
$73$	245.095	0.392961	0.196480	−	0.980508i	$-0.437049\pi$
$73$	245.095	0.392961	0.196480	+	0.980508i	$0.437049\pi$
$74$	−899.188	−1.41255
$75$	−1258.16	−1.93707
$76$	65.1311	0.0983033
$77$	262.329	0.388249
$78$	0	0
$79$	−281.145	−0.400396	−0.200198	−	0.979756i	$-0.564158\pi$
$79$	−281.145	−0.400396	−0.200198	+	0.979756i	$0.564158\pi$
$80$	1729.21	2.41664
$81$	−490.341	−0.672621
$82$	−2347.69	−3.16170
$83$	434.099	0.574080	0.287040	−	0.957919i	$-0.407329\pi$
$83$	434.099	0.574080	0.287040	+	0.957919i	$0.407329\pi$
$84$	1799.06	2.33682
$85$	−2257.92	−2.88125
$86$	−969.884	−1.21611
$87$	381.328	0.469916
$88$	−486.919	−0.589838
$89$	1032.68	1.22993	0.614964	−	0.788555i	$-0.289171\pi$
$89$	1032.68	1.22993	0.614964	+	0.788555i	$0.289171\pi$
$90$	−705.472	−0.826258
$91$	0	0
$92$	−1298.08	−1.47102
$93$	−1093.83	−1.21962
$94$	−1434.41	−1.57392
$95$	77.8109	0.0840339
$96$	−329.309	−0.350104
$97$	802.898	0.840432	0.420216	−	0.907424i	$-0.361954\pi$
$97$	802.898	0.840432	0.420216	+	0.907424i	$0.361954\pi$
$98$	1125.84	1.16048
$99$	77.1768	0.0783491
$100$	4749.48	4.74948
$101$	−1228.44	−1.21024	−0.605118	−	0.796136i	$-0.706874\pi$
$101$	−1228.44	−1.21024	−0.605118	+	0.796136i	$0.706874\pi$
$102$	2497.08	2.42399
$103$	−334.122	−0.319632	−0.159816	−	0.987147i	$-0.551090\pi$
$103$	−334.122	−0.319632	−0.159816	+	0.987147i	$0.551090\pi$
$104$	0	0
$105$	2149.30	1.99762
$106$	−2813.36	−2.57790
$107$	1230.22	1.11149	0.555747	−	0.831351i	$-0.312432\pi$
$107$	1230.22	1.11149	0.555747	+	0.831351i	$0.312432\pi$
$108$	2566.11	2.28633
$109$	−333.762	−0.293290	−0.146645	−	0.989189i	$-0.546847\pi$
$109$	−333.762	−0.293290	−0.146645	+	0.989189i	$0.546847\pi$
$110$	−1106.06	−0.958714
$111$	805.948	0.689164
$112$	−2045.50	−1.72573
$113$	−1369.00	−1.13969	−0.569843	−	0.821753i	$-0.692996\pi$
$113$	−1369.00	−1.13969	−0.569843	+	0.821753i	$0.692996\pi$
$114$	−86.0523	−0.0706977
$115$	−1550.79	−1.25749
$116$	−1439.49	−1.15218
$117$	0	0
$118$	251.535	0.196235
$119$	2670.92	2.05751
$120$	−3989.39	−3.03483
$121$	121.000	0.0909091
$122$	1667.84	1.23770
$123$	2104.25	1.54255
$124$	4129.14	2.99038
$125$	3154.05	2.25685
$126$	834.510	0.590032
$127$	500.653	0.349809	0.174904	−	0.984585i	$-0.444038\pi$
$127$	500.653	0.349809	0.174904	+	0.984585i	$0.444038\pi$
$128$	−2179.19	−1.50480
$129$	869.314	0.593324
$130$	0	0
$131$	205.190	0.136851	0.0684256	−	0.997656i	$-0.478202\pi$
$131$	205.190	0.136851	0.0684256	+	0.997656i	$0.478202\pi$
$132$	829.819	0.547170
$133$	−92.0433	−0.0600088
$134$	−993.886	−0.640736
$135$	3065.68	1.95446
$136$	−4957.60	−3.12581
$137$	2302.23	1.43571	0.717856	−	0.696192i	$-0.245124\pi$
$137$	2302.23	1.43571	0.717856	+	0.696192i	$0.245124\pi$
$138$	1715.04	1.05793
$139$	−469.268	−0.286351	−0.143175	−	0.989697i	$-0.545731\pi$
$139$	−469.268	−0.286351	−0.143175	+	0.989697i	$0.545731\pi$
$140$	−8113.46	−4.89794
$141$	1285.67	0.767895
$142$	758.491	0.448248
$143$	0	0
$144$	−601.782	−0.348253
$145$	−1719.73	−0.984936
$146$	1222.41	0.692928
$147$	−1009.10	−0.566185
$148$	−3042.40	−1.68976
$149$	−749.151	−0.411898	−0.205949	−	0.978563i	$-0.566028\pi$
$149$	−749.151	−0.411898	−0.205949	+	0.978563i	$0.566028\pi$
$150$	−6275.09	−3.41573
$151$	−2358.29	−1.27096	−0.635480	−	0.772117i	$-0.719198\pi$
$151$	−2358.29	−1.27096	−0.635480	+	0.772117i	$0.719198\pi$
$152$	170.845	0.0911669
$153$	785.781	0.415207
$154$	1308.37	0.684620
$155$	4933.00	2.55631
$156$	0	0
$157$	−1366.74	−0.694764	−0.347382	−	0.937724i	$-0.612929\pi$
$157$	−1366.74	−0.694764	−0.347382	+	0.937724i	$0.612929\pi$
$158$	−1402.21	−0.706038
$159$	2521.63	1.25773
$160$	1485.13	0.733812
$161$	1834.45	0.897979
$162$	−2445.58	−1.18607
$163$	2841.66	1.36550	0.682749	−	0.730653i	$-0.260784\pi$
$163$	2841.66	1.36550	0.682749	+	0.730653i	$0.260784\pi$
$164$	−7943.42	−3.78218
$165$	991.368	0.467745
$166$	2165.07	1.01230
$167$	526.823	0.244113	0.122056	−	0.992523i	$-0.461051\pi$
$167$	526.823	0.244113	0.122056	+	0.992523i	$0.461051\pi$
$168$	4719.09	2.16718
$169$	0	0
$170$	−11261.4	−5.08065
$171$	−27.0790	−0.0121098
$172$	−3281.60	−1.45477
$173$	−1622.90	−0.713219	−0.356610	−	0.934254i	$-0.616067\pi$
$173$	−1622.90	−0.713219	−0.356610	+	0.934254i	$0.616067\pi$
$174$	1901.88	0.828626
$175$	−6711.97	−2.89930
$176$	−943.491	−0.404081
$177$	−225.453	−0.0957406
$178$	5150.49	2.16879
$179$	−3536.08	−1.47653	−0.738265	−	0.674510i	$-0.764355\pi$
$179$	−3536.08	−1.47653	−0.738265	+	0.674510i	$0.764355\pi$
$180$	−2386.96	−0.988410
$181$	−3338.97	−1.37118	−0.685590	−	0.727988i	$-0.740456\pi$
$181$	−3338.97	−1.37118	−0.685590	+	0.727988i	$0.740456\pi$
$182$	0	0
$183$	−1494.90	−0.603858
$184$	−3404.98	−1.36423
$185$	−3634.70	−1.44448
$186$	−5455.48	−2.15062
$187$	1231.97	0.481768
$188$	−4853.33	−1.88280
$189$	−3626.42	−1.39568
$190$	388.082	0.148181
$191$	−1085.16	−0.411096	−0.205548	−	0.978647i	$-0.565898\pi$
$191$	−1085.16	−0.411096	−0.205548	+	0.978647i	$0.565898\pi$
$192$	1425.00	0.535629
$193$	1802.02	0.672085	0.336042	−	0.941847i	$-0.390911\pi$
$193$	1802.02	0.672085	0.336042	+	0.941847i	$0.390911\pi$
$194$	4004.46	1.48198
$195$	0	0
$196$	3809.29	1.38823
$197$	2704.82	0.978225	0.489112	−	0.872221i	$-0.337321\pi$
$197$	2704.82	0.978225	0.489112	+	0.872221i	$0.337321\pi$
$198$	384.920	0.138157
$199$	−759.103	−0.270409	−0.135204	−	0.990818i	$-0.543169\pi$
$199$	−759.103	−0.270409	−0.135204	+	0.990818i	$0.543169\pi$
$200$	12458.3	4.40469
$201$	890.827	0.312607
$202$	−6126.83	−2.13407
$203$	2034.29	0.703345
$204$	8448.86	2.89970
$205$	−9489.85	−3.23317
$206$	−1666.44	−0.563622
$207$	539.691	0.181213
$208$	0	0
$209$	−42.4552	−0.0140511
$210$	10719.6	3.52250
$211$	−3908.28	−1.27515	−0.637577	−	0.770387i	$-0.720063\pi$
$211$	−3908.28	−1.27515	−0.637577	+	0.770387i	$0.720063\pi$
$212$	−9519.00	−3.08381
$213$	−679.841	−0.218694
$214$	6135.74	1.95995
$215$	−3920.47	−1.24360
$216$	6731.14	2.12035
$217$	−5835.30	−1.82547
$218$	−1664.64	−0.517173
$219$	−1095.66	−0.338071
$220$	−3742.35	−1.14686
$221$	0	0
$222$	4019.67	1.21524
$223$	4141.64	1.24370	0.621848	−	0.783138i	$-0.286382\pi$
$223$	4141.64	1.24370	0.621848	+	0.783138i	$0.286382\pi$
$224$	−1756.78	−0.524017
$225$	−1974.65	−0.585081
$226$	−6827.89	−2.00967
$227$	−2515.57	−0.735524	−0.367762	−	0.929920i	$-0.619876\pi$
$227$	−2515.57	−0.735524	−0.367762	+	0.929920i	$0.619876\pi$
$228$	−291.158	−0.0845720
$229$	−2143.71	−0.618605	−0.309302	−	0.950964i	$-0.600095\pi$
$229$	−2143.71	−0.618605	−0.309302	+	0.950964i	$0.600095\pi$
$230$	−7734.57	−2.21740
$231$	−1172.70	−0.334017
$232$	−3775.92	−1.06854
$233$	1945.07	0.546893	0.273447	−	0.961887i	$-0.411836\pi$
$233$	1945.07	0.546893	0.273447	+	0.961887i	$0.411836\pi$
$234$	0	0
$235$	−5798.18	−1.60950
$236$	851.071	0.234746
$237$	1256.81	0.344467
$238$	13321.3	3.62810
$239$	5694.26	1.54114	0.770568	−	0.637358i	$-0.219973\pi$
$239$	5694.26	1.54114	0.770568	+	0.637358i	$0.219973\pi$
$240$	−7730.14	−2.07908
$241$	2009.60	0.537137	0.268568	−	0.963261i	$-0.413449\pi$
$241$	2009.60	0.537137	0.268568	+	0.963261i	$0.413449\pi$
$242$	603.489	0.160305
$243$	−1913.72	−0.505207
$244$	5643.15	1.48060
$245$	4550.88	1.18672
$246$	10495.0	2.72006
$247$	0	0
$248$	10831.1	2.77329
$249$	−1940.57	−0.493890
$250$	15730.8	3.97962
$251$	5321.13	1.33812	0.669058	−	0.743210i	$-0.266698\pi$
$251$	5321.13	1.33812	0.669058	+	0.743210i	$0.266698\pi$
$252$	2823.57	0.705825
$253$	846.143	0.210263
$254$	2497.01	0.616836
$255$	10093.7	2.47879
$256$	−8318.55	−2.03090
$257$	3786.94	0.919156	0.459578	−	0.888138i	$-0.348001\pi$
$257$	3786.94	0.919156	0.459578	+	0.888138i	$0.348001\pi$
$258$	4335.71	1.04624
$259$	4299.53	1.03150
$260$	0	0
$261$	598.484	0.141936
$262$	1023.39	0.241317
$263$	−1430.47	−0.335385	−0.167693	−	0.985839i	$-0.553632\pi$
$263$	−1430.47	−0.335385	−0.167693	+	0.985839i	$0.553632\pi$
$264$	2176.69	0.507448
$265$	−11372.2	−2.63617
$266$	−459.067	−0.105817
$267$	−4616.42	−1.05813
$268$	−3362.81	−0.766480
$269$	−3302.24	−0.748481	−0.374240	−	0.927332i	$-0.622096\pi$
$269$	−3302.24	−0.748481	−0.374240	+	0.927332i	$0.622096\pi$
$270$	15290.1	3.44639
$271$	−8402.73	−1.88350	−0.941752	−	0.336308i	$-0.890822\pi$
$271$	−8402.73	−1.88350	−0.941752	+	0.336308i	$0.890822\pi$
$272$	−9606.22	−2.14141
$273$	0	0
$274$	11482.4	2.53166
$275$	−3095.91	−0.678875
$276$	5802.85	1.26555
$277$	−5501.14	−1.19326	−0.596628	−	0.802518i	$-0.703493\pi$
$277$	−5501.14	−1.19326	−0.596628	+	0.802518i	$0.703493\pi$
$278$	−2340.48	−0.504937
$279$	−1716.73	−0.368381
$280$	−21282.4	−4.54237
$281$	−3082.87	−0.654478	−0.327239	−	0.944942i	$-0.606118\pi$
$281$	−3082.87	−0.654478	−0.327239	+	0.944942i	$0.606118\pi$
$282$	6412.31	1.35407
$283$	6542.77	1.37430	0.687151	−	0.726515i	$-0.258861\pi$
$283$	6542.77	1.37430	0.687151	+	0.726515i	$0.258861\pi$
$284$	2566.36	0.536215
$285$	−347.841	−0.0722958
$286$	0	0
$287$	11225.7	2.30881
$288$	−516.841	−0.105747
$289$	7630.39	1.55310
$290$	−8577.17	−1.73679
$291$	−3589.22	−0.723038
$292$	4136.03	0.828914
$293$	5546.77	1.10596	0.552980	−	0.833195i	$-0.313491\pi$
$293$	5546.77	1.10596	0.552980	+	0.833195i	$0.313491\pi$
$294$	−5032.90	−0.998383
$295$	1016.76	0.200671
$296$	−7980.51	−1.56709
$297$	−1672.70	−0.326800
$298$	−3736.40	−0.726321
$299$	0	0
$300$	−21231.8	−4.08606
$301$	4637.57	0.888056
$302$	−11762.0	−2.24115
$303$	5491.52	1.04119
$304$	331.042	0.0624559
$305$	6741.75	1.26568
$306$	3919.09	0.732155
$307$	372.191	0.0691923	0.0345962	−	0.999401i	$-0.488985\pi$
$307$	372.191	0.0691923	0.0345962	+	0.999401i	$0.488985\pi$
$308$	4426.87	0.818975
$309$	1493.64	0.274984
$310$	24603.4	4.50767
$311$	7890.69	1.43871	0.719357	−	0.694640i	$-0.244436\pi$
$311$	7890.69	1.43871	0.719357	+	0.694640i	$0.244436\pi$
$312$	0	0
$313$	348.406	0.0629171	0.0314586	−	0.999505i	$-0.489985\pi$
$313$	348.406	0.0629171	0.0314586	+	0.999505i	$0.489985\pi$
$314$	−6816.64	−1.22511
$315$	3373.26	0.603370
$316$	−4744.39	−0.844597
$317$	−6274.13	−1.11164	−0.555820	−	0.831302i	$-0.687596\pi$
$317$	−6274.13	−1.11164	−0.555820	+	0.831302i	$0.687596\pi$
$318$	12576.7	2.21781
$319$	938.320	0.164689
$320$	−6426.55	−1.12267
$321$	−5499.50	−0.956238
$322$	9149.31	1.58345
$323$	−432.261	−0.0744633
$324$	−8274.62	−1.41883
$325$	0	0
$326$	14172.8	2.40785
$327$	1492.03	0.252322
$328$	−20836.4	−3.50761
$329$	6858.74	1.14934
$330$	4944.46	0.824798
$331$	3876.67	0.643749	0.321875	−	0.946782i	$-0.395687\pi$
$331$	3876.67	0.643749	0.321875	+	0.946782i	$0.395687\pi$
$332$	7325.53	1.21097
$333$	1264.91	0.208159
$334$	2627.54	0.430456
$335$	−4017.49	−0.655220
$336$	9144.07	1.48467
$337$	−5219.32	−0.843663	−0.421831	−	0.906674i	$-0.638613\pi$
$337$	−5219.32	−0.843663	−0.421831	+	0.906674i	$0.638613\pi$
$338$	0	0
$339$	6119.89	0.980492
$340$	−38103.0	−6.07772
$341$	−2691.55	−0.427435
$342$	−135.057	−0.0213539
$343$	2796.61	0.440241
$344$	−8607.96	−1.34916
$345$	6932.55	1.08184
$346$	−8094.23	−1.25766
$347$	7654.63	1.18421	0.592107	−	0.805859i	$-0.298296\pi$
$347$	7654.63	1.18421	0.592107	+	0.805859i	$0.298296\pi$
$348$	6435.00	0.991243
$349$	−6159.99	−0.944804	−0.472402	−	0.881383i	$-0.656613\pi$
$349$	−6159.99	−0.944804	−0.472402	+	0.881383i	$0.656613\pi$
$350$	−33476.0	−5.11248
$351$	0	0
$352$	−810.319	−0.122699
$353$	11219.6	1.69167	0.845835	−	0.533445i	$-0.179103\pi$
$353$	11219.6	1.69167	0.845835	+	0.533445i	$0.179103\pi$
$354$	−1124.45	−0.168824
$355$	3065.97	0.458380
$356$	17426.7	2.59442
$357$	−11939.9	−1.77011
$358$	−17636.2	−2.60364
$359$	−7715.95	−1.13435	−0.567176	−	0.823597i	$-0.691964\pi$
$359$	−7715.95	−1.13435	−0.567176	+	0.823597i	$0.691964\pi$
$360$	−6261.23	−0.916655
$361$	−6844.10	−0.997828
$362$	−16653.1	−2.41787
$363$	−540.911	−0.0782106
$364$	0	0
$365$	4941.23	0.708592
$366$	−7455.82	−1.06481
$367$	5740.64	0.816509	0.408255	−	0.912868i	$-0.366138\pi$
$367$	5740.64	0.816509	0.408255	+	0.912868i	$0.366138\pi$
$368$	−6597.75	−0.934597
$369$	3302.57	0.465921
$370$	−18128.1	−2.54712
$371$	13452.3	1.88250
$372$	−18458.6	−2.57268
$373$	−1439.07	−0.199764	−0.0998820	−	0.994999i	$-0.531847\pi$
$373$	−1439.07	−0.199764	−0.0998820	+	0.994999i	$0.531847\pi$
$374$	6144.46	0.849526
$375$	−14099.7	−1.94161
$376$	−12730.8	−1.74611
$377$	0	0
$378$	−18086.8	−2.46107
$379$	−5751.71	−0.779540	−0.389770	−	0.920912i	$-0.627445\pi$
$379$	−5751.71	−0.779540	−0.389770	+	0.920912i	$0.627445\pi$
$380$	1313.08	0.177262
$381$	−2238.09	−0.300947
$382$	−5412.24	−0.724906
$383$	801.732	0.106962	0.0534812	−	0.998569i	$-0.482968\pi$
$383$	801.732	0.106962	0.0534812	+	0.998569i	$0.482968\pi$
$384$	9741.70	1.29461
$385$	5288.69	0.700096
$386$	8987.60	1.18512
$387$	1364.36	0.179211
$388$	13549.1	1.77281
$389$	−12980.3	−1.69184	−0.845922	−	0.533307i	$-0.820949\pi$
$389$	−12980.3	−1.69184	−0.845922	+	0.533307i	$0.820949\pi$
$390$	0	0
$391$	8615.06	1.11428
$392$	9992.13	1.28745
$393$	−917.268	−0.117735
$394$	13490.3	1.72495
$395$	−5668.02	−0.721998
$396$	1302.38	0.165270
$397$	−3492.52	−0.441523	−0.220762	−	0.975328i	$-0.570854\pi$
$397$	−3492.52	−0.441523	−0.220762	+	0.975328i	$0.570854\pi$
$398$	−3786.03	−0.476826
$399$	411.465	0.0516266
$400$	24140.2	3.01753
$401$	981.877	0.122276	0.0611379	−	0.998129i	$-0.480527\pi$
$401$	981.877	0.122276	0.0611379	+	0.998129i	$0.480527\pi$
$402$	4443.01	0.551236
$403$	0	0
$404$	−20730.2	−2.55288
$405$	−9885.53	−1.21288
$406$	10146.0	1.24024
$407$	1983.17	0.241528
$408$	22162.2	2.68919
$409$	−9119.89	−1.10257	−0.551283	−	0.834318i	$-0.685862\pi$
$409$	−9119.89	−1.10257	−0.551283	+	0.834318i	$0.685862\pi$
$410$	−47330.7	−5.70121
$411$	−10291.7	−1.23517
$412$	−5638.40	−0.674232
$413$	−1202.73	−0.143299
$414$	2691.71	0.319542
$415$	8751.67	1.03519
$416$	0	0
$417$	2097.79	0.246353
$418$	−211.746	−0.0247771
$419$	11055.6	1.28902	0.644512	−	0.764594i	$-0.277061\pi$
$419$	11055.6	1.28902	0.644512	+	0.764594i	$0.277061\pi$
$420$	36269.9	4.21378
$421$	2544.11	0.294519	0.147259	−	0.989098i	$-0.452955\pi$
$421$	2544.11	0.294519	0.147259	+	0.989098i	$0.452955\pi$
$422$	−19492.6	−2.24854
$423$	2017.83	0.231939
$424$	−24969.2	−2.85994
$425$	−31521.3	−3.59766
$426$	−3390.71	−0.385635
$427$	−7974.90	−0.903823
$428$	20760.3	2.34459
$429$	0	0
$430$	−19553.4	−2.19290
$431$	−10692.7	−1.19501	−0.597505	−	0.801865i	$-0.703841\pi$
$431$	−10692.7	−1.19501	−0.597505	+	0.801865i	$0.703841\pi$
$432$	13042.8	1.45259
$433$	2822.50	0.313258	0.156629	−	0.987658i	$-0.449937\pi$
$433$	2822.50	0.313258	0.156629	+	0.987658i	$0.449937\pi$
$434$	−29103.6	−3.21894
$435$	7687.77	0.847357
$436$	−5632.31	−0.618667
$437$	−296.886	−0.0324988
$438$	−5464.59	−0.596138
$439$	3685.12	0.400640	0.200320	−	0.979730i	$-0.435802\pi$
$439$	3685.12	0.400640	0.200320	+	0.979730i	$0.435802\pi$
$440$	−9816.54	−1.06360
$441$	−1583.76	−0.171013
$442$	0	0
$443$	5031.25	0.539598	0.269799	−	0.962917i	$-0.413043\pi$
$443$	5031.25	0.539598	0.269799	+	0.962917i	$0.413043\pi$
$444$	13600.6	1.45373
$445$	20819.3	2.21782
$446$	20656.4	2.19307
$447$	3348.96	0.354363
$448$	7602.04	0.801702
$449$	6659.34	0.699942	0.349971	−	0.936761i	$-0.386191\pi$
$449$	6659.34	0.699942	0.349971	+	0.936761i	$0.386191\pi$
$450$	−9848.58	−1.03170
$451$	5177.86	0.540612
$452$	−23102.2	−2.40406
$453$	10542.4	1.09343
$454$	−12546.4	−1.29699
$455$	0	0
$456$	−763.735	−0.0784324
$457$	12776.1	1.30775	0.653873	−	0.756604i	$-0.273143\pi$
$457$	12776.1	1.30775	0.653873	+	0.756604i	$0.273143\pi$
$458$	−10691.8	−1.09082
$459$	−17030.7	−1.73186
$460$	−26169.9	−2.65256
$461$	−9355.38	−0.945171	−0.472585	−	0.881285i	$-0.656679\pi$
$461$	−9355.38	−0.945171	−0.472585	+	0.881285i	$0.656679\pi$
$462$	−5848.85	−0.588990
$463$	5632.94	0.565410	0.282705	−	0.959207i	$-0.408768\pi$
$463$	5632.94	0.565410	0.282705	+	0.959207i	$0.408768\pi$
$464$	−7316.50	−0.732026
$465$	−22052.2	−2.19924
$466$	9701.08	0.964364
$467$	7557.42	0.748856	0.374428	−	0.927256i	$-0.377839\pi$
$467$	7557.42	0.748856	0.374428	+	0.927256i	$0.377839\pi$
$468$	0	0
$469$	4752.33	0.467894
$470$	−28918.5	−2.83811
$471$	6109.81	0.597718
$472$	2232.44	0.217704
$473$	2139.09	0.207940
$474$	6268.36	0.607416
$475$	1086.26	0.104929
$476$	45072.5	4.34011
$477$	3957.63	0.379890
$478$	28400.2	2.71756
$479$	−461.346	−0.0440072	−0.0220036	−	0.999758i	$-0.507005\pi$
$479$	−461.346	−0.0440072	−0.0220036	+	0.999758i	$0.507005\pi$
$480$	−6639.04	−0.631311
$481$	0	0
$482$	10022.9	0.947161
$483$	−8200.59	−0.772546
$484$	2041.90	0.191764
$485$	16186.8	1.51548
$486$	−9544.70	−0.890857
$487$	8771.88	0.816205	0.408102	−	0.912936i	$-0.366191\pi$
$487$	8771.88	0.816205	0.408102	+	0.912936i	$0.366191\pi$
$488$	14802.5	1.37311
$489$	−12703.2	−1.17476
$490$	22697.6	2.09260
$491$	6631.14	0.609489	0.304745	−	0.952434i	$-0.401429\pi$
$491$	6631.14	0.609489	0.304745	+	0.952434i	$0.401429\pi$
$492$	35509.8	3.25387
$493$	9553.57	0.872761
$494$	0	0
$495$	1555.92	0.141280
$496$	20987.2	1.89990
$497$	−3626.78	−0.327330
$498$	−9678.62	−0.870902
$499$	419.630	0.0376458	0.0188229	−	0.999823i	$-0.494008\pi$
$499$	419.630	0.0376458	0.0188229	+	0.999823i	$0.494008\pi$
$500$	53225.3	4.76062
$501$	−2355.08	−0.210014
$502$	26539.2	2.35957
$503$	1162.41	0.103041	0.0515203	−	0.998672i	$-0.483593\pi$
$503$	1162.41	0.103041	0.0515203	+	0.998672i	$0.483593\pi$
$504$	7406.48	0.654585
$505$	−24765.9	−2.18231
$506$	4220.14	0.370767
$507$	0	0
$508$	8448.64	0.737889
$509$	−9192.32	−0.800476	−0.400238	−	0.916411i	$-0.631073\pi$
$509$	−9192.32	−0.800476	−0.400238	+	0.916411i	$0.631073\pi$
$510$	50342.3	4.37097
$511$	−5845.04	−0.506007
$512$	−24055.4	−2.07638
$513$	586.898	0.0505111
$514$	18887.4	1.62079
$515$	−6736.08	−0.576363
$516$	14669.9	1.25156
$517$	3163.61	0.269121
$518$	21443.9	1.81890
$519$	7254.92	0.613594
$520$	0	0
$521$	−14292.0	−1.20181	−0.600905	−	0.799320i	$-0.705193\pi$
$521$	−14292.0	−1.20181	−0.600905	+	0.799320i	$0.705193\pi$
$522$	2984.94	0.250282
$523$	19647.2	1.64266	0.821329	−	0.570455i	$-0.193233\pi$
$523$	19647.2	1.64266	0.821329	+	0.570455i	$0.193233\pi$
$524$	3462.63	0.288675
$525$	30004.8	2.49432
$526$	−7134.46	−0.591402
$527$	−27404.2	−2.26517
$528$	4217.73	0.347638
$529$	−6250.00	−0.513684
$530$	−56718.7	−4.64850
$531$	−353.842	−0.0289180
$532$	−1553.25	−0.126583
$533$	0	0
$534$	−23024.4	−1.86585
$535$	24801.9	2.00426
$536$	−8820.98	−0.710836
$537$	15807.5	1.27028
$538$	−16470.0	−1.31983
$539$	−2483.06	−0.198428
$540$	51734.0	4.12274
$541$	−3805.59	−0.302431	−0.151216	−	0.988501i	$-0.548319\pi$
$541$	−3805.59	−0.302431	−0.151216	+	0.988501i	$0.548319\pi$
$542$	−41908.7	−3.32128
$543$	14926.3	1.17965
$544$	−8250.32	−0.650238
$545$	−6728.82	−0.528864
$546$	0	0
$547$	4264.30	0.333324	0.166662	−	0.986014i	$-0.446701\pi$
$547$	4264.30	0.333324	0.166662	+	0.986014i	$0.446701\pi$
$548$	38850.6	3.02850
$549$	−2346.20	−0.182392
$550$	−15440.9	−1.19709
$551$	−329.228	−0.0254548
$552$	15221.4	1.17367
$553$	6704.77	0.515580
$554$	−27437.0	−2.10413
$555$	16248.3	1.24271
$556$	−7919.01	−0.604030
$557$	21947.0	1.66952	0.834761	−	0.550612i	$-0.185606\pi$
$557$	21947.0	1.66952	0.834761	+	0.550612i	$0.185606\pi$
$558$	−8562.23	−0.649584
$559$	0	0
$560$	−41238.3	−3.11185
$561$	−5507.32	−0.414473
$562$	−15375.8	−1.15408
$563$	−24846.0	−1.85992	−0.929960	−	0.367660i	$-0.880159\pi$
$563$	−24846.0	−1.85992	−0.929960	+	0.367660i	$0.880159\pi$
$564$	21696.0	1.61980
$565$	−27599.7	−2.05510
$566$	32632.1	2.42338
$567$	11693.7	0.866119
$568$	6731.79	0.497288
$569$	8838.72	0.651210	0.325605	−	0.945506i	$-0.394432\pi$
$569$	8838.72	0.651210	0.325605	+	0.945506i	$0.394432\pi$
$570$	−1734.86	−0.127483
$571$	5535.21	0.405677	0.202838	−	0.979212i	$-0.434983\pi$
$571$	5535.21	0.405677	0.202838	+	0.979212i	$0.434983\pi$
$572$	0	0
$573$	4851.03	0.353673
$574$	55988.0	4.07125
$575$	−21649.5	−1.57016
$576$	2236.51	0.161784
$577$	7216.86	0.520696	0.260348	−	0.965515i	$-0.416163\pi$
$577$	7216.86	0.520696	0.260348	+	0.965515i	$0.416163\pi$
$578$	38056.7	2.73866
$579$	−8055.65	−0.578206
$580$	−29020.9	−2.07763
$581$	−10352.5	−0.739229
$582$	−17901.3	−1.27497
$583$	6204.89	0.440789
$584$	10849.2	0.768738
$585$	0	0
$586$	27664.6	1.95019
$587$	−22137.4	−1.55657	−0.778286	−	0.627910i	$-0.783910\pi$
$587$	−22137.4	−1.55657	−0.778286	+	0.627910i	$0.783910\pi$
$588$	−17028.8	−1.19431
$589$	944.382	0.0660655
$590$	5071.09	0.353853
$591$	−12091.4	−0.841583
$592$	−15463.6	−1.07357
$593$	2759.66	0.191106	0.0955529	−	0.995424i	$-0.469538\pi$
$593$	2759.66	0.191106	0.0955529	+	0.995424i	$0.469538\pi$
$594$	−8342.59	−0.576264
$595$	53847.2	3.71012
$596$	−12642.1	−0.868860
$597$	3393.45	0.232637
$598$	0	0
$599$	8461.04	0.577143	0.288572	−	0.957458i	$-0.406820\pi$
$599$	8461.04	0.577143	0.288572	+	0.957458i	$0.406820\pi$
$600$	−55693.0	−3.78943
$601$	4257.10	0.288936	0.144468	−	0.989509i	$-0.453853\pi$
$601$	4257.10	0.288936	0.144468	+	0.989509i	$0.453853\pi$
$602$	23129.9	1.56595
$603$	1398.13	0.0944215
$604$	−39796.7	−2.68097
$605$	2439.42	0.163928
$606$	27389.0	1.83598
$607$	−25271.1	−1.68982	−0.844912	−	0.534906i	$-0.820347\pi$
$607$	−25271.1	−1.68982	−0.844912	+	0.534906i	$0.820347\pi$
$608$	284.316	0.0189647
$609$	−9093.95	−0.605100
$610$	33624.6	2.23183
$611$	0	0
$612$	13260.2	0.875839
$613$	10020.4	0.660226	0.330113	−	0.943941i	$-0.392913\pi$
$613$	10020.4	0.660226	0.330113	+	0.943941i	$0.392913\pi$
$614$	1856.30	0.122010
$615$	42422.9	2.78155
$616$	11612.1	0.759521
$617$	3621.59	0.236304	0.118152	−	0.992996i	$-0.462303\pi$
$617$	3621.59	0.236304	0.118152	+	0.992996i	$0.462303\pi$
$618$	7449.54	0.484894
$619$	15993.1	1.03847	0.519237	−	0.854630i	$-0.326216\pi$
$619$	15993.1	1.03847	0.519237	+	0.854630i	$0.326216\pi$
$620$	83245.5	5.39229
$621$	−11697.0	−0.755854
$622$	39354.9	2.53696
$623$	−24627.4	−1.58375
$624$	0	0
$625$	28406.4	1.81801
$626$	1737.68	0.110945
$627$	189.789	0.0120884
$628$	−23064.1	−1.46554
$629$	20191.8	1.27997
$630$	16824.2	1.06395
$631$	−11906.1	−0.751148	−0.375574	−	0.926792i	$-0.622554\pi$
$631$	−11906.1	−0.751148	−0.375574	+	0.926792i	$0.622554\pi$
$632$	−12445.0	−0.783282
$633$	17471.4	1.09704
$634$	−31292.3	−1.96021
$635$	10093.4	0.630780
$636$	42553.1	2.65305
$637$	0	0
$638$	4679.88	0.290405
$639$	−1066.99	−0.0660556
$640$	−43933.5	−2.71348
$641$	5547.76	0.341846	0.170923	−	0.985284i	$-0.445325\pi$
$641$	5547.76	0.341846	0.170923	+	0.985284i	$0.445325\pi$
$642$	−27428.8	−1.68618
$643$	8383.25	0.514158	0.257079	−	0.966390i	$-0.417240\pi$
$643$	8383.25	0.514158	0.257079	+	0.966390i	$0.417240\pi$
$644$	30956.7	1.89420
$645$	17525.8	1.06989
$646$	−2155.90	−0.131305
$647$	26350.5	1.60115	0.800575	−	0.599233i	$-0.204528\pi$
$647$	26350.5	1.60115	0.800575	+	0.599233i	$0.204528\pi$
$648$	−21705.1	−1.31583
$649$	−554.764	−0.0335538
$650$	0	0
$651$	26085.8	1.57048
$652$	47953.7	2.88039
$653$	22098.6	1.32433	0.662164	−	0.749359i	$-0.269638\pi$
$653$	22098.6	1.32433	0.662164	+	0.749359i	$0.269638\pi$
$654$	7441.51	0.444933
$655$	4136.73	0.246772
$656$	−40374.1	−2.40296
$657$	−1719.60	−0.102113
$658$	34208.0	2.02670
$659$	5272.65	0.311674	0.155837	−	0.987783i	$-0.450192\pi$
$659$	5272.65	0.311674	0.155837	+	0.987783i	$0.450192\pi$
$660$	16729.6	0.986663
$661$	−19249.3	−1.13270	−0.566348	−	0.824166i	$-0.691644\pi$
$661$	−19249.3	−1.13270	−0.566348	+	0.824166i	$0.691644\pi$
$662$	19334.9	1.13516
$663$	0	0
$664$	19215.6	1.12306
$665$	−1855.64	−0.108209
$666$	6308.77	0.367057
$667$	6561.59	0.380908
$668$	8890.27	0.514933
$669$	−18514.5	−1.06997
$670$	−20037.3	−1.15538
$671$	−3678.44	−0.211631
$672$	7853.40	0.450821
$673$	−32955.4	−1.88757	−0.943787	−	0.330553i	$-0.892765\pi$
$673$	−32955.4	−1.88757	−0.943787	+	0.330553i	$0.892765\pi$
$674$	−26031.4	−1.48767
$675$	42797.7	2.44042
$676$	0	0
$677$	−24793.6	−1.40753	−0.703763	−	0.710435i	$-0.748498\pi$
$677$	−24793.6	−1.40753	−0.703763	+	0.710435i	$0.748498\pi$
$678$	30523.0	1.72895
$679$	−19147.6	−1.08221
$680$	−99947.8	−5.63651
$681$	11245.4	0.632784
$682$	−13424.1	−0.753718
$683$	20604.3	1.15432	0.577161	−	0.816630i	$-0.304160\pi$
$683$	20604.3	1.15432	0.577161	+	0.816630i	$0.304160\pi$
$684$	−456.965	−0.0255446
$685$	46414.1	2.58889
$686$	13948.1	0.776300
$687$	9583.12	0.532196
$688$	−16679.4	−0.924270
$689$	0	0
$690$	34576.2	1.90767
$691$	1561.14	0.0859458	0.0429729	−	0.999076i	$-0.486317\pi$
$691$	1561.14	0.0859458	0.0429729	+	0.999076i	$0.486317\pi$
$692$	−27386.9	−1.50447
$693$	−1840.52	−0.100888
$694$	38177.5	2.08818
$695$	−9460.68	−0.516351
$696$	16879.6	0.919282
$697$	52718.8	2.86494
$698$	−30723.0	−1.66602
$699$	−8695.14	−0.470502
$700$	−113266.	−6.11580
$701$	30999.8	1.67025	0.835125	−	0.550060i	$-0.185395\pi$
$701$	30999.8	1.67025	0.835125	+	0.550060i	$0.185395\pi$
$702$	0	0
$703$	−695.833	−0.0373312
$704$	3506.46	0.187720
$705$	25919.8	1.38468
$706$	55957.9	2.98301
$707$	29295.9	1.55839
$708$	−3804.57	−0.201956
$709$	−36499.5	−1.93338	−0.966690	−	0.255950i	$-0.917612\pi$
$709$	−36499.5	−1.93338	−0.966690	+	0.255950i	$0.917612\pi$
$710$	15291.6	0.808285
$711$	1972.53	0.104045
$712$	45711.8	2.40607
$713$	−18821.7	−0.988612
$714$	−59550.5	−3.12132
$715$	0	0
$716$	−59672.2	−3.11460
$717$	−25455.3	−1.32586
$718$	−38483.4	−2.00026
$719$	−38007.8	−1.97142	−0.985710	−	0.168453i	$-0.946123\pi$
$719$	−38007.8	−1.97142	−0.985710	+	0.168453i	$0.946123\pi$
$720$	−12132.2	−0.627975
$721$	7968.19	0.411582
$722$	−34135.0	−1.75952
$723$	−8983.61	−0.462108
$724$	−56345.9	−2.89237
$725$	−24007.9	−1.22984
$726$	−2697.80	−0.137913
$727$	−20144.5	−1.02768	−0.513838	−	0.857887i	$-0.671777\pi$
$727$	−20144.5	−1.02768	−0.513838	+	0.857887i	$0.671777\pi$
$728$	0	0
$729$	21794.2	1.10726
$730$	24644.4	1.24950
$731$	21779.3	1.10196
$732$	−25226.8	−1.27378
$733$	−13433.0	−0.676889	−0.338444	−	0.940986i	$-0.609901\pi$
$733$	−13433.0	−0.676889	−0.338444	+	0.940986i	$0.609901\pi$
$734$	28631.5	1.43979
$735$	−20344.0	−1.02095
$736$	−5666.49	−0.283790
$737$	2192.02	0.109558
$738$	16471.6	0.821582
$739$	15113.2	0.752300	0.376150	−	0.926559i	$-0.377248\pi$
$739$	15113.2	0.752300	0.376150	+	0.926559i	$0.377248\pi$
$740$	−61336.5	−3.04699
$741$	0	0
$742$	67093.2	3.31950
$743$	−10764.4	−0.531504	−0.265752	−	0.964041i	$-0.585620\pi$
$743$	−10764.4	−0.531504	−0.265752	+	0.964041i	$0.585620\pi$
$744$	−48418.7	−2.38591
$745$	−15103.3	−0.742739
$746$	−7177.35	−0.352254
$747$	−3045.67	−0.149177
$748$	20789.8	1.01624
$749$	−29338.4	−1.43125
$750$	−70322.2	−3.42374
$751$	724.420	0.0351990	0.0175995	−	0.999845i	$-0.494398\pi$
$751$	724.420	0.0351990	0.0175995	+	0.999845i	$0.494398\pi$
$752$	−24668.1	−1.19621
$753$	−23787.3	−1.15120
$754$	0	0
$755$	−47544.4	−2.29181
$756$	−61196.8	−2.94406
$757$	−2475.45	−0.118853	−0.0594265	−	0.998233i	$-0.518927\pi$
$757$	−2475.45	−0.118853	−0.0594265	+	0.998233i	$0.518927\pi$
$758$	−28686.7	−1.37460
$759$	−3782.54	−0.180893
$760$	3444.33	0.164393
$761$	12024.6	0.572786	0.286393	−	0.958112i	$-0.407544\pi$
$761$	12024.6	0.572786	0.286393	+	0.958112i	$0.407544\pi$
$762$	−11162.5	−0.530674
$763$	7959.59	0.377663
$764$	−18312.3	−0.867168
$765$	15841.8	0.748706
$766$	3998.65	0.188612
$767$	0	0
$768$	37186.8	1.74722
$769$	4428.79	0.207681	0.103840	−	0.994594i	$-0.466887\pi$
$769$	4428.79	0.207681	0.103840	+	0.994594i	$0.466887\pi$
$770$	26377.4	1.23451
$771$	−16928.9	−0.790765
$772$	30409.6	1.41770
$773$	−24842.8	−1.15593	−0.577964	−	0.816062i	$-0.696153\pi$
$773$	−24842.8	−1.15593	−0.577964	+	0.816062i	$0.696153\pi$
$774$	6804.78	0.316011
$775$	68866.1	3.19192
$776$	35540.6	1.64411
$777$	−19220.3	−0.887421
$778$	−64739.3	−2.98331
$779$	−1816.75	−0.0835583
$780$	0	0
$781$	−1672.86	−0.0766448
$782$	42967.7	1.96486
$783$	−12971.3	−0.592025
$784$	19361.5	0.881993
$785$	−27554.3	−1.25281
$786$	−4574.88	−0.207609
$787$	41041.0	1.85890	0.929449	−	0.368951i	$-0.120283\pi$
$787$	41041.0	1.85890	0.929449	+	0.368951i	$0.120283\pi$
$788$	45644.5	2.06347
$789$	6394.67	0.288538
$790$	−28269.3	−1.27314
$791$	32648.0	1.46755
$792$	3416.26	0.153272
$793$	0	0
$794$	−17419.0	−0.778561
$795$	50837.4	2.26795
$796$	−12810.0	−0.570402
$797$	30301.7	1.34673	0.673364	−	0.739312i	$-0.264849\pi$
$797$	30301.7	1.34673	0.673364	+	0.739312i	$0.264849\pi$
$798$	2052.18	0.0910358
$799$	32210.5	1.42619
$800$	20732.9	0.916272
$801$	−7245.34	−0.319602
$802$	4897.12	0.215615
$803$	−2696.04	−0.118482
$804$	15032.9	0.659416
$805$	36983.4	1.61925
$806$	0	0
$807$	14762.1	0.643931
$808$	−54377.1	−2.36755
$809$	182.919	0.00794944	0.00397472	−	0.999992i	$-0.498735\pi$
$809$	182.919	0.00794944	0.00397472	+	0.999992i	$0.498735\pi$
$810$	−49304.1	−2.13873
$811$	−18134.4	−0.785186	−0.392593	−	0.919712i	$-0.628422\pi$
$811$	−18134.4	−0.785186	−0.392593	+	0.919712i	$0.628422\pi$
$812$	34329.1	1.48364
$813$	37563.1	1.62041
$814$	9891.07	0.425899
$815$	57289.4	2.46228
$816$	42943.1	1.84229
$817$	−750.541	−0.0321397
$818$	−45485.5	−1.94421
$819$	0	0
$820$	−160144.	−6.82007
$821$	−24718.5	−1.05077	−0.525385	−	0.850865i	$-0.676079\pi$
$821$	−24718.5	−1.05077	−0.525385	+	0.850865i	$0.676079\pi$
$822$	−51330.1	−2.17803
$823$	−13607.1	−0.576322	−0.288161	−	0.957582i	$-0.593044\pi$
$823$	−13607.1	−0.576322	−0.288161	+	0.957582i	$0.593044\pi$
$824$	−14790.0	−0.625286
$825$	13839.8	0.584048
$826$	−5998.65	−0.252687
$827$	−22725.4	−0.955549	−0.477774	−	0.878483i	$-0.658556\pi$
$827$	−22725.4	−0.955549	−0.477774	+	0.878483i	$0.658556\pi$
$828$	9107.41	0.382252
$829$	17207.3	0.720910	0.360455	−	0.932777i	$-0.382622\pi$
$829$	17207.3	0.720910	0.360455	+	0.932777i	$0.382622\pi$
$830$	43649.0	1.82540
$831$	24592.0	1.02658
$832$	0	0
$833$	−25281.4	−1.05156
$834$	10462.7	0.434406
$835$	10621.0	0.440187
$836$	−716.442	−0.0296396
$837$	37207.8	1.53655
$838$	55139.9	2.27300
$839$	22709.3	0.934460	0.467230	−	0.884136i	$-0.345252\pi$
$839$	22709.3	0.934460	0.467230	+	0.884136i	$0.345252\pi$
$840$	95139.4	3.90788
$841$	−17112.6	−0.701652
$842$	12688.8	0.519339
$843$	13781.5	0.563059
$844$	−65953.2	−2.68982
$845$	0	0
$846$	10063.9	0.408990
$847$	−2885.62	−0.117062
$848$	−48382.3	−1.95926
$849$	−29248.4	−1.18234
$850$	−157213.	−6.34394
$851$	13868.1	0.558629
$852$	−11472.5	−0.461315
$853$	−38029.5	−1.52650	−0.763250	−	0.646103i	$-0.776398\pi$
$853$	−38029.5	−1.52650	−0.763250	+	0.646103i	$0.776398\pi$
$854$	−39774.9	−1.59376
$855$	−545.927	−0.0218366
$856$	54456.2	2.17438
$857$	−4498.91	−0.179323	−0.0896616	−	0.995972i	$-0.528579\pi$
$857$	−4498.91	−0.179323	−0.0896616	+	0.995972i	$0.528579\pi$
$858$	0	0
$859$	13450.9	0.534271	0.267135	−	0.963659i	$-0.413923\pi$
$859$	13450.9	0.534271	0.267135	+	0.963659i	$0.413923\pi$
$860$	−66158.9	−2.62325
$861$	−50182.5	−1.98631
$862$	−53330.0	−2.10722
$863$	−4350.45	−0.171600	−0.0858002	−	0.996312i	$-0.527345\pi$
$863$	−4350.45	−0.171600	−0.0858002	+	0.996312i	$0.527345\pi$
$864$	11201.8	0.441080
$865$	−32718.5	−1.28609
$866$	14077.2	0.552384
$867$	−34110.4	−1.33616
$868$	−98472.1	−3.85065
$869$	3092.59	0.120724
$870$	38342.8	1.49419
$871$	0	0
$872$	−14774.1	−0.573754
$873$	−5633.19	−0.218390
$874$	−1480.72	−0.0573067
$875$	−75218.0	−2.90610
$876$	−18489.5	−0.713129
$877$	1982.86	0.0763471	0.0381735	−	0.999271i	$-0.487846\pi$
$877$	1982.86	0.0763471	0.0381735	+	0.999271i	$0.487846\pi$
$878$	18379.6	0.706469
$879$	−24796.0	−0.951475
$880$	−19021.3	−0.728644
$881$	−39887.8	−1.52537	−0.762687	−	0.646768i	$-0.776120\pi$
$881$	−39887.8	−1.52537	−0.762687	+	0.646768i	$0.776120\pi$
$882$	−7898.99	−0.301557
$883$	9886.90	0.376807	0.188404	−	0.982092i	$-0.439669\pi$
$883$	9886.90	0.376807	0.188404	+	0.982092i	$0.439669\pi$
$884$	0	0
$885$	−4545.25	−0.172641
$886$	25093.4	0.951500
$887$	25867.4	0.979189	0.489595	−	0.871950i	$-0.337145\pi$
$887$	25867.4	0.979189	0.489595	+	0.871950i	$0.337145\pi$
$888$	35675.6	1.34819
$889$	−11939.6	−0.450441
$890$	103836.	3.91079
$891$	5393.75	0.202803
$892$	69891.1	2.62346
$893$	−1110.01	−0.0415960
$894$	16703.0	0.624866
$895$	−71289.2	−2.66250
$896$	51969.5	1.93770
$897$	0	0
$898$	33213.5	1.23424
$899$	−20872.2	−0.774333
$900$	−33322.7	−1.23417
$901$	63175.5	2.33594
$902$	25824.6	0.953288
$903$	−20731.5	−0.764010
$904$	−60599.2	−2.22954
$905$	−67315.4	−2.47253
$906$	52580.1	1.92810
$907$	2520.36	0.0922681	0.0461340	−	0.998935i	$-0.485310\pi$
$907$	2520.36	0.0922681	0.0461340	+	0.998935i	$0.485310\pi$
$908$	−42450.8	−1.55152
$909$	8618.79	0.314485
$910$	0	0
$911$	7964.68	0.289662	0.144831	−	0.989456i	$-0.453736\pi$
$911$	7964.68	0.289662	0.144831	+	0.989456i	$0.453736\pi$
$912$	−1479.87	−0.0537318
$913$	−4775.09	−0.173092
$914$	63720.8	2.30601
$915$	−30137.9	−1.08888
$916$	−36175.7	−1.30489
$917$	−4893.39	−0.176220
$918$	−84940.7	−3.05388
$919$	−17048.0	−0.611929	−0.305965	−	0.952043i	$-0.598979\pi$
$919$	−17048.0	−0.611929	−0.305965	+	0.952043i	$0.598979\pi$
$920$	−68646.2	−2.46000
$921$	−1663.82	−0.0595274
$922$	−46660.1	−1.66667
$923$	0	0
$924$	−19789.6	−0.704578
$925$	−50741.5	−1.80364
$926$	28094.3	0.997016
$927$	2344.23	0.0830577
$928$	−6283.79	−0.222280
$929$	28183.3	0.995334	0.497667	−	0.867368i	$-0.334190\pi$
$929$	28183.3	0.995334	0.497667	+	0.867368i	$0.334190\pi$
$930$	−109985.	−3.87802
$931$	871.229	0.0306696
$932$	32823.6	1.15362
$933$	−35274.1	−1.23775
$934$	37692.7	1.32050
$935$	24837.2	0.868730
$936$	0	0
$937$	−31323.9	−1.09211	−0.546055	−	0.837750i	$-0.683871\pi$
$937$	−31323.9	−1.09211	−0.546055	+	0.837750i	$0.683871\pi$
$938$	23702.3	0.825061
$939$	−1557.49	−0.0541287
$940$	−97845.8	−3.39508
$941$	−36257.9	−1.25608	−0.628041	−	0.778181i	$-0.716143\pi$
$941$	−36257.9	−1.25608	−0.628041	+	0.778181i	$0.716143\pi$
$942$	30472.7	1.05399
$943$	36208.3	1.25038
$944$	4325.74	0.149143
$945$	−73110.6	−2.51671
$946$	10668.7	0.366670
$947$	51372.2	1.76280	0.881401	−	0.472369i	$-0.156601\pi$
$947$	51372.2	1.76280	0.881401	+	0.472369i	$0.156601\pi$
$948$	21209.0	0.726621
$949$	0	0
$950$	5417.74	0.185026
$951$	28047.5	0.956363
$952$	118229.	4.02504
$953$	−31677.7	−1.07675	−0.538374	−	0.842706i	$-0.680961\pi$
$953$	−31677.7	−1.07675	−0.538374	+	0.842706i	$0.680961\pi$
$954$	19738.7	0.669879
$955$	−21877.4	−0.741293
$956$	96092.1	3.25088
$957$	−4194.61	−0.141685
$958$	−2300.97	−0.0776001
$959$	−54903.7	−1.84873
$960$	28728.8	0.965853
$961$	30080.2	1.00971
$962$	0	0
$963$	−8631.32	−0.288827
$964$	33912.6	1.13304
$965$	36329.7	1.21191
$966$	−40900.5	−1.36227
$967$	5938.19	0.197476	0.0987381	−	0.995113i	$-0.468519\pi$
$967$	5938.19	0.197476	0.0987381	+	0.995113i	$0.468519\pi$
$968$	5356.11	0.177843
$969$	1932.35	0.0640620
$970$	80732.0	2.67232
$971$	55548.7	1.83588	0.917941	−	0.396717i	$-0.129851\pi$
$971$	55548.7	1.83588	0.917941	+	0.396717i	$0.129851\pi$
$972$	−32294.5	−1.06569
$973$	11191.2	0.368727
$974$	43749.8	1.43926
$975$	0	0
$976$	28682.5	0.940679
$977$	−12029.0	−0.393901	−0.196951	−	0.980413i	$-0.563104\pi$
$977$	−12029.0	−0.393901	−0.196951	+	0.980413i	$0.563104\pi$
$978$	−63357.2	−2.07151
$979$	−11359.4	−0.370837
$980$	76797.3	2.50326
$981$	2341.70	0.0762127
$982$	33072.9	1.07474
$983$	3362.61	0.109106	0.0545528	−	0.998511i	$-0.482627\pi$
$983$	3362.61	0.109106	0.0545528	+	0.998511i	$0.482627\pi$
$984$	93145.5	3.01765
$985$	54530.5	1.76395
$986$	47648.5	1.53898
$987$	−30660.9	−0.988801
$988$	0	0
$989$	14958.5	0.480942
$990$	7760.19	0.249126
$991$	52987.7	1.69850	0.849248	−	0.527994i	$-0.177056\pi$
$991$	52987.7	1.69850	0.849248	+	0.527994i	$0.177056\pi$
$992$	18024.9	0.576906
$993$	−17330.0	−0.553828
$994$	−18088.6	−0.577198
$995$	−15303.9	−0.487605
$996$	−32747.6	−1.04182
$997$	−44929.5	−1.42721	−0.713606	−	0.700547i	$-0.752939\pi$
$997$	−44929.5	−1.42721	−0.713606	+	0.700547i	$0.752939\pi$
$998$	2092.91	0.0663827
$999$	−27415.2	−0.868247

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.j.1.17		18
13.5	odd	4		143.4.b.a.12.3	✓	36
13.8	odd	4		143.4.b.a.12.34	yes	36
13.12	even	2		1859.4.a.k.1.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.3	✓	36	13.5	odd	4
143.4.b.a.12.34	yes	36	13.8	odd	4
1859.4.a.j.1.17		18	1.1	even	1	trivial
1859.4.a.k.1.2		18	13.12	even	2

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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 $\F_{q}$
Belyi maps

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Fields

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

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	1859.4.a.j.1.17

Level	$1859$
Weight	$4$
Character	1859.1
Self dual	yes
Analytic conductor	$109.685$
Analytic rank	$1$
Dimension	$18$
CM	no
Inner twists	$1$