LMFDB - Embedded newform 1840.4.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1840,4,Mod(1,1840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1840, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("1840.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1840 = 2^{4} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1840.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:	$108.563514411$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.318165.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 45x + 60 $ x^3 - x^2 - 45*x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.34735$ of defining polynomial
Character	$\chi$	$=$	1840.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34735 q^{3} +5.00000 q^{5} -32.8794 q^{7} -25.1847 q^{9} +O(q^{10})$	$q+1.34735 q^{3} +5.00000 q^{5} -32.8794 q^{7} -25.1847 q^{9} -58.9379 q^{11} -60.5540 q^{13} +6.73673 q^{15} +31.1792 q^{17} +43.2888 q^{19} -44.2998 q^{21} -23.0000 q^{23} +25.0000 q^{25} -70.3108 q^{27} -13.6015 q^{29} -287.091 q^{31} -79.4097 q^{33} -164.397 q^{35} +279.104 q^{37} -81.5871 q^{39} -419.048 q^{41} -421.243 q^{43} -125.923 q^{45} -117.612 q^{47} +738.052 q^{49} +42.0092 q^{51} +439.207 q^{53} -294.690 q^{55} +58.3250 q^{57} +248.238 q^{59} -186.679 q^{61} +828.055 q^{63} -302.770 q^{65} -888.995 q^{67} -30.9889 q^{69} +444.971 q^{71} +925.588 q^{73} +33.6836 q^{75} +1937.84 q^{77} +755.123 q^{79} +585.253 q^{81} +648.359 q^{83} +155.896 q^{85} -18.3259 q^{87} -542.301 q^{89} +1990.98 q^{91} -386.811 q^{93} +216.444 q^{95} -685.176 q^{97} +1484.33 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{3} + 15 q^{5} - 7 q^{7} + 10 q^{9}+O(q^{10}) $ 3 * q + q^3 + 15 * q^5 - 7 * q^7 + 10 * q^9	$ 3 q + q^{3} + 15 q^{5} - 7 q^{7} + 10 q^{9} - 27 q^{11} + 75 q^{13} + 5 q^{15} + 127 q^{17} + 185 q^{19} - 258 q^{21} - 69 q^{23} + 75 q^{25} - 98 q^{27} + 344 q^{29} - 397 q^{31} + 477 q^{33} - 35 q^{35} + 978 q^{37} - 198 q^{39} - 575 q^{41} - 812 q^{43} + 50 q^{45} + 270 q^{47} + 878 q^{49} - 955 q^{51} + 510 q^{53} - 135 q^{55} + 894 q^{57} - 142 q^{59} - 49 q^{61} + 1356 q^{63} + 375 q^{65} - 1616 q^{67} - 23 q^{69} + 471 q^{71} - 780 q^{73} + 25 q^{75} + 1032 q^{77} + 860 q^{79} - 1193 q^{81} + 288 q^{83} + 635 q^{85} - 1452 q^{87} - 90 q^{89} + 3963 q^{91} - 1592 q^{93} + 925 q^{95} + 1321 q^{97} + 1851 q^{99}+O(q^{100}) $ 3 * q + q^3 + 15 * q^5 - 7 * q^7 + 10 * q^9 - 27 * q^11 + 75 * q^13 + 5 * q^15 + 127 * q^17 + 185 * q^19 - 258 * q^21 - 69 * q^23 + 75 * q^25 - 98 * q^27 + 344 * q^29 - 397 * q^31 + 477 * q^33 - 35 * q^35 + 978 * q^37 - 198 * q^39 - 575 * q^41 - 812 * q^43 + 50 * q^45 + 270 * q^47 + 878 * q^49 - 955 * q^51 + 510 * q^53 - 135 * q^55 + 894 * q^57 - 142 * q^59 - 49 * q^61 + 1356 * q^63 + 375 * q^65 - 1616 * q^67 - 23 * q^69 + 471 * q^71 - 780 * q^73 + 25 * q^75 + 1032 * q^77 + 860 * q^79 - 1193 * q^81 + 288 * q^83 + 635 * q^85 - 1452 * q^87 - 90 * q^89 + 3963 * q^91 - 1592 * q^93 + 925 * q^95 + 1321 * q^97 + 1851 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0	0
$2$	0	0
$3$	1.34735	0.259297	0.129648	−	0.991560i	$-0.458615\pi$
$3$	1.34735	0.259297	0.129648	+	0.991560i	$0.458615\pi$
$4$	0	0
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	−32.8794	−1.77532	−0.887659	−	0.460501i	$-0.847670\pi$
$7$	−32.8794	−1.77532	−0.887659	+	0.460501i	$0.847670\pi$
$8$	0	0
$9$	−25.1847	−0.932765
$10$	0	0
$11$	−58.9379	−1.61550	−0.807748	−	0.589529i	$-0.799314\pi$
$11$	−58.9379	−1.61550	−0.807748	+	0.589529i	$0.799314\pi$
$12$	0	0
$13$	−60.5540	−1.29190	−0.645948	−	0.763381i	$-0.723538\pi$
$13$	−60.5540	−1.29190	−0.645948	+	0.763381i	$0.723538\pi$
$14$	0	0
$15$	6.73673	0.115961
$16$	0	0
$17$	31.1792	0.444827	0.222414	−	0.974952i	$-0.428606\pi$
$17$	31.1792	0.444827	0.222414	+	0.974952i	$0.428606\pi$
$18$	0	0
$19$	43.2888	0.522691	0.261346	−	0.965245i	$-0.415834\pi$
$19$	43.2888	0.522691	0.261346	+	0.965245i	$0.415834\pi$
$20$	0	0
$21$	−44.2998	−0.460334
$22$	0	0
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	−70.3108	−0.501160
$28$	0	0
$29$	−13.6015	−0.0870942	−0.0435471	−	0.999051i	$-0.513866\pi$
$29$	−13.6015	−0.0870942	−0.0435471	+	0.999051i	$0.513866\pi$
$30$	0	0
$31$	−287.091	−1.66333	−0.831664	−	0.555280i	$-0.812611\pi$
$31$	−287.091	−1.66333	−0.831664	+	0.555280i	$0.812611\pi$
$32$	0	0
$33$	−79.4097	−0.418893
$34$	0	0
$35$	−164.397	−0.793946
$36$	0	0
$37$	279.104	1.24012	0.620060	−	0.784554i	$-0.287108\pi$
$37$	279.104	1.24012	0.620060	+	0.784554i	$0.287108\pi$
$38$	0	0
$39$	−81.5871	−0.334985
$40$	0	0
$41$	−419.048	−1.59620	−0.798101	−	0.602524i	$-0.794162\pi$
$41$	−419.048	−1.59620	−0.798101	+	0.602524i	$0.794162\pi$
$42$	0	0
$43$	−421.243	−1.49393	−0.746965	−	0.664864i	$-0.768490\pi$
$43$	−421.243	−1.49393	−0.746965	+	0.664864i	$0.768490\pi$
$44$	0	0
$45$	−125.923	−0.417145
$46$	0	0
$47$	−117.612	−0.365011	−0.182506	−	0.983205i	$-0.558421\pi$
$47$	−117.612	−0.365011	−0.182506	+	0.983205i	$0.558421\pi$
$48$	0	0
$49$	738.052	2.15175
$50$	0	0
$51$	42.0092	0.115342
$52$	0	0
$53$	439.207	1.13830	0.569148	−	0.822235i	$-0.307273\pi$
$53$	439.207	1.13830	0.569148	+	0.822235i	$0.307273\pi$
$54$	0	0
$55$	−294.690	−0.722471
$56$	0	0
$57$	58.3250	0.135532
$58$	0	0
$59$	248.238	0.547760	0.273880	−	0.961764i	$-0.411693\pi$
$59$	248.238	0.547760	0.273880	+	0.961764i	$0.411693\pi$
$60$	0	0
$61$	−186.679	−0.391832	−0.195916	−	0.980621i	$-0.562768\pi$
$61$	−186.679	−0.391832	−0.195916	+	0.980621i	$0.562768\pi$
$62$	0	0
$63$	828.055	1.65595
$64$	0	0
$65$	−302.770	−0.577754
$66$	0	0
$67$	−888.995	−1.62101	−0.810507	−	0.585728i	$-0.800809\pi$
$67$	−888.995	−1.62101	−0.810507	+	0.585728i	$0.800809\pi$
$68$	0	0
$69$	−30.9889	−0.0540671
$70$	0	0
$71$	444.971	0.743779	0.371889	−	0.928277i	$-0.378710\pi$
$71$	444.971	0.743779	0.371889	+	0.928277i	$0.378710\pi$
$72$	0	0
$73$	925.588	1.48400	0.741999	−	0.670401i	$-0.233878\pi$
$73$	925.588	1.48400	0.741999	+	0.670401i	$0.233878\pi$
$74$	0	0
$75$	33.6836	0.0518594
$76$	0	0
$77$	1937.84	2.86802
$78$	0	0
$79$	755.123	1.07542	0.537708	−	0.843131i	$-0.319290\pi$
$79$	755.123	1.07542	0.537708	+	0.843131i	$0.319290\pi$
$80$	0	0
$81$	585.253	0.802816
$82$	0	0
$83$	648.359	0.857429	0.428715	−	0.903440i	$-0.358967\pi$
$83$	648.359	0.857429	0.428715	+	0.903440i	$0.358967\pi$
$84$	0	0
$85$	155.896	0.198933
$86$	0	0
$87$	−18.3259	−0.0225832
$88$	0	0
$89$	−542.301	−0.645885	−0.322943	−	0.946419i	$-0.604672\pi$
$89$	−542.301	−0.645885	−0.322943	+	0.946419i	$0.604672\pi$
$90$	0	0
$91$	1990.98	2.29353
$92$	0	0
$93$	−386.811	−0.431295
$94$	0	0
$95$	216.444	0.233755
$96$	0	0
$97$	−685.176	−0.717207	−0.358604	−	0.933490i	$-0.616747\pi$
$97$	−685.176	−0.717207	−0.358604	+	0.933490i	$0.616747\pi$
$98$	0	0
$99$	1484.33	1.50688
$100$	0	0
$101$	−461.968	−0.455124	−0.227562	−	0.973764i	$-0.573075\pi$
$101$	−461.968	−0.455124	−0.227562	+	0.973764i	$0.573075\pi$
$102$	0	0
$103$	−469.322	−0.448968	−0.224484	−	0.974478i	$-0.572070\pi$
$103$	−469.322	−0.448968	−0.224484	+	0.974478i	$0.572070\pi$
$104$	0	0
$105$	−221.499	−0.205868
$106$	0	0
$107$	516.281	0.466456	0.233228	−	0.972422i	$-0.425071\pi$
$107$	516.281	0.466456	0.233228	+	0.972422i	$0.425071\pi$
$108$	0	0
$109$	−207.099	−0.181986	−0.0909932	−	0.995852i	$-0.529004\pi$
$109$	−207.099	−0.181986	−0.0909932	+	0.995852i	$0.529004\pi$
$110$	0	0
$111$	376.050	0.321559
$112$	0	0
$113$	−1428.14	−1.18892	−0.594462	−	0.804124i	$-0.702635\pi$
$113$	−1428.14	−1.18892	−0.594462	+	0.804124i	$0.702635\pi$
$114$	0	0
$115$	−115.000	−0.0932505
$116$	0	0
$117$	1525.03	1.20504
$118$	0	0
$119$	−1025.15	−0.789710
$120$	0	0
$121$	2142.68	1.60982
$122$	0	0
$123$	−564.602	−0.413890
$124$	0	0
$125$	125.000	0.0894427
$126$	0	0
$127$	1489.09	1.04043	0.520217	−	0.854034i	$-0.325851\pi$
$127$	1489.09	1.04043	0.520217	+	0.854034i	$0.325851\pi$
$128$	0	0
$129$	−567.560	−0.387371
$130$	0	0
$131$	−995.006	−0.663619	−0.331810	−	0.943346i	$-0.607659\pi$
$131$	−995.006	−0.663619	−0.331810	+	0.943346i	$0.607659\pi$
$132$	0	0
$133$	−1423.31	−0.927943
$134$	0	0
$135$	−351.554	−0.224125
$136$	0	0
$137$	2026.45	1.26373	0.631866	−	0.775078i	$-0.282289\pi$
$137$	2026.45	1.26373	0.631866	+	0.775078i	$0.282289\pi$
$138$	0	0
$139$	−752.157	−0.458972	−0.229486	−	0.973312i	$-0.573705\pi$
$139$	−752.157	−0.458972	−0.229486	+	0.973312i	$0.573705\pi$
$140$	0	0
$141$	−158.465	−0.0946463
$142$	0	0
$143$	3568.92	2.08705
$144$	0	0
$145$	−68.0074	−0.0389497
$146$	0	0
$147$	994.411	0.557943
$148$	0	0
$149$	788.585	0.433580	0.216790	−	0.976218i	$-0.430441\pi$
$149$	788.585	0.433580	0.216790	+	0.976218i	$0.430441\pi$
$150$	0	0
$151$	−731.418	−0.394185	−0.197093	−	0.980385i	$-0.563150\pi$
$151$	−731.418	−0.394185	−0.197093	+	0.980385i	$0.563150\pi$
$152$	0	0
$153$	−785.238	−0.414920
$154$	0	0
$155$	−1435.46	−0.743863
$156$	0	0
$157$	−3026.77	−1.53862	−0.769309	−	0.638877i	$-0.779399\pi$
$157$	−3026.77	−1.53862	−0.769309	+	0.638877i	$0.779399\pi$
$158$	0	0
$159$	591.764	0.295157
$160$	0	0
$161$	756.225	0.370179
$162$	0	0
$163$	−1031.99	−0.495899	−0.247949	−	0.968773i	$-0.579757\pi$
$163$	−1031.99	−0.495899	−0.247949	+	0.968773i	$0.579757\pi$
$164$	0	0
$165$	−397.049	−0.187334
$166$	0	0
$167$	−1722.40	−0.798104	−0.399052	−	0.916928i	$-0.630661\pi$
$167$	−1722.40	−0.798104	−0.399052	+	0.916928i	$0.630661\pi$
$168$	0	0
$169$	1469.78	0.668996
$170$	0	0
$171$	−1090.21	−0.487548
$172$	0	0
$173$	−3823.25	−1.68021	−0.840105	−	0.542424i	$-0.817506\pi$
$173$	−3823.25	−1.68021	−0.840105	+	0.542424i	$0.817506\pi$
$174$	0	0
$175$	−821.984	−0.355064
$176$	0	0
$177$	334.462	0.142032
$178$	0	0
$179$	−2139.65	−0.893435	−0.446717	−	0.894675i	$-0.647407\pi$
$179$	−2139.65	−0.893435	−0.446717	+	0.894675i	$0.647407\pi$
$180$	0	0
$181$	1418.09	0.582353	0.291177	−	0.956669i	$-0.405953\pi$
$181$	1418.09	0.582353	0.291177	+	0.956669i	$0.405953\pi$
$182$	0	0
$183$	−251.521	−0.101601
$184$	0	0
$185$	1395.52	0.554598
$186$	0	0
$187$	−1837.64	−0.718617
$188$	0	0
$189$	2311.77	0.889718
$190$	0	0
$191$	2572.03	0.974374	0.487187	−	0.873298i	$-0.338023\pi$
$191$	2572.03	0.974374	0.487187	+	0.873298i	$0.338023\pi$
$192$	0	0
$193$	4326.94	1.61378	0.806891	−	0.590700i	$-0.201148\pi$
$193$	4326.94	1.61378	0.806891	+	0.590700i	$0.201148\pi$
$194$	0	0
$195$	−407.936	−0.149810
$196$	0	0
$197$	141.938	0.0513334	0.0256667	−	0.999671i	$-0.491829\pi$
$197$	141.938	0.0513334	0.0256667	+	0.999671i	$0.491829\pi$
$198$	0	0
$199$	5364.55	1.91097	0.955485	−	0.295040i	$-0.0953329\pi$
$199$	5364.55	1.91097	0.955485	+	0.295040i	$0.0953329\pi$
$200$	0	0
$201$	−1197.78	−0.420324
$202$	0	0
$203$	447.208	0.154620
$204$	0	0
$205$	−2095.24	−0.713843
$206$	0	0
$207$	579.247	0.194495
$208$	0	0
$209$	−2551.35	−0.844405
$210$	0	0
$211$	5557.53	1.81325	0.906625	−	0.421937i	$-0.138650\pi$
$211$	5557.53	1.81325	0.906625	+	0.421937i	$0.138650\pi$
$212$	0	0
$213$	599.529	0.192859
$214$	0	0
$215$	−2106.22	−0.668106
$216$	0	0
$217$	9439.38	2.95294
$218$	0	0
$219$	1247.09	0.384796
$220$	0	0
$221$	−1888.02	−0.574671
$222$	0	0
$223$	−1186.72	−0.356362	−0.178181	−	0.983998i	$-0.557021\pi$
$223$	−1186.72	−0.356362	−0.178181	+	0.983998i	$0.557021\pi$
$224$	0	0
$225$	−629.616	−0.186553
$226$	0	0
$227$	459.495	0.134351	0.0671757	−	0.997741i	$-0.478601\pi$
$227$	459.495	0.134351	0.0671757	+	0.997741i	$0.478601\pi$
$228$	0	0
$229$	−319.746	−0.0922681	−0.0461341	−	0.998935i	$-0.514690\pi$
$229$	−319.746	−0.0922681	−0.0461341	+	0.998935i	$0.514690\pi$
$230$	0	0
$231$	2610.94	0.743668
$232$	0	0
$233$	−5267.68	−1.48111	−0.740553	−	0.671998i	$-0.765436\pi$
$233$	−5267.68	−1.48111	−0.740553	+	0.671998i	$0.765436\pi$
$234$	0	0
$235$	−588.062	−0.163238
$236$	0	0
$237$	1017.41	0.278852
$238$	0	0
$239$	−3647.44	−0.987169	−0.493584	−	0.869698i	$-0.664314\pi$
$239$	−3647.44	−0.987169	−0.493584	+	0.869698i	$0.664314\pi$
$240$	0	0
$241$	1905.34	0.509270	0.254635	−	0.967037i	$-0.418045\pi$
$241$	1905.34	0.509270	0.254635	+	0.967037i	$0.418045\pi$
$242$	0	0
$243$	2686.93	0.709327
$244$	0	0
$245$	3690.26	0.962294
$246$	0	0
$247$	−2621.31	−0.675263
$248$	0	0
$249$	873.564	0.222329
$250$	0	0
$251$	−471.266	−0.118510	−0.0592551	−	0.998243i	$-0.518873\pi$
$251$	−471.266	−0.118510	−0.0592551	+	0.998243i	$0.518873\pi$
$252$	0	0
$253$	1355.57	0.336854
$254$	0	0
$255$	210.046	0.0515827
$256$	0	0
$257$	−4251.66	−1.03195	−0.515975	−	0.856604i	$-0.672570\pi$
$257$	−4251.66	−1.03195	−0.515975	+	0.856604i	$0.672570\pi$
$258$	0	0
$259$	−9176.76	−2.20161
$260$	0	0
$261$	342.549	0.0812384
$262$	0	0
$263$	7725.80	1.81138	0.905691	−	0.423939i	$-0.139353\pi$
$263$	7725.80	1.81138	0.905691	+	0.423939i	$0.139353\pi$
$264$	0	0
$265$	2196.04	0.509062
$266$	0	0
$267$	−730.667	−0.167476
$268$	0	0
$269$	−6381.31	−1.44638	−0.723188	−	0.690651i	$-0.757324\pi$
$269$	−6381.31	−1.44638	−0.723188	+	0.690651i	$0.757324\pi$
$270$	0	0
$271$	2264.86	0.507676	0.253838	−	0.967247i	$-0.418307\pi$
$271$	2264.86	0.507676	0.253838	+	0.967247i	$0.418307\pi$
$272$	0	0
$273$	2682.53	0.594704
$274$	0	0
$275$	−1473.45	−0.323099
$276$	0	0
$277$	4301.92	0.933131	0.466566	−	0.884487i	$-0.345491\pi$
$277$	4301.92	0.933131	0.466566	+	0.884487i	$0.345491\pi$
$278$	0	0
$279$	7230.30	1.55149
$280$	0	0
$281$	−5338.50	−1.13334	−0.566669	−	0.823946i	$-0.691768\pi$
$281$	−5338.50	−1.13334	−0.566669	+	0.823946i	$0.691768\pi$
$282$	0	0
$283$	−5340.79	−1.12183	−0.560914	−	0.827874i	$-0.689550\pi$
$283$	−5340.79	−1.12183	−0.560914	+	0.827874i	$0.689550\pi$
$284$	0	0
$285$	291.625	0.0606118
$286$	0	0
$287$	13778.0	2.83377
$288$	0	0
$289$	−3940.86	−0.802129
$290$	0	0
$291$	−923.169	−0.185970
$292$	0	0
$293$	−693.073	−0.138190	−0.0690951	−	0.997610i	$-0.522011\pi$
$293$	−693.073	−0.138190	−0.0690951	+	0.997610i	$0.522011\pi$
$294$	0	0
$295$	1241.19	0.244966
$296$	0	0
$297$	4143.97	0.809621
$298$	0	0
$299$	1392.74	0.269379
$300$	0	0
$301$	13850.2	2.65220
$302$	0	0
$303$	−622.430	−0.118012
$304$	0	0
$305$	−933.393	−0.175233
$306$	0	0
$307$	3589.95	0.667392	0.333696	−	0.942681i	$-0.391704\pi$
$307$	3589.95	0.667392	0.333696	+	0.942681i	$0.391704\pi$
$308$	0	0
$309$	−632.340	−0.116416
$310$	0	0
$311$	3726.33	0.679424	0.339712	−	0.940530i	$-0.389670\pi$
$311$	3726.33	0.679424	0.339712	+	0.940530i	$0.389670\pi$
$312$	0	0
$313$	−9337.21	−1.68617	−0.843083	−	0.537783i	$-0.819262\pi$
$313$	−9337.21	−1.68617	−0.843083	+	0.537783i	$0.819262\pi$
$314$	0	0
$315$	4140.28	0.740566
$316$	0	0
$317$	−1510.76	−0.267674	−0.133837	−	0.991003i	$-0.542730\pi$
$317$	−1510.76	−0.267674	−0.133837	+	0.991003i	$0.542730\pi$
$318$	0	0
$319$	801.643	0.140700
$320$	0	0
$321$	695.609	0.120951
$322$	0	0
$323$	1349.71	0.232507
$324$	0	0
$325$	−1513.85	−0.258379
$326$	0	0
$327$	−279.034	−0.0471885
$328$	0	0
$329$	3867.02	0.648011
$330$	0	0
$331$	7719.59	1.28189	0.640947	−	0.767585i	$-0.278542\pi$
$331$	7719.59	1.28189	0.640947	+	0.767585i	$0.278542\pi$
$332$	0	0
$333$	−7029.14	−1.15674
$334$	0	0
$335$	−4444.97	−0.724940
$336$	0	0
$337$	−5796.31	−0.936930	−0.468465	−	0.883482i	$-0.655193\pi$
$337$	−5796.31	−0.936930	−0.468465	+	0.883482i	$0.655193\pi$
$338$	0	0
$339$	−1924.20	−0.308284
$340$	0	0
$341$	16920.6	2.68710
$342$	0	0
$343$	−12989.0	−2.04473
$344$	0	0
$345$	−154.945	−0.0241795
$346$	0	0
$347$	−2384.89	−0.368955	−0.184477	−	0.982837i	$-0.559059\pi$
$347$	−2384.89	−0.368955	−0.184477	+	0.982837i	$0.559059\pi$
$348$	0	0
$349$	−7252.62	−1.11239	−0.556195	−	0.831052i	$-0.687739\pi$
$349$	−7252.62	−1.11239	−0.556195	+	0.831052i	$0.687739\pi$
$350$	0	0
$351$	4257.60	0.647446
$352$	0	0
$353$	1030.48	0.155373	0.0776867	−	0.996978i	$-0.475247\pi$
$353$	1030.48	0.155373	0.0776867	+	0.996978i	$0.475247\pi$
$354$	0	0
$355$	2224.85	0.332628
$356$	0	0
$357$	−1381.23	−0.204769
$358$	0	0
$359$	8333.15	1.22509	0.612544	−	0.790436i	$-0.290146\pi$
$359$	8333.15	1.22509	0.612544	+	0.790436i	$0.290146\pi$
$360$	0	0
$361$	−4985.08	−0.726794
$362$	0	0
$363$	2886.93	0.417422
$364$	0	0
$365$	4627.94	0.663664
$366$	0	0
$367$	1604.19	0.228169	0.114084	−	0.993471i	$-0.463607\pi$
$367$	1604.19	0.228169	0.114084	+	0.993471i	$0.463607\pi$
$368$	0	0
$369$	10553.6	1.48888
$370$	0	0
$371$	−14440.8	−2.02084
$372$	0	0
$373$	4811.31	0.667883	0.333941	−	0.942594i	$-0.391621\pi$
$373$	4811.31	0.667883	0.333941	+	0.942594i	$0.391621\pi$
$374$	0	0
$375$	168.418	0.0231922
$376$	0	0
$377$	823.624	0.112517
$378$	0	0
$379$	−3713.11	−0.503245	−0.251622	−	0.967826i	$-0.580964\pi$
$379$	−3713.11	−0.503245	−0.251622	+	0.967826i	$0.580964\pi$
$380$	0	0
$381$	2006.32	0.269781
$382$	0	0
$383$	−13529.2	−1.80498	−0.902490	−	0.430710i	$-0.858263\pi$
$383$	−13529.2	−1.80498	−0.902490	+	0.430710i	$0.858263\pi$
$384$	0	0
$385$	9689.20	1.28262
$386$	0	0
$387$	10608.9	1.39349
$388$	0	0
$389$	9909.90	1.29165	0.645825	−	0.763485i	$-0.276513\pi$
$389$	9909.90	1.29165	0.645825	+	0.763485i	$0.276513\pi$
$390$	0	0
$391$	−717.122	−0.0927529
$392$	0	0
$393$	−1340.62	−0.172074
$394$	0	0
$395$	3775.61	0.480941
$396$	0	0
$397$	−974.000	−0.123133	−0.0615663	−	0.998103i	$-0.519610\pi$
$397$	−974.000	−0.123133	−0.0615663	+	0.998103i	$0.519610\pi$
$398$	0	0
$399$	−1917.69	−0.240613
$400$	0	0
$401$	2272.45	0.282994	0.141497	−	0.989939i	$-0.454808\pi$
$401$	2272.45	0.282994	0.141497	+	0.989939i	$0.454808\pi$
$402$	0	0
$403$	17384.5	2.14885
$404$	0	0
$405$	2926.26	0.359030
$406$	0	0
$407$	−16449.8	−2.00341
$408$	0	0
$409$	−447.137	−0.0540574	−0.0270287	−	0.999635i	$-0.508605\pi$
$409$	−447.137	−0.0540574	−0.0270287	+	0.999635i	$0.508605\pi$
$410$	0	0
$411$	2730.33	0.327681
$412$	0	0
$413$	−8161.91	−0.972448
$414$	0	0
$415$	3241.79	0.383454
$416$	0	0
$417$	−1013.42	−0.119010
$418$	0	0
$419$	−10979.6	−1.28016	−0.640082	−	0.768307i	$-0.721100\pi$
$419$	−10979.6	−1.28016	−0.640082	+	0.768307i	$0.721100\pi$
$420$	0	0
$421$	11679.7	1.35210	0.676050	−	0.736856i	$-0.263690\pi$
$421$	11679.7	1.35210	0.676050	+	0.736856i	$0.263690\pi$
$422$	0	0
$423$	2962.03	0.340470
$424$	0	0
$425$	779.480	0.0889655
$426$	0	0
$427$	6137.87	0.695626
$428$	0	0
$429$	4808.57	0.541166
$430$	0	0
$431$	11584.4	1.29467	0.647333	−	0.762207i	$-0.275884\pi$
$431$	11584.4	1.29467	0.647333	+	0.762207i	$0.275884\pi$
$432$	0	0
$433$	7058.54	0.783399	0.391699	−	0.920093i	$-0.371887\pi$
$433$	7058.54	0.783399	0.391699	+	0.920093i	$0.371887\pi$
$434$	0	0
$435$	−91.6295	−0.0100995
$436$	0	0
$437$	−995.642	−0.108989
$438$	0	0
$439$	−11753.9	−1.27786	−0.638930	−	0.769265i	$-0.720623\pi$
$439$	−11753.9	−1.27786	−0.638930	+	0.769265i	$0.720623\pi$
$440$	0	0
$441$	−18587.6	−2.00708
$442$	0	0
$443$	8026.43	0.860829	0.430415	−	0.902631i	$-0.358367\pi$
$443$	8026.43	0.860829	0.430415	+	0.902631i	$0.358367\pi$
$444$	0	0
$445$	−2711.51	−0.288849
$446$	0	0
$447$	1062.50	0.112426
$448$	0	0
$449$	12992.1	1.36556	0.682780	−	0.730624i	$-0.260771\pi$
$449$	12992.1	1.36556	0.682780	+	0.730624i	$0.260771\pi$
$450$	0	0
$451$	24697.8	2.57866
$452$	0	0
$453$	−985.473	−0.102211
$454$	0	0
$455$	9954.88	1.02570
$456$	0	0
$457$	−7385.09	−0.755930	−0.377965	−	0.925820i	$-0.623376\pi$
$457$	−7385.09	−0.755930	−0.377965	+	0.925820i	$0.623376\pi$
$458$	0	0
$459$	−2192.23	−0.222930
$460$	0	0
$461$	1755.69	0.177376	0.0886881	−	0.996059i	$-0.471733\pi$
$461$	1755.69	0.177376	0.0886881	+	0.996059i	$0.471733\pi$
$462$	0	0
$463$	15292.6	1.53501	0.767503	−	0.641045i	$-0.221499\pi$
$463$	15292.6	1.53501	0.767503	+	0.641045i	$0.221499\pi$
$464$	0	0
$465$	−1934.06	−0.192881
$466$	0	0
$467$	−10139.8	−1.00474	−0.502370	−	0.864652i	$-0.667539\pi$
$467$	−10139.8	−1.00474	−0.502370	+	0.864652i	$0.667539\pi$
$468$	0	0
$469$	29229.6	2.87782
$470$	0	0
$471$	−4078.11	−0.398958
$472$	0	0
$473$	24827.2	2.41344
$474$	0	0
$475$	1082.22	0.104538
$476$	0	0
$477$	−11061.3	−1.06176
$478$	0	0
$479$	794.457	0.0757822	0.0378911	−	0.999282i	$-0.487936\pi$
$479$	794.457	0.0757822	0.0378911	+	0.999282i	$0.487936\pi$
$480$	0	0
$481$	−16900.9	−1.60211
$482$	0	0
$483$	1018.90	0.0959863
$484$	0	0
$485$	−3425.88	−0.320745
$486$	0	0
$487$	−15523.0	−1.44438	−0.722191	−	0.691694i	$-0.756865\pi$
$487$	−15523.0	−1.44438	−0.722191	+	0.691694i	$0.756865\pi$
$488$	0	0
$489$	−1390.44	−0.128585
$490$	0	0
$491$	−8135.21	−0.747733	−0.373866	−	0.927483i	$-0.621968\pi$
$491$	−8135.21	−0.747733	−0.373866	+	0.927483i	$0.621968\pi$
$492$	0	0
$493$	−424.083	−0.0387419
$494$	0	0
$495$	7421.65	0.673896
$496$	0	0
$497$	−14630.3	−1.32044
$498$	0	0
$499$	−14232.2	−1.27680	−0.638398	−	0.769706i	$-0.720403\pi$
$499$	−14232.2	−1.27680	−0.638398	+	0.769706i	$0.720403\pi$
$500$	0	0
$501$	−2320.67	−0.206946
$502$	0	0
$503$	−15130.4	−1.34121	−0.670606	−	0.741814i	$-0.733966\pi$
$503$	−15130.4	−1.34121	−0.670606	+	0.741814i	$0.733966\pi$
$504$	0	0
$505$	−2309.84	−0.203538
$506$	0	0
$507$	1980.31	0.173469
$508$	0	0
$509$	−2656.55	−0.231335	−0.115667	−	0.993288i	$-0.536901\pi$
$509$	−2656.55	−0.231335	−0.115667	+	0.993288i	$0.536901\pi$
$510$	0	0
$511$	−30432.7	−2.63457
$512$	0	0
$513$	−3043.67	−0.261952
$514$	0	0
$515$	−2346.61	−0.200785
$516$	0	0
$517$	6931.83	0.589674
$518$	0	0
$519$	−5151.24	−0.435673
$520$	0	0
$521$	−9505.07	−0.799280	−0.399640	−	0.916672i	$-0.630865\pi$
$521$	−9505.07	−0.799280	−0.399640	+	0.916672i	$0.630865\pi$
$522$	0	0
$523$	−14934.3	−1.24862	−0.624312	−	0.781175i	$-0.714620\pi$
$523$	−14934.3	−1.24862	−0.624312	+	0.781175i	$0.714620\pi$
$524$	0	0
$525$	−1107.50	−0.0920669
$526$	0	0
$527$	−8951.28	−0.739894
$528$	0	0
$529$	529.000	0.0434783
$530$	0	0
$531$	−6251.79	−0.510931
$532$	0	0
$533$	25375.0	2.06213
$534$	0	0
$535$	2581.41	0.208606
$536$	0	0
$537$	−2882.85	−0.231665
$538$	0	0
$539$	−43499.2	−3.47615
$540$	0	0
$541$	10649.7	0.846336	0.423168	−	0.906051i	$-0.360918\pi$
$541$	10649.7	0.846336	0.423168	+	0.906051i	$0.360918\pi$
$542$	0	0
$543$	1910.66	0.151002
$544$	0	0
$545$	−1035.50	−0.0813868
$546$	0	0
$547$	19018.9	1.48664	0.743318	−	0.668938i	$-0.233251\pi$
$547$	19018.9	1.48664	0.743318	+	0.668938i	$0.233251\pi$
$548$	0	0
$549$	4701.44	0.365487
$550$	0	0
$551$	−588.792	−0.0455233
$552$	0	0
$553$	−24827.9	−1.90921
$554$	0	0
$555$	1880.25	0.143806
$556$	0	0
$557$	−8233.93	−0.626360	−0.313180	−	0.949694i	$-0.601394\pi$
$557$	−8233.93	−0.626360	−0.313180	+	0.949694i	$0.601394\pi$
$558$	0	0
$559$	25507.9	1.93000
$560$	0	0
$561$	−2475.93	−0.186335
$562$	0	0
$563$	1778.32	0.133122	0.0665608	−	0.997782i	$-0.478797\pi$
$563$	1778.32	0.133122	0.0665608	+	0.997782i	$0.478797\pi$
$564$	0	0
$565$	−7140.72	−0.531703
$566$	0	0
$567$	−19242.7	−1.42525
$568$	0	0
$569$	−15916.6	−1.17269	−0.586343	−	0.810063i	$-0.699433\pi$
$569$	−15916.6	−1.17269	−0.586343	+	0.810063i	$0.699433\pi$
$570$	0	0
$571$	21037.7	1.54186	0.770928	−	0.636922i	$-0.219793\pi$
$571$	21037.7	1.54186	0.770928	+	0.636922i	$0.219793\pi$
$572$	0	0
$573$	3465.41	0.252652
$574$	0	0
$575$	−575.000	−0.0417029
$576$	0	0
$577$	7799.91	0.562764	0.281382	−	0.959596i	$-0.409207\pi$
$577$	7799.91	0.562764	0.281382	+	0.959596i	$0.409207\pi$
$578$	0	0
$579$	5829.88	0.418449
$580$	0	0
$581$	−21317.6	−1.52221
$582$	0	0
$583$	−25885.9	−1.83891
$584$	0	0
$585$	7625.16	0.538908
$586$	0	0
$587$	25963.6	1.82561	0.912804	−	0.408399i	$-0.133913\pi$
$587$	25963.6	1.82561	0.912804	+	0.408399i	$0.133913\pi$
$588$	0	0
$589$	−12427.8	−0.869406
$590$	0	0
$591$	191.240	0.0133106
$592$	0	0
$593$	−8615.72	−0.596636	−0.298318	−	0.954466i	$-0.596426\pi$
$593$	−8615.72	−0.596636	−0.298318	+	0.954466i	$0.596426\pi$
$594$	0	0
$595$	−5125.76	−0.353169
$596$	0	0
$597$	7227.91	0.495508
$598$	0	0
$599$	9710.43	0.662367	0.331183	−	0.943566i	$-0.392552\pi$
$599$	9710.43	0.662367	0.331183	+	0.943566i	$0.392552\pi$
$600$	0	0
$601$	15589.2	1.05807	0.529034	−	0.848601i	$-0.322554\pi$
$601$	15589.2	1.05807	0.529034	+	0.848601i	$0.322554\pi$
$602$	0	0
$603$	22389.0	1.51203
$604$	0	0
$605$	10713.4	0.719935
$606$	0	0
$607$	14822.3	0.991136	0.495568	−	0.868569i	$-0.334960\pi$
$607$	14822.3	0.991136	0.495568	+	0.868569i	$0.334960\pi$
$608$	0	0
$609$	602.543	0.0400924
$610$	0	0
$611$	7121.90	0.471557
$612$	0	0
$613$	27681.4	1.82389	0.911943	−	0.410316i	$-0.134582\pi$
$613$	27681.4	1.82389	0.911943	+	0.410316i	$0.134582\pi$
$614$	0	0
$615$	−2823.01	−0.185097
$616$	0	0
$617$	−12275.3	−0.800950	−0.400475	−	0.916308i	$-0.631155\pi$
$617$	−12275.3	−0.800950	−0.400475	+	0.916308i	$0.631155\pi$
$618$	0	0
$619$	10827.3	0.703046	0.351523	−	0.936179i	$-0.385664\pi$
$619$	10827.3	0.703046	0.351523	+	0.936179i	$0.385664\pi$
$620$	0	0
$621$	1617.15	0.104499
$622$	0	0
$623$	17830.5	1.14665
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	−3437.55	−0.218951
$628$	0	0
$629$	8702.24	0.551639
$630$	0	0
$631$	−25875.1	−1.63244	−0.816220	−	0.577741i	$-0.803934\pi$
$631$	−25875.1	−1.63244	−0.816220	+	0.577741i	$0.803934\pi$
$632$	0	0
$633$	7487.91	0.470170
$634$	0	0
$635$	7445.44	0.465296
$636$	0	0
$637$	−44692.0	−2.77984
$638$	0	0
$639$	−11206.4	−0.693771
$640$	0	0
$641$	−24318.0	−1.49845	−0.749224	−	0.662317i	$-0.769573\pi$
$641$	−24318.0	−1.49845	−0.749224	+	0.662317i	$0.769573\pi$
$642$	0	0
$643$	8652.57	0.530675	0.265338	−	0.964156i	$-0.414517\pi$
$643$	8652.57	0.530675	0.265338	+	0.964156i	$0.414517\pi$
$644$	0	0
$645$	−2837.80	−0.173238
$646$	0	0
$647$	−31491.1	−1.91351	−0.956756	−	0.290892i	$-0.906048\pi$
$647$	−31491.1	−1.91351	−0.956756	+	0.290892i	$0.906048\pi$
$648$	0	0
$649$	−14630.6	−0.884904
$650$	0	0
$651$	12718.1	0.765687
$652$	0	0
$653$	7520.13	0.450667	0.225334	−	0.974282i	$-0.427653\pi$
$653$	7520.13	0.450667	0.225334	+	0.974282i	$0.427653\pi$
$654$	0	0
$655$	−4975.03	−0.296779
$656$	0	0
$657$	−23310.6	−1.38422
$658$	0	0
$659$	−14075.9	−0.832049	−0.416024	−	0.909353i	$-0.636577\pi$
$659$	−14075.9	−0.832049	−0.416024	+	0.909353i	$0.636577\pi$
$660$	0	0
$661$	−13024.3	−0.766393	−0.383197	−	0.923667i	$-0.625177\pi$
$661$	−13024.3	−0.766393	−0.383197	+	0.923667i	$0.625177\pi$
$662$	0	0
$663$	−2543.82	−0.149010
$664$	0	0
$665$	−7116.54	−0.414989
$666$	0	0
$667$	312.834	0.0181604
$668$	0	0
$669$	−1598.92	−0.0924035
$670$	0	0
$671$	11002.4	0.633002
$672$	0	0
$673$	−11882.1	−0.680568	−0.340284	−	0.940323i	$-0.610523\pi$
$673$	−11882.1	−0.680568	−0.340284	+	0.940323i	$0.610523\pi$
$674$	0	0
$675$	−1757.77	−0.100232
$676$	0	0
$677$	12984.7	0.737141	0.368570	−	0.929600i	$-0.379847\pi$
$677$	12984.7	0.737141	0.368570	+	0.929600i	$0.379847\pi$
$678$	0	0
$679$	22528.1	1.27327
$680$	0	0
$681$	619.099	0.0348369
$682$	0	0
$683$	2319.48	0.129945	0.0649724	−	0.997887i	$-0.479304\pi$
$683$	2319.48	0.129945	0.0649724	+	0.997887i	$0.479304\pi$
$684$	0	0
$685$	10132.2	0.565158
$686$	0	0
$687$	−430.808	−0.0239248
$688$	0	0
$689$	−26595.7	−1.47056
$690$	0	0
$691$	−880.585	−0.0484791	−0.0242395	−	0.999706i	$-0.507716\pi$
$691$	−880.585	−0.0484791	−0.0242395	+	0.999706i	$0.507716\pi$
$692$	0	0
$693$	−48803.8	−2.67519
$694$	0	0
$695$	−3760.79	−0.205259
$696$	0	0
$697$	−13065.6	−0.710035
$698$	0	0
$699$	−7097.39	−0.384046
$700$	0	0
$701$	22417.6	1.20785	0.603924	−	0.797042i	$-0.293603\pi$
$701$	22417.6	1.20785	0.603924	+	0.797042i	$0.293603\pi$
$702$	0	0
$703$	12082.1	0.648200
$704$	0	0
$705$	−792.323	−0.0423271
$706$	0	0
$707$	15189.2	0.807990
$708$	0	0
$709$	−361.105	−0.0191278	−0.00956388	−	0.999954i	$-0.503044\pi$
$709$	−361.105	−0.0191278	−0.00956388	+	0.999954i	$0.503044\pi$
$710$	0	0
$711$	−19017.5	−1.00311
$712$	0	0
$713$	6603.10	0.346828
$714$	0	0
$715$	17844.6	0.933358
$716$	0	0
$717$	−4914.36	−0.255970
$718$	0	0
$719$	27345.9	1.41840	0.709200	−	0.705007i	$-0.249056\pi$
$719$	27345.9	1.41840	0.709200	+	0.705007i	$0.249056\pi$
$720$	0	0
$721$	15431.0	0.797061
$722$	0	0
$723$	2567.16	0.132052
$724$	0	0
$725$	−340.037	−0.0174188
$726$	0	0
$727$	13796.1	0.703807	0.351904	−	0.936036i	$-0.385534\pi$
$727$	13796.1	0.703807	0.351904	+	0.936036i	$0.385534\pi$
$728$	0	0
$729$	−12181.6	−0.618890
$730$	0	0
$731$	−13134.0	−0.664541
$732$	0	0
$733$	−8952.17	−0.451100	−0.225550	−	0.974232i	$-0.572418\pi$
$733$	−8952.17	−0.451100	−0.225550	+	0.974232i	$0.572418\pi$
$734$	0	0
$735$	4972.05	0.249520
$736$	0	0
$737$	52395.5	2.61874
$738$	0	0
$739$	25619.0	1.27525	0.637626	−	0.770346i	$-0.279917\pi$
$739$	25619.0	1.27525	0.637626	+	0.770346i	$0.279917\pi$
$740$	0	0
$741$	−3531.81	−0.175093
$742$	0	0
$743$	20537.2	1.01405	0.507025	−	0.861932i	$-0.330745\pi$
$743$	20537.2	1.01405	0.507025	+	0.861932i	$0.330745\pi$
$744$	0	0
$745$	3942.92	0.193903
$746$	0	0
$747$	−16328.7	−0.799780
$748$	0	0
$749$	−16975.0	−0.828108
$750$	0	0
$751$	−10010.0	−0.486377	−0.243188	−	0.969979i	$-0.578193\pi$
$751$	−10010.0	−0.486377	−0.243188	+	0.969979i	$0.578193\pi$
$752$	0	0
$753$	−634.959	−0.0307293
$754$	0	0
$755$	−3657.09	−0.176285
$756$	0	0
$757$	−6798.63	−0.326420	−0.163210	−	0.986591i	$-0.552185\pi$
$757$	−6798.63	−0.326420	−0.163210	+	0.986591i	$0.552185\pi$
$758$	0	0
$759$	1826.42	0.0873452
$760$	0	0
$761$	21461.0	1.02229	0.511143	−	0.859496i	$-0.329222\pi$
$761$	21461.0	1.02229	0.511143	+	0.859496i	$0.329222\pi$
$762$	0	0
$763$	6809.29	0.323084
$764$	0	0
$765$	−3926.19	−0.185558
$766$	0	0
$767$	−15031.8	−0.707649
$768$	0	0
$769$	27705.6	1.29921	0.649604	−	0.760273i	$-0.274935\pi$
$769$	27705.6	1.29921	0.649604	+	0.760273i	$0.274935\pi$
$770$	0	0
$771$	−5728.45	−0.267581
$772$	0	0
$773$	−1529.78	−0.0711804	−0.0355902	−	0.999366i	$-0.511331\pi$
$773$	−1529.78	−0.0711804	−0.0355902	+	0.999366i	$0.511331\pi$
$774$	0	0
$775$	−7177.29	−0.332665
$776$	0	0
$777$	−12364.3	−0.570870
$778$	0	0
$779$	−18140.1	−0.834321
$780$	0	0
$781$	−26225.6	−1.20157
$782$	0	0
$783$	956.330	0.0436481
$784$	0	0
$785$	−15133.9	−0.688090
$786$	0	0
$787$	−1565.88	−0.0709243	−0.0354622	−	0.999371i	$-0.511290\pi$
$787$	−1565.88	−0.0709243	−0.0354622	+	0.999371i	$0.511290\pi$
$788$	0	0
$789$	10409.3	0.469685
$790$	0	0
$791$	46956.4	2.11072
$792$	0	0
$793$	11304.1	0.506206
$794$	0	0
$795$	2958.82	0.131998
$796$	0	0
$797$	21024.5	0.934413	0.467207	−	0.884148i	$-0.345260\pi$
$797$	21024.5	0.934413	0.467207	+	0.884148i	$0.345260\pi$
$798$	0	0
$799$	−3667.06	−0.162367
$800$	0	0
$801$	13657.7	0.602459
$802$	0	0
$803$	−54552.2	−2.39739
$804$	0	0
$805$	3781.13	0.165549
$806$	0	0
$807$	−8597.83	−0.375041
$808$	0	0
$809$	11085.1	0.481746	0.240873	−	0.970557i	$-0.422566\pi$
$809$	11085.1	0.481746	0.240873	+	0.970557i	$0.422566\pi$
$810$	0	0
$811$	−37708.4	−1.63270	−0.816352	−	0.577555i	$-0.804007\pi$
$811$	−37708.4	−1.63270	−0.816352	+	0.577555i	$0.804007\pi$
$812$	0	0
$813$	3051.55	0.131639
$814$	0	0
$815$	−5159.94	−0.221773
$816$	0	0
$817$	−18235.1	−0.780864
$818$	0	0
$819$	−50142.0	−2.13932
$820$	0	0
$821$	31735.5	1.34906	0.674529	−	0.738248i	$-0.264347\pi$
$821$	31735.5	1.34906	0.674529	+	0.738248i	$0.264347\pi$
$822$	0	0
$823$	2520.71	0.106763	0.0533817	−	0.998574i	$-0.483000\pi$
$823$	2520.71	0.106763	0.0533817	+	0.998574i	$0.483000\pi$
$824$	0	0
$825$	−1985.24	−0.0837785
$826$	0	0
$827$	26109.6	1.09785	0.548923	−	0.835873i	$-0.315038\pi$
$827$	26109.6	1.09785	0.548923	+	0.835873i	$0.315038\pi$
$828$	0	0
$829$	6502.88	0.272442	0.136221	−	0.990678i	$-0.456504\pi$
$829$	6502.88	0.272442	0.136221	+	0.990678i	$0.456504\pi$
$830$	0	0
$831$	5796.17	0.241958
$832$	0	0
$833$	23011.9	0.957159
$834$	0	0
$835$	−8612.00	−0.356923
$836$	0	0
$837$	20185.6	0.833593
$838$	0	0
$839$	29362.9	1.20825	0.604124	−	0.796891i	$-0.293523\pi$
$839$	29362.9	1.20825	0.604124	+	0.796891i	$0.293523\pi$
$840$	0	0
$841$	−24204.0	−0.992415
$842$	0	0
$843$	−7192.80	−0.293871
$844$	0	0
$845$	7348.92	0.299184
$846$	0	0
$847$	−70449.8	−2.85795
$848$	0	0
$849$	−7195.89	−0.290886
$850$	0	0
$851$	−6419.40	−0.258583
$852$	0	0
$853$	10311.6	0.413908	0.206954	−	0.978351i	$-0.433645\pi$
$853$	10311.6	0.413908	0.206954	+	0.978351i	$0.433645\pi$
$854$	0	0
$855$	−5451.07	−0.218038
$856$	0	0
$857$	−16334.5	−0.651080	−0.325540	−	0.945528i	$-0.605546\pi$
$857$	−16334.5	−0.651080	−0.325540	+	0.945528i	$0.605546\pi$
$858$	0	0
$859$	−18191.0	−0.722547	−0.361274	−	0.932460i	$-0.617658\pi$
$859$	−18191.0	−0.722547	−0.361274	+	0.932460i	$0.617658\pi$
$860$	0	0
$861$	18563.8	0.734787
$862$	0	0
$863$	−8181.19	−0.322701	−0.161350	−	0.986897i	$-0.551585\pi$
$863$	−8181.19	−0.322701	−0.161350	+	0.986897i	$0.551585\pi$
$864$	0	0
$865$	−19116.2	−0.751412
$866$	0	0
$867$	−5309.70	−0.207989
$868$	0	0
$869$	−44505.3	−1.73733
$870$	0	0
$871$	53832.2	2.09418
$872$	0	0
$873$	17255.9	0.668986
$874$	0	0
$875$	−4109.92	−0.158789
$876$	0	0
$877$	5408.87	0.208261	0.104130	−	0.994564i	$-0.466794\pi$
$877$	5408.87	0.208261	0.104130	+	0.994564i	$0.466794\pi$
$878$	0	0
$879$	−933.808	−0.0358323
$880$	0	0
$881$	11104.6	0.424656	0.212328	−	0.977198i	$-0.431895\pi$
$881$	11104.6	0.424656	0.212328	+	0.977198i	$0.431895\pi$
$882$	0	0
$883$	−29962.0	−1.14190	−0.570951	−	0.820984i	$-0.693426\pi$
$883$	−29962.0	−1.14190	−0.570951	+	0.820984i	$0.693426\pi$
$884$	0	0
$885$	1672.31	0.0635188
$886$	0	0
$887$	17284.9	0.654305	0.327153	−	0.944972i	$-0.393911\pi$
$887$	17284.9	0.654305	0.327153	+	0.944972i	$0.393911\pi$
$888$	0	0
$889$	−48960.2	−1.84710
$890$	0	0
$891$	−34493.6	−1.29695
$892$	0	0
$893$	−5091.30	−0.190788
$894$	0	0
$895$	−10698.2	−0.399556
$896$	0	0
$897$	1876.50	0.0698491
$898$	0	0
$899$	3904.87	0.144866
$900$	0	0
$901$	13694.1	0.506346
$902$	0	0
$903$	18661.0	0.687707
$904$	0	0
$905$	7090.46	0.260436
$906$	0	0
$907$	−33832.8	−1.23859	−0.619293	−	0.785160i	$-0.712581\pi$
$907$	−33832.8	−1.23859	−0.619293	+	0.785160i	$0.712581\pi$
$908$	0	0
$909$	11634.5	0.424524
$910$	0	0
$911$	3043.81	0.110698	0.0553490	−	0.998467i	$-0.482373\pi$
$911$	3043.81	0.110698	0.0553490	+	0.998467i	$0.482373\pi$
$912$	0	0
$913$	−38212.9	−1.38517
$914$	0	0
$915$	−1257.60	−0.0454372
$916$	0	0
$917$	32715.2	1.17813
$918$	0	0
$919$	21728.9	0.779944	0.389972	−	0.920827i	$-0.372485\pi$
$919$	21728.9	0.779944	0.389972	+	0.920827i	$0.372485\pi$
$920$	0	0
$921$	4836.90	0.173053
$922$	0	0
$923$	−26944.7	−0.960885
$924$	0	0
$925$	6977.60	0.248024
$926$	0	0
$927$	11819.7	0.418782
$928$	0	0
$929$	−36470.6	−1.28801	−0.644005	−	0.765021i	$-0.722728\pi$
$929$	−36470.6	−1.28801	−0.644005	+	0.765021i	$0.722728\pi$
$930$	0	0
$931$	31949.4	1.12470
$932$	0	0
$933$	5020.66	0.176172
$934$	0	0
$935$	−9188.18	−0.321375
$936$	0	0
$937$	−33971.1	−1.18441	−0.592203	−	0.805789i	$-0.701742\pi$
$937$	−33971.1	−1.18441	−0.592203	+	0.805789i	$0.701742\pi$
$938$	0	0
$939$	−12580.4	−0.437218
$940$	0	0
$941$	34956.1	1.21098	0.605492	−	0.795851i	$-0.292976\pi$
$941$	34956.1	1.21098	0.605492	+	0.795851i	$0.292976\pi$
$942$	0	0
$943$	9638.10	0.332831
$944$	0	0
$945$	11558.9	0.397894
$946$	0	0
$947$	−12412.4	−0.425922	−0.212961	−	0.977061i	$-0.568311\pi$
$947$	−12412.4	−0.425922	−0.212961	+	0.977061i	$0.568311\pi$
$948$	0	0
$949$	−56048.0	−1.91717
$950$	0	0
$951$	−2035.52	−0.0694071
$952$	0	0
$953$	−27226.3	−0.925443	−0.462721	−	0.886504i	$-0.653127\pi$
$953$	−27226.3	−0.925443	−0.462721	+	0.886504i	$0.653127\pi$
$954$	0	0
$955$	12860.1	0.435753
$956$	0	0
$957$	1080.09	0.0364831
$958$	0	0
$959$	−66628.3	−2.24353
$960$	0	0
$961$	52630.5	1.76666
$962$	0	0
$963$	−13002.4	−0.435094
$964$	0	0
$965$	21634.7	0.721705
$966$	0	0
$967$	−22421.1	−0.745620	−0.372810	−	0.927908i	$-0.621606\pi$
$967$	−22421.1	−0.745620	−0.372810	+	0.927908i	$0.621606\pi$
$968$	0	0
$969$	1818.53	0.0602884
$970$	0	0
$971$	−45147.2	−1.49211	−0.746057	−	0.665882i	$-0.768055\pi$
$971$	−45147.2	−1.49211	−0.746057	+	0.665882i	$0.768055\pi$
$972$	0	0
$973$	24730.4	0.814822
$974$	0	0
$975$	−2039.68	−0.0669969
$976$	0	0
$977$	−19169.4	−0.627721	−0.313861	−	0.949469i	$-0.601622\pi$
$977$	−19169.4	−0.627721	−0.313861	+	0.949469i	$0.601622\pi$
$978$	0	0
$979$	31962.1	1.04342
$980$	0	0
$981$	5215.73	0.169751
$982$	0	0
$983$	−7749.63	−0.251449	−0.125725	−	0.992065i	$-0.540126\pi$
$983$	−7749.63	−0.251449	−0.125725	+	0.992065i	$0.540126\pi$
$984$	0	0
$985$	709.690	0.0229570
$986$	0	0
$987$	5210.21	0.168027
$988$	0	0
$989$	9688.59	0.311506
$990$	0	0
$991$	−40149.8	−1.28698	−0.643491	−	0.765453i	$-0.722515\pi$
$991$	−40149.8	−1.28698	−0.643491	+	0.765453i	$0.722515\pi$
$992$	0	0
$993$	10401.0	0.332391
$994$	0	0
$995$	26822.8	0.854612
$996$	0	0
$997$	−42247.3	−1.34201	−0.671006	−	0.741452i	$-0.734138\pi$
$997$	−42247.3	−1.34201	−0.671006	+	0.741452i	$0.734138\pi$
$998$	0	0
$999$	−19624.0	−0.621498

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1840.4.a.j.1.2		3
4.3	odd	2		230.4.a.g.1.2	✓	3
12.11	even	2		2070.4.a.ba.1.3		3
20.3	even	4		1150.4.b.l.599.5		6
20.7	even	4		1150.4.b.l.599.2		6
20.19	odd	2		1150.4.a.m.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.g.1.2	✓	3	4.3	odd	2
1150.4.a.m.1.2		3	20.19	odd	2
1150.4.b.l.599.2		6	20.7	even	4
1150.4.b.l.599.5		6	20.3	even	4
1840.4.a.j.1.2		3	1.1	even	1	trivial
2070.4.a.ba.1.3		3	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1840.a (trivial)

\(f(q)\)	\(=\)	\(q+1.34735 q^{3} +5.00000 q^{5} -32.8794 q^{7} -25.1847 q^{9} +O(q^{10})\)	\(q+1.34735 q^{3} +5.00000 q^{5} -32.8794 q^{7} -25.1847 q^{9} -58.9379 q^{11} -60.5540 q^{13} +6.73673 q^{15} +31.1792 q^{17} +43.2888 q^{19} -44.2998 q^{21} -23.0000 q^{23} +25.0000 q^{25} -70.3108 q^{27} -13.6015 q^{29} -287.091 q^{31} -79.4097 q^{33} -164.397 q^{35} +279.104 q^{37} -81.5871 q^{39} -419.048 q^{41} -421.243 q^{43} -125.923 q^{45} -117.612 q^{47} +738.052 q^{49} +42.0092 q^{51} +439.207 q^{53} -294.690 q^{55} +58.3250 q^{57} +248.238 q^{59} -186.679 q^{61} +828.055 q^{63} -302.770 q^{65} -888.995 q^{67} -30.9889 q^{69} +444.971 q^{71} +925.588 q^{73} +33.6836 q^{75} +1937.84 q^{77} +755.123 q^{79} +585.253 q^{81} +648.359 q^{83} +155.896 q^{85} -18.3259 q^{87} -542.301 q^{89} +1990.98 q^{91} -386.811 q^{93} +216.444 q^{95} -685.176 q^{97} +1484.33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{3} + 15 q^{5} - 7 q^{7} + 10 q^{9}+O(q^{10}) \) 3 * q + q^3 + 15 * q^5 - 7 * q^7 + 10 * q^9	\( 3 q + q^{3} + 15 q^{5} - 7 q^{7} + 10 q^{9} - 27 q^{11} + 75 q^{13} + 5 q^{15} + 127 q^{17} + 185 q^{19} - 258 q^{21} - 69 q^{23} + 75 q^{25} - 98 q^{27} + 344 q^{29} - 397 q^{31} + 477 q^{33} - 35 q^{35} + 978 q^{37} - 198 q^{39} - 575 q^{41} - 812 q^{43} + 50 q^{45} + 270 q^{47} + 878 q^{49} - 955 q^{51} + 510 q^{53} - 135 q^{55} + 894 q^{57} - 142 q^{59} - 49 q^{61} + 1356 q^{63} + 375 q^{65} - 1616 q^{67} - 23 q^{69} + 471 q^{71} - 780 q^{73} + 25 q^{75} + 1032 q^{77} + 860 q^{79} - 1193 q^{81} + 288 q^{83} + 635 q^{85} - 1452 q^{87} - 90 q^{89} + 3963 q^{91} - 1592 q^{93} + 925 q^{95} + 1321 q^{97} + 1851 q^{99}+O(q^{100}) \) 3 * q + q^3 + 15 * q^5 - 7 * q^7 + 10 * q^9 - 27 * q^11 + 75 * q^13 + 5 * q^15 + 127 * q^17 + 185 * q^19 - 258 * q^21 - 69 * q^23 + 75 * q^25 - 98 * q^27 + 344 * q^29 - 397 * q^31 + 477 * q^33 - 35 * q^35 + 978 * q^37 - 198 * q^39 - 575 * q^41 - 812 * q^43 + 50 * q^45 + 270 * q^47 + 878 * q^49 - 955 * q^51 + 510 * q^53 - 135 * q^55 + 894 * q^57 - 142 * q^59 - 49 * q^61 + 1356 * q^63 + 375 * q^65 - 1616 * q^67 - 23 * q^69 + 471 * q^71 - 780 * q^73 + 25 * q^75 + 1032 * q^77 + 860 * q^79 - 1193 * q^81 + 288 * q^83 + 635 * q^85 - 1452 * q^87 - 90 * q^89 + 3963 * q^91 - 1592 * q^93 + 925 * q^95 + 1321 * q^97 + 1851 * q^99

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