LMFDB - Embedded newform 1232.4.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,4,Mod(1,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, 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("1232.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1232.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:	$72.6903531271$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.509800.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} + 5x + 15 $ x^4 - x^3 - 10x^2 + 5x + 15
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.11082$ of defining polynomial
Character	$\chi$	$=$	1232.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.17115 q^{3} -10.0822 q^{5} +7.00000 q^{7} -0.259212 q^{9} +O(q^{10})$	$q-5.17115 q^{3} -10.0822 q^{5} +7.00000 q^{7} -0.259212 q^{9} -11.0000 q^{11} -84.5724 q^{13} +52.1367 q^{15} -38.2525 q^{17} +127.283 q^{19} -36.1980 q^{21} -140.378 q^{23} -23.3486 q^{25} +140.961 q^{27} -116.806 q^{29} -338.709 q^{31} +56.8826 q^{33} -70.5756 q^{35} -75.3416 q^{37} +437.337 q^{39} -22.4446 q^{41} -181.844 q^{43} +2.61343 q^{45} -300.530 q^{47} +49.0000 q^{49} +197.810 q^{51} -31.8596 q^{53} +110.905 q^{55} -658.201 q^{57} +68.3030 q^{59} -145.315 q^{61} -1.81448 q^{63} +852.679 q^{65} +668.020 q^{67} +725.916 q^{69} -727.608 q^{71} -416.982 q^{73} +120.739 q^{75} -77.0000 q^{77} -458.805 q^{79} -721.934 q^{81} -355.737 q^{83} +385.671 q^{85} +604.022 q^{87} -1245.97 q^{89} -592.007 q^{91} +1751.51 q^{93} -1283.30 q^{95} -935.338 q^{97} +2.85133 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{3} - 18 q^{5} + 28 q^{7} + 66 q^{9}+O(q^{10}) $ 4 * q + 12 * q^3 - 18 * q^5 + 28 * q^7 + 66 * q^9	$ 4 q + 12 q^{3} - 18 q^{5} + 28 q^{7} + 66 q^{9} - 44 q^{11} - 134 q^{13} + 62 q^{15} - 74 q^{17} + 164 q^{19} + 84 q^{21} - 194 q^{23} + 38 q^{25} + 510 q^{27} - 108 q^{29} + 412 q^{31} - 132 q^{33} - 126 q^{35} + 286 q^{37} + 256 q^{39} - 18 q^{41} + 496 q^{43} + 580 q^{45} - 62 q^{47} + 196 q^{49} + 508 q^{51} - 828 q^{53} + 198 q^{55} + 700 q^{57} + 1224 q^{59} - 350 q^{61} + 462 q^{63} - 396 q^{65} + 1498 q^{67} - 386 q^{69} - 2326 q^{71} - 1630 q^{73} + 1362 q^{75} - 308 q^{77} + 1020 q^{79} + 1128 q^{81} + 1920 q^{83} + 2008 q^{85} - 1640 q^{87} + 1550 q^{89} - 938 q^{91} + 6046 q^{93} - 2332 q^{95} - 2202 q^{97} - 726 q^{99}+O(q^{100}) $ 4 * q + 12 * q^3 - 18 * q^5 + 28 * q^7 + 66 * q^9 - 44 * q^11 - 134 * q^13 + 62 * q^15 - 74 * q^17 + 164 * q^19 + 84 * q^21 - 194 * q^23 + 38 * q^25 + 510 * q^27 - 108 * q^29 + 412 * q^31 - 132 * q^33 - 126 * q^35 + 286 * q^37 + 256 * q^39 - 18 * q^41 + 496 * q^43 + 580 * q^45 - 62 * q^47 + 196 * q^49 + 508 * q^51 - 828 * q^53 + 198 * q^55 + 700 * q^57 + 1224 * q^59 - 350 * q^61 + 462 * q^63 - 396 * q^65 + 1498 * q^67 - 386 * q^69 - 2326 * q^71 - 1630 * q^73 + 1362 * q^75 - 308 * q^77 + 1020 * q^79 + 1128 * q^81 + 1920 * q^83 + 2008 * q^85 - 1640 * q^87 + 1550 * q^89 - 938 * q^91 + 6046 * q^93 - 2332 * q^95 - 2202 * q^97 - 726 * 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
$3$	−5.17115	−0.995188	−0.497594	−	0.867410i	$-0.665783\pi$
$3$	−5.17115	−0.995188	−0.497594	+	0.867410i	$0.665783\pi$
$4$	0	0
$5$	−10.0822	−0.901782	−0.450891	−	0.892579i	$-0.648894\pi$
$5$	−10.0822	−0.901782	−0.450891	+	0.892579i	$0.648894\pi$
$6$	0	0
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	0	0
$9$	−0.259212	−0.00960043
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	0	0
$13$	−84.5724	−1.80432	−0.902161	−	0.431400i	$-0.858020\pi$
$13$	−84.5724	−1.80432	−0.902161	+	0.431400i	$0.858020\pi$
$14$	0	0
$15$	52.1367	0.897443
$16$	0	0
$17$	−38.2525	−0.545741	−0.272871	−	0.962051i	$-0.587973\pi$
$17$	−38.2525	−0.545741	−0.272871	+	0.962051i	$0.587973\pi$
$18$	0	0
$19$	127.283	1.53688	0.768442	−	0.639919i	$-0.221032\pi$
$19$	127.283	1.53688	0.768442	+	0.639919i	$0.221032\pi$
$20$	0	0
$21$	−36.1980	−0.376146
$22$	0	0
$23$	−140.378	−1.27265	−0.636323	−	0.771423i	$-0.719545\pi$
$23$	−140.378	−1.27265	−0.636323	+	0.771423i	$0.719545\pi$
$24$	0	0
$25$	−23.3486	−0.186789
$26$	0	0
$27$	140.961	1.00474
$28$	0	0
$29$	−116.806	−0.747943	−0.373971	−	0.927440i	$-0.622004\pi$
$29$	−116.806	−0.747943	−0.373971	+	0.927440i	$0.622004\pi$
$30$	0	0
$31$	−338.709	−1.96238	−0.981192	−	0.193034i	$-0.938167\pi$
$31$	−338.709	−1.96238	−0.981192	+	0.193034i	$0.938167\pi$
$32$	0	0
$33$	56.8826	0.300061
$34$	0	0
$35$	−70.5756	−0.340842
$36$	0	0
$37$	−75.3416	−0.334759	−0.167379	−	0.985893i	$-0.553531\pi$
$37$	−75.3416	−0.334759	−0.167379	+	0.985893i	$0.553531\pi$
$38$	0	0
$39$	437.337	1.79564
$40$	0	0
$41$	−22.4446	−0.0854941	−0.0427471	−	0.999086i	$-0.513611\pi$
$41$	−22.4446	−0.0854941	−0.0427471	+	0.999086i	$0.513611\pi$
$42$	0	0
$43$	−181.844	−0.644906	−0.322453	−	0.946585i	$-0.604508\pi$
$43$	−181.844	−0.644906	−0.322453	+	0.946585i	$0.604508\pi$
$44$	0	0
$45$	2.61343	0.00865749
$46$	0	0
$47$	−300.530	−0.932698	−0.466349	−	0.884601i	$-0.654431\pi$
$47$	−300.530	−0.932698	−0.466349	+	0.884601i	$0.654431\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	0	0
$51$	197.810	0.543115
$52$	0	0
$53$	−31.8596	−0.0825708	−0.0412854	−	0.999147i	$-0.513145\pi$
$53$	−31.8596	−0.0825708	−0.0412854	+	0.999147i	$0.513145\pi$
$54$	0	0
$55$	110.905	0.271898
$56$	0	0
$57$	−658.201	−1.52949
$58$	0	0
$59$	68.3030	0.150717	0.0753584	−	0.997157i	$-0.475990\pi$
$59$	68.3030	0.150717	0.0753584	+	0.997157i	$0.475990\pi$
$60$	0	0
$61$	−145.315	−0.305012	−0.152506	−	0.988303i	$-0.548734\pi$
$61$	−145.315	−0.305012	−0.152506	+	0.988303i	$0.548734\pi$
$62$	0	0
$63$	−1.81448	−0.00362862
$64$	0	0
$65$	852.679	1.62710
$66$	0	0
$67$	668.020	1.21808	0.609042	−	0.793138i	$-0.291554\pi$
$67$	668.020	1.21808	0.609042	+	0.793138i	$0.291554\pi$
$68$	0	0
$69$	725.916	1.26652
$70$	0	0
$71$	−727.608	−1.21621	−0.608107	−	0.793855i	$-0.708071\pi$
$71$	−727.608	−1.21621	−0.608107	+	0.793855i	$0.708071\pi$
$72$	0	0
$73$	−416.982	−0.668548	−0.334274	−	0.942476i	$-0.608491\pi$
$73$	−416.982	−0.668548	−0.334274	+	0.942476i	$0.608491\pi$
$74$	0	0
$75$	120.739	0.185890
$76$	0	0
$77$	−77.0000	−0.113961
$78$	0	0
$79$	−458.805	−0.653413	−0.326707	−	0.945126i	$-0.605939\pi$
$79$	−458.805	−0.653413	−0.326707	+	0.945126i	$0.605939\pi$
$80$	0	0
$81$	−721.934	−0.990307
$82$	0	0
$83$	−355.737	−0.470449	−0.235224	−	0.971941i	$-0.575582\pi$
$83$	−355.737	−0.470449	−0.235224	+	0.971941i	$0.575582\pi$
$84$	0	0
$85$	385.671	0.492140
$86$	0	0
$87$	604.022	0.744344
$88$	0	0
$89$	−1245.97	−1.48396	−0.741980	−	0.670422i	$-0.766113\pi$
$89$	−1245.97	−1.48396	−0.741980	+	0.670422i	$0.766113\pi$
$90$	0	0
$91$	−592.007	−0.681969
$92$	0	0
$93$	1751.51	1.95294
$94$	0	0
$95$	−1283.30	−1.38594
$96$	0	0
$97$	−935.338	−0.979063	−0.489532	−	0.871986i	$-0.662832\pi$
$97$	−935.338	−0.979063	−0.489532	+	0.871986i	$0.662832\pi$
$98$	0	0
$99$	2.85133	0.00289464
$100$	0	0
$101$	−533.395	−0.525493	−0.262747	−	0.964865i	$-0.584628\pi$
$101$	−533.395	−0.525493	−0.262747	+	0.964865i	$0.584628\pi$
$102$	0	0
$103$	738.096	0.706086	0.353043	−	0.935607i	$-0.385147\pi$
$103$	738.096	0.706086	0.353043	+	0.935607i	$0.385147\pi$
$104$	0	0
$105$	364.957	0.339202
$106$	0	0
$107$	2039.07	1.84228	0.921141	−	0.389229i	$-0.127259\pi$
$107$	2039.07	1.84228	0.921141	+	0.389229i	$0.127259\pi$
$108$	0	0
$109$	1488.69	1.30817	0.654085	−	0.756421i	$-0.273054\pi$
$109$	1488.69	1.30817	0.654085	+	0.756421i	$0.273054\pi$
$110$	0	0
$111$	389.603	0.333148
$112$	0	0
$113$	−532.743	−0.443507	−0.221753	−	0.975103i	$-0.571178\pi$
$113$	−532.743	−0.443507	−0.221753	+	0.975103i	$0.571178\pi$
$114$	0	0
$115$	1415.32	1.14765
$116$	0	0
$117$	21.9222	0.0173223
$118$	0	0
$119$	−267.768	−0.206271
$120$	0	0
$121$	121.000	0.0909091
$122$	0	0
$123$	116.064	0.0850828
$124$	0	0
$125$	1495.68	1.07023
$126$	0	0
$127$	2257.44	1.57729	0.788645	−	0.614849i	$-0.210783\pi$
$127$	2257.44	1.57729	0.788645	+	0.614849i	$0.210783\pi$
$128$	0	0
$129$	940.343	0.641803
$130$	0	0
$131$	−1174.21	−0.783142	−0.391571	−	0.920148i	$-0.628068\pi$
$131$	−1174.21	−0.783142	−0.391571	+	0.920148i	$0.628068\pi$
$132$	0	0
$133$	890.984	0.580888
$134$	0	0
$135$	−1421.21	−0.906059
$136$	0	0
$137$	2690.08	1.67758	0.838792	−	0.544451i	$-0.183262\pi$
$137$	2690.08	1.67758	0.838792	+	0.544451i	$0.183262\pi$
$138$	0	0
$139$	−17.7500	−0.0108312	−0.00541559	−	0.999985i	$-0.501724\pi$
$139$	−17.7500	−0.0108312	−0.00541559	+	0.999985i	$0.501724\pi$
$140$	0	0
$141$	1554.09	0.928210
$142$	0	0
$143$	930.297	0.544023
$144$	0	0
$145$	1177.67	0.674482
$146$	0	0
$147$	−253.386	−0.142170
$148$	0	0
$149$	1517.86	0.834550	0.417275	−	0.908780i	$-0.362985\pi$
$149$	1517.86	0.834550	0.417275	+	0.908780i	$0.362985\pi$
$150$	0	0
$151$	−1948.86	−1.05031	−0.525153	−	0.851008i	$-0.675992\pi$
$151$	−1948.86	−1.05031	−0.525153	+	0.851008i	$0.675992\pi$
$152$	0	0
$153$	9.91550	0.00523935
$154$	0	0
$155$	3414.94	1.76964
$156$	0	0
$157$	−1554.20	−0.790055	−0.395027	−	0.918669i	$-0.629265\pi$
$157$	−1554.20	−0.790055	−0.395027	+	0.918669i	$0.629265\pi$
$158$	0	0
$159$	164.751	0.0821735
$160$	0	0
$161$	−982.647	−0.481015
$162$	0	0
$163$	3472.71	1.66873	0.834367	−	0.551209i	$-0.185833\pi$
$163$	3472.71	1.66873	0.834367	+	0.551209i	$0.185833\pi$
$164$	0	0
$165$	−573.504	−0.270589
$166$	0	0
$167$	2228.90	1.03280	0.516400	−	0.856347i	$-0.327272\pi$
$167$	2228.90	1.03280	0.516400	+	0.856347i	$0.327272\pi$
$168$	0	0
$169$	4955.50	2.25558
$170$	0	0
$171$	−32.9933	−0.0147547
$172$	0	0
$173$	−1008.04	−0.443005	−0.221502	−	0.975160i	$-0.571096\pi$
$173$	−1008.04	−0.443005	−0.221502	+	0.975160i	$0.571096\pi$
$174$	0	0
$175$	−163.440	−0.0705995
$176$	0	0
$177$	−353.205	−0.149992
$178$	0	0
$179$	746.246	0.311603	0.155802	−	0.987788i	$-0.450204\pi$
$179$	746.246	0.311603	0.155802	+	0.987788i	$0.450204\pi$
$180$	0	0
$181$	−2787.76	−1.14482	−0.572410	−	0.819968i	$-0.693991\pi$
$181$	−2787.76	−1.14482	−0.572410	+	0.819968i	$0.693991\pi$
$182$	0	0
$183$	751.447	0.303544
$184$	0	0
$185$	759.611	0.301880
$186$	0	0
$187$	420.778	0.164547
$188$	0	0
$189$	986.730	0.379757
$190$	0	0
$191$	911.917	0.345466	0.172733	−	0.984969i	$-0.444740\pi$
$191$	911.917	0.345466	0.172733	+	0.984969i	$0.444740\pi$
$192$	0	0
$193$	4454.66	1.66142	0.830709	−	0.556707i	$-0.187935\pi$
$193$	4454.66	1.66142	0.830709	+	0.556707i	$0.187935\pi$
$194$	0	0
$195$	−4409.33	−1.61928
$196$	0	0
$197$	−1377.46	−0.498171	−0.249086	−	0.968481i	$-0.580130\pi$
$197$	−1377.46	−0.498171	−0.249086	+	0.968481i	$0.580130\pi$
$198$	0	0
$199$	94.3572	0.0336121	0.0168060	−	0.999859i	$-0.494650\pi$
$199$	94.3572	0.0336121	0.0168060	+	0.999859i	$0.494650\pi$
$200$	0	0
$201$	−3454.43	−1.21222
$202$	0	0
$203$	−817.643	−0.282696
$204$	0	0
$205$	226.292	0.0770971
$206$	0	0
$207$	36.3876	0.0122179
$208$	0	0
$209$	−1400.12	−0.463388
$210$	0	0
$211$	−1174.19	−0.383101	−0.191550	−	0.981483i	$-0.561352\pi$
$211$	−1174.19	−0.383101	−0.191550	+	0.981483i	$0.561352\pi$
$212$	0	0
$213$	3762.57	1.21036
$214$	0	0
$215$	1833.40	0.581565
$216$	0	0
$217$	−2370.96	−0.741712
$218$	0	0
$219$	2156.27	0.665331
$220$	0	0
$221$	3235.11	0.984692
$222$	0	0
$223$	−88.5875	−0.0266021	−0.0133010	−	0.999912i	$-0.504234\pi$
$223$	−88.5875	−0.0266021	−0.0133010	+	0.999912i	$0.504234\pi$
$224$	0	0
$225$	6.05223	0.00179325
$226$	0	0
$227$	−883.312	−0.258271	−0.129135	−	0.991627i	$-0.541220\pi$
$227$	−883.312	−0.258271	−0.129135	+	0.991627i	$0.541220\pi$
$228$	0	0
$229$	1240.26	0.357898	0.178949	−	0.983858i	$-0.442730\pi$
$229$	1240.26	0.357898	0.178949	+	0.983858i	$0.442730\pi$
$230$	0	0
$231$	398.179	0.113412
$232$	0	0
$233$	−5479.93	−1.54078	−0.770392	−	0.637571i	$-0.779939\pi$
$233$	−5479.93	−1.54078	−0.770392	+	0.637571i	$0.779939\pi$
$234$	0	0
$235$	3030.01	0.841090
$236$	0	0
$237$	2372.55	0.650269
$238$	0	0
$239$	−594.006	−0.160766	−0.0803830	−	0.996764i	$-0.525614\pi$
$239$	−594.006	−0.160766	−0.0803830	+	0.996764i	$0.525614\pi$
$240$	0	0
$241$	308.785	0.0825336	0.0412668	−	0.999148i	$-0.486861\pi$
$241$	308.785	0.0825336	0.0412668	+	0.999148i	$0.486861\pi$
$242$	0	0
$243$	−72.7302	−0.0192002
$244$	0	0
$245$	−494.029	−0.128826
$246$	0	0
$247$	−10764.7	−2.77303
$248$	0	0
$249$	1839.57	0.468185
$250$	0	0
$251$	−3487.59	−0.877031	−0.438515	−	0.898724i	$-0.644495\pi$
$251$	−3487.59	−0.877031	−0.438515	+	0.898724i	$0.644495\pi$
$252$	0	0
$253$	1544.16	0.383717
$254$	0	0
$255$	−1994.36	−0.489772
$256$	0	0
$257$	451.445	0.109574	0.0547868	−	0.998498i	$-0.482552\pi$
$257$	451.445	0.109574	0.0547868	+	0.998498i	$0.482552\pi$
$258$	0	0
$259$	−527.391	−0.126527
$260$	0	0
$261$	30.2775	0.00718057
$262$	0	0
$263$	5878.61	1.37829	0.689146	−	0.724622i	$-0.257986\pi$
$263$	5878.61	1.37829	0.689146	+	0.724622i	$0.257986\pi$
$264$	0	0
$265$	321.216	0.0744609
$266$	0	0
$267$	6443.09	1.47682
$268$	0	0
$269$	−52.8516	−0.0119792	−0.00598962	−	0.999982i	$-0.501907\pi$
$269$	−52.8516	−0.0119792	−0.00598962	+	0.999982i	$0.501907\pi$
$270$	0	0
$271$	6822.19	1.52922	0.764610	−	0.644493i	$-0.222931\pi$
$271$	6822.19	1.52922	0.764610	+	0.644493i	$0.222931\pi$
$272$	0	0
$273$	3061.36	0.678688
$274$	0	0
$275$	256.835	0.0563189
$276$	0	0
$277$	469.032	0.101738	0.0508689	−	0.998705i	$-0.483801\pi$
$277$	469.032	0.101738	0.0508689	+	0.998705i	$0.483801\pi$
$278$	0	0
$279$	87.7972	0.0188397
$280$	0	0
$281$	−2305.05	−0.489352	−0.244676	−	0.969605i	$-0.578682\pi$
$281$	−2305.05	−0.489352	−0.244676	+	0.969605i	$0.578682\pi$
$282$	0	0
$283$	7370.80	1.54823	0.774114	−	0.633046i	$-0.218195\pi$
$283$	7370.80	1.54823	0.774114	+	0.633046i	$0.218195\pi$
$284$	0	0
$285$	6636.14	1.37927
$286$	0	0
$287$	−157.112	−0.0323137
$288$	0	0
$289$	−3449.74	−0.702167
$290$	0	0
$291$	4836.77	0.974352
$292$	0	0
$293$	1758.90	0.350702	0.175351	−	0.984506i	$-0.443894\pi$
$293$	1758.90	0.350702	0.175351	+	0.984506i	$0.443894\pi$
$294$	0	0
$295$	−688.646	−0.135914
$296$	0	0
$297$	−1550.58	−0.302941
$298$	0	0
$299$	11872.1	2.29626
$300$	0	0
$301$	−1272.91	−0.243752
$302$	0	0
$303$	2758.27	0.522965
$304$	0	0
$305$	1465.10	0.275054
$306$	0	0
$307$	−3468.10	−0.644739	−0.322369	−	0.946614i	$-0.604479\pi$
$307$	−3468.10	−0.644739	−0.322369	+	0.946614i	$0.604479\pi$
$308$	0	0
$309$	−3816.81	−0.702688
$310$	0	0
$311$	−1983.98	−0.361741	−0.180870	−	0.983507i	$-0.557891\pi$
$311$	−1983.98	−0.361741	−0.180870	+	0.983507i	$0.557891\pi$
$312$	0	0
$313$	−10094.2	−1.82287	−0.911436	−	0.411443i	$-0.865025\pi$
$313$	−10094.2	−1.82287	−0.911436	+	0.411443i	$0.865025\pi$
$314$	0	0
$315$	18.2940	0.00327223
$316$	0	0
$317$	−3051.34	−0.540633	−0.270316	−	0.962772i	$-0.587128\pi$
$317$	−3051.34	−0.540633	−0.270316	+	0.962772i	$0.587128\pi$
$318$	0	0
$319$	1284.87	0.225513
$320$	0	0
$321$	−10544.3	−1.83342
$322$	0	0
$323$	−4868.91	−0.838741
$324$	0	0
$325$	1974.65	0.337027
$326$	0	0
$327$	−7698.23	−1.30187
$328$	0	0
$329$	−2103.71	−0.352527
$330$	0	0
$331$	26.9826	0.00448066	0.00224033	−	0.999997i	$-0.499287\pi$
$331$	26.9826	0.00448066	0.00224033	+	0.999997i	$0.499287\pi$
$332$	0	0
$333$	19.5294	0.00321383
$334$	0	0
$335$	−6735.13	−1.09845
$336$	0	0
$337$	6818.62	1.10218	0.551089	−	0.834447i	$-0.314213\pi$
$337$	6818.62	1.10218	0.551089	+	0.834447i	$0.314213\pi$
$338$	0	0
$339$	2754.90	0.441373
$340$	0	0
$341$	3725.80	0.591681
$342$	0	0
$343$	343.000	0.0539949
$344$	0	0
$345$	−7318.86	−1.14213
$346$	0	0
$347$	−11907.0	−1.84208	−0.921038	−	0.389473i	$-0.872657\pi$
$347$	−11907.0	−1.84208	−0.921038	+	0.389473i	$0.872657\pi$
$348$	0	0
$349$	−4352.72	−0.667609	−0.333805	−	0.942642i	$-0.608333\pi$
$349$	−4352.72	−0.667609	−0.333805	+	0.942642i	$0.608333\pi$
$350$	0	0
$351$	−11921.5	−1.81288
$352$	0	0
$353$	−1326.31	−0.199978	−0.0999891	−	0.994989i	$-0.531881\pi$
$353$	−1326.31	−0.199978	−0.0999891	+	0.994989i	$0.531881\pi$
$354$	0	0
$355$	7335.91	1.09676
$356$	0	0
$357$	1384.67	0.205278
$358$	0	0
$359$	8292.92	1.21917	0.609587	−	0.792719i	$-0.291335\pi$
$359$	8292.92	1.21917	0.609587	+	0.792719i	$0.291335\pi$
$360$	0	0
$361$	9342.06	1.36201
$362$	0	0
$363$	−625.709	−0.0904717
$364$	0	0
$365$	4204.10	0.602885
$366$	0	0
$367$	11027.5	1.56848	0.784241	−	0.620457i	$-0.213053\pi$
$367$	11027.5	1.56848	0.784241	+	0.620457i	$0.213053\pi$
$368$	0	0
$369$	5.81790	0.000820780 0
$370$	0	0
$371$	−223.017	−0.0312088
$372$	0	0
$373$	8245.72	1.14463	0.572316	−	0.820034i	$-0.306045\pi$
$373$	8245.72	1.14463	0.572316	+	0.820034i	$0.306045\pi$
$374$	0	0
$375$	−7734.41	−1.06508
$376$	0	0
$377$	9878.58	1.34953
$378$	0	0
$379$	−10163.4	−1.37747	−0.688734	−	0.725014i	$-0.741833\pi$
$379$	−10163.4	−1.37747	−0.688734	+	0.725014i	$0.741833\pi$
$380$	0	0
$381$	−11673.6	−1.56970
$382$	0	0
$383$	−14338.9	−1.91301	−0.956506	−	0.291714i	$-0.905774\pi$
$383$	−14338.9	−1.91301	−0.956506	+	0.291714i	$0.905774\pi$
$384$	0	0
$385$	776.332	0.102768
$386$	0	0
$387$	47.1361	0.00619138
$388$	0	0
$389$	−2382.91	−0.310587	−0.155294	−	0.987868i	$-0.549632\pi$
$389$	−2382.91	−0.310587	−0.155294	+	0.987868i	$0.549632\pi$
$390$	0	0
$391$	5369.82	0.694535
$392$	0	0
$393$	6072.04	0.779374
$394$	0	0
$395$	4625.78	0.589236
$396$	0	0
$397$	−9868.22	−1.24754	−0.623768	−	0.781609i	$-0.714399\pi$
$397$	−9868.22	−1.24754	−0.623768	+	0.781609i	$0.714399\pi$
$398$	0	0
$399$	−4607.41	−0.578093
$400$	0	0
$401$	−5879.12	−0.732143	−0.366072	−	0.930587i	$-0.619298\pi$
$401$	−5879.12	−0.732143	−0.366072	+	0.930587i	$0.619298\pi$
$402$	0	0
$403$	28645.4	3.54077
$404$	0	0
$405$	7278.71	0.893042
$406$	0	0
$407$	828.758	0.100934
$408$	0	0
$409$	5680.84	0.686796	0.343398	−	0.939190i	$-0.388422\pi$
$409$	5680.84	0.686796	0.343398	+	0.939190i	$0.388422\pi$
$410$	0	0
$411$	−13910.8	−1.66951
$412$	0	0
$413$	478.121	0.0569656
$414$	0	0
$415$	3586.62	0.424242
$416$	0	0
$417$	91.7878	0.0107791
$418$	0	0
$419$	1098.50	0.128079	0.0640395	−	0.997947i	$-0.479602\pi$
$419$	1098.50	0.128079	0.0640395	+	0.997947i	$0.479602\pi$
$420$	0	0
$421$	−5265.06	−0.609509	−0.304754	−	0.952431i	$-0.598574\pi$
$421$	−5265.06	−0.609509	−0.304754	+	0.952431i	$0.598574\pi$
$422$	0	0
$423$	77.9008	0.00895430
$424$	0	0
$425$	893.143	0.101938
$426$	0	0
$427$	−1017.21	−0.115284
$428$	0	0
$429$	−4810.70	−0.541406
$430$	0	0
$431$	−4273.45	−0.477598	−0.238799	−	0.971069i	$-0.576754\pi$
$431$	−4273.45	−0.477598	−0.238799	+	0.971069i	$0.576754\pi$
$432$	0	0
$433$	−8560.19	−0.950061	−0.475031	−	0.879969i	$-0.657563\pi$
$433$	−8560.19	−0.950061	−0.475031	+	0.879969i	$0.657563\pi$
$434$	0	0
$435$	−6089.89	−0.671236
$436$	0	0
$437$	−17867.8	−1.95591
$438$	0	0
$439$	−12664.2	−1.37684	−0.688419	−	0.725314i	$-0.741695\pi$
$439$	−12664.2	−1.37684	−0.688419	+	0.725314i	$0.741695\pi$
$440$	0	0
$441$	−12.7014	−0.00137149
$442$	0	0
$443$	−12368.9	−1.32656	−0.663279	−	0.748372i	$-0.730836\pi$
$443$	−12368.9	−1.32656	−0.663279	+	0.748372i	$0.730836\pi$
$444$	0	0
$445$	12562.2	1.33821
$446$	0	0
$447$	−7849.09	−0.830535
$448$	0	0
$449$	−2092.69	−0.219956	−0.109978	−	0.993934i	$-0.535078\pi$
$449$	−2092.69	−0.219956	−0.109978	+	0.993934i	$0.535078\pi$
$450$	0	0
$451$	246.891	0.0257775
$452$	0	0
$453$	10077.9	1.04525
$454$	0	0
$455$	5968.75	0.614988
$456$	0	0
$457$	7825.71	0.801031	0.400515	−	0.916290i	$-0.368831\pi$
$457$	7825.71	0.801031	0.400515	+	0.916290i	$0.368831\pi$
$458$	0	0
$459$	−5392.13	−0.548329
$460$	0	0
$461$	4775.60	0.482477	0.241238	−	0.970466i	$-0.422446\pi$
$461$	4775.60	0.482477	0.241238	+	0.970466i	$0.422446\pi$
$462$	0	0
$463$	−11518.3	−1.15615	−0.578077	−	0.815982i	$-0.696197\pi$
$463$	−11518.3	−1.15615	−0.578077	+	0.815982i	$0.696197\pi$
$464$	0	0
$465$	−17659.2	−1.76113
$466$	0	0
$467$	7420.17	0.735256	0.367628	−	0.929973i	$-0.380170\pi$
$467$	7420.17	0.735256	0.367628	+	0.929973i	$0.380170\pi$
$468$	0	0
$469$	4676.14	0.460392
$470$	0	0
$471$	8037.00	0.786253
$472$	0	0
$473$	2000.29	0.194447
$474$	0	0
$475$	−2971.89	−0.287073
$476$	0	0
$477$	8.25837	0.000792715 0
$478$	0	0
$479$	−10159.2	−0.969076	−0.484538	−	0.874770i	$-0.661012\pi$
$479$	−10159.2	−0.969076	−0.484538	+	0.874770i	$0.661012\pi$
$480$	0	0
$481$	6371.82	0.604013
$482$	0	0
$483$	5081.41	0.478701
$484$	0	0
$485$	9430.29	0.882902
$486$	0	0
$487$	12344.9	1.14866	0.574331	−	0.818623i	$-0.305262\pi$
$487$	12344.9	1.14866	0.574331	+	0.818623i	$0.305262\pi$
$488$	0	0
$489$	−17957.9	−1.66070
$490$	0	0
$491$	−15344.9	−1.41040	−0.705200	−	0.709009i	$-0.749143\pi$
$491$	−15344.9	−1.41040	−0.705200	+	0.709009i	$0.749143\pi$
$492$	0	0
$493$	4468.13	0.408183
$494$	0	0
$495$	−28.7477	−0.00261033
$496$	0	0
$497$	−5093.26	−0.459686
$498$	0	0
$499$	5022.76	0.450601	0.225300	−	0.974289i	$-0.427664\pi$
$499$	5022.76	0.450601	0.225300	+	0.974289i	$0.427664\pi$
$500$	0	0
$501$	−11526.0	−1.02783
$502$	0	0
$503$	−8735.90	−0.774383	−0.387191	−	0.921999i	$-0.626555\pi$
$503$	−8735.90	−0.774383	−0.387191	+	0.921999i	$0.626555\pi$
$504$	0	0
$505$	5377.82	0.473881
$506$	0	0
$507$	−25625.6	−2.24472
$508$	0	0
$509$	−21805.5	−1.89884	−0.949420	−	0.314008i	$-0.898328\pi$
$509$	−21805.5	−1.89884	−0.949420	+	0.314008i	$0.898328\pi$
$510$	0	0
$511$	−2918.87	−0.252687
$512$	0	0
$513$	17942.1	1.54417
$514$	0	0
$515$	−7441.66	−0.636735
$516$	0	0
$517$	3305.83	0.281219
$518$	0	0
$519$	5212.72	0.440873
$520$	0	0
$521$	−4732.28	−0.397936	−0.198968	−	0.980006i	$-0.563759\pi$
$521$	−4732.28	−0.397936	−0.198968	+	0.980006i	$0.563759\pi$
$522$	0	0
$523$	7511.23	0.627998	0.313999	−	0.949423i	$-0.398331\pi$
$523$	7511.23	0.627998	0.313999	+	0.949423i	$0.398331\pi$
$524$	0	0
$525$	845.174	0.0702598
$526$	0	0
$527$	12956.5	1.07095
$528$	0	0
$529$	7539.02	0.619629
$530$	0	0
$531$	−17.7049	−0.00144695
$532$	0	0
$533$	1898.20	0.154259
$534$	0	0
$535$	−20558.4	−1.66134
$536$	0	0
$537$	−3858.95	−0.310104
$538$	0	0
$539$	−539.000	−0.0430730
$540$	0	0
$541$	−598.410	−0.0475557	−0.0237779	−	0.999717i	$-0.507569\pi$
$541$	−598.410	−0.0475557	−0.0237779	+	0.999717i	$0.507569\pi$
$542$	0	0
$543$	14415.9	1.13931
$544$	0	0
$545$	−15009.3	−1.17968
$546$	0	0
$547$	14042.3	1.09763	0.548816	−	0.835943i	$-0.315079\pi$
$547$	14042.3	1.09763	0.548816	+	0.835943i	$0.315079\pi$
$548$	0	0
$549$	37.6674	0.00292824
$550$	0	0
$551$	−14867.5	−1.14950
$552$	0	0
$553$	−3211.64	−0.246967
$554$	0	0
$555$	−3928.06	−0.300427
$556$	0	0
$557$	4965.87	0.377757	0.188878	−	0.982000i	$-0.439515\pi$
$557$	4965.87	0.377757	0.188878	+	0.982000i	$0.439515\pi$
$558$	0	0
$559$	15379.0	1.16362
$560$	0	0
$561$	−2175.90	−0.163755
$562$	0	0
$563$	15362.4	1.14999	0.574997	−	0.818155i	$-0.305003\pi$
$563$	15362.4	1.14999	0.574997	+	0.818155i	$0.305003\pi$
$564$	0	0
$565$	5371.24	0.399947
$566$	0	0
$567$	−5053.54	−0.374301
$568$	0	0
$569$	17735.3	1.30668	0.653341	−	0.757064i	$-0.273367\pi$
$569$	17735.3	1.30668	0.653341	+	0.757064i	$0.273367\pi$
$570$	0	0
$571$	19818.8	1.45252	0.726262	−	0.687418i	$-0.241256\pi$
$571$	19818.8	1.45252	0.726262	+	0.687418i	$0.241256\pi$
$572$	0	0
$573$	−4715.66	−0.343804
$574$	0	0
$575$	3277.63	0.237716
$576$	0	0
$577$	6579.03	0.474677	0.237339	−	0.971427i	$-0.423725\pi$
$577$	6579.03	0.474677	0.237339	+	0.971427i	$0.423725\pi$
$578$	0	0
$579$	−23035.7	−1.65342
$580$	0	0
$581$	−2490.16	−0.177813
$582$	0	0
$583$	350.455	0.0248960
$584$	0	0
$585$	−221.024	−0.0156209
$586$	0	0
$587$	−13901.5	−0.977470	−0.488735	−	0.872432i	$-0.662541\pi$
$587$	−13901.5	−0.977470	−0.488735	+	0.872432i	$0.662541\pi$
$588$	0	0
$589$	−43112.0	−3.01596
$590$	0	0
$591$	7123.03	0.495774
$592$	0	0
$593$	23928.0	1.65700	0.828502	−	0.559986i	$-0.189193\pi$
$593$	23928.0	1.65700	0.828502	+	0.559986i	$0.189193\pi$
$594$	0	0
$595$	2699.70	0.186011
$596$	0	0
$597$	−487.935	−0.0334503
$598$	0	0
$599$	−24078.9	−1.64247	−0.821233	−	0.570594i	$-0.806713\pi$
$599$	−24078.9	−1.64247	−0.821233	+	0.570594i	$0.806713\pi$
$600$	0	0
$601$	−11806.6	−0.801336	−0.400668	−	0.916223i	$-0.631222\pi$
$601$	−11806.6	−0.801336	−0.400668	+	0.916223i	$0.631222\pi$
$602$	0	0
$603$	−173.158	−0.0116941
$604$	0	0
$605$	−1219.95	−0.0819802
$606$	0	0
$607$	−1957.71	−0.130908	−0.0654539	−	0.997856i	$-0.520850\pi$
$607$	−1957.71	−0.130908	−0.0654539	+	0.997856i	$0.520850\pi$
$608$	0	0
$609$	4228.15	0.281336
$610$	0	0
$611$	25416.6	1.68289
$612$	0	0
$613$	−16029.2	−1.05614	−0.528069	−	0.849201i	$-0.677084\pi$
$613$	−16029.2	−1.05614	−0.528069	+	0.849201i	$0.677084\pi$
$614$	0	0
$615$	−1170.19	−0.0767261
$616$	0	0
$617$	−7153.99	−0.466789	−0.233394	−	0.972382i	$-0.574983\pi$
$617$	−7153.99	−0.466789	−0.233394	+	0.972382i	$0.574983\pi$
$618$	0	0
$619$	11035.9	0.716590	0.358295	−	0.933608i	$-0.383358\pi$
$619$	11035.9	0.716590	0.358295	+	0.933608i	$0.383358\pi$
$620$	0	0
$621$	−19787.9	−1.27868
$622$	0	0
$623$	−8721.78	−0.560884
$624$	0	0
$625$	−12161.3	−0.778321
$626$	0	0
$627$	7240.22	0.461158
$628$	0	0
$629$	2882.01	0.182692
$630$	0	0
$631$	4311.46	0.272007	0.136004	−	0.990708i	$-0.456574\pi$
$631$	4311.46	0.272007	0.136004	+	0.990708i	$0.456574\pi$
$632$	0	0
$633$	6071.89	0.381258
$634$	0	0
$635$	−22760.1	−1.42237
$636$	0	0
$637$	−4144.05	−0.257760
$638$	0	0
$639$	188.604	0.0116762
$640$	0	0
$641$	2692.13	0.165886	0.0829429	−	0.996554i	$-0.473568\pi$
$641$	2692.13	0.165886	0.0829429	+	0.996554i	$0.473568\pi$
$642$	0	0
$643$	−19694.3	−1.20788	−0.603941	−	0.797029i	$-0.706404\pi$
$643$	−19694.3	−1.20788	−0.603941	+	0.797029i	$0.706404\pi$
$644$	0	0
$645$	−9480.76	−0.578767
$646$	0	0
$647$	21225.5	1.28974	0.644870	−	0.764292i	$-0.276911\pi$
$647$	21225.5	1.28974	0.644870	+	0.764292i	$0.276911\pi$
$648$	0	0
$649$	−751.333	−0.0454428
$650$	0	0
$651$	12260.6	0.738143
$652$	0	0
$653$	−12929.7	−0.774850	−0.387425	−	0.921901i	$-0.626635\pi$
$653$	−12929.7	−0.774850	−0.387425	+	0.921901i	$0.626635\pi$
$654$	0	0
$655$	11838.7	0.706224
$656$	0	0
$657$	108.086	0.00641835
$658$	0	0
$659$	20835.3	1.23161	0.615803	−	0.787900i	$-0.288832\pi$
$659$	20835.3	1.23161	0.615803	+	0.787900i	$0.288832\pi$
$660$	0	0
$661$	−1451.06	−0.0853850	−0.0426925	−	0.999088i	$-0.513594\pi$
$661$	−1451.06	−0.0853850	−0.0426925	+	0.999088i	$0.513594\pi$
$662$	0	0
$663$	−16729.2	−0.979954
$664$	0	0
$665$	−8983.10	−0.523834
$666$	0	0
$667$	16397.0	0.951867
$668$	0	0
$669$	458.099	0.0264741
$670$	0	0
$671$	1598.47	0.0919645
$672$	0	0
$673$	−28986.0	−1.66022	−0.830111	−	0.557598i	$-0.811723\pi$
$673$	−28986.0	−1.66022	−0.830111	+	0.557598i	$0.811723\pi$
$674$	0	0
$675$	−3291.25	−0.187675
$676$	0	0
$677$	24818.6	1.40895	0.704474	−	0.709730i	$-0.251183\pi$
$677$	24818.6	1.40895	0.704474	+	0.709730i	$0.251183\pi$
$678$	0	0
$679$	−6547.36	−0.370051
$680$	0	0
$681$	4567.74	0.257028
$682$	0	0
$683$	7450.70	0.417413	0.208706	−	0.977978i	$-0.433075\pi$
$683$	7450.70	0.417413	0.208706	+	0.977978i	$0.433075\pi$
$684$	0	0
$685$	−27122.0	−1.51282
$686$	0	0
$687$	−6413.57	−0.356176
$688$	0	0
$689$	2694.44	0.148984
$690$	0	0
$691$	28469.1	1.56731	0.783657	−	0.621193i	$-0.213352\pi$
$691$	28469.1	1.56731	0.783657	+	0.621193i	$0.213352\pi$
$692$	0	0
$693$	19.9593	0.00109407
$694$	0	0
$695$	178.959	0.00976736
$696$	0	0
$697$	858.563	0.0466577
$698$	0	0
$699$	28337.6	1.53337
$700$	0	0
$701$	20045.7	1.08005	0.540027	−	0.841648i	$-0.318414\pi$
$701$	20045.7	1.08005	0.540027	+	0.841648i	$0.318414\pi$
$702$	0	0
$703$	−9589.73	−0.514486
$704$	0	0
$705$	−15668.6	−0.837043
$706$	0	0
$707$	−3733.77	−0.198618
$708$	0	0
$709$	15326.9	0.811868	0.405934	−	0.913902i	$-0.366946\pi$
$709$	15326.9	0.811868	0.405934	+	0.913902i	$0.366946\pi$
$710$	0	0
$711$	118.928	0.00627304
$712$	0	0
$713$	47547.3	2.49742
$714$	0	0
$715$	−9379.47	−0.490591
$716$	0	0
$717$	3071.70	0.159992
$718$	0	0
$719$	11023.4	0.571770	0.285885	−	0.958264i	$-0.407712\pi$
$719$	11023.4	0.571770	0.285885	+	0.958264i	$0.407712\pi$
$720$	0	0
$721$	5166.68	0.266875
$722$	0	0
$723$	−1596.77	−0.0821365
$724$	0	0
$725$	2727.26	0.139707
$726$	0	0
$727$	−28755.9	−1.46698	−0.733492	−	0.679699i	$-0.762111\pi$
$727$	−28755.9	−1.46698	−0.733492	+	0.679699i	$0.762111\pi$
$728$	0	0
$729$	19868.3	1.00942
$730$	0	0
$731$	6956.00	0.351952
$732$	0	0
$733$	21500.9	1.08343	0.541714	−	0.840563i	$-0.317775\pi$
$733$	21500.9	1.08343	0.541714	+	0.840563i	$0.317775\pi$
$734$	0	0
$735$	2554.70	0.128206
$736$	0	0
$737$	−7348.21	−0.367266
$738$	0	0
$739$	2598.63	0.129353	0.0646767	−	0.997906i	$-0.479398\pi$
$739$	2598.63	0.129353	0.0646767	+	0.997906i	$0.479398\pi$
$740$	0	0
$741$	55665.7	2.75969
$742$	0	0
$743$	−29920.5	−1.47736	−0.738678	−	0.674058i	$-0.764550\pi$
$743$	−29920.5	−1.47736	−0.738678	+	0.674058i	$0.764550\pi$
$744$	0	0
$745$	−15303.4	−0.752583
$746$	0	0
$747$	92.2112	0.00451651
$748$	0	0
$749$	14273.5	0.696317
$750$	0	0
$751$	−17763.1	−0.863096	−0.431548	−	0.902090i	$-0.642032\pi$
$751$	−17763.1	−0.863096	−0.431548	+	0.902090i	$0.642032\pi$
$752$	0	0
$753$	18034.8	0.872810
$754$	0	0
$755$	19648.9	0.947147
$756$	0	0
$757$	6472.04	0.310740	0.155370	−	0.987856i	$-0.450343\pi$
$757$	6472.04	0.310740	0.155370	+	0.987856i	$0.450343\pi$
$758$	0	0
$759$	−7985.08	−0.381871
$760$	0	0
$761$	−33720.2	−1.60625	−0.803126	−	0.595809i	$-0.796831\pi$
$761$	−33720.2	−1.60625	−0.803126	+	0.595809i	$0.796831\pi$
$762$	0	0
$763$	10420.8	0.494441
$764$	0	0
$765$	−99.9703	−0.00472475
$766$	0	0
$767$	−5776.55	−0.271941
$768$	0	0
$769$	−9361.49	−0.438991	−0.219495	−	0.975614i	$-0.570441\pi$
$769$	−9361.49	−0.438991	−0.219495	+	0.975614i	$0.570441\pi$
$770$	0	0
$771$	−2334.49	−0.109046
$772$	0	0
$773$	34886.0	1.62324	0.811618	−	0.584188i	$-0.198587\pi$
$773$	34886.0	1.62324	0.811618	+	0.584188i	$0.198587\pi$
$774$	0	0
$775$	7908.38	0.366551
$776$	0	0
$777$	2727.22	0.125918
$778$	0	0
$779$	−2856.83	−0.131395
$780$	0	0
$781$	8003.69	0.366702
$782$	0	0
$783$	−16465.2	−0.751490
$784$	0	0
$785$	15669.8	0.712458
$786$	0	0
$787$	9526.64	0.431497	0.215748	−	0.976449i	$-0.430781\pi$
$787$	9526.64	0.431497	0.215748	+	0.976449i	$0.430781\pi$
$788$	0	0
$789$	−30399.2	−1.37166
$790$	0	0
$791$	−3729.20	−0.167630
$792$	0	0
$793$	12289.7	0.550339
$794$	0	0
$795$	−1661.05	−0.0741026
$796$	0	0
$797$	−33267.9	−1.47856	−0.739278	−	0.673400i	$-0.764833\pi$
$797$	−33267.9	−1.47856	−0.739278	+	0.673400i	$0.764833\pi$
$798$	0	0
$799$	11496.0	0.509012
$800$	0	0
$801$	322.970	0.0142467
$802$	0	0
$803$	4586.80	0.201575
$804$	0	0
$805$	9907.27	0.433771
$806$	0	0
$807$	273.303	0.0119216
$808$	0	0
$809$	17949.6	0.780069	0.390035	−	0.920800i	$-0.372463\pi$
$809$	17949.6	0.780069	0.390035	+	0.920800i	$0.372463\pi$
$810$	0	0
$811$	−10877.9	−0.470991	−0.235495	−	0.971875i	$-0.575671\pi$
$811$	−10877.9	−0.470991	−0.235495	+	0.971875i	$0.575671\pi$
$812$	0	0
$813$	−35278.6	−1.52186
$814$	0	0
$815$	−35012.7	−1.50484
$816$	0	0
$817$	−23145.7	−0.991147
$818$	0	0
$819$	153.455	0.00654720
$820$	0	0
$821$	−4519.04	−0.192102	−0.0960509	−	0.995376i	$-0.530621\pi$
$821$	−4519.04	−0.192102	−0.0960509	+	0.995376i	$0.530621\pi$
$822$	0	0
$823$	−36987.7	−1.56660	−0.783300	−	0.621644i	$-0.786465\pi$
$823$	−36987.7	−1.56660	−0.783300	+	0.621644i	$0.786465\pi$
$824$	0	0
$825$	−1328.13	−0.0560480
$826$	0	0
$827$	−15325.3	−0.644392	−0.322196	−	0.946673i	$-0.604421\pi$
$827$	−15325.3	−0.644392	−0.322196	+	0.946673i	$0.604421\pi$
$828$	0	0
$829$	26546.3	1.11217	0.556087	−	0.831124i	$-0.312302\pi$
$829$	26546.3	1.11217	0.556087	+	0.831124i	$0.312302\pi$
$830$	0	0
$831$	−2425.43	−0.101248
$832$	0	0
$833$	−1874.37	−0.0779630
$834$	0	0
$835$	−22472.3	−0.931361
$836$	0	0
$837$	−47744.9	−1.97169
$838$	0	0
$839$	−11906.5	−0.489938	−0.244969	−	0.969531i	$-0.578778\pi$
$839$	−11906.5	−0.489938	−0.244969	+	0.969531i	$0.578778\pi$
$840$	0	0
$841$	−10745.3	−0.440581
$842$	0	0
$843$	11919.8	0.486997
$844$	0	0
$845$	−49962.5	−2.03404
$846$	0	0
$847$	847.000	0.0343604
$848$	0	0
$849$	−38115.5	−1.54078
$850$	0	0
$851$	10576.3	0.426030
$852$	0	0
$853$	−6859.53	−0.275341	−0.137670	−	0.990478i	$-0.543961\pi$
$853$	−6859.53	−0.275341	−0.137670	+	0.990478i	$0.543961\pi$
$854$	0	0
$855$	332.646	0.0133056
$856$	0	0
$857$	5193.59	0.207013	0.103506	−	0.994629i	$-0.466994\pi$
$857$	5193.59	0.207013	0.103506	+	0.994629i	$0.466994\pi$
$858$	0	0
$859$	−5265.73	−0.209155	−0.104578	−	0.994517i	$-0.533349\pi$
$859$	−5265.73	−0.209155	−0.104578	+	0.994517i	$0.533349\pi$
$860$	0	0
$861$	812.451	0.0321583
$862$	0	0
$863$	16016.7	0.631767	0.315884	−	0.948798i	$-0.397699\pi$
$863$	16016.7	0.631767	0.315884	+	0.948798i	$0.397699\pi$
$864$	0	0
$865$	10163.3	0.399494
$866$	0	0
$867$	17839.1	0.698788
$868$	0	0
$869$	5046.86	0.197011
$870$	0	0
$871$	−56496.0	−2.19781
$872$	0	0
$873$	242.450	0.00939943
$874$	0	0
$875$	10469.8	0.404507
$876$	0	0
$877$	−11195.5	−0.431065	−0.215533	−	0.976497i	$-0.569149\pi$
$877$	−11195.5	−0.431065	−0.215533	+	0.976497i	$0.569149\pi$
$878$	0	0
$879$	−9095.51	−0.349015
$880$	0	0
$881$	45542.5	1.74162	0.870809	−	0.491621i	$-0.163595\pi$
$881$	45542.5	1.74162	0.870809	+	0.491621i	$0.163595\pi$
$882$	0	0
$883$	−10394.9	−0.396167	−0.198083	−	0.980185i	$-0.563472\pi$
$883$	−10394.9	−0.396167	−0.198083	+	0.980185i	$0.563472\pi$
$884$	0	0
$885$	3561.09	0.135260
$886$	0	0
$887$	4020.51	0.152193	0.0760967	−	0.997100i	$-0.475754\pi$
$887$	4020.51	0.152193	0.0760967	+	0.997100i	$0.475754\pi$
$888$	0	0
$889$	15802.1	0.596159
$890$	0	0
$891$	7941.28	0.298589
$892$	0	0
$893$	−38252.5	−1.43345
$894$	0	0
$895$	−7523.82	−0.280998
$896$	0	0
$897$	−61392.5	−2.28521
$898$	0	0
$899$	39563.3	1.46775
$900$	0	0
$901$	1218.71	0.0450623
$902$	0	0
$903$	6582.40	0.242579
$904$	0	0
$905$	28106.8	1.03238
$906$	0	0
$907$	23907.5	0.875231	0.437615	−	0.899162i	$-0.355823\pi$
$907$	23907.5	0.875231	0.437615	+	0.899162i	$0.355823\pi$
$908$	0	0
$909$	138.262	0.00504496
$910$	0	0
$911$	−40571.4	−1.47551	−0.737755	−	0.675069i	$-0.764114\pi$
$911$	−40571.4	−1.47551	−0.737755	+	0.675069i	$0.764114\pi$
$912$	0	0
$913$	3913.11	0.141846
$914$	0	0
$915$	−7576.26	−0.273731
$916$	0	0
$917$	−8219.50	−0.296000
$918$	0	0
$919$	−20551.0	−0.737667	−0.368834	−	0.929495i	$-0.620243\pi$
$919$	−20551.0	−0.737667	−0.368834	+	0.929495i	$0.620243\pi$
$920$	0	0
$921$	17934.1	0.641637
$922$	0	0
$923$	61535.6	2.19444
$924$	0	0
$925$	1759.12	0.0625292
$926$	0	0
$927$	−191.323	−0.00677872
$928$	0	0
$929$	34068.4	1.20317	0.601587	−	0.798807i	$-0.294535\pi$
$929$	34068.4	1.20317	0.601587	+	0.798807i	$0.294535\pi$
$930$	0	0
$931$	6236.89	0.219555
$932$	0	0
$933$	10259.5	0.360000
$934$	0	0
$935$	−4242.38	−0.148386
$936$	0	0
$937$	15597.9	0.543824	0.271912	−	0.962322i	$-0.412344\pi$
$937$	15597.9	0.543824	0.271912	+	0.962322i	$0.412344\pi$
$938$	0	0
$939$	52198.7	1.81410
$940$	0	0
$941$	−22855.3	−0.791775	−0.395887	−	0.918299i	$-0.629563\pi$
$941$	−22855.3	−0.791775	−0.395887	+	0.918299i	$0.629563\pi$
$942$	0	0
$943$	3150.73	0.108804
$944$	0	0
$945$	−9948.44	−0.342458
$946$	0	0
$947$	−36670.7	−1.25833	−0.629164	−	0.777272i	$-0.716603\pi$
$947$	−36670.7	−1.25833	−0.629164	+	0.777272i	$0.716603\pi$
$948$	0	0
$949$	35265.1	1.20628
$950$	0	0
$951$	15779.0	0.538031
$952$	0	0
$953$	−19922.8	−0.677192	−0.338596	−	0.940932i	$-0.609952\pi$
$953$	−19922.8	−0.677192	−0.338596	+	0.940932i	$0.609952\pi$
$954$	0	0
$955$	−9194.16	−0.311535
$956$	0	0
$957$	−6644.24	−0.224428
$958$	0	0
$959$	18830.6	0.634068
$960$	0	0
$961$	84932.7	2.85095
$962$	0	0
$963$	−528.550	−0.0176867
$964$	0	0
$965$	−44913.0	−1.49824
$966$	0	0
$967$	−24523.8	−0.815545	−0.407772	−	0.913084i	$-0.633694\pi$
$967$	−24523.8	−0.815545	−0.407772	+	0.913084i	$0.633694\pi$
$968$	0	0
$969$	25177.9	0.834705
$970$	0	0
$971$	−4493.82	−0.148520	−0.0742602	−	0.997239i	$-0.523660\pi$
$971$	−4493.82	−0.148520	−0.0742602	+	0.997239i	$0.523660\pi$
$972$	0	0
$973$	−124.250	−0.00409380
$974$	0	0
$975$	−10211.2	−0.335405
$976$	0	0
$977$	−18285.3	−0.598771	−0.299385	−	0.954132i	$-0.596782\pi$
$977$	−18285.3	−0.598771	−0.299385	+	0.954132i	$0.596782\pi$
$978$	0	0
$979$	13705.7	0.447431
$980$	0	0
$981$	−385.885	−0.0125590
$982$	0	0
$983$	25850.8	0.838772	0.419386	−	0.907808i	$-0.362245\pi$
$983$	25850.8	0.838772	0.419386	+	0.907808i	$0.362245\pi$
$984$	0	0
$985$	13887.8	0.449242
$986$	0	0
$987$	10878.6	0.350830
$988$	0	0
$989$	25526.9	0.820738
$990$	0	0
$991$	26842.1	0.860412	0.430206	−	0.902731i	$-0.358441\pi$
$991$	26842.1	0.860412	0.430206	+	0.902731i	$0.358441\pi$
$992$	0	0
$993$	−139.531	−0.00445910
$994$	0	0
$995$	−951.331	−0.0303108
$996$	0	0
$997$	−10468.1	−0.332526	−0.166263	−	0.986081i	$-0.553170\pi$
$997$	−10468.1	−0.332526	−0.166263	+	0.986081i	$0.553170\pi$
$998$	0	0
$999$	−10620.3	−0.336347

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.4.a.w.1.1		4
4.3	odd	2		77.4.a.c.1.2	✓	4
12.11	even	2		693.4.a.m.1.3		4
20.19	odd	2		1925.4.a.q.1.3		4
28.27	even	2		539.4.a.f.1.2		4
44.43	even	2		847.4.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.a.c.1.2	✓	4	4.3	odd	2
539.4.a.f.1.2		4	28.27	even	2
693.4.a.m.1.3		4	12.11	even	2
847.4.a.e.1.3		4	44.43	even	2
1232.4.a.w.1.1		4	1.1	even	1	trivial
1925.4.a.q.1.3		4	20.19	odd	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1232.a (trivial)

\(f(q)\)	\(=\)	\(q-5.17115 q^{3} -10.0822 q^{5} +7.00000 q^{7} -0.259212 q^{9} +O(q^{10})\)	\(q-5.17115 q^{3} -10.0822 q^{5} +7.00000 q^{7} -0.259212 q^{9} -11.0000 q^{11} -84.5724 q^{13} +52.1367 q^{15} -38.2525 q^{17} +127.283 q^{19} -36.1980 q^{21} -140.378 q^{23} -23.3486 q^{25} +140.961 q^{27} -116.806 q^{29} -338.709 q^{31} +56.8826 q^{33} -70.5756 q^{35} -75.3416 q^{37} +437.337 q^{39} -22.4446 q^{41} -181.844 q^{43} +2.61343 q^{45} -300.530 q^{47} +49.0000 q^{49} +197.810 q^{51} -31.8596 q^{53} +110.905 q^{55} -658.201 q^{57} +68.3030 q^{59} -145.315 q^{61} -1.81448 q^{63} +852.679 q^{65} +668.020 q^{67} +725.916 q^{69} -727.608 q^{71} -416.982 q^{73} +120.739 q^{75} -77.0000 q^{77} -458.805 q^{79} -721.934 q^{81} -355.737 q^{83} +385.671 q^{85} +604.022 q^{87} -1245.97 q^{89} -592.007 q^{91} +1751.51 q^{93} -1283.30 q^{95} -935.338 q^{97} +2.85133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{3} - 18 q^{5} + 28 q^{7} + 66 q^{9}+O(q^{10}) \) 4 * q + 12 * q^3 - 18 * q^5 + 28 * q^7 + 66 * q^9	\( 4 q + 12 q^{3} - 18 q^{5} + 28 q^{7} + 66 q^{9} - 44 q^{11} - 134 q^{13} + 62 q^{15} - 74 q^{17} + 164 q^{19} + 84 q^{21} - 194 q^{23} + 38 q^{25} + 510 q^{27} - 108 q^{29} + 412 q^{31} - 132 q^{33} - 126 q^{35} + 286 q^{37} + 256 q^{39} - 18 q^{41} + 496 q^{43} + 580 q^{45} - 62 q^{47} + 196 q^{49} + 508 q^{51} - 828 q^{53} + 198 q^{55} + 700 q^{57} + 1224 q^{59} - 350 q^{61} + 462 q^{63} - 396 q^{65} + 1498 q^{67} - 386 q^{69} - 2326 q^{71} - 1630 q^{73} + 1362 q^{75} - 308 q^{77} + 1020 q^{79} + 1128 q^{81} + 1920 q^{83} + 2008 q^{85} - 1640 q^{87} + 1550 q^{89} - 938 q^{91} + 6046 q^{93} - 2332 q^{95} - 2202 q^{97} - 726 q^{99}+O(q^{100}) \) 4 * q + 12 * q^3 - 18 * q^5 + 28 * q^7 + 66 * q^9 - 44 * q^11 - 134 * q^13 + 62 * q^15 - 74 * q^17 + 164 * q^19 + 84 * q^21 - 194 * q^23 + 38 * q^25 + 510 * q^27 - 108 * q^29 + 412 * q^31 - 132 * q^33 - 126 * q^35 + 286 * q^37 + 256 * q^39 - 18 * q^41 + 496 * q^43 + 580 * q^45 - 62 * q^47 + 196 * q^49 + 508 * q^51 - 828 * q^53 + 198 * q^55 + 700 * q^57 + 1224 * q^59 - 350 * q^61 + 462 * q^63 - 396 * q^65 + 1498 * q^67 - 386 * q^69 - 2326 * q^71 - 1630 * q^73 + 1362 * q^75 - 308 * q^77 + 1020 * q^79 + 1128 * q^81 + 1920 * q^83 + 2008 * q^85 - 1640 * q^87 + 1550 * q^89 - 938 * q^91 + 6046 * q^93 - 2332 * q^95 - 2202 * q^97 - 726 * q^99

Introduction

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