LMFDB - Embedded newform 1936.4.a.bc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1936,4,Mod(1,1936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1936, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1936.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1936 = 2^{4} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1936.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:	$114.227697771$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1936.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.85410 q^{3} -1.61803 q^{5} +14.7984 q^{7} +70.1033 q^{9} +O(q^{10})$	$q+9.85410 q^{3} -1.61803 q^{5} +14.7984 q^{7} +70.1033 q^{9} +50.9230 q^{13} -15.9443 q^{15} +60.3131 q^{17} -26.4377 q^{19} +145.825 q^{21} +29.1672 q^{23} -122.382 q^{25} +424.745 q^{27} +150.267 q^{29} -29.3789 q^{31} -23.9443 q^{35} -224.825 q^{37} +501.800 q^{39} -119.726 q^{41} +213.974 q^{43} -113.430 q^{45} +175.021 q^{47} -124.008 q^{49} +594.331 q^{51} -63.1784 q^{53} -260.520 q^{57} +262.028 q^{59} +708.969 q^{61} +1037.42 q^{63} -82.3951 q^{65} +151.692 q^{67} +287.416 q^{69} -1055.55 q^{71} +31.5197 q^{73} -1205.96 q^{75} +65.1157 q^{79} +2292.69 q^{81} -230.566 q^{83} -97.5886 q^{85} +1480.75 q^{87} -618.952 q^{89} +753.577 q^{91} -289.502 q^{93} +42.7771 q^{95} -1099.99 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 13 q^{3} - q^{5} + 5 q^{7} + 53 q^{9}+O(q^{10}) $ 2 * q + 13 * q^3 - q^5 + 5 * q^7 + 53 * q^9	$ 2 q + 13 q^{3} - q^{5} + 5 q^{7} + 53 q^{9} + 37 q^{13} - 14 q^{15} + 181 q^{17} - 73 q^{19} + 115 q^{21} + 112 q^{23} - 247 q^{25} + 286 q^{27} - 55 q^{29} + 261 q^{31} - 30 q^{35} - 273 q^{37} + 458 q^{39} + 49 q^{41} + 580 q^{43} - 124 q^{45} + 397 q^{47} - 371 q^{49} + 974 q^{51} - 625 q^{53} - 407 q^{57} - 149 q^{59} + 405 q^{61} + 1205 q^{63} - 91 q^{65} + 44 q^{67} + 548 q^{69} - 1125 q^{71} - 51 q^{73} - 1598 q^{75} + 1331 q^{79} + 2318 q^{81} + 601 q^{83} - 23 q^{85} + 835 q^{87} + 864 q^{89} + 890 q^{91} + 624 q^{93} + 14 q^{95} - 713 q^{97}+O(q^{100}) $ 2 * q + 13 * q^3 - q^5 + 5 * q^7 + 53 * q^9 + 37 * q^13 - 14 * q^15 + 181 * q^17 - 73 * q^19 + 115 * q^21 + 112 * q^23 - 247 * q^25 + 286 * q^27 - 55 * q^29 + 261 * q^31 - 30 * q^35 - 273 * q^37 + 458 * q^39 + 49 * q^41 + 580 * q^43 - 124 * q^45 + 397 * q^47 - 371 * q^49 + 974 * q^51 - 625 * q^53 - 407 * q^57 - 149 * q^59 + 405 * q^61 + 1205 * q^63 - 91 * q^65 + 44 * q^67 + 548 * q^69 - 1125 * q^71 - 51 * q^73 - 1598 * q^75 + 1331 * q^79 + 2318 * q^81 + 601 * q^83 - 23 * q^85 + 835 * q^87 + 864 * q^89 + 890 * q^91 + 624 * q^93 + 14 * q^95 - 713 * q^97

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
$3$	9.85410	1.89642	0.948211	−	0.317640i	$-0.102890\pi$
$3$	9.85410	1.89642	0.948211	+	0.317640i	$0.102890\pi$
$4$	0	0
$5$	−1.61803	−0.144721	−0.0723607	−	0.997379i	$-0.523053\pi$
$5$	−1.61803	−0.144721	−0.0723607	+	0.997379i	$0.523053\pi$
$6$	0	0
$7$	14.7984	0.799037	0.399519	−	0.916725i	$-0.369177\pi$
$7$	14.7984	0.799037	0.399519	+	0.916725i	$0.369177\pi$
$8$	0	0
$9$	70.1033	2.59642
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	50.9230	1.08642	0.543211	−	0.839596i	$-0.317208\pi$
$13$	50.9230	1.08642	0.543211	+	0.839596i	$0.317208\pi$
$14$	0	0
$15$	−15.9443	−0.274453
$16$	0	0
$17$	60.3131	0.860475	0.430237	−	0.902716i	$-0.358430\pi$
$17$	60.3131	0.860475	0.430237	+	0.902716i	$0.358430\pi$
$18$	0	0
$19$	−26.4377	−0.319222	−0.159611	−	0.987180i	$-0.551024\pi$
$19$	−26.4377	−0.319222	−0.159611	+	0.987180i	$0.551024\pi$
$20$	0	0
$21$	145.825	1.51531
$22$	0	0
$23$	29.1672	0.264425	0.132213	−	0.991221i	$-0.457792\pi$
$23$	29.1672	0.264425	0.132213	+	0.991221i	$0.457792\pi$
$24$	0	0
$25$	−122.382	−0.979056
$26$	0	0
$27$	424.745	3.02749
$28$	0	0
$29$	150.267	0.962205	0.481103	−	0.876664i	$-0.340236\pi$
$29$	150.267	0.962205	0.481103	+	0.876664i	$0.340236\pi$
$30$	0	0
$31$	−29.3789	−0.170213	−0.0851064	−	0.996372i	$-0.527123\pi$
$31$	−29.3789	−0.170213	−0.0851064	+	0.996372i	$0.527123\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−23.9443	−0.115638
$36$	0	0
$37$	−224.825	−0.998945	−0.499472	−	0.866330i	$-0.666473\pi$
$37$	−224.825	−0.998945	−0.499472	+	0.866330i	$0.666473\pi$
$38$	0	0
$39$	501.800	2.06032
$40$	0	0
$41$	−119.726	−0.456052	−0.228026	−	0.973655i	$-0.573227\pi$
$41$	−119.726	−0.456052	−0.228026	+	0.973655i	$0.573227\pi$
$42$	0	0
$43$	213.974	0.758853	0.379427	−	0.925222i	$-0.376121\pi$
$43$	213.974	0.758853	0.379427	+	0.925222i	$0.376121\pi$
$44$	0	0
$45$	−113.430	−0.375757
$46$	0	0
$47$	175.021	0.543180	0.271590	−	0.962413i	$-0.412450\pi$
$47$	175.021	0.543180	0.271590	+	0.962413i	$0.412450\pi$
$48$	0	0
$49$	−124.008	−0.361540
$50$	0	0
$51$	594.331	1.63182
$52$	0	0
$53$	−63.1784	−0.163740	−0.0818700	−	0.996643i	$-0.526089\pi$
$53$	−63.1784	−0.163740	−0.0818700	+	0.996643i	$0.526089\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−260.520	−0.605380
$58$	0	0
$59$	262.028	0.578189	0.289095	−	0.957301i	$-0.406646\pi$
$59$	262.028	0.578189	0.289095	+	0.957301i	$0.406646\pi$
$60$	0	0
$61$	708.969	1.48810	0.744051	−	0.668123i	$-0.232902\pi$
$61$	708.969	1.48810	0.744051	+	0.668123i	$0.232902\pi$
$62$	0	0
$63$	1037.42	2.07464
$64$	0	0
$65$	−82.3951	−0.157229
$66$	0	0
$67$	151.692	0.276599	0.138299	−	0.990390i	$-0.455836\pi$
$67$	151.692	0.276599	0.138299	+	0.990390i	$0.455836\pi$
$68$	0	0
$69$	287.416	0.501462
$70$	0	0
$71$	−1055.55	−1.76438	−0.882191	−	0.470892i	$-0.843932\pi$
$71$	−1055.55	−1.76438	−0.882191	+	0.470892i	$0.843932\pi$
$72$	0	0
$73$	31.5197	0.0505357	0.0252678	−	0.999681i	$-0.491956\pi$
$73$	31.5197	0.0505357	0.0252678	+	0.999681i	$0.491956\pi$
$74$	0	0
$75$	−1205.96	−1.85670
$76$	0	0
$77$	0	0
$78$	0	0
$79$	65.1157	0.0927354	0.0463677	−	0.998924i	$-0.485235\pi$
$79$	65.1157	0.0927354	0.0463677	+	0.998924i	$0.485235\pi$
$80$	0	0
$81$	2292.69	3.14497
$82$	0	0
$83$	−230.566	−0.304915	−0.152457	−	0.988310i	$-0.548719\pi$
$83$	−230.566	−0.304915	−0.152457	+	0.988310i	$0.548719\pi$
$84$	0	0
$85$	−97.5886	−0.124529
$86$	0	0
$87$	1480.75	1.82475
$88$	0	0
$89$	−618.952	−0.737177	−0.368589	−	0.929593i	$-0.620159\pi$
$89$	−618.952	−0.737177	−0.368589	+	0.929593i	$0.620159\pi$
$90$	0	0
$91$	753.577	0.868092
$92$	0	0
$93$	−289.502	−0.322796
$94$	0	0
$95$	42.7771	0.0461983
$96$	0	0
$97$	−1099.99	−1.15142	−0.575708	−	0.817655i	$-0.695273\pi$
$97$	−1099.99	−1.15142	−0.575708	+	0.817655i	$0.695273\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−1349.28	−1.32929	−0.664643	−	0.747161i	$-0.731416\pi$
$101$	−1349.28	−1.32929	−0.664643	+	0.747161i	$0.731416\pi$
$102$	0	0
$103$	1484.72	1.42033	0.710166	−	0.704035i	$-0.248620\pi$
$103$	1484.72	1.42033	0.710166	+	0.704035i	$0.248620\pi$
$104$	0	0
$105$	−235.949	−0.219298
$106$	0	0
$107$	−1762.19	−1.59212	−0.796062	−	0.605215i	$-0.793087\pi$
$107$	−1762.19	−1.59212	−0.796062	+	0.605215i	$0.793087\pi$
$108$	0	0
$109$	−688.087	−0.604649	−0.302325	−	0.953205i	$-0.597763\pi$
$109$	−688.087	−0.604649	−0.302325	+	0.953205i	$0.597763\pi$
$110$	0	0
$111$	−2215.45	−1.89442
$112$	0	0
$113$	303.195	0.252409	0.126205	−	0.992004i	$-0.459720\pi$
$113$	303.195	0.252409	0.126205	+	0.992004i	$0.459720\pi$
$114$	0	0
$115$	−47.1935	−0.0382680
$116$	0	0
$117$	3569.87	2.82081
$118$	0	0
$119$	892.536	0.687551
$120$	0	0
$121$	0	0
$122$	0	0
$123$	−1179.80	−0.864867
$124$	0	0
$125$	400.272	0.286412
$126$	0	0
$127$	2265.63	1.58301	0.791505	−	0.611162i	$-0.209298\pi$
$127$	2265.63	1.58301	0.791505	+	0.611162i	$0.209298\pi$
$128$	0	0
$129$	2108.52	1.43911
$130$	0	0
$131$	1457.48	0.972068	0.486034	−	0.873940i	$-0.338443\pi$
$131$	1457.48	0.972068	0.486034	+	0.873940i	$0.338443\pi$
$132$	0	0
$133$	−391.235	−0.255070
$134$	0	0
$135$	−687.251	−0.438142
$136$	0	0
$137$	−196.856	−0.122763	−0.0613817	−	0.998114i	$-0.519551\pi$
$137$	−196.856	−0.122763	−0.0613817	+	0.998114i	$0.519551\pi$
$138$	0	0
$139$	−39.6537	−0.0241970	−0.0120985	−	0.999927i	$-0.503851\pi$
$139$	−39.6537	−0.0241970	−0.0120985	+	0.999927i	$0.503851\pi$
$140$	0	0
$141$	1724.68	1.03010
$142$	0	0
$143$	0	0
$144$	0	0
$145$	−243.138	−0.139252
$146$	0	0
$147$	−1221.99	−0.685632
$148$	0	0
$149$	2451.19	1.34771	0.673856	−	0.738863i	$-0.264637\pi$
$149$	2451.19	1.34771	0.673856	+	0.738863i	$0.264637\pi$
$150$	0	0
$151$	2763.52	1.48935	0.744677	−	0.667425i	$-0.232604\pi$
$151$	2763.52	1.48935	0.744677	+	0.667425i	$0.232604\pi$
$152$	0	0
$153$	4228.15	2.23415
$154$	0	0
$155$	47.5360	0.0246334
$156$	0	0
$157$	−3568.04	−1.81376	−0.906881	−	0.421386i	$-0.861544\pi$
$157$	−3568.04	−1.81376	−0.906881	+	0.421386i	$0.861544\pi$
$158$	0	0
$159$	−622.567	−0.310520
$160$	0	0
$161$	431.627	0.211285
$162$	0	0
$163$	70.9741	0.0341051	0.0170525	−	0.999855i	$-0.494572\pi$
$163$	70.9741	0.0341051	0.0170525	+	0.999855i	$0.494572\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	2742.82	1.27093	0.635466	−	0.772129i	$-0.280808\pi$
$167$	2742.82	1.27093	0.635466	+	0.772129i	$0.280808\pi$
$168$	0	0
$169$	396.150	0.180314
$170$	0	0
$171$	−1853.37	−0.828835
$172$	0	0
$173$	−1333.66	−0.586107	−0.293053	−	0.956096i	$-0.594671\pi$
$173$	−1333.66	−0.586107	−0.293053	+	0.956096i	$0.594671\pi$
$174$	0	0
$175$	−1811.05	−0.782302
$176$	0	0
$177$	2582.05	1.09649
$178$	0	0
$179$	−3241.11	−1.35336	−0.676682	−	0.736276i	$-0.736583\pi$
$179$	−3241.11	−1.35336	−0.676682	+	0.736276i	$0.736583\pi$
$180$	0	0
$181$	2660.23	1.09245	0.546225	−	0.837638i	$-0.316064\pi$
$181$	2660.23	1.09245	0.546225	+	0.837638i	$0.316064\pi$
$182$	0	0
$183$	6986.26	2.82207
$184$	0	0
$185$	363.774	0.144569
$186$	0	0
$187$	0	0
$188$	0	0
$189$	6285.53	2.41907
$190$	0	0
$191$	998.627	0.378315	0.189157	−	0.981947i	$-0.439424\pi$
$191$	998.627	0.378315	0.189157	+	0.981947i	$0.439424\pi$
$192$	0	0
$193$	−3841.74	−1.43282	−0.716411	−	0.697678i	$-0.754217\pi$
$193$	−3841.74	−1.43282	−0.716411	+	0.697678i	$0.754217\pi$
$194$	0	0
$195$	−811.930	−0.298172
$196$	0	0
$197$	3386.25	1.22467	0.612335	−	0.790598i	$-0.290230\pi$
$197$	3386.25	1.22467	0.612335	+	0.790598i	$0.290230\pi$
$198$	0	0
$199$	4895.30	1.74381	0.871906	−	0.489674i	$-0.162884\pi$
$199$	4895.30	1.74381	0.871906	+	0.489674i	$0.162884\pi$
$200$	0	0
$201$	1494.79	0.524548
$202$	0	0
$203$	2223.71	0.768838
$204$	0	0
$205$	193.721	0.0660004
$206$	0	0
$207$	2044.72	0.686559
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−1469.43	−0.479430	−0.239715	−	0.970843i	$-0.577054\pi$
$211$	−1469.43	−0.479430	−0.239715	+	0.970843i	$0.577054\pi$
$212$	0	0
$213$	−10401.5	−3.34601
$214$	0	0
$215$	−346.217	−0.109822
$216$	0	0
$217$	−434.759	−0.136006
$218$	0	0
$219$	310.599	0.0958370
$220$	0	0
$221$	3071.32	0.934839
$222$	0	0
$223$	−1745.47	−0.524149	−0.262074	−	0.965048i	$-0.584407\pi$
$223$	−1745.47	−0.524149	−0.262074	+	0.965048i	$0.584407\pi$
$224$	0	0
$225$	−8579.38	−2.54204
$226$	0	0
$227$	2363.87	0.691169	0.345585	−	0.938388i	$-0.387681\pi$
$227$	2363.87	0.691169	0.345585	+	0.938388i	$0.387681\pi$
$228$	0	0
$229$	−3093.75	−0.892754	−0.446377	−	0.894845i	$-0.647286\pi$
$229$	−3093.75	−0.892754	−0.446377	+	0.894845i	$0.647286\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−2700.06	−0.759170	−0.379585	−	0.925157i	$-0.623933\pi$
$233$	−2700.06	−0.759170	−0.379585	+	0.925157i	$0.623933\pi$
$234$	0	0
$235$	−283.190	−0.0786098
$236$	0	0
$237$	641.657	0.175865
$238$	0	0
$239$	357.923	0.0968708	0.0484354	−	0.998826i	$-0.484577\pi$
$239$	357.923	0.0968708	0.0484354	+	0.998826i	$0.484577\pi$
$240$	0	0
$241$	−4290.72	−1.14685	−0.573423	−	0.819260i	$-0.694385\pi$
$241$	−4290.72	−1.14685	−0.573423	+	0.819260i	$0.694385\pi$
$242$	0	0
$243$	11124.3	2.93672
$244$	0	0
$245$	200.649	0.0523225
$246$	0	0
$247$	−1346.29	−0.346810
$248$	0	0
$249$	−2272.02	−0.578247
$250$	0	0
$251$	5392.60	1.35609	0.678044	−	0.735022i	$-0.262828\pi$
$251$	5392.60	1.35609	0.678044	+	0.735022i	$0.262828\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	−961.648	−0.236160
$256$	0	0
$257$	4077.31	0.989632	0.494816	−	0.868998i	$-0.335236\pi$
$257$	4077.31	0.989632	0.494816	+	0.868998i	$0.335236\pi$
$258$	0	0
$259$	−3327.04	−0.798194
$260$	0	0
$261$	10534.2	2.49829
$262$	0	0
$263$	−3256.10	−0.763421	−0.381711	−	0.924282i	$-0.624665\pi$
$263$	−3256.10	−0.763421	−0.381711	+	0.924282i	$0.624665\pi$
$264$	0	0
$265$	102.225	0.0236967
$266$	0	0
$267$	−6099.22	−1.39800
$268$	0	0
$269$	2060.04	0.466925	0.233463	−	0.972366i	$-0.424994\pi$
$269$	2060.04	0.466925	0.233463	+	0.972366i	$0.424994\pi$
$270$	0	0
$271$	−5349.01	−1.19900	−0.599500	−	0.800375i	$-0.704634\pi$
$271$	−5349.01	−1.19900	−0.599500	+	0.800375i	$0.704634\pi$
$272$	0	0
$273$	7425.83	1.64627
$274$	0	0
$275$	0	0
$276$	0	0
$277$	8404.77	1.82308	0.911541	−	0.411209i	$-0.134893\pi$
$277$	8404.77	1.82308	0.911541	+	0.411209i	$0.134893\pi$
$278$	0	0
$279$	−2059.56	−0.441944
$280$	0	0
$281$	−7035.59	−1.49362	−0.746812	−	0.665035i	$-0.768416\pi$
$281$	−7035.59	−1.49362	−0.746812	+	0.665035i	$0.768416\pi$
$282$	0	0
$283$	7553.62	1.58663	0.793314	−	0.608812i	$-0.208354\pi$
$283$	7553.62	1.58663	0.793314	+	0.608812i	$0.208354\pi$
$284$	0	0
$285$	421.530	0.0876115
$286$	0	0
$287$	−1771.76	−0.364402
$288$	0	0
$289$	−1275.33	−0.259583
$290$	0	0
$291$	−10839.4	−2.18357
$292$	0	0
$293$	−3263.90	−0.650782	−0.325391	−	0.945580i	$-0.605496\pi$
$293$	−3263.90	−0.650782	−0.325391	+	0.945580i	$0.605496\pi$
$294$	0	0
$295$	−423.971	−0.0836763
$296$	0	0
$297$	0	0
$298$	0	0
$299$	1485.28	0.287277
$300$	0	0
$301$	3166.46	0.606352
$302$	0	0
$303$	−13295.9	−2.52089
$304$	0	0
$305$	−1147.14	−0.215360
$306$	0	0
$307$	−5505.74	−1.02355	−0.511774	−	0.859120i	$-0.671012\pi$
$307$	−5505.74	−1.02355	−0.511774	+	0.859120i	$0.671012\pi$
$308$	0	0
$309$	14630.6	2.69355
$310$	0	0
$311$	1210.19	0.220654	0.110327	−	0.993895i	$-0.464810\pi$
$311$	1210.19	0.220654	0.110327	+	0.993895i	$0.464810\pi$
$312$	0	0
$313$	−4903.30	−0.885467	−0.442733	−	0.896653i	$-0.645991\pi$
$313$	−4903.30	−0.885467	−0.442733	+	0.896653i	$0.645991\pi$
$314$	0	0
$315$	−1678.57	−0.300244
$316$	0	0
$317$	7689.15	1.36235	0.681176	−	0.732120i	$-0.261469\pi$
$317$	7689.15	1.36235	0.681176	+	0.732120i	$0.261469\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−17364.8	−3.01934
$322$	0	0
$323$	−1594.54	−0.274683
$324$	0	0
$325$	−6232.06	−1.06367
$326$	0	0
$327$	−6780.48	−1.14667
$328$	0	0
$329$	2590.03	0.434021
$330$	0	0
$331$	−3085.35	−0.512344	−0.256172	−	0.966631i	$-0.582461\pi$
$331$	−3085.35	−0.512344	−0.256172	+	0.966631i	$0.582461\pi$
$332$	0	0
$333$	−15761.0	−2.59368
$334$	0	0
$335$	−245.443	−0.0400298
$336$	0	0
$337$	5776.57	0.933738	0.466869	−	0.884327i	$-0.345382\pi$
$337$	5776.57	0.933738	0.466869	+	0.884327i	$0.345382\pi$
$338$	0	0
$339$	2987.72	0.478674
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−6910.96	−1.08792
$344$	0	0
$345$	−465.050	−0.0725722
$346$	0	0
$347$	909.285	0.140671	0.0703357	−	0.997523i	$-0.477593\pi$
$347$	909.285	0.140671	0.0703357	+	0.997523i	$0.477593\pi$
$348$	0	0
$349$	−11434.2	−1.75375	−0.876874	−	0.480720i	$-0.840375\pi$
$349$	−11434.2	−1.75375	−0.876874	+	0.480720i	$0.840375\pi$
$350$	0	0
$351$	21629.3	3.28913
$352$	0	0
$353$	2773.55	0.418190	0.209095	−	0.977895i	$-0.432948\pi$
$353$	2773.55	0.418190	0.209095	+	0.977895i	$0.432948\pi$
$354$	0	0
$355$	1707.92	0.255344
$356$	0	0
$357$	8795.14	1.30389
$358$	0	0
$359$	−2522.86	−0.370895	−0.185448	−	0.982654i	$-0.559373\pi$
$359$	−2522.86	−0.370895	−0.185448	+	0.982654i	$0.559373\pi$
$360$	0	0
$361$	−6160.05	−0.898097
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−51.0000	−0.00731359
$366$	0	0
$367$	−5254.27	−0.747331	−0.373666	−	0.927563i	$-0.621899\pi$
$367$	−5254.27	−0.747331	−0.373666	+	0.927563i	$0.621899\pi$
$368$	0	0
$369$	−8393.22	−1.18410
$370$	0	0
$371$	−934.938	−0.130834
$372$	0	0
$373$	−316.370	−0.0439169	−0.0219585	−	0.999759i	$-0.506990\pi$
$373$	−316.370	−0.0439169	−0.0219585	+	0.999759i	$0.506990\pi$
$374$	0	0
$375$	3944.33	0.543158
$376$	0	0
$377$	7652.06	1.04536
$378$	0	0
$379$	−5257.04	−0.712497	−0.356248	−	0.934391i	$-0.615944\pi$
$379$	−5257.04	−0.712497	−0.356248	+	0.934391i	$0.615944\pi$
$380$	0	0
$381$	22325.8	3.00206
$382$	0	0
$383$	1424.22	0.190011	0.0950057	−	0.995477i	$-0.469713\pi$
$383$	1424.22	0.190011	0.0950057	+	0.995477i	$0.469713\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	15000.3	1.97030
$388$	0	0
$389$	−1970.12	−0.256784	−0.128392	−	0.991724i	$-0.540982\pi$
$389$	−1970.12	−0.256784	−0.128392	+	0.991724i	$0.540982\pi$
$390$	0	0
$391$	1759.16	0.227531
$392$	0	0
$393$	14362.2	1.84345
$394$	0	0
$395$	−105.359	−0.0134208
$396$	0	0
$397$	−4148.62	−0.524467	−0.262233	−	0.965004i	$-0.584459\pi$
$397$	−4148.62	−0.524467	−0.262233	+	0.965004i	$0.584459\pi$
$398$	0	0
$399$	−3855.27	−0.483721
$400$	0	0
$401$	−7710.20	−0.960171	−0.480086	−	0.877222i	$-0.659394\pi$
$401$	−7710.20	−0.960171	−0.480086	+	0.877222i	$0.659394\pi$
$402$	0	0
$403$	−1496.06	−0.184923
$404$	0	0
$405$	−3709.64	−0.455145
$406$	0	0
$407$	0	0
$408$	0	0
$409$	3495.64	0.422612	0.211306	−	0.977420i	$-0.432228\pi$
$409$	3495.64	0.422612	0.211306	+	0.977420i	$0.432228\pi$
$410$	0	0
$411$	−1939.84	−0.232811
$412$	0	0
$413$	3877.59	0.461995
$414$	0	0
$415$	373.064	0.0441277
$416$	0	0
$417$	−390.751	−0.0458877
$418$	0	0
$419$	−6493.78	−0.757140	−0.378570	−	0.925573i	$-0.623584\pi$
$419$	−6493.78	−0.757140	−0.378570	+	0.925573i	$0.623584\pi$
$420$	0	0
$421$	−9961.59	−1.15320	−0.576601	−	0.817026i	$-0.695621\pi$
$421$	−9961.59	−1.15320	−0.576601	+	0.817026i	$0.695621\pi$
$422$	0	0
$423$	12269.6	1.41032
$424$	0	0
$425$	−7381.23	−0.842453
$426$	0	0
$427$	10491.6	1.18905
$428$	0	0
$429$	0	0
$430$	0	0
$431$	5496.82	0.614321	0.307161	−	0.951658i	$-0.400621\pi$
$431$	5496.82	0.614321	0.307161	+	0.951658i	$0.400621\pi$
$432$	0	0
$433$	98.3315	0.0109134	0.00545671	−	0.999985i	$-0.498263\pi$
$433$	98.3315	0.0109134	0.00545671	+	0.999985i	$0.498263\pi$
$434$	0	0
$435$	−2395.90	−0.264080
$436$	0	0
$437$	−771.113	−0.0844104
$438$	0	0
$439$	−1951.20	−0.212131	−0.106065	−	0.994359i	$-0.533825\pi$
$439$	−1951.20	−0.212131	−0.106065	+	0.994359i	$0.533825\pi$
$440$	0	0
$441$	−8693.38	−0.938709
$442$	0	0
$443$	−9438.69	−1.01229	−0.506146	−	0.862448i	$-0.668930\pi$
$443$	−9438.69	−1.01229	−0.506146	+	0.862448i	$0.668930\pi$
$444$	0	0
$445$	1001.49	0.106685
$446$	0	0
$447$	24154.2	2.55583
$448$	0	0
$449$	12878.8	1.35365	0.676825	−	0.736144i	$-0.263355\pi$
$449$	12878.8	1.35365	0.676825	+	0.736144i	$0.263355\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	27232.0	2.82444
$454$	0	0
$455$	−1219.31	−0.125631
$456$	0	0
$457$	7757.62	0.794061	0.397031	−	0.917805i	$-0.370041\pi$
$457$	7757.62	0.794061	0.397031	+	0.917805i	$0.370041\pi$
$458$	0	0
$459$	25617.7	2.60508
$460$	0	0
$461$	−13529.3	−1.36686	−0.683432	−	0.730014i	$-0.739513\pi$
$461$	−13529.3	−1.36686	−0.683432	+	0.730014i	$0.739513\pi$
$462$	0	0
$463$	14558.3	1.46130	0.730651	−	0.682752i	$-0.239217\pi$
$463$	14558.3	1.46130	0.730651	+	0.682752i	$0.239217\pi$
$464$	0	0
$465$	468.425	0.0467154
$466$	0	0
$467$	4633.16	0.459094	0.229547	−	0.973298i	$-0.426275\pi$
$467$	4633.16	0.459094	0.229547	+	0.973298i	$0.426275\pi$
$468$	0	0
$469$	2244.79	0.221013
$470$	0	0
$471$	−35159.8	−3.43966
$472$	0	0
$473$	0	0
$474$	0	0
$475$	3235.50	0.312536
$476$	0	0
$477$	−4429.02	−0.425138
$478$	0	0
$479$	19601.1	1.86972	0.934860	−	0.355018i	$-0.115525\pi$
$479$	19601.1	1.86972	0.934860	+	0.355018i	$0.115525\pi$
$480$	0	0
$481$	−11448.7	−1.08528
$482$	0	0
$483$	4253.30	0.400687
$484$	0	0
$485$	1779.83	0.166634
$486$	0	0
$487$	3675.21	0.341971	0.170985	−	0.985274i	$-0.445305\pi$
$487$	3675.21	0.341971	0.170985	+	0.985274i	$0.445305\pi$
$488$	0	0
$489$	699.386	0.0646776
$490$	0	0
$491$	20571.1	1.89075	0.945377	−	0.325980i	$-0.105694\pi$
$491$	20571.1	1.89075	0.945377	+	0.325980i	$0.105694\pi$
$492$	0	0
$493$	9063.09	0.827953
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−15620.5	−1.40981
$498$	0	0
$499$	−968.806	−0.0869133	−0.0434566	−	0.999055i	$-0.513837\pi$
$499$	−968.806	−0.0869133	−0.0434566	+	0.999055i	$0.513837\pi$
$500$	0	0
$501$	27028.0	2.41022
$502$	0	0
$503$	−12912.5	−1.14461	−0.572307	−	0.820040i	$-0.693951\pi$
$503$	−12912.5	−1.14461	−0.572307	+	0.820040i	$0.693951\pi$
$504$	0	0
$505$	2183.17	0.192376
$506$	0	0
$507$	3903.71	0.341952
$508$	0	0
$509$	−2401.08	−0.209088	−0.104544	−	0.994520i	$-0.533338\pi$
$509$	−2401.08	−0.209088	−0.104544	+	0.994520i	$0.533338\pi$
$510$	0	0
$511$	466.441	0.0403799
$512$	0	0
$513$	−11229.3	−0.966441
$514$	0	0
$515$	−2402.33	−0.205552
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−13142.0	−1.11151
$520$	0	0
$521$	14283.4	1.20109	0.600544	−	0.799591i	$-0.294951\pi$
$521$	14283.4	1.20109	0.600544	+	0.799591i	$0.294951\pi$
$522$	0	0
$523$	−9266.32	−0.774737	−0.387369	−	0.921925i	$-0.626616\pi$
$523$	−9266.32	−0.774737	−0.387369	+	0.921925i	$0.626616\pi$
$524$	0	0
$525$	−17846.3	−1.48358
$526$	0	0
$527$	−1771.93	−0.146464
$528$	0	0
$529$	−11316.3	−0.930079
$530$	0	0
$531$	18369.1	1.50122
$532$	0	0
$533$	−6096.82	−0.495465
$534$	0	0
$535$	2851.28	0.230414
$536$	0	0
$537$	−31938.2	−2.56655
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−5268.19	−0.418664	−0.209332	−	0.977845i	$-0.567129\pi$
$541$	−5268.19	−0.418664	−0.209332	+	0.977845i	$0.567129\pi$
$542$	0	0
$543$	26214.2	2.07175
$544$	0	0
$545$	1113.35	0.0875056
$546$	0	0
$547$	−19377.9	−1.51470	−0.757348	−	0.653012i	$-0.773505\pi$
$547$	−19377.9	−1.51470	−0.757348	+	0.653012i	$0.773505\pi$
$548$	0	0
$549$	49701.1	3.86374
$550$	0	0
$551$	−3972.72	−0.307157
$552$	0	0
$553$	963.607	0.0740990
$554$	0	0
$555$	3584.67	0.274163
$556$	0	0
$557$	5309.74	0.403915	0.201958	−	0.979394i	$-0.435270\pi$
$557$	5309.74	0.403915	0.201958	+	0.979394i	$0.435270\pi$
$558$	0	0
$559$	10896.2	0.824435
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−4494.72	−0.336465	−0.168232	−	0.985747i	$-0.553806\pi$
$563$	−4494.72	−0.336465	−0.168232	+	0.985747i	$0.553806\pi$
$564$	0	0
$565$	−490.580	−0.0365290
$566$	0	0
$567$	33928.0	2.51295
$568$	0	0
$569$	22234.4	1.63816	0.819082	−	0.573676i	$-0.194483\pi$
$569$	22234.4	1.63816	0.819082	+	0.573676i	$0.194483\pi$
$570$	0	0
$571$	2370.18	0.173711	0.0868554	−	0.996221i	$-0.472318\pi$
$571$	2370.18	0.173711	0.0868554	+	0.996221i	$0.472318\pi$
$572$	0	0
$573$	9840.57	0.717445
$574$	0	0
$575$	−3569.54	−0.258887
$576$	0	0
$577$	−13848.0	−0.999136	−0.499568	−	0.866275i	$-0.666508\pi$
$577$	−13848.0	−0.999136	−0.499568	+	0.866275i	$0.666508\pi$
$578$	0	0
$579$	−37856.9	−2.71724
$580$	0	0
$581$	−3412.00	−0.243638
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−5776.17	−0.408231
$586$	0	0
$587$	19878.7	1.39776	0.698879	−	0.715240i	$-0.253683\pi$
$587$	19878.7	1.39776	0.698879	+	0.715240i	$0.253683\pi$
$588$	0	0
$589$	776.709	0.0543357
$590$	0	0
$591$	33368.4	2.32249
$592$	0	0
$593$	−23426.3	−1.62226	−0.811132	−	0.584863i	$-0.801148\pi$
$593$	−23426.3	−1.62226	−0.811132	+	0.584863i	$0.801148\pi$
$594$	0	0
$595$	−1444.15	−0.0995034
$596$	0	0
$597$	48238.8	3.30700
$598$	0	0
$599$	884.679	0.0603456	0.0301728	−	0.999545i	$-0.490394\pi$
$599$	884.679	0.0603456	0.0301728	+	0.999545i	$0.490394\pi$
$600$	0	0
$601$	6902.37	0.468475	0.234238	−	0.972179i	$-0.424741\pi$
$601$	6902.37	0.468475	0.234238	+	0.972179i	$0.424741\pi$
$602$	0	0
$603$	10634.1	0.718167
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−18984.5	−1.26945	−0.634726	−	0.772738i	$-0.718887\pi$
$607$	−18984.5	−1.26945	−0.634726	+	0.772738i	$0.718887\pi$
$608$	0	0
$609$	21912.7	1.45804
$610$	0	0
$611$	8912.61	0.590124
$612$	0	0
$613$	18129.4	1.19452	0.597261	−	0.802047i	$-0.296256\pi$
$613$	18129.4	1.19452	0.597261	+	0.802047i	$0.296256\pi$
$614$	0	0
$615$	1908.95	0.125165
$616$	0	0
$617$	−15257.7	−0.995549	−0.497774	−	0.867307i	$-0.665849\pi$
$617$	−15257.7	−0.995549	−0.497774	+	0.867307i	$0.665849\pi$
$618$	0	0
$619$	7610.30	0.494158	0.247079	−	0.968995i	$-0.420529\pi$
$619$	7610.30	0.494158	0.247079	+	0.968995i	$0.420529\pi$
$620$	0	0
$621$	12388.6	0.800544
$622$	0	0
$623$	−9159.48	−0.589032
$624$	0	0
$625$	14650.1	0.937606
$626$	0	0
$627$	0	0
$628$	0	0
$629$	−13559.9	−0.859567
$630$	0	0
$631$	26065.6	1.64446	0.822231	−	0.569154i	$-0.192729\pi$
$631$	26065.6	1.64446	0.822231	+	0.569154i	$0.192729\pi$
$632$	0	0
$633$	−14479.9	−0.909201
$634$	0	0
$635$	−3665.87	−0.229095
$636$	0	0
$637$	−6314.86	−0.392785
$638$	0	0
$639$	−73997.8	−4.58107
$640$	0	0
$641$	−22980.0	−1.41600	−0.708000	−	0.706212i	$-0.750402\pi$
$641$	−22980.0	−1.41600	−0.708000	+	0.706212i	$0.750402\pi$
$642$	0	0
$643$	−6551.27	−0.401799	−0.200900	−	0.979612i	$-0.564386\pi$
$643$	−6551.27	−0.401799	−0.200900	+	0.979612i	$0.564386\pi$
$644$	0	0
$645$	−3411.65	−0.208269
$646$	0	0
$647$	6281.33	0.381676	0.190838	−	0.981622i	$-0.438879\pi$
$647$	6281.33	0.381676	0.190838	+	0.981622i	$0.438879\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−4284.16	−0.257926
$652$	0	0
$653$	1178.52	0.0706266	0.0353133	−	0.999376i	$-0.488757\pi$
$653$	1178.52	0.0706266	0.0353133	+	0.999376i	$0.488757\pi$
$654$	0	0
$655$	−2358.26	−0.140679
$656$	0	0
$657$	2209.64	0.131212
$658$	0	0
$659$	−15421.0	−0.911561	−0.455781	−	0.890092i	$-0.650640\pi$
$659$	−15421.0	−0.911561	−0.455781	+	0.890092i	$0.650640\pi$
$660$	0	0
$661$	−9587.68	−0.564172	−0.282086	−	0.959389i	$-0.591026\pi$
$661$	−9587.68	−0.564172	−0.282086	+	0.959389i	$0.591026\pi$
$662$	0	0
$663$	30265.1	1.77285
$664$	0	0
$665$	633.031	0.0369141
$666$	0	0
$667$	4382.88	0.254431
$668$	0	0
$669$	−17200.0	−0.994008
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−16151.6	−0.925108	−0.462554	−	0.886591i	$-0.653067\pi$
$673$	−16151.6	−0.925108	−0.462554	+	0.886591i	$0.653067\pi$
$674$	0	0
$675$	−51981.1	−2.96408
$676$	0	0
$677$	8026.53	0.455664	0.227832	−	0.973700i	$-0.426836\pi$
$677$	8026.53	0.455664	0.227832	+	0.973700i	$0.426836\pi$
$678$	0	0
$679$	−16278.1	−0.920024
$680$	0	0
$681$	23293.8	1.31075
$682$	0	0
$683$	17912.7	1.00353	0.501765	−	0.865004i	$-0.332684\pi$
$683$	17912.7	1.00353	0.501765	+	0.865004i	$0.332684\pi$
$684$	0	0
$685$	318.520	0.0177665
$686$	0	0
$687$	−30486.1	−1.69304
$688$	0	0
$689$	−3217.23	−0.177891
$690$	0	0
$691$	−27493.4	−1.51360	−0.756800	−	0.653646i	$-0.773238\pi$
$691$	−27493.4	−1.51360	−0.756800	+	0.653646i	$0.773238\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	64.1610	0.00350182
$696$	0	0
$697$	−7221.07	−0.392421
$698$	0	0
$699$	−26606.6	−1.43971
$700$	0	0
$701$	−2238.33	−0.120600	−0.0603000	−	0.998180i	$-0.519206\pi$
$701$	−2238.33	−0.120600	−0.0603000	+	0.998180i	$0.519206\pi$
$702$	0	0
$703$	5943.85	0.318885
$704$	0	0
$705$	−2790.59	−0.149077
$706$	0	0
$707$	−19967.1	−1.06215
$708$	0	0
$709$	24224.5	1.28317	0.641586	−	0.767051i	$-0.278277\pi$
$709$	24224.5	1.28317	0.641586	+	0.767051i	$0.278277\pi$
$710$	0	0
$711$	4564.83	0.240780
$712$	0	0
$713$	−856.899	−0.0450086
$714$	0	0
$715$	0	0
$716$	0	0
$717$	3527.01	0.183708
$718$	0	0
$719$	−9744.02	−0.505411	−0.252705	−	0.967543i	$-0.581320\pi$
$719$	−9744.02	−0.505411	−0.252705	+	0.967543i	$0.581320\pi$
$720$	0	0
$721$	21971.5	1.13490
$722$	0	0
$723$	−42281.2	−2.17490
$724$	0	0
$725$	−18390.0	−0.942053
$726$	0	0
$727$	−14917.2	−0.761002	−0.380501	−	0.924781i	$-0.624248\pi$
$727$	−14917.2	−0.761002	−0.380501	+	0.924781i	$0.624248\pi$
$728$	0	0
$729$	47717.1	2.42428
$730$	0	0
$731$	12905.4	0.652974
$732$	0	0
$733$	7094.38	0.357485	0.178743	−	0.983896i	$-0.442797\pi$
$733$	7094.38	0.357485	0.178743	+	0.983896i	$0.442797\pi$
$734$	0	0
$735$	1977.22	0.0992256
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−29689.9	−1.47789	−0.738944	−	0.673767i	$-0.764675\pi$
$739$	−29689.9	−1.47789	−0.738944	+	0.673767i	$0.764675\pi$
$740$	0	0
$741$	−13266.4	−0.657699
$742$	0	0
$743$	−19302.6	−0.953089	−0.476545	−	0.879150i	$-0.658111\pi$
$743$	−19302.6	−0.953089	−0.476545	+	0.879150i	$0.658111\pi$
$744$	0	0
$745$	−3966.10	−0.195043
$746$	0	0
$747$	−16163.5	−0.791687
$748$	0	0
$749$	−26077.5	−1.27217
$750$	0	0
$751$	−12582.7	−0.611384	−0.305692	−	0.952130i	$-0.598888\pi$
$751$	−12582.7	−0.611384	−0.305692	+	0.952130i	$0.598888\pi$
$752$	0	0
$753$	53139.2	2.57172
$754$	0	0
$755$	−4471.48	−0.215541
$756$	0	0
$757$	2728.73	0.131014	0.0655068	−	0.997852i	$-0.479134\pi$
$757$	2728.73	0.131014	0.0655068	+	0.997852i	$0.479134\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	21134.6	1.00674	0.503371	−	0.864070i	$-0.332093\pi$
$761$	21134.6	1.00674	0.503371	+	0.864070i	$0.332093\pi$
$762$	0	0
$763$	−10182.6	−0.483137
$764$	0	0
$765$	−6841.29	−0.323330
$766$	0	0
$767$	13343.3	0.628158
$768$	0	0
$769$	−10493.4	−0.492068	−0.246034	−	0.969261i	$-0.579127\pi$
$769$	−10493.4	−0.492068	−0.246034	+	0.969261i	$0.579127\pi$
$770$	0	0
$771$	40178.2	1.87676
$772$	0	0
$773$	−14732.9	−0.685516	−0.342758	−	0.939424i	$-0.611361\pi$
$773$	−14732.9	−0.685516	−0.342758	+	0.939424i	$0.611361\pi$
$774$	0	0
$775$	3595.44	0.166648
$776$	0	0
$777$	−32785.0	−1.51371
$778$	0	0
$779$	3165.29	0.145582
$780$	0	0
$781$	0	0
$782$	0	0
$783$	63825.3	2.91306
$784$	0	0
$785$	5773.21	0.262490
$786$	0	0
$787$	−25252.0	−1.14376	−0.571879	−	0.820338i	$-0.693785\pi$
$787$	−25252.0	−1.14376	−0.571879	+	0.820338i	$0.693785\pi$
$788$	0	0
$789$	−32085.9	−1.44777
$790$	0	0
$791$	4486.80	0.201684
$792$	0	0
$793$	36102.8	1.61671
$794$	0	0
$795$	1007.33	0.0449389
$796$	0	0
$797$	−29313.5	−1.30281	−0.651403	−	0.758732i	$-0.725819\pi$
$797$	−29313.5	−1.30281	−0.651403	+	0.758732i	$0.725819\pi$
$798$	0	0
$799$	10556.1	0.467393
$800$	0	0
$801$	−43390.6	−1.91402
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−698.387	−0.0305775
$806$	0	0
$807$	20299.8	0.885487
$808$	0	0
$809$	−7235.09	−0.314428	−0.157214	−	0.987565i	$-0.550251\pi$
$809$	−7235.09	−0.314428	−0.157214	+	0.987565i	$0.550251\pi$
$810$	0	0
$811$	−18954.3	−0.820685	−0.410342	−	0.911932i	$-0.634591\pi$
$811$	−18954.3	−0.820685	−0.410342	+	0.911932i	$0.634591\pi$
$812$	0	0
$813$	−52709.7	−2.27381
$814$	0	0
$815$	−114.839	−0.00493573
$816$	0	0
$817$	−5656.97	−0.242243
$818$	0	0
$819$	52828.3	2.25393
$820$	0	0
$821$	−12893.1	−0.548077	−0.274039	−	0.961719i	$-0.588360\pi$
$821$	−12893.1	−0.548077	−0.274039	+	0.961719i	$0.588360\pi$
$822$	0	0
$823$	17780.4	0.753083	0.376542	−	0.926400i	$-0.377113\pi$
$823$	17780.4	0.753083	0.376542	+	0.926400i	$0.377113\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	19993.0	0.840659	0.420329	−	0.907372i	$-0.361915\pi$
$827$	19993.0	0.840659	0.420329	+	0.907372i	$0.361915\pi$
$828$	0	0
$829$	−3499.09	−0.146596	−0.0732982	−	0.997310i	$-0.523352\pi$
$829$	−3499.09	−0.146596	−0.0732982	+	0.997310i	$0.523352\pi$
$830$	0	0
$831$	82821.5	3.45734
$832$	0	0
$833$	−7479.31	−0.311096
$834$	0	0
$835$	−4437.97	−0.183931
$836$	0	0
$837$	−12478.5	−0.515317
$838$	0	0
$839$	−18827.6	−0.774734	−0.387367	−	0.921926i	$-0.626615\pi$
$839$	−18827.6	−0.774734	−0.387367	+	0.921926i	$0.626615\pi$
$840$	0	0
$841$	−1808.71	−0.0741608
$842$	0	0
$843$	−69329.4	−2.83254
$844$	0	0
$845$	−640.985	−0.0260953
$846$	0	0
$847$	0	0
$848$	0	0
$849$	74434.1	3.00892
$850$	0	0
$851$	−6557.50	−0.264146
$852$	0	0
$853$	−28919.7	−1.16083	−0.580417	−	0.814320i	$-0.697110\pi$
$853$	−28919.7	−1.16083	−0.580417	+	0.814320i	$0.697110\pi$
$854$	0	0
$855$	2998.82	0.119950
$856$	0	0
$857$	13906.3	0.554294	0.277147	−	0.960827i	$-0.410611\pi$
$857$	13906.3	0.554294	0.277147	+	0.960827i	$0.410611\pi$
$858$	0	0
$859$	−18829.8	−0.747923	−0.373962	−	0.927444i	$-0.622001\pi$
$859$	−18829.8	−0.747923	−0.373962	+	0.927444i	$0.622001\pi$
$860$	0	0
$861$	−17459.1	−0.691061
$862$	0	0
$863$	−26157.4	−1.03176	−0.515879	−	0.856661i	$-0.672535\pi$
$863$	−26157.4	−1.03176	−0.515879	+	0.856661i	$0.672535\pi$
$864$	0	0
$865$	2157.91	0.0848222
$866$	0	0
$867$	−12567.3	−0.492279
$868$	0	0
$869$	0	0
$870$	0	0
$871$	7724.61	0.300503
$872$	0	0
$873$	−77113.1	−2.98956
$874$	0	0
$875$	5923.38	0.228854
$876$	0	0
$877$	−1415.24	−0.0544917	−0.0272458	−	0.999629i	$-0.508674\pi$
$877$	−1415.24	−0.0544917	−0.0272458	+	0.999629i	$0.508674\pi$
$878$	0	0
$879$	−32162.8	−1.23416
$880$	0	0
$881$	−5355.31	−0.204796	−0.102398	−	0.994744i	$-0.532651\pi$
$881$	−5355.31	−0.204796	−0.102398	+	0.994744i	$0.532651\pi$
$882$	0	0
$883$	−48865.1	−1.86234	−0.931168	−	0.364590i	$-0.881209\pi$
$883$	−48865.1	−1.86234	−0.931168	+	0.364590i	$0.881209\pi$
$884$	0	0
$885$	−4177.85	−0.158686
$886$	0	0
$887$	12614.5	0.477511	0.238755	−	0.971080i	$-0.423261\pi$
$887$	12614.5	0.477511	0.238755	+	0.971080i	$0.423261\pi$
$888$	0	0
$889$	33527.7	1.26488
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−4627.16	−0.173395
$894$	0	0
$895$	5244.23	0.195861
$896$	0	0
$897$	14636.1	0.544800
$898$	0	0
$899$	−4414.69	−0.163780
$900$	0	0
$901$	−3810.49	−0.140894
$902$	0	0
$903$	31202.6	1.14990
$904$	0	0
$905$	−4304.35	−0.158101
$906$	0	0
$907$	−5592.74	−0.204745	−0.102373	−	0.994746i	$-0.532643\pi$
$907$	−5592.74	−0.204745	−0.102373	+	0.994746i	$0.532643\pi$
$908$	0	0
$909$	−94588.7	−3.45138
$910$	0	0
$911$	22598.1	0.821854	0.410927	−	0.911668i	$-0.365205\pi$
$911$	22598.1	0.821854	0.410927	+	0.911668i	$0.365205\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−11304.0	−0.408414
$916$	0	0
$917$	21568.4	0.776718
$918$	0	0
$919$	−6798.94	−0.244044	−0.122022	−	0.992527i	$-0.538938\pi$
$919$	−6798.94	−0.244044	−0.122022	+	0.992527i	$0.538938\pi$
$920$	0	0
$921$	−54254.2	−1.94108
$922$	0	0
$923$	−53751.9	−1.91686
$924$	0	0
$925$	27514.5	0.978022
$926$	0	0
$927$	104084.	3.68778
$928$	0	0
$929$	−15869.5	−0.560453	−0.280227	−	0.959934i	$-0.590410\pi$
$929$	−15869.5	−0.560453	−0.280227	+	0.959934i	$0.590410\pi$
$930$	0	0
$931$	3278.49	0.115412
$932$	0	0
$933$	11925.3	0.418453
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−20320.0	−0.708457	−0.354229	−	0.935159i	$-0.615257\pi$
$937$	−20320.0	−0.708457	−0.354229	+	0.935159i	$0.615257\pi$
$938$	0	0
$939$	−48317.7	−1.67922
$940$	0	0
$941$	−2080.02	−0.0720583	−0.0360292	−	0.999351i	$-0.511471\pi$
$941$	−2080.02	−0.0720583	−0.0360292	+	0.999351i	$0.511471\pi$
$942$	0	0
$943$	−3492.08	−0.120592
$944$	0	0
$945$	−10170.2	−0.350092
$946$	0	0
$947$	21613.7	0.741658	0.370829	−	0.928701i	$-0.379074\pi$
$947$	21613.7	0.741658	0.370829	+	0.928701i	$0.379074\pi$
$948$	0	0
$949$	1605.08	0.0549031
$950$	0	0
$951$	75769.7	2.58360
$952$	0	0
$953$	15318.4	0.520685	0.260342	−	0.965516i	$-0.416165\pi$
$953$	15318.4	0.520685	0.260342	+	0.965516i	$0.416165\pi$
$954$	0	0
$955$	−1615.81	−0.0547502
$956$	0	0
$957$	0	0
$958$	0	0
$959$	−2913.16	−0.0980925
$960$	0	0
$961$	−28927.9	−0.971028
$962$	0	0
$963$	−123535.	−4.13382
$964$	0	0
$965$	6216.07	0.207360
$966$	0	0
$967$	−33356.0	−1.10926	−0.554631	−	0.832096i	$-0.687141\pi$
$967$	−33356.0	−1.10926	−0.554631	+	0.832096i	$0.687141\pi$
$968$	0	0
$969$	−15712.7	−0.520915
$970$	0	0
$971$	24491.3	0.809436	0.404718	−	0.914442i	$-0.367370\pi$
$971$	24491.3	0.809436	0.404718	+	0.914442i	$0.367370\pi$
$972$	0	0
$973$	−586.810	−0.0193343
$974$	0	0
$975$	−61411.3	−2.01716
$976$	0	0
$977$	43967.8	1.43977	0.719885	−	0.694093i	$-0.244194\pi$
$977$	43967.8	1.43977	0.719885	+	0.694093i	$0.244194\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−48237.2	−1.56992
$982$	0	0
$983$	−34681.2	−1.12529	−0.562644	−	0.826699i	$-0.690216\pi$
$983$	−34681.2	−1.12529	−0.562644	+	0.826699i	$0.690216\pi$
$984$	0	0
$985$	−5479.06	−0.177236
$986$	0	0
$987$	25522.4	0.823088
$988$	0	0
$989$	6241.01	0.200660
$990$	0	0
$991$	−42734.1	−1.36982	−0.684910	−	0.728627i	$-0.740159\pi$
$991$	−42734.1	−1.36982	−0.684910	+	0.728627i	$0.740159\pi$
$992$	0	0
$993$	−30403.3	−0.971622
$994$	0	0
$995$	−7920.76	−0.252367
$996$	0	0
$997$	−32108.6	−1.01995	−0.509975	−	0.860189i	$-0.670345\pi$
$997$	−32108.6	−1.01995	−0.509975	+	0.860189i	$0.670345\pi$
$998$	0	0
$999$	−95493.1	−3.02429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1936.4.a.bc.1.2		2
4.3	odd	2		242.4.a.h.1.1		2
11.2	odd	10		176.4.m.a.81.1		4
11.6	odd	10		176.4.m.a.113.1		4
11.10	odd	2		1936.4.a.bb.1.2		2
12.11	even	2		2178.4.a.bi.1.2		2
44.3	odd	10		242.4.c.m.9.1		4
44.7	even	10		242.4.c.f.27.1		4
44.15	odd	10		242.4.c.m.27.1		4
44.19	even	10		242.4.c.f.9.1		4
44.27	odd	10		242.4.c.j.3.1		4
44.31	odd	10		242.4.c.j.81.1		4
44.35	even	10		22.4.c.a.15.1	yes	4
44.39	even	10		22.4.c.a.3.1	✓	4
44.43	even	2		242.4.a.k.1.1		2
132.35	odd	10		198.4.f.b.37.1		4
132.83	odd	10		198.4.f.b.91.1		4
132.131	odd	2		2178.4.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.a.3.1	✓	4	44.39	even	10
22.4.c.a.15.1	yes	4	44.35	even	10
176.4.m.a.81.1		4	11.2	odd	10
176.4.m.a.113.1		4	11.6	odd	10
198.4.f.b.37.1		4	132.35	odd	10
198.4.f.b.91.1		4	132.83	odd	10
242.4.a.h.1.1		2	4.3	odd	2
242.4.a.k.1.1		2	44.43	even	2
242.4.c.f.9.1		4	44.19	even	10
242.4.c.f.27.1		4	44.7	even	10
242.4.c.j.3.1		4	44.27	odd	10
242.4.c.j.81.1		4	44.31	odd	10
242.4.c.m.9.1		4	44.3	odd	10
242.4.c.m.27.1		4	44.15	odd	10
1936.4.a.bb.1.2		2	11.10	odd	2
1936.4.a.bc.1.2		2	1.1	even	1	trivial
2178.4.a.z.1.2		2	132.131	odd	2
2178.4.a.bi.1.2		2	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:	\( N \)	\(=\)	\( 1936 = 2^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1936.a (trivial)

\(f(q)\)	\(=\)	\(q+9.85410 q^{3} -1.61803 q^{5} +14.7984 q^{7} +70.1033 q^{9} +O(q^{10})\)	\(q+9.85410 q^{3} -1.61803 q^{5} +14.7984 q^{7} +70.1033 q^{9} +50.9230 q^{13} -15.9443 q^{15} +60.3131 q^{17} -26.4377 q^{19} +145.825 q^{21} +29.1672 q^{23} -122.382 q^{25} +424.745 q^{27} +150.267 q^{29} -29.3789 q^{31} -23.9443 q^{35} -224.825 q^{37} +501.800 q^{39} -119.726 q^{41} +213.974 q^{43} -113.430 q^{45} +175.021 q^{47} -124.008 q^{49} +594.331 q^{51} -63.1784 q^{53} -260.520 q^{57} +262.028 q^{59} +708.969 q^{61} +1037.42 q^{63} -82.3951 q^{65} +151.692 q^{67} +287.416 q^{69} -1055.55 q^{71} +31.5197 q^{73} -1205.96 q^{75} +65.1157 q^{79} +2292.69 q^{81} -230.566 q^{83} -97.5886 q^{85} +1480.75 q^{87} -618.952 q^{89} +753.577 q^{91} -289.502 q^{93} +42.7771 q^{95} -1099.99 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 13 q^{3} - q^{5} + 5 q^{7} + 53 q^{9}+O(q^{10}) \) 2 * q + 13 * q^3 - q^5 + 5 * q^7 + 53 * q^9	\( 2 q + 13 q^{3} - q^{5} + 5 q^{7} + 53 q^{9} + 37 q^{13} - 14 q^{15} + 181 q^{17} - 73 q^{19} + 115 q^{21} + 112 q^{23} - 247 q^{25} + 286 q^{27} - 55 q^{29} + 261 q^{31} - 30 q^{35} - 273 q^{37} + 458 q^{39} + 49 q^{41} + 580 q^{43} - 124 q^{45} + 397 q^{47} - 371 q^{49} + 974 q^{51} - 625 q^{53} - 407 q^{57} - 149 q^{59} + 405 q^{61} + 1205 q^{63} - 91 q^{65} + 44 q^{67} + 548 q^{69} - 1125 q^{71} - 51 q^{73} - 1598 q^{75} + 1331 q^{79} + 2318 q^{81} + 601 q^{83} - 23 q^{85} + 835 q^{87} + 864 q^{89} + 890 q^{91} + 624 q^{93} + 14 q^{95} - 713 q^{97}+O(q^{100}) \) 2 * q + 13 * q^3 - q^5 + 5 * q^7 + 53 * q^9 + 37 * q^13 - 14 * q^15 + 181 * q^17 - 73 * q^19 + 115 * q^21 + 112 * q^23 - 247 * q^25 + 286 * q^27 - 55 * q^29 + 261 * q^31 - 30 * q^35 - 273 * q^37 + 458 * q^39 + 49 * q^41 + 580 * q^43 - 124 * q^45 + 397 * q^47 - 371 * q^49 + 974 * q^51 - 625 * q^53 - 407 * q^57 - 149 * q^59 + 405 * q^61 + 1205 * q^63 - 91 * q^65 + 44 * q^67 + 548 * q^69 - 1125 * q^71 - 51 * q^73 - 1598 * q^75 + 1331 * q^79 + 2318 * q^81 + 601 * q^83 - 23 * q^85 + 835 * q^87 + 864 * q^89 + 890 * q^91 + 624 * q^93 + 14 * q^95 - 713 * q^97

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