LMFDB - Embedded newform 1232.4.a.i.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:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$

$=$

$q+10.0000 q^{3} -14.0000 q^{5} -7.00000 q^{7} +73.0000 q^{9} +O(q^{10})$

$q+10.0000 q^{3} -14.0000 q^{5} -7.00000 q^{7} +73.0000 q^{9} +11.0000 q^{11} -16.0000 q^{13} -140.000 q^{15} +108.000 q^{17} -116.000 q^{19} -70.0000 q^{21} -68.0000 q^{23} +71.0000 q^{25} +460.000 q^{27} +122.000 q^{29} +262.000 q^{31} +110.000 q^{33} +98.0000 q^{35} +130.000 q^{37} -160.000 q^{39} +204.000 q^{41} +396.000 q^{43} -1022.00 q^{45} -166.000 q^{47} +49.0000 q^{49} +1080.00 q^{51} +442.000 q^{53} -154.000 q^{55} -1160.00 q^{57} -702.000 q^{59} +196.000 q^{61} -511.000 q^{63} +224.000 q^{65} +416.000 q^{67} -680.000 q^{69} -492.000 q^{71} +408.000 q^{73} +710.000 q^{75} -77.0000 q^{77} -600.000 q^{79} +2629.00 q^{81} +1212.00 q^{83} -1512.00 q^{85} +1220.00 q^{87} +1146.00 q^{89} +112.000 q^{91} +2620.00 q^{93} +1624.00 q^{95} -482.000 q^{97} +803.000 q^{99} +O(q^{100})$

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
$3$	10.0000	1.92450	0.962250	−	0.272166i	$-0.0877398\pi$
$3$	10.0000	1.92450	0.962250	+	0.272166i	$0.0877398\pi$
$4$	0	0
$5$	−14.0000	−1.25220	−0.626099	−	0.779744i	$-0.715349\pi$
$5$	−14.0000	−1.25220	−0.626099	+	0.779744i	$0.715349\pi$
$6$	0	0
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	0	0
$9$	73.0000	2.70370
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	0	0
$13$	−16.0000	−0.341354	−0.170677	−	0.985327i	$-0.554595\pi$
$13$	−16.0000	−0.341354	−0.170677	+	0.985327i	$0.554595\pi$
$14$	0	0
$15$	−140.000	−2.40986
$16$	0	0
$17$	108.000	1.54081	0.770407	−	0.637552i	$-0.220053\pi$
$17$	108.000	1.54081	0.770407	+	0.637552i	$0.220053\pi$
$18$	0	0
$19$	−116.000	−1.40064	−0.700322	−	0.713827i	$-0.746960\pi$
$19$	−116.000	−1.40064	−0.700322	+	0.713827i	$0.746960\pi$
$20$	0	0
$21$	−70.0000	−0.727393
$22$	0	0
$23$	−68.0000	−0.616477	−0.308239	−	0.951309i	$-0.599740\pi$
$23$	−68.0000	−0.616477	−0.308239	+	0.951309i	$0.599740\pi$
$24$	0	0
$25$	71.0000	0.568000
$26$	0	0
$27$	460.000	3.27878
$28$	0	0
$29$	122.000	0.781201	0.390601	−	0.920560i	$-0.372267\pi$
$29$	122.000	0.781201	0.390601	+	0.920560i	$0.372267\pi$
$30$	0	0
$31$	262.000	1.51795	0.758977	−	0.651117i	$-0.225699\pi$
$31$	262.000	1.51795	0.758977	+	0.651117i	$0.225699\pi$
$32$	0	0
$33$	110.000	0.580259
$34$	0	0
$35$	98.0000	0.473286
$36$	0	0
$37$	130.000	0.577618	0.288809	−	0.957387i	$-0.406741\pi$
$37$	130.000	0.577618	0.288809	+	0.957387i	$0.406741\pi$
$38$	0	0
$39$	−160.000	−0.656936
$40$	0	0
$41$	204.000	0.777060	0.388530	−	0.921436i	$-0.372983\pi$
$41$	204.000	0.777060	0.388530	+	0.921436i	$0.372983\pi$
$42$	0	0
$43$	396.000	1.40441	0.702203	−	0.711977i	$-0.252200\pi$
$43$	396.000	1.40441	0.702203	+	0.711977i	$0.252200\pi$
$44$	0	0
$45$	−1022.00	−3.38557
$46$	0	0
$47$	−166.000	−0.515183	−0.257591	−	0.966254i	$-0.582929\pi$
$47$	−166.000	−0.515183	−0.257591	+	0.966254i	$0.582929\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	0	0
$51$	1080.00	2.96530
$52$	0	0
$53$	442.000	1.14554	0.572768	−	0.819718i	$-0.305870\pi$
$53$	442.000	1.14554	0.572768	+	0.819718i	$0.305870\pi$
$54$	0	0
$55$	−154.000	−0.377552
$56$	0	0
$57$	−1160.00	−2.69554
$58$	0	0
$59$	−702.000	−1.54903	−0.774514	−	0.632557i	$-0.782005\pi$
$59$	−702.000	−1.54903	−0.774514	+	0.632557i	$0.782005\pi$
$60$	0	0
$61$	196.000	0.411397	0.205699	−	0.978615i	$-0.434053\pi$
$61$	196.000	0.411397	0.205699	+	0.978615i	$0.434053\pi$
$62$	0	0
$63$	−511.000	−1.02190
$64$	0	0
$65$	224.000	0.427443
$66$	0	0
$67$	416.000	0.758545	0.379272	−	0.925285i	$-0.376174\pi$
$67$	416.000	0.758545	0.379272	+	0.925285i	$0.376174\pi$
$68$	0	0
$69$	−680.000	−1.18641
$70$	0	0
$71$	−492.000	−0.822390	−0.411195	−	0.911548i	$-0.634888\pi$
$71$	−492.000	−0.822390	−0.411195	+	0.911548i	$0.634888\pi$
$72$	0	0
$73$	408.000	0.654148	0.327074	−	0.944999i	$-0.393937\pi$
$73$	408.000	0.654148	0.327074	+	0.944999i	$0.393937\pi$
$74$	0	0
$75$	710.000	1.09312
$76$	0	0
$77$	−77.0000	−0.113961
$78$	0	0
$79$	−600.000	−0.854497	−0.427249	−	0.904134i	$-0.640517\pi$
$79$	−600.000	−0.854497	−0.427249	+	0.904134i	$0.640517\pi$
$80$	0	0
$81$	2629.00	3.60631
$82$	0	0
$83$	1212.00	1.60282	0.801411	−	0.598114i	$-0.204083\pi$
$83$	1212.00	1.60282	0.801411	+	0.598114i	$0.204083\pi$
$84$	0	0
$85$	−1512.00	−1.92941
$86$	0	0
$87$	1220.00	1.50342
$88$	0	0
$89$	1146.00	1.36490	0.682448	−	0.730934i	$-0.260915\pi$
$89$	1146.00	1.36490	0.682448	+	0.730934i	$0.260915\pi$
$90$	0	0
$91$	112.000	0.129020
$92$	0	0
$93$	2620.00	2.92130
$94$	0	0
$95$	1624.00	1.75388
$96$	0	0
$97$	−482.000	−0.504533	−0.252266	−	0.967658i	$-0.581176\pi$
$97$	−482.000	−0.504533	−0.252266	+	0.967658i	$0.581176\pi$
$98$	0	0
$99$	803.000	0.815197
$100$	0	0
$101$	1216.00	1.19799	0.598993	−	0.800754i	$-0.295568\pi$
$101$	1216.00	1.19799	0.598993	+	0.800754i	$0.295568\pi$
$102$	0	0
$103$	−1406.00	−1.34502	−0.672511	−	0.740087i	$-0.734784\pi$
$103$	−1406.00	−1.34502	−0.672511	+	0.740087i	$0.734784\pi$
$104$	0	0
$105$	980.000	0.910840
$106$	0	0
$107$	588.000	0.531253	0.265627	−	0.964076i	$-0.414421\pi$
$107$	588.000	0.531253	0.265627	+	0.964076i	$0.414421\pi$
$108$	0	0
$109$	154.000	0.135326	0.0676630	−	0.997708i	$-0.478446\pi$
$109$	154.000	0.135326	0.0676630	+	0.997708i	$0.478446\pi$
$110$	0	0
$111$	1300.00	1.11163
$112$	0	0
$113$	−1902.00	−1.58341	−0.791704	−	0.610905i	$-0.790806\pi$
$113$	−1902.00	−1.58341	−0.791704	+	0.610905i	$0.790806\pi$
$114$	0	0
$115$	952.000	0.771952
$116$	0	0
$117$	−1168.00	−0.922920
$118$	0	0
$119$	−756.000	−0.582373
$120$	0	0
$121$	121.000	0.0909091
$122$	0	0
$123$	2040.00	1.49545
$124$	0	0
$125$	756.000	0.540950
$126$	0	0
$127$	−64.0000	−0.0447172	−0.0223586	−	0.999750i	$-0.507118\pi$
$127$	−64.0000	−0.0447172	−0.0223586	+	0.999750i	$0.507118\pi$
$128$	0	0
$129$	3960.00	2.70278
$130$	0	0
$131$	1584.00	1.05645	0.528224	−	0.849105i	$-0.322858\pi$
$131$	1584.00	1.05645	0.528224	+	0.849105i	$0.322858\pi$
$132$	0	0
$133$	812.000	0.529393
$134$	0	0
$135$	−6440.00	−4.10568
$136$	0	0
$137$	998.000	0.622371	0.311186	−	0.950349i	$-0.399274\pi$
$137$	998.000	0.622371	0.311186	+	0.950349i	$0.399274\pi$
$138$	0	0
$139$	−276.000	−0.168417	−0.0842087	−	0.996448i	$-0.526836\pi$
$139$	−276.000	−0.168417	−0.0842087	+	0.996448i	$0.526836\pi$
$140$	0	0
$141$	−1660.00	−0.991470
$142$	0	0
$143$	−176.000	−0.102922
$144$	0	0
$145$	−1708.00	−0.978218
$146$	0	0
$147$	490.000	0.274929
$148$	0	0
$149$	1318.00	0.724663	0.362331	−	0.932049i	$-0.381981\pi$
$149$	1318.00	0.724663	0.362331	+	0.932049i	$0.381981\pi$
$150$	0	0
$151$	984.000	0.530310	0.265155	−	0.964206i	$-0.414577\pi$
$151$	984.000	0.530310	0.265155	+	0.964206i	$0.414577\pi$
$152$	0	0
$153$	7884.00	4.16591
$154$	0	0
$155$	−3668.00	−1.90078
$156$	0	0
$157$	1706.00	0.867221	0.433610	−	0.901101i	$-0.357239\pi$
$157$	1706.00	0.867221	0.433610	+	0.901101i	$0.357239\pi$
$158$	0	0
$159$	4420.00	2.20458
$160$	0	0
$161$	476.000	0.233007
$162$	0	0
$163$	−1168.00	−0.561257	−0.280628	−	0.959817i	$-0.590543\pi$
$163$	−1168.00	−0.561257	−0.280628	+	0.959817i	$0.590543\pi$
$164$	0	0
$165$	−1540.00	−0.726599
$166$	0	0
$167$	−72.0000	−0.0333624	−0.0166812	−	0.999861i	$-0.505310\pi$
$167$	−72.0000	−0.0333624	−0.0166812	+	0.999861i	$0.505310\pi$
$168$	0	0
$169$	−1941.00	−0.883477
$170$	0	0
$171$	−8468.00	−3.78692
$172$	0	0
$173$	−4328.00	−1.90203	−0.951017	−	0.309140i	$-0.899959\pi$
$173$	−4328.00	−1.90203	−0.951017	+	0.309140i	$0.899959\pi$
$174$	0	0
$175$	−497.000	−0.214684
$176$	0	0
$177$	−7020.00	−2.98110
$178$	0	0
$179$	1924.00	0.803388	0.401694	−	0.915774i	$-0.368421\pi$
$179$	1924.00	0.803388	0.401694	+	0.915774i	$0.368421\pi$
$180$	0	0
$181$	2230.00	0.915771	0.457886	−	0.889011i	$-0.348607\pi$
$181$	2230.00	0.915771	0.457886	+	0.889011i	$0.348607\pi$
$182$	0	0
$183$	1960.00	0.791734
$184$	0	0
$185$	−1820.00	−0.723292
$186$	0	0
$187$	1188.00	0.464573
$188$	0	0
$189$	−3220.00	−1.23926
$190$	0	0
$191$	−2176.00	−0.824345	−0.412172	−	0.911106i	$-0.635230\pi$
$191$	−2176.00	−0.824345	−0.412172	+	0.911106i	$0.635230\pi$
$192$	0	0
$193$	−3126.00	−1.16588	−0.582939	−	0.812516i	$-0.698097\pi$
$193$	−3126.00	−1.16588	−0.582939	+	0.812516i	$0.698097\pi$
$194$	0	0
$195$	2240.00	0.822614
$196$	0	0
$197$	−1122.00	−0.405783	−0.202891	−	0.979201i	$-0.565034\pi$
$197$	−1122.00	−0.405783	−0.202891	+	0.979201i	$0.565034\pi$
$198$	0	0
$199$	5586.00	1.98985	0.994927	−	0.100597i	$-0.0320753\pi$
$199$	5586.00	1.98985	0.994927	+	0.100597i	$0.0320753\pi$
$200$	0	0
$201$	4160.00	1.45982
$202$	0	0
$203$	−854.000	−0.295266
$204$	0	0
$205$	−2856.00	−0.973033
$206$	0	0
$207$	−4964.00	−1.66677
$208$	0	0
$209$	−1276.00	−0.422310
$210$	0	0
$211$	−3372.00	−1.10018	−0.550090	−	0.835105i	$-0.685407\pi$
$211$	−3372.00	−1.10018	−0.550090	+	0.835105i	$0.685407\pi$
$212$	0	0
$213$	−4920.00	−1.58269
$214$	0	0
$215$	−5544.00	−1.75859
$216$	0	0
$217$	−1834.00	−0.573733
$218$	0	0
$219$	4080.00	1.25891
$220$	0	0
$221$	−1728.00	−0.525963
$222$	0	0
$223$	−606.000	−0.181977	−0.0909883	−	0.995852i	$-0.529003\pi$
$223$	−606.000	−0.181977	−0.0909883	+	0.995852i	$0.529003\pi$
$224$	0	0
$225$	5183.00	1.53570
$226$	0	0
$227$	−144.000	−0.0421040	−0.0210520	−	0.999778i	$-0.506702\pi$
$227$	−144.000	−0.0421040	−0.0210520	+	0.999778i	$0.506702\pi$
$228$	0	0
$229$	−1010.00	−0.291453	−0.145726	−	0.989325i	$-0.546552\pi$
$229$	−1010.00	−0.291453	−0.145726	+	0.989325i	$0.546552\pi$
$230$	0	0
$231$	−770.000	−0.219317
$232$	0	0
$233$	3790.00	1.06563	0.532814	−	0.846233i	$-0.321135\pi$
$233$	3790.00	1.06563	0.532814	+	0.846233i	$0.321135\pi$
$234$	0	0
$235$	2324.00	0.645111
$236$	0	0
$237$	−6000.00	−1.64448
$238$	0	0
$239$	−2184.00	−0.591093	−0.295546	−	0.955328i	$-0.595502\pi$
$239$	−2184.00	−0.591093	−0.295546	+	0.955328i	$0.595502\pi$
$240$	0	0
$241$	−4268.00	−1.14077	−0.570386	−	0.821377i	$-0.693206\pi$
$241$	−4268.00	−1.14077	−0.570386	+	0.821377i	$0.693206\pi$
$242$	0	0
$243$	13870.0	3.66157
$244$	0	0
$245$	−686.000	−0.178885
$246$	0	0
$247$	1856.00	0.478115
$248$	0	0
$249$	12120.0	3.08463
$250$	0	0
$251$	−7922.00	−1.99216	−0.996080	−	0.0884559i	$-0.971807\pi$
$251$	−7922.00	−1.99216	−0.996080	+	0.0884559i	$0.971807\pi$
$252$	0	0
$253$	−748.000	−0.185875
$254$	0	0
$255$	−15120.0	−3.71314
$256$	0	0
$257$	4002.00	0.971354	0.485677	−	0.874138i	$-0.338573\pi$
$257$	4002.00	0.971354	0.485677	+	0.874138i	$0.338573\pi$
$258$	0	0
$259$	−910.000	−0.218319
$260$	0	0
$261$	8906.00	2.11214
$262$	0	0
$263$	3960.00	0.928457	0.464228	−	0.885716i	$-0.346332\pi$
$263$	3960.00	0.928457	0.464228	+	0.885716i	$0.346332\pi$
$264$	0	0
$265$	−6188.00	−1.43444
$266$	0	0
$267$	11460.0	2.62674
$268$	0	0
$269$	1878.00	0.425664	0.212832	−	0.977089i	$-0.431731\pi$
$269$	1878.00	0.425664	0.212832	+	0.977089i	$0.431731\pi$
$270$	0	0
$271$	4740.00	1.06249	0.531244	−	0.847219i	$-0.321725\pi$
$271$	4740.00	1.06249	0.531244	+	0.847219i	$0.321725\pi$
$272$	0	0
$273$	1120.00	0.248298
$274$	0	0
$275$	781.000	0.171258
$276$	0	0
$277$	710.000	0.154006	0.0770032	−	0.997031i	$-0.475465\pi$
$277$	710.000	0.154006	0.0770032	+	0.997031i	$0.475465\pi$
$278$	0	0
$279$	19126.0	4.10410
$280$	0	0
$281$	−90.0000	−0.0191066	−0.00955329	−	0.999954i	$-0.503041\pi$
$281$	−90.0000	−0.0191066	−0.00955329	+	0.999954i	$0.503041\pi$
$282$	0	0
$283$	3448.00	0.724248	0.362124	−	0.932130i	$-0.382052\pi$
$283$	3448.00	0.724248	0.362124	+	0.932130i	$0.382052\pi$
$284$	0	0
$285$	16240.0	3.37535
$286$	0	0
$287$	−1428.00	−0.293701
$288$	0	0
$289$	6751.00	1.37411
$290$	0	0
$291$	−4820.00	−0.970974
$292$	0	0
$293$	−2804.00	−0.559083	−0.279542	−	0.960134i	$-0.590183\pi$
$293$	−2804.00	−0.559083	−0.279542	+	0.960134i	$0.590183\pi$
$294$	0	0
$295$	9828.00	1.93969
$296$	0	0
$297$	5060.00	0.988589
$298$	0	0
$299$	1088.00	0.210437
$300$	0	0
$301$	−2772.00	−0.530815
$302$	0	0
$303$	12160.0	2.30552
$304$	0	0
$305$	−2744.00	−0.515151
$306$	0	0
$307$	−1320.00	−0.245395	−0.122698	−	0.992444i	$-0.539155\pi$
$307$	−1320.00	−0.245395	−0.122698	+	0.992444i	$0.539155\pi$
$308$	0	0
$309$	−14060.0	−2.58850
$310$	0	0
$311$	1066.00	0.194364	0.0971822	−	0.995267i	$-0.469017\pi$
$311$	1066.00	0.194364	0.0971822	+	0.995267i	$0.469017\pi$
$312$	0	0
$313$	−9254.00	−1.67114	−0.835570	−	0.549384i	$-0.814863\pi$
$313$	−9254.00	−1.67114	−0.835570	+	0.549384i	$0.814863\pi$
$314$	0	0
$315$	7154.00	1.27963
$316$	0	0
$317$	−9722.00	−1.72253	−0.861265	−	0.508156i	$-0.830327\pi$
$317$	−9722.00	−1.72253	−0.861265	+	0.508156i	$0.830327\pi$
$318$	0	0
$319$	1342.00	0.235541
$320$	0	0
$321$	5880.00	1.02240
$322$	0	0
$323$	−12528.0	−2.15813
$324$	0	0
$325$	−1136.00	−0.193889
$326$	0	0
$327$	1540.00	0.260435
$328$	0	0
$329$	1162.00	0.194721
$330$	0	0
$331$	−2620.00	−0.435070	−0.217535	−	0.976053i	$-0.569802\pi$
$331$	−2620.00	−0.435070	−0.217535	+	0.976053i	$0.569802\pi$
$332$	0	0
$333$	9490.00	1.56171
$334$	0	0
$335$	−5824.00	−0.949848
$336$	0	0
$337$	2806.00	0.453568	0.226784	−	0.973945i	$-0.427179\pi$
$337$	2806.00	0.453568	0.226784	+	0.973945i	$0.427179\pi$
$338$	0	0
$339$	−19020.0	−3.04727
$340$	0	0
$341$	2882.00	0.457680
$342$	0	0
$343$	−343.000	−0.0539949
$344$	0	0
$345$	9520.00	1.48562
$346$	0	0
$347$	−5564.00	−0.860781	−0.430391	−	0.902643i	$-0.641624\pi$
$347$	−5564.00	−0.860781	−0.430391	+	0.902643i	$0.641624\pi$
$348$	0	0
$349$	10060.0	1.54298	0.771489	−	0.636242i	$-0.219512\pi$
$349$	10060.0	1.54298	0.771489	+	0.636242i	$0.219512\pi$
$350$	0	0
$351$	−7360.00	−1.11922
$352$	0	0
$353$	−5102.00	−0.769269	−0.384635	−	0.923069i	$-0.625673\pi$
$353$	−5102.00	−0.769269	−0.384635	+	0.923069i	$0.625673\pi$
$354$	0	0
$355$	6888.00	1.02979
$356$	0	0
$357$	−7560.00	−1.12078
$358$	0	0
$359$	−7976.00	−1.17258	−0.586291	−	0.810100i	$-0.699413\pi$
$359$	−7976.00	−1.17258	−0.586291	+	0.810100i	$0.699413\pi$
$360$	0	0
$361$	6597.00	0.961802
$362$	0	0
$363$	1210.00	0.174955
$364$	0	0
$365$	−5712.00	−0.819123
$366$	0	0
$367$	1234.00	0.175516	0.0877579	−	0.996142i	$-0.472030\pi$
$367$	1234.00	0.175516	0.0877579	+	0.996142i	$0.472030\pi$
$368$	0	0
$369$	14892.0	2.10094
$370$	0	0
$371$	−3094.00	−0.432972
$372$	0	0
$373$	8030.00	1.11469	0.557343	−	0.830283i	$-0.311821\pi$
$373$	8030.00	1.11469	0.557343	+	0.830283i	$0.311821\pi$
$374$	0	0
$375$	7560.00	1.04106
$376$	0	0
$377$	−1952.00	−0.266666
$378$	0	0
$379$	5184.00	0.702597	0.351298	−	0.936264i	$-0.385740\pi$
$379$	5184.00	0.702597	0.351298	+	0.936264i	$0.385740\pi$
$380$	0	0
$381$	−640.000	−0.0860583
$382$	0	0
$383$	−7570.00	−1.00994	−0.504972	−	0.863135i	$-0.668497\pi$
$383$	−7570.00	−1.00994	−0.504972	+	0.863135i	$0.668497\pi$
$384$	0	0
$385$	1078.00	0.142701
$386$	0	0
$387$	28908.0	3.79710
$388$	0	0
$389$	−5370.00	−0.699922	−0.349961	−	0.936764i	$-0.613805\pi$
$389$	−5370.00	−0.699922	−0.349961	+	0.936764i	$0.613805\pi$
$390$	0	0
$391$	−7344.00	−0.949877
$392$	0	0
$393$	15840.0	2.03314
$394$	0	0
$395$	8400.00	1.07000
$396$	0	0
$397$	11442.0	1.44649	0.723246	−	0.690590i	$-0.242649\pi$
$397$	11442.0	1.44649	0.723246	+	0.690590i	$0.242649\pi$
$398$	0	0
$399$	8120.00	1.01882
$400$	0	0
$401$	2362.00	0.294146	0.147073	−	0.989126i	$-0.453015\pi$
$401$	2362.00	0.294146	0.147073	+	0.989126i	$0.453015\pi$
$402$	0	0
$403$	−4192.00	−0.518160
$404$	0	0
$405$	−36806.0	−4.51581
$406$	0	0
$407$	1430.00	0.174158
$408$	0	0
$409$	−16.0000	−0.00193435	−0.000967175	−	1.00000i	$-0.500308\pi$
$409$	−16.0000	−0.00193435	−0.000967175		1.00000i	$0.500308\pi$
$410$	0	0
$411$	9980.00	1.19775
$412$	0	0
$413$	4914.00	0.585477
$414$	0	0
$415$	−16968.0	−2.00705
$416$	0	0
$417$	−2760.00	−0.324119
$418$	0	0
$419$	−9462.00	−1.10322	−0.551610	−	0.834102i	$-0.685986\pi$
$419$	−9462.00	−1.10322	−0.551610	+	0.834102i	$0.685986\pi$
$420$	0	0
$421$	−6302.00	−0.729550	−0.364775	−	0.931096i	$-0.618854\pi$
$421$	−6302.00	−0.729550	−0.364775	+	0.931096i	$0.618854\pi$
$422$	0	0
$423$	−12118.0	−1.39290
$424$	0	0
$425$	7668.00	0.875183
$426$	0	0
$427$	−1372.00	−0.155494
$428$	0	0
$429$	−1760.00	−0.198074
$430$	0	0
$431$	−7816.00	−0.873512	−0.436756	−	0.899580i	$-0.643873\pi$
$431$	−7816.00	−0.873512	−0.436756	+	0.899580i	$0.643873\pi$
$432$	0	0
$433$	−9506.00	−1.05503	−0.527516	−	0.849545i	$-0.676877\pi$
$433$	−9506.00	−1.05503	−0.527516	+	0.849545i	$0.676877\pi$
$434$	0	0
$435$	−17080.0	−1.88258
$436$	0	0
$437$	7888.00	0.863465
$438$	0	0
$439$	8228.00	0.894535	0.447268	−	0.894400i	$-0.352397\pi$
$439$	8228.00	0.894535	0.447268	+	0.894400i	$0.352397\pi$
$440$	0	0
$441$	3577.00	0.386243
$442$	0	0
$443$	−7668.00	−0.822388	−0.411194	−	0.911548i	$-0.634888\pi$
$443$	−7668.00	−0.822388	−0.411194	+	0.911548i	$0.634888\pi$
$444$	0	0
$445$	−16044.0	−1.70912
$446$	0	0
$447$	13180.0	1.39461
$448$	0	0
$449$	−922.000	−0.0969084	−0.0484542	−	0.998825i	$-0.515429\pi$
$449$	−922.000	−0.0969084	−0.0484542	+	0.998825i	$0.515429\pi$
$450$	0	0
$451$	2244.00	0.234292
$452$	0	0
$453$	9840.00	1.02058
$454$	0	0
$455$	−1568.00	−0.161558
$456$	0	0
$457$	3386.00	0.346587	0.173294	−	0.984870i	$-0.444559\pi$
$457$	3386.00	0.346587	0.173294	+	0.984870i	$0.444559\pi$
$458$	0	0
$459$	49680.0	5.05199
$460$	0	0
$461$	−3300.00	−0.333398	−0.166699	−	0.986008i	$-0.553311\pi$
$461$	−3300.00	−0.333398	−0.166699	+	0.986008i	$0.553311\pi$
$462$	0	0
$463$	−14236.0	−1.42895	−0.714474	−	0.699662i	$-0.753334\pi$
$463$	−14236.0	−1.42895	−0.714474	+	0.699662i	$0.753334\pi$
$464$	0	0
$465$	−36680.0	−3.65805
$466$	0	0
$467$	−3770.00	−0.373565	−0.186782	−	0.982401i	$-0.559806\pi$
$467$	−3770.00	−0.373565	−0.186782	+	0.982401i	$0.559806\pi$
$468$	0	0
$469$	−2912.00	−0.286703
$470$	0	0
$471$	17060.0	1.66897
$472$	0	0
$473$	4356.00	0.423444
$474$	0	0
$475$	−8236.00	−0.795565
$476$	0	0
$477$	32266.0	3.09719
$478$	0	0
$479$	−17796.0	−1.69754	−0.848768	−	0.528765i	$-0.822655\pi$
$479$	−17796.0	−1.69754	−0.848768	+	0.528765i	$0.822655\pi$
$480$	0	0
$481$	−2080.00	−0.197172
$482$	0	0
$483$	4760.00	0.448421
$484$	0	0
$485$	6748.00	0.631775
$486$	0	0
$487$	3684.00	0.342788	0.171394	−	0.985203i	$-0.445173\pi$
$487$	3684.00	0.342788	0.171394	+	0.985203i	$0.445173\pi$
$488$	0	0
$489$	−11680.0	−1.08014
$490$	0	0
$491$	17236.0	1.58422	0.792108	−	0.610381i	$-0.208984\pi$
$491$	17236.0	1.58422	0.792108	+	0.610381i	$0.208984\pi$
$492$	0	0
$493$	13176.0	1.20369
$494$	0	0
$495$	−11242.0	−1.02079
$496$	0	0
$497$	3444.00	0.310834
$498$	0	0
$499$	−13176.0	−1.18204	−0.591021	−	0.806656i	$-0.701275\pi$
$499$	−13176.0	−1.18204	−0.591021	+	0.806656i	$0.701275\pi$
$500$	0	0
$501$	−720.000	−0.0642060
$502$	0	0
$503$	−15428.0	−1.36760	−0.683798	−	0.729672i	$-0.739673\pi$
$503$	−15428.0	−1.36760	−0.683798	+	0.729672i	$0.739673\pi$
$504$	0	0
$505$	−17024.0	−1.50011
$506$	0	0
$507$	−19410.0	−1.70025
$508$	0	0
$509$	−7842.00	−0.682889	−0.341445	−	0.939902i	$-0.610916\pi$
$509$	−7842.00	−0.682889	−0.341445	+	0.939902i	$0.610916\pi$
$510$	0	0
$511$	−2856.00	−0.247245
$512$	0	0
$513$	−53360.0	−4.59240
$514$	0	0
$515$	19684.0	1.68423
$516$	0	0
$517$	−1826.00	−0.155333
$518$	0	0
$519$	−43280.0	−3.66046
$520$	0	0
$521$	−17250.0	−1.45055	−0.725275	−	0.688460i	$-0.758287\pi$
$521$	−17250.0	−1.45055	−0.725275	+	0.688460i	$0.758287\pi$
$522$	0	0
$523$	−1032.00	−0.0862834	−0.0431417	−	0.999069i	$-0.513737\pi$
$523$	−1032.00	−0.0862834	−0.0431417	+	0.999069i	$0.513737\pi$
$524$	0	0
$525$	−4970.00	−0.413159
$526$	0	0
$527$	28296.0	2.33889
$528$	0	0
$529$	−7543.00	−0.619956
$530$	0	0
$531$	−51246.0	−4.18811
$532$	0	0
$533$	−3264.00	−0.265252
$534$	0	0
$535$	−8232.00	−0.665234
$536$	0	0
$537$	19240.0	1.54612
$538$	0	0
$539$	539.000	0.0430730
$540$	0	0
$541$	94.0000	0.00747020	0.00373510	−	0.999993i	$-0.498811\pi$
$541$	94.0000	0.00747020	0.00373510	+	0.999993i	$0.498811\pi$
$542$	0	0
$543$	22300.0	1.76240
$544$	0	0
$545$	−2156.00	−0.169455
$546$	0	0
$547$	11676.0	0.912669	0.456334	−	0.889808i	$-0.349162\pi$
$547$	11676.0	0.912669	0.456334	+	0.889808i	$0.349162\pi$
$548$	0	0
$549$	14308.0	1.11230
$550$	0	0
$551$	−14152.0	−1.09418
$552$	0	0
$553$	4200.00	0.322970
$554$	0	0
$555$	−18200.0	−1.39198
$556$	0	0
$557$	−1858.00	−0.141339	−0.0706696	−	0.997500i	$-0.522514\pi$
$557$	−1858.00	−0.141339	−0.0706696	+	0.997500i	$0.522514\pi$
$558$	0	0
$559$	−6336.00	−0.479399
$560$	0	0
$561$	11880.0	0.894071
$562$	0	0
$563$	23028.0	1.72383	0.861913	−	0.507056i	$-0.169266\pi$
$563$	23028.0	1.72383	0.861913	+	0.507056i	$0.169266\pi$
$564$	0	0
$565$	26628.0	1.98274
$566$	0	0
$567$	−18403.0	−1.36306
$568$	0	0
$569$	−17066.0	−1.25737	−0.628685	−	0.777660i	$-0.716407\pi$
$569$	−17066.0	−1.25737	−0.628685	+	0.777660i	$0.716407\pi$
$570$	0	0
$571$	10252.0	0.751371	0.375686	−	0.926747i	$-0.377407\pi$
$571$	10252.0	0.751371	0.375686	+	0.926747i	$0.377407\pi$
$572$	0	0
$573$	−21760.0	−1.58645
$574$	0	0
$575$	−4828.00	−0.350159
$576$	0	0
$577$	2142.00	0.154545	0.0772726	−	0.997010i	$-0.475379\pi$
$577$	2142.00	0.154545	0.0772726	+	0.997010i	$0.475379\pi$
$578$	0	0
$579$	−31260.0	−2.24373
$580$	0	0
$581$	−8484.00	−0.605810
$582$	0	0
$583$	4862.00	0.345392
$584$	0	0
$585$	16352.0	1.15568
$586$	0	0
$587$	−3474.00	−0.244271	−0.122136	−	0.992513i	$-0.538974\pi$
$587$	−3474.00	−0.244271	−0.122136	+	0.992513i	$0.538974\pi$
$588$	0	0
$589$	−30392.0	−2.12611
$590$	0	0
$591$	−11220.0	−0.780929
$592$	0	0
$593$	−17424.0	−1.20661	−0.603303	−	0.797512i	$-0.706149\pi$
$593$	−17424.0	−1.20661	−0.603303	+	0.797512i	$0.706149\pi$
$594$	0	0
$595$	10584.0	0.729247
$596$	0	0
$597$	55860.0	3.82948
$598$	0	0
$599$	−6916.00	−0.471753	−0.235877	−	0.971783i	$-0.575796\pi$
$599$	−6916.00	−0.471753	−0.235877	+	0.971783i	$0.575796\pi$
$600$	0	0
$601$	16468.0	1.11771	0.558855	−	0.829265i	$-0.311241\pi$
$601$	16468.0	1.11771	0.558855	+	0.829265i	$0.311241\pi$
$602$	0	0
$603$	30368.0	2.05088
$604$	0	0
$605$	−1694.00	−0.113836
$606$	0	0
$607$	17176.0	1.14852	0.574261	−	0.818673i	$-0.305290\pi$
$607$	17176.0	1.14852	0.574261	+	0.818673i	$0.305290\pi$
$608$	0	0
$609$	−8540.00	−0.568240
$610$	0	0
$611$	2656.00	0.175860
$612$	0	0
$613$	11402.0	0.751260	0.375630	−	0.926770i	$-0.377426\pi$
$613$	11402.0	0.751260	0.375630	+	0.926770i	$0.377426\pi$
$614$	0	0
$615$	−28560.0	−1.87260
$616$	0	0
$617$	3654.00	0.238419	0.119209	−	0.992869i	$-0.461964\pi$
$617$	3654.00	0.238419	0.119209	+	0.992869i	$0.461964\pi$
$618$	0	0
$619$	11318.0	0.734909	0.367455	−	0.930041i	$-0.380229\pi$
$619$	11318.0	0.734909	0.367455	+	0.930041i	$0.380229\pi$
$620$	0	0
$621$	−31280.0	−2.02129
$622$	0	0
$623$	−8022.00	−0.515882
$624$	0	0
$625$	−19459.0	−1.24538
$626$	0	0
$627$	−12760.0	−0.812736
$628$	0	0
$629$	14040.0	0.890002
$630$	0	0
$631$	23872.0	1.50607	0.753034	−	0.657981i	$-0.228589\pi$
$631$	23872.0	1.50607	0.753034	+	0.657981i	$0.228589\pi$
$632$	0	0
$633$	−33720.0	−2.11730
$634$	0	0
$635$	896.000	0.0559948
$636$	0	0
$637$	−784.000	−0.0487649
$638$	0	0
$639$	−35916.0	−2.22350
$640$	0	0
$641$	−27026.0	−1.66531	−0.832654	−	0.553793i	$-0.813180\pi$
$641$	−27026.0	−1.66531	−0.832654	+	0.553793i	$0.813180\pi$
$642$	0	0
$643$	−6498.00	−0.398532	−0.199266	−	0.979945i	$-0.563856\pi$
$643$	−6498.00	−0.398532	−0.199266	+	0.979945i	$0.563856\pi$
$644$	0	0
$645$	−55440.0	−3.38442
$646$	0	0
$647$	6422.00	0.390224	0.195112	−	0.980781i	$-0.437493\pi$
$647$	6422.00	0.390224	0.195112	+	0.980781i	$0.437493\pi$
$648$	0	0
$649$	−7722.00	−0.467049
$650$	0	0
$651$	−18340.0	−1.10415
$652$	0	0
$653$	23670.0	1.41850	0.709249	−	0.704958i	$-0.249034\pi$
$653$	23670.0	1.41850	0.709249	+	0.704958i	$0.249034\pi$
$654$	0	0
$655$	−22176.0	−1.32288
$656$	0	0
$657$	29784.0	1.76862
$658$	0	0
$659$	9812.00	0.580002	0.290001	−	0.957026i	$-0.406344\pi$
$659$	9812.00	0.580002	0.290001	+	0.957026i	$0.406344\pi$
$660$	0	0
$661$	−5190.00	−0.305397	−0.152699	−	0.988273i	$-0.548796\pi$
$661$	−5190.00	−0.305397	−0.152699	+	0.988273i	$0.548796\pi$
$662$	0	0
$663$	−17280.0	−1.01222
$664$	0	0
$665$	−11368.0	−0.662905
$666$	0	0
$667$	−8296.00	−0.481593
$668$	0	0
$669$	−6060.00	−0.350214
$670$	0	0
$671$	2156.00	0.124041
$672$	0	0
$673$	94.0000	0.00538400	0.00269200	−	0.999996i	$-0.499143\pi$
$673$	94.0000	0.00538400	0.00269200	+	0.999996i	$0.499143\pi$
$674$	0	0
$675$	32660.0	1.86235
$676$	0	0
$677$	−12432.0	−0.705762	−0.352881	−	0.935668i	$-0.614798\pi$
$677$	−12432.0	−0.705762	−0.352881	+	0.935668i	$0.614798\pi$
$678$	0	0
$679$	3374.00	0.190695
$680$	0	0
$681$	−1440.00	−0.0810293
$682$	0	0
$683$	2308.00	0.129302	0.0646509	−	0.997908i	$-0.479407\pi$
$683$	2308.00	0.129302	0.0646509	+	0.997908i	$0.479407\pi$
$684$	0	0
$685$	−13972.0	−0.779332
$686$	0	0
$687$	−10100.0	−0.560901
$688$	0	0
$689$	−7072.00	−0.391033
$690$	0	0
$691$	−26446.0	−1.45594	−0.727969	−	0.685610i	$-0.759536\pi$
$691$	−26446.0	−1.45594	−0.727969	+	0.685610i	$0.759536\pi$
$692$	0	0
$693$	−5621.00	−0.308116
$694$	0	0
$695$	3864.00	0.210892
$696$	0	0
$697$	22032.0	1.19730
$698$	0	0
$699$	37900.0	2.05080
$700$	0	0
$701$	26450.0	1.42511	0.712555	−	0.701616i	$-0.247538\pi$
$701$	26450.0	1.42511	0.712555	+	0.701616i	$0.247538\pi$
$702$	0	0
$703$	−15080.0	−0.809037
$704$	0	0
$705$	23240.0	1.24152
$706$	0	0
$707$	−8512.00	−0.452796
$708$	0	0
$709$	17102.0	0.905894	0.452947	−	0.891537i	$-0.350373\pi$
$709$	17102.0	0.905894	0.452947	+	0.891537i	$0.350373\pi$
$710$	0	0
$711$	−43800.0	−2.31031
$712$	0	0
$713$	−17816.0	−0.935785
$714$	0	0
$715$	2464.00	0.128879
$716$	0	0
$717$	−21840.0	−1.13756
$718$	0	0
$719$	16854.0	0.874198	0.437099	−	0.899413i	$-0.356006\pi$
$719$	16854.0	0.874198	0.437099	+	0.899413i	$0.356006\pi$
$720$	0	0
$721$	9842.00	0.508371
$722$	0	0
$723$	−42680.0	−2.19542
$724$	0	0
$725$	8662.00	0.443722
$726$	0	0
$727$	34670.0	1.76869	0.884346	−	0.466832i	$-0.154605\pi$
$727$	34670.0	1.76869	0.884346	+	0.466832i	$0.154605\pi$
$728$	0	0
$729$	67717.0	3.44038
$730$	0	0
$731$	42768.0	2.16393
$732$	0	0
$733$	11716.0	0.590369	0.295184	−	0.955440i	$-0.404619\pi$
$733$	11716.0	0.590369	0.295184	+	0.955440i	$0.404619\pi$
$734$	0	0
$735$	−6860.00	−0.344265
$736$	0	0
$737$	4576.00	0.228710
$738$	0	0
$739$	−29772.0	−1.48198	−0.740988	−	0.671518i	$-0.765643\pi$
$739$	−29772.0	−1.48198	−0.740988	+	0.671518i	$0.765643\pi$
$740$	0	0
$741$	18560.0	0.920133
$742$	0	0
$743$	24928.0	1.23085	0.615424	−	0.788196i	$-0.288985\pi$
$743$	24928.0	1.23085	0.615424	+	0.788196i	$0.288985\pi$
$744$	0	0
$745$	−18452.0	−0.907421
$746$	0	0
$747$	88476.0	4.33356
$748$	0	0
$749$	−4116.00	−0.200795
$750$	0	0
$751$	4652.00	0.226037	0.113019	−	0.993593i	$-0.463948\pi$
$751$	4652.00	0.226037	0.113019	+	0.993593i	$0.463948\pi$
$752$	0	0
$753$	−79220.0	−3.83391
$754$	0	0
$755$	−13776.0	−0.664053
$756$	0	0
$757$	−1802.00	−0.0865189	−0.0432594	−	0.999064i	$-0.513774\pi$
$757$	−1802.00	−0.0865189	−0.0432594	+	0.999064i	$0.513774\pi$
$758$	0	0
$759$	−7480.00	−0.357716
$760$	0	0
$761$	−808.000	−0.0384888	−0.0192444	−	0.999815i	$-0.506126\pi$
$761$	−808.000	−0.0384888	−0.0192444	+	0.999815i	$0.506126\pi$
$762$	0	0
$763$	−1078.00	−0.0511484
$764$	0	0
$765$	−110376.	−5.21654
$766$	0	0
$767$	11232.0	0.528767
$768$	0	0
$769$	23144.0	1.08530	0.542649	−	0.839960i	$-0.317421\pi$
$769$	23144.0	1.08530	0.542649	+	0.839960i	$0.317421\pi$
$770$	0	0
$771$	40020.0	1.86937
$772$	0	0
$773$	−27466.0	−1.27799	−0.638993	−	0.769212i	$-0.720649\pi$
$773$	−27466.0	−1.27799	−0.638993	+	0.769212i	$0.720649\pi$
$774$	0	0
$775$	18602.0	0.862198
$776$	0	0
$777$	−9100.00	−0.420155
$778$	0	0
$779$	−23664.0	−1.08838
$780$	0	0
$781$	−5412.00	−0.247960
$782$	0	0
$783$	56120.0	2.56139
$784$	0	0
$785$	−23884.0	−1.08593
$786$	0	0
$787$	−23604.0	−1.06911	−0.534556	−	0.845133i	$-0.679521\pi$
$787$	−23604.0	−1.06911	−0.534556	+	0.845133i	$0.679521\pi$
$788$	0	0
$789$	39600.0	1.78682
$790$	0	0
$791$	13314.0	0.598472
$792$	0	0
$793$	−3136.00	−0.140432
$794$	0	0
$795$	−61880.0	−2.76058
$796$	0	0
$797$	4122.00	0.183198	0.0915990	−	0.995796i	$-0.470802\pi$
$797$	4122.00	0.183198	0.0915990	+	0.995796i	$0.470802\pi$
$798$	0	0
$799$	−17928.0	−0.793801
$800$	0	0
$801$	83658.0	3.69027
$802$	0	0
$803$	4488.00	0.197233
$804$	0	0
$805$	−6664.00	−0.291770
$806$	0	0
$807$	18780.0	0.819191
$808$	0	0
$809$	−9110.00	−0.395909	−0.197955	−	0.980211i	$-0.563430\pi$
$809$	−9110.00	−0.395909	−0.197955	+	0.980211i	$0.563430\pi$
$810$	0	0
$811$	28352.0	1.22759	0.613794	−	0.789466i	$-0.289643\pi$
$811$	28352.0	1.22759	0.613794	+	0.789466i	$0.289643\pi$
$812$	0	0
$813$	47400.0	2.04476
$814$	0	0
$815$	16352.0	0.702804
$816$	0	0
$817$	−45936.0	−1.96707
$818$	0	0
$819$	8176.00	0.348831
$820$	0	0
$821$	−14002.0	−0.595217	−0.297609	−	0.954688i	$-0.596189\pi$
$821$	−14002.0	−0.595217	−0.297609	+	0.954688i	$0.596189\pi$
$822$	0	0
$823$	14848.0	0.628881	0.314440	−	0.949277i	$-0.398183\pi$
$823$	14848.0	0.628881	0.314440	+	0.949277i	$0.398183\pi$
$824$	0	0
$825$	7810.00	0.329587
$826$	0	0
$827$	−10500.0	−0.441500	−0.220750	−	0.975330i	$-0.570851\pi$
$827$	−10500.0	−0.441500	−0.220750	+	0.975330i	$0.570851\pi$
$828$	0	0
$829$	23890.0	1.00089	0.500443	−	0.865770i	$-0.333171\pi$
$829$	23890.0	1.00089	0.500443	+	0.865770i	$0.333171\pi$
$830$	0	0
$831$	7100.00	0.296385
$832$	0	0
$833$	5292.00	0.220116
$834$	0	0
$835$	1008.00	0.0417764
$836$	0	0
$837$	120520.	4.97704
$838$	0	0
$839$	670.000	0.0275697	0.0137848	−	0.999905i	$-0.495612\pi$
$839$	670.000	0.0275697	0.0137848	+	0.999905i	$0.495612\pi$
$840$	0	0
$841$	−9505.00	−0.389725
$842$	0	0
$843$	−900.000	−0.0367706
$844$	0	0
$845$	27174.0	1.10629
$846$	0	0
$847$	−847.000	−0.0343604
$848$	0	0
$849$	34480.0	1.39382
$850$	0	0
$851$	−8840.00	−0.356088
$852$	0	0
$853$	−4776.00	−0.191708	−0.0958541	−	0.995395i	$-0.530558\pi$
$853$	−4776.00	−0.191708	−0.0958541	+	0.995395i	$0.530558\pi$
$854$	0	0
$855$	118552.	4.74198
$856$	0	0
$857$	−13024.0	−0.519126	−0.259563	−	0.965726i	$-0.583579\pi$
$857$	−13024.0	−0.519126	−0.259563	+	0.965726i	$0.583579\pi$
$858$	0	0
$859$	32998.0	1.31068	0.655342	−	0.755332i	$-0.272525\pi$
$859$	32998.0	1.31068	0.655342	+	0.755332i	$0.272525\pi$
$860$	0	0
$861$	−14280.0	−0.565228
$862$	0	0
$863$	−22272.0	−0.878503	−0.439251	−	0.898364i	$-0.644756\pi$
$863$	−22272.0	−0.878503	−0.439251	+	0.898364i	$0.644756\pi$
$864$	0	0
$865$	60592.0	2.38172
$866$	0	0
$867$	67510.0	2.64447
$868$	0	0
$869$	−6600.00	−0.257641
$870$	0	0
$871$	−6656.00	−0.258932
$872$	0	0
$873$	−35186.0	−1.36411
$874$	0	0
$875$	−5292.00	−0.204460
$876$	0	0
$877$	−30398.0	−1.17043	−0.585215	−	0.810878i	$-0.698990\pi$
$877$	−30398.0	−1.17043	−0.585215	+	0.810878i	$0.698990\pi$
$878$	0	0
$879$	−28040.0	−1.07596
$880$	0	0
$881$	1630.00	0.0623338	0.0311669	−	0.999514i	$-0.490078\pi$
$881$	1630.00	0.0623338	0.0311669	+	0.999514i	$0.490078\pi$
$882$	0	0
$883$	20228.0	0.770925	0.385462	−	0.922724i	$-0.374042\pi$
$883$	20228.0	0.770925	0.385462	+	0.922724i	$0.374042\pi$
$884$	0	0
$885$	98280.0	3.73293
$886$	0	0
$887$	−38908.0	−1.47283	−0.736416	−	0.676528i	$-0.763484\pi$
$887$	−38908.0	−1.47283	−0.736416	+	0.676528i	$0.763484\pi$
$888$	0	0
$889$	448.000	0.0169015
$890$	0	0
$891$	28919.0	1.08734
$892$	0	0
$893$	19256.0	0.721587
$894$	0	0
$895$	−26936.0	−1.00600
$896$	0	0
$897$	10880.0	0.404986
$898$	0	0
$899$	31964.0	1.18583
$900$	0	0
$901$	47736.0	1.76506
$902$	0	0
$903$	−27720.0	−1.02155
$904$	0	0
$905$	−31220.0	−1.14673
$906$	0	0
$907$	20936.0	0.766448	0.383224	−	0.923655i	$-0.374814\pi$
$907$	20936.0	0.766448	0.383224	+	0.923655i	$0.374814\pi$
$908$	0	0
$909$	88768.0	3.23900
$910$	0	0
$911$	−48204.0	−1.75310	−0.876548	−	0.481315i	$-0.840159\pi$
$911$	−48204.0	−1.75310	−0.876548	+	0.481315i	$0.840159\pi$
$912$	0	0
$913$	13332.0	0.483269
$914$	0	0
$915$	−27440.0	−0.991408
$916$	0	0
$917$	−11088.0	−0.399300
$918$	0	0
$919$	27304.0	0.980061	0.490030	−	0.871705i	$-0.336986\pi$
$919$	27304.0	0.980061	0.490030	+	0.871705i	$0.336986\pi$
$920$	0	0
$921$	−13200.0	−0.472264
$922$	0	0
$923$	7872.00	0.280726
$924$	0	0
$925$	9230.00	0.328087
$926$	0	0
$927$	−102638.	−3.63654
$928$	0	0
$929$	30.0000	0.00105949	0.000529746	−	1.00000i	$-0.499831\pi$
$929$	30.0000	0.00105949	0.000529746		1.00000i	$0.499831\pi$
$930$	0	0
$931$	−5684.00	−0.200092
$932$	0	0
$933$	10660.0	0.374054
$934$	0	0
$935$	−16632.0	−0.581737
$936$	0	0
$937$	4736.00	0.165121	0.0825605	−	0.996586i	$-0.473690\pi$
$937$	4736.00	0.165121	0.0825605	+	0.996586i	$0.473690\pi$
$938$	0	0
$939$	−92540.0	−3.21611
$940$	0	0
$941$	19996.0	0.692722	0.346361	−	0.938101i	$-0.387417\pi$
$941$	19996.0	0.692722	0.346361	+	0.938101i	$0.387417\pi$
$942$	0	0
$943$	−13872.0	−0.479040
$944$	0	0
$945$	45080.0	1.55180
$946$	0	0
$947$	1252.00	0.0429615	0.0214807	−	0.999769i	$-0.493162\pi$
$947$	1252.00	0.0429615	0.0214807	+	0.999769i	$0.493162\pi$
$948$	0	0
$949$	−6528.00	−0.223296
$950$	0	0
$951$	−97220.0	−3.31501
$952$	0	0
$953$	17986.0	0.611357	0.305679	−	0.952135i	$-0.401117\pi$
$953$	17986.0	0.611357	0.305679	+	0.952135i	$0.401117\pi$
$954$	0	0
$955$	30464.0	1.03224
$956$	0	0
$957$	13420.0	0.453299
$958$	0	0
$959$	−6986.00	−0.235234
$960$	0	0
$961$	38853.0	1.30419
$962$	0	0
$963$	42924.0	1.43635
$964$	0	0
$965$	43764.0	1.45991
$966$	0	0
$967$	−14256.0	−0.474087	−0.237043	−	0.971499i	$-0.576178\pi$
$967$	−14256.0	−0.474087	−0.237043	+	0.971499i	$0.576178\pi$
$968$	0	0
$969$	−125280.	−4.15333
$970$	0	0
$971$	50214.0	1.65957	0.829786	−	0.558082i	$-0.188463\pi$
$971$	50214.0	1.65957	0.829786	+	0.558082i	$0.188463\pi$
$972$	0	0
$973$	1932.00	0.0636558
$974$	0	0
$975$	−11360.0	−0.373140
$976$	0	0
$977$	−35814.0	−1.17276	−0.586382	−	0.810034i	$-0.699448\pi$
$977$	−35814.0	−1.17276	−0.586382	+	0.810034i	$0.699448\pi$
$978$	0	0
$979$	12606.0	0.411532
$980$	0	0
$981$	11242.0	0.365881
$982$	0	0
$983$	19274.0	0.625377	0.312688	−	0.949856i	$-0.398770\pi$
$983$	19274.0	0.625377	0.312688	+	0.949856i	$0.398770\pi$
$984$	0	0
$985$	15708.0	0.508120
$986$	0	0
$987$	11620.0	0.374740
$988$	0	0
$989$	−26928.0	−0.865784
$990$	0	0
$991$	−59996.0	−1.92314	−0.961572	−	0.274553i	$-0.911470\pi$
$991$	−59996.0	−1.92314	−0.961572	+	0.274553i	$0.911470\pi$
$992$	0	0
$993$	−26200.0	−0.837293
$994$	0	0
$995$	−78204.0	−2.49169
$996$	0	0
$997$	24344.0	0.773302	0.386651	−	0.922226i	$-0.373632\pi$
$997$	24344.0	0.773302	0.386651	+	0.922226i	$0.373632\pi$
$998$	0	0
$999$	59800.0	1.89388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.4.a.i.1.1		1
4.3	odd	2		154.4.a.c.1.1	✓	1
12.11	even	2		1386.4.a.g.1.1		1
28.27	even	2		1078.4.a.h.1.1		1
44.43	even	2		1694.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.a.c.1.1	✓	1	4.3	odd	2
1078.4.a.h.1.1		1	28.27	even	2
1232.4.a.i.1.1		1	1.1	even	1	trivial
1386.4.a.g.1.1		1	12.11	even	2
1694.4.a.a.1.1		1	44.43	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1232.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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