LMFDB - Embedded newform 232.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,6,Mod(1,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("232.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	232.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:	$37.2090461966$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	232.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+16.0000 q^{3} +54.0000 q^{5} +112.000 q^{7} +13.0000 q^{9} +O(q^{10})$

$q+16.0000 q^{3} +54.0000 q^{5} +112.000 q^{7} +13.0000 q^{9} +472.000 q^{11} -290.000 q^{13} +864.000 q^{15} +738.000 q^{17} +1616.00 q^{19} +1792.00 q^{21} -1504.00 q^{23} -209.000 q^{25} -3680.00 q^{27} +841.000 q^{29} +5324.00 q^{31} +7552.00 q^{33} +6048.00 q^{35} -2650.00 q^{37} -4640.00 q^{39} -4470.00 q^{41} +2824.00 q^{43} +702.000 q^{45} +3028.00 q^{47} -4263.00 q^{49} +11808.0 q^{51} +5574.00 q^{53} +25488.0 q^{55} +25856.0 q^{57} -22764.0 q^{59} +654.000 q^{61} +1456.00 q^{63} -15660.0 q^{65} +54612.0 q^{67} -24064.0 q^{69} +5480.00 q^{71} +49370.0 q^{73} -3344.00 q^{75} +52864.0 q^{77} -8020.00 q^{79} -62039.0 q^{81} -17508.0 q^{83} +39852.0 q^{85} +13456.0 q^{87} +63114.0 q^{89} -32480.0 q^{91} +85184.0 q^{93} +87264.0 q^{95} -5614.00 q^{97} +6136.00 q^{99} +O(q^{100})$

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
$3$	16.0000	1.02640	0.513200	−	0.858269i	$-0.328460\pi$
$3$	16.0000	1.02640	0.513200	+	0.858269i	$0.328460\pi$
$4$	0	0
$5$	54.0000	0.965981	0.482991	−	0.875625i	$-0.339550\pi$
$5$	54.0000	0.965981	0.482991	+	0.875625i	$0.339550\pi$
$6$	0	0
$7$	112.000	0.863919	0.431959	−	0.901893i	$-0.357822\pi$
$7$	112.000	0.863919	0.431959	+	0.901893i	$0.357822\pi$
$8$	0	0
$9$	13.0000	0.0534979
$10$	0	0
$11$	472.000	1.17614	0.588072	−	0.808809i	$-0.299887\pi$
$11$	472.000	1.17614	0.588072	+	0.808809i	$0.299887\pi$
$12$	0	0
$13$	−290.000	−0.475926	−0.237963	−	0.971274i	$-0.576480\pi$
$13$	−290.000	−0.475926	−0.237963	+	0.971274i	$0.576480\pi$
$14$	0	0
$15$	864.000	0.991484
$16$	0	0
$17$	738.000	0.619347	0.309674	−	0.950843i	$-0.399780\pi$
$17$	738.000	0.619347	0.309674	+	0.950843i	$0.399780\pi$
$18$	0	0
$19$	1616.00	1.02697	0.513485	−	0.858099i	$-0.328354\pi$
$19$	1616.00	1.02697	0.513485	+	0.858099i	$0.328354\pi$
$20$	0	0
$21$	1792.00	0.886727
$22$	0	0
$23$	−1504.00	−0.592827	−0.296414	−	0.955060i	$-0.595791\pi$
$23$	−1504.00	−0.592827	−0.296414	+	0.955060i	$0.595791\pi$
$24$	0	0
$25$	−209.000	−0.0668800
$26$	0	0
$27$	−3680.00	−0.971490
$28$	0	0
$29$	841.000	0.185695
$29$	841.000	0.185695
$30$	0	0
$31$	5324.00	0.995025	0.497512	−	0.867457i	$-0.334247\pi$
$31$	5324.00	0.995025	0.497512	+	0.867457i	$0.334247\pi$
$32$	0	0
$33$	7552.00	1.20719
$34$	0	0
$35$	6048.00	0.834529
$36$	0	0
$37$	−2650.00	−0.318230	−0.159115	−	0.987260i	$-0.550864\pi$
$37$	−2650.00	−0.318230	−0.159115	+	0.987260i	$0.550864\pi$
$38$	0	0
$39$	−4640.00	−0.488491
$40$	0	0
$41$	−4470.00	−0.415287	−0.207643	−	0.978205i	$-0.566579\pi$
$41$	−4470.00	−0.415287	−0.207643	+	0.978205i	$0.566579\pi$
$42$	0	0
$43$	2824.00	0.232913	0.116456	−	0.993196i	$-0.462846\pi$
$43$	2824.00	0.232913	0.116456	+	0.993196i	$0.462846\pi$
$44$	0	0
$45$	702.000	0.0516780
$46$	0	0
$47$	3028.00	0.199945	0.0999727	−	0.994990i	$-0.468124\pi$
$47$	3028.00	0.199945	0.0999727	+	0.994990i	$0.468124\pi$
$48$	0	0
$49$	−4263.00	−0.253644
$50$	0	0
$51$	11808.0	0.635698
$52$	0	0
$53$	5574.00	0.272570	0.136285	−	0.990670i	$-0.456484\pi$
$53$	5574.00	0.272570	0.136285	+	0.990670i	$0.456484\pi$
$54$	0	0
$55$	25488.0	1.13613
$56$	0	0
$57$	25856.0	1.05408
$58$	0	0
$59$	−22764.0	−0.851370	−0.425685	−	0.904871i	$-0.639967\pi$
$59$	−22764.0	−0.851370	−0.425685	+	0.904871i	$0.639967\pi$
$60$	0	0
$61$	654.000	0.0225037	0.0112518	−	0.999937i	$-0.496418\pi$
$61$	654.000	0.0225037	0.0112518	+	0.999937i	$0.496418\pi$
$62$	0	0
$63$	1456.00	0.0462179
$64$	0	0
$65$	−15660.0	−0.459736
$66$	0	0
$67$	54612.0	1.48628	0.743141	−	0.669135i	$-0.233335\pi$
$67$	54612.0	1.48628	0.743141	+	0.669135i	$0.233335\pi$
$68$	0	0
$69$	−24064.0	−0.608478
$70$	0	0
$71$	5480.00	0.129013	0.0645067	−	0.997917i	$-0.479453\pi$
$71$	5480.00	0.129013	0.0645067	+	0.997917i	$0.479453\pi$
$72$	0	0
$73$	49370.0	1.08432	0.542158	−	0.840276i	$-0.317607\pi$
$73$	49370.0	1.08432	0.542158	+	0.840276i	$0.317607\pi$
$74$	0	0
$75$	−3344.00	−0.0686457
$76$	0	0
$77$	52864.0	1.01609
$78$	0	0
$79$	−8020.00	−0.144579	−0.0722897	−	0.997384i	$-0.523031\pi$
$79$	−8020.00	−0.144579	−0.0722897	+	0.997384i	$0.523031\pi$
$80$	0	0
$81$	−62039.0	−1.05064
$82$	0	0
$83$	−17508.0	−0.278960	−0.139480	−	0.990225i	$-0.544543\pi$
$83$	−17508.0	−0.278960	−0.139480	+	0.990225i	$0.544543\pi$
$84$	0	0
$85$	39852.0	0.598278
$86$	0	0
$87$	13456.0	0.190598
$88$	0	0
$89$	63114.0	0.844599	0.422300	−	0.906456i	$-0.361223\pi$
$89$	63114.0	0.844599	0.422300	+	0.906456i	$0.361223\pi$
$90$	0	0
$91$	−32480.0	−0.411162
$92$	0	0
$93$	85184.0	1.02129
$94$	0	0
$95$	87264.0	0.992033
$96$	0	0
$97$	−5614.00	−0.0605819	−0.0302910	−	0.999541i	$-0.509643\pi$
$97$	−5614.00	−0.0605819	−0.0302910	+	0.999541i	$0.509643\pi$
$98$	0	0
$99$	6136.00	0.0629213
$100$	0	0
$101$	85766.0	0.836588	0.418294	−	0.908312i	$-0.362628\pi$
$101$	85766.0	0.836588	0.418294	+	0.908312i	$0.362628\pi$
$102$	0	0
$103$	90880.0	0.844064	0.422032	−	0.906581i	$-0.361317\pi$
$103$	90880.0	0.844064	0.422032	+	0.906581i	$0.361317\pi$
$104$	0	0
$105$	96768.0	0.856561
$106$	0	0
$107$	−204492.	−1.72670	−0.863350	−	0.504606i	$-0.831638\pi$
$107$	−204492.	−1.72670	−0.863350	+	0.504606i	$0.831638\pi$
$108$	0	0
$109$	34974.0	0.281955	0.140977	−	0.990013i	$-0.454976\pi$
$109$	34974.0	0.281955	0.140977	+	0.990013i	$0.454976\pi$
$110$	0	0
$111$	−42400.0	−0.326632
$112$	0	0
$113$	248274.	1.82909	0.914545	−	0.404484i	$-0.132549\pi$
$113$	248274.	1.82909	0.914545	+	0.404484i	$0.132549\pi$
$114$	0	0
$115$	−81216.0	−0.572660
$116$	0	0
$117$	−3770.00	−0.0254611
$118$	0	0
$119$	82656.0	0.535066
$120$	0	0
$121$	61733.0	0.383313
$122$	0	0
$123$	−71520.0	−0.426250
$124$	0	0
$125$	−180036.	−1.03059
$126$	0	0
$127$	−263300.	−1.44858	−0.724288	−	0.689497i	$-0.757832\pi$
$127$	−263300.	−1.44858	−0.724288	+	0.689497i	$0.757832\pi$
$128$	0	0
$129$	45184.0	0.239062
$130$	0	0
$131$	−144136.	−0.733828	−0.366914	−	0.930255i	$-0.619586\pi$
$131$	−144136.	−0.733828	−0.366914	+	0.930255i	$0.619586\pi$
$132$	0	0
$133$	180992.	0.887218
$134$	0	0
$135$	−198720.	−0.938441
$136$	0	0
$137$	204074.	0.928937	0.464468	−	0.885590i	$-0.346245\pi$
$137$	204074.	0.928937	0.464468	+	0.885590i	$0.346245\pi$
$138$	0	0
$139$	−311148.	−1.36593	−0.682967	−	0.730449i	$-0.739311\pi$
$139$	−311148.	−1.36593	−0.682967	+	0.730449i	$0.739311\pi$
$140$	0	0
$141$	48448.0	0.205224
$142$	0	0
$143$	−136880.	−0.559757
$144$	0	0
$145$	45414.0	0.179378
$146$	0	0
$147$	−68208.0	−0.260341
$148$	0	0
$149$	−132282.	−0.488130	−0.244065	−	0.969759i	$-0.578481\pi$
$149$	−132282.	−0.488130	−0.244065	+	0.969759i	$0.578481\pi$
$150$	0	0
$151$	−139544.	−0.498045	−0.249023	−	0.968498i	$-0.580109\pi$
$151$	−139544.	−0.498045	−0.249023	+	0.968498i	$0.580109\pi$
$152$	0	0
$153$	9594.00	0.0331338
$154$	0	0
$155$	287496.	0.961175
$156$	0	0
$157$	−120722.	−0.390874	−0.195437	−	0.980716i	$-0.562613\pi$
$157$	−120722.	−0.390874	−0.195437	+	0.980716i	$0.562613\pi$
$158$	0	0
$159$	89184.0	0.279765
$160$	0	0
$161$	−168448.	−0.512155
$162$	0	0
$163$	−162344.	−0.478594	−0.239297	−	0.970946i	$-0.576917\pi$
$163$	−162344.	−0.478594	−0.239297	+	0.970946i	$0.576917\pi$
$164$	0	0
$165$	407808.	1.16613
$166$	0	0
$167$	−678744.	−1.88328	−0.941640	−	0.336622i	$-0.890716\pi$
$167$	−678744.	−1.88328	−0.941640	+	0.336622i	$0.890716\pi$
$168$	0	0
$169$	−287193.	−0.773494
$170$	0	0
$171$	21008.0	0.0549407
$172$	0	0
$173$	−473954.	−1.20398	−0.601992	−	0.798502i	$-0.705626\pi$
$173$	−473954.	−1.20398	−0.601992	+	0.798502i	$0.705626\pi$
$174$	0	0
$175$	−23408.0	−0.0577789
$176$	0	0
$177$	−364224.	−0.873847
$178$	0	0
$179$	−362908.	−0.846572	−0.423286	−	0.905996i	$-0.639123\pi$
$179$	−362908.	−0.846572	−0.423286	+	0.905996i	$0.639123\pi$
$180$	0	0
$181$	−506842.	−1.14994	−0.574971	−	0.818174i	$-0.694987\pi$
$181$	−506842.	−1.14994	−0.574971	+	0.818174i	$0.694987\pi$
$182$	0	0
$183$	10464.0	0.0230978
$184$	0	0
$185$	−143100.	−0.307405
$186$	0	0
$187$	348336.	0.728441
$188$	0	0
$189$	−412160.	−0.839289
$190$	0	0
$191$	−209828.	−0.416179	−0.208089	−	0.978110i	$-0.566725\pi$
$191$	−209828.	−0.416179	−0.208089	+	0.978110i	$0.566725\pi$
$192$	0	0
$193$	−291214.	−0.562755	−0.281377	−	0.959597i	$-0.590791\pi$
$193$	−291214.	−0.562755	−0.281377	+	0.959597i	$0.590791\pi$
$194$	0	0
$195$	−250560.	−0.471873
$196$	0	0
$197$	−438186.	−0.804439	−0.402219	−	0.915543i	$-0.631761\pi$
$197$	−438186.	−0.804439	−0.402219	+	0.915543i	$0.631761\pi$
$198$	0	0
$199$	642256.	1.14968	0.574838	−	0.818267i	$-0.305065\pi$
$199$	642256.	1.14968	0.574838	+	0.818267i	$0.305065\pi$
$200$	0	0
$201$	873792.	1.52552
$202$	0	0
$203$	94192.0	0.160426
$204$	0	0
$205$	−241380.	−0.401159
$206$	0	0
$207$	−19552.0	−0.0317150
$208$	0	0
$209$	762752.	1.20786
$210$	0	0
$211$	507400.	0.784593	0.392296	−	0.919839i	$-0.371681\pi$
$211$	507400.	0.784593	0.392296	+	0.919839i	$0.371681\pi$
$212$	0	0
$213$	87680.0	0.132419
$214$	0	0
$215$	152496.	0.224990
$216$	0	0
$217$	596288.	0.859620
$218$	0	0
$219$	789920.	1.11294
$220$	0	0
$221$	−214020.	−0.294763
$222$	0	0
$223$	−229288.	−0.308759	−0.154379	−	0.988012i	$-0.549338\pi$
$223$	−229288.	−0.308759	−0.154379	+	0.988012i	$0.549338\pi$
$224$	0	0
$225$	−2717.00	−0.00357794
$226$	0	0
$227$	−367092.	−0.472836	−0.236418	−	0.971651i	$-0.575973\pi$
$227$	−367092.	−0.472836	−0.236418	+	0.971651i	$0.575973\pi$
$228$	0	0
$229$	−371130.	−0.467668	−0.233834	−	0.972277i	$-0.575127\pi$
$229$	−371130.	−0.467668	−0.233834	+	0.972277i	$0.575127\pi$
$230$	0	0
$231$	845824.	1.04292
$232$	0	0
$233$	822346.	0.992350	0.496175	−	0.868223i	$-0.334737\pi$
$233$	822346.	0.992350	0.496175	+	0.868223i	$0.334737\pi$
$234$	0	0
$235$	163512.	0.193143
$236$	0	0
$237$	−128320.	−0.148396
$238$	0	0
$239$	−1.05420e6	−1.19379	−0.596895	−	0.802319i	$-0.703599\pi$
$239$	−1.05420e6	−1.19379	−0.596895	+	0.802319i	$0.703599\pi$
$240$	0	0
$241$	1.14799e6	1.27319	0.636596	−	0.771197i	$-0.280342\pi$
$241$	1.14799e6	1.27319	0.636596	+	0.771197i	$0.280342\pi$
$242$	0	0
$243$	−98384.0	−0.106883
$244$	0	0
$245$	−230202.	−0.245016
$246$	0	0
$247$	−468640.	−0.488761
$248$	0	0
$249$	−280128.	−0.286324
$250$	0	0
$251$	269848.	0.270355	0.135178	−	0.990821i	$-0.456839\pi$
$251$	269848.	0.270355	0.135178	+	0.990821i	$0.456839\pi$
$252$	0	0
$253$	−709888.	−0.697250
$254$	0	0
$255$	637632.	0.614073
$256$	0	0
$257$	1.36869e6	1.29262	0.646312	−	0.763073i	$-0.276310\pi$
$257$	1.36869e6	1.29262	0.646312	+	0.763073i	$0.276310\pi$
$258$	0	0
$259$	−296800.	−0.274925
$260$	0	0
$261$	10933.0	0.00993432
$262$	0	0
$263$	−1.36785e6	−1.21941	−0.609705	−	0.792628i	$-0.708712\pi$
$263$	−1.36785e6	−1.21941	−0.609705	+	0.792628i	$0.708712\pi$
$264$	0	0
$265$	300996.	0.263297
$266$	0	0
$267$	1.00982e6	0.866897
$268$	0	0
$269$	−343250.	−0.289221	−0.144611	−	0.989489i	$-0.546193\pi$
$269$	−343250.	−0.289221	−0.144611	+	0.989489i	$0.546193\pi$
$270$	0	0
$271$	−1.37643e6	−1.13849	−0.569246	−	0.822167i	$-0.692765\pi$
$271$	−1.37643e6	−1.13849	−0.569246	+	0.822167i	$0.692765\pi$
$272$	0	0
$273$	−519680.	−0.422016
$274$	0	0
$275$	−98648.0	−0.0786605
$276$	0	0
$277$	−1.15334e6	−0.903144	−0.451572	−	0.892235i	$-0.649137\pi$
$277$	−1.15334e6	−0.903144	−0.451572	+	0.892235i	$0.649137\pi$
$278$	0	0
$279$	69212.0	0.0532318
$280$	0	0
$281$	1.42022e6	1.07297	0.536487	−	0.843909i	$-0.319751\pi$
$281$	1.42022e6	1.07297	0.536487	+	0.843909i	$0.319751\pi$
$282$	0	0
$283$	1.24809e6	0.926362	0.463181	−	0.886264i	$-0.346708\pi$
$283$	1.24809e6	0.926362	0.463181	+	0.886264i	$0.346708\pi$
$284$	0	0
$285$	1.39622e6	1.01822
$286$	0	0
$287$	−500640.	−0.358774
$288$	0	0
$289$	−875213.	−0.616409
$290$	0	0
$291$	−89824.0	−0.0621813
$292$	0	0
$293$	586806.	0.399324	0.199662	−	0.979865i	$-0.436016\pi$
$293$	586806.	0.399324	0.199662	+	0.979865i	$0.436016\pi$
$294$	0	0
$295$	−1.22926e6	−0.822408
$296$	0	0
$297$	−1.73696e6	−1.14261
$298$	0	0
$299$	436160.	0.282142
$300$	0	0
$301$	316288.	0.201218
$302$	0	0
$303$	1.37226e6	0.858675
$304$	0	0
$305$	35316.0	0.0217381
$306$	0	0
$307$	1.38016e6	0.835764	0.417882	−	0.908501i	$-0.362773\pi$
$307$	1.38016e6	0.835764	0.417882	+	0.908501i	$0.362773\pi$
$308$	0	0
$309$	1.45408e6	0.866347
$310$	0	0
$311$	529620.	0.310501	0.155251	−	0.987875i	$-0.450381\pi$
$311$	529620.	0.310501	0.155251	+	0.987875i	$0.450381\pi$
$312$	0	0
$313$	−1.21679e6	−0.702029	−0.351014	−	0.936370i	$-0.614163\pi$
$313$	−1.21679e6	−0.702029	−0.351014	+	0.936370i	$0.614163\pi$
$314$	0	0
$315$	78624.0	0.0446456
$316$	0	0
$317$	899438.	0.502716	0.251358	−	0.967894i	$-0.419123\pi$
$317$	899438.	0.502716	0.251358	+	0.967894i	$0.419123\pi$
$318$	0	0
$319$	396952.	0.218404
$320$	0	0
$321$	−3.27187e6	−1.77229
$322$	0	0
$323$	1.19261e6	0.636050
$324$	0	0
$325$	60610.0	0.0318299
$326$	0	0
$327$	559584.	0.289398
$328$	0	0
$329$	339136.	0.172737
$330$	0	0
$331$	1.22888e6	0.616509	0.308255	−	0.951304i	$-0.400255\pi$
$331$	1.22888e6	0.616509	0.308255	+	0.951304i	$0.400255\pi$
$332$	0	0
$333$	−34450.0	−0.0170247
$334$	0	0
$335$	2.94905e6	1.43572
$336$	0	0
$337$	−2.49486e6	−1.19666	−0.598331	−	0.801249i	$-0.704169\pi$
$337$	−2.49486e6	−1.19666	−0.598331	+	0.801249i	$0.704169\pi$
$338$	0	0
$339$	3.97238e6	1.87738
$340$	0	0
$341$	2.51293e6	1.17029
$342$	0	0
$343$	−2.35984e6	−1.08305
$344$	0	0
$345$	−1.29946e6	−0.587779
$346$	0	0
$347$	4.07372e6	1.81622	0.908109	−	0.418734i	$-0.137526\pi$
$347$	4.07372e6	1.81622	0.908109	+	0.418734i	$0.137526\pi$
$348$	0	0
$349$	1.19473e6	0.525058	0.262529	−	0.964924i	$-0.415443\pi$
$349$	1.19473e6	0.525058	0.262529	+	0.964924i	$0.415443\pi$
$350$	0	0
$351$	1.06720e6	0.462358
$352$	0	0
$353$	1.63883e6	0.700000	0.350000	−	0.936750i	$-0.386182\pi$
$353$	1.63883e6	0.700000	0.350000	+	0.936750i	$0.386182\pi$
$354$	0	0
$355$	295920.	0.124625
$356$	0	0
$357$	1.32250e6	0.549192
$358$	0	0
$359$	−340988.	−0.139638	−0.0698189	−	0.997560i	$-0.522242\pi$
$359$	−340988.	−0.139638	−0.0698189	+	0.997560i	$0.522242\pi$
$360$	0	0
$361$	135357.	0.0546654
$362$	0	0
$363$	987728.	0.393433
$364$	0	0
$365$	2.66598e6	1.04743
$366$	0	0
$367$	1.37534e6	0.533022	0.266511	−	0.963832i	$-0.414129\pi$
$367$	1.37534e6	0.533022	0.266511	+	0.963832i	$0.414129\pi$
$368$	0	0
$369$	−58110.0	−0.0222170
$370$	0	0
$371$	624288.	0.235478
$372$	0	0
$373$	−197210.	−0.0733934	−0.0366967	−	0.999326i	$-0.511684\pi$
$373$	−197210.	−0.0733934	−0.0366967	+	0.999326i	$0.511684\pi$
$374$	0	0
$375$	−2.88058e6	−1.05779
$376$	0	0
$377$	−243890.	−0.0883773
$378$	0	0
$379$	−3.27500e6	−1.17115	−0.585576	−	0.810617i	$-0.699132\pi$
$379$	−3.27500e6	−1.17115	−0.585576	+	0.810617i	$0.699132\pi$
$380$	0	0
$381$	−4.21280e6	−1.48682
$382$	0	0
$383$	−3.10310e6	−1.08093	−0.540467	−	0.841365i	$-0.681753\pi$
$383$	−3.10310e6	−1.08093	−0.540467	+	0.841365i	$0.681753\pi$
$384$	0	0
$385$	2.85466e6	0.981526
$386$	0	0
$387$	36712.0	0.0124604
$388$	0	0
$389$	4.28837e6	1.43687	0.718437	−	0.695592i	$-0.244858\pi$
$389$	4.28837e6	1.43687	0.718437	+	0.695592i	$0.244858\pi$
$390$	0	0
$391$	−1.10995e6	−0.367166
$392$	0	0
$393$	−2.30618e6	−0.753201
$394$	0	0
$395$	−433080.	−0.139661
$396$	0	0
$397$	−4.22234e6	−1.34455	−0.672275	−	0.740302i	$-0.734683\pi$
$397$	−4.22234e6	−1.34455	−0.672275	+	0.740302i	$0.734683\pi$
$398$	0	0
$399$	2.89587e6	0.910641
$400$	0	0
$401$	−3.08657e6	−0.958552	−0.479276	−	0.877664i	$-0.659101\pi$
$401$	−3.08657e6	−0.958552	−0.479276	+	0.877664i	$0.659101\pi$
$402$	0	0
$403$	−1.54396e6	−0.473558
$404$	0	0
$405$	−3.35011e6	−1.01489
$406$	0	0
$407$	−1.25080e6	−0.374285
$408$	0	0
$409$	−624262.	−0.184526	−0.0922632	−	0.995735i	$-0.529410\pi$
$409$	−624262.	−0.184526	−0.0922632	+	0.995735i	$0.529410\pi$
$410$	0	0
$411$	3.26518e6	0.953461
$412$	0	0
$413$	−2.54957e6	−0.735515
$414$	0	0
$415$	−945432.	−0.269470
$416$	0	0
$417$	−4.97837e6	−1.40200
$418$	0	0
$419$	−401868.	−0.111827	−0.0559137	−	0.998436i	$-0.517807\pi$
$419$	−401868.	−0.111827	−0.0559137	+	0.998436i	$0.517807\pi$
$420$	0	0
$421$	1.89185e6	0.520212	0.260106	−	0.965580i	$-0.416242\pi$
$421$	1.89185e6	0.520212	0.260106	+	0.965580i	$0.416242\pi$
$422$	0	0
$423$	39364.0	0.0106967
$424$	0	0
$425$	−154242.	−0.0414219
$426$	0	0
$427$	73248.0	0.0194413
$428$	0	0
$429$	−2.19008e6	−0.574535
$430$	0	0
$431$	6.91650e6	1.79347	0.896734	−	0.442571i	$-0.145933\pi$
$431$	6.91650e6	1.79347	0.896734	+	0.442571i	$0.145933\pi$
$432$	0	0
$433$	−6.66253e6	−1.70773	−0.853865	−	0.520495i	$-0.825748\pi$
$433$	−6.66253e6	−1.70773	−0.853865	+	0.520495i	$0.825748\pi$
$434$	0	0
$435$	726624.	0.184114
$436$	0	0
$437$	−2.43046e6	−0.608815
$438$	0	0
$439$	−3.64329e6	−0.902261	−0.451131	−	0.892458i	$-0.648979\pi$
$439$	−3.64329e6	−0.902261	−0.451131	+	0.892458i	$0.648979\pi$
$440$	0	0
$441$	−55419.0	−0.0135694
$442$	0	0
$443$	1.77842e6	0.430550	0.215275	−	0.976553i	$-0.430935\pi$
$443$	1.77842e6	0.430550	0.215275	+	0.976553i	$0.430935\pi$
$444$	0	0
$445$	3.40816e6	0.815867
$446$	0	0
$447$	−2.11651e6	−0.501016
$448$	0	0
$449$	−336974.	−0.0788825	−0.0394412	−	0.999222i	$-0.512558\pi$
$449$	−336974.	−0.0788825	−0.0394412	+	0.999222i	$0.512558\pi$
$450$	0	0
$451$	−2.10984e6	−0.488437
$452$	0	0
$453$	−2.23270e6	−0.511194
$454$	0	0
$455$	−1.75392e6	−0.397174
$456$	0	0
$457$	1.02108e6	0.228702	0.114351	−	0.993440i	$-0.463521\pi$
$457$	1.02108e6	0.228702	0.114351	+	0.993440i	$0.463521\pi$
$458$	0	0
$459$	−2.71584e6	−0.601690
$460$	0	0
$461$	−5.60853e6	−1.22913	−0.614563	−	0.788867i	$-0.710668\pi$
$461$	−5.60853e6	−1.22913	−0.614563	+	0.788867i	$0.710668\pi$
$462$	0	0
$463$	−7.28480e6	−1.57930	−0.789651	−	0.613556i	$-0.789738\pi$
$463$	−7.28480e6	−1.57930	−0.789651	+	0.613556i	$0.789738\pi$
$464$	0	0
$465$	4.59994e6	0.986551
$466$	0	0
$467$	5.64931e6	1.19868	0.599340	−	0.800494i	$-0.295430\pi$
$467$	5.64931e6	1.19868	0.599340	+	0.800494i	$0.295430\pi$
$468$	0	0
$469$	6.11654e6	1.28403
$470$	0	0
$471$	−1.93155e6	−0.401194
$472$	0	0
$473$	1.33293e6	0.273939
$474$	0	0
$475$	−337744.	−0.0686837
$476$	0	0
$477$	72462.0	0.0145819
$478$	0	0
$479$	2.60965e6	0.519689	0.259845	−	0.965650i	$-0.416329\pi$
$479$	2.60965e6	0.519689	0.259845	+	0.965650i	$0.416329\pi$
$480$	0	0
$481$	768500.	0.151454
$482$	0	0
$483$	−2.69517e6	−0.525676
$484$	0	0
$485$	−303156.	−0.0585210
$486$	0	0
$487$	−2.05502e6	−0.392640	−0.196320	−	0.980540i	$-0.562899\pi$
$487$	−2.05502e6	−0.392640	−0.196320	+	0.980540i	$0.562899\pi$
$488$	0	0
$489$	−2.59750e6	−0.491229
$490$	0	0
$491$	−3.68539e6	−0.689890	−0.344945	−	0.938623i	$-0.612102\pi$
$491$	−3.68539e6	−0.689890	−0.344945	+	0.938623i	$0.612102\pi$
$492$	0	0
$493$	620658.	0.115010
$494$	0	0
$495$	331344.	0.0607808
$496$	0	0
$497$	613760.	0.111457
$498$	0	0
$499$	−199756.	−0.0359127	−0.0179564	−	0.999839i	$-0.505716\pi$
$499$	−199756.	−0.0359127	−0.0179564	+	0.999839i	$0.505716\pi$
$500$	0	0
$501$	−1.08599e7	−1.93300
$502$	0	0
$503$	−503524.	−0.0887361	−0.0443680	−	0.999015i	$-0.514127\pi$
$503$	−503524.	−0.0887361	−0.0443680	+	0.999015i	$0.514127\pi$
$504$	0	0
$505$	4.63136e6	0.808129
$506$	0	0
$507$	−4.59509e6	−0.793915
$508$	0	0
$509$	−2.73749e6	−0.468337	−0.234168	−	0.972196i	$-0.575237\pi$
$509$	−2.73749e6	−0.468337	−0.234168	+	0.972196i	$0.575237\pi$
$510$	0	0
$511$	5.52944e6	0.936761
$512$	0	0
$513$	−5.94688e6	−0.997690
$514$	0	0
$515$	4.90752e6	0.815350
$516$	0	0
$517$	1.42922e6	0.235164
$518$	0	0
$519$	−7.58326e6	−1.23577
$520$	0	0
$521$	1.04455e7	1.68592	0.842958	−	0.537979i	$-0.180812\pi$
$521$	1.04455e7	1.68592	0.842958	+	0.537979i	$0.180812\pi$
$522$	0	0
$523$	−5.68844e6	−0.909367	−0.454684	−	0.890653i	$-0.650248\pi$
$523$	−5.68844e6	−0.909367	−0.454684	+	0.890653i	$0.650248\pi$
$524$	0	0
$525$	−374528.	−0.0593043
$526$	0	0
$527$	3.92911e6	0.616266
$528$	0	0
$529$	−4.17433e6	−0.648556
$530$	0	0
$531$	−295932.	−0.0455466
$532$	0	0
$533$	1.29630e6	0.197646
$534$	0	0
$535$	−1.10426e7	−1.66796
$536$	0	0
$537$	−5.80653e6	−0.868922
$538$	0	0
$539$	−2.01214e6	−0.298322
$540$	0	0
$541$	8.03243e6	1.17992	0.589962	−	0.807431i	$-0.299143\pi$
$541$	8.03243e6	1.17992	0.589962	+	0.807431i	$0.299143\pi$
$542$	0	0
$543$	−8.10947e6	−1.18030
$544$	0	0
$545$	1.88860e6	0.272363
$546$	0	0
$547$	1.30291e7	1.86185	0.930926	−	0.365209i	$-0.119002\pi$
$547$	1.30291e7	1.86185	0.930926	+	0.365209i	$0.119002\pi$
$548$	0	0
$549$	8502.00	0.00120390
$550$	0	0
$551$	1.35906e6	0.190703
$552$	0	0
$553$	−898240.	−0.124905
$554$	0	0
$555$	−2.28960e6	−0.315520
$556$	0	0
$557$	6.20592e6	0.847555	0.423778	−	0.905766i	$-0.360704\pi$
$557$	6.20592e6	0.847555	0.423778	+	0.905766i	$0.360704\pi$
$558$	0	0
$559$	−818960.	−0.110849
$560$	0	0
$561$	5.57338e6	0.747672
$562$	0	0
$563$	1.23562e7	1.64290	0.821452	−	0.570277i	$-0.193164\pi$
$563$	1.23562e7	1.64290	0.821452	+	0.570277i	$0.193164\pi$
$564$	0	0
$565$	1.34068e7	1.76687
$566$	0	0
$567$	−6.94837e6	−0.907664
$568$	0	0
$569$	423930.	0.0548926	0.0274463	−	0.999623i	$-0.491262\pi$
$569$	423930.	0.0548926	0.0274463	+	0.999623i	$0.491262\pi$
$570$	0	0
$571$	9.48250e6	1.21712	0.608559	−	0.793509i	$-0.291748\pi$
$571$	9.48250e6	1.21712	0.608559	+	0.793509i	$0.291748\pi$
$572$	0	0
$573$	−3.35725e6	−0.427166
$574$	0	0
$575$	314336.	0.0396483
$576$	0	0
$577$	2.87360e6	0.359325	0.179662	−	0.983728i	$-0.442499\pi$
$577$	2.87360e6	0.359325	0.179662	+	0.983728i	$0.442499\pi$
$578$	0	0
$579$	−4.65942e6	−0.577611
$580$	0	0
$581$	−1.96090e6	−0.240998
$582$	0	0
$583$	2.63093e6	0.320581
$584$	0	0
$585$	−203580.	−0.0245949
$586$	0	0
$587$	−1.71704e6	−0.205676	−0.102838	−	0.994698i	$-0.532792\pi$
$587$	−1.71704e6	−0.205676	−0.102838	+	0.994698i	$0.532792\pi$
$588$	0	0
$589$	8.60358e6	1.02186
$590$	0	0
$591$	−7.01098e6	−0.825676
$592$	0	0
$593$	−1.04001e7	−1.21451	−0.607254	−	0.794508i	$-0.707729\pi$
$593$	−1.04001e7	−1.21451	−0.607254	+	0.794508i	$0.707729\pi$
$594$	0	0
$595$	4.46342e6	0.516863
$596$	0	0
$597$	1.02761e7	1.18003
$598$	0	0
$599$	−665228.	−0.0757536	−0.0378768	−	0.999282i	$-0.512059\pi$
$599$	−665228.	−0.0757536	−0.0378768	+	0.999282i	$0.512059\pi$
$600$	0	0
$601$	1.74958e7	1.97582	0.987908	−	0.155041i	$-0.0495511\pi$
$601$	1.74958e7	1.97582	0.987908	+	0.155041i	$0.0495511\pi$
$602$	0	0
$603$	709956.	0.0795130
$604$	0	0
$605$	3.33358e6	0.370274
$606$	0	0
$607$	−110668.	−0.0121913	−0.00609565	−	0.999981i	$-0.501940\pi$
$607$	−110668.	−0.0121913	−0.00609565	+	0.999981i	$0.501940\pi$
$608$	0	0
$609$	1.50707e6	0.164661
$610$	0	0
$611$	−878120.	−0.0951592
$612$	0	0
$613$	1.47975e7	1.59051	0.795254	−	0.606276i	$-0.207337\pi$
$613$	1.47975e7	1.59051	0.795254	+	0.606276i	$0.207337\pi$
$614$	0	0
$615$	−3.86208e6	−0.411750
$616$	0	0
$617$	6.49455e6	0.686810	0.343405	−	0.939187i	$-0.388420\pi$
$617$	6.49455e6	0.686810	0.343405	+	0.939187i	$0.388420\pi$
$618$	0	0
$619$	−1.30042e7	−1.36414	−0.682069	−	0.731288i	$-0.738920\pi$
$619$	−1.30042e7	−1.36414	−0.682069	+	0.731288i	$0.738920\pi$
$620$	0	0
$621$	5.53472e6	0.575926
$622$	0	0
$623$	7.06877e6	0.729665
$624$	0	0
$625$	−9.06882e6	−0.928647
$626$	0	0
$627$	1.22040e7	1.23975
$628$	0	0
$629$	−1.95570e6	−0.197095
$630$	0	0
$631$	−1.13304e7	−1.13285	−0.566424	−	0.824114i	$-0.691673\pi$
$631$	−1.13304e7	−1.13285	−0.566424	+	0.824114i	$0.691673\pi$
$632$	0	0
$633$	8.11840e6	0.805306
$634$	0	0
$635$	−1.42182e7	−1.39930
$636$	0	0
$637$	1.23627e6	0.120716
$638$	0	0
$639$	71240.0	0.00690195
$640$	0	0
$641$	1.35011e7	1.29785	0.648925	−	0.760853i	$-0.275219\pi$
$641$	1.35011e7	1.29785	0.648925	+	0.760853i	$0.275219\pi$
$642$	0	0
$643$	−6.03508e6	−0.575647	−0.287823	−	0.957684i	$-0.592932\pi$
$643$	−6.03508e6	−0.575647	−0.287823	+	0.957684i	$0.592932\pi$
$644$	0	0
$645$	2.43994e6	0.230929
$646$	0	0
$647$	1.21143e7	1.13773	0.568865	−	0.822431i	$-0.307383\pi$
$647$	1.21143e7	1.13773	0.568865	+	0.822431i	$0.307383\pi$
$648$	0	0
$649$	−1.07446e7	−1.00133
$650$	0	0
$651$	9.54061e6	0.882315
$652$	0	0
$653$	2.09009e6	0.191815	0.0959076	−	0.995390i	$-0.469425\pi$
$653$	2.09009e6	0.191815	0.0959076	+	0.995390i	$0.469425\pi$
$654$	0	0
$655$	−7.78334e6	−0.708864
$656$	0	0
$657$	641810.	0.0580087
$658$	0	0
$659$	1.83184e6	0.164314	0.0821569	−	0.996619i	$-0.473819\pi$
$659$	1.83184e6	0.164314	0.0821569	+	0.996619i	$0.473819\pi$
$660$	0	0
$661$	−1.91164e7	−1.70177	−0.850887	−	0.525349i	$-0.823935\pi$
$661$	−1.91164e7	−1.70177	−0.850887	+	0.525349i	$0.823935\pi$
$662$	0	0
$663$	−3.42432e6	−0.302545
$664$	0	0
$665$	9.77357e6	0.857036
$666$	0	0
$667$	−1.26486e6	−0.110085
$668$	0	0
$669$	−3.66861e6	−0.316910
$670$	0	0
$671$	308688.	0.0264675
$672$	0	0
$673$	−1.09686e7	−0.933496	−0.466748	−	0.884390i	$-0.654575\pi$
$673$	−1.09686e7	−0.933496	−0.466748	+	0.884390i	$0.654575\pi$
$674$	0	0
$675$	769120.	0.0649733
$676$	0	0
$677$	4.28247e6	0.359106	0.179553	−	0.983748i	$-0.442535\pi$
$677$	4.28247e6	0.359106	0.179553	+	0.983748i	$0.442535\pi$
$678$	0	0
$679$	−628768.	−0.0523379
$680$	0	0
$681$	−5.87347e6	−0.485319
$682$	0	0
$683$	1.09554e7	0.898623	0.449312	−	0.893375i	$-0.351669\pi$
$683$	1.09554e7	0.898623	0.449312	+	0.893375i	$0.351669\pi$
$684$	0	0
$685$	1.10200e7	0.897336
$686$	0	0
$687$	−5.93808e6	−0.480014
$688$	0	0
$689$	−1.61646e6	−0.129723
$690$	0	0
$691$	1.15087e7	0.916917	0.458458	−	0.888716i	$-0.348402\pi$
$691$	1.15087e7	0.916917	0.458458	+	0.888716i	$0.348402\pi$
$692$	0	0
$693$	687232.	0.0543589
$694$	0	0
$695$	−1.68020e7	−1.31947
$696$	0	0
$697$	−3.29886e6	−0.257207
$698$	0	0
$699$	1.31575e7	1.01855
$700$	0	0
$701$	1.73867e7	1.33635	0.668177	−	0.744003i	$-0.267075\pi$
$701$	1.73867e7	1.33635	0.668177	+	0.744003i	$0.267075\pi$
$702$	0	0
$703$	−4.28240e6	−0.326813
$704$	0	0
$705$	2.61619e6	0.198243
$706$	0	0
$707$	9.60579e6	0.722744
$708$	0	0
$709$	−7.16062e6	−0.534977	−0.267488	−	0.963561i	$-0.586194\pi$
$709$	−7.16062e6	−0.534977	−0.267488	+	0.963561i	$0.586194\pi$
$710$	0	0
$711$	−104260.	−0.00773470
$712$	0	0
$713$	−8.00730e6	−0.589878
$714$	0	0
$715$	−7.39152e6	−0.540715
$716$	0	0
$717$	−1.68672e7	−1.22531
$718$	0	0
$719$	2.73521e6	0.197319	0.0986593	−	0.995121i	$-0.468545\pi$
$719$	2.73521e6	0.197319	0.0986593	+	0.995121i	$0.468545\pi$
$720$	0	0
$721$	1.01786e7	0.729203
$722$	0	0
$723$	1.83678e7	1.30681
$724$	0	0
$725$	−175769.	−0.0124193
$726$	0	0
$727$	−2.10004e7	−1.47364	−0.736821	−	0.676088i	$-0.763674\pi$
$727$	−2.10004e7	−1.47364	−0.736821	+	0.676088i	$0.763674\pi$
$728$	0	0
$729$	1.35013e7	0.940931
$730$	0	0
$731$	2.08411e6	0.144254
$732$	0	0
$733$	−1.23913e7	−0.851838	−0.425919	−	0.904761i	$-0.640049\pi$
$733$	−1.23913e7	−0.851838	−0.425919	+	0.904761i	$0.640049\pi$
$734$	0	0
$735$	−3.68323e6	−0.251484
$736$	0	0
$737$	2.57769e7	1.74808
$738$	0	0
$739$	3.89810e6	0.262568	0.131284	−	0.991345i	$-0.458090\pi$
$739$	3.89810e6	0.262568	0.131284	+	0.991345i	$0.458090\pi$
$740$	0	0
$741$	−7.49824e6	−0.501665
$742$	0	0
$743$	2.16703e7	1.44010	0.720050	−	0.693922i	$-0.244119\pi$
$743$	2.16703e7	1.44010	0.720050	+	0.693922i	$0.244119\pi$
$744$	0	0
$745$	−7.14323e6	−0.471524
$746$	0	0
$747$	−227604.	−0.0149238
$748$	0	0
$749$	−2.29031e7	−1.49173
$750$	0	0
$751$	−2.50477e7	−1.62057	−0.810285	−	0.586036i	$-0.800688\pi$
$751$	−2.50477e7	−1.62057	−0.810285	+	0.586036i	$0.800688\pi$
$752$	0	0
$753$	4.31757e6	0.277493
$754$	0	0
$755$	−7.53538e6	−0.481102
$756$	0	0
$757$	1.72701e7	1.09535	0.547677	−	0.836690i	$-0.315512\pi$
$757$	1.72701e7	1.09535	0.547677	+	0.836690i	$0.315512\pi$
$758$	0	0
$759$	−1.13582e7	−0.715658
$760$	0	0
$761$	1.35992e7	0.851240	0.425620	−	0.904902i	$-0.360056\pi$
$761$	1.35992e7	0.851240	0.425620	+	0.904902i	$0.360056\pi$
$762$	0	0
$763$	3.91709e6	0.243586
$764$	0	0
$765$	518076.	0.0320066
$766$	0	0
$767$	6.60156e6	0.405189
$768$	0	0
$769$	−2.71274e7	−1.65422	−0.827109	−	0.562041i	$-0.810016\pi$
$769$	−2.71274e7	−1.65422	−0.827109	+	0.562041i	$0.810016\pi$
$770$	0	0
$771$	2.18990e7	1.32675
$772$	0	0
$773$	−2.39816e7	−1.44354	−0.721772	−	0.692131i	$-0.756672\pi$
$773$	−2.39816e7	−1.44354	−0.721772	+	0.692131i	$0.756672\pi$
$774$	0	0
$775$	−1.11272e6	−0.0665472
$776$	0	0
$777$	−4.74880e6	−0.282183
$778$	0	0
$779$	−7.22352e6	−0.426486
$780$	0	0
$781$	2.58656e6	0.151738
$782$	0	0
$783$	−3.09488e6	−0.180401
$784$	0	0
$785$	−6.51899e6	−0.377577
$786$	0	0
$787$	2.57481e7	1.48187	0.740933	−	0.671579i	$-0.234383\pi$
$787$	2.57481e7	1.48187	0.740933	+	0.671579i	$0.234383\pi$
$788$	0	0
$789$	−2.18856e7	−1.25160
$790$	0	0
$791$	2.78067e7	1.58019
$792$	0	0
$793$	−189660.	−0.0107101
$794$	0	0
$795$	4.81594e6	0.270248
$796$	0	0
$797$	3.89139e6	0.217000	0.108500	−	0.994096i	$-0.465395\pi$
$797$	3.89139e6	0.217000	0.108500	+	0.994096i	$0.465395\pi$
$798$	0	0
$799$	2.23466e6	0.123836
$800$	0	0
$801$	820482.	0.0451843
$802$	0	0
$803$	2.33026e7	1.27531
$804$	0	0
$805$	−9.09619e6	−0.494732
$806$	0	0
$807$	−5.49200e6	−0.296857
$808$	0	0
$809$	1.75197e7	0.941142	0.470571	−	0.882362i	$-0.344048\pi$
$809$	1.75197e7	0.941142	0.470571	+	0.882362i	$0.344048\pi$
$810$	0	0
$811$	−1.33567e7	−0.713094	−0.356547	−	0.934277i	$-0.616046\pi$
$811$	−1.33567e7	−0.713094	−0.356547	+	0.934277i	$0.616046\pi$
$812$	0	0
$813$	−2.20228e7	−1.16855
$814$	0	0
$815$	−8.76658e6	−0.462313
$816$	0	0
$817$	4.56358e6	0.239194
$818$	0	0
$819$	−422240.	−0.0219963
$820$	0	0
$821$	3.69768e7	1.91457	0.957286	−	0.289141i	$-0.0933698\pi$
$821$	3.69768e7	1.91457	0.957286	+	0.289141i	$0.0933698\pi$
$822$	0	0
$823$	1.62419e7	0.835869	0.417935	−	0.908477i	$-0.362754\pi$
$823$	1.62419e7	0.835869	0.417935	+	0.908477i	$0.362754\pi$
$824$	0	0
$825$	−1.57837e6	−0.0807371
$826$	0	0
$827$	1.73165e7	0.880432	0.440216	−	0.897892i	$-0.354902\pi$
$827$	1.73165e7	0.880432	0.440216	+	0.897892i	$0.354902\pi$
$828$	0	0
$829$	1.27462e7	0.644160	0.322080	−	0.946712i	$-0.395618\pi$
$829$	1.27462e7	0.644160	0.322080	+	0.946712i	$0.395618\pi$
$830$	0	0
$831$	−1.84534e7	−0.926988
$832$	0	0
$833$	−3.14609e6	−0.157094
$834$	0	0
$835$	−3.66522e7	−1.81921
$836$	0	0
$837$	−1.95923e7	−0.966657
$838$	0	0
$839$	−1.13330e7	−0.555829	−0.277914	−	0.960606i	$-0.589643\pi$
$839$	−1.13330e7	−0.555829	−0.277914	+	0.960606i	$0.589643\pi$
$840$	0	0
$841$	707281.	0.0344828
$842$	0	0
$843$	2.27235e7	1.10130
$844$	0	0
$845$	−1.55084e7	−0.747181
$846$	0	0
$847$	6.91410e6	0.331152
$848$	0	0
$849$	1.99695e7	0.950818
$850$	0	0
$851$	3.98560e6	0.188656
$852$	0	0
$853$	−1.48026e7	−0.696569	−0.348284	−	0.937389i	$-0.613236\pi$
$853$	−1.48026e7	−0.696569	−0.348284	+	0.937389i	$0.613236\pi$
$854$	0	0
$855$	1.13443e6	0.0530717
$856$	0	0
$857$	−2.24724e7	−1.04519	−0.522597	−	0.852580i	$-0.675037\pi$
$857$	−2.24724e7	−1.04519	−0.522597	+	0.852580i	$0.675037\pi$
$858$	0	0
$859$	−2.32066e6	−0.107307	−0.0536535	−	0.998560i	$-0.517087\pi$
$859$	−2.32066e6	−0.107307	−0.0536535	+	0.998560i	$0.517087\pi$
$860$	0	0
$861$	−8.01024e6	−0.368246
$862$	0	0
$863$	−879104.	−0.0401803	−0.0200902	−	0.999798i	$-0.506395\pi$
$863$	−879104.	−0.0401803	−0.0200902	+	0.999798i	$0.506395\pi$
$864$	0	0
$865$	−2.55935e7	−1.16303
$866$	0	0
$867$	−1.40034e7	−0.632683
$868$	0	0
$869$	−3.78544e6	−0.170046
$870$	0	0
$871$	−1.58375e7	−0.707360
$872$	0	0
$873$	−72982.0	−0.00324101
$874$	0	0
$875$	−2.01640e7	−0.890343
$876$	0	0
$877$	4.28102e6	0.187953	0.0939763	−	0.995574i	$-0.470042\pi$
$877$	4.28102e6	0.187953	0.0939763	+	0.995574i	$0.470042\pi$
$878$	0	0
$879$	9.38890e6	0.409866
$880$	0	0
$881$	7.95599e6	0.345346	0.172673	−	0.984979i	$-0.444760\pi$
$881$	7.95599e6	0.345346	0.172673	+	0.984979i	$0.444760\pi$
$882$	0	0
$883$	−2.67903e7	−1.15631	−0.578156	−	0.815926i	$-0.696228\pi$
$883$	−2.67903e7	−1.15631	−0.578156	+	0.815926i	$0.696228\pi$
$884$	0	0
$885$	−1.96681e7	−0.844120
$886$	0	0
$887$	−8.24062e6	−0.351683	−0.175841	−	0.984419i	$-0.556265\pi$
$887$	−8.24062e6	−0.351683	−0.175841	+	0.984419i	$0.556265\pi$
$888$	0	0
$889$	−2.94896e7	−1.25145
$890$	0	0
$891$	−2.92824e7	−1.23570
$892$	0	0
$893$	4.89325e6	0.205338
$894$	0	0
$895$	−1.95970e7	−0.817773
$896$	0	0
$897$	6.97856e6	0.289591
$898$	0	0
$899$	4.47748e6	0.184771
$900$	0	0
$901$	4.11361e6	0.168815
$902$	0	0
$903$	5.06061e6	0.206530
$904$	0	0
$905$	−2.73695e7	−1.11082
$906$	0	0
$907$	1.92772e7	0.778081	0.389041	−	0.921221i	$-0.372807\pi$
$907$	1.92772e7	0.778081	0.389041	+	0.921221i	$0.372807\pi$
$908$	0	0
$909$	1.11496e6	0.0447557
$910$	0	0
$911$	2.12865e7	0.849784	0.424892	−	0.905244i	$-0.360312\pi$
$911$	2.12865e7	0.849784	0.424892	+	0.905244i	$0.360312\pi$
$912$	0	0
$913$	−8.26378e6	−0.328096
$914$	0	0
$915$	565056.	0.0223120
$916$	0	0
$917$	−1.61432e7	−0.633968
$918$	0	0
$919$	−8.11730e6	−0.317046	−0.158523	−	0.987355i	$-0.550673\pi$
$919$	−8.11730e6	−0.317046	−0.158523	+	0.987355i	$0.550673\pi$
$920$	0	0
$921$	2.20826e7	0.857828
$922$	0	0
$923$	−1.58920e6	−0.0614008
$924$	0	0
$925$	553850.	0.0212832
$926$	0	0
$927$	1.18144e6	0.0451557
$928$	0	0
$929$	−2.69633e6	−0.102502	−0.0512512	−	0.998686i	$-0.516321\pi$
$929$	−2.69633e6	−0.102502	−0.0512512	+	0.998686i	$0.516321\pi$
$930$	0	0
$931$	−6.88901e6	−0.260485
$932$	0	0
$933$	8.47392e6	0.318699
$934$	0	0
$935$	1.88101e7	0.703660
$936$	0	0
$937$	1.86751e7	0.694888	0.347444	−	0.937701i	$-0.387050\pi$
$937$	1.86751e7	0.694888	0.347444	+	0.937701i	$0.387050\pi$
$938$	0	0
$939$	−1.94686e7	−0.720562
$940$	0	0
$941$	−1.80767e7	−0.665494	−0.332747	−	0.943016i	$-0.607976\pi$
$941$	−1.80767e7	−0.665494	−0.332747	+	0.943016i	$0.607976\pi$
$942$	0	0
$943$	6.72288e6	0.246193
$944$	0	0
$945$	−2.22566e7	−0.810737
$946$	0	0
$947$	−1.41297e7	−0.511986	−0.255993	−	0.966679i	$-0.582402\pi$
$947$	−1.41297e7	−0.511986	−0.255993	+	0.966679i	$0.582402\pi$
$948$	0	0
$949$	−1.43173e7	−0.516055
$950$	0	0
$951$	1.43910e7	0.515988
$952$	0	0
$953$	1.02005e7	0.363821	0.181911	−	0.983315i	$-0.441772\pi$
$953$	1.02005e7	0.363821	0.181911	+	0.983315i	$0.441772\pi$
$954$	0	0
$955$	−1.13307e7	−0.402021
$956$	0	0
$957$	6.35123e6	0.224170
$958$	0	0
$959$	2.28563e7	0.802526
$960$	0	0
$961$	−284175.	−0.00992607
$962$	0	0
$963$	−2.65840e6	−0.0923749
$964$	0	0
$965$	−1.57256e7	−0.543610
$966$	0	0
$967$	520940.	0.0179152	0.00895760	−	0.999960i	$-0.497149\pi$
$967$	520940.	0.0179152	0.00895760	+	0.999960i	$0.497149\pi$
$968$	0	0
$969$	1.90817e7	0.652842
$970$	0	0
$971$	−8.25620e6	−0.281017	−0.140508	−	0.990079i	$-0.544874\pi$
$971$	−8.25620e6	−0.281017	−0.140508	+	0.990079i	$0.544874\pi$
$972$	0	0
$973$	−3.48486e7	−1.18006
$974$	0	0
$975$	969760.	0.0326703
$976$	0	0
$977$	−4.03373e7	−1.35198	−0.675990	−	0.736910i	$-0.736284\pi$
$977$	−4.03373e7	−1.35198	−0.675990	+	0.736910i	$0.736284\pi$
$978$	0	0
$979$	2.97898e7	0.993370
$980$	0	0
$981$	454662.	0.0150840
$982$	0	0
$983$	−4.72753e7	−1.56045	−0.780227	−	0.625497i	$-0.784896\pi$
$983$	−4.72753e7	−1.56045	−0.780227	+	0.625497i	$0.784896\pi$
$984$	0	0
$985$	−2.36620e7	−0.777073
$986$	0	0
$987$	5.42618e6	0.177297
$988$	0	0
$989$	−4.24730e6	−0.138077
$990$	0	0
$991$	−1.14415e7	−0.370083	−0.185041	−	0.982731i	$-0.559242\pi$
$991$	−1.14415e7	−0.370083	−0.185041	+	0.982731i	$0.559242\pi$
$992$	0	0
$993$	1.96621e7	0.632785
$994$	0	0
$995$	3.46818e7	1.11057
$996$	0	0
$997$	−8.43603e6	−0.268782	−0.134391	−	0.990928i	$-0.542908\pi$
$997$	−8.43603e6	−0.268782	−0.134391	+	0.990928i	$0.542908\pi$
$998$	0	0
$999$	9.75200e6	0.309158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.6.a.a.1.1	✓	1
4.3	odd	2		464.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.6.a.a.1.1	✓	1	1.1	even	1	trivial
464.6.a.a.1.1		1	4.3	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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	232.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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