LMFDB - Embedded newform 7800.2.a.bj.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7800,2,Mod(1,7800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7800, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("7800.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7800.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:	$62.2833135766$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1560)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.12489$ of defining polynomial
Character	$\chi$	$=$	7800.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{9} +O(q^{10})$	$q-1.00000 q^{3} +1.00000 q^{9} -4.64002 q^{11} -1.00000 q^{13} -4.24977 q^{17} -6.24977 q^{19} -2.24977 q^{23} -1.00000 q^{27} -9.21949 q^{29} +9.28005 q^{31} +4.64002 q^{33} -7.28005 q^{37} +1.00000 q^{39} -5.67030 q^{41} +4.24977 q^{43} -2.88979 q^{47} -7.00000 q^{49} +4.24977 q^{51} +9.21949 q^{53} +6.24977 q^{57} +5.92007 q^{59} +0.969724 q^{61} +1.93945 q^{67} +2.24977 q^{69} +5.60975 q^{71} +12.5601 q^{73} +12.2498 q^{79} +1.00000 q^{81} +3.67030 q^{83} +9.21949 q^{87} -9.67030 q^{89} -9.28005 q^{93} +6.00000 q^{97} -4.64002 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 3 * q^9	$ 3 q - 3 q^{3} + 3 q^{9} - 6 q^{11} - 3 q^{13} + 4 q^{17} - 2 q^{19} + 10 q^{23} - 3 q^{27} - 10 q^{29} + 12 q^{31} + 6 q^{33} - 6 q^{37} + 3 q^{39} - 10 q^{41} - 4 q^{43} + 16 q^{47} - 21 q^{49} - 4 q^{51} + 10 q^{53} + 2 q^{57} - 6 q^{59} + 2 q^{61} + 4 q^{67} - 10 q^{69} + 8 q^{71} + 6 q^{73} + 20 q^{79} + 3 q^{81} + 4 q^{83} + 10 q^{87} - 22 q^{89} - 12 q^{93} + 18 q^{97} - 6 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 3 * q^9 - 6 * q^11 - 3 * q^13 + 4 * q^17 - 2 * q^19 + 10 * q^23 - 3 * q^27 - 10 * q^29 + 12 * q^31 + 6 * q^33 - 6 * q^37 + 3 * q^39 - 10 * q^41 - 4 * q^43 + 16 * q^47 - 21 * q^49 - 4 * q^51 + 10 * q^53 + 2 * q^57 - 6 * q^59 + 2 * q^61 + 4 * q^67 - 10 * q^69 + 8 * q^71 + 6 * q^73 + 20 * q^79 + 3 * q^81 + 4 * q^83 + 10 * q^87 - 22 * q^89 - 12 * q^93 + 18 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.64002	−1.39902	−0.699510	−	0.714623i	$-0.746598\pi$
$11$	−4.64002	−1.39902	−0.699510	+	0.714623i	$0.746598\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−4.24977	−1.03072	−0.515360	−	0.856974i	$-0.672342\pi$
$17$	−4.24977	−1.03072	−0.515360	+	0.856974i	$0.672342\pi$
$18$	0	0
$19$	−6.24977	−1.43380	−0.716898	−	0.697178i	$-0.754439\pi$
$19$	−6.24977	−1.43380	−0.716898	+	0.697178i	$0.754439\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−2.24977	−0.469110	−0.234555	−	0.972103i	$-0.575363\pi$
$23$	−2.24977	−0.469110	−0.234555	+	0.972103i	$0.575363\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−9.21949	−1.71202	−0.856009	−	0.516962i	$-0.827063\pi$
$29$	−9.21949	−1.71202	−0.856009	+	0.516962i	$0.827063\pi$
$30$	0	0
$31$	9.28005	1.66675	0.833373	−	0.552711i	$-0.186407\pi$
$31$	9.28005	1.66675	0.833373	+	0.552711i	$0.186407\pi$
$32$	0	0
$33$	4.64002	0.807724
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−7.28005	−1.19683	−0.598416	−	0.801185i	$-0.704203\pi$
$37$	−7.28005	−1.19683	−0.598416	+	0.801185i	$0.704203\pi$
$38$	0	0
$39$	1.00000	0.160128
$40$	0	0
$41$	−5.67030	−0.885552	−0.442776	−	0.896632i	$-0.646006\pi$
$41$	−5.67030	−0.885552	−0.442776	+	0.896632i	$0.646006\pi$
$42$	0	0
$43$	4.24977	0.648084	0.324042	−	0.946043i	$-0.394958\pi$
$43$	4.24977	0.648084	0.324042	+	0.946043i	$0.394958\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−2.88979	−0.421520	−0.210760	−	0.977538i	$-0.567594\pi$
$47$	−2.88979	−0.421520	−0.210760	+	0.977538i	$0.567594\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	4.24977	0.595087
$52$	0	0
$53$	9.21949	1.26639	0.633197	−	0.773990i	$-0.281742\pi$
$53$	9.21949	1.26639	0.633197	+	0.773990i	$0.281742\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	6.24977	0.827802
$58$	0	0
$59$	5.92007	0.770728	0.385364	−	0.922765i	$-0.374076\pi$
$59$	5.92007	0.770728	0.385364	+	0.922765i	$0.374076\pi$
$60$	0	0
$61$	0.969724	0.124160	0.0620802	−	0.998071i	$-0.480227\pi$
$61$	0.969724	0.124160	0.0620802	+	0.998071i	$0.480227\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	1.93945	0.236941	0.118471	−	0.992958i	$-0.462201\pi$
$67$	1.93945	0.236941	0.118471	+	0.992958i	$0.462201\pi$
$68$	0	0
$69$	2.24977	0.270841
$70$	0	0
$71$	5.60975	0.665755	0.332877	−	0.942970i	$-0.391981\pi$
$71$	5.60975	0.665755	0.332877	+	0.942970i	$0.391981\pi$
$72$	0	0
$73$	12.5601	1.47005	0.735024	−	0.678041i	$-0.237171\pi$
$73$	12.5601	1.47005	0.735024	+	0.678041i	$0.237171\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	12.2498	1.37821	0.689103	−	0.724663i	$-0.258005\pi$
$79$	12.2498	1.37821	0.689103	+	0.724663i	$0.258005\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	3.67030	0.402868	0.201434	−	0.979502i	$-0.435440\pi$
$83$	3.67030	0.402868	0.201434	+	0.979502i	$0.435440\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	9.21949	0.988434
$88$	0	0
$89$	−9.67030	−1.02505	−0.512525	−	0.858672i	$-0.671290\pi$
$89$	−9.67030	−1.02505	−0.512525	+	0.858672i	$0.671290\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−9.28005	−0.962296
$94$	0	0
$95$	0	0
$96$	0	0
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	0	0
$99$	−4.64002	−0.466340
$100$	0	0
$101$	−15.2800	−1.52042	−0.760211	−	0.649677i	$-0.774904\pi$
$101$	−15.2800	−1.52042	−0.760211	+	0.649677i	$0.774904\pi$
$102$	0	0
$103$	−1.21949	−0.120160	−0.0600802	−	0.998194i	$-0.519136\pi$
$103$	−1.21949	−0.120160	−0.0600802	+	0.998194i	$0.519136\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	5.28005	0.510441	0.255221	−	0.966883i	$-0.417852\pi$
$107$	5.28005	0.510441	0.255221	+	0.966883i	$0.417852\pi$
$108$	0	0
$109$	−10.1892	−0.975950	−0.487975	−	0.872858i	$-0.662264\pi$
$109$	−10.1892	−0.975950	−0.487975	+	0.872858i	$0.662264\pi$
$110$	0	0
$111$	7.28005	0.690991
$112$	0	0
$113$	−1.03028	−0.0969202	−0.0484601	−	0.998825i	$-0.515431\pi$
$113$	−1.03028	−0.0969202	−0.0484601	+	0.998825i	$0.515431\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	0	0
$120$	0	0
$121$	10.5298	0.957256
$122$	0	0
$123$	5.67030	0.511274
$124$	0	0
$125$	0	0
$126$	0	0
$127$	11.0303	0.978779	0.489389	−	0.872065i	$-0.337220\pi$
$127$	11.0303	0.978779	0.489389	+	0.872065i	$0.337220\pi$
$128$	0	0
$129$	−4.24977	−0.374171
$130$	0	0
$131$	7.21949	0.630770	0.315385	−	0.948964i	$-0.397866\pi$
$131$	7.21949	0.630770	0.315385	+	0.948964i	$0.397866\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−8.10929	−0.692823	−0.346412	−	0.938083i	$-0.612600\pi$
$137$	−8.10929	−0.692823	−0.346412	+	0.938083i	$0.612600\pi$
$138$	0	0
$139$	−19.0596	−1.61662	−0.808309	−	0.588759i	$-0.799617\pi$
$139$	−19.0596	−1.61662	−0.808309	+	0.588759i	$0.799617\pi$
$140$	0	0
$141$	2.88979	0.243365
$142$	0	0
$143$	4.64002	0.388018
$144$	0	0
$145$	0	0
$146$	0	0
$147$	7.00000	0.577350
$148$	0	0
$149$	3.92007	0.321145	0.160572	−	0.987024i	$-0.448666\pi$
$149$	3.92007	0.321145	0.160572	+	0.987024i	$0.448666\pi$
$150$	0	0
$151$	21.7796	1.77240	0.886199	−	0.463305i	$-0.153337\pi$
$151$	21.7796	1.77240	0.886199	+	0.463305i	$0.153337\pi$
$152$	0	0
$153$	−4.24977	−0.343574
$154$	0	0
$155$	0	0
$156$	0	0
$157$	21.5904	1.72310	0.861550	−	0.507673i	$-0.169494\pi$
$157$	21.5904	1.72310	0.861550	+	0.507673i	$0.169494\pi$
$158$	0	0
$159$	−9.21949	−0.731153
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−1.28005	−0.100261	−0.0501305	−	0.998743i	$-0.515964\pi$
$163$	−1.28005	−0.100261	−0.0501305	+	0.998743i	$0.515964\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	18.8898	1.46174	0.730868	−	0.682519i	$-0.239115\pi$
$167$	18.8898	1.46174	0.730868	+	0.682519i	$0.239115\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	−6.24977	−0.477932
$172$	0	0
$173$	22.9991	1.74859	0.874294	−	0.485397i	$-0.161325\pi$
$173$	22.9991	1.74859	0.874294	+	0.485397i	$0.161325\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−5.92007	−0.444980
$178$	0	0
$179$	−4.49954	−0.336312	−0.168156	−	0.985760i	$-0.553781\pi$
$179$	−4.49954	−0.336312	−0.168156	+	0.985760i	$0.553781\pi$
$180$	0	0
$181$	−21.0596	−1.56535	−0.782675	−	0.622430i	$-0.786145\pi$
$181$	−21.0596	−1.56535	−0.782675	+	0.622430i	$0.786145\pi$
$182$	0	0
$183$	−0.969724	−0.0716841
$184$	0	0
$185$	0	0
$186$	0	0
$187$	19.7190	1.44200
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−14.4390	−1.04477	−0.522384	−	0.852710i	$-0.674957\pi$
$191$	−14.4390	−1.04477	−0.522384	+	0.852710i	$0.674957\pi$
$192$	0	0
$193$	−21.7190	−1.56337	−0.781685	−	0.623673i	$-0.785640\pi$
$193$	−21.7190	−1.56337	−0.781685	+	0.623673i	$0.785640\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	13.0109	0.926988	0.463494	−	0.886100i	$-0.346596\pi$
$197$	13.0109	0.926988	0.463494	+	0.886100i	$0.346596\pi$
$198$	0	0
$199$	18.6888	1.32481	0.662406	−	0.749145i	$-0.269536\pi$
$199$	18.6888	1.32481	0.662406	+	0.749145i	$0.269536\pi$
$200$	0	0
$201$	−1.93945	−0.136798
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−2.24977	−0.156370
$208$	0	0
$209$	28.9991	2.00591
$210$	0	0
$211$	−8.24977	−0.567938	−0.283969	−	0.958834i	$-0.591651\pi$
$211$	−8.24977	−0.567938	−0.283969	+	0.958834i	$0.591651\pi$
$212$	0	0
$213$	−5.60975	−0.384374
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−12.5601	−0.848732
$220$	0	0
$221$	4.24977	0.285871
$222$	0	0
$223$	−9.77959	−0.654890	−0.327445	−	0.944870i	$-0.606188\pi$
$223$	−9.77959	−0.654890	−0.327445	+	0.944870i	$0.606188\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−25.4499	−1.68917	−0.844584	−	0.535423i	$-0.820152\pi$
$227$	−25.4499	−1.68917	−0.844584	+	0.535423i	$0.820152\pi$
$228$	0	0
$229$	−8.24977	−0.545160	−0.272580	−	0.962133i	$-0.587877\pi$
$229$	−8.24977	−0.545160	−0.272580	+	0.962133i	$0.587877\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−11.5904	−0.759310	−0.379655	−	0.925128i	$-0.623957\pi$
$233$	−11.5904	−0.759310	−0.379655	+	0.925128i	$0.623957\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−12.2498	−0.795708
$238$	0	0
$239$	−6.88979	−0.445664	−0.222832	−	0.974857i	$-0.571530\pi$
$239$	−6.88979	−0.445664	−0.222832	+	0.974857i	$0.571530\pi$
$240$	0	0
$241$	21.2195	1.36687	0.683434	−	0.730012i	$-0.260486\pi$
$241$	21.2195	1.36687	0.683434	+	0.730012i	$0.260486\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	6.24977	0.397663
$248$	0	0
$249$	−3.67030	−0.232596
$250$	0	0
$251$	−24.3397	−1.53631	−0.768154	−	0.640266i	$-0.778824\pi$
$251$	−24.3397	−1.53631	−0.768154	+	0.640266i	$0.778824\pi$
$252$	0	0
$253$	10.4390	0.656294
$254$	0	0
$255$	0	0
$256$	0	0
$257$	23.4693	1.46397	0.731986	−	0.681319i	$-0.238593\pi$
$257$	23.4693	1.46397	0.731986	+	0.681319i	$0.238593\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−9.21949	−0.570672
$262$	0	0
$263$	22.6282	1.39532	0.697658	−	0.716431i	$-0.254226\pi$
$263$	22.6282	1.39532	0.697658	+	0.716431i	$0.254226\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	9.67030	0.591813
$268$	0	0
$269$	12.2791	0.748672	0.374336	−	0.927293i	$-0.377871\pi$
$269$	12.2791	0.748672	0.374336	+	0.927293i	$0.377871\pi$
$270$	0	0
$271$	−22.9385	−1.39342	−0.696708	−	0.717355i	$-0.745353\pi$
$271$	−22.9385	−1.39342	−0.696708	+	0.717355i	$0.745353\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−11.5298	−0.692760	−0.346380	−	0.938094i	$-0.612589\pi$
$277$	−11.5298	−0.692760	−0.346380	+	0.938094i	$0.612589\pi$
$278$	0	0
$279$	9.28005	0.555582
$280$	0	0
$281$	−11.3288	−0.675819	−0.337909	−	0.941179i	$-0.609720\pi$
$281$	−11.3288	−0.675819	−0.337909	+	0.941179i	$0.609720\pi$
$282$	0	0
$283$	−20.9991	−1.24827	−0.624133	−	0.781318i	$-0.714548\pi$
$283$	−20.9991	−1.24827	−0.624133	+	0.781318i	$0.714548\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	1.06055	0.0623854
$290$	0	0
$291$	−6.00000	−0.351726
$292$	0	0
$293$	4.26915	0.249406	0.124703	−	0.992194i	$-0.460202\pi$
$293$	4.26915	0.249406	0.124703	+	0.992194i	$0.460202\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	4.64002	0.269241
$298$	0	0
$299$	2.24977	0.130108
$300$	0	0
$301$	0	0
$302$	0	0
$303$	15.2800	0.877816
$304$	0	0
$305$	0	0
$306$	0	0
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	0	0
$309$	1.21949	0.0693746
$310$	0	0
$311$	3.71904	0.210887	0.105444	−	0.994425i	$-0.466374\pi$
$311$	3.71904	0.210887	0.105444	+	0.994425i	$0.466374\pi$
$312$	0	0
$313$	−1.52982	−0.0864704	−0.0432352	−	0.999065i	$-0.513766\pi$
$313$	−1.52982	−0.0864704	−0.0432352	+	0.999065i	$0.513766\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−16.1093	−0.904788	−0.452394	−	0.891818i	$-0.649430\pi$
$317$	−16.1093	−0.904788	−0.452394	+	0.891818i	$0.649430\pi$
$318$	0	0
$319$	42.7787	2.39515
$320$	0	0
$321$	−5.28005	−0.294703
$322$	0	0
$323$	26.5601	1.47784
$324$	0	0
$325$	0	0
$326$	0	0
$327$	10.1892	0.563465
$328$	0	0
$329$	0	0
$330$	0	0
$331$	15.5298	0.853596	0.426798	−	0.904347i	$-0.359642\pi$
$331$	15.5298	0.853596	0.426798	+	0.904347i	$0.359642\pi$
$332$	0	0
$333$	−7.28005	−0.398944
$334$	0	0
$335$	0	0
$336$	0	0
$337$	21.4087	1.16621	0.583103	−	0.812398i	$-0.301838\pi$
$337$	21.4087	1.16621	0.583103	+	0.812398i	$0.301838\pi$
$338$	0	0
$339$	1.03028	0.0559569
$340$	0	0
$341$	−43.0596	−2.33181
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	4.62065	0.248049	0.124025	−	0.992279i	$-0.460420\pi$
$347$	4.62065	0.248049	0.124025	+	0.992279i	$0.460420\pi$
$348$	0	0
$349$	23.9688	1.28302	0.641510	−	0.767114i	$-0.278308\pi$
$349$	23.9688	1.28302	0.641510	+	0.767114i	$0.278308\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	0	0
$353$	0.511357	0.0272168	0.0136084	−	0.999907i	$-0.495668\pi$
$353$	0.511357	0.0272168	0.0136084	+	0.999907i	$0.495668\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−12.6694	−0.668664	−0.334332	−	0.942455i	$-0.608511\pi$
$359$	−12.6694	−0.668664	−0.334332	+	0.942455i	$0.608511\pi$
$360$	0	0
$361$	20.0596	1.05577
$362$	0	0
$363$	−10.5298	−0.552672
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0.841057	0.0439028	0.0219514	−	0.999759i	$-0.493012\pi$
$367$	0.841057	0.0439028	0.0219514	+	0.999759i	$0.493012\pi$
$368$	0	0
$369$	−5.67030	−0.295184
$370$	0	0
$371$	0	0
$372$	0	0
$373$	29.0596	1.50465	0.752325	−	0.658792i	$-0.228932\pi$
$373$	29.0596	1.50465	0.752325	+	0.658792i	$0.228932\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	9.21949	0.474828
$378$	0	0
$379$	9.75023	0.500836	0.250418	−	0.968138i	$-0.419432\pi$
$379$	9.75023	0.500836	0.250418	+	0.968138i	$0.419432\pi$
$380$	0	0
$381$	−11.0303	−0.565098
$382$	0	0
$383$	7.38934	0.377577	0.188789	−	0.982018i	$-0.439544\pi$
$383$	7.38934	0.377577	0.188789	+	0.982018i	$0.439544\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	4.24977	0.216028
$388$	0	0
$389$	−14.0000	−0.709828	−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000	−0.709828	−0.354914	+	0.934899i	$0.615490\pi$
$390$	0	0
$391$	9.56101	0.483521
$392$	0	0
$393$	−7.21949	−0.364175
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−26.2186	−1.31587	−0.657936	−	0.753074i	$-0.728570\pi$
$397$	−26.2186	−1.31587	−0.657936	+	0.753074i	$0.728570\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	10.2909	0.513905	0.256953	−	0.966424i	$-0.417282\pi$
$401$	10.2909	0.513905	0.256953	+	0.966424i	$0.417282\pi$
$402$	0	0
$403$	−9.28005	−0.462272
$404$	0	0
$405$	0	0
$406$	0	0
$407$	33.7796	1.67439
$408$	0	0
$409$	−11.9007	−0.588451	−0.294226	−	0.955736i	$-0.595062\pi$
$409$	−11.9007	−0.588451	−0.294226	+	0.955736i	$0.595062\pi$
$410$	0	0
$411$	8.10929	0.400002
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	19.0596	0.933354
$418$	0	0
$419$	26.2791	1.28382	0.641910	−	0.766780i	$-0.278142\pi$
$419$	26.2791	1.28382	0.641910	+	0.766780i	$0.278142\pi$
$420$	0	0
$421$	22.3103	1.08734	0.543669	−	0.839300i	$-0.317035\pi$
$421$	22.3103	1.08734	0.543669	+	0.839300i	$0.317035\pi$
$422$	0	0
$423$	−2.88979	−0.140507
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−4.64002	−0.224022
$430$	0	0
$431$	12.0487	0.580367	0.290184	−	0.956971i	$-0.406284\pi$
$431$	12.0487	0.580367	0.290184	+	0.956971i	$0.406284\pi$
$432$	0	0
$433$	−27.5904	−1.32591	−0.662954	−	0.748660i	$-0.730698\pi$
$433$	−27.5904	−1.32591	−0.662954	+	0.748660i	$0.730698\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	14.0606	0.672607
$438$	0	0
$439$	19.8789	0.948768	0.474384	−	0.880318i	$-0.342671\pi$
$439$	19.8789	0.948768	0.474384	+	0.880318i	$0.342671\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	0	0
$443$	−17.9007	−0.850488	−0.425244	−	0.905079i	$-0.639812\pi$
$443$	−17.9007	−0.850488	−0.425244	+	0.905079i	$0.639812\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−3.92007	−0.185413
$448$	0	0
$449$	−17.2682	−0.814938	−0.407469	−	0.913219i	$-0.633589\pi$
$449$	−17.2682	−0.814938	−0.407469	+	0.913219i	$0.633589\pi$
$450$	0	0
$451$	26.3103	1.23890
$452$	0	0
$453$	−21.7796	−1.02329
$454$	0	0
$455$	0	0
$456$	0	0
$457$	30.4995	1.42671	0.713354	−	0.700804i	$-0.247175\pi$
$457$	30.4995	1.42671	0.713354	+	0.700804i	$0.247175\pi$
$458$	0	0
$459$	4.24977	0.198362
$460$	0	0
$461$	−2.64002	−0.122958	−0.0614791	−	0.998108i	$-0.519582\pi$
$461$	−2.64002	−0.122958	−0.0614791	+	0.998108i	$0.519582\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	4.78051	0.221215	0.110608	−	0.993864i	$-0.464720\pi$
$467$	4.78051	0.221215	0.110608	+	0.993864i	$0.464720\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−21.5904	−0.994832
$472$	0	0
$473$	−19.7190	−0.906682
$474$	0	0
$475$	0	0
$476$	0	0
$477$	9.21949	0.422132
$478$	0	0
$479$	9.11021	0.416256	0.208128	−	0.978102i	$-0.433263\pi$
$479$	9.11021	0.416256	0.208128	+	0.978102i	$0.433263\pi$
$480$	0	0
$481$	7.28005	0.331942
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	26.2791	1.19082	0.595411	−	0.803422i	$-0.296989\pi$
$487$	26.2791	1.19082	0.595411	+	0.803422i	$0.296989\pi$
$488$	0	0
$489$	1.28005	0.0578857
$490$	0	0
$491$	5.40115	0.243751	0.121875	−	0.992545i	$-0.461109\pi$
$491$	5.40115	0.243751	0.121875	+	0.992545i	$0.461109\pi$
$492$	0	0
$493$	39.1807	1.76461
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	22.9092	1.02556	0.512778	−	0.858521i	$-0.328617\pi$
$499$	22.9092	1.02556	0.512778	+	0.858521i	$0.328617\pi$
$500$	0	0
$501$	−18.8898	−0.843934
$502$	0	0
$503$	−37.3094	−1.66354	−0.831772	−	0.555117i	$-0.812673\pi$
$503$	−37.3094	−1.66354	−0.831772	+	0.555117i	$0.812673\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−1.00000	−0.0444116
$508$	0	0
$509$	−0.700576	−0.0310525	−0.0155262	−	0.999879i	$-0.504942\pi$
$509$	−0.700576	−0.0310525	−0.0155262	+	0.999879i	$0.504942\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	6.24977	0.275934
$514$	0	0
$515$	0	0
$516$	0	0
$517$	13.4087	0.589715
$518$	0	0
$519$	−22.9991	−1.00955
$520$	0	0
$521$	13.8401	0.606348	0.303174	−	0.952935i	$-0.401954\pi$
$521$	13.8401	0.606348	0.303174	+	0.952935i	$0.401954\pi$
$522$	0	0
$523$	43.6878	1.91034	0.955168	−	0.296064i	$-0.0956743\pi$
$523$	43.6878	1.91034	0.955168	+	0.296064i	$0.0956743\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−39.4381	−1.71795
$528$	0	0
$529$	−17.9385	−0.779936
$530$	0	0
$531$	5.92007	0.256909
$532$	0	0
$533$	5.67030	0.245608
$534$	0	0
$535$	0	0
$536$	0	0
$537$	4.49954	0.194170
$538$	0	0
$539$	32.4802	1.39902
$540$	0	0
$541$	14.1892	0.610042	0.305021	−	0.952346i	$-0.401336\pi$
$541$	14.1892	0.610042	0.305021	+	0.952346i	$0.401336\pi$
$542$	0	0
$543$	21.0596	0.903755
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−44.3085	−1.89449	−0.947247	−	0.320504i	$-0.896148\pi$
$547$	−44.3085	−1.89449	−0.947247	+	0.320504i	$0.896148\pi$
$548$	0	0
$549$	0.969724	0.0413868
$550$	0	0
$551$	57.6197	2.45468
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	39.2077	1.66128	0.830641	−	0.556808i	$-0.187974\pi$
$557$	39.2077	1.66128	0.830641	+	0.556808i	$0.187974\pi$
$558$	0	0
$559$	−4.24977	−0.179746
$560$	0	0
$561$	−19.7190	−0.832538
$562$	0	0
$563$	18.0606	0.761162	0.380581	−	0.924748i	$-0.375724\pi$
$563$	18.0606	0.761162	0.380581	+	0.924748i	$0.375724\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−42.3397	−1.77497	−0.887486	−	0.460835i	$-0.847550\pi$
$569$	−42.3397	−1.77497	−0.887486	+	0.460835i	$0.847550\pi$
$570$	0	0
$571$	−39.9301	−1.67102	−0.835510	−	0.549475i	$-0.814828\pi$
$571$	−39.9301	−1.67102	−0.835510	+	0.549475i	$0.814828\pi$
$572$	0	0
$573$	14.4390	0.603197
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−21.3406	−0.888421	−0.444210	−	0.895923i	$-0.646516\pi$
$577$	−21.3406	−0.888421	−0.444210	+	0.895923i	$0.646516\pi$
$578$	0	0
$579$	21.7190	0.902612
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−42.7787	−1.77171
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−32.7905	−1.35341	−0.676704	−	0.736255i	$-0.736592\pi$
$587$	−32.7905	−1.35341	−0.676704	+	0.736255i	$0.736592\pi$
$588$	0	0
$589$	−57.9982	−2.38977
$590$	0	0
$591$	−13.0109	−0.535197
$592$	0	0
$593$	−6.66938	−0.273879	−0.136939	−	0.990579i	$-0.543727\pi$
$593$	−6.66938	−0.273879	−0.136939	+	0.990579i	$0.543727\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−18.6888	−0.764880
$598$	0	0
$599$	1.40115	0.0572495	0.0286247	−	0.999590i	$-0.490887\pi$
$599$	1.40115	0.0572495	0.0286247	+	0.999590i	$0.490887\pi$
$600$	0	0
$601$	0.349078	0.0142392	0.00711959	−	0.999975i	$-0.497734\pi$
$601$	0.349078	0.0142392	0.00711959	+	0.999975i	$0.497734\pi$
$602$	0	0
$603$	1.93945	0.0789804
$604$	0	0
$605$	0	0
$606$	0	0
$607$	27.2800	1.10726	0.553631	−	0.832762i	$-0.313242\pi$
$607$	27.2800	1.10726	0.553631	+	0.832762i	$0.313242\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	2.88979	0.116909
$612$	0	0
$613$	−9.34060	−0.377263	−0.188632	−	0.982048i	$-0.560405\pi$
$613$	−9.34060	−0.377263	−0.188632	+	0.982048i	$0.560405\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	34.6694	1.39574	0.697868	−	0.716226i	$-0.254132\pi$
$617$	34.6694	1.39574	0.697868	+	0.716226i	$0.254132\pi$
$618$	0	0
$619$	19.6509	0.789837	0.394919	−	0.918716i	$-0.370773\pi$
$619$	19.6509	0.789837	0.394919	+	0.918716i	$0.370773\pi$
$620$	0	0
$621$	2.24977	0.0902802
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−28.9991	−1.15811
$628$	0	0
$629$	30.9385	1.23360
$630$	0	0
$631$	−43.3993	−1.72770	−0.863850	−	0.503749i	$-0.831953\pi$
$631$	−43.3993	−1.72770	−0.863850	+	0.503749i	$0.831953\pi$
$632$	0	0
$633$	8.24977	0.327899
$634$	0	0
$635$	0	0
$636$	0	0
$637$	7.00000	0.277350
$638$	0	0
$639$	5.60975	0.221918
$640$	0	0
$641$	−4.56009	−0.180113	−0.0900564	−	0.995937i	$-0.528705\pi$
$641$	−4.56009	−0.180113	−0.0900564	+	0.995937i	$0.528705\pi$
$642$	0	0
$643$	8.62065	0.339965	0.169983	−	0.985447i	$-0.445629\pi$
$643$	8.62065	0.339965	0.169983	+	0.985447i	$0.445629\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	7.40871	0.291267	0.145633	−	0.989339i	$-0.453478\pi$
$647$	7.40871	0.291267	0.145633	+	0.989339i	$0.453478\pi$
$648$	0	0
$649$	−27.4693	−1.07826
$650$	0	0
$651$	0	0
$652$	0	0
$653$	2.00000	0.0782660	0.0391330	−	0.999234i	$-0.487540\pi$
$653$	2.00000	0.0782660	0.0391330	+	0.999234i	$0.487540\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	12.5601	0.490016
$658$	0	0
$659$	40.3784	1.57292	0.786460	−	0.617641i	$-0.211911\pi$
$659$	40.3784	1.57292	0.786460	+	0.617641i	$0.211911\pi$
$660$	0	0
$661$	39.0284	1.51803	0.759015	−	0.651073i	$-0.225681\pi$
$661$	39.0284	1.51803	0.759015	+	0.651073i	$0.225681\pi$
$662$	0	0
$663$	−4.24977	−0.165047
$664$	0	0
$665$	0	0
$666$	0	0
$667$	20.7418	0.803124
$668$	0	0
$669$	9.77959	0.378101
$670$	0	0
$671$	−4.49954	−0.173703
$672$	0	0
$673$	11.1807	0.430986	0.215493	−	0.976505i	$-0.430864\pi$
$673$	11.1807	0.430986	0.215493	+	0.976505i	$0.430864\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	33.3406	1.28138	0.640692	−	0.767798i	$-0.278648\pi$
$677$	33.3406	1.28138	0.640692	+	0.767798i	$0.278648\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	25.4499	0.975242
$682$	0	0
$683$	31.8889	1.22019	0.610097	−	0.792327i	$-0.291130\pi$
$683$	31.8889	1.22019	0.610097	+	0.792327i	$0.291130\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	8.24977	0.314748
$688$	0	0
$689$	−9.21949	−0.351235
$690$	0	0
$691$	39.0303	1.48478	0.742391	−	0.669967i	$-0.233692\pi$
$691$	39.0303	1.48478	0.742391	+	0.669967i	$0.233692\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	24.0975	0.912757
$698$	0	0
$699$	11.5904	0.438388
$700$	0	0
$701$	−44.5601	−1.68301	−0.841506	−	0.540248i	$-0.818330\pi$
$701$	−44.5601	−1.68301	−0.841506	+	0.540248i	$0.818330\pi$
$702$	0	0
$703$	45.4986	1.71601
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	23.4305	0.879951	0.439976	−	0.898010i	$-0.354987\pi$
$709$	23.4305	0.879951	0.439976	+	0.898010i	$0.354987\pi$
$710$	0	0
$711$	12.2498	0.459402
$712$	0	0
$713$	−20.8780	−0.781886
$714$	0	0
$715$	0	0
$716$	0	0
$717$	6.88979	0.257304
$718$	0	0
$719$	−15.0984	−0.563075	−0.281537	−	0.959550i	$-0.590844\pi$
$719$	−15.0984	−0.563075	−0.281537	+	0.959550i	$0.590844\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−21.2195	−0.789162
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−3.40871	−0.126422	−0.0632111	−	0.998000i	$-0.520134\pi$
$727$	−3.40871	−0.126422	−0.0632111	+	0.998000i	$0.520134\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−18.0606	−0.667994
$732$	0	0
$733$	−12.4390	−0.459445	−0.229722	−	0.973256i	$-0.573782\pi$
$733$	−12.4390	−0.459445	−0.229722	+	0.973256i	$0.573782\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−8.99908	−0.331485
$738$	0	0
$739$	−13.4693	−0.495475	−0.247737	−	0.968827i	$-0.579687\pi$
$739$	−13.4693	−0.495475	−0.247737	+	0.968827i	$0.579687\pi$
$740$	0	0
$741$	−6.24977	−0.229591
$742$	0	0
$743$	45.4111	1.66597	0.832986	−	0.553293i	$-0.186629\pi$
$743$	45.4111	1.66597	0.832986	+	0.553293i	$0.186629\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	3.67030	0.134289
$748$	0	0
$749$	0	0
$750$	0	0
$751$	1.56101	0.0569621	0.0284810	−	0.999594i	$-0.490933\pi$
$751$	1.56101	0.0569621	0.0284810	+	0.999594i	$0.490933\pi$
$752$	0	0
$753$	24.3397	0.886987
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−38.8780	−1.41304	−0.706522	−	0.707691i	$-0.749737\pi$
$757$	−38.8780	−1.41304	−0.706522	+	0.707691i	$0.749737\pi$
$758$	0	0
$759$	−10.4390	−0.378911
$760$	0	0
$761$	5.42809	0.196768	0.0983841	−	0.995149i	$-0.468633\pi$
$761$	5.42809	0.196768	0.0983841	+	0.995149i	$0.468633\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−5.92007	−0.213761
$768$	0	0
$769$	16.4390	0.592805	0.296403	−	0.955063i	$-0.404213\pi$
$769$	16.4390	0.592805	0.296403	+	0.955063i	$0.404213\pi$
$770$	0	0
$771$	−23.4693	−0.845225
$772$	0	0
$773$	−42.3884	−1.52461	−0.762303	−	0.647221i	$-0.775931\pi$
$773$	−42.3884	−1.52461	−0.762303	+	0.647221i	$0.775931\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	35.4381	1.26970
$780$	0	0
$781$	−26.0294	−0.931404
$782$	0	0
$783$	9.21949	0.329478
$784$	0	0
$785$	0	0
$786$	0	0
$787$	15.5592	0.554625	0.277312	−	0.960780i	$-0.410556\pi$
$787$	15.5592	0.554625	0.277312	+	0.960780i	$0.410556\pi$
$788$	0	0
$789$	−22.6282	−0.805586
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−0.969724	−0.0344359
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−36.4002	−1.28936	−0.644681	−	0.764452i	$-0.723010\pi$
$797$	−36.4002	−1.28936	−0.644681	+	0.764452i	$0.723010\pi$
$798$	0	0
$799$	12.2810	0.434469
$800$	0	0
$801$	−9.67030	−0.341683
$802$	0	0
$803$	−58.2791	−2.05663
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−12.2791	−0.432246
$808$	0	0
$809$	5.59793	0.196813	0.0984064	−	0.995146i	$-0.468625\pi$
$809$	5.59793	0.196813	0.0984064	+	0.995146i	$0.468625\pi$
$810$	0	0
$811$	28.1892	0.989857	0.494929	−	0.868934i	$-0.335194\pi$
$811$	28.1892	0.989857	0.494929	+	0.868934i	$0.335194\pi$
$812$	0	0
$813$	22.9385	0.804489
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−26.5601	−0.929220
$818$	0	0
$819$	0	0
$820$	0	0
$821$	33.8208	1.18035	0.590176	−	0.807274i	$-0.299058\pi$
$821$	33.8208	1.18035	0.590176	+	0.807274i	$0.299058\pi$
$822$	0	0
$823$	2.53830	0.0884795	0.0442397	−	0.999021i	$-0.485913\pi$
$823$	2.53830	0.0884795	0.0442397	+	0.999021i	$0.485913\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	12.6694	0.440558	0.220279	−	0.975437i	$-0.429303\pi$
$827$	12.6694	0.440558	0.220279	+	0.975437i	$0.429303\pi$
$828$	0	0
$829$	−37.4693	−1.30136	−0.650681	−	0.759351i	$-0.725516\pi$
$829$	−37.4693	−1.30136	−0.650681	+	0.759351i	$0.725516\pi$
$830$	0	0
$831$	11.5298	0.399965
$832$	0	0
$833$	29.7484	1.03072
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−9.28005	−0.320765
$838$	0	0
$839$	−19.3893	−0.669394	−0.334697	−	0.942326i	$-0.608634\pi$
$839$	−19.3893	−0.669394	−0.334697	+	0.942326i	$0.608634\pi$
$840$	0	0
$841$	55.9991	1.93100
$842$	0	0
$843$	11.3288	0.390184
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	20.9991	0.720687
$850$	0	0
$851$	16.3784	0.561446
$852$	0	0
$853$	7.77959	0.266368	0.133184	−	0.991091i	$-0.457480\pi$
$853$	7.77959	0.266368	0.133184	+	0.991091i	$0.457480\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	26.9697	0.921268	0.460634	−	0.887590i	$-0.347622\pi$
$857$	26.9697	0.921268	0.460634	+	0.887590i	$0.347622\pi$
$858$	0	0
$859$	5.93189	0.202393	0.101197	−	0.994866i	$-0.467733\pi$
$859$	5.93189	0.202393	0.101197	+	0.994866i	$0.467733\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−33.3288	−1.13452	−0.567262	−	0.823537i	$-0.691998\pi$
$863$	−33.3288	−1.13452	−0.567262	+	0.823537i	$0.691998\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−1.06055	−0.0360182
$868$	0	0
$869$	−56.8392	−1.92814
$870$	0	0
$871$	−1.93945	−0.0657157
$872$	0	0
$873$	6.00000	0.203069
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−19.1589	−0.646952	−0.323476	−	0.946236i	$-0.604851\pi$
$877$	−19.1589	−0.646952	−0.323476	+	0.946236i	$0.604851\pi$
$878$	0	0
$879$	−4.26915	−0.143995
$880$	0	0
$881$	53.8989	1.81590	0.907949	−	0.419080i	$-0.137647\pi$
$881$	53.8989	1.81590	0.907949	+	0.419080i	$0.137647\pi$
$882$	0	0
$883$	22.9385	0.771943	0.385972	−	0.922511i	$-0.373866\pi$
$883$	22.9385	0.771943	0.385972	+	0.922511i	$0.373866\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−47.5298	−1.59590	−0.797948	−	0.602727i	$-0.794081\pi$
$887$	−47.5298	−1.59590	−0.797948	+	0.602727i	$0.794081\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−4.64002	−0.155447
$892$	0	0
$893$	18.0606	0.604373
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−2.24977	−0.0751177
$898$	0	0
$899$	−85.5573	−2.85350
$900$	0	0
$901$	−39.1807	−1.30530
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−20.6206	−0.684697	−0.342349	−	0.939573i	$-0.611222\pi$
$907$	−20.6206	−0.684697	−0.342349	+	0.939573i	$0.611222\pi$
$908$	0	0
$909$	−15.2800	−0.506807
$910$	0	0
$911$	−41.2413	−1.36638	−0.683192	−	0.730238i	$-0.739409\pi$
$911$	−41.2413	−1.36638	−0.683192	+	0.730238i	$0.739409\pi$
$912$	0	0
$913$	−17.0303	−0.563620
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	37.2489	1.22873	0.614363	−	0.789023i	$-0.289413\pi$
$919$	37.2489	1.22873	0.614363	+	0.789023i	$0.289413\pi$
$920$	0	0
$921$	−20.0000	−0.659022
$922$	0	0
$923$	−5.60975	−0.184647
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−1.21949	−0.0400535
$928$	0	0
$929$	−59.0091	−1.93602	−0.968012	−	0.250903i	$-0.919273\pi$
$929$	−59.0091	−1.93602	−0.968012	+	0.250903i	$0.919273\pi$
$930$	0	0
$931$	43.7484	1.43380
$932$	0	0
$933$	−3.71904	−0.121756
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−56.9679	−1.86106	−0.930530	−	0.366216i	$-0.880653\pi$
$937$	−56.9679	−1.86106	−0.930530	+	0.366216i	$0.880653\pi$
$938$	0	0
$939$	1.52982	0.0499237
$940$	0	0
$941$	2.35906	0.0769032	0.0384516	−	0.999260i	$-0.487757\pi$
$941$	2.35906	0.0769032	0.0384516	+	0.999260i	$0.487757\pi$
$942$	0	0
$943$	12.7569	0.415421
$944$	0	0
$945$	0	0
$946$	0	0
$947$	43.4481	1.41187	0.705936	−	0.708276i	$-0.250527\pi$
$947$	43.4481	1.41187	0.705936	+	0.708276i	$0.250527\pi$
$948$	0	0
$949$	−12.5601	−0.407718
$950$	0	0
$951$	16.1093	0.522379
$952$	0	0
$953$	23.5904	0.764167	0.382084	−	0.924128i	$-0.375207\pi$
$953$	23.5904	0.764167	0.382084	+	0.924128i	$0.375207\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−42.7787	−1.38284
$958$	0	0
$959$	0	0
$960$	0	0
$961$	55.1193	1.77804
$962$	0	0
$963$	5.28005	0.170147
$964$	0	0
$965$	0	0
$966$	0	0
$967$	31.5979	1.01612	0.508060	−	0.861321i	$-0.330363\pi$
$967$	31.5979	1.01612	0.508060	+	0.861321i	$0.330363\pi$
$968$	0	0
$969$	−26.5601	−0.853233
$970$	0	0
$971$	−0.499542	−0.0160311	−0.00801553	−	0.999968i	$-0.502551\pi$
$971$	−0.499542	−0.0160311	−0.00801553	+	0.999968i	$0.502551\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	18.7081	0.598526	0.299263	−	0.954171i	$-0.403259\pi$
$977$	18.7081	0.598526	0.299263	+	0.954171i	$0.403259\pi$
$978$	0	0
$979$	44.8704	1.43406
$980$	0	0
$981$	−10.1892	−0.325317
$982$	0	0
$983$	−3.83016	−0.122163	−0.0610815	−	0.998133i	$-0.519455\pi$
$983$	−3.83016	−0.122163	−0.0610815	+	0.998133i	$0.519455\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−9.56101	−0.304022
$990$	0	0
$991$	6.43899	0.204541	0.102271	−	0.994757i	$-0.467389\pi$
$991$	6.43899	0.204541	0.102271	+	0.994757i	$0.467389\pi$
$992$	0	0
$993$	−15.5298	−0.492824
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−12.1505	−0.384809	−0.192405	−	0.981316i	$-0.561629\pi$
$997$	−12.1505	−0.384809	−0.192405	+	0.981316i	$0.561629\pi$
$998$	0	0
$999$	7.28005	0.230330

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7800.2.a.bj.1.1		3
5.2	odd	4		1560.2.l.c.1249.6	yes	6
5.3	odd	4		1560.2.l.c.1249.3	✓	6
5.4	even	2		7800.2.a.bp.1.1		3
15.2	even	4		4680.2.l.e.2809.2		6
15.8	even	4		4680.2.l.e.2809.1		6
20.3	even	4		3120.2.l.m.1249.6		6
20.7	even	4		3120.2.l.m.1249.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.l.c.1249.3	✓	6	5.3	odd	4
1560.2.l.c.1249.6	yes	6	5.2	odd	4
3120.2.l.m.1249.3		6	20.7	even	4
3120.2.l.m.1249.6		6	20.3	even	4
4680.2.l.e.2809.1		6	15.8	even	4
4680.2.l.e.2809.2		6	15.2	even	4
7800.2.a.bj.1.1		3	1.1	even	1	trivial
7800.2.a.bp.1.1		3	5.4	even	2

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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:	\( N \)	\(=\)	\( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7800.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{9} -4.64002 q^{11} -1.00000 q^{13} -4.24977 q^{17} -6.24977 q^{19} -2.24977 q^{23} -1.00000 q^{27} -9.21949 q^{29} +9.28005 q^{31} +4.64002 q^{33} -7.28005 q^{37} +1.00000 q^{39} -5.67030 q^{41} +4.24977 q^{43} -2.88979 q^{47} -7.00000 q^{49} +4.24977 q^{51} +9.21949 q^{53} +6.24977 q^{57} +5.92007 q^{59} +0.969724 q^{61} +1.93945 q^{67} +2.24977 q^{69} +5.60975 q^{71} +12.5601 q^{73} +12.2498 q^{79} +1.00000 q^{81} +3.67030 q^{83} +9.21949 q^{87} -9.67030 q^{89} -9.28005 q^{93} +6.00000 q^{97} -4.64002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 3 * q^9	\( 3 q - 3 q^{3} + 3 q^{9} - 6 q^{11} - 3 q^{13} + 4 q^{17} - 2 q^{19} + 10 q^{23} - 3 q^{27} - 10 q^{29} + 12 q^{31} + 6 q^{33} - 6 q^{37} + 3 q^{39} - 10 q^{41} - 4 q^{43} + 16 q^{47} - 21 q^{49} - 4 q^{51} + 10 q^{53} + 2 q^{57} - 6 q^{59} + 2 q^{61} + 4 q^{67} - 10 q^{69} + 8 q^{71} + 6 q^{73} + 20 q^{79} + 3 q^{81} + 4 q^{83} + 10 q^{87} - 22 q^{89} - 12 q^{93} + 18 q^{97} - 6 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 3 * q^9 - 6 * q^11 - 3 * q^13 + 4 * q^17 - 2 * q^19 + 10 * q^23 - 3 * q^27 - 10 * q^29 + 12 * q^31 + 6 * q^33 - 6 * q^37 + 3 * q^39 - 10 * q^41 - 4 * q^43 + 16 * q^47 - 21 * q^49 - 4 * q^51 + 10 * q^53 + 2 * q^57 - 6 * q^59 + 2 * q^61 + 4 * q^67 - 10 * q^69 + 8 * q^71 + 6 * q^73 + 20 * q^79 + 3 * q^81 + 4 * q^83 + 10 * q^87 - 22 * q^89 - 12 * q^93 + 18 * q^97 - 6 * q^99

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