LMFDB - Embedded newform 126.14.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,14,Mod(1,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("126.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	126.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:	$135.110970479$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	126.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+64.0000 q^{2} +4096.00 q^{4} -34758.0 q^{5} +117649. q^{7} +262144. q^{8} +O(q^{10})$

\(q+64.0000 q^{2} +4096.00 q^{4} -34758.0 q^{5} +117649. q^{7} +262144. q^{8} -2.22451e6 q^{10} +9.57488e6 q^{11} -4.78107e6 q^{13} +7.52954e6 q^{14} +1.67772e7 q^{16} +1.41818e8 q^{17} -2.23101e8 q^{19} -1.42369e8 q^{20} +6.12793e8 q^{22} -1.94422e8 q^{23} -1.25846e7 q^{25} -3.05989e8 q^{26} +4.81890e8 q^{28} -2.81676e9 q^{29} -2.53185e8 q^{31} +1.07374e9 q^{32} +9.07635e9 q^{34} -4.08924e9 q^{35} -3.67033e9 q^{37} -1.42785e10 q^{38} -9.11160e9 q^{40} -1.49802e10 q^{41} -1.97968e10 q^{43} +3.92187e10 q^{44} -1.24430e10 q^{46} +7.96848e10 q^{47} +1.38413e10 q^{49} -8.05412e8 q^{50} -1.95833e10 q^{52} +1.72786e11 q^{53} -3.32804e11 q^{55} +3.08410e10 q^{56} -1.80272e11 q^{58} +5.35163e11 q^{59} +9.51435e9 q^{61} -1.62038e10 q^{62} +6.87195e10 q^{64} +1.66181e11 q^{65} +1.19377e12 q^{67} +5.80887e11 q^{68} -2.61712e11 q^{70} +2.05393e12 q^{71} -2.91598e11 q^{73} -2.34901e11 q^{74} -9.13824e11 q^{76} +1.12648e12 q^{77} +8.67537e11 q^{79} -5.83142e11 q^{80} -9.58731e11 q^{82} -3.56643e12 q^{83} -4.92931e12 q^{85} -1.26699e12 q^{86} +2.51000e12 q^{88} -8.11580e11 q^{89} -5.62489e11 q^{91} -7.96351e11 q^{92} +5.09983e12 q^{94} +7.75456e12 q^{95} +1.07329e13 q^{97} +8.85842e11 q^{98} +O(q^{100})\)

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 $

$2$	64.0000	0.707107
$2$	64.0000	0.707107
$3$	0	0
$3$	0	0
$4$	4096.00	0.500000
$5$	−34758.0	−0.994832	−0.497416	−	0.867512i	$-0.665718\pi$
$5$	−34758.0	−0.994832	−0.497416	+	0.867512i	$0.665718\pi$
$6$	0	0
$7$	117649.	0.377964
$7$	117649.	0.377964
$8$	262144.	0.353553
$9$	0	0
$10$	−2.22451e6	−0.703452
$11$	9.57488e6	1.62960	0.814800	−	0.579742i	$-0.196847\pi$
$11$	9.57488e6	1.62960	0.814800	+	0.579742i	$0.196847\pi$
$12$	0	0
$13$	−4.78107e6	−0.274722	−0.137361	−	0.990521i	$-0.543862\pi$
$13$	−4.78107e6	−0.274722	−0.137361	+	0.990521i	$0.543862\pi$
$14$	7.52954e6	0.267261
$15$	0	0
$16$	1.67772e7	0.250000
$17$	1.41818e8	1.42500	0.712498	−	0.701675i	$-0.247564\pi$
$17$	1.41818e8	1.42500	0.712498	+	0.701675i	$0.247564\pi$
$18$	0	0
$19$	−2.23101e8	−1.08794	−0.543969	−	0.839105i	$-0.683079\pi$
$19$	−2.23101e8	−1.08794	−0.543969	+	0.839105i	$0.683079\pi$
$20$	−1.42369e8	−0.497416
$21$	0	0
$22$	6.12793e8	1.15230
$23$	−1.94422e8	−0.273850	−0.136925	−	0.990581i	$-0.543722\pi$
$23$	−1.94422e8	−0.273850	−0.136925	+	0.990581i	$0.543722\pi$
$24$	0	0
$25$	−1.25846e7	−0.0103093
$26$	−3.05989e8	−0.194258
$27$	0	0
$28$	4.81890e8	0.188982
$29$	−2.81676e9	−0.879351	−0.439676	−	0.898157i	$-0.644907\pi$
$29$	−2.81676e9	−0.879351	−0.439676	+	0.898157i	$0.644907\pi$
$30$	0	0
$31$	−2.53185e8	−0.0512373	−0.0256187	−	0.999672i	$-0.508156\pi$
$31$	−2.53185e8	−0.0512373	−0.0256187	+	0.999672i	$0.508156\pi$
$32$	1.07374e9	0.176777
$33$	0	0
$34$	9.07635e9	1.00762
$35$	−4.08924e9	−0.376011
$36$	0	0
$37$	−3.67033e9	−0.235176	−0.117588	−	0.993062i	$-0.537516\pi$
$37$	−3.67033e9	−0.235176	−0.117588	+	0.993062i	$0.537516\pi$
$38$	−1.42785e10	−0.769288
$39$	0	0
$40$	−9.11160e9	−0.351726
$41$	−1.49802e10	−0.492518	−0.246259	−	0.969204i	$-0.579201\pi$
$41$	−1.49802e10	−0.492518	−0.246259	+	0.969204i	$0.579201\pi$
$42$	0	0
$43$	−1.97968e10	−0.477584	−0.238792	−	0.971071i	$-0.576751\pi$
$43$	−1.97968e10	−0.477584	−0.238792	+	0.971071i	$0.576751\pi$
$44$	3.92187e10	0.814800
$45$	0	0
$46$	−1.24430e10	−0.193641
$47$	7.96848e10	1.07830	0.539150	−	0.842210i	$-0.318746\pi$
$47$	7.96848e10	1.07830	0.539150	+	0.842210i	$0.318746\pi$
$48$	0	0
$49$	1.38413e10	0.142857
$50$	−8.05412e8	−0.00728976
$51$	0	0
$52$	−1.95833e10	−0.137361
$53$	1.72786e11	1.07082	0.535408	−	0.844594i	$-0.320158\pi$
$53$	1.72786e11	1.07082	0.535408	+	0.844594i	$0.320158\pi$
$54$	0	0
$55$	−3.32804e11	−1.62118
$56$	3.08410e10	0.133631
$57$	0	0
$58$	−1.80272e11	−0.621795
$59$	5.35163e11	1.65176	0.825882	−	0.563843i	$-0.190678\pi$
$59$	5.35163e11	1.65176	0.825882	+	0.563843i	$0.190678\pi$
$60$	0	0
$61$	9.51435e9	0.0236448	0.0118224	−	0.999930i	$-0.496237\pi$
$61$	9.51435e9	0.0236448	0.0118224	+	0.999930i	$0.496237\pi$
$62$	−1.62038e10	−0.0362303
$63$	0	0
$64$	6.87195e10	0.125000
$65$	1.66181e11	0.273302
$66$	0	0
$67$	1.19377e12	1.61225	0.806127	−	0.591742i	$-0.201560\pi$
$67$	1.19377e12	1.61225	0.806127	+	0.591742i	$0.201560\pi$
$68$	5.80887e11	0.712498
$69$	0	0
$70$	−2.61712e11	−0.265880
$71$	2.05393e12	1.90286	0.951429	−	0.307868i	$-0.0996155\pi$
$71$	2.05393e12	1.90286	0.951429	+	0.307868i	$0.0996155\pi$
$72$	0	0
$73$	−2.91598e11	−0.225520	−0.112760	−	0.993622i	$-0.535969\pi$
$73$	−2.91598e11	−0.225520	−0.112760	+	0.993622i	$0.535969\pi$
$74$	−2.34901e11	−0.166295
$75$	0	0
$76$	−9.13824e11	−0.543969
$77$	1.12648e12	0.615931
$78$	0	0
$79$	8.67537e11	0.401524	0.200762	−	0.979640i	$-0.435658\pi$
$79$	8.67537e11	0.401524	0.200762	+	0.979640i	$0.435658\pi$
$80$	−5.83142e11	−0.248708
$81$	0	0
$82$	−9.58731e11	−0.348263
$83$	−3.56643e12	−1.19736	−0.598682	−	0.800987i	$-0.704309\pi$
$83$	−3.56643e12	−1.19736	−0.598682	+	0.800987i	$0.704309\pi$
$84$	0	0
$85$	−4.92931e12	−1.41763
$86$	−1.26699e12	−0.337703
$87$	0	0
$88$	2.51000e12	0.576151
$89$	−8.11580e11	−0.173100	−0.0865498	−	0.996248i	$-0.527584\pi$
$89$	−8.11580e11	−0.173100	−0.0865498	+	0.996248i	$0.527584\pi$
$90$	0	0
$91$	−5.62489e11	−0.103835
$92$	−7.96351e11	−0.136925
$93$	0	0
$94$	5.09983e12	0.762473
$95$	7.75456e12	1.08232
$96$	0	0
$97$	1.07329e13	1.30828	0.654139	−	0.756374i	$-0.273031\pi$
$97$	1.07329e13	1.30828	0.654139	+	0.756374i	$0.273031\pi$
$98$	8.85842e11	0.101015
$99$	0	0
$100$	−5.15464e10	−0.00515464
$101$	5.98031e12	0.560576	0.280288	−	0.959916i	$-0.409570\pi$
$101$	5.98031e12	0.560576	0.280288	+	0.959916i	$0.409570\pi$
$102$	0	0
$103$	−5.34251e12	−0.440863	−0.220431	−	0.975402i	$-0.570746\pi$
$103$	−5.34251e12	−0.440863	−0.220431	+	0.975402i	$0.570746\pi$
$104$	−1.25333e12	−0.0971289
$105$	0	0
$106$	1.10583e13	0.757181
$107$	2.00751e13	1.29320	0.646598	−	0.762831i	$-0.276191\pi$
$107$	2.00751e13	1.29320	0.646598	+	0.762831i	$0.276191\pi$
$108$	0	0
$109$	1.30494e13	0.745277	0.372639	−	0.927977i	$-0.378453\pi$
$109$	1.30494e13	0.745277	0.372639	+	0.927977i	$0.378453\pi$
$110$	−2.12994e13	−1.14635
$111$	0	0
$112$	1.97382e12	0.0944911
$113$	−8.92136e12	−0.403108	−0.201554	−	0.979477i	$-0.564599\pi$
$113$	−8.92136e12	−0.403108	−0.201554	+	0.979477i	$0.564599\pi$
$114$	0	0
$115$	6.75770e12	0.272435
$116$	−1.15374e13	−0.439676
$117$	0	0
$118$	3.42504e13	1.16797
$119$	1.66847e13	0.538598
$120$	0	0
$121$	5.71557e13	1.65560
$122$	6.08918e11	0.0167194
$123$	0	0
$124$	−1.03704e12	−0.0256187
$125$	4.28666e13	1.00509
$126$	0	0
$127$	−6.69049e12	−0.141493	−0.0707463	−	0.997494i	$-0.522538\pi$
$127$	−6.69049e12	−0.141493	−0.0707463	+	0.997494i	$0.522538\pi$
$128$	4.39805e12	0.0883883
$129$	0	0
$130$	1.06356e13	0.193254
$131$	−9.72766e13	−1.68169	−0.840843	−	0.541278i	$-0.817941\pi$
$131$	−9.72766e13	−1.68169	−0.840843	+	0.541278i	$0.817941\pi$
$132$	0	0
$133$	−2.62477e13	−0.411202
$134$	7.64011e13	1.14004
$135$	0	0
$136$	3.71767e13	0.503812
$137$	7.00280e13	0.904874	0.452437	−	0.891796i	$-0.350555\pi$
$137$	7.00280e13	0.904874	0.452437	+	0.891796i	$0.350555\pi$
$138$	0	0
$139$	−1.52288e14	−1.79089	−0.895445	−	0.445173i	$-0.853142\pi$
$139$	−1.52288e14	−1.79089	−0.895445	+	0.445173i	$0.853142\pi$
$140$	−1.67495e13	−0.188006
$141$	0	0
$142$	1.31452e14	1.34552
$143$	−4.57782e13	−0.447687
$144$	0	0
$145$	9.79048e13	0.874807
$146$	−1.86622e13	−0.159467
$147$	0	0
$148$	−1.50337e13	−0.117588
$149$	2.24697e14	1.68223	0.841117	−	0.540853i	$-0.181899\pi$
$149$	2.24697e14	1.68223	0.841117	+	0.540853i	$0.181899\pi$
$150$	0	0
$151$	−1.54962e14	−1.06384	−0.531918	−	0.846796i	$-0.678529\pi$
$151$	−1.54962e14	−1.06384	−0.531918	+	0.846796i	$0.678529\pi$
$152$	−5.84847e13	−0.384644
$153$	0	0
$154$	7.20944e13	0.435529
$155$	8.80020e12	0.0509726
$156$	0	0
$157$	−9.65485e13	−0.514515	−0.257257	−	0.966343i	$-0.582819\pi$
$157$	−9.65485e13	−0.514515	−0.257257	+	0.966343i	$0.582819\pi$
$158$	5.55223e13	0.283921
$159$	0	0
$160$	−3.73211e13	−0.175863
$161$	−2.28735e13	−0.103506
$162$	0	0
$163$	2.49306e14	1.04115	0.520575	−	0.853816i	$-0.325718\pi$
$163$	2.49306e14	1.04115	0.520575	+	0.853816i	$0.325718\pi$
$164$	−6.13588e13	−0.246259
$165$	0	0
$166$	−2.28252e14	−0.846664
$167$	−2.86038e14	−1.02039	−0.510195	−	0.860059i	$-0.670427\pi$
$167$	−2.86038e14	−1.02039	−0.510195	+	0.860059i	$0.670427\pi$
$168$	0	0
$169$	−2.80016e14	−0.924528
$170$	−3.15476e14	−1.00242
$171$	0	0
$172$	−8.10876e13	−0.238792
$173$	3.64751e14	1.03442	0.517210	−	0.855859i	$-0.326971\pi$
$173$	3.64751e14	1.03442	0.517210	+	0.855859i	$0.326971\pi$
$174$	0	0
$175$	−1.48056e12	−0.00389654
$176$	1.60640e14	0.407400
$177$	0	0
$178$	−5.19411e13	−0.122400
$179$	7.39111e14	1.67944	0.839720	−	0.543019i	$-0.182719\pi$
$179$	7.39111e14	1.67944	0.839720	+	0.543019i	$0.182719\pi$
$180$	0	0
$181$	6.16121e14	1.30243	0.651217	−	0.758892i	$-0.274259\pi$
$181$	6.16121e14	1.30243	0.651217	+	0.758892i	$0.274259\pi$
$182$	−3.59993e13	−0.0734226
$183$	0	0
$184$	−5.09664e13	−0.0968207
$185$	1.27573e14	0.233961
$186$	0	0
$187$	1.35789e15	2.32217
$188$	3.26389e14	0.539150
$189$	0	0
$190$	4.96292e14	0.765312
$191$	−1.00757e15	−1.50161	−0.750804	−	0.660525i	$-0.770334\pi$
$191$	−1.00757e15	−1.50161	−0.750804	+	0.660525i	$0.770334\pi$
$192$	0	0
$193$	1.18652e15	1.65255	0.826273	−	0.563270i	$-0.190457\pi$
$193$	1.18652e15	1.65255	0.826273	+	0.563270i	$0.190457\pi$
$194$	6.86905e14	0.925093
$195$	0	0
$196$	5.66939e13	0.0714286
$197$	5.28577e14	0.644285	0.322142	−	0.946691i	$-0.395597\pi$
$197$	5.28577e14	0.644285	0.322142	+	0.946691i	$0.395597\pi$
$198$	0	0
$199$	1.22197e15	1.39481	0.697407	−	0.716676i	$-0.254337\pi$
$199$	1.22197e15	1.39481	0.697407	+	0.716676i	$0.254337\pi$
$200$	−3.29897e12	−0.00364488
$201$	0	0
$202$	3.82740e14	0.396387
$203$	−3.31389e14	−0.332363
$204$	0	0
$205$	5.20681e14	0.489972
$206$	−3.41921e14	−0.311737
$207$	0	0
$208$	−8.02131e13	−0.0686805
$209$	−2.13617e15	−1.77290
$210$	0	0
$211$	−5.73085e14	−0.447078	−0.223539	−	0.974695i	$-0.571761\pi$
$211$	−5.73085e14	−0.447078	−0.223539	+	0.974695i	$0.571761\pi$
$212$	7.07731e14	0.535408
$213$	0	0
$214$	1.28481e15	0.914427
$215$	6.88096e14	0.475115
$216$	0	0
$217$	−2.97869e13	−0.0193659
$218$	8.35161e14	0.526990
$219$	0	0
$220$	−1.36316e15	−0.810589
$221$	−6.78042e14	−0.391478
$222$	0	0
$223$	2.43219e15	1.32439	0.662196	−	0.749331i	$-0.269625\pi$
$223$	2.43219e15	1.32439	0.662196	+	0.749331i	$0.269625\pi$
$224$	1.26325e14	0.0668153
$225$	0	0
$226$	−5.70967e14	−0.285040
$227$	8.01244e14	0.388684	0.194342	−	0.980934i	$-0.437743\pi$
$227$	8.01244e14	0.388684	0.194342	+	0.980934i	$0.437743\pi$
$228$	0	0
$229$	1.42037e15	0.650836	0.325418	−	0.945570i	$-0.394495\pi$
$229$	1.42037e15	0.650836	0.325418	+	0.945570i	$0.394495\pi$
$230$	4.32493e14	0.192641
$231$	0	0
$232$	−7.38396e14	−0.310898
$233$	1.68574e15	0.690205	0.345103	−	0.938565i	$-0.387844\pi$
$233$	1.68574e15	0.690205	0.345103	+	0.938565i	$0.387844\pi$
$234$	0	0
$235$	−2.76968e15	−1.07273
$236$	2.19203e15	0.825882
$237$	0	0
$238$	1.06782e15	0.380846
$239$	1.04065e15	0.361175	0.180588	−	0.983559i	$-0.442200\pi$
$239$	1.04065e15	0.361175	0.180588	+	0.983559i	$0.442200\pi$
$240$	0	0
$241$	5.01902e14	0.165009	0.0825046	−	0.996591i	$-0.473708\pi$
$241$	5.01902e14	0.165009	0.0825046	+	0.996591i	$0.473708\pi$
$242$	3.65796e15	1.17068
$243$	0	0
$244$	3.89708e13	0.0118224
$245$	−4.81095e14	−0.142119
$246$	0	0
$247$	1.06666e15	0.298881
$248$	−6.63709e13	−0.0181151
$249$	0	0
$250$	2.74346e15	0.710705
$251$	−4.60207e15	−1.16165	−0.580823	−	0.814030i	$-0.697269\pi$
$251$	−4.60207e15	−1.16165	−0.580823	+	0.814030i	$0.697269\pi$
$252$	0	0
$253$	−1.86156e15	−0.446267
$254$	−4.28191e14	−0.100050
$255$	0	0
$256$	2.81475e14	0.0625000
$257$	−1.83358e15	−0.396949	−0.198474	−	0.980106i	$-0.563599\pi$
$257$	−1.83358e15	−0.396949	−0.198474	+	0.980106i	$0.563599\pi$
$258$	0	0
$259$	−4.31811e14	−0.0888883
$260$	6.80676e14	0.136651
$261$	0	0
$262$	−6.22570e15	−1.18913
$263$	5.86908e15	1.09360	0.546799	−	0.837264i	$-0.315846\pi$
$263$	5.86908e15	1.09360	0.546799	+	0.837264i	$0.315846\pi$
$264$	0	0
$265$	−6.00569e15	−1.06528
$266$	−1.67985e15	−0.290764
$267$	0	0
$268$	4.88967e15	0.806127
$269$	7.45041e15	1.19892	0.599460	−	0.800404i	$-0.295382\pi$
$269$	7.45041e15	1.19892	0.599460	+	0.800404i	$0.295382\pi$
$270$	0	0
$271$	−1.21323e16	−1.86056	−0.930280	−	0.366850i	$-0.880436\pi$
$271$	−1.21323e16	−1.86056	−0.930280	+	0.366850i	$0.880436\pi$
$272$	2.37931e15	0.356249
$273$	0	0
$274$	4.48179e15	0.639843
$275$	−1.20496e14	−0.0168000
$276$	0	0
$277$	1.21392e16	1.61463	0.807314	−	0.590123i	$-0.200921\pi$
$277$	1.21392e16	1.61463	0.807314	+	0.590123i	$0.200921\pi$
$278$	−9.74641e15	−1.26635
$279$	0	0
$280$	−1.07197e15	−0.132940
$281$	−7.84561e15	−0.950682	−0.475341	−	0.879802i	$-0.657675\pi$
$281$	−7.84561e15	−0.950682	−0.475341	+	0.879802i	$0.657675\pi$
$282$	0	0
$283$	−9.23915e15	−1.06910	−0.534552	−	0.845136i	$-0.679520\pi$
$283$	−9.23915e15	−1.06910	−0.534552	+	0.845136i	$0.679520\pi$
$284$	8.41290e15	0.951429
$285$	0	0
$286$	−2.92981e15	−0.316563
$287$	−1.76240e15	−0.186154
$288$	0	0
$289$	1.02078e16	1.03061
$290$	6.26591e15	0.618582
$291$	0	0
$292$	−1.19438e15	−0.112760
$293$	−1.74771e15	−0.161373	−0.0806865	−	0.996740i	$-0.525711\pi$
$293$	−1.74771e15	−0.161373	−0.0806865	+	0.996740i	$0.525711\pi$
$294$	0	0
$295$	−1.86012e16	−1.64323
$296$	−9.62155e14	−0.0831474
$297$	0	0
$298$	1.43806e16	1.18952
$299$	9.29544e14	0.0752328
$300$	0	0
$301$	−2.32907e15	−0.180510
$302$	−9.91756e15	−0.752246
$303$	0	0
$304$	−3.74302e15	−0.271984
$305$	−3.30700e14	−0.0235226
$306$	0	0
$307$	−4.26817e15	−0.290966	−0.145483	−	0.989361i	$-0.546474\pi$
$307$	−4.26817e15	−0.290966	−0.145483	+	0.989361i	$0.546474\pi$
$308$	4.61404e15	0.307965
$309$	0	0
$310$	5.63213e14	0.0360430
$311$	−1.66954e16	−1.04630	−0.523149	−	0.852241i	$-0.675243\pi$
$311$	−1.66954e16	−1.04630	−0.523149	+	0.852241i	$0.675243\pi$
$312$	0	0
$313$	−1.41380e16	−0.849867	−0.424933	−	0.905225i	$-0.639703\pi$
$313$	−1.41380e16	−0.849867	−0.424933	+	0.905225i	$0.639703\pi$
$314$	−6.17910e15	−0.363817
$315$	0	0
$316$	3.55343e15	0.200762
$317$	−3.27228e16	−1.81119	−0.905597	−	0.424139i	$-0.860577\pi$
$317$	−3.27228e16	−1.81119	−0.905597	+	0.424139i	$0.860577\pi$
$318$	0	0
$319$	−2.69701e16	−1.43299
$320$	−2.38855e15	−0.124354
$321$	0	0
$322$	−1.46390e15	−0.0731896
$323$	−3.16398e16	−1.55031
$324$	0	0
$325$	6.01677e13	0.00283219
$326$	1.59556e16	0.736204
$327$	0	0
$328$	−3.92696e15	−0.174131
$329$	9.37484e15	0.407559
$330$	0	0
$331$	1.56765e16	0.655191	0.327596	−	0.944818i	$-0.393762\pi$
$331$	1.56765e16	0.655191	0.327596	+	0.944818i	$0.393762\pi$
$332$	−1.46081e16	−0.598682
$333$	0	0
$334$	−1.83064e16	−0.721525
$335$	−4.14930e16	−1.60392
$336$	0	0
$337$	−2.23724e16	−0.831990	−0.415995	−	0.909367i	$-0.636567\pi$
$337$	−2.23724e16	−0.831990	−0.415995	+	0.909367i	$0.636567\pi$
$338$	−1.79211e16	−0.653740
$339$	0	0
$340$	−2.01905e16	−0.708815
$341$	−2.42422e15	−0.0834964
$342$	0	0
$343$	1.62841e15	0.0539949
$344$	−5.18960e15	−0.168851
$345$	0	0
$346$	2.33441e16	0.731445
$347$	2.05570e16	0.632147	0.316074	−	0.948735i	$-0.397635\pi$
$347$	2.05570e16	0.632147	0.316074	+	0.948735i	$0.397635\pi$
$348$	0	0
$349$	3.10128e16	0.918705	0.459352	−	0.888254i	$-0.348081\pi$
$349$	3.10128e16	0.918705	0.459352	+	0.888254i	$0.348081\pi$
$350$	−9.47559e13	−0.00275527
$351$	0	0
$352$	1.02810e16	0.288075
$353$	−3.62709e16	−0.997753	−0.498876	−	0.866673i	$-0.666254\pi$
$353$	−3.62709e16	−0.997753	−0.498876	+	0.866673i	$0.666254\pi$
$354$	0	0
$355$	−7.13905e16	−1.89302
$356$	−3.32423e15	−0.0865498
$357$	0	0
$358$	4.73031e16	1.18754
$359$	2.27310e16	0.560408	0.280204	−	0.959940i	$-0.409598\pi$
$359$	2.27310e16	0.560408	0.280204	+	0.959940i	$0.409598\pi$
$360$	0	0
$361$	7.72129e15	0.183609
$362$	3.94318e16	0.920959
$363$	0	0
$364$	−2.30395e15	−0.0519176
$365$	1.01354e16	0.224355
$366$	0	0
$367$	−7.71920e16	−1.64909	−0.824543	−	0.565800i	$-0.808567\pi$
$367$	−7.71920e16	−1.64909	−0.824543	+	0.565800i	$0.808567\pi$
$368$	−3.26185e15	−0.0684626
$369$	0	0
$370$	8.16469e15	0.165435
$371$	2.03281e16	0.404730
$372$	0	0
$373$	2.70701e15	0.0520454	0.0260227	−	0.999661i	$-0.491716\pi$
$373$	2.70701e15	0.0520454	0.0260227	+	0.999661i	$0.491716\pi$
$374$	8.69050e16	1.64202
$375$	0	0
$376$	2.08889e16	0.381236
$377$	1.34671e16	0.241577
$378$	0	0
$379$	2.32185e16	0.402419	0.201210	−	0.979548i	$-0.435513\pi$
$379$	2.32185e16	0.402419	0.201210	+	0.979548i	$0.435513\pi$
$380$	3.17627e16	0.541158
$381$	0	0
$382$	−6.44843e16	−1.06180
$383$	8.49278e16	1.37486	0.687429	−	0.726251i	$-0.258739\pi$
$383$	8.49278e16	1.37486	0.687429	+	0.726251i	$0.258739\pi$
$384$	0	0
$385$	−3.91540e16	−0.612748
$386$	7.59374e16	1.16853
$387$	0	0
$388$	4.39619e16	0.654139
$389$	−7.24806e16	−1.06059	−0.530297	−	0.847812i	$-0.677920\pi$
$389$	−7.24806e16	−1.06059	−0.530297	+	0.847812i	$0.677920\pi$
$390$	0	0
$391$	−2.75725e16	−0.390236
$392$	3.62841e15	0.0505076
$393$	0	0
$394$	3.38289e16	0.455578
$395$	−3.01538e16	−0.399449
$396$	0	0
$397$	−2.09568e16	−0.268650	−0.134325	−	0.990937i	$-0.542887\pi$
$397$	−2.09568e16	−0.268650	−0.134325	+	0.990937i	$0.542887\pi$
$398$	7.82062e16	0.986282
$399$	0	0
$400$	−2.11134e14	−0.00257732
$401$	−1.46222e17	−1.75620	−0.878101	−	0.478476i	$-0.841189\pi$
$401$	−1.46222e17	−1.75620	−0.878101	+	0.478476i	$0.841189\pi$
$402$	0	0
$403$	1.21050e15	0.0140760
$404$	2.44953e16	0.280288
$405$	0	0
$406$	−2.12089e16	−0.235016
$407$	−3.51430e16	−0.383244
$408$	0	0
$409$	−4.28456e16	−0.452589	−0.226295	−	0.974059i	$-0.572661\pi$
$409$	−4.28456e16	−0.452589	−0.226295	+	0.974059i	$0.572661\pi$
$410$	3.33236e16	0.346463
$411$	0	0
$412$	−2.18829e16	−0.220431
$413$	6.29614e16	0.624308
$414$	0	0
$415$	1.23962e17	1.19118
$416$	−5.13364e15	−0.0485645
$417$	0	0
$418$	−1.36715e17	−1.25363
$419$	2.80121e16	0.252903	0.126452	−	0.991973i	$-0.459641\pi$
$419$	2.80121e16	0.252903	0.126452	+	0.991973i	$0.459641\pi$
$420$	0	0
$421$	1.77702e17	1.55546	0.777730	−	0.628599i	$-0.216371\pi$
$421$	1.77702e17	1.55546	0.777730	+	0.628599i	$0.216371\pi$
$422$	−3.66774e16	−0.316132
$423$	0	0
$424$	4.52948e16	0.378591
$425$	−1.78472e15	−0.0146907
$426$	0	0
$427$	1.11935e15	0.00893689
$428$	8.22278e16	0.646598
$429$	0	0
$430$	4.40382e16	0.335957
$431$	1.09605e17	0.823620	0.411810	−	0.911270i	$-0.364897\pi$
$431$	1.09605e17	0.823620	0.411810	+	0.911270i	$0.364897\pi$
$432$	0	0
$433$	1.64040e17	1.19613	0.598066	−	0.801447i	$-0.295936\pi$
$433$	1.64040e17	1.19613	0.598066	+	0.801447i	$0.295936\pi$
$434$	−1.90636e15	−0.0136938
$435$	0	0
$436$	5.34503e16	0.372639
$437$	4.33757e16	0.297932
$438$	0	0
$439$	1.00369e17	0.669238	0.334619	−	0.942354i	$-0.391392\pi$
$439$	1.00369e17	0.669238	0.334619	+	0.942354i	$0.391392\pi$
$440$	−8.72425e16	−0.573173
$441$	0	0
$442$	−4.33947e16	−0.276817
$443$	−2.69413e17	−1.69354	−0.846768	−	0.531963i	$-0.821455\pi$
$443$	−2.69413e17	−1.69354	−0.846768	+	0.531963i	$0.821455\pi$
$444$	0	0
$445$	2.82089e16	0.172205
$446$	1.55660e17	0.936486
$447$	0	0
$448$	8.08478e15	0.0472456
$449$	−1.97230e17	−1.13598	−0.567992	−	0.823034i	$-0.692279\pi$
$449$	−1.97230e17	−1.13598	−0.567992	+	0.823034i	$0.692279\pi$
$450$	0	0
$451$	−1.43433e17	−0.802607
$452$	−3.65419e16	−0.201554
$453$	0	0
$454$	5.12796e16	0.274841
$455$	1.95510e16	0.103299
$456$	0	0
$457$	1.01391e17	0.520650	0.260325	−	0.965521i	$-0.416170\pi$
$457$	1.01391e17	0.520650	0.260325	+	0.965521i	$0.416170\pi$
$458$	9.09038e16	0.460211
$459$	0	0
$460$	2.76796e16	0.136218
$461$	−7.94271e16	−0.385401	−0.192700	−	0.981258i	$-0.561725\pi$
$461$	−7.94271e16	−0.385401	−0.192700	+	0.981258i	$0.561725\pi$
$462$	0	0
$463$	1.48361e17	0.699911	0.349956	−	0.936766i	$-0.386197\pi$
$463$	1.48361e17	0.699911	0.349956	+	0.936766i	$0.386197\pi$
$464$	−4.72573e16	−0.219838
$465$	0	0
$466$	1.07888e17	0.488049
$467$	−2.26060e17	−1.00847	−0.504235	−	0.863566i	$-0.668226\pi$
$467$	−2.26060e17	−1.00847	−0.504235	+	0.863566i	$0.668226\pi$
$468$	0	0
$469$	1.40446e17	0.609375
$470$	−1.77260e17	−0.758532
$471$	0	0
$472$	1.40290e17	0.583987
$473$	−1.89552e17	−0.778270
$474$	0	0
$475$	2.80763e15	0.0112158
$476$	6.83407e16	0.269299
$477$	0	0
$478$	6.66016e16	0.255390
$479$	4.68429e17	1.77200	0.885998	−	0.463690i	$-0.153475\pi$
$479$	4.68429e17	1.77200	0.885998	+	0.463690i	$0.153475\pi$
$480$	0	0
$481$	1.75481e16	0.0646082
$482$	3.21217e16	0.116679
$483$	0	0
$484$	2.34110e17	0.827798
$485$	−3.73054e17	−1.30152
$486$	0	0
$487$	−1.17591e17	−0.399426	−0.199713	−	0.979854i	$-0.564001\pi$
$487$	−1.17591e17	−0.399426	−0.199713	+	0.979854i	$0.564001\pi$
$488$	2.49413e15	0.00835969
$489$	0	0
$490$	−3.07901e16	−0.100493
$491$	4.35990e17	1.40426	0.702128	−	0.712051i	$-0.252233\pi$
$491$	4.35990e17	1.40426	0.702128	+	0.712051i	$0.252233\pi$
$492$	0	0
$493$	−3.99467e17	−1.25307
$494$	6.82665e16	0.211341
$495$	0	0
$496$	−4.24774e15	−0.0128093
$497$	2.41643e17	0.719213
$498$	0	0
$499$	4.52325e17	1.31159	0.655793	−	0.754941i	$-0.272335\pi$
$499$	4.52325e17	1.31159	0.655793	+	0.754941i	$0.272335\pi$
$500$	1.75582e17	0.502544
$501$	0	0
$502$	−2.94532e17	−0.821408
$503$	3.80178e17	1.04664	0.523318	−	0.852138i	$-0.324694\pi$
$503$	3.80178e17	1.04664	0.523318	+	0.852138i	$0.324694\pi$
$504$	0	0
$505$	−2.07864e17	−0.557679
$506$	−1.19140e17	−0.315558
$507$	0	0
$508$	−2.74042e16	−0.0707463
$509$	−1.52059e17	−0.387567	−0.193783	−	0.981044i	$-0.562076\pi$
$509$	−1.52059e17	−0.387567	−0.193783	+	0.981044i	$0.562076\pi$
$510$	0	0
$511$	−3.43062e16	−0.0852386
$512$	1.80144e16	0.0441942
$513$	0	0
$514$	−1.17349e17	−0.280685
$515$	1.85695e17	0.438584
$516$	0	0
$517$	7.62973e17	1.75720
$518$	−2.76359e16	−0.0628535
$519$	0	0
$520$	4.35632e16	0.0966270
$521$	2.80630e17	0.614737	0.307369	−	0.951591i	$-0.400552\pi$
$521$	2.80630e17	0.614737	0.307369	+	0.951591i	$0.400552\pi$
$522$	0	0
$523$	−2.46266e17	−0.526191	−0.263095	−	0.964770i	$-0.584743\pi$
$523$	−2.46266e17	−0.526191	−0.263095	+	0.964770i	$0.584743\pi$
$524$	−3.98445e17	−0.840843
$525$	0	0
$526$	3.75621e17	0.773290
$527$	−3.59062e16	−0.0730130
$528$	0	0
$529$	−4.66237e17	−0.925006
$530$	−3.84364e17	−0.753268
$531$	0	0
$532$	−1.07510e17	−0.205601
$533$	7.16213e16	0.135306
$534$	0	0
$535$	−6.97772e17	−1.28651
$536$	3.12939e17	0.570018
$537$	0	0
$538$	4.76826e17	0.847765
$539$	1.32529e17	0.232800
$540$	0	0
$541$	−1.29998e17	−0.222922	−0.111461	−	0.993769i	$-0.535553\pi$
$541$	−1.29998e17	−0.222922	−0.111461	+	0.993769i	$0.535553\pi$
$542$	−7.76469e17	−1.31561
$543$	0	0
$544$	1.52276e17	0.251906
$545$	−4.53570e17	−0.741425
$546$	0	0
$547$	−9.18761e17	−1.46651	−0.733255	−	0.679954i	$-0.762000\pi$
$547$	−9.18761e17	−1.46651	−0.733255	+	0.679954i	$0.762000\pi$
$548$	2.86835e17	0.452437
$549$	0	0
$550$	−7.71173e15	−0.0118794
$551$	6.28422e17	0.956679
$552$	0	0
$553$	1.02065e17	0.151762
$554$	7.76910e17	1.14171
$555$	0	0
$556$	−6.23771e17	−0.895445
$557$	4.21515e17	0.598073	0.299036	−	0.954242i	$-0.403335\pi$
$557$	4.21515e17	0.598073	0.299036	+	0.954242i	$0.403335\pi$
$558$	0	0
$559$	9.46498e16	0.131203
$560$	−6.86061e16	−0.0940028
$561$	0	0
$562$	−5.02119e17	−0.672234
$563$	−8.17298e17	−1.08162	−0.540811	−	0.841144i	$-0.681883\pi$
$563$	−8.17298e17	−1.08162	−0.540811	+	0.841144i	$0.681883\pi$
$564$	0	0
$565$	3.10089e17	0.401025
$566$	−5.91305e17	−0.755971
$567$	0	0
$568$	5.38425e17	0.672762
$569$	−6.14047e16	−0.0758529	−0.0379265	−	0.999281i	$-0.512075\pi$
$569$	−6.14047e16	−0.0758529	−0.0379265	+	0.999281i	$0.512075\pi$
$570$	0	0
$571$	−8.37967e17	−1.01179	−0.505897	−	0.862594i	$-0.668838\pi$
$571$	−8.37967e17	−1.01179	−0.505897	+	0.862594i	$0.668838\pi$
$572$	−1.87508e17	−0.223844
$573$	0	0
$574$	−1.12794e17	−0.131631
$575$	2.44671e15	0.00282320
$576$	0	0
$577$	6.93506e17	0.782361	0.391181	−	0.920314i	$-0.372067\pi$
$577$	6.93506e17	0.782361	0.391181	+	0.920314i	$0.372067\pi$
$578$	6.53297e17	0.728752
$579$	0	0
$580$	4.01018e17	0.437403
$581$	−4.19587e17	−0.452561
$582$	0	0
$583$	1.65440e18	1.74500
$584$	−7.64406e16	−0.0797334
$585$	0	0
$586$	−1.11854e17	−0.114108
$587$	1.73073e18	1.74615	0.873074	−	0.487588i	$-0.162123\pi$
$587$	1.73073e18	1.74615	0.873074	+	0.487588i	$0.162123\pi$
$588$	0	0
$589$	5.64859e16	0.0557430
$590$	−1.19048e18	−1.16194
$591$	0	0
$592$	−6.15779e16	−0.0587941
$593$	8.17983e17	0.772483	0.386241	−	0.922398i	$-0.373773\pi$
$593$	8.17983e17	0.772483	0.386241	+	0.922398i	$0.373773\pi$
$594$	0	0
$595$	−5.79928e17	−0.535814
$596$	9.20359e17	0.841117
$597$	0	0
$598$	5.94908e16	0.0531976
$599$	3.47555e17	0.307432	0.153716	−	0.988115i	$-0.450876\pi$
$599$	3.47555e17	0.307432	0.153716	+	0.988115i	$0.450876\pi$
$600$	0	0
$601$	−7.44681e17	−0.644594	−0.322297	−	0.946639i	$-0.604455\pi$
$601$	−7.44681e17	−0.644594	−0.322297	+	0.946639i	$0.604455\pi$
$602$	−1.49060e17	−0.127640
$603$	0	0
$604$	−6.34724e17	−0.531918
$605$	−1.98662e18	−1.64704
$606$	0	0
$607$	3.92604e17	0.318587	0.159293	−	0.987231i	$-0.449078\pi$
$607$	3.92604e17	0.318587	0.159293	+	0.987231i	$0.449078\pi$
$608$	−2.39553e17	−0.192322
$609$	0	0
$610$	−2.11648e16	−0.0166330
$611$	−3.80979e17	−0.296233
$612$	0	0
$613$	1.57710e18	1.20051	0.600257	−	0.799807i	$-0.295065\pi$
$613$	1.57710e18	1.20051	0.600257	+	0.799807i	$0.295065\pi$
$614$	−2.73163e17	−0.205744
$615$	0	0
$616$	2.95299e17	0.217764
$617$	1.68095e18	1.22660	0.613298	−	0.789852i	$-0.289843\pi$
$617$	1.68095e18	1.22660	0.613298	+	0.789852i	$0.289843\pi$
$618$	0	0
$619$	−2.34927e18	−1.67859	−0.839294	−	0.543677i	$-0.817032\pi$
$619$	−2.34927e18	−1.67859	−0.839294	+	0.543677i	$0.817032\pi$
$620$	3.60456e16	0.0254863
$621$	0	0
$622$	−1.06851e18	−0.739845
$623$	−9.54815e16	−0.0654255
$624$	0	0
$625$	−1.47460e18	−0.989584
$626$	−9.04834e17	−0.600947
$627$	0	0
$628$	−3.95463e17	−0.257257
$629$	−5.20519e17	−0.335125
$630$	0	0
$631$	−6.40695e17	−0.404074	−0.202037	−	0.979378i	$-0.564756\pi$
$631$	−6.40695e17	−0.404074	−0.202037	+	0.979378i	$0.564756\pi$
$632$	2.27420e17	0.141960
$633$	0	0
$634$	−2.09426e18	−1.28071
$635$	2.32548e17	0.140761
$636$	0	0
$637$	−6.61762e16	−0.0392460
$638$	−1.72609e18	−1.01328
$639$	0	0
$640$	−1.52867e17	−0.0879316
$641$	−2.25043e18	−1.28141	−0.640706	−	0.767786i	$-0.721358\pi$
$641$	−2.25043e18	−1.28141	−0.640706	+	0.767786i	$0.721358\pi$
$642$	0	0
$643$	−1.96875e18	−1.09855	−0.549274	−	0.835642i	$-0.685096\pi$
$643$	−1.96875e18	−1.09855	−0.549274	+	0.835642i	$0.685096\pi$
$644$	−9.36898e16	−0.0517529
$645$	0	0
$646$	−2.02495e18	−1.09623
$647$	−1.19575e18	−0.640860	−0.320430	−	0.947272i	$-0.603827\pi$
$647$	−1.19575e18	−0.640860	−0.320430	+	0.947272i	$0.603827\pi$
$648$	0	0
$649$	5.12412e18	2.69171
$650$	3.85073e15	0.00200266
$651$	0	0
$652$	1.02116e18	0.520575
$653$	−3.08192e18	−1.55556	−0.777778	−	0.628539i	$-0.783653\pi$
$653$	−3.08192e18	−1.55556	−0.777778	+	0.628539i	$0.783653\pi$
$654$	0	0
$655$	3.38114e18	1.67300
$656$	−2.51326e17	−0.123129
$657$	0	0
$658$	5.99990e17	0.288188
$659$	−1.53129e18	−0.728287	−0.364144	−	0.931343i	$-0.618638\pi$
$659$	−1.53129e18	−0.728287	−0.364144	+	0.931343i	$0.618638\pi$
$660$	0	0
$661$	1.18647e18	0.553284	0.276642	−	0.960973i	$-0.410778\pi$
$661$	1.18647e18	0.553284	0.276642	+	0.960973i	$0.410778\pi$
$662$	1.00330e18	0.463290
$663$	0	0
$664$	−9.34918e17	−0.423332
$665$	9.12316e17	0.409077
$666$	0	0
$667$	5.47638e17	0.240811
$668$	−1.17161e18	−0.510195
$669$	0	0
$670$	−2.65555e18	−1.13414
$671$	9.10988e16	0.0385315
$672$	0	0
$673$	−1.47771e17	−0.0613043	−0.0306522	−	0.999530i	$-0.509758\pi$
$673$	−1.47771e17	−0.0613043	−0.0306522	+	0.999530i	$0.509758\pi$
$674$	−1.43183e18	−0.588305
$675$	0	0
$676$	−1.14695e18	−0.462264
$677$	8.37412e17	0.334282	0.167141	−	0.985933i	$-0.446546\pi$
$677$	8.37412e17	0.334282	0.167141	+	0.985933i	$0.446546\pi$
$678$	0	0
$679$	1.26271e18	0.494483
$680$	−1.29219e18	−0.501208
$681$	0	0
$682$	−1.55150e17	−0.0590409
$683$	3.29808e18	1.24316	0.621580	−	0.783351i	$-0.286491\pi$
$683$	3.29808e18	1.24316	0.621580	+	0.783351i	$0.286491\pi$
$684$	0	0
$685$	−2.43403e18	−0.900198
$686$	1.04218e17	0.0381802
$687$	0	0
$688$	−3.32135e17	−0.119396
$689$	−8.26102e17	−0.294177
$690$	0	0
$691$	−5.29545e17	−0.185053	−0.0925264	−	0.995710i	$-0.529494\pi$
$691$	−5.29545e17	−0.185053	−0.0925264	+	0.995710i	$0.529494\pi$
$692$	1.49402e18	0.517210
$693$	0	0
$694$	1.31565e18	0.446996
$695$	5.29322e18	1.78163
$696$	0	0
$697$	−2.12446e18	−0.701835
$698$	1.98482e18	0.649623
$699$	0	0
$700$	−6.06438e15	−0.00194827
$701$	4.66224e18	1.48398	0.741990	−	0.670411i	$-0.233882\pi$
$701$	4.66224e18	1.48398	0.741990	+	0.670411i	$0.233882\pi$
$702$	0	0
$703$	8.18856e17	0.255857
$704$	6.57981e17	0.203700
$705$	0	0
$706$	−2.32134e18	−0.705518
$707$	7.03577e17	0.211878
$708$	0	0
$709$	−6.32550e18	−1.87023	−0.935113	−	0.354350i	$-0.884702\pi$
$709$	−6.32550e18	−1.87023	−0.935113	+	0.354350i	$0.884702\pi$
$710$	−4.56899e18	−1.33857
$711$	0	0
$712$	−2.12751e17	−0.0611999
$713$	4.92246e16	0.0140314
$714$	0	0
$715$	1.59116e18	0.445374
$716$	3.02740e18	0.839720
$717$	0	0
$718$	1.45478e18	0.396268
$719$	−6.63423e18	−1.79082	−0.895412	−	0.445238i	$-0.853119\pi$
$719$	−6.63423e18	−1.79082	−0.895412	+	0.445238i	$0.853119\pi$
$720$	0	0
$721$	−6.28541e17	−0.166630
$722$	4.94162e17	0.129831
$723$	0	0
$724$	2.52363e18	0.651217
$725$	3.54476e16	0.00906547
$726$	0	0
$727$	−2.80242e18	−0.703979	−0.351989	−	0.936004i	$-0.614495\pi$
$727$	−2.80242e18	−0.703979	−0.351989	+	0.936004i	$0.614495\pi$
$728$	−1.47453e17	−0.0367113
$729$	0	0
$730$	6.48662e17	0.158643
$731$	−2.80754e18	−0.680554
$732$	0	0
$733$	−2.85631e18	−0.680189	−0.340094	−	0.940391i	$-0.610459\pi$
$733$	−2.85631e18	−0.680189	−0.340094	+	0.940391i	$0.610459\pi$
$734$	−4.94029e18	−1.16608
$735$	0	0
$736$	−2.08759e17	−0.0484104
$737$	1.14302e19	2.62733
$738$	0	0
$739$	7.32659e18	1.65468	0.827338	−	0.561705i	$-0.189854\pi$
$739$	7.32659e18	1.65468	0.827338	+	0.561705i	$0.189854\pi$
$740$	5.22540e17	0.116981
$741$	0	0
$742$	1.30100e18	0.286188
$743$	2.23791e17	0.0487996	0.0243998	−	0.999702i	$-0.492233\pi$
$743$	2.23791e17	0.0487996	0.0243998	+	0.999702i	$0.492233\pi$
$744$	0	0
$745$	−7.81002e18	−1.67354
$746$	1.73248e17	0.0368016
$747$	0	0
$748$	5.56192e18	1.16109
$749$	2.36182e18	0.488782
$750$	0	0
$751$	−3.07828e18	−0.626107	−0.313053	−	0.949736i	$-0.601352\pi$
$751$	−3.07828e18	−0.626107	−0.313053	+	0.949736i	$0.601352\pi$
$752$	1.33689e18	0.269575
$753$	0	0
$754$	8.61896e17	0.170821
$755$	5.38617e18	1.05834
$756$	0	0
$757$	2.41361e18	0.466169	0.233085	−	0.972456i	$-0.425118\pi$
$757$	2.41361e18	0.466169	0.233085	+	0.972456i	$0.425118\pi$
$758$	1.48598e18	0.284554
$759$	0	0
$760$	2.03281e18	0.382656
$761$	−5.47321e18	−1.02151	−0.510754	−	0.859727i	$-0.670634\pi$
$761$	−5.47321e18	−1.02151	−0.510754	+	0.859727i	$0.670634\pi$
$762$	0	0
$763$	1.53525e18	0.281688
$764$	−4.12699e18	−0.750804
$765$	0	0
$766$	5.43538e18	0.972172
$767$	−2.55865e18	−0.453776
$768$	0	0
$769$	4.99087e18	0.870273	0.435136	−	0.900365i	$-0.356700\pi$
$769$	4.99087e18	0.870273	0.435136	+	0.900365i	$0.356700\pi$
$770$	−2.50586e18	−0.433278
$771$	0	0
$772$	4.86000e18	0.826273
$773$	1.12721e17	0.0190038	0.00950188	−	0.999955i	$-0.496975\pi$
$773$	1.12721e17	0.0190038	0.00950188	+	0.999955i	$0.496975\pi$
$774$	0	0
$775$	3.18622e15	0.000528220 0
$776$	2.81356e18	0.462546
$777$	0	0
$778$	−4.63876e18	−0.749953
$779$	3.34210e18	0.535829
$780$	0	0
$781$	1.96661e19	3.10090
$782$	−1.76464e18	−0.275938
$783$	0	0
$784$	2.32218e17	0.0357143
$785$	3.35583e18	0.511856
$786$	0	0
$787$	6.20473e18	0.930866	0.465433	−	0.885083i	$-0.345899\pi$
$787$	6.20473e18	0.930866	0.465433	+	0.885083i	$0.345899\pi$
$788$	2.16505e18	0.322142
$789$	0	0
$790$	−1.92985e18	−0.282453
$791$	−1.04959e18	−0.152360
$792$	0	0
$793$	−4.54888e16	−0.00649574
$794$	−1.34124e18	−0.189964
$795$	0	0
$796$	5.00519e18	0.697407
$797$	5.15496e18	0.712436	0.356218	−	0.934403i	$-0.384066\pi$
$797$	5.15496e18	0.712436	0.356218	+	0.934403i	$0.384066\pi$
$798$	0	0
$799$	1.13007e19	1.53657
$800$	−1.35126e16	−0.00182244
$801$	0	0
$802$	−9.35821e18	−1.24182
$803$	−2.79201e18	−0.367508
$804$	0	0
$805$	7.95037e17	0.102971
$806$	7.74717e16	0.00995326
$807$	0	0
$808$	1.56770e18	0.198194
$809$	−1.23760e19	−1.55209	−0.776043	−	0.630680i	$-0.782776\pi$
$809$	−1.23760e19	−1.55209	−0.776043	+	0.630680i	$0.782776\pi$
$810$	0	0
$811$	−5.50347e18	−0.679205	−0.339603	−	0.940569i	$-0.610293\pi$
$811$	−5.50347e18	−0.679205	−0.339603	+	0.940569i	$0.610293\pi$
$812$	−1.35737e18	−0.166182
$813$	0	0
$814$	−2.24915e18	−0.270994
$815$	−8.66537e18	−1.03577
$816$	0	0
$817$	4.41669e18	0.519581
$818$	−2.74212e18	−0.320029
$819$	0	0
$820$	2.13271e18	0.244986
$821$	2.10796e17	0.0240232	0.0120116	−	0.999928i	$-0.496176\pi$
$821$	2.10796e17	0.0240232	0.0120116	+	0.999928i	$0.496176\pi$
$822$	0	0
$823$	−1.13797e19	−1.27654	−0.638268	−	0.769814i	$-0.720349\pi$
$823$	−1.13797e19	−1.27654	−0.638268	+	0.769814i	$0.720349\pi$
$824$	−1.40051e18	−0.155869
$825$	0	0
$826$	4.02953e18	0.441452
$827$	9.80788e18	1.06608	0.533040	−	0.846090i	$-0.321050\pi$
$827$	9.80788e18	1.06608	0.533040	+	0.846090i	$0.321050\pi$
$828$	0	0
$829$	8.58043e18	0.918131	0.459066	−	0.888402i	$-0.348184\pi$
$829$	8.58043e18	0.918131	0.459066	+	0.888402i	$0.348184\pi$
$830$	7.93357e18	0.842289
$831$	0	0
$832$	−3.28553e17	−0.0343403
$833$	1.96294e18	0.203571
$834$	0	0
$835$	9.94210e18	1.01512
$836$	−8.74976e18	−0.886452
$837$	0	0
$838$	1.79277e18	0.178829
$839$	9.55862e18	0.946112	0.473056	−	0.881032i	$-0.343151\pi$
$839$	9.55862e18	0.946112	0.473056	+	0.881032i	$0.343151\pi$
$840$	0	0
$841$	−2.32651e18	−0.226742
$842$	1.13729e19	1.09988
$843$	0	0
$844$	−2.34736e18	−0.223539
$845$	9.73281e18	0.919750
$846$	0	0
$847$	6.72431e18	0.625757
$848$	2.89886e18	0.267704
$849$	0	0
$850$	−1.14222e17	−0.0103879
$851$	7.13591e17	0.0644032
$852$	0	0
$853$	−7.53554e18	−0.669800	−0.334900	−	0.942254i	$-0.608703\pi$
$853$	−7.53554e18	−0.669800	−0.334900	+	0.942254i	$0.608703\pi$
$854$	7.16386e16	0.00631933
$855$	0	0
$856$	5.26258e18	0.457213
$857$	1.28698e19	1.10968	0.554839	−	0.831957i	$-0.312780\pi$
$857$	1.28698e19	1.10968	0.554839	+	0.831957i	$0.312780\pi$
$858$	0	0
$859$	−5.62168e18	−0.477431	−0.238715	−	0.971090i	$-0.576726\pi$
$859$	−5.62168e18	−0.477431	−0.238715	+	0.971090i	$0.576726\pi$
$860$	2.81844e18	0.237558
$861$	0	0
$862$	7.01470e18	0.582387
$863$	−1.93836e19	−1.59722	−0.798609	−	0.601850i	$-0.794430\pi$
$863$	−1.93836e19	−1.59722	−0.798609	+	0.601850i	$0.794430\pi$
$864$	0	0
$865$	−1.26780e19	−1.02907
$866$	1.04986e19	0.845793
$867$	0	0
$868$	−1.22007e17	−0.00968295
$869$	8.30656e18	0.654324
$870$	0	0
$871$	−5.70749e18	−0.442922
$872$	3.42082e18	0.263495
$873$	0	0
$874$	2.77605e18	0.210670
$875$	5.04321e18	0.379888
$876$	0	0
$877$	−9.59713e18	−0.712269	−0.356135	−	0.934435i	$-0.615906\pi$
$877$	−9.59713e18	−0.712269	−0.356135	+	0.934435i	$0.615906\pi$
$878$	6.42362e18	0.473223
$879$	0	0
$880$	−5.58352e18	−0.405295
$881$	7.01364e18	0.505359	0.252680	−	0.967550i	$-0.418688\pi$
$881$	7.01364e18	0.505359	0.252680	+	0.967550i	$0.418688\pi$
$882$	0	0
$883$	−7.87780e18	−0.559320	−0.279660	−	0.960099i	$-0.590222\pi$
$883$	−7.87780e18	−0.559320	−0.279660	+	0.960099i	$0.590222\pi$
$884$	−2.77726e18	−0.195739
$885$	0	0
$886$	−1.72424e19	−1.19751
$887$	−1.80776e19	−1.24635	−0.623173	−	0.782084i	$-0.714157\pi$
$887$	−1.80776e19	−1.24635	−0.623173	+	0.782084i	$0.714157\pi$
$888$	0	0
$889$	−7.87129e17	−0.0534791
$890$	1.80537e18	0.121767
$891$	0	0
$892$	9.96226e18	0.662196
$893$	−1.77778e19	−1.17312
$894$	0	0
$895$	−2.56900e19	−1.67076
$896$	5.17426e17	0.0334077
$897$	0	0
$898$	−1.26227e19	−0.803262
$899$	7.13160e17	0.0450556
$900$	0	0
$901$	2.45041e19	1.52591
$902$	−9.17974e18	−0.567529
$903$	0	0
$904$	−2.33868e18	−0.142520
$905$	−2.14151e19	−1.29570
$906$	0	0
$907$	8.58062e18	0.511766	0.255883	−	0.966708i	$-0.417634\pi$
$907$	8.58062e18	0.511766	0.255883	+	0.966708i	$0.417634\pi$
$908$	3.28189e18	0.194342
$909$	0	0
$910$	1.25126e18	0.0730431
$911$	1.93827e19	1.12342	0.561712	−	0.827333i	$-0.310143\pi$
$911$	1.93827e19	1.12342	0.561712	+	0.827333i	$0.310143\pi$
$912$	0	0
$913$	−3.41482e19	−1.95122
$914$	6.48905e18	0.368155
$915$	0	0
$916$	5.81785e18	0.325418
$917$	−1.14445e19	−0.635618
$918$	0	0
$919$	2.08729e19	1.14296	0.571480	−	0.820616i	$-0.306369\pi$
$919$	2.08729e19	1.14296	0.571480	+	0.820616i	$0.306369\pi$
$920$	1.77149e18	0.0963204
$921$	0	0
$922$	−5.08333e18	−0.272520
$923$	−9.81999e18	−0.522757
$924$	0	0
$925$	4.61895e16	0.00242450
$926$	9.49510e18	0.494912
$927$	0	0
$928$	−3.02447e18	−0.155449
$929$	−2.35794e19	−1.20346	−0.601729	−	0.798701i	$-0.705521\pi$
$929$	−2.35794e19	−1.20346	−0.601729	+	0.798701i	$0.705521\pi$
$930$	0	0
$931$	−3.08801e18	−0.155420
$932$	6.90481e18	0.345103
$933$	0	0
$934$	−1.44678e19	−0.713097
$935$	−4.71976e19	−2.31017
$936$	0	0
$937$	−3.34817e19	−1.61622	−0.808111	−	0.589031i	$-0.799510\pi$
$937$	−3.34817e19	−1.61622	−0.808111	+	0.589031i	$0.799510\pi$
$938$	8.98851e18	0.430893
$939$	0	0
$940$	−1.13446e19	−0.536363
$941$	−1.53564e19	−0.721037	−0.360518	−	0.932752i	$-0.617400\pi$
$941$	−1.53564e19	−0.721037	−0.360518	+	0.932752i	$0.617400\pi$
$942$	0	0
$943$	2.91247e18	0.134876
$944$	8.97854e18	0.412941
$945$	0	0
$946$	−1.21313e19	−0.550320
$947$	−9.60751e18	−0.432848	−0.216424	−	0.976299i	$-0.569439\pi$
$947$	−9.60751e18	−0.432848	−0.216424	+	0.976299i	$0.569439\pi$
$948$	0	0
$949$	1.39415e18	0.0619554
$950$	1.79689e17	0.00793080
$951$	0	0
$952$	4.37381e18	0.190423
$953$	1.00611e18	0.0435053	0.0217526	−	0.999763i	$-0.493075\pi$
$953$	1.00611e18	0.0435053	0.0217526	+	0.999763i	$0.493075\pi$
$954$	0	0
$955$	3.50210e19	1.49385
$956$	4.26250e18	0.180588
$957$	0	0
$958$	2.99794e19	1.25299
$959$	8.23873e18	0.342010
$960$	0	0
$961$	−2.43534e19	−0.997375
$962$	1.12308e18	0.0456849
$963$	0	0
$964$	2.05579e18	0.0825046
$965$	−4.12411e19	−1.64401
$966$	0	0
$967$	−3.54711e19	−1.39509	−0.697545	−	0.716541i	$-0.745724\pi$
$967$	−3.54711e19	−1.39509	−0.697545	+	0.716541i	$0.745724\pi$
$968$	1.49830e19	0.585342
$969$	0	0
$970$	−2.38754e19	−0.920312
$971$	−2.21331e19	−0.847457	−0.423728	−	0.905789i	$-0.639279\pi$
$971$	−2.21331e19	−0.847457	−0.423728	+	0.905789i	$0.639279\pi$
$972$	0	0
$973$	−1.79165e19	−0.676892
$974$	−7.52583e18	−0.282437
$975$	0	0
$976$	1.59624e17	0.00591119
$977$	5.00647e18	0.184169	0.0920847	−	0.995751i	$-0.470647\pi$
$977$	5.00647e18	0.184169	0.0920847	+	0.995751i	$0.470647\pi$
$978$	0	0
$979$	−7.77078e18	−0.282083
$980$	−1.97057e18	−0.0710594
$981$	0	0
$982$	2.79033e19	0.992959
$983$	3.61782e19	1.27894	0.639469	−	0.768817i	$-0.279154\pi$
$983$	3.61782e19	1.27894	0.639469	+	0.768817i	$0.279154\pi$
$984$	0	0
$985$	−1.83723e19	−0.640955
$986$	−2.55659e19	−0.886055
$987$	0	0
$988$	4.36906e18	0.149440
$989$	3.84892e18	0.130786
$990$	0	0
$991$	2.54381e19	0.853110	0.426555	−	0.904462i	$-0.359727\pi$
$991$	2.54381e19	0.853110	0.426555	+	0.904462i	$0.359727\pi$
$992$	−2.71855e17	−0.00905757
$993$	0	0
$994$	1.54651e19	0.508560
$995$	−4.24733e19	−1.38760
$996$	0	0
$997$	−5.37949e19	−1.73469	−0.867346	−	0.497705i	$-0.834176\pi$
$997$	−5.37949e19	−1.73469	−0.867346	+	0.497705i	$0.834176\pi$
$998$	2.89488e19	0.927431
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.14.a.d.1.1		1
3.2	odd	2		42.14.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.14.a.b.1.1	✓	1	3.2	odd	2
126.14.a.d.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	126.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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