LMFDB - Embedded newform 1100.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,6,Mod(1,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, 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("1100.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1100.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:	$176.422201794$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-7.00000 q^{3} +50.0000 q^{7} -194.000 q^{9} +O(q^{10})$

$q-7.00000 q^{3} +50.0000 q^{7} -194.000 q^{9} +121.000 q^{11} +380.000 q^{13} +1154.00 q^{17} -1824.00 q^{19} -350.000 q^{21} -3591.00 q^{23} +3059.00 q^{27} +8032.00 q^{29} -2945.00 q^{31} -847.000 q^{33} -6979.00 q^{37} -2660.00 q^{39} -520.000 q^{41} +2486.00 q^{43} +6920.00 q^{47} -14307.0 q^{49} -8078.00 q^{51} +13718.0 q^{53} +12768.0 q^{57} -31779.0 q^{59} +34156.0 q^{61} -9700.00 q^{63} +61503.0 q^{67} +25137.0 q^{69} -14971.0 q^{71} +36444.0 q^{73} +6050.00 q^{77} -28538.0 q^{79} +25729.0 q^{81} -77482.0 q^{83} -56224.0 q^{87} +36271.0 q^{89} +19000.0 q^{91} +20615.0 q^{93} +49799.0 q^{97} -23474.0 q^{99} +O(q^{100})$

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
$3$	−7.00000	−0.449050	−0.224525	−	0.974468i	$-0.572083\pi$
$3$	−7.00000	−0.449050	−0.224525	+	0.974468i	$0.572083\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	50.0000	0.385678	0.192839	−	0.981230i	$-0.438230\pi$
$7$	50.0000	0.385678	0.192839	+	0.981230i	$0.438230\pi$
$8$	0	0
$9$	−194.000	−0.798354
$10$	0	0
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	0	0
$13$	380.000	0.623627	0.311814	−	0.950143i	$-0.399064\pi$
$13$	380.000	0.623627	0.311814	+	0.950143i	$0.399064\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	1154.00	0.968464	0.484232	−	0.874940i	$-0.339099\pi$
$17$	1154.00	0.968464	0.484232	+	0.874940i	$0.339099\pi$
$18$	0	0
$19$	−1824.00	−1.15915	−0.579577	−	0.814918i	$-0.696782\pi$
$19$	−1824.00	−1.15915	−0.579577	+	0.814918i	$0.696782\pi$
$20$	0	0
$21$	−350.000	−0.173189
$22$	0	0
$23$	−3591.00	−1.41545	−0.707727	−	0.706486i	$-0.750279\pi$
$23$	−3591.00	−1.41545	−0.707727	+	0.706486i	$0.750279\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	3059.00	0.807551
$28$	0	0
$29$	8032.00	1.77349	0.886745	−	0.462259i	$-0.152961\pi$
$29$	8032.00	1.77349	0.886745	+	0.462259i	$0.152961\pi$
$30$	0	0
$31$	−2945.00	−0.550403	−0.275202	−	0.961387i	$-0.588745\pi$
$31$	−2945.00	−0.550403	−0.275202	+	0.961387i	$0.588745\pi$
$32$	0	0
$33$	−847.000	−0.135394
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−6979.00	−0.838087	−0.419043	−	0.907966i	$-0.637634\pi$
$37$	−6979.00	−0.838087	−0.419043	+	0.907966i	$0.637634\pi$
$38$	0	0
$39$	−2660.00	−0.280040
$40$	0	0
$41$	−520.000	−0.0483107	−0.0241554	−	0.999708i	$-0.507690\pi$
$41$	−520.000	−0.0483107	−0.0241554	+	0.999708i	$0.507690\pi$
$42$	0	0
$43$	2486.00	0.205036	0.102518	−	0.994731i	$-0.467310\pi$
$43$	2486.00	0.205036	0.102518	+	0.994731i	$0.467310\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	6920.00	0.456942	0.228471	−	0.973551i	$-0.426627\pi$
$47$	6920.00	0.456942	0.228471	+	0.973551i	$0.426627\pi$
$48$	0	0
$49$	−14307.0	−0.851252
$50$	0	0
$51$	−8078.00	−0.434889
$52$	0	0
$53$	13718.0	0.670812	0.335406	−	0.942074i	$-0.391126\pi$
$53$	13718.0	0.670812	0.335406	+	0.942074i	$0.391126\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	12768.0	0.520518
$58$	0	0
$59$	−31779.0	−1.18853	−0.594265	−	0.804269i	$-0.702557\pi$
$59$	−31779.0	−1.18853	−0.594265	+	0.804269i	$0.702557\pi$
$60$	0	0
$61$	34156.0	1.17528	0.587641	−	0.809121i	$-0.300057\pi$
$61$	34156.0	1.17528	0.587641	+	0.809121i	$0.300057\pi$
$62$	0	0
$63$	−9700.00	−0.307908
$64$	0	0
$65$	0	0
$66$	0	0
$67$	61503.0	1.67382	0.836911	−	0.547339i	$-0.184359\pi$
$67$	61503.0	1.67382	0.836911	+	0.547339i	$0.184359\pi$
$68$	0	0
$69$	25137.0	0.635610
$70$	0	0
$71$	−14971.0	−0.352456	−0.176228	−	0.984349i	$-0.556390\pi$
$71$	−14971.0	−0.352456	−0.176228	+	0.984349i	$0.556390\pi$
$72$	0	0
$73$	36444.0	0.800422	0.400211	−	0.916423i	$-0.368937\pi$
$73$	36444.0	0.800422	0.400211	+	0.916423i	$0.368937\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	6050.00	0.116286
$78$	0	0
$79$	−28538.0	−0.514465	−0.257232	−	0.966350i	$-0.582811\pi$
$79$	−28538.0	−0.514465	−0.257232	+	0.966350i	$0.582811\pi$
$80$	0	0
$81$	25729.0	0.435723
$82$	0	0
$83$	−77482.0	−1.23454	−0.617271	−	0.786751i	$-0.711762\pi$
$83$	−77482.0	−1.23454	−0.617271	+	0.786751i	$0.711762\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−56224.0	−0.796386
$88$	0	0
$89$	36271.0	0.485383	0.242691	−	0.970104i	$-0.421970\pi$
$89$	36271.0	0.485383	0.242691	+	0.970104i	$0.421970\pi$
$90$	0	0
$91$	19000.0	0.240519
$92$	0	0
$93$	20615.0	0.247159
$94$	0	0
$95$	0	0
$96$	0	0
$97$	49799.0	0.537392	0.268696	−	0.963225i	$-0.413407\pi$
$97$	49799.0	0.537392	0.268696	+	0.963225i	$0.413407\pi$
$98$	0	0
$99$	−23474.0	−0.240713
$100$	0	0
$101$	−153406.	−1.49637	−0.748185	−	0.663490i	$-0.769074\pi$
$101$	−153406.	−1.49637	−0.748185	+	0.663490i	$0.769074\pi$
$102$	0	0
$103$	134720.	1.25124	0.625618	−	0.780130i	$-0.284847\pi$
$103$	134720.	1.25124	0.625618	+	0.780130i	$0.284847\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−169218.	−1.42885	−0.714426	−	0.699711i	$-0.753312\pi$
$107$	−169218.	−1.42885	−0.714426	+	0.699711i	$0.753312\pi$
$108$	0	0
$109$	−233206.	−1.88007	−0.940034	−	0.341081i	$-0.889207\pi$
$109$	−233206.	−1.88007	−0.940034	+	0.341081i	$0.889207\pi$
$110$	0	0
$111$	48853.0	0.376343
$112$	0	0
$113$	−94329.0	−0.694943	−0.347471	−	0.937691i	$-0.612960\pi$
$113$	−94329.0	−0.694943	−0.347471	+	0.937691i	$0.612960\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−73720.0	−0.497875
$118$	0	0
$119$	57700.0	0.373515
$120$	0	0
$121$	14641.0	0.0909091
$122$	0	0
$123$	3640.00	0.0216939
$124$	0	0
$125$	0	0
$126$	0	0
$127$	259480.	1.42756	0.713780	−	0.700370i	$-0.246981\pi$
$127$	259480.	1.42756	0.713780	+	0.700370i	$0.246981\pi$
$128$	0	0
$129$	−17402.0	−0.0920714
$130$	0	0
$131$	−85410.0	−0.434841	−0.217420	−	0.976078i	$-0.569764\pi$
$131$	−85410.0	−0.434841	−0.217420	+	0.976078i	$0.569764\pi$
$132$	0	0
$133$	−91200.0	−0.447060
$134$	0	0
$135$	0	0
$136$	0	0
$137$	427703.	1.94689	0.973444	−	0.228926i	$-0.0735214\pi$
$137$	427703.	1.94689	0.973444	+	0.228926i	$0.0735214\pi$
$138$	0	0
$139$	309690.	1.35953	0.679767	−	0.733428i	$-0.262081\pi$
$139$	309690.	1.35953	0.679767	+	0.733428i	$0.262081\pi$
$140$	0	0
$141$	−48440.0	−0.205190
$142$	0	0
$143$	45980.0	0.188031
$144$	0	0
$145$	0	0
$146$	0	0
$147$	100149.	0.382255
$148$	0	0
$149$	449846.	1.65996	0.829981	−	0.557792i	$-0.188351\pi$
$149$	449846.	1.65996	0.829981	+	0.557792i	$0.188351\pi$
$150$	0	0
$151$	405074.	1.44575	0.722873	−	0.690981i	$-0.242821\pi$
$151$	405074.	1.44575	0.722873	+	0.690981i	$0.242821\pi$
$152$	0	0
$153$	−223876.	−0.773177
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−339321.	−1.09866	−0.549328	−	0.835607i	$-0.685116\pi$
$157$	−339321.	−1.09866	−0.549328	+	0.835607i	$0.685116\pi$
$158$	0	0
$159$	−96026.0	−0.301228
$160$	0	0
$161$	−179550.	−0.545910
$162$	0	0
$163$	−271396.	−0.800082	−0.400041	−	0.916497i	$-0.631004\pi$
$163$	−271396.	−0.800082	−0.400041	+	0.916497i	$0.631004\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−72468.0	−0.201074	−0.100537	−	0.994933i	$-0.532056\pi$
$167$	−72468.0	−0.201074	−0.100537	+	0.994933i	$0.532056\pi$
$168$	0	0
$169$	−226893.	−0.611089
$170$	0	0
$171$	353856.	0.925414
$172$	0	0
$173$	−479226.	−1.21738	−0.608689	−	0.793409i	$-0.708304\pi$
$173$	−479226.	−1.21738	−0.608689	+	0.793409i	$0.708304\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	222453.	0.533710
$178$	0	0
$179$	−40935.0	−0.0954910	−0.0477455	−	0.998860i	$-0.515204\pi$
$179$	−40935.0	−0.0954910	−0.0477455	+	0.998860i	$0.515204\pi$
$180$	0	0
$181$	−90169.0	−0.204579	−0.102289	−	0.994755i	$-0.532617\pi$
$181$	−90169.0	−0.204579	−0.102289	+	0.994755i	$0.532617\pi$
$182$	0	0
$183$	−239092.	−0.527761
$184$	0	0
$185$	0	0
$186$	0	0
$187$	139634.	0.292003
$188$	0	0
$189$	152950.	0.311455
$190$	0	0
$191$	−260375.	−0.516435	−0.258218	−	0.966087i	$-0.583135\pi$
$191$	−260375.	−0.516435	−0.258218	+	0.966087i	$0.583135\pi$
$192$	0	0
$193$	−524324.	−1.01323	−0.506613	−	0.862173i	$-0.669103\pi$
$193$	−524324.	−1.01323	−0.506613	+	0.862173i	$0.669103\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−759582.	−1.39447	−0.697235	−	0.716843i	$-0.745587\pi$
$197$	−759582.	−1.39447	−0.697235	+	0.716843i	$0.745587\pi$
$198$	0	0
$199$	−882736.	−1.58015	−0.790075	−	0.613011i	$-0.789958\pi$
$199$	−882736.	−1.58015	−0.790075	+	0.613011i	$0.789958\pi$
$200$	0	0
$201$	−430521.	−0.751630
$202$	0	0
$203$	401600.	0.683996
$204$	0	0
$205$	0	0
$206$	0	0
$207$	696654.	1.13003
$208$	0	0
$209$	−220704.	−0.349498
$210$	0	0
$211$	−1.15285e6	−1.78266	−0.891328	−	0.453360i	$-0.850225\pi$
$211$	−1.15285e6	−1.78266	−0.891328	+	0.453360i	$0.850225\pi$
$212$	0	0
$213$	104797.	0.158270
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−147250.	−0.212278
$218$	0	0
$219$	−255108.	−0.359430
$220$	0	0
$221$	438520.	0.603961
$222$	0	0
$223$	65893.0	0.0887314	0.0443657	−	0.999015i	$-0.485873\pi$
$223$	65893.0	0.0887314	0.0443657	+	0.999015i	$0.485873\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	314526.	0.405128	0.202564	−	0.979269i	$-0.435073\pi$
$227$	314526.	0.405128	0.202564	+	0.979269i	$0.435073\pi$
$228$	0	0
$229$	1.03846e6	1.30859	0.654293	−	0.756241i	$-0.272966\pi$
$229$	1.03846e6	1.30859	0.654293	+	0.756241i	$0.272966\pi$
$230$	0	0
$231$	−42350.0	−0.0522184
$232$	0	0
$233$	−509976.	−0.615403	−0.307702	−	0.951483i	$-0.599560\pi$
$233$	−509976.	−0.615403	−0.307702	+	0.951483i	$0.599560\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	199766.	0.231021
$238$	0	0
$239$	−444494.	−0.503351	−0.251676	−	0.967812i	$-0.580982\pi$
$239$	−444494.	−0.503351	−0.251676	+	0.967812i	$0.580982\pi$
$240$	0	0
$241$	−283464.	−0.314380	−0.157190	−	0.987568i	$-0.550244\pi$
$241$	−283464.	−0.314380	−0.157190	+	0.987568i	$0.550244\pi$
$242$	0	0
$243$	−923440.	−1.00321
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−693120.	−0.722880
$248$	0	0
$249$	542374.	0.554371
$250$	0	0
$251$	−773807.	−0.775262	−0.387631	−	0.921815i	$-0.626706\pi$
$251$	−773807.	−0.775262	−0.387631	+	0.921815i	$0.626706\pi$
$252$	0	0
$253$	−434511.	−0.426775
$254$	0	0
$255$	0	0
$256$	0	0
$257$	387714.	0.366167	0.183083	−	0.983097i	$-0.441392\pi$
$257$	387714.	0.366167	0.183083	+	0.983097i	$0.441392\pi$
$258$	0	0
$259$	−348950.	−0.323232
$260$	0	0
$261$	−1.55821e6	−1.41587
$262$	0	0
$263$	197602.	0.176158	0.0880789	−	0.996113i	$-0.471927\pi$
$263$	197602.	0.176158	0.0880789	+	0.996113i	$0.471927\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−253897.	−0.217961
$268$	0	0
$269$	−262694.	−0.221345	−0.110672	−	0.993857i	$-0.535300\pi$
$269$	−262694.	−0.221345	−0.110672	+	0.993857i	$0.535300\pi$
$270$	0	0
$271$	−159068.	−0.131571	−0.0657854	−	0.997834i	$-0.520955\pi$
$271$	−159068.	−0.131571	−0.0657854	+	0.997834i	$0.520955\pi$
$272$	0	0
$273$	−133000.	−0.108005
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−1.29385e6	−1.01318	−0.506589	−	0.862188i	$-0.669094\pi$
$277$	−1.29385e6	−1.01318	−0.506589	+	0.862188i	$0.669094\pi$
$278$	0	0
$279$	571330.	0.439417
$280$	0	0
$281$	−1.78114e6	−1.34565	−0.672824	−	0.739802i	$-0.734919\pi$
$281$	−1.78114e6	−1.34565	−0.672824	+	0.739802i	$0.734919\pi$
$282$	0	0
$283$	−1.98279e6	−1.47167	−0.735835	−	0.677161i	$-0.763210\pi$
$283$	−1.98279e6	−1.47167	−0.735835	+	0.677161i	$0.763210\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−26000.0	−0.0186324
$288$	0	0
$289$	−88141.0	−0.0620774
$290$	0	0
$291$	−348593.	−0.241316
$292$	0	0
$293$	−578360.	−0.393577	−0.196788	−	0.980446i	$-0.563051\pi$
$293$	−578360.	−0.393577	−0.196788	+	0.980446i	$0.563051\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	370139.	0.243486
$298$	0	0
$299$	−1.36458e6	−0.882716
$300$	0	0
$301$	124300.	0.0790779
$302$	0	0
$303$	1.07384e6	0.671945
$304$	0	0
$305$	0	0
$306$	0	0
$307$	3.07602e6	1.86270	0.931352	−	0.364120i	$-0.118630\pi$
$307$	3.07602e6	1.86270	0.931352	+	0.364120i	$0.118630\pi$
$308$	0	0
$309$	−943040.	−0.561868
$310$	0	0
$311$	−3.13757e6	−1.83947	−0.919735	−	0.392540i	$-0.871597\pi$
$311$	−3.13757e6	−1.83947	−0.919735	+	0.392540i	$0.871597\pi$
$312$	0	0
$313$	−2.61784e6	−1.51037	−0.755183	−	0.655514i	$-0.772452\pi$
$313$	−2.61784e6	−1.51037	−0.755183	+	0.655514i	$0.772452\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	2.49220e6	1.39294	0.696472	−	0.717584i	$-0.254752\pi$
$317$	2.49220e6	1.39294	0.696472	+	0.717584i	$0.254752\pi$
$318$	0	0
$319$	971872.	0.534727
$320$	0	0
$321$	1.18453e6	0.641626
$322$	0	0
$323$	−2.10490e6	−1.12260
$324$	0	0
$325$	0	0
$326$	0	0
$327$	1.63244e6	0.844245
$328$	0	0
$329$	346000.	0.176233
$330$	0	0
$331$	−2.70125e6	−1.35517	−0.677586	−	0.735443i	$-0.736974\pi$
$331$	−2.70125e6	−1.35517	−0.677586	+	0.735443i	$0.736974\pi$
$332$	0	0
$333$	1.35393e6	0.669090
$334$	0	0
$335$	0	0
$336$	0	0
$337$	1.42610e6	0.684031	0.342016	−	0.939694i	$-0.388890\pi$
$337$	1.42610e6	0.684031	0.342016	+	0.939694i	$0.388890\pi$
$338$	0	0
$339$	660303.	0.312064
$340$	0	0
$341$	−356345.	−0.165953
$342$	0	0
$343$	−1.55570e6	−0.713987
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−2.86374e6	−1.27676	−0.638381	−	0.769721i	$-0.720396\pi$
$347$	−2.86374e6	−1.27676	−0.638381	+	0.769721i	$0.720396\pi$
$348$	0	0
$349$	296350.	0.130239	0.0651195	−	0.997877i	$-0.479257\pi$
$349$	296350.	0.130239	0.0651195	+	0.997877i	$0.479257\pi$
$350$	0	0
$351$	1.16242e6	0.503611
$352$	0	0
$353$	2.12114e6	0.906010	0.453005	−	0.891508i	$-0.350352\pi$
$353$	2.12114e6	0.906010	0.453005	+	0.891508i	$0.350352\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−403900.	−0.167727
$358$	0	0
$359$	−3.47512e6	−1.42310	−0.711548	−	0.702638i	$-0.752006\pi$
$359$	−3.47512e6	−1.42310	−0.711548	+	0.702638i	$0.752006\pi$
$360$	0	0
$361$	850877.	0.343636
$362$	0	0
$363$	−102487.	−0.0408227
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−1.56190e6	−0.605322	−0.302661	−	0.953098i	$-0.597875\pi$
$367$	−1.56190e6	−0.605322	−0.302661	+	0.953098i	$0.597875\pi$
$368$	0	0
$369$	100880.	0.0385691
$370$	0	0
$371$	685900.	0.258718
$372$	0	0
$373$	−1.93773e6	−0.721144	−0.360572	−	0.932731i	$-0.617419\pi$
$373$	−1.93773e6	−0.721144	−0.360572	+	0.932731i	$0.617419\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	3.05216e6	1.10600
$378$	0	0
$379$	3.07495e6	1.09961	0.549806	−	0.835292i	$-0.314702\pi$
$379$	3.07495e6	1.09961	0.549806	+	0.835292i	$0.314702\pi$
$380$	0	0
$381$	−1.81636e6	−0.641046
$382$	0	0
$383$	−4.31553e6	−1.50327	−0.751635	−	0.659579i	$-0.770734\pi$
$383$	−4.31553e6	−1.50327	−0.751635	+	0.659579i	$0.770734\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−482284.	−0.163691
$388$	0	0
$389$	2.36251e6	0.791590	0.395795	−	0.918339i	$-0.370469\pi$
$389$	2.36251e6	0.791590	0.395795	+	0.918339i	$0.370469\pi$
$390$	0	0
$391$	−4.14401e6	−1.37082
$392$	0	0
$393$	597870.	0.195265
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−1.77598e6	−0.565539	−0.282769	−	0.959188i	$-0.591253\pi$
$397$	−1.77598e6	−0.565539	−0.282769	+	0.959188i	$0.591253\pi$
$398$	0	0
$399$	638400.	0.200752
$400$	0	0
$401$	1.56967e6	0.487468	0.243734	−	0.969842i	$-0.421628\pi$
$401$	1.56967e6	0.487468	0.243734	+	0.969842i	$0.421628\pi$
$402$	0	0
$403$	−1.11910e6	−0.343247
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−844459.	−0.252693
$408$	0	0
$409$	1.29485e6	0.382746	0.191373	−	0.981517i	$-0.438706\pi$
$409$	1.29485e6	0.382746	0.191373	+	0.981517i	$0.438706\pi$
$410$	0	0
$411$	−2.99392e6	−0.874250
$412$	0	0
$413$	−1.58895e6	−0.458390
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−2.16783e6	−0.610499
$418$	0	0
$419$	272916.	0.0759441	0.0379720	−	0.999279i	$-0.487910\pi$
$419$	272916.	0.0759441	0.0379720	+	0.999279i	$0.487910\pi$
$420$	0	0
$421$	−2.61801e6	−0.719890	−0.359945	−	0.932974i	$-0.617205\pi$
$421$	−2.61801e6	−0.719890	−0.359945	+	0.932974i	$0.617205\pi$
$422$	0	0
$423$	−1.34248e6	−0.364802
$424$	0	0
$425$	0	0
$426$	0	0
$427$	1.70780e6	0.453281
$428$	0	0
$429$	−321860.	−0.0844352
$430$	0	0
$431$	2.81037e6	0.728735	0.364368	−	0.931255i	$-0.381285\pi$
$431$	2.81037e6	0.728735	0.364368	+	0.931255i	$0.381285\pi$
$432$	0	0
$433$	−5.98509e6	−1.53409	−0.767046	−	0.641593i	$-0.778274\pi$
$433$	−5.98509e6	−1.53409	−0.767046	+	0.641593i	$0.778274\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	6.54998e6	1.64073
$438$	0	0
$439$	−7.50486e6	−1.85858	−0.929290	−	0.369352i	$-0.879580\pi$
$439$	−7.50486e6	−1.85858	−0.929290	+	0.369352i	$0.879580\pi$
$440$	0	0
$441$	2.77556e6	0.679601
$442$	0	0
$443$	−1.56806e6	−0.379624	−0.189812	−	0.981820i	$-0.560788\pi$
$443$	−1.56806e6	−0.379624	−0.189812	+	0.981820i	$0.560788\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−3.14892e6	−0.745406
$448$	0	0
$449$	−4.04044e6	−0.945831	−0.472915	−	0.881108i	$-0.656798\pi$
$449$	−4.04044e6	−0.945831	−0.472915	+	0.881108i	$0.656798\pi$
$450$	0	0
$451$	−62920.0	−0.0145662
$452$	0	0
$453$	−2.83552e6	−0.649213
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−2.21132e6	−0.495291	−0.247645	−	0.968851i	$-0.579657\pi$
$457$	−2.21132e6	−0.495291	−0.247645	+	0.968851i	$0.579657\pi$
$458$	0	0
$459$	3.53009e6	0.782084
$460$	0	0
$461$	−3.56735e6	−0.781795	−0.390898	−	0.920434i	$-0.627835\pi$
$461$	−3.56735e6	−0.781795	−0.390898	+	0.920434i	$0.627835\pi$
$462$	0	0
$463$	−747757.	−0.162109	−0.0810547	−	0.996710i	$-0.525829\pi$
$463$	−747757.	−0.162109	−0.0810547	+	0.996710i	$0.525829\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	5.44511e6	1.15535	0.577676	−	0.816266i	$-0.303960\pi$
$467$	5.44511e6	1.15535	0.577676	+	0.816266i	$0.303960\pi$
$468$	0	0
$469$	3.07515e6	0.645556
$470$	0	0
$471$	2.37525e6	0.493352
$472$	0	0
$473$	300806.	0.0618207
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−2.66129e6	−0.535546
$478$	0	0
$479$	−6.22046e6	−1.23875	−0.619375	−	0.785095i	$-0.712614\pi$
$479$	−6.22046e6	−1.23875	−0.619375	+	0.785095i	$0.712614\pi$
$480$	0	0
$481$	−2.65202e6	−0.522654
$482$	0	0
$483$	1.25685e6	0.245141
$484$	0	0
$485$	0	0
$486$	0	0
$487$	3.34398e6	0.638913	0.319457	−	0.947601i	$-0.396500\pi$
$487$	3.34398e6	0.638913	0.319457	+	0.947601i	$0.396500\pi$
$488$	0	0
$489$	1.89977e6	0.359277
$490$	0	0
$491$	5.58646e6	1.04576	0.522881	−	0.852406i	$-0.324857\pi$
$491$	5.58646e6	1.04576	0.522881	+	0.852406i	$0.324857\pi$
$492$	0	0
$493$	9.26893e6	1.71756
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−748550.	−0.135935
$498$	0	0
$499$	−8.29348e6	−1.49103	−0.745514	−	0.666490i	$-0.767796\pi$
$499$	−8.29348e6	−1.49103	−0.745514	+	0.666490i	$0.767796\pi$
$500$	0	0
$501$	507276.	0.0902922
$502$	0	0
$503$	−5.29951e6	−0.933933	−0.466967	−	0.884275i	$-0.654653\pi$
$503$	−5.29951e6	−0.933933	−0.466967	+	0.884275i	$0.654653\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	1.58825e6	0.274410
$508$	0	0
$509$	24415.0	0.00417698	0.00208849	−	0.999998i	$-0.499335\pi$
$509$	24415.0	0.00417698	0.00208849	+	0.999998i	$0.499335\pi$
$510$	0	0
$511$	1.82220e6	0.308705
$512$	0	0
$513$	−5.57962e6	−0.936076
$514$	0	0
$515$	0	0
$516$	0	0
$517$	837320.	0.137773
$518$	0	0
$519$	3.35458e6	0.546663
$520$	0	0
$521$	4.76275e6	0.768712	0.384356	−	0.923185i	$-0.374424\pi$
$521$	4.76275e6	0.768712	0.384356	+	0.923185i	$0.374424\pi$
$522$	0	0
$523$	−735248.	−0.117538	−0.0587692	−	0.998272i	$-0.518718\pi$
$523$	−735248.	−0.117538	−0.0587692	+	0.998272i	$0.518718\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−3.39853e6	−0.533046
$528$	0	0
$529$	6.45894e6	1.00351
$530$	0	0
$531$	6.16513e6	0.948868
$532$	0	0
$533$	−197600.	−0.0301279
$534$	0	0
$535$	0	0
$536$	0	0
$537$	286545.	0.0428802
$538$	0	0
$539$	−1.73115e6	−0.256662
$540$	0	0
$541$	−3.19649e6	−0.469548	−0.234774	−	0.972050i	$-0.575435\pi$
$541$	−3.19649e6	−0.469548	−0.234774	+	0.972050i	$0.575435\pi$
$542$	0	0
$543$	631183.	0.0918662
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−8.85902e6	−1.26595	−0.632976	−	0.774171i	$-0.718167\pi$
$547$	−8.85902e6	−1.26595	−0.632976	+	0.774171i	$0.718167\pi$
$548$	0	0
$549$	−6.62626e6	−0.938292
$550$	0	0
$551$	−1.46504e7	−2.05575
$552$	0	0
$553$	−1.42690e6	−0.198418
$554$	0	0
$555$	0	0
$556$	0	0
$557$	1.74512e6	0.238335	0.119167	−	0.992874i	$-0.461977\pi$
$557$	1.74512e6	0.238335	0.119167	+	0.992874i	$0.461977\pi$
$558$	0	0
$559$	944680.	0.127866
$560$	0	0
$561$	−977438.	−0.131124
$562$	0	0
$563$	1.32333e7	1.75953	0.879764	−	0.475410i	$-0.157700\pi$
$563$	1.32333e7	1.75953	0.879764	+	0.475410i	$0.157700\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	1.28645e6	0.168049
$568$	0	0
$569$	1.04156e7	1.34867	0.674335	−	0.738426i	$-0.264430\pi$
$569$	1.04156e7	1.34867	0.674335	+	0.738426i	$0.264430\pi$
$570$	0	0
$571$	−2.48163e6	−0.318527	−0.159264	−	0.987236i	$-0.550912\pi$
$571$	−2.48163e6	−0.318527	−0.159264	+	0.987236i	$0.550912\pi$
$572$	0	0
$573$	1.82262e6	0.231905
$574$	0	0
$575$	0	0
$576$	0	0
$577$	1.31244e7	1.64112	0.820562	−	0.571557i	$-0.193661\pi$
$577$	1.31244e7	1.64112	0.820562	+	0.571557i	$0.193661\pi$
$578$	0	0
$579$	3.67027e6	0.454989
$580$	0	0
$581$	−3.87410e6	−0.476135
$582$	0	0
$583$	1.65988e6	0.202258
$584$	0	0
$585$	0	0
$586$	0	0
$587$	4.86010e6	0.582170	0.291085	−	0.956697i	$-0.405984\pi$
$587$	4.86010e6	0.582170	0.291085	+	0.956697i	$0.405984\pi$
$588$	0	0
$589$	5.37168e6	0.638002
$590$	0	0
$591$	5.31707e6	0.626187
$592$	0	0
$593$	1.58559e6	0.185163	0.0925814	−	0.995705i	$-0.470488\pi$
$593$	1.58559e6	0.185163	0.0925814	+	0.995705i	$0.470488\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	6.17915e6	0.709566
$598$	0	0
$599$	9.04294e6	1.02978	0.514888	−	0.857258i	$-0.327834\pi$
$599$	9.04294e6	1.02978	0.514888	+	0.857258i	$0.327834\pi$
$600$	0	0
$601$	729186.	0.0823478	0.0411739	−	0.999152i	$-0.486890\pi$
$601$	729186.	0.0823478	0.0411739	+	0.999152i	$0.486890\pi$
$602$	0	0
$603$	−1.19316e7	−1.33630
$604$	0	0
$605$	0	0
$606$	0	0
$607$	3.91130e6	0.430873	0.215437	−	0.976518i	$-0.430883\pi$
$607$	3.91130e6	0.430873	0.215437	+	0.976518i	$0.430883\pi$
$608$	0	0
$609$	−2.81120e6	−0.307149
$610$	0	0
$611$	2.62960e6	0.284962
$612$	0	0
$613$	5.52184e6	0.593516	0.296758	−	0.954953i	$-0.404094\pi$
$613$	5.52184e6	0.593516	0.296758	+	0.954953i	$0.404094\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	4.88539e6	0.516638	0.258319	−	0.966060i	$-0.416831\pi$
$617$	4.88539e6	0.516638	0.258319	+	0.966060i	$0.416831\pi$
$618$	0	0
$619$	−4.11150e6	−0.431295	−0.215647	−	0.976471i	$-0.569186\pi$
$619$	−4.11150e6	−0.431295	−0.215647	+	0.976471i	$0.569186\pi$
$620$	0	0
$621$	−1.09849e7	−1.14305
$622$	0	0
$623$	1.81355e6	0.187202
$624$	0	0
$625$	0	0
$626$	0	0
$627$	1.54493e6	0.156942
$628$	0	0
$629$	−8.05377e6	−0.811657
$630$	0	0
$631$	8.24910e6	0.824771	0.412385	−	0.911009i	$-0.364696\pi$
$631$	8.24910e6	0.824771	0.412385	+	0.911009i	$0.364696\pi$
$632$	0	0
$633$	8.06996e6	0.800502
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−5.43666e6	−0.530864
$638$	0	0
$639$	2.90437e6	0.281385
$640$	0	0
$641$	−4.29330e6	−0.412711	−0.206355	−	0.978477i	$-0.566160\pi$
$641$	−4.29330e6	−0.412711	−0.206355	+	0.978477i	$0.566160\pi$
$642$	0	0
$643$	1.63045e7	1.55518	0.777588	−	0.628774i	$-0.216443\pi$
$643$	1.63045e7	1.55518	0.777588	+	0.628774i	$0.216443\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−4.42624e6	−0.415695	−0.207847	−	0.978161i	$-0.566646\pi$
$647$	−4.42624e6	−0.415695	−0.207847	+	0.978161i	$0.566646\pi$
$648$	0	0
$649$	−3.84526e6	−0.358355
$650$	0	0
$651$	1.03075e6	0.0953237
$652$	0	0
$653$	6.27529e6	0.575905	0.287952	−	0.957645i	$-0.407025\pi$
$653$	6.27529e6	0.575905	0.287952	+	0.957645i	$0.407025\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−7.07014e6	−0.639020
$658$	0	0
$659$	−1.09748e7	−0.984422	−0.492211	−	0.870476i	$-0.663811\pi$
$659$	−1.09748e7	−0.984422	−0.492211	+	0.870476i	$0.663811\pi$
$660$	0	0
$661$	2.02025e7	1.79846	0.899229	−	0.437478i	$-0.144128\pi$
$661$	2.02025e7	1.79846	0.899229	+	0.437478i	$0.144128\pi$
$662$	0	0
$663$	−3.06964e6	−0.271209
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−2.88429e7	−2.51029
$668$	0	0
$669$	−461251.	−0.0398448
$670$	0	0
$671$	4.13288e6	0.354361
$672$	0	0
$673$	−1.14233e7	−0.972200	−0.486100	−	0.873903i	$-0.661581\pi$
$673$	−1.14233e7	−0.972200	−0.486100	+	0.873903i	$0.661581\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	2.43918e6	0.204537	0.102268	−	0.994757i	$-0.467390\pi$
$677$	2.43918e6	0.204537	0.102268	+	0.994757i	$0.467390\pi$
$678$	0	0
$679$	2.48995e6	0.207260
$680$	0	0
$681$	−2.20168e6	−0.181923
$682$	0	0
$683$	−1.01384e6	−0.0831606	−0.0415803	−	0.999135i	$-0.513239\pi$
$683$	−1.01384e6	−0.0831606	−0.0415803	+	0.999135i	$0.513239\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−7.26924e6	−0.587621
$688$	0	0
$689$	5.21284e6	0.418337
$690$	0	0
$691$	−8.03186e6	−0.639913	−0.319957	−	0.947432i	$-0.603668\pi$
$691$	−8.03186e6	−0.639913	−0.319957	+	0.947432i	$0.603668\pi$
$692$	0	0
$693$	−1.17370e6	−0.0928376
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−600080.	−0.0467872
$698$	0	0
$699$	3.56983e6	0.276347
$700$	0	0
$701$	−259806.	−0.0199689	−0.00998445	−	0.999950i	$-0.503178\pi$
$701$	−259806.	−0.0199689	−0.00998445	+	0.999950i	$0.503178\pi$
$702$	0	0
$703$	1.27297e7	0.971471
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−7.67030e6	−0.577117
$708$	0	0
$709$	−1.92848e7	−1.44079	−0.720393	−	0.693566i	$-0.756039\pi$
$709$	−1.92848e7	−1.44079	−0.720393	+	0.693566i	$0.756039\pi$
$710$	0	0
$711$	5.53637e6	0.410725
$712$	0	0
$713$	1.05755e7	0.779071
$714$	0	0
$715$	0	0
$716$	0	0
$717$	3.11146e6	0.226030
$718$	0	0
$719$	926119.	0.0668105	0.0334052	−	0.999442i	$-0.489365\pi$
$719$	926119.	0.0668105	0.0334052	+	0.999442i	$0.489365\pi$
$720$	0	0
$721$	6.73600e6	0.482574
$722$	0	0
$723$	1.98425e6	0.141173
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−2.02599e7	−1.42168	−0.710840	−	0.703354i	$-0.751685\pi$
$727$	−2.02599e7	−1.42168	−0.710840	+	0.703354i	$0.751685\pi$
$728$	0	0
$729$	211933.	0.0147700
$730$	0	0
$731$	2.86884e6	0.198570
$732$	0	0
$733$	−1.10982e7	−0.762944	−0.381472	−	0.924380i	$-0.624583\pi$
$733$	−1.10982e7	−0.762944	−0.381472	+	0.924380i	$0.624583\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	7.44186e6	0.504676
$738$	0	0
$739$	624962.	0.0420962	0.0210481	−	0.999778i	$-0.493300\pi$
$739$	624962.	0.0420962	0.0210481	+	0.999778i	$0.493300\pi$
$740$	0	0
$741$	4.85184e6	0.324609
$742$	0	0
$743$	−46436.0	−0.00308591	−0.00154295	−	0.999999i	$-0.500491\pi$
$743$	−46436.0	−0.00308591	−0.00154295	+	0.999999i	$0.500491\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	1.50315e7	0.985601
$748$	0	0
$749$	−8.46090e6	−0.551077
$750$	0	0
$751$	−6.12144e6	−0.396053	−0.198027	−	0.980197i	$-0.563453\pi$
$751$	−6.12144e6	−0.396053	−0.198027	+	0.980197i	$0.563453\pi$
$752$	0	0
$753$	5.41665e6	0.348131
$754$	0	0
$755$	0	0
$756$	0	0
$757$	3.26458e6	0.207056	0.103528	−	0.994627i	$-0.466987\pi$
$757$	3.26458e6	0.207056	0.103528	+	0.994627i	$0.466987\pi$
$758$	0	0
$759$	3.04158e6	0.191644
$760$	0	0
$761$	1.60311e7	1.00346	0.501732	−	0.865023i	$-0.332696\pi$
$761$	1.60311e7	1.00346	0.501732	+	0.865023i	$0.332696\pi$
$762$	0	0
$763$	−1.16603e7	−0.725101
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−1.20760e7	−0.741200
$768$	0	0
$769$	2.64617e7	1.61362	0.806811	−	0.590810i	$-0.201192\pi$
$769$	2.64617e7	1.61362	0.806811	+	0.590810i	$0.201192\pi$
$770$	0	0
$771$	−2.71400e6	−0.164427
$772$	0	0
$773$	2.63836e7	1.58813	0.794063	−	0.607836i	$-0.207962\pi$
$773$	2.63836e7	1.58813	0.794063	+	0.607836i	$0.207962\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	2.44265e6	0.145147
$778$	0	0
$779$	948480.	0.0559995
$780$	0	0
$781$	−1.81149e6	−0.106269
$782$	0	0
$783$	2.45699e7	1.43218
$784$	0	0
$785$	0	0
$786$	0	0
$787$	5.68115e6	0.326964	0.163482	−	0.986546i	$-0.447727\pi$
$787$	5.68115e6	0.326964	0.163482	+	0.986546i	$0.447727\pi$
$788$	0	0
$789$	−1.38321e6	−0.0791037
$790$	0	0
$791$	−4.71645e6	−0.268024
$792$	0	0
$793$	1.29793e7	0.732939
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−9.99383e6	−0.557296	−0.278648	−	0.960393i	$-0.589886\pi$
$797$	−9.99383e6	−0.557296	−0.278648	+	0.960393i	$0.589886\pi$
$798$	0	0
$799$	7.98568e6	0.442532
$800$	0	0
$801$	−7.03657e6	−0.387507
$802$	0	0
$803$	4.40972e6	0.241336
$804$	0	0
$805$	0	0
$806$	0	0
$807$	1.83886e6	0.0993950
$808$	0	0
$809$	2.32455e7	1.24873	0.624364	−	0.781134i	$-0.285358\pi$
$809$	2.32455e7	1.24873	0.624364	+	0.781134i	$0.285358\pi$
$810$	0	0
$811$	1.27367e7	0.679991	0.339995	−	0.940427i	$-0.389574\pi$
$811$	1.27367e7	0.679991	0.339995	+	0.940427i	$0.389574\pi$
$812$	0	0
$813$	1.11348e6	0.0590819
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−4.53446e6	−0.237668
$818$	0	0
$819$	−3.68600e6	−0.192020
$820$	0	0
$821$	−7.85748e6	−0.406842	−0.203421	−	0.979091i	$-0.565206\pi$
$821$	−7.85748e6	−0.406842	−0.203421	+	0.979091i	$0.565206\pi$
$822$	0	0
$823$	1.09499e7	0.563524	0.281762	−	0.959484i	$-0.409081\pi$
$823$	1.09499e7	0.563524	0.281762	+	0.959484i	$0.409081\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−2.20638e7	−1.12180	−0.560901	−	0.827883i	$-0.689545\pi$
$827$	−2.20638e7	−1.12180	−0.560901	+	0.827883i	$0.689545\pi$
$828$	0	0
$829$	7.05255e6	0.356418	0.178209	−	0.983993i	$-0.442970\pi$
$829$	7.05255e6	0.356418	0.178209	+	0.983993i	$0.442970\pi$
$830$	0	0
$831$	9.05698e6	0.454968
$832$	0	0
$833$	−1.65103e7	−0.824407
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−9.00876e6	−0.444479
$838$	0	0
$839$	−2.26195e7	−1.10937	−0.554686	−	0.832060i	$-0.687162\pi$
$839$	−2.26195e7	−1.10937	−0.554686	+	0.832060i	$0.687162\pi$
$840$	0	0
$841$	4.40019e7	2.14527
$842$	0	0
$843$	1.24680e7	0.604264
$844$	0	0
$845$	0	0
$846$	0	0
$847$	732050.	0.0350616
$848$	0	0
$849$	1.38795e7	0.660853
$850$	0	0
$851$	2.50616e7	1.18627
$852$	0	0
$853$	−9.46645e6	−0.445466	−0.222733	−	0.974880i	$-0.571498\pi$
$853$	−9.46645e6	−0.445466	−0.222733	+	0.974880i	$0.571498\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−941480.	−0.0437884	−0.0218942	−	0.999760i	$-0.506970\pi$
$857$	−941480.	−0.0437884	−0.0218942	+	0.999760i	$0.506970\pi$
$858$	0	0
$859$	−806423.	−0.0372889	−0.0186445	−	0.999826i	$-0.505935\pi$
$859$	−806423.	−0.0372889	−0.0186445	+	0.999826i	$0.505935\pi$
$860$	0	0
$861$	182000.	0.00836688
$862$	0	0
$863$	−1.19485e7	−0.546119	−0.273059	−	0.961997i	$-0.588036\pi$
$863$	−1.19485e7	−0.546119	−0.273059	+	0.961997i	$0.588036\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	616987.	0.0278759
$868$	0	0
$869$	−3.45310e6	−0.155117
$870$	0	0
$871$	2.33711e7	1.04384
$872$	0	0
$873$	−9.66101e6	−0.429029
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−7.84853e6	−0.344580	−0.172290	−	0.985046i	$-0.555117\pi$
$877$	−7.84853e6	−0.344580	−0.172290	+	0.985046i	$0.555117\pi$
$878$	0	0
$879$	4.04852e6	0.176736
$880$	0	0
$881$	−1.73933e7	−0.754991	−0.377496	−	0.926011i	$-0.623215\pi$
$881$	−1.73933e7	−0.754991	−0.377496	+	0.926011i	$0.623215\pi$
$882$	0	0
$883$	4.31619e7	1.86294	0.931470	−	0.363818i	$-0.118527\pi$
$883$	4.31619e7	1.86294	0.931470	+	0.363818i	$0.118527\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	9.25652e6	0.395038	0.197519	−	0.980299i	$-0.436712\pi$
$887$	9.25652e6	0.395038	0.197519	+	0.980299i	$0.436712\pi$
$888$	0	0
$889$	1.29740e7	0.550579
$890$	0	0
$891$	3.11321e6	0.131375
$892$	0	0
$893$	−1.26221e7	−0.529666
$894$	0	0
$895$	0	0
$896$	0	0
$897$	9.55206e6	0.396384
$898$	0	0
$899$	−2.36542e7	−0.976135
$900$	0	0
$901$	1.58306e7	0.649658
$902$	0	0
$903$	−870100.	−0.0355099
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−4.47293e7	−1.80540	−0.902700	−	0.430270i	$-0.858418\pi$
$907$	−4.47293e7	−1.80540	−0.902700	+	0.430270i	$0.858418\pi$
$908$	0	0
$909$	2.97608e7	1.19463
$910$	0	0
$911$	2.57577e7	1.02828	0.514139	−	0.857707i	$-0.328112\pi$
$911$	2.57577e7	1.02828	0.514139	+	0.857707i	$0.328112\pi$
$912$	0	0
$913$	−9.37532e6	−0.372228
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−4.27050e6	−0.167709
$918$	0	0
$919$	−3.63488e7	−1.41972	−0.709858	−	0.704344i	$-0.751241\pi$
$919$	−3.63488e7	−1.41972	−0.709858	+	0.704344i	$0.751241\pi$
$920$	0	0
$921$	−2.15322e7	−0.836447
$922$	0	0
$923$	−5.68898e6	−0.219801
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−2.61357e7	−0.998929
$928$	0	0
$929$	−3.96617e6	−0.150776	−0.0753880	−	0.997154i	$-0.524020\pi$
$929$	−3.96617e6	−0.150776	−0.0753880	+	0.997154i	$0.524020\pi$
$930$	0	0
$931$	2.60960e7	0.986732
$932$	0	0
$933$	2.19630e7	0.826014
$934$	0	0
$935$	0	0
$936$	0	0
$937$	3.50528e7	1.30429	0.652145	−	0.758094i	$-0.273869\pi$
$937$	3.50528e7	1.30429	0.652145	+	0.758094i	$0.273869\pi$
$938$	0	0
$939$	1.83249e7	0.678230
$940$	0	0
$941$	−1.40738e7	−0.518130	−0.259065	−	0.965860i	$-0.583414\pi$
$941$	−1.40738e7	−0.518130	−0.259065	+	0.965860i	$0.583414\pi$
$942$	0	0
$943$	1.86732e6	0.0683816
$944$	0	0
$945$	0	0
$946$	0	0
$947$	3.73759e7	1.35431	0.677153	−	0.735842i	$-0.263214\pi$
$947$	3.73759e7	1.35431	0.677153	+	0.735842i	$0.263214\pi$
$948$	0	0
$949$	1.38487e7	0.499165
$950$	0	0
$951$	−1.74454e7	−0.625502
$952$	0	0
$953$	3.18424e7	1.13572	0.567862	−	0.823124i	$-0.307771\pi$
$953$	3.18424e7	1.13572	0.567862	+	0.823124i	$0.307771\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−6.80310e6	−0.240119
$958$	0	0
$959$	2.13852e7	0.750872
$960$	0	0
$961$	−1.99561e7	−0.697056
$962$	0	0
$963$	3.28283e7	1.14073
$964$	0	0
$965$	0	0
$966$	0	0
$967$	3.16276e7	1.08768	0.543838	−	0.839190i	$-0.316971\pi$
$967$	3.16276e7	1.08768	0.543838	+	0.839190i	$0.316971\pi$
$968$	0	0
$969$	1.47343e7	0.504103
$970$	0	0
$971$	−2.73412e7	−0.930614	−0.465307	−	0.885149i	$-0.654056\pi$
$971$	−2.73412e7	−0.930614	−0.465307	+	0.885149i	$0.654056\pi$
$972$	0	0
$973$	1.54845e7	0.524343
$974$	0	0
$975$	0	0
$976$	0	0
$977$	5.81630e6	0.194944	0.0974721	−	0.995238i	$-0.468924\pi$
$977$	5.81630e6	0.194944	0.0974721	+	0.995238i	$0.468924\pi$
$978$	0	0
$979$	4.38879e6	0.146348
$980$	0	0
$981$	4.52420e7	1.50096
$982$	0	0
$983$	3.81817e7	1.26029	0.630146	−	0.776476i	$-0.282995\pi$
$983$	3.81817e7	1.26029	0.630146	+	0.776476i	$0.282995\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−2.42200e6	−0.0791373
$988$	0	0
$989$	−8.92723e6	−0.290219
$990$	0	0
$991$	5.44564e6	0.176143	0.0880714	−	0.996114i	$-0.471930\pi$
$991$	5.44564e6	0.176143	0.0880714	+	0.996114i	$0.471930\pi$
$992$	0	0
$993$	1.89087e7	0.608541
$994$	0	0
$995$	0	0
$996$	0	0
$997$	3.77967e6	0.120425	0.0602125	−	0.998186i	$-0.480822\pi$
$997$	3.77967e6	0.120425	0.0602125	+	0.998186i	$0.480822\pi$
$998$	0	0
$999$	−2.13488e7	−0.676798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.6.a.a.1.1		1
5.2	odd	4		1100.6.b.a.749.2		2
5.3	odd	4		1100.6.b.a.749.1		2
5.4	even	2		44.6.a.a.1.1	✓	1
15.14	odd	2		396.6.a.e.1.1		1
20.19	odd	2		176.6.a.a.1.1		1
40.19	odd	2		704.6.a.g.1.1		1
40.29	even	2		704.6.a.d.1.1		1
55.54	odd	2		484.6.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.6.a.a.1.1	✓	1	5.4	even	2
176.6.a.a.1.1		1	20.19	odd	2
396.6.a.e.1.1		1	15.14	odd	2
484.6.a.b.1.1		1	55.54	odd	2
704.6.a.d.1.1		1	40.29	even	2
704.6.a.g.1.1		1	40.19	odd	2
1100.6.a.a.1.1		1	1.1	even	1	trivial
1100.6.b.a.749.1		2	5.3	odd	4
1100.6.b.a.749.2		2	5.2	odd	4

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:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1100.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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