LMFDB - Embedded newform 1050.6.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,6,Mod(1,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, 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("1050.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1050.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:	$168.403010804$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1050.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$

\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} -154.000 q^{11} -144.000 q^{12} +404.000 q^{13} -196.000 q^{14} +256.000 q^{16} -2182.00 q^{17} +324.000 q^{18} -2494.00 q^{19} +441.000 q^{21} -616.000 q^{22} +3472.00 q^{23} -576.000 q^{24} +1616.00 q^{26} -729.000 q^{27} -784.000 q^{28} +5958.00 q^{29} -6410.00 q^{31} +1024.00 q^{32} +1386.00 q^{33} -8728.00 q^{34} +1296.00 q^{36} +11150.0 q^{37} -9976.00 q^{38} -3636.00 q^{39} +7834.00 q^{41} +1764.00 q^{42} -16236.0 q^{43} -2464.00 q^{44} +13888.0 q^{46} +2800.00 q^{47} -2304.00 q^{48} +2401.00 q^{49} +19638.0 q^{51} +6464.00 q^{52} +30924.0 q^{53} -2916.00 q^{54} -3136.00 q^{56} +22446.0 q^{57} +23832.0 q^{58} -11536.0 q^{59} -38834.0 q^{61} -25640.0 q^{62} -3969.00 q^{63} +4096.00 q^{64} +5544.00 q^{66} +48756.0 q^{67} -34912.0 q^{68} -31248.0 q^{69} -77882.0 q^{71} +5184.00 q^{72} +47540.0 q^{73} +44600.0 q^{74} -39904.0 q^{76} +7546.00 q^{77} -14544.0 q^{78} -36480.0 q^{79} +6561.00 q^{81} +31336.0 q^{82} -25716.0 q^{83} +7056.00 q^{84} -64944.0 q^{86} -53622.0 q^{87} -9856.00 q^{88} -100826. q^{89} -19796.0 q^{91} +55552.0 q^{92} +57690.0 q^{93} +11200.0 q^{94} -9216.00 q^{96} +89024.0 q^{97} +9604.00 q^{98} -12474.0 q^{99} +O(q^{100})\)

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	−36.0000	−0.408248
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	0	0
$11$	−154.000	−0.383742	−0.191871	−	0.981420i	$-0.561455\pi$
$11$	−154.000	−0.383742	−0.191871	+	0.981420i	$0.561455\pi$
$12$	−144.000	−0.288675
$13$	404.000	0.663014	0.331507	−	0.943453i	$-0.392443\pi$
$13$	404.000	0.663014	0.331507	+	0.943453i	$0.392443\pi$
$14$	−196.000	−0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	−2182.00	−1.83119	−0.915593	−	0.402106i	$-0.868278\pi$
$17$	−2182.00	−1.83119	−0.915593	+	0.402106i	$0.868278\pi$
$18$	324.000	0.235702
$19$	−2494.00	−1.58494	−0.792469	−	0.609912i	$-0.791205\pi$
$19$	−2494.00	−1.58494	−0.792469	+	0.609912i	$0.791205\pi$
$20$	0	0
$21$	441.000	0.218218
$22$	−616.000	−0.271346
$23$	3472.00	1.36855	0.684274	−	0.729225i	$-0.260119\pi$
$23$	3472.00	1.36855	0.684274	+	0.729225i	$0.260119\pi$
$24$	−576.000	−0.204124
$25$	0	0
$26$	1616.00	0.468822
$27$	−729.000	−0.192450
$28$	−784.000	−0.188982
$29$	5958.00	1.31554	0.657772	−	0.753217i	$-0.271499\pi$
$29$	5958.00	1.31554	0.657772	+	0.753217i	$0.271499\pi$
$30$	0	0
$31$	−6410.00	−1.19799	−0.598996	−	0.800752i	$-0.704433\pi$
$31$	−6410.00	−1.19799	−0.598996	+	0.800752i	$0.704433\pi$
$32$	1024.00	0.176777
$33$	1386.00	0.221553
$34$	−8728.00	−1.29484
$35$	0	0
$36$	1296.00	0.166667
$37$	11150.0	1.33897	0.669485	−	0.742826i	$-0.266515\pi$
$37$	11150.0	1.33897	0.669485	+	0.742826i	$0.266515\pi$
$38$	−9976.00	−1.12072
$39$	−3636.00	−0.382792
$40$	0	0
$41$	7834.00	0.727820	0.363910	−	0.931434i	$-0.381442\pi$
$41$	7834.00	0.727820	0.363910	+	0.931434i	$0.381442\pi$
$42$	1764.00	0.154303
$43$	−16236.0	−1.33908	−0.669542	−	0.742774i	$-0.733510\pi$
$43$	−16236.0	−1.33908	−0.669542	+	0.742774i	$0.733510\pi$
$44$	−2464.00	−0.191871
$45$	0	0
$46$	13888.0	0.967710
$47$	2800.00	0.184890	0.0924450	−	0.995718i	$-0.470532\pi$
$47$	2800.00	0.184890	0.0924450	+	0.995718i	$0.470532\pi$
$48$	−2304.00	−0.144338
$49$	2401.00	0.142857
$50$	0	0
$51$	19638.0	1.05724
$52$	6464.00	0.331507
$53$	30924.0	1.51219	0.756094	−	0.654463i	$-0.227105\pi$
$53$	30924.0	1.51219	0.756094	+	0.654463i	$0.227105\pi$
$54$	−2916.00	−0.136083
$55$	0	0
$56$	−3136.00	−0.133631
$57$	22446.0	0.915065
$58$	23832.0	0.930230
$59$	−11536.0	−0.431445	−0.215722	−	0.976455i	$-0.569211\pi$
$59$	−11536.0	−0.431445	−0.215722	+	0.976455i	$0.569211\pi$
$60$	0	0
$61$	−38834.0	−1.33625	−0.668125	−	0.744049i	$-0.732903\pi$
$61$	−38834.0	−1.33625	−0.668125	+	0.744049i	$0.732903\pi$
$62$	−25640.0	−0.847108
$63$	−3969.00	−0.125988
$64$	4096.00	0.125000
$65$	0	0
$66$	5544.00	0.156662
$67$	48756.0	1.32691	0.663454	−	0.748217i	$-0.269090\pi$
$67$	48756.0	1.32691	0.663454	+	0.748217i	$0.269090\pi$
$68$	−34912.0	−0.915593
$69$	−31248.0	−0.790132
$70$	0	0
$71$	−77882.0	−1.83354	−0.916772	−	0.399411i	$-0.869214\pi$
$71$	−77882.0	−1.83354	−0.916772	+	0.399411i	$0.869214\pi$
$72$	5184.00	0.117851
$73$	47540.0	1.04412	0.522062	−	0.852908i	$-0.325163\pi$
$73$	47540.0	1.04412	0.522062	+	0.852908i	$0.325163\pi$
$74$	44600.0	0.946794
$75$	0	0
$76$	−39904.0	−0.792469
$77$	7546.00	0.145041
$78$	−14544.0	−0.270675
$79$	−36480.0	−0.657638	−0.328819	−	0.944393i	$-0.606651\pi$
$79$	−36480.0	−0.657638	−0.328819	+	0.944393i	$0.606651\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	31336.0	0.514646
$83$	−25716.0	−0.409740	−0.204870	−	0.978789i	$-0.565677\pi$
$83$	−25716.0	−0.409740	−0.204870	+	0.978789i	$0.565677\pi$
$84$	7056.00	0.109109
$85$	0	0
$86$	−64944.0	−0.946876
$87$	−53622.0	−0.759530
$88$	−9856.00	−0.135673
$89$	−100826.	−1.34927	−0.674633	−	0.738153i	$-0.735698\pi$
$89$	−100826.	−1.34927	−0.674633	+	0.738153i	$0.735698\pi$
$90$	0	0
$91$	−19796.0	−0.250596
$92$	55552.0	0.684274
$93$	57690.0	0.691661
$94$	11200.0	0.130737
$95$	0	0
$96$	−9216.00	−0.102062
$97$	89024.0	0.960678	0.480339	−	0.877083i	$-0.340514\pi$
$97$	89024.0	0.960678	0.480339	+	0.877083i	$0.340514\pi$
$98$	9604.00	0.101015
$99$	−12474.0	−0.127914
$100$	0	0
$101$	135318.	1.31993	0.659967	−	0.751295i	$-0.270570\pi$
$101$	135318.	1.31993	0.659967	+	0.751295i	$0.270570\pi$
$102$	78552.0	0.747579
$103$	32272.0	0.299732	0.149866	−	0.988706i	$-0.452116\pi$
$103$	32272.0	0.299732	0.149866	+	0.988706i	$0.452116\pi$
$104$	25856.0	0.234411
$105$	0	0
$106$	123696.	1.06928
$107$	105328.	0.889374	0.444687	−	0.895686i	$-0.353315\pi$
$107$	105328.	0.889374	0.444687	+	0.895686i	$0.353315\pi$
$108$	−11664.0	−0.0962250
$109$	169618.	1.36743	0.683716	−	0.729748i	$-0.260363\pi$
$109$	169618.	1.36743	0.683716	+	0.729748i	$0.260363\pi$
$110$	0	0
$111$	−100350.	−0.773054
$112$	−12544.0	−0.0944911
$113$	−222176.	−1.63682	−0.818410	−	0.574634i	$-0.805144\pi$
$113$	−222176.	−1.63682	−0.818410	+	0.574634i	$0.805144\pi$
$114$	89784.0	0.647048
$115$	0	0
$116$	95328.0	0.657772
$117$	32724.0	0.221005
$118$	−46144.0	−0.305078
$119$	106918.	0.692123
$120$	0	0
$121$	−137335.	−0.852742
$122$	−155336.	−0.944871
$123$	−70506.0	−0.420207
$124$	−102560.	−0.598996
$125$	0	0
$126$	−15876.0	−0.0890871
$127$	201720.	1.10979	0.554894	−	0.831921i	$-0.312759\pi$
$127$	201720.	1.10979	0.554894	+	0.831921i	$0.312759\pi$
$128$	16384.0	0.0883883
$129$	146124.	0.773121
$130$	0	0
$131$	191940.	0.977209	0.488604	−	0.872506i	$-0.337506\pi$
$131$	191940.	0.977209	0.488604	+	0.872506i	$0.337506\pi$
$132$	22176.0	0.110777
$133$	122206.	0.599050
$134$	195024.	0.938266
$135$	0	0
$136$	−139648.	−0.647422
$137$	263020.	1.19726	0.598628	−	0.801027i	$-0.295713\pi$
$137$	263020.	1.19726	0.598628	+	0.801027i	$0.295713\pi$
$138$	−124992.	−0.558707
$139$	304874.	1.33839	0.669196	−	0.743086i	$-0.266639\pi$
$139$	304874.	1.33839	0.669196	+	0.743086i	$0.266639\pi$
$140$	0	0
$141$	−25200.0	−0.106746
$142$	−311528.	−1.29651
$143$	−62216.0	−0.254426
$144$	20736.0	0.0833333
$145$	0	0
$146$	190160.	0.738307
$147$	−21609.0	−0.0824786
$148$	178400.	0.669485
$149$	415986.	1.53502	0.767508	−	0.641039i	$-0.221496\pi$
$149$	415986.	1.53502	0.767508	+	0.641039i	$0.221496\pi$
$150$	0	0
$151$	66572.0	0.237602	0.118801	−	0.992918i	$-0.462095\pi$
$151$	66572.0	0.237602	0.118801	+	0.992918i	$0.462095\pi$
$152$	−159616.	−0.560360
$153$	−176742.	−0.610395
$154$	30184.0	0.102559
$155$	0	0
$156$	−58176.0	−0.191396
$157$	−210200.	−0.680587	−0.340293	−	0.940319i	$-0.610526\pi$
$157$	−210200.	−0.680587	−0.340293	+	0.940319i	$0.610526\pi$
$158$	−145920.	−0.465021
$159$	−278316.	−0.873063
$160$	0	0
$161$	−170128.	−0.517263
$162$	26244.0	0.0785674
$163$	−257220.	−0.758291	−0.379145	−	0.925337i	$-0.623782\pi$
$163$	−257220.	−0.758291	−0.379145	+	0.925337i	$0.623782\pi$
$164$	125344.	0.363910
$165$	0	0
$166$	−102864.	−0.289730
$167$	446768.	1.23963	0.619813	−	0.784749i	$-0.287208\pi$
$167$	446768.	1.23963	0.619813	+	0.784749i	$0.287208\pi$
$168$	28224.0	0.0771517
$169$	−208077.	−0.560412
$170$	0	0
$171$	−202014.	−0.528313
$172$	−259776.	−0.669542
$173$	385418.	0.979077	0.489538	−	0.871982i	$-0.337165\pi$
$173$	385418.	0.979077	0.489538	+	0.871982i	$0.337165\pi$
$174$	−214488.	−0.537069
$175$	0	0
$176$	−39424.0	−0.0959354
$177$	103824.	0.249095
$178$	−403304.	−0.954075
$179$	651398.	1.51955	0.759773	−	0.650188i	$-0.225310\pi$
$179$	651398.	1.51955	0.759773	+	0.650188i	$0.225310\pi$
$180$	0	0
$181$	−143038.	−0.324530	−0.162265	−	0.986747i	$-0.551880\pi$
$181$	−143038.	−0.324530	−0.162265	+	0.986747i	$0.551880\pi$
$182$	−79184.0	−0.177198
$183$	349506.	0.771484
$184$	222208.	0.483855
$185$	0	0
$186$	230760.	0.489078
$187$	336028.	0.702702
$188$	44800.0	0.0924450
$189$	35721.0	0.0727393
$190$	0	0
$191$	601330.	1.19270	0.596348	−	0.802726i	$-0.296618\pi$
$191$	601330.	1.19270	0.596348	+	0.802726i	$0.296618\pi$
$192$	−36864.0	−0.0721688
$193$	540038.	1.04359	0.521796	−	0.853070i	$-0.325262\pi$
$193$	540038.	1.04359	0.521796	+	0.853070i	$0.325262\pi$
$194$	356096.	0.679302
$195$	0	0
$196$	38416.0	0.0714286
$197$	−939240.	−1.72429	−0.862146	−	0.506659i	$-0.830880\pi$
$197$	−939240.	−1.72429	−0.862146	+	0.506659i	$0.830880\pi$
$198$	−49896.0	−0.0904488
$199$	202358.	0.362233	0.181116	−	0.983462i	$-0.442029\pi$
$199$	202358.	0.362233	0.181116	+	0.983462i	$0.442029\pi$
$200$	0	0
$201$	−438804.	−0.766091
$202$	541272.	0.933334
$203$	−291942.	−0.497229
$204$	314208.	0.528618
$205$	0	0
$206$	129088.	0.211942
$207$	281232.	0.456183
$208$	103424.	0.165754
$209$	384076.	0.608207
$210$	0	0
$211$	−20140.0	−0.0311425	−0.0155712	−	0.999879i	$-0.504957\pi$
$211$	−20140.0	−0.0311425	−0.0155712	+	0.999879i	$0.504957\pi$
$212$	494784.	0.756094
$213$	700938.	1.05860
$214$	421312.	0.628882
$215$	0	0
$216$	−46656.0	−0.0680414
$217$	314090.	0.452798
$218$	678472.	0.966920
$219$	−427860.	−0.602825
$220$	0	0
$221$	−881528.	−1.21410
$222$	−401400.	−0.546632
$223$	813156.	1.09499	0.547497	−	0.836808i	$-0.315581\pi$
$223$	813156.	1.09499	0.547497	+	0.836808i	$0.315581\pi$
$224$	−50176.0	−0.0668153
$225$	0	0
$226$	−888704.	−1.15741
$227$	91668.0	0.118074	0.0590368	−	0.998256i	$-0.481197\pi$
$227$	91668.0	0.118074	0.0590368	+	0.998256i	$0.481197\pi$
$228$	359136.	0.457532
$229$	825358.	1.04005	0.520024	−	0.854151i	$-0.325923\pi$
$229$	825358.	1.04005	0.520024	+	0.854151i	$0.325923\pi$
$230$	0	0
$231$	−67914.0	−0.0837393
$232$	381312.	0.465115
$233$	−437288.	−0.527689	−0.263844	−	0.964565i	$-0.584991\pi$
$233$	−437288.	−0.527689	−0.263844	+	0.964565i	$0.584991\pi$
$234$	130896.	0.156274
$235$	0	0
$236$	−184576.	−0.215722
$237$	328320.	0.379688
$238$	427672.	0.489405
$239$	−685850.	−0.776666	−0.388333	−	0.921519i	$-0.626949\pi$
$239$	−685850.	−0.776666	−0.388333	+	0.921519i	$0.626949\pi$
$240$	0	0
$241$	1.69186e6	1.87639	0.938193	−	0.346112i	$-0.112498\pi$
$241$	1.69186e6	1.87639	0.938193	+	0.346112i	$0.112498\pi$
$242$	−549340.	−0.602980
$243$	−59049.0	−0.0641500
$244$	−621344.	−0.668125
$245$	0	0
$246$	−282024.	−0.297131
$247$	−1.00758e6	−1.05084
$248$	−410240.	−0.423554
$249$	231444.	0.236563
$250$	0	0
$251$	−491032.	−0.491955	−0.245978	−	0.969276i	$-0.579109\pi$
$251$	−491032.	−0.491955	−0.245978	+	0.969276i	$0.579109\pi$
$252$	−63504.0	−0.0629941
$253$	−534688.	−0.525169
$254$	806880.	0.784738
$255$	0	0
$256$	65536.0	0.0625000
$257$	628910.	0.593958	0.296979	−	0.954884i	$-0.404021\pi$
$257$	628910.	0.593958	0.296979	+	0.954884i	$0.404021\pi$
$258$	584496.	0.546679
$259$	−546350.	−0.506083
$260$	0	0
$261$	482598.	0.438515
$262$	767760.	0.690991
$263$	−318276.	−0.283736	−0.141868	−	0.989886i	$-0.545311\pi$
$263$	−318276.	−0.283736	−0.141868	+	0.989886i	$0.545311\pi$
$264$	88704.0	0.0783309
$265$	0	0
$266$	488824.	0.423593
$267$	907434.	0.778999
$268$	780096.	0.663454
$269$	473622.	0.399072	0.199536	−	0.979891i	$-0.436057\pi$
$269$	473622.	0.399072	0.199536	+	0.979891i	$0.436057\pi$
$270$	0	0
$271$	−1.68579e6	−1.39438	−0.697189	−	0.716888i	$-0.745566\pi$
$271$	−1.68579e6	−1.39438	−0.697189	+	0.716888i	$0.745566\pi$
$272$	−558592.	−0.457796
$273$	178164.	0.144682
$274$	1.05208e6	0.846588
$275$	0	0
$276$	−499968.	−0.395066
$277$	−123050.	−0.0963568	−0.0481784	−	0.998839i	$-0.515342\pi$
$277$	−123050.	−0.0963568	−0.0481784	+	0.998839i	$0.515342\pi$
$278$	1.21950e6	0.946386
$279$	−519210.	−0.399331
$280$	0	0
$281$	−685114.	−0.517603	−0.258802	−	0.965930i	$-0.583328\pi$
$281$	−685114.	−0.517603	−0.258802	+	0.965930i	$0.583328\pi$
$282$	−100800.	−0.0754810
$283$	305956.	0.227087	0.113544	−	0.993533i	$-0.463780\pi$
$283$	305956.	0.227087	0.113544	+	0.993533i	$0.463780\pi$
$284$	−1.24611e6	−0.916772
$285$	0	0
$286$	−248864.	−0.179907
$287$	−383866.	−0.275090
$288$	82944.0	0.0589256
$289$	3.34127e6	2.35324
$290$	0	0
$291$	−801216.	−0.554648
$292$	760640.	0.522062
$293$	−341790.	−0.232590	−0.116295	−	0.993215i	$-0.537102\pi$
$293$	−341790.	−0.232590	−0.116295	+	0.993215i	$0.537102\pi$
$294$	−86436.0	−0.0583212
$295$	0	0
$296$	713600.	0.473397
$297$	112266.	0.0738511
$298$	1.66394e6	1.08542
$299$	1.40269e6	0.907367
$300$	0	0
$301$	795564.	0.506126
$302$	266288.	0.168010
$303$	−1.21786e6	−0.762064
$304$	−638464.	−0.396235
$305$	0	0
$306$	−706968.	−0.431615
$307$	−1.61509e6	−0.978026	−0.489013	−	0.872277i	$-0.662643\pi$
$307$	−1.61509e6	−0.978026	−0.489013	+	0.872277i	$0.662643\pi$
$308$	120736.	0.0725204
$309$	−290448.	−0.173050
$310$	0	0
$311$	2.44535e6	1.43364	0.716820	−	0.697258i	$-0.245597\pi$
$311$	2.44535e6	1.43364	0.716820	+	0.697258i	$0.245597\pi$
$312$	−232704.	−0.135337
$313$	2.47844e6	1.42994	0.714970	−	0.699156i	$-0.246441\pi$
$313$	2.47844e6	1.42994	0.714970	+	0.699156i	$0.246441\pi$
$314$	−840800.	−0.481248
$315$	0	0
$316$	−583680.	−0.328819
$317$	1.59019e6	0.888792	0.444396	−	0.895830i	$-0.353418\pi$
$317$	1.59019e6	0.888792	0.444396	+	0.895830i	$0.353418\pi$
$318$	−1.11326e6	−0.617348
$319$	−917532.	−0.504829
$320$	0	0
$321$	−947952.	−0.513480
$322$	−680512.	−0.365760
$323$	5.44191e6	2.90232
$324$	104976.	0.0555556
$325$	0	0
$326$	−1.02888e6	−0.536192
$327$	−1.52656e6	−0.789487
$328$	501376.	0.257323
$329$	−137200.	−0.0698818
$330$	0	0
$331$	76636.0	0.0384470	0.0192235	−	0.999815i	$-0.493881\pi$
$331$	76636.0	0.0384470	0.0192235	+	0.999815i	$0.493881\pi$
$332$	−411456.	−0.204870
$333$	903150.	0.446323
$334$	1.78707e6	0.876548
$335$	0	0
$336$	112896.	0.0545545
$337$	2.94098e6	1.41064	0.705322	−	0.708887i	$-0.250802\pi$
$337$	2.94098e6	1.41064	0.705322	+	0.708887i	$0.250802\pi$
$338$	−832308.	−0.396271
$339$	1.99958e6	0.945019
$340$	0	0
$341$	987140.	0.459719
$342$	−808056.	−0.373574
$343$	−117649.	−0.0539949
$344$	−1.03910e6	−0.473438
$345$	0	0
$346$	1.54167e6	0.692312
$347$	3.35015e6	1.49362	0.746810	−	0.665037i	$-0.231584\pi$
$347$	3.35015e6	1.49362	0.746810	+	0.665037i	$0.231584\pi$
$348$	−857952.	−0.379765
$349$	2.00658e6	0.881847	0.440924	−	0.897545i	$-0.354651\pi$
$349$	2.00658e6	0.881847	0.440924	+	0.897545i	$0.354651\pi$
$350$	0	0
$351$	−294516.	−0.127597
$352$	−157696.	−0.0678366
$353$	−1.57875e6	−0.674336	−0.337168	−	0.941444i	$-0.609469\pi$
$353$	−1.57875e6	−0.674336	−0.337168	+	0.941444i	$0.609469\pi$
$354$	415296.	0.176137
$355$	0	0
$356$	−1.61322e6	−0.674633
$357$	−962262.	−0.399598
$358$	2.60559e6	1.07448
$359$	735842.	0.301334	0.150667	−	0.988585i	$-0.451858\pi$
$359$	735842.	0.301334	0.150667	+	0.988585i	$0.451858\pi$
$360$	0	0
$361$	3.74394e6	1.51203
$362$	−572152.	−0.229477
$363$	1.23602e6	0.492331
$364$	−316736.	−0.125298
$365$	0	0
$366$	1.39802e6	0.545522
$367$	−1.73849e6	−0.673764	−0.336882	−	0.941547i	$-0.609372\pi$
$367$	−1.73849e6	−0.673764	−0.336882	+	0.941547i	$0.609372\pi$
$368$	888832.	0.342137
$369$	634554.	0.242607
$370$	0	0
$371$	−1.51528e6	−0.571554
$372$	923040.	0.345830
$373$	1.44138e6	0.536421	0.268211	−	0.963360i	$-0.413568\pi$
$373$	1.44138e6	0.536421	0.268211	+	0.963360i	$0.413568\pi$
$374$	1.34411e6	0.496886
$375$	0	0
$376$	179200.	0.0653685
$377$	2.40703e6	0.872225
$378$	142884.	0.0514344
$379$	2.23672e6	0.799859	0.399930	−	0.916546i	$-0.369035\pi$
$379$	2.23672e6	0.799859	0.399930	+	0.916546i	$0.369035\pi$
$380$	0	0
$381$	−1.81548e6	−0.640736
$382$	2.40532e6	0.843363
$383$	208656.	0.0726832	0.0363416	−	0.999339i	$-0.488430\pi$
$383$	208656.	0.0726832	0.0363416	+	0.999339i	$0.488430\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	2.16015e6	0.737932
$387$	−1.31512e6	−0.446361
$388$	1.42438e6	0.480339
$389$	−3.35989e6	−1.12577	−0.562886	−	0.826534i	$-0.690309\pi$
$389$	−3.35989e6	−1.12577	−0.562886	+	0.826534i	$0.690309\pi$
$390$	0	0
$391$	−7.57590e6	−2.50607
$392$	153664.	0.0505076
$393$	−1.72746e6	−0.564192
$394$	−3.75696e6	−1.21926
$395$	0	0
$396$	−199584.	−0.0639570
$397$	−4.45592e6	−1.41893	−0.709465	−	0.704741i	$-0.751063\pi$
$397$	−4.45592e6	−1.41893	−0.709465	+	0.704741i	$0.751063\pi$
$398$	809432.	0.256137
$399$	−1.09985e6	−0.345862
$400$	0	0
$401$	2.34278e6	0.727562	0.363781	−	0.931484i	$-0.381486\pi$
$401$	2.34278e6	0.727562	0.363781	+	0.931484i	$0.381486\pi$
$402$	−1.75522e6	−0.541708
$403$	−2.58964e6	−0.794286
$404$	2.16509e6	0.659967
$405$	0	0
$406$	−1.16777e6	−0.351594
$407$	−1.71710e6	−0.513818
$408$	1.25683e6	0.373789
$409$	5.74830e6	1.69915	0.849574	−	0.527470i	$-0.176859\pi$
$409$	5.74830e6	1.69915	0.849574	+	0.527470i	$0.176859\pi$
$410$	0	0
$411$	−2.36718e6	−0.691237
$412$	516352.	0.149866
$413$	565264.	0.163071
$414$	1.12493e6	0.322570
$415$	0	0
$416$	413696.	0.117206
$417$	−2.74387e6	−0.772721
$418$	1.53630e6	0.430067
$419$	3.12572e6	0.869792	0.434896	−	0.900481i	$-0.356785\pi$
$419$	3.12572e6	0.869792	0.434896	+	0.900481i	$0.356785\pi$
$420$	0	0
$421$	−4.27807e6	−1.17637	−0.588184	−	0.808727i	$-0.700157\pi$
$421$	−4.27807e6	−1.17637	−0.588184	+	0.808727i	$0.700157\pi$
$422$	−80560.0	−0.0220211
$423$	226800.	0.0616300
$424$	1.97914e6	0.534639
$425$	0	0
$426$	2.80375e6	0.748541
$427$	1.90287e6	0.505055
$428$	1.68525e6	0.444687
$429$	559944.	0.146893
$430$	0	0
$431$	−4.85877e6	−1.25989	−0.629946	−	0.776639i	$-0.716923\pi$
$431$	−4.85877e6	−1.25989	−0.629946	+	0.776639i	$0.716923\pi$
$432$	−186624.	−0.0481125
$433$	−6.17695e6	−1.58327	−0.791634	−	0.610995i	$-0.790769\pi$
$433$	−6.17695e6	−1.58327	−0.791634	+	0.610995i	$0.790769\pi$
$434$	1.25636e6	0.320177
$435$	0	0
$436$	2.71389e6	0.683716
$437$	−8.65917e6	−2.16907
$438$	−1.71144e6	−0.426262
$439$	−3.35463e6	−0.830776	−0.415388	−	0.909644i	$-0.636354\pi$
$439$	−3.35463e6	−0.830776	−0.415388	+	0.909644i	$0.636354\pi$
$440$	0	0
$441$	194481.	0.0476190
$442$	−3.52611e6	−0.858500
$443$	2.34016e6	0.566548	0.283274	−	0.959039i	$-0.408579\pi$
$443$	2.34016e6	0.566548	0.283274	+	0.959039i	$0.408579\pi$
$444$	−1.60560e6	−0.386527
$445$	0	0
$446$	3.25262e6	0.774278
$447$	−3.74387e6	−0.886242
$448$	−200704.	−0.0472456
$449$	−6.57665e6	−1.53953	−0.769766	−	0.638326i	$-0.779627\pi$
$449$	−6.57665e6	−1.53953	−0.769766	+	0.638326i	$0.779627\pi$
$450$	0	0
$451$	−1.20644e6	−0.279295
$452$	−3.55482e6	−0.818410
$453$	−599148.	−0.137179
$454$	366672.	0.0834907
$455$	0	0
$456$	1.43654e6	0.323524
$457$	−522430.	−0.117014	−0.0585070	−	0.998287i	$-0.518634\pi$
$457$	−522430.	−0.117014	−0.0585070	+	0.998287i	$0.518634\pi$
$458$	3.30143e6	0.735425
$459$	1.59068e6	0.352412
$460$	0	0
$461$	3.31808e6	0.727168	0.363584	−	0.931561i	$-0.381553\pi$
$461$	3.31808e6	0.727168	0.363584	+	0.931561i	$0.381553\pi$
$462$	−271656.	−0.0592126
$463$	−3.59461e6	−0.779290	−0.389645	−	0.920965i	$-0.627402\pi$
$463$	−3.59461e6	−0.779290	−0.389645	+	0.920965i	$0.627402\pi$
$464$	1.52525e6	0.328886
$465$	0	0
$466$	−1.74915e6	−0.373132
$467$	−1.53871e6	−0.326486	−0.163243	−	0.986586i	$-0.552195\pi$
$467$	−1.53871e6	−0.326486	−0.163243	+	0.986586i	$0.552195\pi$
$468$	523584.	0.110502
$469$	−2.38904e6	−0.501524
$470$	0	0
$471$	1.89180e6	0.392937
$472$	−738304.	−0.152539
$473$	2.50034e6	0.513862
$474$	1.31328e6	0.268480
$475$	0	0
$476$	1.71069e6	0.346062
$477$	2.50484e6	0.504063
$478$	−2.74340e6	−0.549186
$479$	−8.23054e6	−1.63904	−0.819520	−	0.573051i	$-0.805760\pi$
$479$	−8.23054e6	−1.63904	−0.819520	+	0.573051i	$0.805760\pi$
$480$	0	0
$481$	4.50460e6	0.887756
$482$	6.76745e6	1.32681
$483$	1.53115e6	0.298642
$484$	−2.19736e6	−0.426371
$485$	0	0
$486$	−236196.	−0.0453609
$487$	7.86643e6	1.50299	0.751494	−	0.659740i	$-0.229334\pi$
$487$	7.86643e6	1.50299	0.751494	+	0.659740i	$0.229334\pi$
$488$	−2.48538e6	−0.472436
$489$	2.31498e6	0.437799
$490$	0	0
$491$	−3.03074e6	−0.567342	−0.283671	−	0.958922i	$-0.591552\pi$
$491$	−3.03074e6	−0.567342	−0.283671	+	0.958922i	$0.591552\pi$
$492$	−1.12810e6	−0.210104
$493$	−1.30004e7	−2.40901
$494$	−4.03030e6	−0.743054
$495$	0	0
$496$	−1.64096e6	−0.299498
$497$	3.81622e6	0.693014
$498$	925776.	0.167276
$499$	8.30966e6	1.49393	0.746967	−	0.664861i	$-0.231509\pi$
$499$	8.30966e6	1.49393	0.746967	+	0.664861i	$0.231509\pi$
$500$	0	0
$501$	−4.02091e6	−0.715699
$502$	−1.96413e6	−0.347865
$503$	−1.57054e6	−0.276777	−0.138389	−	0.990378i	$-0.544192\pi$
$503$	−1.57054e6	−0.276777	−0.138389	+	0.990378i	$0.544192\pi$
$504$	−254016.	−0.0445435
$505$	0	0
$506$	−2.13875e6	−0.371351
$507$	1.87269e6	0.323554
$508$	3.22752e6	0.554894
$509$	6.18245e6	1.05771	0.528854	−	0.848713i	$-0.322622\pi$
$509$	6.18245e6	1.05771	0.528854	+	0.848713i	$0.322622\pi$
$510$	0	0
$511$	−2.32946e6	−0.394642
$512$	262144.	0.0441942
$513$	1.81813e6	0.305022
$514$	2.51564e6	0.419992
$515$	0	0
$516$	2.33798e6	0.386560
$517$	−431200.	−0.0709500
$518$	−2.18540e6	−0.357855
$519$	−3.46876e6	−0.565270
$520$	0	0
$521$	−4.77457e6	−0.770619	−0.385309	−	0.922787i	$-0.625905\pi$
$521$	−4.77457e6	−0.770619	−0.385309	+	0.922787i	$0.625905\pi$
$522$	1.93039e6	0.310077
$523$	−1.72880e6	−0.276370	−0.138185	−	0.990406i	$-0.544127\pi$
$523$	−1.72880e6	−0.276370	−0.138185	+	0.990406i	$0.544127\pi$
$524$	3.07104e6	0.488604
$525$	0	0
$526$	−1.27310e6	−0.200632
$527$	1.39866e7	2.19375
$528$	354816.	0.0553883
$529$	5.61844e6	0.872924
$530$	0	0
$531$	−934416.	−0.143815
$532$	1.95530e6	0.299525
$533$	3.16494e6	0.482555
$534$	3.62974e6	0.550835
$535$	0	0
$536$	3.12038e6	0.469133
$537$	−5.86258e6	−0.877310
$538$	1.89449e6	0.282186
$539$	−369754.	−0.0548202
$540$	0	0
$541$	−8.15665e6	−1.19817	−0.599085	−	0.800685i	$-0.704469\pi$
$541$	−8.15665e6	−1.19817	−0.599085	+	0.800685i	$0.704469\pi$
$542$	−6.74316e6	−0.985974
$543$	1.28734e6	0.187368
$544$	−2.23437e6	−0.323711
$545$	0	0
$546$	712656.	0.102305
$547$	1.83873e6	0.262754	0.131377	−	0.991332i	$-0.458060\pi$
$547$	1.83873e6	0.262754	0.131377	+	0.991332i	$0.458060\pi$
$548$	4.20832e6	0.598628
$549$	−3.14555e6	−0.445416
$550$	0	0
$551$	−1.48593e7	−2.08506
$552$	−1.99987e6	−0.279354
$553$	1.78752e6	0.248564
$554$	−492200.	−0.0681345
$555$	0	0
$556$	4.87798e6	0.669196
$557$	3.90389e6	0.533163	0.266581	−	0.963812i	$-0.414106\pi$
$557$	3.90389e6	0.533163	0.266581	+	0.963812i	$0.414106\pi$
$558$	−2.07684e6	−0.282369
$559$	−6.55934e6	−0.887832
$560$	0	0
$561$	−3.02425e6	−0.405705
$562$	−2.74046e6	−0.366001
$563$	2.29096e6	0.304611	0.152306	−	0.988333i	$-0.451330\pi$
$563$	2.29096e6	0.304611	0.152306	+	0.988333i	$0.451330\pi$
$564$	−403200.	−0.0533731
$565$	0	0
$566$	1.22382e6	0.160575
$567$	−321489.	−0.0419961
$568$	−4.98445e6	−0.648256
$569$	−3.91597e6	−0.507059	−0.253529	−	0.967328i	$-0.581591\pi$
$569$	−3.91597e6	−0.507059	−0.253529	+	0.967328i	$0.581591\pi$
$570$	0	0
$571$	−2.34541e6	−0.301043	−0.150521	−	0.988607i	$-0.548095\pi$
$571$	−2.34541e6	−0.301043	−0.150521	+	0.988607i	$0.548095\pi$
$572$	−995456.	−0.127213
$573$	−5.41197e6	−0.688603
$574$	−1.53546e6	−0.194518
$575$	0	0
$576$	331776.	0.0416667
$577$	2.94434e6	0.368170	0.184085	−	0.982910i	$-0.441068\pi$
$577$	2.94434e6	0.368170	0.184085	+	0.982910i	$0.441068\pi$
$578$	1.33651e7	1.66399
$579$	−4.86034e6	−0.602519
$580$	0	0
$581$	1.26008e6	0.154867
$582$	−3.20486e6	−0.392195
$583$	−4.76230e6	−0.580290
$584$	3.04256e6	0.369154
$585$	0	0
$586$	−1.36716e6	−0.164466
$587$	−2.02909e6	−0.243056	−0.121528	−	0.992588i	$-0.538779\pi$
$587$	−2.02909e6	−0.243056	−0.121528	+	0.992588i	$0.538779\pi$
$588$	−345744.	−0.0412393
$589$	1.59865e7	1.89874
$590$	0	0
$591$	8.45316e6	0.995521
$592$	2.85440e6	0.334742
$593$	−1.35165e7	−1.57844	−0.789220	−	0.614111i	$-0.789515\pi$
$593$	−1.35165e7	−1.57844	−0.789220	+	0.614111i	$0.789515\pi$
$594$	449064.	0.0522206
$595$	0	0
$596$	6.65578e6	0.767508
$597$	−1.82122e6	−0.209135
$598$	5.61075e6	0.641606
$599$	2.32035e6	0.264233	0.132117	−	0.991234i	$-0.457823\pi$
$599$	2.32035e6	0.264233	0.132117	+	0.991234i	$0.457823\pi$
$600$	0	0
$601$	1.25049e6	0.141219	0.0706094	−	0.997504i	$-0.477506\pi$
$601$	1.25049e6	0.141219	0.0706094	+	0.997504i	$0.477506\pi$
$602$	3.18226e6	0.357885
$603$	3.94924e6	0.442303
$604$	1.06515e6	0.118801
$605$	0	0
$606$	−4.87145e6	−0.538861
$607$	−551388.	−0.0607415	−0.0303708	−	0.999539i	$-0.509669\pi$
$607$	−551388.	−0.0607415	−0.0303708	+	0.999539i	$0.509669\pi$
$608$	−2.55386e6	−0.280180
$609$	2.62748e6	0.287075
$610$	0	0
$611$	1.13120e6	0.122585
$612$	−2.82787e6	−0.305198
$613$	1.69792e7	1.82501	0.912506	−	0.409064i	$-0.134145\pi$
$613$	1.69792e7	1.82501	0.912506	+	0.409064i	$0.134145\pi$
$614$	−6.46035e6	−0.691569
$615$	0	0
$616$	482944.	0.0512796
$617$	6.50147e6	0.687541	0.343771	−	0.939054i	$-0.388296\pi$
$617$	6.50147e6	0.687541	0.343771	+	0.939054i	$0.388296\pi$
$618$	−1.16179e6	−0.122365
$619$	−2.00377e6	−0.210195	−0.105097	−	0.994462i	$-0.533515\pi$
$619$	−2.00377e6	−0.210195	−0.105097	+	0.994462i	$0.533515\pi$
$620$	0	0
$621$	−2.53109e6	−0.263377
$622$	9.78141e6	1.01374
$623$	4.94047e6	0.509975
$624$	−930816.	−0.0956979
$625$	0	0
$626$	9.91376e6	1.01112
$627$	−3.45668e6	−0.351149
$628$	−3.36320e6	−0.340293
$629$	−2.43293e7	−2.45190
$630$	0	0
$631$	1.09500e7	1.09482	0.547410	−	0.836865i	$-0.315614\pi$
$631$	1.09500e7	1.09482	0.547410	+	0.836865i	$0.315614\pi$
$632$	−2.33472e6	−0.232510
$633$	181260.	0.0179801
$634$	6.36075e6	0.628471
$635$	0	0
$636$	−4.45306e6	−0.436531
$637$	970004.	0.0947163
$638$	−3.67013e6	−0.356968
$639$	−6.30844e6	−0.611181
$640$	0	0
$641$	2.82070e6	0.271152	0.135576	−	0.990767i	$-0.456712\pi$
$641$	2.82070e6	0.271152	0.135576	+	0.990767i	$0.456712\pi$
$642$	−3.79181e6	−0.363085
$643$	−2.86202e6	−0.272989	−0.136494	−	0.990641i	$-0.543584\pi$
$643$	−2.86202e6	−0.272989	−0.136494	+	0.990641i	$0.543584\pi$
$644$	−2.72205e6	−0.258631
$645$	0	0
$646$	2.17676e7	2.05225
$647$	2.56106e6	0.240524	0.120262	−	0.992742i	$-0.461627\pi$
$647$	2.56106e6	0.240524	0.120262	+	0.992742i	$0.461627\pi$
$648$	419904.	0.0392837
$649$	1.77654e6	0.165563
$650$	0	0
$651$	−2.82681e6	−0.261423
$652$	−4.11552e6	−0.379145
$653$	8.10229e6	0.743575	0.371787	−	0.928318i	$-0.378745\pi$
$653$	8.10229e6	0.743575	0.371787	+	0.928318i	$0.378745\pi$
$654$	−6.10625e6	−0.558252
$655$	0	0
$656$	2.00550e6	0.181955
$657$	3.85074e6	0.348041
$658$	−548800.	−0.0494139
$659$	−1.73968e7	−1.56047	−0.780234	−	0.625488i	$-0.784900\pi$
$659$	−1.73968e7	−1.56047	−0.780234	+	0.625488i	$0.784900\pi$
$660$	0	0
$661$	−6.22052e6	−0.553762	−0.276881	−	0.960904i	$-0.589301\pi$
$661$	−6.22052e6	−0.553762	−0.276881	+	0.960904i	$0.589301\pi$
$662$	306544.	0.0271862
$663$	7.93375e6	0.700963
$664$	−1.64582e6	−0.144865
$665$	0	0
$666$	3.61260e6	0.315598
$667$	2.06862e7	1.80039
$668$	7.14829e6	0.619813
$669$	−7.31840e6	−0.632195
$670$	0	0
$671$	5.98044e6	0.512775
$672$	451584.	0.0385758
$673$	−5.12142e6	−0.435866	−0.217933	−	0.975964i	$-0.569931\pi$
$673$	−5.12142e6	−0.435866	−0.217933	+	0.975964i	$0.569931\pi$
$674$	1.17639e7	0.997476
$675$	0	0
$676$	−3.32923e6	−0.280206
$677$	504738.	0.0423247	0.0211624	−	0.999776i	$-0.493263\pi$
$677$	504738.	0.0423247	0.0211624	+	0.999776i	$0.493263\pi$
$678$	7.99834e6	0.668229
$679$	−4.36218e6	−0.363102
$680$	0	0
$681$	−825012.	−0.0681699
$682$	3.94856e6	0.325071
$683$	−6.38249e6	−0.523526	−0.261763	−	0.965132i	$-0.584304\pi$
$683$	−6.38249e6	−0.523526	−0.261763	+	0.965132i	$0.584304\pi$
$684$	−3.23222e6	−0.264156
$685$	0	0
$686$	−470596.	−0.0381802
$687$	−7.42822e6	−0.600472
$688$	−4.15642e6	−0.334771
$689$	1.24933e7	1.00260
$690$	0	0
$691$	−1.93077e7	−1.53828	−0.769141	−	0.639080i	$-0.779315\pi$
$691$	−1.93077e7	−1.53828	−0.769141	+	0.639080i	$0.779315\pi$
$692$	6.16669e6	0.489538
$693$	611226.	0.0483469
$694$	1.34006e7	1.05615
$695$	0	0
$696$	−3.43181e6	−0.268534
$697$	−1.70938e7	−1.33277
$698$	8.02633e6	0.623560
$699$	3.93559e6	0.304661
$700$	0	0
$701$	−1.12652e7	−0.865849	−0.432925	−	0.901430i	$-0.642518\pi$
$701$	−1.12652e7	−0.865849	−0.432925	+	0.901430i	$0.642518\pi$
$702$	−1.17806e6	−0.0902248
$703$	−2.78081e7	−2.12218
$704$	−630784.	−0.0479677
$705$	0	0
$706$	−6.31500e6	−0.476828
$707$	−6.63058e6	−0.498888
$708$	1.66118e6	0.124547
$709$	7.33135e6	0.547732	0.273866	−	0.961768i	$-0.411697\pi$
$709$	7.33135e6	0.547732	0.273866	+	0.961768i	$0.411697\pi$
$710$	0	0
$711$	−2.95488e6	−0.219213
$712$	−6.45286e6	−0.477038
$713$	−2.22555e7	−1.63951
$714$	−3.84905e6	−0.282558
$715$	0	0
$716$	1.04224e7	0.759773
$717$	6.17265e6	0.448408
$718$	2.94337e6	0.213075
$719$	4.50534e6	0.325016	0.162508	−	0.986707i	$-0.448042\pi$
$719$	4.50534e6	0.325016	0.162508	+	0.986707i	$0.448042\pi$
$720$	0	0
$721$	−1.58133e6	−0.113288
$722$	1.49757e7	1.06917
$723$	−1.52268e7	−1.08333
$724$	−2.28861e6	−0.162265
$725$	0	0
$726$	4.94406e6	0.348131
$727$	2.03907e7	1.43086	0.715430	−	0.698684i	$-0.246231\pi$
$727$	2.03907e7	1.43086	0.715430	+	0.698684i	$0.246231\pi$
$728$	−1.26694e6	−0.0885990
$729$	531441.	0.0370370
$730$	0	0
$731$	3.54270e7	2.45211
$732$	5.59210e6	0.385742
$733$	−1.22592e7	−0.842759	−0.421380	−	0.906884i	$-0.638454\pi$
$733$	−1.22592e7	−0.842759	−0.421380	+	0.906884i	$0.638454\pi$
$734$	−6.95397e6	−0.476423
$735$	0	0
$736$	3.55533e6	0.241927
$737$	−7.50842e6	−0.509190
$738$	2.53822e6	0.171549
$739$	−1.90266e7	−1.28159	−0.640795	−	0.767712i	$-0.721395\pi$
$739$	−1.90266e7	−1.28159	−0.640795	+	0.767712i	$0.721395\pi$
$740$	0	0
$741$	9.06818e6	0.606701
$742$	−6.06110e6	−0.404149
$743$	−1.71290e7	−1.13831	−0.569154	−	0.822231i	$-0.692729\pi$
$743$	−1.71290e7	−1.13831	−0.569154	+	0.822231i	$0.692729\pi$
$744$	3.69216e6	0.244539
$745$	0	0
$746$	5.76551e6	0.379307
$747$	−2.08300e6	−0.136580
$748$	5.37645e6	0.351351
$749$	−5.16107e6	−0.336152
$750$	0	0
$751$	−1.36251e7	−0.881534	−0.440767	−	0.897622i	$-0.645293\pi$
$751$	−1.36251e7	−0.881534	−0.440767	+	0.897622i	$0.645293\pi$
$752$	716800.	0.0462225
$753$	4.41929e6	0.284030
$754$	9.62813e6	0.616756
$755$	0	0
$756$	571536.	0.0363696
$757$	−7.38705e6	−0.468523	−0.234262	−	0.972174i	$-0.575267\pi$
$757$	−7.38705e6	−0.468523	−0.234262	+	0.972174i	$0.575267\pi$
$758$	8.94688e6	0.565586
$759$	4.81219e6	0.303206
$760$	0	0
$761$	2.37994e7	1.48972	0.744858	−	0.667223i	$-0.232517\pi$
$761$	2.37994e7	1.48972	0.744858	+	0.667223i	$0.232517\pi$
$762$	−7.26192e6	−0.453069
$763$	−8.31128e6	−0.516841
$764$	9.62128e6	0.596348
$765$	0	0
$766$	834624.	0.0513948
$767$	−4.66054e6	−0.286054
$768$	−589824.	−0.0360844
$769$	2.31023e7	1.40877	0.704385	−	0.709819i	$-0.251223\pi$
$769$	2.31023e7	1.40877	0.704385	+	0.709819i	$0.251223\pi$
$770$	0	0
$771$	−5.66019e6	−0.342922
$772$	8.64061e6	0.521796
$773$	−2.12954e7	−1.28185	−0.640924	−	0.767605i	$-0.721448\pi$
$773$	−2.12954e7	−1.28185	−0.640924	+	0.767605i	$0.721448\pi$
$774$	−5.26046e6	−0.315625
$775$	0	0
$776$	5.69754e6	0.339651
$777$	4.91715e6	0.292187
$778$	−1.34395e7	−0.796041
$779$	−1.95380e7	−1.15355
$780$	0	0
$781$	1.19938e7	0.703607
$782$	−3.03036e7	−1.77206
$783$	−4.34338e6	−0.253177
$784$	614656.	0.0357143
$785$	0	0
$786$	−6.90984e6	−0.398944
$787$	1.28443e7	0.739222	0.369611	−	0.929187i	$-0.379491\pi$
$787$	1.28443e7	0.739222	0.369611	+	0.929187i	$0.379491\pi$
$788$	−1.50278e7	−0.862146
$789$	2.86448e6	0.163815
$790$	0	0
$791$	1.08866e7	0.618660
$792$	−798336.	−0.0452244
$793$	−1.56889e7	−0.885953
$794$	−1.78237e7	−1.00333
$795$	0	0
$796$	3.23773e6	0.181116
$797$	−1.47704e7	−0.823660	−0.411830	−	0.911261i	$-0.635110\pi$
$797$	−1.47704e7	−0.823660	−0.411830	+	0.911261i	$0.635110\pi$
$798$	−4.39942e6	−0.244561
$799$	−6.10960e6	−0.338568
$800$	0	0
$801$	−8.16691e6	−0.449755
$802$	9.37111e6	0.514464
$803$	−7.32116e6	−0.400674
$804$	−7.02086e6	−0.383046
$805$	0	0
$806$	−1.03586e7	−0.561645
$807$	−4.26260e6	−0.230404
$808$	8.66035e6	0.466667
$809$	1.46840e7	0.788813	0.394406	−	0.918936i	$-0.370950\pi$
$809$	1.46840e7	0.788813	0.394406	+	0.918936i	$0.370950\pi$
$810$	0	0
$811$	3.10515e7	1.65779	0.828897	−	0.559401i	$-0.188969\pi$
$811$	3.10515e7	1.65779	0.828897	+	0.559401i	$0.188969\pi$
$812$	−4.67107e6	−0.248615
$813$	1.51721e7	0.805044
$814$	−6.86840e6	−0.363324
$815$	0	0
$816$	5.02733e6	0.264309
$817$	4.04926e7	2.12237
$818$	2.29932e7	1.20148
$819$	−1.60348e6	−0.0835320
$820$	0	0
$821$	−4.60748e6	−0.238564	−0.119282	−	0.992860i	$-0.538059\pi$
$821$	−4.60748e6	−0.238564	−0.119282	+	0.992860i	$0.538059\pi$
$822$	−9.46872e6	−0.488778
$823$	−1.08449e7	−0.558120	−0.279060	−	0.960274i	$-0.590023\pi$
$823$	−1.08449e7	−0.558120	−0.279060	+	0.960274i	$0.590023\pi$
$824$	2.06541e6	0.105971
$825$	0	0
$826$	2.26106e6	0.115308
$827$	−3.53332e7	−1.79647	−0.898233	−	0.439520i	$-0.855149\pi$
$827$	−3.53332e7	−1.79647	−0.898233	+	0.439520i	$0.855149\pi$
$828$	4.49971e6	0.228091
$829$	−5.05313e6	−0.255372	−0.127686	−	0.991815i	$-0.540755\pi$
$829$	−5.05313e6	−0.255372	−0.127686	+	0.991815i	$0.540755\pi$
$830$	0	0
$831$	1.10745e6	0.0556316
$832$	1.65478e6	0.0828768
$833$	−5.23898e6	−0.261598
$834$	−1.09755e7	−0.546396
$835$	0	0
$836$	6.14522e6	0.304104
$837$	4.67289e6	0.230554
$838$	1.25029e7	0.615036
$839$	−1.07551e7	−0.527484	−0.263742	−	0.964593i	$-0.584957\pi$
$839$	−1.07551e7	−0.527484	−0.263742	+	0.964593i	$0.584957\pi$
$840$	0	0
$841$	1.49866e7	0.730657
$842$	−1.71123e7	−0.831818
$843$	6.16603e6	0.298838
$844$	−322240.	−0.0155712
$845$	0	0
$846$	907200.	0.0435790
$847$	6.72942e6	0.322306
$848$	7.91654e6	0.378047
$849$	−2.75360e6	−0.131109
$850$	0	0
$851$	3.87128e7	1.83244
$852$	1.12150e7	0.529298
$853$	−9.88836e6	−0.465320	−0.232660	−	0.972558i	$-0.574743\pi$
$853$	−9.88836e6	−0.465320	−0.232660	+	0.972558i	$0.574743\pi$
$854$	7.61146e6	0.357128
$855$	0	0
$856$	6.74099e6	0.314441
$857$	−1.40820e7	−0.654954	−0.327477	−	0.944859i	$-0.606198\pi$
$857$	−1.40820e7	−0.654954	−0.327477	+	0.944859i	$0.606198\pi$
$858$	2.23978e6	0.103869
$859$	4.81499e6	0.222645	0.111322	−	0.993784i	$-0.464491\pi$
$859$	4.81499e6	0.222645	0.111322	+	0.993784i	$0.464491\pi$
$860$	0	0
$861$	3.45479e6	0.158823
$862$	−1.94351e7	−0.890878
$863$	−2.69454e7	−1.23157	−0.615784	−	0.787915i	$-0.711161\pi$
$863$	−2.69454e7	−1.23157	−0.615784	+	0.787915i	$0.711161\pi$
$864$	−746496.	−0.0340207
$865$	0	0
$866$	−2.47078e7	−1.11954
$867$	−3.00714e7	−1.35864
$868$	5.02544e6	0.226399
$869$	5.61792e6	0.252363
$870$	0	0
$871$	1.96974e7	0.879760
$872$	1.08556e7	0.483460
$873$	7.21094e6	0.320226
$874$	−3.46367e7	−1.53376
$875$	0	0
$876$	−6.84576e6	−0.301413
$877$	3.61198e7	1.58579	0.792896	−	0.609357i	$-0.208572\pi$
$877$	3.61198e7	1.58579	0.792896	+	0.609357i	$0.208572\pi$
$878$	−1.34185e7	−0.587447
$879$	3.07611e6	0.134286
$880$	0	0
$881$	−3.02037e7	−1.31105	−0.655526	−	0.755172i	$-0.727553\pi$
$881$	−3.02037e7	−1.31105	−0.655526	+	0.755172i	$0.727553\pi$
$882$	777924.	0.0336718
$883$	2.02606e7	0.874480	0.437240	−	0.899345i	$-0.355956\pi$
$883$	2.02606e7	0.874480	0.437240	+	0.899345i	$0.355956\pi$
$884$	−1.41044e7	−0.607051
$885$	0	0
$886$	9.36066e6	0.400610
$887$	−1.94200e7	−0.828782	−0.414391	−	0.910099i	$-0.636005\pi$
$887$	−1.94200e7	−0.828782	−0.414391	+	0.910099i	$0.636005\pi$
$888$	−6.42240e6	−0.273316
$889$	−9.88428e6	−0.419460
$890$	0	0
$891$	−1.01039e6	−0.0426380
$892$	1.30105e7	0.547497
$893$	−6.98320e6	−0.293039
$894$	−1.49755e7	−0.626668
$895$	0	0
$896$	−802816.	−0.0334077
$897$	−1.26242e7	−0.523869
$898$	−2.63066e7	−1.08861
$899$	−3.81908e7	−1.57601
$900$	0	0
$901$	−6.74762e7	−2.76910
$902$	−4.82574e6	−0.197491
$903$	−7.16008e6	−0.292212
$904$	−1.42193e7	−0.578703
$905$	0	0
$906$	−2.39659e6	−0.0970004
$907$	1.89253e7	0.763879	0.381940	−	0.924187i	$-0.375256\pi$
$907$	1.89253e7	0.763879	0.381940	+	0.924187i	$0.375256\pi$
$908$	1.46669e6	0.0590368
$909$	1.09608e7	0.439978
$910$	0	0
$911$	−2.90586e7	−1.16006	−0.580028	−	0.814596i	$-0.696959\pi$
$911$	−2.90586e7	−1.16006	−0.580028	+	0.814596i	$0.696959\pi$
$912$	5.74618e6	0.228766
$913$	3.96026e6	0.157234
$914$	−2.08972e6	−0.0827414
$915$	0	0
$916$	1.32057e7	0.520024
$917$	−9.40506e6	−0.369350
$918$	6.36271e6	0.249193
$919$	4.54288e6	0.177436	0.0887182	−	0.996057i	$-0.471723\pi$
$919$	4.54288e6	0.177436	0.0887182	+	0.996057i	$0.471723\pi$
$920$	0	0
$921$	1.45358e7	0.564663
$922$	1.32723e7	0.514185
$923$	−3.14643e7	−1.21567
$924$	−1.08662e6	−0.0418697
$925$	0	0
$926$	−1.43784e7	−0.551041
$927$	2.61403e6	0.0999106
$928$	6.10099e6	0.232558
$929$	2.18175e7	0.829402	0.414701	−	0.909958i	$-0.363886\pi$
$929$	2.18175e7	0.829402	0.414701	+	0.909958i	$0.363886\pi$
$930$	0	0
$931$	−5.98809e6	−0.226420
$932$	−6.99661e6	−0.263844
$933$	−2.20082e7	−0.827713
$934$	−6.15483e6	−0.230860
$935$	0	0
$936$	2.09434e6	0.0781370
$937$	5.04862e7	1.87855	0.939277	−	0.343161i	$-0.111498\pi$
$937$	5.04862e7	1.87855	0.939277	+	0.343161i	$0.111498\pi$
$938$	−9.55618e6	−0.354631
$939$	−2.23060e7	−0.825576
$940$	0	0
$941$	−1.24950e7	−0.460005	−0.230002	−	0.973190i	$-0.573873\pi$
$941$	−1.24950e7	−0.460005	−0.230002	+	0.973190i	$0.573873\pi$
$942$	7.56720e6	0.277848
$943$	2.71996e7	0.996057
$944$	−2.95322e6	−0.107861
$945$	0	0
$946$	1.00014e7	0.363356
$947$	4.09419e7	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$947$	4.09419e7	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$948$	5.25312e6	0.189844
$949$	1.92062e7	0.692269
$950$	0	0
$951$	−1.43117e7	−0.513145
$952$	6.84275e6	0.244703
$953$	8.37038e6	0.298547	0.149274	−	0.988796i	$-0.452306\pi$
$953$	8.37038e6	0.298547	0.149274	+	0.988796i	$0.452306\pi$
$954$	1.00194e7	0.356426
$955$	0	0
$956$	−1.09736e7	−0.388333
$957$	8.25779e6	0.291463
$958$	−3.29221e7	−1.15898
$959$	−1.28880e7	−0.452521
$960$	0	0
$961$	1.24589e7	0.435184
$962$	1.80184e7	0.627738
$963$	8.53157e6	0.296458
$964$	2.70698e7	0.938193
$965$	0	0
$966$	6.12461e6	0.211172
$967$	1.32135e6	0.0454415	0.0227207	−	0.999742i	$-0.492767\pi$
$967$	1.32135e6	0.0454415	0.0227207	+	0.999742i	$0.492767\pi$
$968$	−8.78944e6	−0.301490
$969$	−4.89772e7	−1.67565
$970$	0	0
$971$	−6.52939e6	−0.222241	−0.111121	−	0.993807i	$-0.535444\pi$
$971$	−6.52939e6	−0.222241	−0.111121	+	0.993807i	$0.535444\pi$
$972$	−944784.	−0.0320750
$973$	−1.49388e7	−0.505865
$974$	3.14657e7	1.06277
$975$	0	0
$976$	−9.94150e6	−0.334062
$977$	−4.03344e7	−1.35188	−0.675942	−	0.736954i	$-0.736263\pi$
$977$	−4.03344e7	−1.35188	−0.675942	+	0.736954i	$0.736263\pi$
$978$	9.25992e6	0.309571
$979$	1.55272e7	0.517770
$980$	0	0
$981$	1.37391e7	0.455811
$982$	−1.21230e7	−0.401171
$983$	2.91053e7	0.960700	0.480350	−	0.877077i	$-0.340510\pi$
$983$	2.91053e7	0.960700	0.480350	+	0.877077i	$0.340510\pi$
$984$	−4.51238e6	−0.148566
$985$	0	0
$986$	−5.20014e7	−1.70342
$987$	1.23480e6	0.0403463
$988$	−1.61212e7	−0.525419
$989$	−5.63714e7	−1.83260
$990$	0	0
$991$	−1.53423e7	−0.496257	−0.248128	−	0.968727i	$-0.579815\pi$
$991$	−1.53423e7	−0.496257	−0.248128	+	0.968727i	$0.579815\pi$
$992$	−6.56384e6	−0.211777
$993$	−689724.	−0.0221974
$994$	1.52649e7	0.490035
$995$	0	0
$996$	3.70310e6	0.118282
$997$	−2.65828e7	−0.846960	−0.423480	−	0.905905i	$-0.639192\pi$
$997$	−2.65828e7	−0.846960	−0.423480	+	0.905905i	$0.639192\pi$
$998$	3.32386e7	1.05637
$999$	−8.12835e6	−0.257685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.6.a.h.1.1		1
5.2	odd	4		1050.6.g.f.799.2		2
5.3	odd	4		1050.6.g.f.799.1		2
5.4	even	2		210.6.a.e.1.1	✓	1
15.14	odd	2		630.6.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.6.a.e.1.1	✓	1	5.4	even	2
630.6.a.p.1.1		1	15.14	odd	2
1050.6.a.h.1.1		1	1.1	even	1	trivial
1050.6.g.f.799.1		2	5.3	odd	4
1050.6.g.f.799.2		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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1050.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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