LMFDB - Embedded newform 300.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,6,Mod(1,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, 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("300.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	300.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:	$48.1151459439$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 60)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	300.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-9.00000 q^{3} -56.0000 q^{7} +81.0000 q^{9} +O(q^{10})$

$q-9.00000 q^{3} -56.0000 q^{7} +81.0000 q^{9} +156.000 q^{11} -350.000 q^{13} -786.000 q^{17} +740.000 q^{19} +504.000 q^{21} -2376.00 q^{23} -729.000 q^{27} +2574.00 q^{29} -4576.00 q^{31} -1404.00 q^{33} +12202.0 q^{37} +3150.00 q^{39} -10230.0 q^{41} +16084.0 q^{43} -864.000 q^{47} -13671.0 q^{49} +7074.00 q^{51} +17658.0 q^{53} -6660.00 q^{57} +48684.0 q^{59} -33778.0 q^{61} -4536.00 q^{63} -3524.00 q^{67} +21384.0 q^{69} +38280.0 q^{71} +79702.0 q^{73} -8736.00 q^{77} +99248.0 q^{79} +6561.00 q^{81} +22284.0 q^{83} -23166.0 q^{87} +94650.0 q^{89} +19600.0 q^{91} +41184.0 q^{93} -9122.00 q^{97} +12636.0 q^{99} +O(q^{100})$

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
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−56.0000	−0.431959	−0.215980	−	0.976398i	$-0.569295\pi$
$7$	−56.0000	−0.431959	−0.215980	+	0.976398i	$0.569295\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	156.000	0.388725	0.194363	−	0.980930i	$-0.437736\pi$
$11$	156.000	0.388725	0.194363	+	0.980930i	$0.437736\pi$
$12$	0	0
$13$	−350.000	−0.574394	−0.287197	−	0.957872i	$-0.592723\pi$
$13$	−350.000	−0.574394	−0.287197	+	0.957872i	$0.592723\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−786.000	−0.659630	−0.329815	−	0.944046i	$-0.606986\pi$
$17$	−786.000	−0.659630	−0.329815	+	0.944046i	$0.606986\pi$
$18$	0	0
$19$	740.000	0.470270	0.235135	−	0.971963i	$-0.424447\pi$
$19$	740.000	0.470270	0.235135	+	0.971963i	$0.424447\pi$
$20$	0	0
$21$	504.000	0.249392
$22$	0	0
$23$	−2376.00	−0.936541	−0.468271	−	0.883585i	$-0.655123\pi$
$23$	−2376.00	−0.936541	−0.468271	+	0.883585i	$0.655123\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−729.000	−0.192450
$28$	0	0
$29$	2574.00	0.568347	0.284173	−	0.958773i	$-0.408281\pi$
$29$	2574.00	0.568347	0.284173	+	0.958773i	$0.408281\pi$
$30$	0	0
$31$	−4576.00	−0.855228	−0.427614	−	0.903961i	$-0.640646\pi$
$31$	−4576.00	−0.855228	−0.427614	+	0.903961i	$0.640646\pi$
$32$	0	0
$33$	−1404.00	−0.224431
$34$	0	0
$35$	0	0
$36$	0	0
$37$	12202.0	1.46530	0.732650	−	0.680605i	$-0.238283\pi$
$37$	12202.0	1.46530	0.732650	+	0.680605i	$0.238283\pi$
$38$	0	0
$39$	3150.00	0.331626
$40$	0	0
$41$	−10230.0	−0.950421	−0.475210	−	0.879872i	$-0.657628\pi$
$41$	−10230.0	−0.950421	−0.475210	+	0.879872i	$0.657628\pi$
$42$	0	0
$43$	16084.0	1.32655	0.663274	−	0.748377i	$-0.269166\pi$
$43$	16084.0	1.32655	0.663274	+	0.748377i	$0.269166\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−864.000	−0.0570518	−0.0285259	−	0.999593i	$-0.509081\pi$
$47$	−864.000	−0.0570518	−0.0285259	+	0.999593i	$0.509081\pi$
$48$	0	0
$49$	−13671.0	−0.813411
$50$	0	0
$51$	7074.00	0.380837
$52$	0	0
$53$	17658.0	0.863479	0.431740	−	0.901998i	$-0.357900\pi$
$53$	17658.0	0.863479	0.431740	+	0.901998i	$0.357900\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−6660.00	−0.271511
$58$	0	0
$59$	48684.0	1.82077	0.910387	−	0.413757i	$-0.135784\pi$
$59$	48684.0	1.82077	0.910387	+	0.413757i	$0.135784\pi$
$60$	0	0
$61$	−33778.0	−1.16228	−0.581138	−	0.813805i	$-0.697392\pi$
$61$	−33778.0	−1.16228	−0.581138	+	0.813805i	$0.697392\pi$
$62$	0	0
$63$	−4536.00	−0.143986
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−3524.00	−0.0959067	−0.0479533	−	0.998850i	$-0.515270\pi$
$67$	−3524.00	−0.0959067	−0.0479533	+	0.998850i	$0.515270\pi$
$68$	0	0
$69$	21384.0	0.540712
$70$	0	0
$71$	38280.0	0.901210	0.450605	−	0.892723i	$-0.351208\pi$
$71$	38280.0	0.901210	0.450605	+	0.892723i	$0.351208\pi$
$72$	0	0
$73$	79702.0	1.75050	0.875250	−	0.483671i	$-0.160697\pi$
$73$	79702.0	1.75050	0.875250	+	0.483671i	$0.160697\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−8736.00	−0.167914
$78$	0	0
$79$	99248.0	1.78918	0.894590	−	0.446888i	$-0.147468\pi$
$79$	99248.0	1.78918	0.894590	+	0.446888i	$0.147468\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	22284.0	0.355057	0.177528	−	0.984116i	$-0.443190\pi$
$83$	22284.0	0.355057	0.177528	+	0.984116i	$0.443190\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−23166.0	−0.328135
$88$	0	0
$89$	94650.0	1.26662	0.633309	−	0.773899i	$-0.281696\pi$
$89$	94650.0	1.26662	0.633309	+	0.773899i	$0.281696\pi$
$90$	0	0
$91$	19600.0	0.248115
$92$	0	0
$93$	41184.0	0.493766
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−9122.00	−0.0984375	−0.0492188	−	0.998788i	$-0.515673\pi$
$97$	−9122.00	−0.0984375	−0.0492188	+	0.998788i	$0.515673\pi$
$98$	0	0
$99$	12636.0	0.129575
$100$	0	0
$101$	−71562.0	−0.698038	−0.349019	−	0.937116i	$-0.613485\pi$
$101$	−71562.0	−0.698038	−0.349019	+	0.937116i	$0.613485\pi$
$102$	0	0
$103$	31816.0	0.295497	0.147748	−	0.989025i	$-0.452797\pi$
$103$	31816.0	0.295497	0.147748	+	0.989025i	$0.452797\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	175092.	1.47845	0.739225	−	0.673458i	$-0.235192\pi$
$107$	175092.	1.47845	0.739225	+	0.673458i	$0.235192\pi$
$108$	0	0
$109$	41918.0	0.337936	0.168968	−	0.985622i	$-0.445957\pi$
$109$	41918.0	0.337936	0.168968	+	0.985622i	$0.445957\pi$
$110$	0	0
$111$	−109818.	−0.845992
$112$	0	0
$113$	149262.	1.09965	0.549823	−	0.835281i	$-0.314695\pi$
$113$	149262.	1.09965	0.549823	+	0.835281i	$0.314695\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−28350.0	−0.191465
$118$	0	0
$119$	44016.0	0.284933
$120$	0	0
$121$	−136715.	−0.848893
$122$	0	0
$123$	92070.0	0.548726
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−60176.0	−0.331066	−0.165533	−	0.986204i	$-0.552934\pi$
$127$	−60176.0	−0.331066	−0.165533	+	0.986204i	$0.552934\pi$
$128$	0	0
$129$	−144756.	−0.765883
$130$	0	0
$131$	−167628.	−0.853431	−0.426715	−	0.904386i	$-0.640329\pi$
$131$	−167628.	−0.853431	−0.426715	+	0.904386i	$0.640329\pi$
$132$	0	0
$133$	−41440.0	−0.203138
$134$	0	0
$135$	0	0
$136$	0	0
$137$	115542.	0.525943	0.262971	−	0.964804i	$-0.415298\pi$
$137$	115542.	0.525943	0.262971	+	0.964804i	$0.415298\pi$
$138$	0	0
$139$	163196.	0.716428	0.358214	−	0.933640i	$-0.383386\pi$
$139$	163196.	0.716428	0.358214	+	0.933640i	$0.383386\pi$
$140$	0	0
$141$	7776.00	0.0329389
$142$	0	0
$143$	−54600.0	−0.223281
$144$	0	0
$145$	0	0
$146$	0	0
$147$	123039.	0.469623
$148$	0	0
$149$	299238.	1.10421	0.552104	−	0.833775i	$-0.313825\pi$
$149$	299238.	1.10421	0.552104	+	0.833775i	$0.313825\pi$
$150$	0	0
$151$	288440.	1.02947	0.514734	−	0.857350i	$-0.327891\pi$
$151$	288440.	1.02947	0.514734	+	0.857350i	$0.327891\pi$
$152$	0	0
$153$	−63666.0	−0.219877
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−430382.	−1.39349	−0.696747	−	0.717317i	$-0.745370\pi$
$157$	−430382.	−1.39349	−0.696747	+	0.717317i	$0.745370\pi$
$158$	0	0
$159$	−158922.	−0.498530
$160$	0	0
$161$	133056.	0.404548
$162$	0	0
$163$	−260420.	−0.767724	−0.383862	−	0.923390i	$-0.625406\pi$
$163$	−260420.	−0.767724	−0.383862	+	0.923390i	$0.625406\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	465672.	1.29208	0.646039	−	0.763304i	$-0.276424\pi$
$167$	465672.	1.29208	0.646039	+	0.763304i	$0.276424\pi$
$168$	0	0
$169$	−248793.	−0.670072
$170$	0	0
$171$	59940.0	0.156757
$172$	0	0
$173$	−527454.	−1.33989	−0.669945	−	0.742410i	$-0.733682\pi$
$173$	−527454.	−1.33989	−0.669945	+	0.742410i	$0.733682\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−438156.	−1.05122
$178$	0	0
$179$	6084.00	0.0141924	0.00709621	−	0.999975i	$-0.497741\pi$
$179$	6084.00	0.0141924	0.00709621	+	0.999975i	$0.497741\pi$
$180$	0	0
$181$	109670.	0.248824	0.124412	−	0.992231i	$-0.460296\pi$
$181$	109670.	0.248824	0.124412	+	0.992231i	$0.460296\pi$
$182$	0	0
$183$	304002.	0.671040
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−122616.	−0.256415
$188$	0	0
$189$	40824.0	0.0831306
$190$	0	0
$191$	285984.	0.567229	0.283614	−	0.958938i	$-0.408466\pi$
$191$	285984.	0.567229	0.283614	+	0.958938i	$0.408466\pi$
$192$	0	0
$193$	263806.	0.509790	0.254895	−	0.966969i	$-0.417959\pi$
$193$	263806.	0.509790	0.254895	+	0.966969i	$0.417959\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−297174.	−0.545563	−0.272782	−	0.962076i	$-0.587944\pi$
$197$	−297174.	−0.545563	−0.272782	+	0.962076i	$0.587944\pi$
$198$	0	0
$199$	−945592.	−1.69267	−0.846333	−	0.532655i	$-0.821194\pi$
$199$	−945592.	−1.69267	−0.846333	+	0.532655i	$0.821194\pi$
$200$	0	0
$201$	31716.0	0.0553718
$202$	0	0
$203$	−144144.	−0.245503
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−192456.	−0.312180
$208$	0	0
$209$	115440.	0.182806
$210$	0	0
$211$	178820.	0.276509	0.138255	−	0.990397i	$-0.455851\pi$
$211$	178820.	0.276509	0.138255	+	0.990397i	$0.455851\pi$
$212$	0	0
$213$	−344520.	−0.520314
$214$	0	0
$215$	0	0
$216$	0	0
$217$	256256.	0.369424
$218$	0	0
$219$	−717318.	−1.01065
$220$	0	0
$221$	275100.	0.378887
$222$	0	0
$223$	343600.	0.462691	0.231345	−	0.972872i	$-0.425687\pi$
$223$	343600.	0.462691	0.231345	+	0.972872i	$0.425687\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	1.32438e6	1.70588	0.852939	−	0.522011i	$-0.174818\pi$
$227$	1.32438e6	1.70588	0.852939	+	0.522011i	$0.174818\pi$
$228$	0	0
$229$	−1.39959e6	−1.76365	−0.881827	−	0.471573i	$-0.843686\pi$
$229$	−1.39959e6	−1.76365	−0.881827	+	0.471573i	$0.843686\pi$
$230$	0	0
$231$	78624.0	0.0969449
$232$	0	0
$233$	−1.02849e6	−1.24111	−0.620555	−	0.784163i	$-0.713093\pi$
$233$	−1.02849e6	−1.24111	−0.620555	+	0.784163i	$0.713093\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−893232.	−1.03298
$238$	0	0
$239$	−517392.	−0.585902	−0.292951	−	0.956127i	$-0.594637\pi$
$239$	−517392.	−0.585902	−0.292951	+	0.956127i	$0.594637\pi$
$240$	0	0
$241$	−1.57166e6	−1.74308	−0.871538	−	0.490327i	$-0.836877\pi$
$241$	−1.57166e6	−1.74308	−0.871538	+	0.490327i	$0.836877\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−259000.	−0.270120
$248$	0	0
$249$	−200556.	−0.204992
$250$	0	0
$251$	1.26779e6	1.27017	0.635086	−	0.772442i	$-0.280965\pi$
$251$	1.26779e6	1.27017	0.635086	+	0.772442i	$0.280965\pi$
$252$	0	0
$253$	−370656.	−0.364057
$254$	0	0
$255$	0	0
$256$	0	0
$257$	1.27174e6	1.20106	0.600532	−	0.799601i	$-0.294955\pi$
$257$	1.27174e6	1.20106	0.600532	+	0.799601i	$0.294955\pi$
$258$	0	0
$259$	−683312.	−0.632950
$260$	0	0
$261$	208494.	0.189449
$262$	0	0
$263$	−1.21030e6	−1.07895	−0.539476	−	0.842001i	$-0.681378\pi$
$263$	−1.21030e6	−1.07895	−0.539476	+	0.842001i	$0.681378\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−851850.	−0.731282
$268$	0	0
$269$	2.29453e6	1.93336	0.966679	−	0.255992i	$-0.0824019\pi$
$269$	2.29453e6	1.93336	0.966679	+	0.255992i	$0.0824019\pi$
$270$	0	0
$271$	1.27726e6	1.05647	0.528235	−	0.849098i	$-0.322854\pi$
$271$	1.27726e6	1.05647	0.528235	+	0.849098i	$0.322854\pi$
$272$	0	0
$273$	−176400.	−0.143249
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−1.06938e6	−0.837401	−0.418700	−	0.908124i	$-0.637514\pi$
$277$	−1.06938e6	−0.837401	−0.418700	+	0.908124i	$0.637514\pi$
$278$	0	0
$279$	−370656.	−0.285076
$280$	0	0
$281$	−739974.	−0.559050	−0.279525	−	0.960138i	$-0.590177\pi$
$281$	−739974.	−0.559050	−0.279525	+	0.960138i	$0.590177\pi$
$282$	0	0
$283$	−1.33891e6	−0.993767	−0.496884	−	0.867817i	$-0.665522\pi$
$283$	−1.33891e6	−0.993767	−0.496884	+	0.867817i	$0.665522\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	572880.	0.410543
$288$	0	0
$289$	−802061.	−0.564889
$290$	0	0
$291$	82098.0	0.0568329
$292$	0	0
$293$	−836598.	−0.569309	−0.284654	−	0.958630i	$-0.591879\pi$
$293$	−836598.	−0.569309	−0.284654	+	0.958630i	$0.591879\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−113724.	−0.0748102
$298$	0	0
$299$	831600.	0.537943
$300$	0	0
$301$	−900704.	−0.573015
$302$	0	0
$303$	644058.	0.403012
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−1.55839e6	−0.943691	−0.471845	−	0.881681i	$-0.656412\pi$
$307$	−1.55839e6	−0.943691	−0.471845	+	0.881681i	$0.656412\pi$
$308$	0	0
$309$	−286344.	−0.170605
$310$	0	0
$311$	108984.	0.0638942	0.0319471	−	0.999490i	$-0.489829\pi$
$311$	108984.	0.0638942	0.0319471	+	0.999490i	$0.489829\pi$
$312$	0	0
$313$	1.46417e6	0.844752	0.422376	−	0.906421i	$-0.361196\pi$
$313$	1.46417e6	0.844752	0.422376	+	0.906421i	$0.361196\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	997074.	0.557287	0.278644	−	0.960395i	$-0.410115\pi$
$317$	997074.	0.557287	0.278644	+	0.960395i	$0.410115\pi$
$318$	0	0
$319$	401544.	0.220931
$320$	0	0
$321$	−1.57583e6	−0.853584
$322$	0	0
$323$	−581640.	−0.310204
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−377262.	−0.195107
$328$	0	0
$329$	48384.0	0.0246440
$330$	0	0
$331$	1.91145e6	0.958944	0.479472	−	0.877557i	$-0.340828\pi$
$331$	1.91145e6	0.958944	0.479472	+	0.877557i	$0.340828\pi$
$332$	0	0
$333$	988362.	0.488434
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−375698.	−0.180204	−0.0901019	−	0.995933i	$-0.528719\pi$
$337$	−375698.	−0.180204	−0.0901019	+	0.995933i	$0.528719\pi$
$338$	0	0
$339$	−1.34336e6	−0.634881
$340$	0	0
$341$	−713856.	−0.332449
$342$	0	0
$343$	1.70677e6	0.783320
$344$	0	0
$345$	0	0
$346$	0	0
$347$	4.41805e6	1.96973	0.984866	−	0.173318i	$-0.0554487\pi$
$347$	4.41805e6	1.96973	0.984866	+	0.173318i	$0.0554487\pi$
$348$	0	0
$349$	2.83365e6	1.24532	0.622662	−	0.782491i	$-0.286051\pi$
$349$	2.83365e6	1.24532	0.622662	+	0.782491i	$0.286051\pi$
$350$	0	0
$351$	255150.	0.110542
$352$	0	0
$353$	3.63094e6	1.55090	0.775448	−	0.631412i	$-0.217524\pi$
$353$	3.63094e6	1.55090	0.775448	+	0.631412i	$0.217524\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−396144.	−0.164506
$358$	0	0
$359$	3.07802e6	1.26048	0.630240	−	0.776400i	$-0.282957\pi$
$359$	3.07802e6	1.26048	0.630240	+	0.776400i	$0.282957\pi$
$360$	0	0
$361$	−1.92850e6	−0.778846
$362$	0	0
$363$	1.23044e6	0.490108
$364$	0	0
$365$	0	0
$366$	0	0
$367$	165184.	0.0640181	0.0320091	−	0.999488i	$-0.489809\pi$
$367$	165184.	0.0640181	0.0320091	+	0.999488i	$0.489809\pi$
$368$	0	0
$369$	−828630.	−0.316807
$370$	0	0
$371$	−988848.	−0.372988
$372$	0	0
$373$	587674.	0.218708	0.109354	−	0.994003i	$-0.465122\pi$
$373$	587674.	0.218708	0.109354	+	0.994003i	$0.465122\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−900900.	−0.326455
$378$	0	0
$379$	691628.	0.247329	0.123664	−	0.992324i	$-0.460535\pi$
$379$	691628.	0.247329	0.123664	+	0.992324i	$0.460535\pi$
$380$	0	0
$381$	541584.	0.191141
$382$	0	0
$383$	4.05835e6	1.41369	0.706843	−	0.707371i	$-0.250119\pi$
$383$	4.05835e6	1.41369	0.706843	+	0.707371i	$0.250119\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	1.30280e6	0.442183
$388$	0	0
$389$	3.44041e6	1.15275	0.576376	−	0.817185i	$-0.304466\pi$
$389$	3.44041e6	1.15275	0.576376	+	0.817185i	$0.304466\pi$
$390$	0	0
$391$	1.86754e6	0.617770
$392$	0	0
$393$	1.50865e6	0.492729
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−3.38320e6	−1.07734	−0.538668	−	0.842518i	$-0.681072\pi$
$397$	−3.38320e6	−1.07734	−0.538668	+	0.842518i	$0.681072\pi$
$398$	0	0
$399$	372960.	0.117282
$400$	0	0
$401$	−4.06001e6	−1.26086	−0.630430	−	0.776246i	$-0.717121\pi$
$401$	−4.06001e6	−1.26086	−0.630430	+	0.776246i	$0.717121\pi$
$402$	0	0
$403$	1.60160e6	0.491237
$404$	0	0
$405$	0	0
$406$	0	0
$407$	1.90351e6	0.569599
$408$	0	0
$409$	3.53139e6	1.04385	0.521924	−	0.852992i	$-0.325215\pi$
$409$	3.53139e6	1.04385	0.521924	+	0.852992i	$0.325215\pi$
$410$	0	0
$411$	−1.03988e6	−0.303653
$412$	0	0
$413$	−2.72630e6	−0.786501
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−1.46876e6	−0.413630
$418$	0	0
$419$	995892.	0.277126	0.138563	−	0.990354i	$-0.455752\pi$
$419$	995892.	0.277126	0.138563	+	0.990354i	$0.455752\pi$
$420$	0	0
$421$	−251050.	−0.0690327	−0.0345164	−	0.999404i	$-0.510989\pi$
$421$	−251050.	−0.0690327	−0.0345164	+	0.999404i	$0.510989\pi$
$422$	0	0
$423$	−69984.0	−0.0190173
$424$	0	0
$425$	0	0
$426$	0	0
$427$	1.89157e6	0.502056
$428$	0	0
$429$	491400.	0.128912
$430$	0	0
$431$	5.88341e6	1.52558	0.762791	−	0.646645i	$-0.223828\pi$
$431$	5.88341e6	1.52558	0.762791	+	0.646645i	$0.223828\pi$
$432$	0	0
$433$	−1.83403e6	−0.470097	−0.235049	−	0.971984i	$-0.575525\pi$
$433$	−1.83403e6	−0.470097	−0.235049	+	0.971984i	$0.575525\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−1.75824e6	−0.440428
$438$	0	0
$439$	−667912.	−0.165409	−0.0827043	−	0.996574i	$-0.526356\pi$
$439$	−667912.	−0.165409	−0.0827043	+	0.996574i	$0.526356\pi$
$440$	0	0
$441$	−1.10735e6	−0.271137
$442$	0	0
$443$	−1.27148e6	−0.307823	−0.153912	−	0.988085i	$-0.549187\pi$
$443$	−1.27148e6	−0.307823	−0.153912	+	0.988085i	$0.549187\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−2.69314e6	−0.637515
$448$	0	0
$449$	5.04602e6	1.18123	0.590613	−	0.806955i	$-0.298886\pi$
$449$	5.04602e6	1.18123	0.590613	+	0.806955i	$0.298886\pi$
$450$	0	0
$451$	−1.59588e6	−0.369453
$452$	0	0
$453$	−2.59596e6	−0.594364
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.66577e6	−0.373099	−0.186550	−	0.982446i	$-0.559731\pi$
$457$	−1.66577e6	−0.373099	−0.186550	+	0.982446i	$0.559731\pi$
$458$	0	0
$459$	572994.	0.126946
$460$	0	0
$461$	427326.	0.0936498	0.0468249	−	0.998903i	$-0.485090\pi$
$461$	427326.	0.0936498	0.0468249	+	0.998903i	$0.485090\pi$
$462$	0	0
$463$	5.19731e6	1.12675	0.563373	−	0.826202i	$-0.309503\pi$
$463$	5.19731e6	1.12675	0.563373	+	0.826202i	$0.309503\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−166548.	−0.0353384	−0.0176692	−	0.999844i	$-0.505625\pi$
$467$	−166548.	−0.0353384	−0.0176692	+	0.999844i	$0.505625\pi$
$468$	0	0
$469$	197344.	0.0414278
$470$	0	0
$471$	3.87344e6	0.804534
$472$	0	0
$473$	2.50910e6	0.515663
$474$	0	0
$475$	0	0
$476$	0	0
$477$	1.43030e6	0.287826
$478$	0	0
$479$	−2.63530e6	−0.524796	−0.262398	−	0.964960i	$-0.584513\pi$
$479$	−2.63530e6	−0.524796	−0.262398	+	0.964960i	$0.584513\pi$
$480$	0	0
$481$	−4.27070e6	−0.841659
$482$	0	0
$483$	−1.19750e6	−0.233566
$484$	0	0
$485$	0	0
$486$	0	0
$487$	8.44497e6	1.61352	0.806762	−	0.590876i	$-0.201218\pi$
$487$	8.44497e6	1.61352	0.806762	+	0.590876i	$0.201218\pi$
$488$	0	0
$489$	2.34378e6	0.443246
$490$	0	0
$491$	−5.48884e6	−1.02749	−0.513744	−	0.857944i	$-0.671742\pi$
$491$	−5.48884e6	−1.02749	−0.513744	+	0.857944i	$0.671742\pi$
$492$	0	0
$493$	−2.02316e6	−0.374899
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−2.14368e6	−0.389286
$498$	0	0
$499$	−6.41984e6	−1.15418	−0.577089	−	0.816681i	$-0.695811\pi$
$499$	−6.41984e6	−1.15418	−0.577089	+	0.816681i	$0.695811\pi$
$500$	0	0
$501$	−4.19105e6	−0.745982
$502$	0	0
$503$	−7.21226e6	−1.27102	−0.635509	−	0.772094i	$-0.719210\pi$
$503$	−7.21226e6	−1.27102	−0.635509	+	0.772094i	$0.719210\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	2.23914e6	0.386866
$508$	0	0
$509$	−1.03776e7	−1.77543	−0.887714	−	0.460395i	$-0.847708\pi$
$509$	−1.03776e7	−1.77543	−0.887714	+	0.460395i	$0.847708\pi$
$510$	0	0
$511$	−4.46331e6	−0.756145
$512$	0	0
$513$	−539460.	−0.0905036
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−134784.	−0.0221775
$518$	0	0
$519$	4.74709e6	0.773586
$520$	0	0
$521$	6.39652e6	1.03240	0.516202	−	0.856467i	$-0.327345\pi$
$521$	6.39652e6	1.03240	0.516202	+	0.856467i	$0.327345\pi$
$522$	0	0
$523$	680692.	0.108817	0.0544085	−	0.998519i	$-0.482673\pi$
$523$	680692.	0.108817	0.0544085	+	0.998519i	$0.482673\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	3.59674e6	0.564134
$528$	0	0
$529$	−790967.	−0.122891
$530$	0	0
$531$	3.94340e6	0.606925
$532$	0	0
$533$	3.58050e6	0.545916
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−54756.0	−0.00819400
$538$	0	0
$539$	−2.13268e6	−0.316194
$540$	0	0
$541$	−1.01096e6	−0.148505	−0.0742526	−	0.997239i	$-0.523657\pi$
$541$	−1.01096e6	−0.148505	−0.0742526	+	0.997239i	$0.523657\pi$
$542$	0	0
$543$	−987030.	−0.143658
$544$	0	0
$545$	0	0
$546$	0	0
$547$	5.39907e6	0.771526	0.385763	−	0.922598i	$-0.373938\pi$
$547$	5.39907e6	0.771526	0.385763	+	0.922598i	$0.373938\pi$
$548$	0	0
$549$	−2.73602e6	−0.387425
$550$	0	0
$551$	1.90476e6	0.267277
$552$	0	0
$553$	−5.55789e6	−0.772853
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−1.33673e7	−1.82560	−0.912798	−	0.408412i	$-0.866083\pi$
$557$	−1.33673e7	−1.82560	−0.912798	+	0.408412i	$0.866083\pi$
$558$	0	0
$559$	−5.62940e6	−0.761961
$560$	0	0
$561$	1.10354e6	0.148041
$562$	0	0
$563$	−1.82370e6	−0.242484	−0.121242	−	0.992623i	$-0.538688\pi$
$563$	−1.82370e6	−0.242484	−0.121242	+	0.992623i	$0.538688\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−367416.	−0.0479955
$568$	0	0
$569$	−7.08125e6	−0.916916	−0.458458	−	0.888716i	$-0.651598\pi$
$569$	−7.08125e6	−0.916916	−0.458458	+	0.888716i	$0.651598\pi$
$570$	0	0
$571$	8.92526e6	1.14559	0.572797	−	0.819697i	$-0.305858\pi$
$571$	8.92526e6	1.14559	0.572797	+	0.819697i	$0.305858\pi$
$572$	0	0
$573$	−2.57386e6	−0.327490
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−4.71648e6	−0.589765	−0.294882	−	0.955534i	$-0.595280\pi$
$577$	−4.71648e6	−0.589765	−0.294882	+	0.955534i	$0.595280\pi$
$578$	0	0
$579$	−2.37425e6	−0.294327
$580$	0	0
$581$	−1.24790e6	−0.153370
$582$	0	0
$583$	2.75465e6	0.335656
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−9.58456e6	−1.14809	−0.574046	−	0.818823i	$-0.694627\pi$
$587$	−9.58456e6	−1.14809	−0.574046	+	0.818823i	$0.694627\pi$
$588$	0	0
$589$	−3.38624e6	−0.402188
$590$	0	0
$591$	2.67457e6	0.314981
$592$	0	0
$593$	134574.	0.0157154	0.00785768	−	0.999969i	$-0.497499\pi$
$593$	134574.	0.0157154	0.00785768	+	0.999969i	$0.497499\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	8.51033e6	0.977261
$598$	0	0
$599$	−6.51290e6	−0.741665	−0.370832	−	0.928700i	$-0.620928\pi$
$599$	−6.51290e6	−0.741665	−0.370832	+	0.928700i	$0.620928\pi$
$600$	0	0
$601$	1.07623e7	1.21540	0.607699	−	0.794167i	$-0.292093\pi$
$601$	1.07623e7	1.21540	0.607699	+	0.794167i	$0.292093\pi$
$602$	0	0
$603$	−285444.	−0.0319689
$604$	0	0
$605$	0	0
$606$	0	0
$607$	1.70459e6	0.187780	0.0938899	−	0.995583i	$-0.470070\pi$
$607$	1.70459e6	0.187780	0.0938899	+	0.995583i	$0.470070\pi$
$608$	0	0
$609$	1.29730e6	0.141741
$610$	0	0
$611$	302400.	0.0327702
$612$	0	0
$613$	−1.23488e7	−1.32731	−0.663655	−	0.748039i	$-0.730996\pi$
$613$	−1.23488e7	−1.32731	−0.663655	+	0.748039i	$0.730996\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−4.16423e6	−0.440375	−0.220187	−	0.975458i	$-0.570667\pi$
$617$	−4.16423e6	−0.440375	−0.220187	+	0.975458i	$0.570667\pi$
$618$	0	0
$619$	1.10614e7	1.16034	0.580168	−	0.814497i	$-0.302987\pi$
$619$	1.10614e7	1.16034	0.580168	+	0.814497i	$0.302987\pi$
$620$	0	0
$621$	1.73210e6	0.180237
$622$	0	0
$623$	−5.30040e6	−0.547127
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−1.03896e6	−0.105543
$628$	0	0
$629$	−9.59077e6	−0.966556
$630$	0	0
$631$	7.69935e6	0.769805	0.384903	−	0.922957i	$-0.374235\pi$
$631$	7.69935e6	0.769805	0.384903	+	0.922957i	$0.374235\pi$
$632$	0	0
$633$	−1.60938e6	−0.159643
$634$	0	0
$635$	0	0
$636$	0	0
$637$	4.78485e6	0.467218
$638$	0	0
$639$	3.10068e6	0.300403
$640$	0	0
$641$	2.20307e6	0.211780	0.105890	−	0.994378i	$-0.466231\pi$
$641$	2.20307e6	0.211780	0.105890	+	0.994378i	$0.466231\pi$
$642$	0	0
$643$	−1.77333e7	−1.69146	−0.845730	−	0.533611i	$-0.820835\pi$
$643$	−1.77333e7	−1.69146	−0.845730	+	0.533611i	$0.820835\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−1.89374e7	−1.77852	−0.889260	−	0.457401i	$-0.848780\pi$
$647$	−1.89374e7	−1.77852	−0.889260	+	0.457401i	$0.848780\pi$
$648$	0	0
$649$	7.59470e6	0.707781
$650$	0	0
$651$	−2.30630e6	−0.213287
$652$	0	0
$653$	1.77695e7	1.63077	0.815383	−	0.578922i	$-0.196526\pi$
$653$	1.77695e7	1.63077	0.815383	+	0.578922i	$0.196526\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	6.45586e6	0.583500
$658$	0	0
$659$	−1.66587e7	−1.49426	−0.747130	−	0.664678i	$-0.768569\pi$
$659$	−1.66587e7	−1.49426	−0.747130	+	0.664678i	$0.768569\pi$
$660$	0	0
$661$	1.61236e6	0.143535	0.0717675	−	0.997421i	$-0.477136\pi$
$661$	1.61236e6	0.143535	0.0717675	+	0.997421i	$0.477136\pi$
$662$	0	0
$663$	−2.47590e6	−0.218751
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−6.11582e6	−0.532280
$668$	0	0
$669$	−3.09240e6	−0.267135
$670$	0	0
$671$	−5.26937e6	−0.451806
$672$	0	0
$673$	−2.87933e6	−0.245049	−0.122525	−	0.992465i	$-0.539099\pi$
$673$	−2.87933e6	−0.245049	−0.122525	+	0.992465i	$0.539099\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	6.86375e6	0.575559	0.287780	−	0.957697i	$-0.407083\pi$
$677$	6.86375e6	0.575559	0.287780	+	0.957697i	$0.407083\pi$
$678$	0	0
$679$	510832.	0.0425210
$680$	0	0
$681$	−1.19194e7	−0.984889
$682$	0	0
$683$	−1.16896e7	−0.958847	−0.479424	−	0.877584i	$-0.659154\pi$
$683$	−1.16896e7	−0.958847	−0.479424	+	0.877584i	$0.659154\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	1.25963e7	1.01825
$688$	0	0
$689$	−6.18030e6	−0.495977
$690$	0	0
$691$	−1.65161e6	−0.131587	−0.0657935	−	0.997833i	$-0.520958\pi$
$691$	−1.65161e6	−0.131587	−0.0657935	+	0.997833i	$0.520958\pi$
$692$	0	0
$693$	−707616.	−0.0559712
$694$	0	0
$695$	0	0
$696$	0	0
$697$	8.04078e6	0.626926
$698$	0	0
$699$	9.25641e6	0.716555
$700$	0	0
$701$	−7.03835e6	−0.540974	−0.270487	−	0.962724i	$-0.587185\pi$
$701$	−7.03835e6	−0.540974	−0.270487	+	0.962724i	$0.587185\pi$
$702$	0	0
$703$	9.02948e6	0.689088
$704$	0	0
$705$	0	0
$706$	0	0
$707$	4.00747e6	0.301524
$708$	0	0
$709$	−1.42009e7	−1.06096	−0.530482	−	0.847696i	$-0.677989\pi$
$709$	−1.42009e7	−1.06096	−0.530482	+	0.847696i	$0.677989\pi$
$710$	0	0
$711$	8.03909e6	0.596393
$712$	0	0
$713$	1.08726e7	0.800956
$714$	0	0
$715$	0	0
$716$	0	0
$717$	4.65653e6	0.338271
$718$	0	0
$719$	−2.10187e6	−0.151630	−0.0758148	−	0.997122i	$-0.524156\pi$
$719$	−2.10187e6	−0.151630	−0.0758148	+	0.997122i	$0.524156\pi$
$720$	0	0
$721$	−1.78170e6	−0.127643
$722$	0	0
$723$	1.41450e7	1.00637
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−4.95687e6	−0.347834	−0.173917	−	0.984760i	$-0.555642\pi$
$727$	−4.95687e6	−0.347834	−0.173917	+	0.984760i	$0.555642\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	−1.26420e7	−0.875030
$732$	0	0
$733$	−810926.	−0.0557470	−0.0278735	−	0.999611i	$-0.508874\pi$
$733$	−810926.	−0.0557470	−0.0278735	+	0.999611i	$0.508874\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−549744.	−0.0372814
$738$	0	0
$739$	1.89432e7	1.27598	0.637988	−	0.770046i	$-0.279767\pi$
$739$	1.89432e7	1.27598	0.637988	+	0.770046i	$0.279767\pi$
$740$	0	0
$741$	2.33100e6	0.155954
$742$	0	0
$743$	782376.	0.0519928	0.0259964	−	0.999662i	$-0.491724\pi$
$743$	782376.	0.0519928	0.0259964	+	0.999662i	$0.491724\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	1.80500e6	0.118352
$748$	0	0
$749$	−9.80515e6	−0.638631
$750$	0	0
$751$	−2.63061e7	−1.70199	−0.850995	−	0.525174i	$-0.824000\pi$
$751$	−2.63061e7	−1.70199	−0.850995	+	0.525174i	$0.824000\pi$
$752$	0	0
$753$	−1.14101e7	−0.733334
$754$	0	0
$755$	0	0
$756$	0	0
$757$	2.07709e7	1.31739	0.658697	−	0.752408i	$-0.271108\pi$
$757$	2.07709e7	1.31739	0.658697	+	0.752408i	$0.271108\pi$
$758$	0	0
$759$	3.33590e6	0.210189
$760$	0	0
$761$	1.35574e7	0.848623	0.424312	−	0.905516i	$-0.360516\pi$
$761$	1.35574e7	0.848623	0.424312	+	0.905516i	$0.360516\pi$
$762$	0	0
$763$	−2.34741e6	−0.145975
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−1.70394e7	−1.04584
$768$	0	0
$769$	2.91206e7	1.77576	0.887882	−	0.460072i	$-0.152176\pi$
$769$	2.91206e7	1.77576	0.887882	+	0.460072i	$0.152176\pi$
$770$	0	0
$771$	−1.14457e7	−0.693435
$772$	0	0
$773$	8.49278e6	0.511212	0.255606	−	0.966781i	$-0.417725\pi$
$773$	8.49278e6	0.511212	0.255606	+	0.966781i	$0.417725\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	6.14981e6	0.365434
$778$	0	0
$779$	−7.57020e6	−0.446955
$780$	0	0
$781$	5.97168e6	0.350323
$782$	0	0
$783$	−1.87645e6	−0.109378
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−1.07177e7	−0.616826	−0.308413	−	0.951253i	$-0.599798\pi$
$787$	−1.07177e7	−0.616826	−0.308413	+	0.951253i	$0.599798\pi$
$788$	0	0
$789$	1.08927e7	0.622933
$790$	0	0
$791$	−8.35867e6	−0.475003
$792$	0	0
$793$	1.18223e7	0.667604
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−1.50302e7	−0.838146	−0.419073	−	0.907953i	$-0.637645\pi$
$797$	−1.50302e7	−0.838146	−0.419073	+	0.907953i	$0.637645\pi$
$798$	0	0
$799$	679104.	0.0376330
$800$	0	0
$801$	7.66665e6	0.422206
$802$	0	0
$803$	1.24335e7	0.680464
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−2.06507e7	−1.11622
$808$	0	0
$809$	3.09263e7	1.66134	0.830668	−	0.556769i	$-0.187959\pi$
$809$	3.09263e7	1.66134	0.830668	+	0.556769i	$0.187959\pi$
$810$	0	0
$811$	1.25898e7	0.672152	0.336076	−	0.941835i	$-0.390900\pi$
$811$	1.25898e7	0.672152	0.336076	+	0.941835i	$0.390900\pi$
$812$	0	0
$813$	−1.14954e7	−0.609954
$814$	0	0
$815$	0	0
$816$	0	0
$817$	1.19022e7	0.623836
$818$	0	0
$819$	1.58760e6	0.0827049
$820$	0	0
$821$	2.24592e7	1.16288	0.581442	−	0.813588i	$-0.302489\pi$
$821$	2.24592e7	1.16288	0.581442	+	0.813588i	$0.302489\pi$
$822$	0	0
$823$	1.69776e7	0.873729	0.436864	−	0.899527i	$-0.356089\pi$
$823$	1.69776e7	0.873729	0.436864	+	0.899527i	$0.356089\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	2.21783e6	0.112762	0.0563812	−	0.998409i	$-0.482044\pi$
$827$	2.21783e6	0.112762	0.0563812	+	0.998409i	$0.482044\pi$
$828$	0	0
$829$	−5.02290e6	−0.253845	−0.126922	−	0.991913i	$-0.540510\pi$
$829$	−5.02290e6	−0.253845	−0.126922	+	0.991913i	$0.540510\pi$
$830$	0	0
$831$	9.62444e6	0.483474
$832$	0	0
$833$	1.07454e7	0.536550
$834$	0	0
$835$	0	0
$836$	0	0
$837$	3.33590e6	0.164589
$838$	0	0
$839$	3.11575e7	1.52812	0.764062	−	0.645143i	$-0.223202\pi$
$839$	3.11575e7	1.52812	0.764062	+	0.645143i	$0.223202\pi$
$840$	0	0
$841$	−1.38857e7	−0.676982
$842$	0	0
$843$	6.65977e6	0.322768
$844$	0	0
$845$	0	0
$846$	0	0
$847$	7.65604e6	0.366687
$848$	0	0
$849$	1.20502e7	0.573752
$850$	0	0
$851$	−2.89920e7	−1.37231
$852$	0	0
$853$	3.88710e6	0.182917	0.0914583	−	0.995809i	$-0.470847\pi$
$853$	3.88710e6	0.182917	0.0914583	+	0.995809i	$0.470847\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−1.67000e7	−0.776718	−0.388359	−	0.921508i	$-0.626958\pi$
$857$	−1.67000e7	−0.776718	−0.388359	+	0.921508i	$0.626958\pi$
$858$	0	0
$859$	1.20088e7	0.555285	0.277643	−	0.960684i	$-0.410447\pi$
$859$	1.20088e7	0.555285	0.277643	+	0.960684i	$0.410447\pi$
$860$	0	0
$861$	−5.15592e6	−0.237027
$862$	0	0
$863$	8.45525e6	0.386455	0.193228	−	0.981154i	$-0.438104\pi$
$863$	8.45525e6	0.386455	0.193228	+	0.981154i	$0.438104\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	7.21855e6	0.326139
$868$	0	0
$869$	1.54827e7	0.695500
$870$	0	0
$871$	1.23340e6	0.0550882
$872$	0	0
$873$	−738882.	−0.0328125
$874$	0	0
$875$	0	0
$876$	0	0
$877$	3.46298e7	1.52038	0.760189	−	0.649703i	$-0.225107\pi$
$877$	3.46298e7	1.52038	0.760189	+	0.649703i	$0.225107\pi$
$878$	0	0
$879$	7.52938e6	0.328690
$880$	0	0
$881$	3.36583e7	1.46101	0.730503	−	0.682909i	$-0.239285\pi$
$881$	3.36583e7	1.46101	0.730503	+	0.682909i	$0.239285\pi$
$882$	0	0
$883$	2.86606e7	1.23704	0.618519	−	0.785770i	$-0.287733\pi$
$883$	2.86606e7	1.23704	0.618519	+	0.785770i	$0.287733\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−3.46222e6	−0.147756	−0.0738780	−	0.997267i	$-0.523538\pi$
$887$	−3.46222e6	−0.147756	−0.0738780	+	0.997267i	$0.523538\pi$
$888$	0	0
$889$	3.36986e6	0.143007
$890$	0	0
$891$	1.02352e6	0.0431917
$892$	0	0
$893$	−639360.	−0.0268298
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−7.48440e6	−0.310582
$898$	0	0
$899$	−1.17786e7	−0.486066
$900$	0	0
$901$	−1.38792e7	−0.569577
$902$	0	0
$903$	8.10634e6	0.330830
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−3.11793e7	−1.25849	−0.629243	−	0.777209i	$-0.716635\pi$
$907$	−3.11793e7	−1.25849	−0.629243	+	0.777209i	$0.716635\pi$
$908$	0	0
$909$	−5.79652e6	−0.232679
$910$	0	0
$911$	−3.89155e7	−1.55355	−0.776777	−	0.629776i	$-0.783147\pi$
$911$	−3.89155e7	−1.55355	−0.776777	+	0.629776i	$0.783147\pi$
$912$	0	0
$913$	3.47630e6	0.138020
$914$	0	0
$915$	0	0
$916$	0	0
$917$	9.38717e6	0.368647
$918$	0	0
$919$	−5.38871e6	−0.210473	−0.105236	−	0.994447i	$-0.533560\pi$
$919$	−5.38871e6	−0.210473	−0.105236	+	0.994447i	$0.533560\pi$
$920$	0	0
$921$	1.40255e7	0.544840
$922$	0	0
$923$	−1.33980e7	−0.517649
$924$	0	0
$925$	0	0
$926$	0	0
$927$	2.57710e6	0.0984989
$928$	0	0
$929$	3.51050e6	0.133453	0.0667267	−	0.997771i	$-0.478744\pi$
$929$	3.51050e6	0.133453	0.0667267	+	0.997771i	$0.478744\pi$
$930$	0	0
$931$	−1.01165e7	−0.382523
$932$	0	0
$933$	−980856.	−0.0368894
$934$	0	0
$935$	0	0
$936$	0	0
$937$	1.33541e7	0.496896	0.248448	−	0.968645i	$-0.420079\pi$
$937$	1.33541e7	0.496896	0.248448	+	0.968645i	$0.420079\pi$
$938$	0	0
$939$	−1.31775e7	−0.487718
$940$	0	0
$941$	3.24365e7	1.19415	0.597077	−	0.802184i	$-0.296329\pi$
$941$	3.24365e7	1.19415	0.597077	+	0.802184i	$0.296329\pi$
$942$	0	0
$943$	2.43065e7	0.890108
$944$	0	0
$945$	0	0
$946$	0	0
$947$	2.79207e7	1.01170	0.505849	−	0.862622i	$-0.331179\pi$
$947$	2.79207e7	1.01170	0.505849	+	0.862622i	$0.331179\pi$
$948$	0	0
$949$	−2.78957e7	−1.00548
$950$	0	0
$951$	−8.97367e6	−0.321750
$952$	0	0
$953$	4.72306e7	1.68458	0.842289	−	0.539027i	$-0.181208\pi$
$953$	4.72306e7	1.68458	0.842289	+	0.539027i	$0.181208\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−3.61390e6	−0.127555
$958$	0	0
$959$	−6.47035e6	−0.227186
$960$	0	0
$961$	−7.68938e6	−0.268586
$962$	0	0
$963$	1.41825e7	0.492817
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−6.85484e6	−0.235739	−0.117869	−	0.993029i	$-0.537606\pi$
$967$	−6.85484e6	−0.235739	−0.117869	+	0.993029i	$0.537606\pi$
$968$	0	0
$969$	5.23476e6	0.179097
$970$	0	0
$971$	−4.03763e7	−1.37429	−0.687145	−	0.726520i	$-0.741136\pi$
$971$	−4.03763e7	−1.37429	−0.687145	+	0.726520i	$0.741136\pi$
$972$	0	0
$973$	−9.13898e6	−0.309468
$974$	0	0
$975$	0	0
$976$	0	0
$977$	6.30200e6	0.211223	0.105612	−	0.994407i	$-0.466320\pi$
$977$	6.30200e6	0.211223	0.105612	+	0.994407i	$0.466320\pi$
$978$	0	0
$979$	1.47654e7	0.492366
$980$	0	0
$981$	3.39536e6	0.112645
$982$	0	0
$983$	−5.08854e7	−1.67962	−0.839808	−	0.542884i	$-0.817332\pi$
$983$	−5.08854e7	−1.67962	−0.839808	+	0.542884i	$0.817332\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−435456.	−0.0142282
$988$	0	0
$989$	−3.82156e7	−1.24237
$990$	0	0
$991$	−6.05891e6	−0.195979	−0.0979897	−	0.995187i	$-0.531241\pi$
$991$	−6.05891e6	−0.195979	−0.0979897	+	0.995187i	$0.531241\pi$
$992$	0	0
$993$	−1.72031e7	−0.553647
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−2.28661e7	−0.728542	−0.364271	−	0.931293i	$-0.618682\pi$
$997$	−2.28661e7	−0.728542	−0.364271	+	0.931293i	$0.618682\pi$
$998$	0	0
$999$	−8.89526e6	−0.281997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.6.a.b.1.1		1
3.2	odd	2		900.6.a.e.1.1		1
5.2	odd	4		300.6.d.d.49.2		2
5.3	odd	4		300.6.d.d.49.1		2
5.4	even	2		60.6.a.d.1.1	✓	1
15.2	even	4		900.6.d.c.649.1		2
15.8	even	4		900.6.d.c.649.2		2
15.14	odd	2		180.6.a.b.1.1		1
20.19	odd	2		240.6.a.e.1.1		1
40.19	odd	2		960.6.a.p.1.1		1
40.29	even	2		960.6.a.e.1.1		1
60.59	even	2		720.6.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.a.d.1.1	✓	1	5.4	even	2
180.6.a.b.1.1		1	15.14	odd	2
240.6.a.e.1.1		1	20.19	odd	2
300.6.a.b.1.1		1	1.1	even	1	trivial
300.6.d.d.49.1		2	5.3	odd	4
300.6.d.d.49.2		2	5.2	odd	4
720.6.a.d.1.1		1	60.59	even	2
900.6.a.e.1.1		1	3.2	odd	2
900.6.d.c.649.1		2	15.2	even	4
900.6.d.c.649.2		2	15.8	even	4
960.6.a.e.1.1		1	40.29	even	2
960.6.a.p.1.1		1	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	300.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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