LMFDB - Embedded newform 294.6.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("294.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.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:	$47.1528430250$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	294.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +54.0000 q^{5} -36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$

\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +54.0000 q^{5} -36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} -216.000 q^{10} +216.000 q^{11} +144.000 q^{12} -998.000 q^{13} +486.000 q^{15} +256.000 q^{16} -1302.00 q^{17} -324.000 q^{18} -884.000 q^{19} +864.000 q^{20} -864.000 q^{22} -2268.00 q^{23} -576.000 q^{24} -209.000 q^{25} +3992.00 q^{26} +729.000 q^{27} -1482.00 q^{29} -1944.00 q^{30} -8360.00 q^{31} -1024.00 q^{32} +1944.00 q^{33} +5208.00 q^{34} +1296.00 q^{36} -4714.00 q^{37} +3536.00 q^{38} -8982.00 q^{39} -3456.00 q^{40} +9786.00 q^{41} +19436.0 q^{43} +3456.00 q^{44} +4374.00 q^{45} +9072.00 q^{46} -22200.0 q^{47} +2304.00 q^{48} +836.000 q^{50} -11718.0 q^{51} -15968.0 q^{52} +26790.0 q^{53} -2916.00 q^{54} +11664.0 q^{55} -7956.00 q^{57} +5928.00 q^{58} -28092.0 q^{59} +7776.00 q^{60} +38866.0 q^{61} +33440.0 q^{62} +4096.00 q^{64} -53892.0 q^{65} -7776.00 q^{66} +23948.0 q^{67} -20832.0 q^{68} -20412.0 q^{69} -20628.0 q^{71} -5184.00 q^{72} -290.000 q^{73} +18856.0 q^{74} -1881.00 q^{75} -14144.0 q^{76} +35928.0 q^{78} -99544.0 q^{79} +13824.0 q^{80} +6561.00 q^{81} -39144.0 q^{82} -19308.0 q^{83} -70308.0 q^{85} -77744.0 q^{86} -13338.0 q^{87} -13824.0 q^{88} -36390.0 q^{89} -17496.0 q^{90} -36288.0 q^{92} -75240.0 q^{93} +88800.0 q^{94} -47736.0 q^{95} -9216.00 q^{96} +79078.0 q^{97} +17496.0 q^{99} +O(q^{100})\)

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
$5$	54.0000	0.965981	0.482991	−	0.875625i	$-0.339550\pi$
$5$	54.0000	0.965981	0.482991	+	0.875625i	$0.339550\pi$
$6$	−36.0000	−0.408248
$7$	0	0
$7$	0	0
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−216.000	−0.683052
$11$	216.000	0.538235	0.269118	−	0.963107i	$-0.413268\pi$
$11$	216.000	0.538235	0.269118	+	0.963107i	$0.413268\pi$
$12$	144.000	0.288675
$13$	−998.000	−1.63784	−0.818921	−	0.573906i	$-0.805428\pi$
$13$	−998.000	−1.63784	−0.818921	+	0.573906i	$0.805428\pi$
$14$	0	0
$15$	486.000	0.557710
$16$	256.000	0.250000
$17$	−1302.00	−1.09267	−0.546335	−	0.837567i	$-0.683977\pi$
$17$	−1302.00	−1.09267	−0.546335	+	0.837567i	$0.683977\pi$
$18$	−324.000	−0.235702
$19$	−884.000	−0.561783	−0.280891	−	0.959740i	$-0.590630\pi$
$19$	−884.000	−0.561783	−0.280891	+	0.959740i	$0.590630\pi$
$20$	864.000	0.482991
$21$	0	0
$22$	−864.000	−0.380590
$23$	−2268.00	−0.893971	−0.446986	−	0.894541i	$-0.647502\pi$
$23$	−2268.00	−0.893971	−0.446986	+	0.894541i	$0.647502\pi$
$24$	−576.000	−0.204124
$25$	−209.000	−0.0668800
$26$	3992.00	1.15813
$27$	729.000	0.192450
$28$	0	0
$29$	−1482.00	−0.327230	−0.163615	−	0.986524i	$-0.552315\pi$
$29$	−1482.00	−0.327230	−0.163615	+	0.986524i	$0.552315\pi$
$30$	−1944.00	−0.394360
$31$	−8360.00	−1.56244	−0.781218	−	0.624259i	$-0.785401\pi$
$31$	−8360.00	−1.56244	−0.781218	+	0.624259i	$0.785401\pi$
$32$	−1024.00	−0.176777
$33$	1944.00	0.310750
$34$	5208.00	0.772634
$35$	0	0
$36$	1296.00	0.166667
$37$	−4714.00	−0.566090	−0.283045	−	0.959107i	$-0.591345\pi$
$37$	−4714.00	−0.566090	−0.283045	+	0.959107i	$0.591345\pi$
$38$	3536.00	0.397240
$39$	−8982.00	−0.945609
$40$	−3456.00	−0.341526
$41$	9786.00	0.909171	0.454585	−	0.890703i	$-0.349787\pi$
$41$	9786.00	0.909171	0.454585	+	0.890703i	$0.349787\pi$
$42$	0	0
$43$	19436.0	1.60301	0.801504	−	0.597989i	$-0.204033\pi$
$43$	19436.0	1.60301	0.801504	+	0.597989i	$0.204033\pi$
$44$	3456.00	0.269118
$45$	4374.00	0.321994
$46$	9072.00	0.632133
$47$	−22200.0	−1.46591	−0.732957	−	0.680275i	$-0.761860\pi$
$47$	−22200.0	−1.46591	−0.732957	+	0.680275i	$0.761860\pi$
$48$	2304.00	0.144338
$49$	0	0
$50$	836.000	0.0472913
$51$	−11718.0	−0.630853
$52$	−15968.0	−0.818921
$53$	26790.0	1.31004	0.655018	−	0.755614i	$-0.272661\pi$
$53$	26790.0	1.31004	0.655018	+	0.755614i	$0.272661\pi$
$54$	−2916.00	−0.136083
$55$	11664.0	0.519925
$56$	0	0
$57$	−7956.00	−0.324345
$58$	5928.00	0.231387
$59$	−28092.0	−1.05064	−0.525318	−	0.850906i	$-0.676054\pi$
$59$	−28092.0	−1.05064	−0.525318	+	0.850906i	$0.676054\pi$
$60$	7776.00	0.278855
$61$	38866.0	1.33735	0.668675	−	0.743555i	$-0.266862\pi$
$61$	38866.0	1.33735	0.668675	+	0.743555i	$0.266862\pi$
$62$	33440.0	1.10481
$63$	0	0
$64$	4096.00	0.125000
$65$	−53892.0	−1.58213
$66$	−7776.00	−0.219734
$67$	23948.0	0.651752	0.325876	−	0.945413i	$-0.394341\pi$
$67$	23948.0	0.651752	0.325876	+	0.945413i	$0.394341\pi$
$68$	−20832.0	−0.546335
$69$	−20412.0	−0.516134
$70$	0	0
$71$	−20628.0	−0.485636	−0.242818	−	0.970072i	$-0.578072\pi$
$71$	−20628.0	−0.485636	−0.242818	+	0.970072i	$0.578072\pi$
$72$	−5184.00	−0.117851
$73$	−290.000	−0.00636929	−0.00318464	−	0.999995i	$-0.501014\pi$
$73$	−290.000	−0.00636929	−0.00318464	+	0.999995i	$0.501014\pi$
$74$	18856.0	0.400286
$75$	−1881.00	−0.0386132
$76$	−14144.0	−0.280891
$77$	0	0
$78$	35928.0	0.668646
$79$	−99544.0	−1.79452	−0.897258	−	0.441506i	$-0.854444\pi$
$79$	−99544.0	−1.79452	−0.897258	+	0.441506i	$0.854444\pi$
$80$	13824.0	0.241495
$81$	6561.00	0.111111
$82$	−39144.0	−0.642881
$83$	−19308.0	−0.307639	−0.153820	−	0.988099i	$-0.549158\pi$
$83$	−19308.0	−0.307639	−0.153820	+	0.988099i	$0.549158\pi$
$84$	0	0
$85$	−70308.0	−1.05550
$86$	−77744.0	−1.13350
$87$	−13338.0	−0.188926
$88$	−13824.0	−0.190295
$89$	−36390.0	−0.486975	−0.243488	−	0.969904i	$-0.578292\pi$
$89$	−36390.0	−0.486975	−0.243488	+	0.969904i	$0.578292\pi$
$90$	−17496.0	−0.227684
$91$	0	0
$92$	−36288.0	−0.446986
$93$	−75240.0	−0.902072
$94$	88800.0	1.03656
$95$	−47736.0	−0.542671
$96$	−9216.00	−0.102062
$97$	79078.0	0.853348	0.426674	−	0.904405i	$-0.359685\pi$
$97$	79078.0	0.853348	0.426674	+	0.904405i	$0.359685\pi$
$98$	0	0
$99$	17496.0	0.179412
$100$	−3344.00	−0.0334400
$101$	−184626.	−1.80090	−0.900450	−	0.434960i	$-0.856762\pi$
$101$	−184626.	−1.80090	−0.900450	+	0.434960i	$0.856762\pi$
$102$	46872.0	0.446080
$103$	−64592.0	−0.599909	−0.299955	−	0.953953i	$-0.596972\pi$
$103$	−64592.0	−0.599909	−0.299955	+	0.953953i	$0.596972\pi$
$104$	63872.0	0.579065
$105$	0	0
$106$	−107160.	−0.926335
$107$	149592.	1.26313	0.631566	−	0.775322i	$-0.282412\pi$
$107$	149592.	1.26313	0.631566	+	0.775322i	$0.282412\pi$
$108$	11664.0	0.0962250
$109$	−63826.0	−0.514555	−0.257277	−	0.966338i	$-0.582825\pi$
$109$	−63826.0	−0.514555	−0.257277	+	0.966338i	$0.582825\pi$
$110$	−46656.0	−0.367643
$111$	−42426.0	−0.326832
$112$	0	0
$113$	−71022.0	−0.523235	−0.261618	−	0.965172i	$-0.584256\pi$
$113$	−71022.0	−0.523235	−0.261618	+	0.965172i	$0.584256\pi$
$114$	31824.0	0.229347
$115$	−122472.	−0.863559
$116$	−23712.0	−0.163615
$117$	−80838.0	−0.545948
$118$	112368.	0.742912
$119$	0	0
$120$	−31104.0	−0.197180
$121$	−114395.	−0.710303
$122$	−155464.	−0.945650
$123$	88074.0	0.524910
$124$	−133760.	−0.781218
$125$	−180036.	−1.03059
$126$	0	0
$127$	269624.	1.48337	0.741685	−	0.670749i	$-0.234027\pi$
$127$	269624.	1.48337	0.741685	+	0.670749i	$0.234027\pi$
$128$	−16384.0	−0.0883883
$129$	174924.	0.925497
$130$	215568.	1.11873
$131$	−81180.0	−0.413305	−0.206653	−	0.978414i	$-0.566257\pi$
$131$	−81180.0	−0.413305	−0.206653	+	0.978414i	$0.566257\pi$
$132$	31104.0	0.155375
$133$	0	0
$134$	−95792.0	−0.460858
$135$	39366.0	0.185903
$136$	83328.0	0.386317
$137$	−260910.	−1.18765	−0.593826	−	0.804593i	$-0.702383\pi$
$137$	−260910.	−1.18765	−0.593826	+	0.804593i	$0.702383\pi$
$138$	81648.0	0.364962
$139$	297964.	1.30806	0.654029	−	0.756470i	$-0.273078\pi$
$139$	297964.	1.30806	0.654029	+	0.756470i	$0.273078\pi$
$140$	0	0
$141$	−199800.	−0.846346
$142$	82512.0	0.343397
$143$	−215568.	−0.881544
$144$	20736.0	0.0833333
$145$	−80028.0	−0.316098
$146$	1160.00	0.00450377
$147$	0	0
$148$	−75424.0	−0.283045
$149$	−398970.	−1.47223	−0.736113	−	0.676859i	$-0.763341\pi$
$149$	−398970.	−1.47223	−0.736113	+	0.676859i	$0.763341\pi$
$150$	7524.00	0.0273036
$151$	−224968.	−0.802931	−0.401466	−	0.915874i	$-0.631499\pi$
$151$	−224968.	−0.802931	−0.401466	+	0.915874i	$0.631499\pi$
$152$	56576.0	0.198620
$153$	−105462.	−0.364223
$154$	0	0
$155$	−451440.	−1.50928
$156$	−143712.	−0.472804
$157$	233218.	0.755115	0.377557	−	0.925986i	$-0.376764\pi$
$157$	233218.	0.755115	0.377557	+	0.925986i	$0.376764\pi$
$158$	398176.	1.26891
$159$	241110.	0.756349
$160$	−55296.0	−0.170763
$161$	0	0
$162$	−26244.0	−0.0785674
$163$	466220.	1.37443	0.687214	−	0.726455i	$-0.258834\pi$
$163$	466220.	1.37443	0.687214	+	0.726455i	$0.258834\pi$
$164$	156576.	0.454585
$165$	104976.	0.300179
$166$	77232.0	0.217534
$167$	100848.	0.279818	0.139909	−	0.990164i	$-0.455319\pi$
$167$	100848.	0.279818	0.139909	+	0.990164i	$0.455319\pi$
$168$	0	0
$169$	624711.	1.68253
$170$	281232.	0.746350
$171$	−71604.0	−0.187261
$172$	310976.	0.801504
$173$	668838.	1.69905	0.849524	−	0.527550i	$-0.176889\pi$
$173$	668838.	1.69905	0.849524	+	0.527550i	$0.176889\pi$
$174$	53352.0	0.133591
$175$	0	0
$176$	55296.0	0.134559
$177$	−252828.	−0.606585
$178$	145560.	0.344344
$179$	−614856.	−1.43430	−0.717151	−	0.696917i	$-0.754554\pi$
$179$	−614856.	−1.43430	−0.717151	+	0.696917i	$0.754554\pi$
$180$	69984.0	0.160997
$181$	−540686.	−1.22673	−0.613365	−	0.789800i	$-0.710184\pi$
$181$	−540686.	−1.22673	−0.613365	+	0.789800i	$0.710184\pi$
$182$	0	0
$183$	349794.	0.772120
$184$	145152.	0.316066
$185$	−254556.	−0.546832
$186$	300960.	0.637862
$187$	−281232.	−0.588113
$188$	−355200.	−0.732957
$189$	0	0
$190$	190944.	0.383727
$191$	−41916.0	−0.0831374	−0.0415687	−	0.999136i	$-0.513236\pi$
$191$	−41916.0	−0.0831374	−0.0415687	+	0.999136i	$0.513236\pi$
$192$	36864.0	0.0721688
$193$	−533998.	−1.03192	−0.515960	−	0.856612i	$-0.672565\pi$
$193$	−533998.	−1.03192	−0.515960	+	0.856612i	$0.672565\pi$
$194$	−316312.	−0.603408
$195$	−485028.	−0.913441
$196$	0	0
$197$	824886.	1.51436	0.757179	−	0.653208i	$-0.226577\pi$
$197$	824886.	1.51436	0.757179	+	0.653208i	$0.226577\pi$
$198$	−69984.0	−0.126863
$199$	399544.	0.715207	0.357604	−	0.933873i	$-0.383594\pi$
$199$	399544.	0.715207	0.357604	+	0.933873i	$0.383594\pi$
$200$	13376.0	0.0236457
$201$	215532.	0.376289
$202$	738504.	1.27343
$203$	0	0
$204$	−187488.	−0.315426
$205$	528444.	0.878242
$206$	258368.	0.424200
$207$	−183708.	−0.297990
$208$	−255488.	−0.409461
$209$	−190944.	−0.302371
$210$	0	0
$211$	868868.	1.34353	0.671765	−	0.740764i	$-0.265536\pi$
$211$	868868.	1.34353	0.671765	+	0.740764i	$0.265536\pi$
$212$	428640.	0.655018
$213$	−185652.	−0.280382
$214$	−598368.	−0.893170
$215$	1.04954e6	1.54848
$216$	−46656.0	−0.0680414
$217$	0	0
$218$	255304.	0.363845
$219$	−2610.00	−0.00367731
$220$	186624.	0.259963
$221$	1.29940e6	1.78962
$222$	169704.	0.231105
$223$	626656.	0.843853	0.421927	−	0.906630i	$-0.361354\pi$
$223$	626656.	0.843853	0.421927	+	0.906630i	$0.361354\pi$
$224$	0	0
$225$	−16929.0	−0.0222933
$226$	284088.	0.369983
$227$	450396.	0.580136	0.290068	−	0.957006i	$-0.406322\pi$
$227$	450396.	0.580136	0.290068	+	0.957006i	$0.406322\pi$
$228$	−127296.	−0.162173
$229$	1.06453e6	1.34143	0.670717	−	0.741714i	$-0.265987\pi$
$229$	1.06453e6	1.34143	0.670717	+	0.741714i	$0.265987\pi$
$230$	489888.	0.610629
$231$	0	0
$232$	94848.0	0.115693
$233$	1.43618e6	1.73308	0.866540	−	0.499108i	$-0.166339\pi$
$233$	1.43618e6	1.73308	0.866540	+	0.499108i	$0.166339\pi$
$234$	323352.	0.386043
$235$	−1.19880e6	−1.41605
$236$	−449472.	−0.525318
$237$	−895896.	−1.03606
$238$	0	0
$239$	−997860.	−1.12999	−0.564995	−	0.825094i	$-0.691122\pi$
$239$	−997860.	−1.12999	−0.564995	+	0.825094i	$0.691122\pi$
$240$	124416.	0.139427
$241$	227974.	0.252838	0.126419	−	0.991977i	$-0.459652\pi$
$241$	227974.	0.252838	0.126419	+	0.991977i	$0.459652\pi$
$242$	457580.	0.502260
$243$	59049.0	0.0641500
$244$	621856.	0.668675
$245$	0	0
$246$	−352296.	−0.371168
$247$	882232.	0.920111
$248$	535040.	0.552404
$249$	−173772.	−0.177616
$250$	720144.	0.728734
$251$	−1.51657e6	−1.51942	−0.759712	−	0.650260i	$-0.774660\pi$
$251$	−1.51657e6	−1.51942	−0.759712	+	0.650260i	$0.774660\pi$
$252$	0	0
$253$	−489888.	−0.481167
$254$	−1.07850e6	−1.04890
$255$	−632772.	−0.609392
$256$	65536.0	0.0625000
$257$	−455886.	−0.430550	−0.215275	−	0.976553i	$-0.569065\pi$
$257$	−455886.	−0.430550	−0.215275	+	0.976553i	$0.569065\pi$
$258$	−699696.	−0.654425
$259$	0	0
$260$	−862272.	−0.791063
$261$	−120042.	−0.109077
$262$	324720.	0.292251
$263$	−752652.	−0.670973	−0.335486	−	0.942045i	$-0.608901\pi$
$263$	−752652.	−0.670973	−0.335486	+	0.942045i	$0.608901\pi$
$264$	−124416.	−0.109867
$265$	1.44666e6	1.26547
$266$	0	0
$267$	−327510.	−0.281155
$268$	383168.	0.325876
$269$	−143682.	−0.121066	−0.0605329	−	0.998166i	$-0.519280\pi$
$269$	−143682.	−0.121066	−0.0605329	+	0.998166i	$0.519280\pi$
$270$	−157464.	−0.131453
$271$	−757496.	−0.626552	−0.313276	−	0.949662i	$-0.601426\pi$
$271$	−757496.	−0.626552	−0.313276	+	0.949662i	$0.601426\pi$
$272$	−333312.	−0.273167
$273$	0	0
$274$	1.04364e6	0.839797
$275$	−45144.0	−0.0359972
$276$	−326592.	−0.258067
$277$	−1.16214e6	−0.910035	−0.455018	−	0.890482i	$-0.650367\pi$
$277$	−1.16214e6	−0.910035	−0.455018	+	0.890482i	$0.650367\pi$
$278$	−1.19186e6	−0.924936
$279$	−677160.	−0.520812
$280$	0	0
$281$	−414366.	−0.313053	−0.156527	−	0.987674i	$-0.550030\pi$
$281$	−414366.	−0.313053	−0.156527	+	0.987674i	$0.550030\pi$
$282$	799200.	0.598457
$283$	−120428.	−0.0893843	−0.0446922	−	0.999001i	$-0.514231\pi$
$283$	−120428.	−0.0893843	−0.0446922	+	0.999001i	$0.514231\pi$
$284$	−330048.	−0.242818
$285$	−429624.	−0.313312
$286$	862272.	0.623346
$287$	0	0
$288$	−82944.0	−0.0589256
$289$	275347.	0.193926
$290$	320112.	0.223515
$291$	711702.	0.492681
$292$	−4640.00	−0.00318464
$293$	−2.20159e6	−1.49819	−0.749094	−	0.662463i	$-0.769511\pi$
$293$	−2.20159e6	−1.49819	−0.749094	+	0.662463i	$0.769511\pi$
$294$	0	0
$295$	−1.51697e6	−1.01490
$296$	301696.	0.200143
$297$	157464.	0.103583
$298$	1.59588e6	1.04102
$299$	2.26346e6	1.46418
$300$	−30096.0	−0.0193066
$301$	0	0
$302$	899872.	0.567758
$303$	−1.66163e6	−1.03975
$304$	−226304.	−0.140446
$305$	2.09876e6	1.29186
$306$	421848.	0.257545
$307$	−110900.	−0.0671561	−0.0335781	−	0.999436i	$-0.510690\pi$
$307$	−110900.	−0.0671561	−0.0335781	+	0.999436i	$0.510690\pi$
$308$	0	0
$309$	−581328.	−0.346358
$310$	1.80576e6	1.06722
$311$	910608.	0.533864	0.266932	−	0.963715i	$-0.413990\pi$
$311$	910608.	0.533864	0.266932	+	0.963715i	$0.413990\pi$
$312$	574848.	0.334323
$313$	−3.12247e6	−1.80152	−0.900758	−	0.434322i	$-0.856988\pi$
$313$	−3.12247e6	−1.80152	−0.900758	+	0.434322i	$0.856988\pi$
$314$	−932872.	−0.533947
$315$	0	0
$316$	−1.59270e6	−0.897258
$317$	−2.76688e6	−1.54647	−0.773237	−	0.634117i	$-0.781364\pi$
$317$	−2.76688e6	−1.54647	−0.773237	+	0.634117i	$0.781364\pi$
$318$	−964440.	−0.534820
$319$	−320112.	−0.176127
$320$	221184.	0.120748
$321$	1.34633e6	0.729270
$322$	0	0
$323$	1.15097e6	0.613842
$324$	104976.	0.0555556
$325$	208582.	0.109539
$326$	−1.86488e6	−0.971867
$327$	−574434.	−0.297078
$328$	−626304.	−0.321440
$329$	0	0
$330$	−419904.	−0.212259
$331$	3.22257e6	1.61671	0.808356	−	0.588694i	$-0.200358\pi$
$331$	3.22257e6	1.61671	0.808356	+	0.588694i	$0.200358\pi$
$332$	−308928.	−0.153820
$333$	−381834.	−0.188697
$334$	−403392.	−0.197861
$335$	1.29319e6	0.629580
$336$	0	0
$337$	1.63306e6	0.783298	0.391649	−	0.920115i	$-0.371905\pi$
$337$	1.63306e6	0.783298	0.391649	+	0.920115i	$0.371905\pi$
$338$	−2.49884e6	−1.18973
$339$	−639198.	−0.302090
$340$	−1.12493e6	−0.527749
$341$	−1.80576e6	−0.840958
$342$	286416.	0.132413
$343$	0	0
$344$	−1.24390e6	−0.566749
$345$	−1.10225e6	−0.498576
$346$	−2.67535e6	−1.20141
$347$	1.03642e6	0.462073	0.231036	−	0.972945i	$-0.425788\pi$
$347$	1.03642e6	0.462073	0.231036	+	0.972945i	$0.425788\pi$
$348$	−213408.	−0.0944632
$349$	4.22999e6	1.85898	0.929491	−	0.368844i	$-0.120246\pi$
$349$	4.22999e6	1.85898	0.929491	+	0.368844i	$0.120246\pi$
$350$	0	0
$351$	−727542.	−0.315203
$352$	−221184.	−0.0951474
$353$	−238806.	−0.102002	−0.0510010	−	0.998699i	$-0.516241\pi$
$353$	−238806.	−0.102002	−0.0510010	+	0.998699i	$0.516241\pi$
$354$	1.01131e6	0.428921
$355$	−1.11391e6	−0.469116
$356$	−582240.	−0.243488
$357$	0	0
$358$	2.45942e6	1.01421
$359$	−2.66428e6	−1.09105	−0.545523	−	0.838096i	$-0.683669\pi$
$359$	−2.66428e6	−1.09105	−0.545523	+	0.838096i	$0.683669\pi$
$360$	−279936.	−0.113842
$361$	−1.69464e6	−0.684400
$362$	2.16274e6	0.867429
$363$	−1.02956e6	−0.410094
$364$	0	0
$365$	−15660.0	−0.00615261
$366$	−1.39918e6	−0.545971
$367$	1.71083e6	0.663044	0.331522	−	0.943448i	$-0.392438\pi$
$367$	1.71083e6	0.663044	0.331522	+	0.943448i	$0.392438\pi$
$368$	−580608.	−0.223493
$369$	792666.	0.303057
$370$	1.01822e6	0.386669
$371$	0	0
$372$	−1.20384e6	−0.451036
$373$	−3.96649e6	−1.47616	−0.738081	−	0.674712i	$-0.764268\pi$
$373$	−3.96649e6	−1.47616	−0.738081	+	0.674712i	$0.764268\pi$
$374$	1.12493e6	0.415859
$375$	−1.62032e6	−0.595009
$376$	1.42080e6	0.518279
$377$	1.47904e6	0.535951
$378$	0	0
$379$	828668.	0.296335	0.148167	−	0.988962i	$-0.452663\pi$
$379$	828668.	0.296335	0.148167	+	0.988962i	$0.452663\pi$
$380$	−763776.	−0.271336
$381$	2.42662e6	0.856424
$382$	167664.	0.0587870
$383$	2.55686e6	0.890657	0.445329	−	0.895367i	$-0.353087\pi$
$383$	2.55686e6	0.890657	0.445329	+	0.895367i	$0.353087\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	2.13599e6	0.729678
$387$	1.57432e6	0.534336
$388$	1.26525e6	0.426674
$389$	2.91785e6	0.977664	0.488832	−	0.872378i	$-0.337423\pi$
$389$	2.91785e6	0.977664	0.488832	+	0.872378i	$0.337423\pi$
$390$	1.94011e6	0.645900
$391$	2.95294e6	0.976815
$392$	0	0
$393$	−730620.	−0.238622
$394$	−3.29954e6	−1.07081
$395$	−5.37538e6	−1.73347
$396$	279936.	0.0897059
$397$	−2.50715e6	−0.798370	−0.399185	−	0.916870i	$-0.630707\pi$
$397$	−2.50715e6	−0.798370	−0.399185	+	0.916870i	$0.630707\pi$
$398$	−1.59818e6	−0.505728
$399$	0	0
$400$	−53504.0	−0.0167200
$401$	990666.	0.307657	0.153828	−	0.988098i	$-0.450840\pi$
$401$	990666.	0.307657	0.153828	+	0.988098i	$0.450840\pi$
$402$	−862128.	−0.266077
$403$	8.34328e6	2.55902
$404$	−2.95402e6	−0.900450
$405$	354294.	0.107331
$406$	0	0
$407$	−1.01822e6	−0.304689
$408$	749952.	0.223040
$409$	−4.51824e6	−1.33555	−0.667777	−	0.744362i	$-0.732754\pi$
$409$	−4.51824e6	−1.33555	−0.667777	+	0.744362i	$0.732754\pi$
$410$	−2.11378e6	−0.621011
$411$	−2.34819e6	−0.685691
$412$	−1.03347e6	−0.299955
$413$	0	0
$414$	734832.	0.210711
$415$	−1.04263e6	−0.297174
$416$	1.02195e6	0.289532
$417$	2.68168e6	0.755207
$418$	763776.	0.213809
$419$	−605220.	−0.168414	−0.0842070	−	0.996448i	$-0.526836\pi$
$419$	−605220.	−0.168414	−0.0842070	+	0.996448i	$0.526836\pi$
$420$	0	0
$421$	4.49893e6	1.23710	0.618549	−	0.785746i	$-0.287721\pi$
$421$	4.49893e6	1.23710	0.618549	+	0.785746i	$0.287721\pi$
$422$	−3.47547e6	−0.950020
$423$	−1.79820e6	−0.488638
$424$	−1.71456e6	−0.463167
$425$	272118.	0.0730777
$426$	742608.	0.198260
$427$	0	0
$428$	2.39347e6	0.631566
$429$	−1.94011e6	−0.508960
$430$	−4.19818e6	−1.09494
$431$	5.37594e6	1.39400	0.696998	−	0.717074i	$-0.254519\pi$
$431$	5.37594e6	1.39400	0.696998	+	0.717074i	$0.254519\pi$
$432$	186624.	0.0481125
$433$	1.98561e6	0.508950	0.254475	−	0.967079i	$-0.418097\pi$
$433$	1.98561e6	0.508950	0.254475	+	0.967079i	$0.418097\pi$
$434$	0	0
$435$	−720252.	−0.182499
$436$	−1.02122e6	−0.257277
$437$	2.00491e6	0.502217
$438$	10440.0	0.00260025
$439$	−3.38727e6	−0.838859	−0.419429	−	0.907788i	$-0.637770\pi$
$439$	−3.38727e6	−0.838859	−0.419429	+	0.907788i	$0.637770\pi$
$440$	−746496.	−0.183821
$441$	0	0
$442$	−5.19758e6	−1.26545
$443$	2.14094e6	0.518318	0.259159	−	0.965835i	$-0.416555\pi$
$443$	2.14094e6	0.518318	0.259159	+	0.965835i	$0.416555\pi$
$444$	−678816.	−0.163416
$445$	−1.96506e6	−0.470409
$446$	−2.50662e6	−0.596695
$447$	−3.59073e6	−0.849990
$448$	0	0
$449$	−6.97808e6	−1.63350	−0.816752	−	0.576990i	$-0.804227\pi$
$449$	−6.97808e6	−1.63350	−0.816752	+	0.576990i	$0.804227\pi$
$450$	67716.0	0.0157638
$451$	2.11378e6	0.489348
$452$	−1.13635e6	−0.261618
$453$	−2.02471e6	−0.463573
$454$	−1.80158e6	−0.410218
$455$	0	0
$456$	509184.	0.114673
$457$	−5.17999e6	−1.16021	−0.580107	−	0.814540i	$-0.696989\pi$
$457$	−5.17999e6	−1.16021	−0.580107	+	0.814540i	$0.696989\pi$
$458$	−4.25812e6	−0.948537
$459$	−949158.	−0.210284
$460$	−1.95955e6	−0.431780
$461$	7.83001e6	1.71597	0.857985	−	0.513674i	$-0.171716\pi$
$461$	7.83001e6	1.71597	0.857985	+	0.513674i	$0.171716\pi$
$462$	0	0
$463$	165320.	0.0358404	0.0179202	−	0.999839i	$-0.494296\pi$
$463$	165320.	0.0358404	0.0179202	+	0.999839i	$0.494296\pi$
$464$	−379392.	−0.0818075
$465$	−4.06296e6	−0.871385
$466$	−5.74471e6	−1.22547
$467$	1.79329e6	0.380504	0.190252	−	0.981735i	$-0.439070\pi$
$467$	1.79329e6	0.380504	0.190252	+	0.981735i	$0.439070\pi$
$468$	−1.29341e6	−0.272974
$469$	0	0
$470$	4.79520e6	1.00130
$471$	2.09896e6	0.435966
$472$	1.79789e6	0.371456
$473$	4.19818e6	0.862795
$474$	3.58358e6	0.732608
$475$	184756.	0.0375720
$476$	0	0
$477$	2.16999e6	0.436678
$478$	3.99144e6	0.799024
$479$	6.59657e6	1.31365	0.656824	−	0.754044i	$-0.271899\pi$
$479$	6.59657e6	1.31365	0.656824	+	0.754044i	$0.271899\pi$
$480$	−497664.	−0.0985901
$481$	4.70457e6	0.927166
$482$	−911896.	−0.178784
$483$	0	0
$484$	−1.83032e6	−0.355151
$485$	4.27021e6	0.824319
$486$	−236196.	−0.0453609
$487$	−5.97393e6	−1.14140	−0.570700	−	0.821159i	$-0.693328\pi$
$487$	−5.97393e6	−1.14140	−0.570700	+	0.821159i	$0.693328\pi$
$488$	−2.48742e6	−0.472825
$489$	4.19598e6	0.793526
$490$	0	0
$491$	381264.	0.0713710	0.0356855	−	0.999363i	$-0.488639\pi$
$491$	381264.	0.0713710	0.0356855	+	0.999363i	$0.488639\pi$
$492$	1.40918e6	0.262455
$493$	1.92956e6	0.357554
$494$	−3.52893e6	−0.650617
$495$	944784.	0.173308
$496$	−2.14016e6	−0.390609
$497$	0	0
$498$	695088.	0.125593
$499$	1.54351e6	0.277497	0.138748	−	0.990328i	$-0.455692\pi$
$499$	1.54351e6	0.277497	0.138748	+	0.990328i	$0.455692\pi$
$500$	−2.88058e6	−0.515293
$501$	907632.	0.161553
$502$	6.06629e6	1.07439
$503$	4.02300e6	0.708974	0.354487	−	0.935061i	$-0.384656\pi$
$503$	4.02300e6	0.708974	0.354487	+	0.935061i	$0.384656\pi$
$504$	0	0
$505$	−9.96980e6	−1.73964
$506$	1.95955e6	0.340236
$507$	5.62240e6	0.971408
$508$	4.31398e6	0.741685
$509$	1.94715e6	0.333123	0.166562	−	0.986031i	$-0.446734\pi$
$509$	1.94715e6	0.333123	0.166562	+	0.986031i	$0.446734\pi$
$510$	2.53109e6	0.430905
$511$	0	0
$512$	−262144.	−0.0441942
$513$	−644436.	−0.108115
$514$	1.82354e6	0.304445
$515$	−3.48797e6	−0.579501
$516$	2.79878e6	0.462749
$517$	−4.79520e6	−0.789006
$518$	0	0
$519$	6.01954e6	0.980946
$520$	3.44909e6	0.559366
$521$	−7.38569e6	−1.19206	−0.596028	−	0.802963i	$-0.703255\pi$
$521$	−7.38569e6	−1.19206	−0.596028	+	0.802963i	$0.703255\pi$
$522$	480168.	0.0771289
$523$	329740.	0.0527130	0.0263565	−	0.999653i	$-0.491610\pi$
$523$	329740.	0.0527130	0.0263565	+	0.999653i	$0.491610\pi$
$524$	−1.29888e6	−0.206653
$525$	0	0
$526$	3.01061e6	0.474449
$527$	1.08847e7	1.70722
$528$	497664.	0.0776875
$529$	−1.29252e6	−0.200816
$530$	−5.78664e6	−0.894822
$531$	−2.27545e6	−0.350212
$532$	0	0
$533$	−9.76643e6	−1.48908
$534$	1.31004e6	0.198807
$535$	8.07797e6	1.22016
$536$	−1.53267e6	−0.230429
$537$	−5.53370e6	−0.828095
$538$	574728.	0.0856065
$539$	0	0
$540$	629856.	0.0929516
$541$	87086.0	0.0127925	0.00639625	−	0.999980i	$-0.497964\pi$
$541$	87086.0	0.0127925	0.00639625	+	0.999980i	$0.497964\pi$
$542$	3.02998e6	0.443039
$543$	−4.86617e6	−0.708252
$544$	1.33325e6	0.193158
$545$	−3.44660e6	−0.497050
$546$	0	0
$547$	6.91531e6	0.988196	0.494098	−	0.869406i	$-0.335498\pi$
$547$	6.91531e6	0.988196	0.494098	+	0.869406i	$0.335498\pi$
$548$	−4.17456e6	−0.593826
$549$	3.14815e6	0.445784
$550$	180576.	0.0254538
$551$	1.31009e6	0.183832
$552$	1.30637e6	0.182481
$553$	0	0
$554$	4.64855e6	0.643492
$555$	−2.29100e6	−0.315714
$556$	4.76742e6	0.654029
$557$	−1.52258e6	−0.207942	−0.103971	−	0.994580i	$-0.533155\pi$
$557$	−1.52258e6	−0.207942	−0.103971	+	0.994580i	$0.533155\pi$
$558$	2.70864e6	0.368270
$559$	−1.93971e7	−2.62548
$560$	0	0
$561$	−2.53109e6	−0.339547
$562$	1.65746e6	0.221362
$563$	7.86462e6	1.04570	0.522850	−	0.852425i	$-0.324869\pi$
$563$	7.86462e6	1.04570	0.522850	+	0.852425i	$0.324869\pi$
$564$	−3.19680e6	−0.423173
$565$	−3.83519e6	−0.505435
$566$	481712.	0.0632043
$567$	0	0
$568$	1.32019e6	0.171698
$569$	−1.46321e6	−0.189464	−0.0947321	−	0.995503i	$-0.530199\pi$
$569$	−1.46321e6	−0.189464	−0.0947321	+	0.995503i	$0.530199\pi$
$570$	1.71850e6	0.221545
$571$	9.19855e6	1.18067	0.590336	−	0.807158i	$-0.298995\pi$
$571$	9.19855e6	1.18067	0.590336	+	0.807158i	$0.298995\pi$
$572$	−3.44909e6	−0.440772
$573$	−377244.	−0.0479994
$574$	0	0
$575$	474012.	0.0597888
$576$	331776.	0.0416667
$577$	−3.28939e6	−0.411317	−0.205658	−	0.978624i	$-0.565934\pi$
$577$	−3.28939e6	−0.411317	−0.205658	+	0.978624i	$0.565934\pi$
$578$	−1.10139e6	−0.137126
$579$	−4.80598e6	−0.595780
$580$	−1.28045e6	−0.158049
$581$	0	0
$582$	−2.84681e6	−0.348378
$583$	5.78664e6	0.705107
$584$	18560.0	0.00225188
$585$	−4.36525e6	−0.527375
$586$	8.80634e6	1.05938
$587$	−5.12929e6	−0.614416	−0.307208	−	0.951642i	$-0.599395\pi$
$587$	−5.12929e6	−0.614416	−0.307208	+	0.951642i	$0.599395\pi$
$588$	0	0
$589$	7.39024e6	0.877749
$590$	6.06787e6	0.717640
$591$	7.42397e6	0.874315
$592$	−1.20678e6	−0.141522
$593$	2.75433e6	0.321647	0.160823	−	0.986983i	$-0.448585\pi$
$593$	2.75433e6	0.321647	0.160823	+	0.986983i	$0.448585\pi$
$594$	−629856.	−0.0732445
$595$	0	0
$596$	−6.38352e6	−0.736113
$597$	3.59590e6	0.412925
$598$	−9.05386e6	−1.03533
$599$	−9.88616e6	−1.12580	−0.562899	−	0.826525i	$-0.690314\pi$
$599$	−9.88616e6	−1.12580	−0.562899	+	0.826525i	$0.690314\pi$
$600$	120384.	0.0136518
$601$	−1.37039e7	−1.54760	−0.773798	−	0.633433i	$-0.781645\pi$
$601$	−1.37039e7	−1.54760	−0.773798	+	0.633433i	$0.781645\pi$
$602$	0	0
$603$	1.93979e6	0.217251
$604$	−3.59949e6	−0.401466
$605$	−6.17733e6	−0.686139
$606$	6.64654e6	0.735214
$607$	7.85310e6	0.865107	0.432553	−	0.901608i	$-0.357613\pi$
$607$	7.85310e6	0.865107	0.432553	+	0.901608i	$0.357613\pi$
$608$	905216.	0.0993101
$609$	0	0
$610$	−8.39506e6	−0.913480
$611$	2.21556e7	2.40094
$612$	−1.68739e6	−0.182112
$613$	1.46977e7	1.57978	0.789892	−	0.613246i	$-0.210136\pi$
$613$	1.46977e7	1.57978	0.789892	+	0.613246i	$0.210136\pi$
$614$	443600.	0.0474865
$615$	4.75600e6	0.507053
$616$	0	0
$617$	6.28370e6	0.664511	0.332256	−	0.943189i	$-0.392190\pi$
$617$	6.28370e6	0.664511	0.332256	+	0.943189i	$0.392190\pi$
$618$	2.32531e6	0.244912
$619$	2.26692e6	0.237799	0.118900	−	0.992906i	$-0.462063\pi$
$619$	2.26692e6	0.237799	0.118900	+	0.992906i	$0.462063\pi$
$620$	−7.22304e6	−0.754642
$621$	−1.65337e6	−0.172045
$622$	−3.64243e6	−0.377499
$623$	0	0
$624$	−2.29939e6	−0.236402
$625$	−9.06882e6	−0.928647
$626$	1.24899e7	1.27386
$627$	−1.71850e6	−0.174574
$628$	3.73149e6	0.377557
$629$	6.13763e6	0.618549
$630$	0	0
$631$	−1.17477e7	−1.17457	−0.587285	−	0.809380i	$-0.699803\pi$
$631$	−1.17477e7	−1.17457	−0.587285	+	0.809380i	$0.699803\pi$
$632$	6.37082e6	0.634457
$633$	7.81981e6	0.775688
$634$	1.10675e7	1.09352
$635$	1.45597e7	1.43291
$636$	3.85776e6	0.378175
$637$	0	0
$638$	1.28045e6	0.124540
$639$	−1.67087e6	−0.161879
$640$	−884736.	−0.0853815
$641$	5.93231e6	0.570268	0.285134	−	0.958488i	$-0.407962\pi$
$641$	5.93231e6	0.570268	0.285134	+	0.958488i	$0.407962\pi$
$642$	−5.38531e6	−0.515672
$643$	6.94443e6	0.662383	0.331191	−	0.943564i	$-0.392549\pi$
$643$	6.94443e6	0.662383	0.331191	+	0.943564i	$0.392549\pi$
$644$	0	0
$645$	9.44590e6	0.894013
$646$	−4.60387e6	−0.434052
$647$	4.97050e6	0.466809	0.233404	−	0.972380i	$-0.425013\pi$
$647$	4.97050e6	0.466809	0.233404	+	0.972380i	$0.425013\pi$
$648$	−419904.	−0.0392837
$649$	−6.06787e6	−0.565490
$650$	−834328.	−0.0774557
$651$	0	0
$652$	7.45952e6	0.687214
$653$	−1.83355e7	−1.68271	−0.841354	−	0.540484i	$-0.818241\pi$
$653$	−1.83355e7	−1.68271	−0.841354	+	0.540484i	$0.818241\pi$
$654$	2.29774e6	0.210066
$655$	−4.38372e6	−0.399245
$656$	2.50522e6	0.227293
$657$	−23490.0	−0.00212310
$658$	0	0
$659$	9.01402e6	0.808546	0.404273	−	0.914638i	$-0.367525\pi$
$659$	9.01402e6	0.808546	0.404273	+	0.914638i	$0.367525\pi$
$660$	1.67962e6	0.150089
$661$	−699398.	−0.0622617	−0.0311308	−	0.999515i	$-0.509911\pi$
$661$	−699398.	−0.0622617	−0.0311308	+	0.999515i	$0.509911\pi$
$662$	−1.28903e7	−1.14319
$663$	1.16946e7	1.03324
$664$	1.23571e6	0.108767
$665$	0	0
$666$	1.52734e6	0.133429
$667$	3.36118e6	0.292534
$668$	1.61357e6	0.139909
$669$	5.63990e6	0.487199
$670$	−5.17277e6	−0.445180
$671$	8.39506e6	0.719809
$672$	0	0
$673$	−5.80603e6	−0.494130	−0.247065	−	0.968999i	$-0.579466\pi$
$673$	−5.80603e6	−0.494130	−0.247065	+	0.968999i	$0.579466\pi$
$674$	−6.53223e6	−0.553875
$675$	−152361.	−0.0128711
$676$	9.99538e6	0.841264
$677$	−985074.	−0.0826033	−0.0413016	−	0.999147i	$-0.513150\pi$
$677$	−985074.	−0.0826033	−0.0413016	+	0.999147i	$0.513150\pi$
$678$	2.55679e6	0.213610
$679$	0	0
$680$	4.49971e6	0.373175
$681$	4.05356e6	0.334942
$682$	7.22304e6	0.594647
$683$	−1.88208e7	−1.54379	−0.771894	−	0.635752i	$-0.780690\pi$
$683$	−1.88208e7	−1.54379	−0.771894	+	0.635752i	$0.780690\pi$
$684$	−1.14566e6	−0.0936304
$685$	−1.40891e7	−1.14725
$686$	0	0
$687$	9.58077e6	0.774477
$688$	4.97562e6	0.400752
$689$	−2.67364e7	−2.14563
$690$	4.40899e6	0.352547
$691$	1.93385e7	1.54073	0.770366	−	0.637601i	$-0.220073\pi$
$691$	1.93385e7	1.54073	0.770366	+	0.637601i	$0.220073\pi$
$692$	1.07014e7	0.849524
$693$	0	0
$694$	−4.14566e6	−0.326735
$695$	1.60901e7	1.26356
$696$	853632.	0.0667956
$697$	−1.27414e7	−0.993423
$698$	−1.69199e7	−1.31450
$699$	1.29256e7	1.00059
$700$	0	0
$701$	−1.41489e6	−0.108750	−0.0543748	−	0.998521i	$-0.517317\pi$
$701$	−1.41489e6	−0.108750	−0.0543748	+	0.998521i	$0.517317\pi$
$702$	2.91017e6	0.222882
$703$	4.16718e6	0.318019
$704$	884736.	0.0672794
$705$	−1.07892e7	−0.817554
$706$	955224.	0.0721263
$707$	0	0
$708$	−4.04525e6	−0.303293
$709$	−754906.	−0.0563998	−0.0281999	−	0.999602i	$-0.508977\pi$
$709$	−754906.	−0.0563998	−0.0281999	+	0.999602i	$0.508977\pi$
$710$	4.45565e6	0.331715
$711$	−8.06306e6	−0.598172
$712$	2.32896e6	0.172172
$713$	1.89605e7	1.39677
$714$	0	0
$715$	−1.16407e7	−0.851555
$716$	−9.83770e6	−0.717151
$717$	−8.98074e6	−0.652400
$718$	1.06571e7	0.771486
$719$	−1.08854e6	−0.0785279	−0.0392639	−	0.999229i	$-0.512501\pi$
$719$	−1.08854e6	−0.0785279	−0.0392639	+	0.999229i	$0.512501\pi$
$720$	1.11974e6	0.0804984
$721$	0	0
$722$	6.77857e6	0.483944
$723$	2.05177e6	0.145976
$724$	−8.65098e6	−0.613365
$725$	309738.	0.0218851
$726$	4.11822e6	0.289980
$727$	755392.	0.0530074	0.0265037	−	0.999649i	$-0.491563\pi$
$727$	755392.	0.0530074	0.0265037	+	0.999649i	$0.491563\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	62640.0	0.00435055
$731$	−2.53057e7	−1.75156
$732$	5.59670e6	0.386060
$733$	−1.56369e6	−0.107495	−0.0537477	−	0.998555i	$-0.517117\pi$
$733$	−1.56369e6	−0.107495	−0.0537477	+	0.998555i	$0.517117\pi$
$734$	−6.84333e6	−0.468843
$735$	0	0
$736$	2.32243e6	0.158033
$737$	5.17277e6	0.350796
$738$	−3.17066e6	−0.214294
$739$	−1.05544e7	−0.710922	−0.355461	−	0.934691i	$-0.615676\pi$
$739$	−1.05544e7	−0.710922	−0.355461	+	0.934691i	$0.615676\pi$
$740$	−4.07290e6	−0.273416
$741$	7.94009e6	0.531227
$742$	0	0
$743$	1.73678e7	1.15418	0.577088	−	0.816682i	$-0.304189\pi$
$743$	1.73678e7	1.15418	0.577088	+	0.816682i	$0.304189\pi$
$744$	4.81536e6	0.318931
$745$	−2.15444e7	−1.42214
$746$	1.58660e7	1.04380
$747$	−1.56395e6	−0.102546
$748$	−4.49971e6	−0.294056
$749$	0	0
$750$	6.48130e6	0.420735
$751$	−2.80181e7	−1.81276	−0.906378	−	0.422467i	$-0.861164\pi$
$751$	−2.80181e7	−1.81276	−0.906378	+	0.422467i	$0.861164\pi$
$752$	−5.68320e6	−0.366478
$753$	−1.36491e7	−0.877239
$754$	−5.91614e6	−0.378975
$755$	−1.21483e7	−0.775617
$756$	0	0
$757$	−1.01979e7	−0.646801	−0.323401	−	0.946262i	$-0.604826\pi$
$757$	−1.01979e7	−0.646801	−0.323401	+	0.946262i	$0.604826\pi$
$758$	−3.31467e6	−0.209540
$759$	−4.40899e6	−0.277802
$760$	3.05510e6	0.191863
$761$	−2.57535e6	−0.161204	−0.0806018	−	0.996746i	$-0.525684\pi$
$761$	−2.57535e6	−0.161204	−0.0806018	+	0.996746i	$0.525684\pi$
$762$	−9.70646e6	−0.605583
$763$	0	0
$764$	−670656.	−0.0415687
$765$	−5.69495e6	−0.351833
$766$	−1.02275e7	−0.629790
$767$	2.80358e7	1.72078
$768$	589824.	0.0360844
$769$	−971234.	−0.0592254	−0.0296127	−	0.999561i	$-0.509427\pi$
$769$	−971234.	−0.0592254	−0.0296127	+	0.999561i	$0.509427\pi$
$770$	0	0
$771$	−4.10297e6	−0.248578
$772$	−8.54397e6	−0.515960
$773$	1.72921e7	1.04088	0.520439	−	0.853899i	$-0.325768\pi$
$773$	1.72921e7	1.04088	0.520439	+	0.853899i	$0.325768\pi$
$774$	−6.29726e6	−0.377833
$775$	1.74724e6	0.104496
$776$	−5.06099e6	−0.301704
$777$	0	0
$778$	−1.16714e7	−0.691313
$779$	−8.65082e6	−0.510756
$780$	−7.76045e6	−0.456720
$781$	−4.45565e6	−0.261387
$782$	−1.18117e7	−0.690712
$783$	−1.08038e6	−0.0629755
$784$	0	0
$785$	1.25938e7	0.729427
$786$	2.92248e6	0.168731
$787$	1.65515e7	0.952576	0.476288	−	0.879289i	$-0.341982\pi$
$787$	1.65515e7	0.952576	0.476288	+	0.879289i	$0.341982\pi$
$788$	1.31982e7	0.757179
$789$	−6.77387e6	−0.387386
$790$	2.15015e7	1.22575
$791$	0	0
$792$	−1.11974e6	−0.0634316
$793$	−3.87883e7	−2.19037
$794$	1.00286e7	0.564533
$795$	1.30199e7	0.730619
$796$	6.39270e6	0.357604
$797$	−2.91057e6	−0.162305	−0.0811526	−	0.996702i	$-0.525860\pi$
$797$	−2.91057e6	−0.162305	−0.0811526	+	0.996702i	$0.525860\pi$
$798$	0	0
$799$	2.89044e7	1.60176
$800$	214016.	0.0118228
$801$	−2.94759e6	−0.162325
$802$	−3.96266e6	−0.217546
$803$	−62640.0	−0.00342817
$804$	3.44851e6	0.188145
$805$	0	0
$806$	−3.33731e7	−1.80950
$807$	−1.29314e6	−0.0698974
$808$	1.18161e7	0.636714
$809$	−1.16252e7	−0.624496	−0.312248	−	0.950001i	$-0.601082\pi$
$809$	−1.16252e7	−0.624496	−0.312248	+	0.950001i	$0.601082\pi$
$810$	−1.41718e6	−0.0758947
$811$	−3.09020e7	−1.64981	−0.824906	−	0.565270i	$-0.808772\pi$
$811$	−3.09020e7	−1.64981	−0.824906	+	0.565270i	$0.808772\pi$
$812$	0	0
$813$	−6.81746e6	−0.361740
$814$	4.07290e6	0.215448
$815$	2.51759e7	1.32767
$816$	−2.99981e6	−0.157713
$817$	−1.71814e7	−0.900542
$818$	1.80730e7	0.944379
$819$	0	0
$820$	8.45510e6	0.439121
$821$	−2.22870e7	−1.15397	−0.576984	−	0.816755i	$-0.695771\pi$
$821$	−2.22870e7	−1.15397	−0.576984	+	0.816755i	$0.695771\pi$
$822$	9.39276e6	0.484857
$823$	−1.64895e7	−0.848610	−0.424305	−	0.905519i	$-0.639482\pi$
$823$	−1.64895e7	−0.848610	−0.424305	+	0.905519i	$0.639482\pi$
$824$	4.13389e6	0.212100
$825$	−406296.	−0.0207830
$826$	0	0
$827$	−2.37457e7	−1.20732	−0.603658	−	0.797244i	$-0.706291\pi$
$827$	−2.37457e7	−1.20732	−0.603658	+	0.797244i	$0.706291\pi$
$828$	−2.93933e6	−0.148995
$829$	−2.60865e7	−1.31835	−0.659173	−	0.751991i	$-0.729094\pi$
$829$	−2.60865e7	−1.31835	−0.659173	+	0.751991i	$0.729094\pi$
$830$	4.17053e6	0.210134
$831$	−1.04592e7	−0.525409
$832$	−4.08781e6	−0.204730
$833$	0	0
$834$	−1.07267e7	−0.534012
$835$	5.44579e6	0.270299
$836$	−3.05510e6	−0.151186
$837$	−6.09444e6	−0.300691
$838$	2.42088e6	0.119087
$839$	−1.00872e7	−0.494729	−0.247365	−	0.968922i	$-0.579565\pi$
$839$	−1.00872e7	−0.494729	−0.247365	+	0.968922i	$0.579565\pi$
$840$	0	0
$841$	−1.83148e7	−0.892920
$842$	−1.79957e7	−0.874761
$843$	−3.72929e6	−0.180741
$844$	1.39019e7	0.671765
$845$	3.37344e7	1.62529
$846$	7.19280e6	0.345519
$847$	0	0
$848$	6.85824e6	0.327509
$849$	−1.08385e6	−0.0516061
$850$	−1.08847e6	−0.0516737
$851$	1.06914e7	0.506068
$852$	−2.97043e6	−0.140191
$853$	2.43630e7	1.14646	0.573229	−	0.819395i	$-0.305691\pi$
$853$	2.43630e7	1.14646	0.573229	+	0.819395i	$0.305691\pi$
$854$	0	0
$855$	−3.86662e6	−0.180890
$856$	−9.57389e6	−0.446585
$857$	−2.45612e6	−0.114234	−0.0571172	−	0.998367i	$-0.518191\pi$
$857$	−2.45612e6	−0.114234	−0.0571172	+	0.998367i	$0.518191\pi$
$858$	7.76045e6	0.359889
$859$	−8.62982e6	−0.399042	−0.199521	−	0.979894i	$-0.563939\pi$
$859$	−8.62982e6	−0.399042	−0.199521	+	0.979894i	$0.563939\pi$
$860$	1.67927e7	0.774238
$861$	0	0
$862$	−2.15038e7	−0.985703
$863$	1.05199e7	0.480824	0.240412	−	0.970671i	$-0.422717\pi$
$863$	1.05199e7	0.480824	0.240412	+	0.970671i	$0.422717\pi$
$864$	−746496.	−0.0340207
$865$	3.61173e7	1.64125
$866$	−7.94246e6	−0.359882
$867$	2.47812e6	0.111963
$868$	0	0
$869$	−2.15015e7	−0.965872
$870$	2.88101e6	0.129047
$871$	−2.39001e7	−1.06747
$872$	4.08486e6	0.181922
$873$	6.40532e6	0.284449
$874$	−8.01965e6	−0.355121
$875$	0	0
$876$	−41760.0	−0.00183865
$877$	−1.14540e7	−0.502872	−0.251436	−	0.967874i	$-0.580903\pi$
$877$	−1.14540e7	−0.502872	−0.251436	+	0.967874i	$0.580903\pi$
$878$	1.35491e7	0.593163
$879$	−1.98143e7	−0.864980
$880$	2.98598e6	0.129981
$881$	1.18134e7	0.512786	0.256393	−	0.966573i	$-0.417466\pi$
$881$	1.18134e7	0.512786	0.256393	+	0.966573i	$0.417466\pi$
$882$	0	0
$883$	4.63221e6	0.199934	0.0999670	−	0.994991i	$-0.468126\pi$
$883$	4.63221e6	0.199934	0.0999670	+	0.994991i	$0.468126\pi$
$884$	2.07903e7	0.894810
$885$	−1.36527e7	−0.585950
$886$	−8.56378e6	−0.366506
$887$	−4.47728e7	−1.91075	−0.955377	−	0.295388i	$-0.904551\pi$
$887$	−4.47728e7	−1.91075	−0.955377	+	0.295388i	$0.904551\pi$
$888$	2.71526e6	0.115553
$889$	0	0
$890$	7.86024e6	0.332630
$891$	1.41718e6	0.0598039
$892$	1.00265e7	0.421927
$893$	1.96248e7	0.823525
$894$	1.43629e7	0.601034
$895$	−3.32022e7	−1.38551
$896$	0	0
$897$	2.03712e7	0.845347
$898$	2.79123e7	1.15506
$899$	1.23895e7	0.511276
$900$	−270864.	−0.0111467
$901$	−3.48806e7	−1.43144
$902$	−8.45510e6	−0.346021
$903$	0	0
$904$	4.54541e6	0.184992
$905$	−2.91970e7	−1.18500
$906$	8.09885e6	0.327795
$907$	−2.08357e7	−0.840986	−0.420493	−	0.907296i	$-0.638143\pi$
$907$	−2.08357e7	−0.840986	−0.420493	+	0.907296i	$0.638143\pi$
$908$	7.20634e6	0.290068
$909$	−1.49547e7	−0.600300
$910$	0	0
$911$	5.27869e6	0.210732	0.105366	−	0.994434i	$-0.466399\pi$
$911$	5.27869e6	0.210732	0.105366	+	0.994434i	$0.466399\pi$
$912$	−2.03674e6	−0.0810863
$913$	−4.17053e6	−0.165582
$914$	2.07200e7	0.820396
$915$	1.88889e7	0.745853
$916$	1.70325e7	0.670717
$917$	0	0
$918$	3.79663e6	0.148693
$919$	2.51286e7	0.981477	0.490738	−	0.871307i	$-0.336727\pi$
$919$	2.51286e7	0.981477	0.490738	+	0.871307i	$0.336727\pi$
$920$	7.83821e6	0.305314
$921$	−998100.	−0.0387726
$922$	−3.13200e7	−1.21337
$923$	2.05867e7	0.795396
$924$	0	0
$925$	985226.	0.0378601
$926$	−661280.	−0.0253430
$927$	−5.23195e6	−0.199970
$928$	1.51757e6	0.0578467
$929$	−1.38042e7	−0.524774	−0.262387	−	0.964963i	$-0.584510\pi$
$929$	−1.38042e7	−0.524774	−0.262387	+	0.964963i	$0.584510\pi$
$930$	1.62518e7	0.616162
$931$	0	0
$932$	2.29788e7	0.866540
$933$	8.19547e6	0.308226
$934$	−7.17317e6	−0.269057
$935$	−1.51865e7	−0.568106
$936$	5.17363e6	0.193022
$937$	4.73307e7	1.76114	0.880570	−	0.473915i	$-0.157160\pi$
$937$	4.73307e7	1.76114	0.880570	+	0.473915i	$0.157160\pi$
$938$	0	0
$939$	−2.81023e7	−1.04011
$940$	−1.91808e7	−0.708023
$941$	3.25570e7	1.19859	0.599295	−	0.800528i	$-0.295448\pi$
$941$	3.25570e7	1.19859	0.599295	+	0.800528i	$0.295448\pi$
$942$	−8.39585e6	−0.308274
$943$	−2.21946e7	−0.812773
$944$	−7.19155e6	−0.262659
$945$	0	0
$946$	−1.67927e7	−0.610088
$947$	−5.27117e6	−0.190999	−0.0954997	−	0.995429i	$-0.530445\pi$
$947$	−5.27117e6	−0.190999	−0.0954997	+	0.995429i	$0.530445\pi$
$948$	−1.43343e7	−0.518032
$949$	289420.	0.0104319
$950$	−739024.	−0.0265674
$951$	−2.49019e7	−0.892857
$952$	0	0
$953$	8.20579e6	0.292677	0.146338	−	0.989235i	$-0.453251\pi$
$953$	8.20579e6	0.292677	0.146338	+	0.989235i	$0.453251\pi$
$954$	−8.67996e6	−0.308778
$955$	−2.26346e6	−0.0803092
$956$	−1.59658e7	−0.564995
$957$	−2.88101e6	−0.101687
$958$	−2.63863e7	−0.928890
$959$	0	0
$960$	1.99066e6	0.0697137
$961$	4.12604e7	1.44120
$962$	−1.88183e7	−0.655605
$963$	1.21170e7	0.421044
$964$	3.64758e6	0.126419
$965$	−2.88359e7	−0.996816
$966$	0	0
$967$	−1.18118e7	−0.406210	−0.203105	−	0.979157i	$-0.565103\pi$
$967$	−1.18118e7	−0.406210	−0.203105	+	0.979157i	$0.565103\pi$
$968$	7.32128e6	0.251130
$969$	1.03587e7	0.354402
$970$	−1.70808e7	−0.582881
$971$	3.67702e7	1.25155	0.625774	−	0.780004i	$-0.284783\pi$
$971$	3.67702e7	1.25155	0.625774	+	0.780004i	$0.284783\pi$
$972$	944784.	0.0320750
$973$	0	0
$974$	2.38957e7	0.807091
$975$	1.87724e6	0.0632423
$976$	9.94970e6	0.334338
$977$	−1.85183e7	−0.620674	−0.310337	−	0.950627i	$-0.600442\pi$
$977$	−1.85183e7	−0.620674	−0.310337	+	0.950627i	$0.600442\pi$
$978$	−1.67839e7	−0.561108
$979$	−7.86024e6	−0.262107
$980$	0	0
$981$	−5.16991e6	−0.171518
$982$	−1.52506e6	−0.0504670
$983$	−2.72169e7	−0.898370	−0.449185	−	0.893439i	$-0.648286\pi$
$983$	−2.72169e7	−0.898370	−0.449185	+	0.893439i	$0.648286\pi$
$984$	−5.63674e6	−0.185584
$985$	4.45438e7	1.46284
$986$	−7.71826e6	−0.252829
$987$	0	0
$988$	1.41157e7	0.460056
$989$	−4.40808e7	−1.43304
$990$	−3.77914e6	−0.122548
$991$	1.63398e7	0.528522	0.264261	−	0.964451i	$-0.414872\pi$
$991$	1.63398e7	0.528522	0.264261	+	0.964451i	$0.414872\pi$
$992$	8.56064e6	0.276202
$993$	2.90031e7	0.933409
$994$	0	0
$995$	2.15754e7	0.690877
$996$	−2.78035e6	−0.0888079
$997$	3.02062e7	0.962406	0.481203	−	0.876609i	$-0.340200\pi$
$997$	3.02062e7	0.962406	0.481203	+	0.876609i	$0.340200\pi$
$998$	−6.17403e6	−0.196220
$999$	−3.43651e6	−0.108944

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.a.h.1.1		1
3.2	odd	2		882.6.a.o.1.1		1
7.2	even	3		294.6.e.h.67.1		2
7.3	odd	6		294.6.e.r.79.1		2
7.4	even	3		294.6.e.h.79.1		2
7.5	odd	6		294.6.e.r.67.1		2
7.6	odd	2		42.6.a.a.1.1	✓	1
21.20	even	2		126.6.a.k.1.1		1
28.27	even	2		336.6.a.j.1.1		1
35.13	even	4		1050.6.g.o.799.2		2
35.27	even	4		1050.6.g.o.799.1		2
35.34	odd	2		1050.6.a.n.1.1		1
84.83	odd	2		1008.6.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.a.a.1.1	✓	1	7.6	odd	2
126.6.a.k.1.1		1	21.20	even	2
294.6.a.h.1.1		1	1.1	even	1	trivial
294.6.e.h.67.1		2	7.2	even	3
294.6.e.h.79.1		2	7.4	even	3
294.6.e.r.67.1		2	7.5	odd	6
294.6.e.r.79.1		2	7.3	odd	6
336.6.a.j.1.1		1	28.27	even	2
882.6.a.o.1.1		1	3.2	odd	2
1008.6.a.x.1.1		1	84.83	odd	2
1050.6.a.n.1.1		1	35.34	odd	2
1050.6.g.o.799.1		2	35.27	even	4
1050.6.g.o.799.2		2	35.13	even	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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