LMFDB - Embedded newform 17.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,6,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	17.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:	$2.72652493682$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -18.0000 q^{3} -31.0000 q^{4} -16.0000 q^{5} -18.0000 q^{6} +28.0000 q^{7} -63.0000 q^{8} +81.0000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -18.0000 q^{3} -31.0000 q^{4} -16.0000 q^{5} -18.0000 q^{6} +28.0000 q^{7} -63.0000 q^{8} +81.0000 q^{9} -16.0000 q^{10} -138.000 q^{11} +558.000 q^{12} +82.0000 q^{13} +28.0000 q^{14} +288.000 q^{15} +929.000 q^{16} -289.000 q^{17} +81.0000 q^{18} -2260.00 q^{19} +496.000 q^{20} -504.000 q^{21} -138.000 q^{22} -3424.00 q^{23} +1134.00 q^{24} -2869.00 q^{25} +82.0000 q^{26} +2916.00 q^{27} -868.000 q^{28} +8304.00 q^{29} +288.000 q^{30} -4580.00 q^{31} +2945.00 q^{32} +2484.00 q^{33} -289.000 q^{34} -448.000 q^{35} -2511.00 q^{36} +5932.00 q^{37} -2260.00 q^{38} -1476.00 q^{39} +1008.00 q^{40} +9990.00 q^{41} -504.000 q^{42} -12776.0 q^{43} +4278.00 q^{44} -1296.00 q^{45} -3424.00 q^{46} -768.000 q^{47} -16722.0 q^{48} -16023.0 q^{49} -2869.00 q^{50} +5202.00 q^{51} -2542.00 q^{52} -12630.0 q^{53} +2916.00 q^{54} +2208.00 q^{55} -1764.00 q^{56} +40680.0 q^{57} +8304.00 q^{58} +37968.0 q^{59} -8928.00 q^{60} +18476.0 q^{61} -4580.00 q^{62} +2268.00 q^{63} -26783.0 q^{64} -1312.00 q^{65} +2484.00 q^{66} -51272.0 q^{67} +8959.00 q^{68} +61632.0 q^{69} -448.000 q^{70} -10592.0 q^{71} -5103.00 q^{72} -70974.0 q^{73} +5932.00 q^{74} +51642.0 q^{75} +70060.0 q^{76} -3864.00 q^{77} -1476.00 q^{78} -25944.0 q^{79} -14864.0 q^{80} -72171.0 q^{81} +9990.00 q^{82} -63056.0 q^{83} +15624.0 q^{84} +4624.00 q^{85} -12776.0 q^{86} -149472. q^{87} +8694.00 q^{88} +7706.00 q^{89} -1296.00 q^{90} +2296.00 q^{91} +106144. q^{92} +82440.0 q^{93} -768.000 q^{94} +36160.0 q^{95} -53010.0 q^{96} +99662.0 q^{97} -16023.0 q^{98} -11178.0 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.176777	0.0883883	−	0.996086i	$-0.471828\pi$
$2$	1.00000	0.176777	0.0883883	+	0.996086i	$0.471828\pi$
$3$	−18.0000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−18.0000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−31.0000	−0.968750
$5$	−16.0000	−0.286217	−0.143108	−	0.989707i	$-0.545710\pi$
$5$	−16.0000	−0.286217	−0.143108	+	0.989707i	$0.545710\pi$
$6$	−18.0000	−0.204124
$7$	28.0000	0.215980	0.107990	−	0.994152i	$-0.465559\pi$
$7$	28.0000	0.215980	0.107990	+	0.994152i	$0.465559\pi$
$8$	−63.0000	−0.348029
$9$	81.0000	0.333333
$10$	−16.0000	−0.0505964
$11$	−138.000	−0.343872	−0.171936	−	0.985108i	$-0.555002\pi$
$11$	−138.000	−0.343872	−0.171936	+	0.985108i	$0.555002\pi$
$12$	558.000	1.11862
$13$	82.0000	0.134572	0.0672861	−	0.997734i	$-0.478566\pi$
$13$	82.0000	0.134572	0.0672861	+	0.997734i	$0.478566\pi$
$14$	28.0000	0.0381802
$15$	288.000	0.330495
$16$	929.000	0.907227
$17$	−289.000	−0.242536
$17$	−289.000	−0.242536
$18$	81.0000	0.0589256
$19$	−2260.00	−1.43623	−0.718116	−	0.695924i	$-0.754995\pi$
$19$	−2260.00	−1.43623	−0.718116	+	0.695924i	$0.754995\pi$
$20$	496.000	0.277272
$21$	−504.000	−0.249392
$22$	−138.000	−0.0607886
$23$	−3424.00	−1.34963	−0.674814	−	0.737988i	$-0.735776\pi$
$23$	−3424.00	−1.34963	−0.674814	+	0.737988i	$0.735776\pi$
$24$	1134.00	0.401869
$25$	−2869.00	−0.918080
$26$	82.0000	0.0237892
$27$	2916.00	0.769800
$28$	−868.000	−0.209230
$29$	8304.00	1.83355	0.916774	−	0.399406i	$-0.130784\pi$
$29$	8304.00	1.83355	0.916774	+	0.399406i	$0.130784\pi$
$30$	288.000	0.0584237
$31$	−4580.00	−0.855975	−0.427988	−	0.903785i	$-0.640777\pi$
$31$	−4580.00	−0.855975	−0.427988	+	0.903785i	$0.640777\pi$
$32$	2945.00	0.508406
$33$	2484.00	0.397070
$34$	−289.000	−0.0428746
$35$	−448.000	−0.0618170
$36$	−2511.00	−0.322917
$37$	5932.00	0.712356	0.356178	−	0.934418i	$-0.384080\pi$
$37$	5932.00	0.712356	0.356178	+	0.934418i	$0.384080\pi$
$38$	−2260.00	−0.253892
$39$	−1476.00	−0.155391
$40$	1008.00	0.0996117
$41$	9990.00	0.928124	0.464062	−	0.885803i	$-0.346392\pi$
$41$	9990.00	0.928124	0.464062	+	0.885803i	$0.346392\pi$
$42$	−504.000	−0.0440867
$43$	−12776.0	−1.05372	−0.526858	−	0.849953i	$-0.676630\pi$
$43$	−12776.0	−1.05372	−0.526858	+	0.849953i	$0.676630\pi$
$44$	4278.00	0.333126
$45$	−1296.00	−0.0954056
$46$	−3424.00	−0.238583
$47$	−768.000	−0.0507127	−0.0253563	−	0.999678i	$-0.508072\pi$
$47$	−768.000	−0.0507127	−0.0253563	+	0.999678i	$0.508072\pi$
$48$	−16722.0	−1.04758
$49$	−16023.0	−0.953353
$50$	−2869.00	−0.162295
$51$	5202.00	0.280056
$52$	−2542.00	−0.130367
$53$	−12630.0	−0.617609	−0.308805	−	0.951126i	$-0.599929\pi$
$53$	−12630.0	−0.617609	−0.308805	+	0.951126i	$0.599929\pi$
$54$	2916.00	0.136083
$55$	2208.00	0.0984220
$56$	−1764.00	−0.0751672
$57$	40680.0	1.65842
$58$	8304.00	0.324129
$59$	37968.0	1.42000	0.709999	−	0.704203i	$-0.248695\pi$
$59$	37968.0	1.42000	0.709999	+	0.704203i	$0.248695\pi$
$60$	−8928.00	−0.320167
$61$	18476.0	0.635746	0.317873	−	0.948133i	$-0.397032\pi$
$61$	18476.0	0.635746	0.317873	+	0.948133i	$0.397032\pi$
$62$	−4580.00	−0.151316
$63$	2268.00	0.0719932
$64$	−26783.0	−0.817352
$65$	−1312.00	−0.0385168
$66$	2484.00	0.0701927
$67$	−51272.0	−1.39538	−0.697691	−	0.716399i	$-0.745789\pi$
$67$	−51272.0	−1.39538	−0.697691	+	0.716399i	$0.745789\pi$
$68$	8959.00	0.234956
$69$	61632.0	1.55842
$70$	−448.000	−0.0109278
$71$	−10592.0	−0.249363	−0.124682	−	0.992197i	$-0.539791\pi$
$71$	−10592.0	−0.249363	−0.124682	+	0.992197i	$0.539791\pi$
$72$	−5103.00	−0.116010
$73$	−70974.0	−1.55881	−0.779403	−	0.626523i	$-0.784478\pi$
$73$	−70974.0	−1.55881	−0.779403	+	0.626523i	$0.784478\pi$
$74$	5932.00	0.125928
$75$	51642.0	1.06011
$76$	70060.0	1.39135
$77$	−3864.00	−0.0742695
$78$	−1476.00	−0.0274694
$79$	−25944.0	−0.467702	−0.233851	−	0.972272i	$-0.575133\pi$
$79$	−25944.0	−0.467702	−0.233851	+	0.972272i	$0.575133\pi$
$80$	−14864.0	−0.259663
$81$	−72171.0	−1.22222
$82$	9990.00	0.164071
$83$	−63056.0	−1.00469	−0.502344	−	0.864668i	$-0.667529\pi$
$83$	−63056.0	−1.00469	−0.502344	+	0.864668i	$0.667529\pi$
$84$	15624.0	0.241598
$85$	4624.00	0.0694177
$86$	−12776.0	−0.186273
$87$	−149472.	−2.11720
$88$	8694.00	0.119678
$89$	7706.00	0.103123	0.0515613	−	0.998670i	$-0.483580\pi$
$89$	7706.00	0.103123	0.0515613	+	0.998670i	$0.483580\pi$
$90$	−1296.00	−0.0168655
$91$	2296.00	0.0290649
$92$	106144.	1.30745
$93$	82440.0	0.988395
$94$	−768.000	−0.00896482
$95$	36160.0	0.411073
$96$	−53010.0	−0.587056
$97$	99662.0	1.07547	0.537737	−	0.843112i	$-0.319279\pi$
$97$	99662.0	1.07547	0.537737	+	0.843112i	$0.319279\pi$
$98$	−16023.0	−0.168531
$99$	−11178.0	−0.114624
$100$	88939.0	0.889390
$101$	24514.0	0.239117	0.119559	−	0.992827i	$-0.461852\pi$
$101$	24514.0	0.239117	0.119559	+	0.992827i	$0.461852\pi$
$102$	5202.00	0.0495074
$103$	126992.	1.17946	0.589730	−	0.807600i	$-0.299234\pi$
$103$	126992.	1.17946	0.589730	+	0.807600i	$0.299234\pi$
$104$	−5166.00	−0.0468351
$105$	8064.00	0.0713801
$106$	−12630.0	−0.109179
$107$	−160598.	−1.35607	−0.678033	−	0.735032i	$-0.737167\pi$
$107$	−160598.	−1.35607	−0.678033	+	0.735032i	$0.737167\pi$
$108$	−90396.0	−0.745744
$109$	143712.	1.15858	0.579291	−	0.815121i	$-0.303329\pi$
$109$	143712.	1.15858	0.579291	+	0.815121i	$0.303329\pi$
$110$	2208.00	0.0173987
$111$	−106776.	−0.822557
$112$	26012.0	0.195943
$113$	19514.0	0.143764	0.0718820	−	0.997413i	$-0.477099\pi$
$113$	19514.0	0.143764	0.0718820	+	0.997413i	$0.477099\pi$
$114$	40680.0	0.293170
$115$	54784.0	0.386286
$116$	−257424.	−1.77625
$117$	6642.00	0.0448574
$118$	37968.0	0.251023
$119$	−8092.00	−0.0523828
$120$	−18144.0	−0.115022
$121$	−142007.	−0.881752
$122$	18476.0	0.112385
$123$	−179820.	−1.07170
$124$	141980.	0.829226
$125$	95904.0	0.548987
$126$	2268.00	0.0127267
$127$	−187792.	−1.03316	−0.516580	−	0.856239i	$-0.672795\pi$
$127$	−187792.	−1.03316	−0.516580	+	0.856239i	$0.672795\pi$
$128$	−121023.	−0.652894
$129$	229968.	1.21673
$130$	−1312.00	−0.00680888
$131$	128426.	0.653845	0.326922	−	0.945051i	$-0.393988\pi$
$131$	128426.	0.653845	0.326922	+	0.945051i	$0.393988\pi$
$132$	−77004.0	−0.384661
$133$	−63280.0	−0.310197
$134$	−51272.0	−0.246671
$135$	−46656.0	−0.220330
$136$	18207.0	0.0844095
$137$	−55962.0	−0.254737	−0.127368	−	0.991855i	$-0.540653\pi$
$137$	−55962.0	−0.254737	−0.127368	+	0.991855i	$0.540653\pi$
$138$	61632.0	0.275492
$139$	258994.	1.13698	0.568490	−	0.822690i	$-0.307528\pi$
$139$	258994.	1.13698	0.568490	+	0.822690i	$0.307528\pi$
$140$	13888.0	0.0598852
$141$	13824.0	0.0585580
$142$	−10592.0	−0.0440816
$143$	−11316.0	−0.0462757
$144$	75249.0	0.302409
$145$	−132864.	−0.524792
$146$	−70974.0	−0.275561
$147$	288414.	1.10084
$148$	−183892.	−0.690094
$149$	320566.	1.18291	0.591455	−	0.806338i	$-0.298554\pi$
$149$	320566.	1.18291	0.591455	+	0.806338i	$0.298554\pi$
$150$	51642.0	0.187402
$151$	−78832.0	−0.281359	−0.140679	−	0.990055i	$-0.544929\pi$
$151$	−78832.0	−0.281359	−0.140679	+	0.990055i	$0.544929\pi$
$152$	142380.	0.499850
$153$	−23409.0	−0.0808452
$154$	−3864.00	−0.0131291
$155$	73280.0	0.244994
$156$	45756.0	0.150535
$157$	131806.	0.426762	0.213381	−	0.976969i	$-0.431552\pi$
$157$	131806.	0.426762	0.213381	+	0.976969i	$0.431552\pi$
$158$	−25944.0	−0.0826788
$159$	227340.	0.713154
$160$	−47120.0	−0.145514
$161$	−95872.0	−0.291492
$162$	−72171.0	−0.216060
$163$	−163662.	−0.482479	−0.241240	−	0.970466i	$-0.577554\pi$
$163$	−163662.	−0.482479	−0.241240	+	0.970466i	$0.577554\pi$
$164$	−309690.	−0.899120
$165$	−39744.0	−0.113648
$166$	−63056.0	−0.177605
$167$	213292.	0.591811	0.295906	−	0.955217i	$-0.404379\pi$
$167$	213292.	0.591811	0.295906	+	0.955217i	$0.404379\pi$
$168$	31752.0	0.0867956
$169$	−364569.	−0.981890
$170$	4624.00	0.0122714
$171$	−183060.	−0.478744
$172$	396056.	1.02079
$173$	−622456.	−1.58122	−0.790612	−	0.612317i	$-0.790237\pi$
$173$	−622456.	−1.58122	−0.790612	+	0.612317i	$0.790237\pi$
$174$	−149472.	−0.374271
$175$	−80332.0	−0.198287
$176$	−128202.	−0.311970
$177$	−683424.	−1.63967
$178$	7706.00	0.0182297
$179$	847356.	1.97667	0.988333	−	0.152308i	$-0.0486705\pi$
$179$	847356.	1.97667	0.988333	+	0.152308i	$0.0486705\pi$
$180$	40176.0	0.0924241
$181$	27436.0	0.0622479	0.0311239	−	0.999516i	$-0.490091\pi$
$181$	27436.0	0.0622479	0.0311239	+	0.999516i	$0.490091\pi$
$182$	2296.00	0.00513799
$183$	−332568.	−0.734096
$184$	215712.	0.469710
$185$	−94912.0	−0.203888
$186$	82440.0	0.174725
$187$	39882.0	0.0834013
$188$	23808.0	0.0491279
$189$	81648.0	0.166261
$190$	36160.0	0.0726682
$191$	775528.	1.53820	0.769102	−	0.639126i	$-0.220704\pi$
$191$	775528.	1.53820	0.769102	+	0.639126i	$0.220704\pi$
$192$	482094.	0.943797
$193$	−358282.	−0.692360	−0.346180	−	0.938168i	$-0.612521\pi$
$193$	−358282.	−0.692360	−0.346180	+	0.938168i	$0.612521\pi$
$194$	99662.0	0.190119
$195$	23616.0	0.0444754
$196$	496713.	0.923560
$197$	−956508.	−1.75599	−0.877997	−	0.478666i	$-0.841120\pi$
$197$	−956508.	−1.75599	−0.877997	+	0.478666i	$0.841120\pi$
$198$	−11178.0	−0.0202629
$199$	−653744.	−1.17024	−0.585120	−	0.810947i	$-0.698953\pi$
$199$	−653744.	−1.17024	−0.585120	+	0.810947i	$0.698953\pi$
$200$	180747.	0.319519
$201$	922896.	1.61125
$202$	24514.0	0.0422703
$203$	232512.	0.396009
$204$	−161262.	−0.271304
$205$	−159840.	−0.265644
$206$	126992.	0.208501
$207$	−277344.	−0.449876
$208$	76178.0	0.122088
$209$	311880.	0.493880
$210$	8064.00	0.0126183
$211$	−499738.	−0.772745	−0.386373	−	0.922343i	$-0.626272\pi$
$211$	−499738.	−0.772745	−0.386373	+	0.922343i	$0.626272\pi$
$212$	391530.	0.598309
$213$	190656.	0.287940
$214$	−160598.	−0.239721
$215$	204416.	0.301591
$216$	−183708.	−0.267913
$217$	−128240.	−0.184873
$218$	143712.	0.204810
$219$	1.27753e6	1.79995
$220$	−68448.0	−0.0953463
$221$	−23698.0	−0.0326386
$222$	−106776.	−0.145409
$223$	498696.	0.671543	0.335771	−	0.941943i	$-0.391003\pi$
$223$	498696.	0.671543	0.335771	+	0.941943i	$0.391003\pi$
$224$	82460.0	0.109805
$225$	−232389.	−0.306027
$226$	19514.0	0.0254141
$227$	−235542.	−0.303392	−0.151696	−	0.988427i	$-0.548473\pi$
$227$	−235542.	−0.303392	−0.151696	+	0.988427i	$0.548473\pi$
$228$	−1.26108e6	−1.60659
$229$	−1.44909e6	−1.82602	−0.913012	−	0.407932i	$-0.866250\pi$
$229$	−1.44909e6	−1.82602	−0.913012	+	0.407932i	$0.866250\pi$
$230$	54784.0	0.0682864
$231$	69552.0	0.0857590
$232$	−523152.	−0.638128
$233$	254226.	0.306782	0.153391	−	0.988166i	$-0.450981\pi$
$233$	254226.	0.306782	0.153391	+	0.988166i	$0.450981\pi$
$234$	6642.00	0.00792975
$235$	12288.0	0.0145148
$236$	−1.17701e6	−1.37562
$237$	466992.	0.540056
$238$	−8092.00	−0.00926005
$239$	−1.36561e6	−1.54643	−0.773217	−	0.634142i	$-0.781354\pi$
$239$	−1.36561e6	−1.54643	−0.773217	+	0.634142i	$0.781354\pi$
$240$	267552.	0.299833
$241$	−204426.	−0.226722	−0.113361	−	0.993554i	$-0.536162\pi$
$241$	−204426.	−0.226722	−0.113361	+	0.993554i	$0.536162\pi$
$242$	−142007.	−0.155873
$243$	590490.	0.641500
$244$	−572756.	−0.615879
$245$	256368.	0.272865
$246$	−179820.	−0.189452
$247$	−185320.	−0.193277
$248$	288540.	0.297904
$249$	1.13501e6	1.16011
$250$	95904.0	0.0970480
$251$	1.28729e6	1.28971	0.644854	−	0.764306i	$-0.276918\pi$
$251$	1.28729e6	1.28971	0.644854	+	0.764306i	$0.276918\pi$
$252$	−70308.0	−0.0697434
$253$	472512.	0.464100
$254$	−187792.	−0.182639
$255$	−83232.0	−0.0801567
$256$	736033.	0.701936
$257$	1.29236e6	1.22053	0.610267	−	0.792196i	$-0.291062\pi$
$257$	1.29236e6	1.22053	0.610267	+	0.792196i	$0.291062\pi$
$258$	229968.	0.215089
$259$	166096.	0.153854
$260$	40672.0	0.0373132
$261$	672624.	0.611183
$262$	128426.	0.115585
$263$	−1.30177e6	−1.16050	−0.580249	−	0.814439i	$-0.697045\pi$
$263$	−1.30177e6	−1.16050	−0.580249	+	0.814439i	$0.697045\pi$
$264$	−156492.	−0.138192
$265$	202080.	0.176770
$266$	−63280.0	−0.0548356
$267$	−138708.	−0.119076
$268$	1.58943e6	1.35178
$269$	−1.23844e6	−1.04350	−0.521752	−	0.853097i	$-0.674721\pi$
$269$	−1.23844e6	−1.04350	−0.521752	+	0.853097i	$0.674721\pi$
$270$	−46656.0	−0.0389492
$271$	338504.	0.279989	0.139994	−	0.990152i	$-0.455292\pi$
$271$	338504.	0.279989	0.139994	+	0.990152i	$0.455292\pi$
$272$	−268481.	−0.220035
$273$	−41328.0	−0.0335612
$274$	−55962.0	−0.0450315
$275$	395922.	0.315702
$276$	−1.91059e6	−1.50972
$277$	206840.	0.161970	0.0809851	−	0.996715i	$-0.474193\pi$
$277$	206840.	0.161970	0.0809851	+	0.996715i	$0.474193\pi$
$278$	258994.	0.200992
$279$	−370980.	−0.285325
$280$	28224.0	0.0215141
$281$	−1.62115e6	−1.22478	−0.612388	−	0.790558i	$-0.709791\pi$
$281$	−1.62115e6	−1.22478	−0.612388	+	0.790558i	$0.709791\pi$
$282$	13824.0	0.0103517
$283$	1.82349e6	1.35343	0.676716	−	0.736244i	$-0.263403\pi$
$283$	1.82349e6	1.35343	0.676716	+	0.736244i	$0.263403\pi$
$284$	328352.	0.241570
$285$	−650880.	−0.474667
$286$	−11316.0	−0.00818046
$287$	279720.	0.200456
$288$	238545.	0.169469
$289$	83521.0	0.0588235
$290$	−132864.	−0.0927710
$291$	−1.79392e6	−1.24185
$292$	2.20019e6	1.51009
$293$	2.03295e6	1.38343	0.691716	−	0.722170i	$-0.256855\pi$
$293$	2.03295e6	1.38343	0.691716	+	0.722170i	$0.256855\pi$
$294$	288414.	0.194602
$295$	−607488.	−0.406427
$296$	−373716.	−0.247920
$297$	−402408.	−0.264713
$298$	320566.	0.209111
$299$	−280768.	−0.181622
$300$	−1.60090e6	−1.02698
$301$	−357728.	−0.227581
$302$	−78832.0	−0.0497376
$303$	−441252.	−0.276109
$304$	−2.09954e6	−1.30299
$305$	−295616.	−0.181961
$306$	−23409.0	−0.0142915
$307$	−262716.	−0.159089	−0.0795446	−	0.996831i	$-0.525347\pi$
$307$	−262716.	−0.159089	−0.0795446	+	0.996831i	$0.525347\pi$
$308$	119784.	0.0719485
$309$	−2.28586e6	−1.36192
$310$	73280.0	0.0433093
$311$	−1.36008e6	−0.797379	−0.398689	−	0.917086i	$-0.630535\pi$
$311$	−1.36008e6	−0.797379	−0.398689	+	0.917086i	$0.630535\pi$
$312$	92988.0	0.0540805
$313$	2.32566e6	1.34179	0.670897	−	0.741551i	$-0.265909\pi$
$313$	2.32566e6	1.34179	0.670897	+	0.741551i	$0.265909\pi$
$314$	131806.	0.0754416
$315$	−36288.0	−0.0206057
$316$	804264.	0.453086
$317$	−1.30550e6	−0.729674	−0.364837	−	0.931071i	$-0.618875\pi$
$317$	−1.30550e6	−0.729674	−0.364837	+	0.931071i	$0.618875\pi$
$318$	227340.	0.126069
$319$	−1.14595e6	−0.630507
$320$	428528.	0.233940
$321$	2.89076e6	1.56585
$322$	−95872.0	−0.0515290
$323$	653140.	0.348337
$324$	2.23730e6	1.18403
$325$	−235258.	−0.123548
$326$	−163662.	−0.0852911
$327$	−2.58682e6	−1.33782
$328$	−629370.	−0.323014
$329$	−21504.0	−0.0109529
$330$	−39744.0	−0.0200903
$331$	2.46938e6	1.23885	0.619423	−	0.785058i	$-0.287367\pi$
$331$	2.46938e6	1.23885	0.619423	+	0.785058i	$0.287367\pi$
$332$	1.95474e6	0.973291
$333$	480492.	0.237452
$334$	213292.	0.104618
$335$	820352.	0.399382
$336$	−468216.	−0.226255
$337$	1.56183e6	0.749135	0.374568	−	0.927200i	$-0.377791\pi$
$337$	1.56183e6	0.749135	0.374568	+	0.927200i	$0.377791\pi$
$338$	−364569.	−0.173575
$339$	−351252.	−0.166004
$340$	−143344.	−0.0672484
$341$	632040.	0.294346
$342$	−183060.	−0.0846308
$343$	−919240.	−0.421885
$344$	804888.	0.366724
$345$	−986112.	−0.446045
$346$	−622456.	−0.279524
$347$	2.59827e6	1.15841	0.579204	−	0.815183i	$-0.303364\pi$
$347$	2.59827e6	1.15841	0.579204	+	0.815183i	$0.303364\pi$
$348$	4.63363e6	2.05104
$349$	−1.58300e6	−0.695692	−0.347846	−	0.937552i	$-0.613087\pi$
$349$	−1.58300e6	−0.695692	−0.347846	+	0.937552i	$0.613087\pi$
$350$	−80332.0	−0.0350525
$351$	239112.	0.103594
$352$	−406410.	−0.174827
$353$	−4.37279e6	−1.86777	−0.933883	−	0.357580i	$-0.883602\pi$
$353$	−4.37279e6	−1.86777	−0.933883	+	0.357580i	$0.883602\pi$
$354$	−683424.	−0.289856
$355$	169472.	0.0713719
$356$	−238886.	−0.0999000
$357$	145656.	0.0604864
$358$	847356.	0.349429
$359$	−3.85140e6	−1.57718	−0.788592	−	0.614916i	$-0.789190\pi$
$359$	−3.85140e6	−1.57718	−0.788592	+	0.614916i	$0.789190\pi$
$360$	81648.0	0.0332039
$361$	2.63150e6	1.06276
$362$	27436.0	0.0110040
$363$	2.55613e6	1.01816
$364$	−71176.0	−0.0281566
$365$	1.13558e6	0.446156
$366$	−332568.	−0.129771
$367$	−2.36254e6	−0.915619	−0.457809	−	0.889050i	$-0.651366\pi$
$367$	−2.36254e6	−0.915619	−0.457809	+	0.889050i	$0.651366\pi$
$368$	−3.18090e6	−1.22442
$369$	809190.	0.309375
$370$	−94912.0	−0.0360427
$371$	−353640.	−0.133391
$372$	−2.55564e6	−0.957508
$373$	−1.81815e6	−0.676640	−0.338320	−	0.941031i	$-0.609859\pi$
$373$	−1.81815e6	−0.676640	−0.338320	+	0.941031i	$0.609859\pi$
$374$	39882.0	0.0147434
$375$	−1.72627e6	−0.633915
$376$	48384.0	0.0176495
$377$	680928.	0.246745
$378$	81648.0	0.0293911
$379$	−3.40032e6	−1.21597	−0.607984	−	0.793949i	$-0.708021\pi$
$379$	−3.40032e6	−1.21597	−0.607984	+	0.793949i	$0.708021\pi$
$380$	−1.12096e6	−0.398227
$381$	3.38026e6	1.19299
$382$	775528.	0.271919
$383$	2.45508e6	0.855202	0.427601	−	0.903968i	$-0.359359\pi$
$383$	2.45508e6	0.855202	0.427601	+	0.903968i	$0.359359\pi$
$384$	2.17841e6	0.753898
$385$	61824.0	0.0212572
$386$	−358282.	−0.122393
$387$	−1.03486e6	−0.351239
$388$	−3.08952e6	−1.04187
$389$	−1.27403e6	−0.426881	−0.213441	−	0.976956i	$-0.568467\pi$
$389$	−1.27403e6	−0.426881	−0.213441	+	0.976956i	$0.568467\pi$
$390$	23616.0	0.00786221
$391$	989536.	0.327333
$392$	1.00945e6	0.331795
$393$	−2.31167e6	−0.754995
$394$	−956508.	−0.310419
$395$	415104.	0.133864
$396$	346518.	0.111042
$397$	3.92596e6	1.25017	0.625085	−	0.780557i	$-0.285064\pi$
$397$	3.92596e6	1.25017	0.625085	+	0.780557i	$0.285064\pi$
$398$	−653744.	−0.206871
$399$	1.13904e6	0.358184
$400$	−2.66530e6	−0.832907
$401$	3.26320e6	1.01340	0.506702	−	0.862121i	$-0.330864\pi$
$401$	3.26320e6	1.01340	0.506702	+	0.862121i	$0.330864\pi$
$402$	922896.	0.284831
$403$	−375560.	−0.115191
$404$	−759934.	−0.231645
$405$	1.15474e6	0.349820
$406$	232512.	0.0700052
$407$	−818616.	−0.244959
$408$	−327726.	−0.0974676
$409$	3.92802e6	1.16109	0.580545	−	0.814228i	$-0.302840\pi$
$409$	3.92802e6	1.16109	0.580545	+	0.814228i	$0.302840\pi$
$410$	−159840.	−0.0469598
$411$	1.00732e6	0.294145
$412$	−3.93675e6	−1.14260
$413$	1.06310e6	0.306691
$414$	−277344.	−0.0795276
$415$	1.00890e6	0.287558
$416$	241490.	0.0684173
$417$	−4.66189e6	−1.31287
$418$	311880.	0.0873065
$419$	2.88354e6	0.802399	0.401200	−	0.915991i	$-0.368593\pi$
$419$	2.88354e6	0.802399	0.401200	+	0.915991i	$0.368593\pi$
$420$	−249984.	−0.0691495
$421$	4.14047e6	1.13853	0.569264	−	0.822155i	$-0.307228\pi$
$421$	4.14047e6	1.13853	0.569264	+	0.822155i	$0.307228\pi$
$422$	−499738.	−0.136603
$423$	−62208.0	−0.0169042
$424$	795690.	0.214946
$425$	829141.	0.222667
$426$	190656.	0.0509010
$427$	517328.	0.137308
$428$	4.97854e6	1.31369
$429$	203688.	0.0534346
$430$	204416.	0.0533143
$431$	1.15135e6	0.298549	0.149274	−	0.988796i	$-0.452306\pi$
$431$	1.15135e6	0.298549	0.149274	+	0.988796i	$0.452306\pi$
$432$	2.70896e6	0.698383
$433$	−4.60857e6	−1.18126	−0.590632	−	0.806941i	$-0.701121\pi$
$433$	−4.60857e6	−1.18126	−0.590632	+	0.806941i	$0.701121\pi$
$434$	−128240.	−0.0326813
$435$	2.39155e6	0.605978
$436$	−4.45507e6	−1.12238
$437$	7.73824e6	1.93838
$438$	1.27753e6	0.318190
$439$	−5.69026e6	−1.40920	−0.704598	−	0.709607i	$-0.748872\pi$
$439$	−5.69026e6	−1.40920	−0.704598	+	0.709607i	$0.748872\pi$
$440$	−139104.	−0.0342537
$441$	−1.29786e6	−0.317784
$442$	−23698.0	−0.00576974
$443$	−2.51726e6	−0.609422	−0.304711	−	0.952445i	$-0.598560\pi$
$443$	−2.51726e6	−0.609422	−0.304711	+	0.952445i	$0.598560\pi$
$444$	3.31006e6	0.796852
$445$	−123296.	−0.0295154
$446$	498696.	0.118713
$447$	−5.77019e6	−1.36591
$448$	−749924.	−0.176532
$449$	−3.08360e6	−0.721843	−0.360921	−	0.932596i	$-0.617538\pi$
$449$	−3.08360e6	−0.721843	−0.360921	+	0.932596i	$0.617538\pi$
$450$	−232389.	−0.0540984
$451$	−1.37862e6	−0.319156
$452$	−604934.	−0.139271
$453$	1.41898e6	0.324885
$454$	−235542.	−0.0536326
$455$	−36736.0	−0.00831885
$456$	−2.56284e6	−0.577177
$457$	−1.36685e6	−0.306148	−0.153074	−	0.988215i	$-0.548917\pi$
$457$	−1.36685e6	−0.306148	−0.153074	+	0.988215i	$0.548917\pi$
$458$	−1.44909e6	−0.322799
$459$	−842724.	−0.186704
$460$	−1.69830e6	−0.374215
$461$	−4.41305e6	−0.967133	−0.483566	−	0.875308i	$-0.660659\pi$
$461$	−4.41305e6	−0.967133	−0.483566	+	0.875308i	$0.660659\pi$
$462$	69552.0	0.0151602
$463$	−2.61890e6	−0.567761	−0.283881	−	0.958860i	$-0.591622\pi$
$463$	−2.61890e6	−0.567761	−0.283881	+	0.958860i	$0.591622\pi$
$464$	7.71442e6	1.66344
$465$	−1.31904e6	−0.282895
$466$	254226.	0.0542319
$467$	−5.63629e6	−1.19592	−0.597959	−	0.801527i	$-0.704021\pi$
$467$	−5.63629e6	−1.19592	−0.597959	+	0.801527i	$0.704021\pi$
$468$	−205902.	−0.0434556
$469$	−1.43562e6	−0.301374
$470$	12288.0	0.00256588
$471$	−2.37251e6	−0.492783
$472$	−2.39198e6	−0.494201
$473$	1.76309e6	0.362344
$474$	466992.	0.0954693
$475$	6.48394e6	1.31858
$476$	250852.	0.0507458
$477$	−1.02303e6	−0.205870
$478$	−1.36561e6	−0.273373
$479$	3.70207e6	0.737235	0.368618	−	0.929581i	$-0.379831\pi$
$479$	3.70207e6	0.737235	0.368618	+	0.929581i	$0.379831\pi$
$480$	848160.	0.168025
$481$	486424.	0.0958633
$482$	−204426.	−0.0400792
$483$	1.72570e6	0.336586
$484$	4.40222e6	0.854197
$485$	−1.59459e6	−0.307819
$486$	590490.	0.113402
$487$	6.68919e6	1.27806	0.639030	−	0.769182i	$-0.279336\pi$
$487$	6.68919e6	1.27806	0.639030	+	0.769182i	$0.279336\pi$
$488$	−1.16399e6	−0.221258
$489$	2.94592e6	0.557119
$490$	256368.	0.0482363
$491$	1.89024e6	0.353846	0.176923	−	0.984225i	$-0.443386\pi$
$491$	1.89024e6	0.353846	0.176923	+	0.984225i	$0.443386\pi$
$492$	5.57442e6	1.03821
$493$	−2.39986e6	−0.444701
$494$	−185320.	−0.0341668
$495$	178848.	0.0328073
$496$	−4.25482e6	−0.776564
$497$	−296576.	−0.0538574
$498$	1.13501e6	0.205081
$499$	−3.04659e6	−0.547726	−0.273863	−	0.961769i	$-0.588301\pi$
$499$	−3.04659e6	−0.547726	−0.273863	+	0.961769i	$0.588301\pi$
$500$	−2.97302e6	−0.531831
$501$	−3.83926e6	−0.683365
$502$	1.28729e6	0.227990
$503$	1.87726e6	0.330829	0.165414	−	0.986224i	$-0.447104\pi$
$503$	1.87726e6	0.330829	0.165414	+	0.986224i	$0.447104\pi$
$504$	−142884.	−0.0250557
$505$	−392224.	−0.0684393
$506$	472512.	0.0820421
$507$	6.56224e6	1.13379
$508$	5.82155e6	1.00087
$509$	−4.18203e6	−0.715473	−0.357736	−	0.933823i	$-0.616451\pi$
$509$	−4.18203e6	−0.715473	−0.357736	+	0.933823i	$0.616451\pi$
$510$	−83232.0	−0.0141698
$511$	−1.98727e6	−0.336670
$512$	4.60877e6	0.776980
$513$	−6.59016e6	−1.10561
$514$	1.29236e6	0.215762
$515$	−2.03187e6	−0.337581
$516$	−7.12901e6	−1.17870
$517$	105984.	0.0174387
$518$	166096.	0.0271979
$519$	1.12042e7	1.82584
$520$	82656.0	0.0134050
$521$	−7.13429e6	−1.15148	−0.575740	−	0.817633i	$-0.695286\pi$
$521$	−7.13429e6	−1.15148	−0.575740	+	0.817633i	$0.695286\pi$
$522$	672624.	0.108043
$523$	3.88339e6	0.620808	0.310404	−	0.950605i	$-0.399536\pi$
$523$	3.88339e6	0.620808	0.310404	+	0.950605i	$0.399536\pi$
$524$	−3.98121e6	−0.633412
$525$	1.44598e6	0.228962
$526$	−1.30177e6	−0.205149
$527$	1.32362e6	0.207605
$528$	2.30764e6	0.360232
$529$	5.28743e6	0.821496
$530$	202080.	0.0312488
$531$	3.07541e6	0.473333
$532$	1.96168e6	0.300503
$533$	819180.	0.124900
$534$	−138708.	−0.0210498
$535$	2.56957e6	0.388129
$536$	3.23014e6	0.485634
$537$	−1.52524e7	−2.28246
$538$	−1.23844e6	−0.184467
$539$	2.21117e6	0.327832
$540$	1.44634e6	0.213444
$541$	1.32610e7	1.94797	0.973987	−	0.226606i	$-0.0727628\pi$
$541$	1.32610e7	1.94797	0.973987	+	0.226606i	$0.0727628\pi$
$542$	338504.	0.0494955
$543$	−493848.	−0.0718776
$544$	−851105.	−0.123306
$545$	−2.29939e6	−0.331606
$546$	−41328.0	−0.00593284
$547$	−2.92014e6	−0.417288	−0.208644	−	0.977992i	$-0.566905\pi$
$547$	−2.92014e6	−0.417288	−0.208644	+	0.977992i	$0.566905\pi$
$548$	1.73482e6	0.246776
$549$	1.49656e6	0.211915
$550$	395922.	0.0558088
$551$	−1.87670e7	−2.63340
$552$	−3.88282e6	−0.542374
$553$	−726432.	−0.101014
$554$	206840.	0.0286326
$555$	1.70842e6	0.235430
$556$	−8.02881e6	−1.10145
$557$	−1.28247e7	−1.75150	−0.875749	−	0.482766i	$-0.839632\pi$
$557$	−1.28247e7	−1.75150	−0.875749	+	0.482766i	$0.839632\pi$
$558$	−370980.	−0.0504388
$559$	−1.04763e6	−0.141801
$560$	−416192.	−0.0560820
$561$	−717876.	−0.0963035
$562$	−1.62115e6	−0.216512
$563$	3.08514e6	0.410208	0.205104	−	0.978740i	$-0.434247\pi$
$563$	3.08514e6	0.410208	0.205104	+	0.978740i	$0.434247\pi$
$564$	−428544.	−0.0567280
$565$	−312224.	−0.0411477
$566$	1.82349e6	0.239255
$567$	−2.02079e6	−0.263975
$568$	667296.	0.0867856
$569$	−335998.	−0.0435067	−0.0217533	−	0.999763i	$-0.506925\pi$
$569$	−335998.	−0.0435067	−0.0217533	+	0.999763i	$0.506925\pi$
$570$	−650880.	−0.0839100
$571$	847498.	0.108780	0.0543899	−	0.998520i	$-0.482679\pi$
$571$	847498.	0.108780	0.0543899	+	0.998520i	$0.482679\pi$
$572$	350796.	0.0448296
$573$	−1.39595e7	−1.77617
$574$	279720.	0.0354359
$575$	9.82346e6	1.23907
$576$	−2.16942e6	−0.272451
$577$	−148274.	−0.0185407	−0.00927034	−	0.999957i	$-0.502951\pi$
$577$	−148274.	−0.0185407	−0.00927034	+	0.999957i	$0.502951\pi$
$578$	83521.0	0.0103986
$579$	6.44908e6	0.799468
$580$	4.11878e6	0.508392
$581$	−1.76557e6	−0.216992
$582$	−1.79392e6	−0.219530
$583$	1.74294e6	0.212379
$584$	4.47136e6	0.542510
$585$	−106272.	−0.0128389
$586$	2.03295e6	0.244558
$587$	1.14026e7	1.36587	0.682933	−	0.730481i	$-0.260704\pi$
$587$	1.14026e7	1.36587	0.682933	+	0.730481i	$0.260704\pi$
$588$	−8.94083e6	−1.06644
$589$	1.03508e7	1.22938
$590$	−607488.	−0.0718468
$591$	1.72171e7	2.02765
$592$	5.51083e6	0.646268
$593$	−3.20163e6	−0.373882	−0.186941	−	0.982371i	$-0.559857\pi$
$593$	−3.20163e6	−0.373882	−0.186941	+	0.982371i	$0.559857\pi$
$594$	−402408.	−0.0467951
$595$	129472.	0.0149928
$596$	−9.93755e6	−1.14594
$597$	1.17674e7	1.35128
$598$	−280768.	−0.0321066
$599$	4.94638e6	0.563274	0.281637	−	0.959521i	$-0.409123\pi$
$599$	4.94638e6	0.563274	0.281637	+	0.959521i	$0.409123\pi$
$600$	−3.25345e6	−0.368948
$601$	6.33013e6	0.714869	0.357434	−	0.933938i	$-0.383652\pi$
$601$	6.33013e6	0.714869	0.357434	+	0.933938i	$0.383652\pi$
$602$	−357728.	−0.0402311
$603$	−4.15303e6	−0.465127
$604$	2.44379e6	0.272566
$605$	2.27211e6	0.252372
$606$	−441252.	−0.0488096
$607$	−5.54369e6	−0.610699	−0.305350	−	0.952240i	$-0.598773\pi$
$607$	−5.54369e6	−0.610699	−0.305350	+	0.952240i	$0.598773\pi$
$608$	−6.65570e6	−0.730188
$609$	−4.18522e6	−0.457272
$610$	−295616.	−0.0321665
$611$	−62976.0	−0.00682452
$612$	725679.	0.0783188
$613$	2.21837e6	0.238442	0.119221	−	0.992868i	$-0.461960\pi$
$613$	2.21837e6	0.238442	0.119221	+	0.992868i	$0.461960\pi$
$614$	−262716.	−0.0281233
$615$	2.87712e6	0.306740
$616$	243432.	0.0258479
$617$	1.29573e7	1.37025	0.685127	−	0.728424i	$-0.259747\pi$
$617$	1.29573e7	1.37025	0.685127	+	0.728424i	$0.259747\pi$
$618$	−2.28586e6	−0.240756
$619$	−5.72261e6	−0.600299	−0.300150	−	0.953892i	$-0.597037\pi$
$619$	−5.72261e6	−0.600299	−0.300150	+	0.953892i	$0.597037\pi$
$620$	−2.27168e6	−0.237338
$621$	−9.98438e6	−1.03894
$622$	−1.36008e6	−0.140958
$623$	215768.	0.0222724
$624$	−1.37120e6	−0.140975
$625$	7.43116e6	0.760951
$626$	2.32566e6	0.237198
$627$	−5.61384e6	−0.570284
$628$	−4.08599e6	−0.413426
$629$	−1.71435e6	−0.172772
$630$	−36288.0	−0.00364260
$631$	610216.	0.0610113	0.0305056	−	0.999535i	$-0.490288\pi$
$631$	610216.	0.0610113	0.0305056	+	0.999535i	$0.490288\pi$
$632$	1.63447e6	0.162774
$633$	8.99528e6	0.892289
$634$	−1.30550e6	−0.128989
$635$	3.00467e6	0.295708
$636$	−7.04754e6	−0.690867
$637$	−1.31389e6	−0.128295
$638$	−1.14595e6	−0.111459
$639$	−857952.	−0.0831210
$640$	1.93637e6	0.186869
$641$	1.32737e7	1.27599	0.637995	−	0.770041i	$-0.279764\pi$
$641$	1.32737e7	1.27599	0.637995	+	0.770041i	$0.279764\pi$
$642$	2.89076e6	0.276806
$643$	−1.11903e7	−1.06737	−0.533683	−	0.845685i	$-0.679192\pi$
$643$	−1.11903e7	−1.06737	−0.533683	+	0.845685i	$0.679192\pi$
$644$	2.97203e6	0.282383
$645$	−3.67949e6	−0.348248
$646$	653140.	0.0615779
$647$	−1.63568e7	−1.53616	−0.768080	−	0.640354i	$-0.778788\pi$
$647$	−1.63568e7	−1.53616	−0.768080	+	0.640354i	$0.778788\pi$
$648$	4.54677e6	0.425369
$649$	−5.23958e6	−0.488298
$650$	−235258.	−0.0218404
$651$	2.30832e6	0.213473
$652$	5.07352e6	0.467402
$653$	−1.13851e7	−1.04485	−0.522427	−	0.852684i	$-0.674973\pi$
$653$	−1.13851e7	−1.04485	−0.522427	+	0.852684i	$0.674973\pi$
$654$	−2.58682e6	−0.236495
$655$	−2.05482e6	−0.187141
$656$	9.28071e6	0.842018
$657$	−5.74889e6	−0.519602
$658$	−21504.0	−0.00193622
$659$	−6.89916e6	−0.618846	−0.309423	−	0.950924i	$-0.600136\pi$
$659$	−6.89916e6	−0.618846	−0.309423	+	0.950924i	$0.600136\pi$
$660$	1.23206e6	0.110096
$661$	1.06861e7	0.951300	0.475650	−	0.879635i	$-0.342213\pi$
$661$	1.06861e7	0.951300	0.475650	+	0.879635i	$0.342213\pi$
$662$	2.46938e6	0.218999
$663$	426564.	0.0376878
$664$	3.97253e6	0.349661
$665$	1.01248e6	0.0887835
$666$	480492.	0.0419760
$667$	−2.84329e7	−2.47461
$668$	−6.61205e6	−0.573317
$669$	−8.97653e6	−0.775431
$670$	820352.	0.0706014
$671$	−2.54969e6	−0.218615
$672$	−1.48428e6	−0.126792
$673$	5.94743e6	0.506164	0.253082	−	0.967445i	$-0.418556\pi$
$673$	5.94743e6	0.506164	0.253082	+	0.967445i	$0.418556\pi$
$674$	1.56183e6	0.132430
$675$	−8.36600e6	−0.706738
$676$	1.13016e7	0.951206
$677$	−1.22521e7	−1.02739	−0.513697	−	0.857971i	$-0.671725\pi$
$677$	−1.22521e7	−1.02739	−0.513697	+	0.857971i	$0.671725\pi$
$678$	−351252.	−0.0293457
$679$	2.79054e6	0.232281
$680$	−291312.	−0.0241594
$681$	4.23976e6	0.350327
$682$	632040.	0.0520336
$683$	1.54440e6	0.126680	0.0633399	−	0.997992i	$-0.479825\pi$
$683$	1.54440e6	0.126680	0.0633399	+	0.997992i	$0.479825\pi$
$684$	5.67486e6	0.463783
$685$	895392.	0.0729099
$686$	−919240.	−0.0745794
$687$	2.60836e7	2.10851
$688$	−1.18689e7	−0.955960
$689$	−1.03566e6	−0.0831130
$690$	−986112.	−0.0788503
$691$	−4.67446e6	−0.372423	−0.186211	−	0.982510i	$-0.559621\pi$
$691$	−4.67446e6	−0.372423	−0.186211	+	0.982510i	$0.559621\pi$
$692$	1.92961e7	1.53181
$693$	−312984.	−0.0247565
$694$	2.59827e6	0.204779
$695$	−4.14390e6	−0.325423
$696$	9.41674e6	0.736847
$697$	−2.88711e6	−0.225103
$698$	−1.58300e6	−0.122982
$699$	−4.57607e6	−0.354242
$700$	2.49029e6	0.192090
$701$	1.56326e7	1.20154	0.600768	−	0.799424i	$-0.294862\pi$
$701$	1.56326e7	1.20154	0.600768	+	0.799424i	$0.294862\pi$
$702$	239112.	0.0183130
$703$	−1.34063e7	−1.02311
$704$	3.69605e6	0.281065
$705$	−221184.	−0.0167603
$706$	−4.37279e6	−0.330177
$707$	686392.	0.0516445
$708$	2.11861e7	1.58843
$709$	3.00982e6	0.224867	0.112433	−	0.993659i	$-0.464135\pi$
$709$	3.00982e6	0.224867	0.112433	+	0.993659i	$0.464135\pi$
$710$	169472.	0.0126169
$711$	−2.10146e6	−0.155901
$712$	−485478.	−0.0358897
$713$	1.56819e7	1.15525
$714$	145656.	0.0106926
$715$	181056.	0.0132449
$716$	−2.62680e7	−1.91490
$717$	2.45809e7	1.78567
$718$	−3.85140e6	−0.278809
$719$	1.75685e7	1.26739	0.633697	−	0.773581i	$-0.281537\pi$
$719$	1.75685e7	1.26739	0.633697	+	0.773581i	$0.281537\pi$
$720$	−1.20398e6	−0.0865545
$721$	3.55578e6	0.254739
$722$	2.63150e6	0.187871
$723$	3.67967e6	0.261796
$724$	−850516.	−0.0603026
$725$	−2.38242e7	−1.68334
$726$	2.55613e6	0.179987
$727$	−2.38686e7	−1.67491	−0.837455	−	0.546506i	$-0.815957\pi$
$727$	−2.38686e7	−1.67491	−0.837455	+	0.546506i	$0.815957\pi$
$728$	−144648.	−0.0101154
$729$	6.90873e6	0.481481
$730$	1.13558e6	0.0788700
$731$	3.69226e6	0.255564
$732$	1.03096e7	0.711155
$733$	−1.23100e7	−0.846250	−0.423125	−	0.906071i	$-0.639067\pi$
$733$	−1.23100e7	−0.846250	−0.423125	+	0.906071i	$0.639067\pi$
$734$	−2.36254e6	−0.161860
$735$	−4.61462e6	−0.315078
$736$	−1.00837e7	−0.686159
$737$	7.07554e6	0.479834
$738$	809190.	0.0546902
$739$	8.29133e6	0.558487	0.279244	−	0.960220i	$-0.409916\pi$
$739$	8.29133e6	0.558487	0.279244	+	0.960220i	$0.409916\pi$
$740$	2.94227e6	0.197517
$741$	3.33576e6	0.223177
$742$	−353640.	−0.0235804
$743$	2.38814e7	1.58704	0.793520	−	0.608544i	$-0.208246\pi$
$743$	2.38814e7	1.58704	0.793520	+	0.608544i	$0.208246\pi$
$744$	−5.19372e6	−0.343990
$745$	−5.12906e6	−0.338569
$746$	−1.81815e6	−0.119614
$747$	−5.10754e6	−0.334896
$748$	−1.23634e6	−0.0807950
$749$	−4.49674e6	−0.292883
$750$	−1.72627e6	−0.112061
$751$	−7.25327e6	−0.469282	−0.234641	−	0.972082i	$-0.575391\pi$
$751$	−7.25327e6	−0.469282	−0.234641	+	0.972082i	$0.575391\pi$
$752$	−713472.	−0.0460079
$753$	−2.31712e7	−1.48923
$754$	680928.	0.0436187
$755$	1.26131e6	0.0805295
$756$	−2.53109e6	−0.161066
$757$	−8.49948e6	−0.539079	−0.269540	−	0.962989i	$-0.586872\pi$
$757$	−8.49948e6	−0.539079	−0.269540	+	0.962989i	$0.586872\pi$
$758$	−3.40032e6	−0.214955
$759$	−8.50522e6	−0.535896
$760$	−2.27808e6	−0.143066
$761$	1.11285e7	0.696586	0.348293	−	0.937386i	$-0.386762\pi$
$761$	1.11285e7	0.696586	0.348293	+	0.937386i	$0.386762\pi$
$762$	3.38026e6	0.210893
$763$	4.02394e6	0.250230
$764$	−2.40414e7	−1.49014
$765$	374544.	0.0231392
$766$	2.45508e6	0.151180
$767$	3.11338e6	0.191092
$768$	−1.32486e7	−0.810526
$769$	−3.81682e6	−0.232748	−0.116374	−	0.993205i	$-0.537127\pi$
$769$	−3.81682e6	−0.232748	−0.116374	+	0.993205i	$0.537127\pi$
$770$	61824.0	0.00375777
$771$	−2.32624e7	−1.40935
$772$	1.11067e7	0.670723
$773$	2.44139e7	1.46956	0.734782	−	0.678304i	$-0.237285\pi$
$773$	2.44139e7	1.46956	0.734782	+	0.678304i	$0.237285\pi$
$774$	−1.03486e6	−0.0620908
$775$	1.31400e7	0.785854
$776$	−6.27871e6	−0.374297
$777$	−2.98973e6	−0.177656
$778$	−1.27403e6	−0.0754626
$779$	−2.25774e7	−1.33300
$780$	−732096.	−0.0430855
$781$	1.46170e6	0.0857491
$782$	989536.	0.0578648
$783$	2.42145e7	1.41147
$784$	−1.48854e7	−0.864907
$785$	−2.10890e6	−0.122146
$786$	−2.31167e6	−0.133466
$787$	−8.67597e6	−0.499322	−0.249661	−	0.968333i	$-0.580319\pi$
$787$	−8.67597e6	−0.499322	−0.249661	+	0.968333i	$0.580319\pi$
$788$	2.96517e7	1.70112
$789$	2.34318e7	1.34003
$790$	415104.	0.0236641
$791$	546392.	0.0310501
$792$	704214.	0.0398925
$793$	1.51503e6	0.0855537
$794$	3.92596e6	0.221001
$795$	−3.63744e6	−0.204116
$796$	2.02661e7	1.13367
$797$	−2.09139e7	−1.16624	−0.583121	−	0.812386i	$-0.698169\pi$
$797$	−2.09139e7	−1.16624	−0.583121	+	0.812386i	$0.698169\pi$
$798$	1.13904e6	0.0633187
$799$	221952.	0.0122996
$800$	−8.44921e6	−0.466757
$801$	624186.	0.0343742
$802$	3.26320e6	0.179146
$803$	9.79441e6	0.536031
$804$	−2.86098e7	−1.56090
$805$	1.53395e6	0.0834300
$806$	−375560.	−0.0203630
$807$	2.22919e7	1.20494
$808$	−1.54438e6	−0.0832197
$809$	375646.	0.0201794	0.0100897	−	0.999949i	$-0.496788\pi$
$809$	375646.	0.0201794	0.0100897	+	0.999949i	$0.496788\pi$
$810$	1.15474e6	0.0618401
$811$	−3.37751e7	−1.80320	−0.901601	−	0.432569i	$-0.857607\pi$
$811$	−3.37751e7	−1.80320	−0.901601	+	0.432569i	$0.857607\pi$
$812$	−7.20787e6	−0.383634
$813$	−6.09307e6	−0.323303
$814$	−818616.	−0.0433031
$815$	2.61859e6	0.138094
$816$	4.83266e6	0.254074
$817$	2.88738e7	1.51338
$818$	3.92802e6	0.205254
$819$	185976.	0.00968829
$820$	4.95504e6	0.257343
$821$	1.30751e7	0.676997	0.338499	−	0.940967i	$-0.390081\pi$
$821$	1.30751e7	0.676997	0.338499	+	0.940967i	$0.390081\pi$
$822$	1.00732e6	0.0519979
$823$	1.04272e7	0.536622	0.268311	−	0.963332i	$-0.413534\pi$
$823$	1.04272e7	0.536622	0.268311	+	0.963332i	$0.413534\pi$
$824$	−8.00050e6	−0.410487
$825$	−7.12660e6	−0.364542
$826$	1.06310e6	0.0542158
$827$	894198.	0.0454642	0.0227321	−	0.999742i	$-0.492764\pi$
$827$	894198.	0.0454642	0.0227321	+	0.999742i	$0.492764\pi$
$828$	8.59766e6	0.435817
$829$	−1.40788e7	−0.711509	−0.355755	−	0.934579i	$-0.615776\pi$
$829$	−1.40788e7	−0.711509	−0.355755	+	0.934579i	$0.615776\pi$
$830$	1.00890e6	0.0508336
$831$	−3.72312e6	−0.187027
$832$	−2.19621e6	−0.109993
$833$	4.63065e6	0.231222
$834$	−4.66189e6	−0.232085
$835$	−3.41267e6	−0.169386
$836$	−9.66828e6	−0.478447
$837$	−1.33553e7	−0.658930
$838$	2.88354e6	0.141846
$839$	3.64266e7	1.78654	0.893271	−	0.449519i	$-0.148404\pi$
$839$	3.64266e7	1.78654	0.893271	+	0.449519i	$0.148404\pi$
$840$	−508032.	−0.0248424
$841$	4.84453e7	2.36190
$842$	4.14047e6	0.201265
$843$	2.91806e7	1.41425
$844$	1.54919e7	0.748597
$845$	5.83310e6	0.281033
$846$	−62208.0	−0.00298827
$847$	−3.97620e6	−0.190440
$848$	−1.17333e7	−0.560311
$849$	−3.28227e7	−1.56281
$850$	829141.	0.0393624
$851$	−2.03112e7	−0.961415
$852$	−5.91034e6	−0.278942
$853$	2.25356e7	1.06047	0.530233	−	0.847852i	$-0.322104\pi$
$853$	2.25356e7	1.06047	0.530233	+	0.847852i	$0.322104\pi$
$854$	517328.	0.0242729
$855$	2.92896e6	0.137024
$856$	1.01177e7	0.471950
$857$	−5.42063e6	−0.252114	−0.126057	−	0.992023i	$-0.540232\pi$
$857$	−5.42063e6	−0.252114	−0.126057	+	0.992023i	$0.540232\pi$
$858$	203688.	0.00944598
$859$	−5.23558e6	−0.242093	−0.121046	−	0.992647i	$-0.538625\pi$
$859$	−5.23558e6	−0.242093	−0.121046	+	0.992647i	$0.538625\pi$
$860$	−6.33690e6	−0.292167
$861$	−5.03496e6	−0.231467
$862$	1.15135e6	0.0527764
$863$	−1.68411e7	−0.769739	−0.384870	−	0.922971i	$-0.625754\pi$
$863$	−1.68411e7	−0.769739	−0.384870	+	0.922971i	$0.625754\pi$
$864$	8.58762e6	0.391371
$865$	9.95930e6	0.452573
$866$	−4.60857e6	−0.208820
$867$	−1.50338e6	−0.0679236
$868$	3.97544e6	0.179096
$869$	3.58027e6	0.160830
$870$	2.39155e6	0.107123
$871$	−4.20430e6	−0.187780
$872$	−9.05386e6	−0.403220
$873$	8.07262e6	0.358492
$874$	7.73824e6	0.342660
$875$	2.68531e6	0.118570
$876$	−3.96035e7	−1.74371
$877$	−4.47184e7	−1.96330	−0.981651	−	0.190686i	$-0.938929\pi$
$877$	−4.47184e7	−1.96330	−0.981651	+	0.190686i	$0.938929\pi$
$878$	−5.69026e6	−0.249113
$879$	−3.65931e7	−1.59745
$880$	2.05123e6	0.0892911
$881$	−1.94946e7	−0.846205	−0.423102	−	0.906082i	$-0.639059\pi$
$881$	−1.94946e7	−0.846205	−0.423102	+	0.906082i	$0.639059\pi$
$882$	−1.29786e6	−0.0561769
$883$	8.11594e6	0.350297	0.175149	−	0.984542i	$-0.443959\pi$
$883$	8.11594e6	0.350297	0.175149	+	0.984542i	$0.443959\pi$
$884$	734638.	0.0316186
$885$	1.09348e7	0.469302
$886$	−2.51726e6	−0.107732
$887$	−6.41959e6	−0.273967	−0.136984	−	0.990573i	$-0.543741\pi$
$887$	−6.41959e6	−0.273967	−0.136984	+	0.990573i	$0.543741\pi$
$888$	6.72689e6	0.286274
$889$	−5.25818e6	−0.223142
$890$	−123296.	−0.00521764
$891$	9.95960e6	0.420289
$892$	−1.54596e7	−0.650557
$893$	1.73568e6	0.0728351
$894$	−5.77019e6	−0.241461
$895$	−1.35577e7	−0.565755
$896$	−3.38864e6	−0.141012
$897$	5.05382e6	0.209720
$898$	−3.08360e6	−0.127605
$899$	−3.80323e7	−1.56947
$900$	7.20406e6	0.296463
$901$	3.65007e6	0.149792
$902$	−1.37862e6	−0.0564194
$903$	6.43910e6	0.262788
$904$	−1.22938e6	−0.0500341
$905$	−438976.	−0.0178164
$906$	1.41898e6	0.0574321
$907$	−2.44531e7	−0.986998	−0.493499	−	0.869746i	$-0.664282\pi$
$907$	−2.44531e7	−0.986998	−0.493499	+	0.869746i	$0.664282\pi$
$908$	7.30180e6	0.293911
$909$	1.98563e6	0.0797057
$910$	−36736.0	−0.00147058
$911$	3.07240e7	1.22654	0.613270	−	0.789873i	$-0.289854\pi$
$911$	3.07240e7	1.22654	0.613270	+	0.789873i	$0.289854\pi$
$912$	3.77917e7	1.50456
$913$	8.70173e6	0.345484
$914$	−1.36685e6	−0.0541199
$915$	5.32109e6	0.210110
$916$	4.49218e7	1.76896
$917$	3.59593e6	0.141217
$918$	−842724.	−0.0330049
$919$	2.91180e7	1.13729	0.568647	−	0.822582i	$-0.307467\pi$
$919$	2.91180e7	1.13729	0.568647	+	0.822582i	$0.307467\pi$
$920$	−3.45139e6	−0.134439
$921$	4.72889e6	0.183700
$922$	−4.41305e6	−0.170967
$923$	−868544.	−0.0335573
$924$	−2.15611e6	−0.0830790
$925$	−1.70189e7	−0.653999
$926$	−2.61890e6	−0.100367
$927$	1.02864e7	0.393153
$928$	2.44553e7	0.932186
$929$	−2.72558e7	−1.03614	−0.518071	−	0.855338i	$-0.673350\pi$
$929$	−2.72558e7	−1.03614	−0.518071	+	0.855338i	$0.673350\pi$
$930$	−1.31904e6	−0.0500093
$931$	3.62120e7	1.36924
$932$	−7.88101e6	−0.297195
$933$	2.44815e7	0.920734
$934$	−5.63629e6	−0.211410
$935$	−638112.	−0.0238709
$936$	−418446.	−0.0156117
$937$	1.77108e7	0.659007	0.329503	−	0.944154i	$-0.393119\pi$
$937$	1.77108e7	0.659007	0.329503	+	0.944154i	$0.393119\pi$
$938$	−1.43562e6	−0.0532759
$939$	−4.18619e7	−1.54937
$940$	−380928.	−0.0140612
$941$	−2.62616e7	−0.966822	−0.483411	−	0.875394i	$-0.660602\pi$
$941$	−2.62616e7	−0.966822	−0.483411	+	0.875394i	$0.660602\pi$
$942$	−2.37251e6	−0.0871125
$943$	−3.42058e7	−1.25262
$944$	3.52723e7	1.28826
$945$	−1.30637e6	−0.0475867
$946$	1.76309e6	0.0640540
$947$	4.72817e7	1.71324	0.856619	−	0.515949i	$-0.172561\pi$
$947$	4.72817e7	1.71324	0.856619	+	0.515949i	$0.172561\pi$
$948$	−1.44768e7	−0.523179
$949$	−5.81987e6	−0.209772
$950$	6.48394e6	0.233093
$951$	2.34990e7	0.842555
$952$	509796.	0.0182307
$953$	−4.23885e7	−1.51187	−0.755937	−	0.654644i	$-0.772818\pi$
$953$	−4.23885e7	−1.51187	−0.755937	+	0.654644i	$0.772818\pi$
$954$	−1.02303e6	−0.0363930
$955$	−1.24084e7	−0.440260
$956$	4.23338e7	1.49811
$957$	2.06271e7	0.728046
$958$	3.70207e6	0.130326
$959$	−1.56694e6	−0.0550180
$960$	−7.71350e6	−0.270131
$961$	−7.65275e6	−0.267306
$962$	486424.	0.0169464
$963$	−1.30084e7	−0.452022
$964$	6.33721e6	0.219637
$965$	5.73251e6	0.198165
$966$	1.72570e6	0.0595006
$967$	−2.63718e7	−0.906931	−0.453466	−	0.891274i	$-0.649813\pi$
$967$	−2.63718e7	−0.906931	−0.453466	+	0.891274i	$0.649813\pi$
$968$	8.94644e6	0.306875
$969$	−1.17565e7	−0.402225
$970$	−1.59459e6	−0.0544152
$971$	−2.54493e7	−0.866219	−0.433109	−	0.901341i	$-0.642584\pi$
$971$	−2.54493e7	−0.866219	−0.433109	+	0.901341i	$0.642584\pi$
$972$	−1.83052e7	−0.621453
$973$	7.25183e6	0.245565
$974$	6.68919e6	0.225931
$975$	4.23464e6	0.142661
$976$	1.71642e7	0.576765
$977$	−1.15428e7	−0.386879	−0.193439	−	0.981112i	$-0.561964\pi$
$977$	−1.15428e7	−0.386879	−0.193439	+	0.981112i	$0.561964\pi$
$978$	2.94592e6	0.0984857
$979$	−1.06343e6	−0.0354610
$980$	−7.94741e6	−0.264338
$981$	1.16407e7	0.386194
$982$	1.89024e6	0.0625517
$983$	1.91193e7	0.631084	0.315542	−	0.948912i	$-0.397814\pi$
$983$	1.91193e7	0.631084	0.315542	+	0.948912i	$0.397814\pi$
$984$	1.13287e7	0.372985
$985$	1.53041e7	0.502595
$986$	−2.39986e6	−0.0786127
$987$	387072.	0.0126473
$988$	5.74492e6	0.187237
$989$	4.37450e7	1.42213
$990$	178848.	0.00579957
$991$	1.81353e7	0.586598	0.293299	−	0.956021i	$-0.405247\pi$
$991$	1.81353e7	0.586598	0.293299	+	0.956021i	$0.405247\pi$
$992$	−1.34881e7	−0.435183
$993$	−4.44488e7	−1.43050
$994$	−296576.	−0.00952073
$995$	1.04599e7	0.334942
$996$	−3.51852e7	−1.12386
$997$	3.97825e7	1.26752	0.633760	−	0.773530i	$-0.281511\pi$
$997$	3.97825e7	1.26752	0.633760	+	0.773530i	$0.281511\pi$
$998$	−3.04659e6	−0.0968252
$999$	1.72977e7	0.548372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.6.a.b.1.1	✓	1
3.2	odd	2		153.6.a.a.1.1		1
4.3	odd	2		272.6.a.d.1.1		1
5.4	even	2		425.6.a.a.1.1		1
7.6	odd	2		833.6.a.b.1.1		1
8.3	odd	2		1088.6.a.b.1.1		1
8.5	even	2		1088.6.a.i.1.1		1
17.16	even	2		289.6.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.6.a.b.1.1	✓	1	1.1	even	1	trivial
153.6.a.a.1.1		1	3.2	odd	2
272.6.a.d.1.1		1	4.3	odd	2
289.6.a.b.1.1		1	17.16	even	2
425.6.a.a.1.1		1	5.4	even	2
833.6.a.b.1.1		1	7.6	odd	2
1088.6.a.b.1.1		1	8.3	odd	2
1088.6.a.i.1.1		1	8.5	even	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more