LMFDB - Embedded newform 240.6.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,6,Mod(1,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("240.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	240.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:	$38.4921167551$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 120)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	240.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+9.00000 q^{3} -25.0000 q^{5} +100.000 q^{7} +81.0000 q^{9} +O(q^{10})$

$q+9.00000 q^{3} -25.0000 q^{5} +100.000 q^{7} +81.0000 q^{9} +136.000 q^{11} +82.0000 q^{13} -225.000 q^{15} +358.000 q^{17} -796.000 q^{19} +900.000 q^{21} -488.000 q^{23} +625.000 q^{25} +729.000 q^{27} +7466.00 q^{29} -2728.00 q^{31} +1224.00 q^{33} -2500.00 q^{35} +7794.00 q^{37} +738.000 q^{39} +18234.0 q^{41} +2444.00 q^{43} -2025.00 q^{45} +2200.00 q^{47} -6807.00 q^{49} +3222.00 q^{51} +10122.0 q^{53} -3400.00 q^{55} -7164.00 q^{57} +6776.00 q^{59} +23398.0 q^{61} +8100.00 q^{63} -2050.00 q^{65} +9676.00 q^{67} -4392.00 q^{69} -13728.0 q^{71} -27390.0 q^{73} +5625.00 q^{75} +13600.0 q^{77} +93288.0 q^{79} +6561.00 q^{81} +23276.0 q^{83} -8950.00 q^{85} +67194.0 q^{87} +102354. q^{89} +8200.00 q^{91} -24552.0 q^{93} +19900.0 q^{95} -49502.0 q^{97} +11016.0 q^{99} +O(q^{100})$

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
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	0	0
$7$	100.000	0.771356	0.385678	−	0.922633i	$-0.373968\pi$
$7$	100.000	0.771356	0.385678	+	0.922633i	$0.373968\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	136.000	0.338889	0.169444	−	0.985540i	$-0.445803\pi$
$11$	136.000	0.338889	0.169444	+	0.985540i	$0.445803\pi$
$12$	0	0
$13$	82.0000	0.134572	0.0672861	−	0.997734i	$-0.478566\pi$
$13$	82.0000	0.134572	0.0672861	+	0.997734i	$0.478566\pi$
$14$	0	0
$15$	−225.000	−0.258199
$16$	0	0
$17$	358.000	0.300442	0.150221	−	0.988652i	$-0.452001\pi$
$17$	358.000	0.300442	0.150221	+	0.988652i	$0.452001\pi$
$18$	0	0
$19$	−796.000	−0.505859	−0.252929	−	0.967485i	$-0.581394\pi$
$19$	−796.000	−0.505859	−0.252929	+	0.967485i	$0.581394\pi$
$20$	0	0
$21$	900.000	0.445343
$22$	0	0
$23$	−488.000	−0.192354	−0.0961768	−	0.995364i	$-0.530661\pi$
$23$	−488.000	−0.192354	−0.0961768	+	0.995364i	$0.530661\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	729.000	0.192450
$28$	0	0
$29$	7466.00	1.64852	0.824258	−	0.566215i	$-0.191593\pi$
$29$	7466.00	1.64852	0.824258	+	0.566215i	$0.191593\pi$
$30$	0	0
$31$	−2728.00	−0.509847	−0.254924	−	0.966961i	$-0.582050\pi$
$31$	−2728.00	−0.509847	−0.254924	+	0.966961i	$0.582050\pi$
$32$	0	0
$33$	1224.00	0.195658
$34$	0	0
$35$	−2500.00	−0.344961
$36$	0	0
$37$	7794.00	0.935957	0.467979	−	0.883740i	$-0.344982\pi$
$37$	7794.00	0.935957	0.467979	+	0.883740i	$0.344982\pi$
$38$	0	0
$39$	738.000	0.0776953
$40$	0	0
$41$	18234.0	1.69403	0.847017	−	0.531565i	$-0.178396\pi$
$41$	18234.0	1.69403	0.847017	+	0.531565i	$0.178396\pi$
$42$	0	0
$43$	2444.00	0.201572	0.100786	−	0.994908i	$-0.467864\pi$
$43$	2444.00	0.201572	0.100786	+	0.994908i	$0.467864\pi$
$44$	0	0
$45$	−2025.00	−0.149071
$46$	0	0
$47$	2200.00	0.145271	0.0726354	−	0.997359i	$-0.476859\pi$
$47$	2200.00	0.145271	0.0726354	+	0.997359i	$0.476859\pi$
$48$	0	0
$49$	−6807.00	−0.405010
$50$	0	0
$51$	3222.00	0.173460
$52$	0	0
$53$	10122.0	0.494967	0.247484	−	0.968892i	$-0.420396\pi$
$53$	10122.0	0.494967	0.247484	+	0.968892i	$0.420396\pi$
$54$	0	0
$55$	−3400.00	−0.151556
$56$	0	0
$57$	−7164.00	−0.292058
$58$	0	0
$59$	6776.00	0.253421	0.126711	−	0.991940i	$-0.459558\pi$
$59$	6776.00	0.253421	0.126711	+	0.991940i	$0.459558\pi$
$60$	0	0
$61$	23398.0	0.805108	0.402554	−	0.915396i	$-0.368123\pi$
$61$	23398.0	0.805108	0.402554	+	0.915396i	$0.368123\pi$
$62$	0	0
$63$	8100.00	0.257119
$64$	0	0
$65$	−2050.00	−0.0601825
$66$	0	0
$67$	9676.00	0.263335	0.131668	−	0.991294i	$-0.457967\pi$
$67$	9676.00	0.263335	0.131668	+	0.991294i	$0.457967\pi$
$68$	0	0
$69$	−4392.00	−0.111055
$70$	0	0
$71$	−13728.0	−0.323193	−0.161596	−	0.986857i	$-0.551664\pi$
$71$	−13728.0	−0.323193	−0.161596	+	0.986857i	$0.551664\pi$
$72$	0	0
$73$	−27390.0	−0.601568	−0.300784	−	0.953692i	$-0.597248\pi$
$73$	−27390.0	−0.601568	−0.300784	+	0.953692i	$0.597248\pi$
$74$	0	0
$75$	5625.00	0.115470
$76$	0	0
$77$	13600.0	0.261404
$78$	0	0
$79$	93288.0	1.68174	0.840868	−	0.541240i	$-0.182045\pi$
$79$	93288.0	1.68174	0.840868	+	0.541240i	$0.182045\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	23276.0	0.370863	0.185431	−	0.982657i	$-0.440632\pi$
$83$	23276.0	0.370863	0.185431	+	0.982657i	$0.440632\pi$
$84$	0	0
$85$	−8950.00	−0.134362
$86$	0	0
$87$	67194.0	0.951771
$88$	0	0
$89$	102354.	1.36971	0.684857	−	0.728678i	$-0.259865\pi$
$89$	102354.	1.36971	0.684857	+	0.728678i	$0.259865\pi$
$90$	0	0
$91$	8200.00	0.103803
$92$	0	0
$93$	−24552.0	−0.294360
$94$	0	0
$95$	19900.0	0.226227
$96$	0	0
$97$	−49502.0	−0.534187	−0.267094	−	0.963671i	$-0.586063\pi$
$97$	−49502.0	−0.534187	−0.267094	+	0.963671i	$0.586063\pi$
$98$	0	0
$99$	11016.0	0.112963
$100$	0	0
$101$	107682.	1.05036	0.525182	−	0.850990i	$-0.323997\pi$
$101$	107682.	1.05036	0.525182	+	0.850990i	$0.323997\pi$
$102$	0	0
$103$	214676.	1.99384	0.996920	−	0.0784215i	$-0.0249880\pi$
$103$	214676.	1.99384	0.996920	+	0.0784215i	$0.0249880\pi$
$104$	0	0
$105$	−22500.0	−0.199163
$106$	0	0
$107$	−50892.0	−0.429724	−0.214862	−	0.976644i	$-0.568930\pi$
$107$	−50892.0	−0.429724	−0.214862	+	0.976644i	$0.568930\pi$
$108$	0	0
$109$	−17242.0	−0.139002	−0.0695011	−	0.997582i	$-0.522141\pi$
$109$	−17242.0	−0.139002	−0.0695011	+	0.997582i	$0.522141\pi$
$110$	0	0
$111$	70146.0	0.540375
$112$	0	0
$113$	−40338.0	−0.297179	−0.148590	−	0.988899i	$-0.547473\pi$
$113$	−40338.0	−0.297179	−0.148590	+	0.988899i	$0.547473\pi$
$114$	0	0
$115$	12200.0	0.0860231
$116$	0	0
$117$	6642.00	0.0448574
$118$	0	0
$119$	35800.0	0.231748
$120$	0	0
$121$	−142555.	−0.885154
$122$	0	0
$123$	164106.	0.978051
$124$	0	0
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−243828.	−1.34145	−0.670725	−	0.741706i	$-0.734017\pi$
$127$	−243828.	−1.34145	−0.670725	+	0.741706i	$0.734017\pi$
$128$	0	0
$129$	21996.0	0.116378
$130$	0	0
$131$	−303336.	−1.54435	−0.772175	−	0.635410i	$-0.780831\pi$
$131$	−303336.	−1.54435	−0.772175	+	0.635410i	$0.780831\pi$
$132$	0	0
$133$	−79600.0	−0.390197
$134$	0	0
$135$	−18225.0	−0.0860663
$136$	0	0
$137$	224486.	1.02185	0.510926	−	0.859625i	$-0.329303\pi$
$137$	224486.	1.02185	0.510926	+	0.859625i	$0.329303\pi$
$138$	0	0
$139$	−239628.	−1.05196	−0.525982	−	0.850496i	$-0.676302\pi$
$139$	−239628.	−1.05196	−0.525982	+	0.850496i	$0.676302\pi$
$140$	0	0
$141$	19800.0	0.0838721
$142$	0	0
$143$	11152.0	0.0456050
$144$	0	0
$145$	−186650.	−0.737238
$146$	0	0
$147$	−61263.0	−0.233833
$148$	0	0
$149$	387754.	1.43084	0.715419	−	0.698695i	$-0.246236\pi$
$149$	387754.	1.43084	0.715419	+	0.698695i	$0.246236\pi$
$150$	0	0
$151$	−532184.	−1.89941	−0.949707	−	0.313141i	$-0.898619\pi$
$151$	−532184.	−1.89941	−0.949707	+	0.313141i	$0.898619\pi$
$152$	0	0
$153$	28998.0	0.100147
$154$	0	0
$155$	68200.0	0.228011
$156$	0	0
$157$	46162.0	0.149464	0.0747318	−	0.997204i	$-0.476190\pi$
$157$	46162.0	0.149464	0.0747318	+	0.997204i	$0.476190\pi$
$158$	0	0
$159$	91098.0	0.285770
$160$	0	0
$161$	−48800.0	−0.148373
$162$	0	0
$163$	−185188.	−0.545939	−0.272969	−	0.962023i	$-0.588006\pi$
$163$	−185188.	−0.545939	−0.272969	+	0.962023i	$0.588006\pi$
$164$	0	0
$165$	−30600.0	−0.0875007
$166$	0	0
$167$	−456696.	−1.26717	−0.633587	−	0.773672i	$-0.718418\pi$
$167$	−456696.	−1.26717	−0.633587	+	0.773672i	$0.718418\pi$
$168$	0	0
$169$	−364569.	−0.981890
$170$	0	0
$171$	−64476.0	−0.168620
$172$	0	0
$173$	−202526.	−0.514476	−0.257238	−	0.966348i	$-0.582813\pi$
$173$	−202526.	−0.514476	−0.257238	+	0.966348i	$0.582813\pi$
$174$	0	0
$175$	62500.0	0.154271
$176$	0	0
$177$	60984.0	0.146313
$178$	0	0
$179$	7808.00	0.0182141	0.00910704	−	0.999959i	$-0.497101\pi$
$179$	7808.00	0.0182141	0.00910704	+	0.999959i	$0.497101\pi$
$180$	0	0
$181$	194366.	0.440985	0.220493	−	0.975389i	$-0.429234\pi$
$181$	194366.	0.440985	0.220493	+	0.975389i	$0.429234\pi$
$182$	0	0
$183$	210582.	0.464829
$184$	0	0
$185$	−194850.	−0.418573
$186$	0	0
$187$	48688.0	0.101816
$188$	0	0
$189$	72900.0	0.148448
$190$	0	0
$191$	−383560.	−0.760764	−0.380382	−	0.924829i	$-0.624207\pi$
$191$	−383560.	−0.760764	−0.380382	+	0.924829i	$0.624207\pi$
$192$	0	0
$193$	−718262.	−1.38800	−0.694000	−	0.719975i	$-0.744153\pi$
$193$	−718262.	−1.38800	−0.694000	+	0.719975i	$0.744153\pi$
$194$	0	0
$195$	−18450.0	−0.0347464
$196$	0	0
$197$	342218.	0.628257	0.314128	−	0.949380i	$-0.398288\pi$
$197$	342218.	0.628257	0.314128	+	0.949380i	$0.398288\pi$
$198$	0	0
$199$	−311336.	−0.557310	−0.278655	−	0.960391i	$-0.589889\pi$
$199$	−311336.	−0.557310	−0.278655	+	0.960391i	$0.589889\pi$
$200$	0	0
$201$	87084.0	0.152037
$202$	0	0
$203$	746600.	1.27159
$204$	0	0
$205$	−455850.	−0.757595
$206$	0	0
$207$	−39528.0	−0.0641179
$208$	0	0
$209$	−108256.	−0.171430
$210$	0	0
$211$	−684500.	−1.05844	−0.529221	−	0.848484i	$-0.677516\pi$
$211$	−684500.	−1.05844	−0.529221	+	0.848484i	$0.677516\pi$
$212$	0	0
$213$	−123552.	−0.186595
$214$	0	0
$215$	−61100.0	−0.0901457
$216$	0	0
$217$	−272800.	−0.393274
$218$	0	0
$219$	−246510.	−0.347316
$220$	0	0
$221$	29356.0	0.0404312
$222$	0	0
$223$	−32708.0	−0.0440445	−0.0220223	−	0.999757i	$-0.507010\pi$
$223$	−32708.0	−0.0440445	−0.0220223	+	0.999757i	$0.507010\pi$
$224$	0	0
$225$	50625.0	0.0666667
$226$	0	0
$227$	1.20301e6	1.54955	0.774775	−	0.632238i	$-0.217863\pi$
$227$	1.20301e6	1.54955	0.774775	+	0.632238i	$0.217863\pi$
$228$	0	0
$229$	90022.0	0.113438	0.0567192	−	0.998390i	$-0.481936\pi$
$229$	90022.0	0.113438	0.0567192	+	0.998390i	$0.481936\pi$
$230$	0	0
$231$	122400.	0.150922
$232$	0	0
$233$	−1.61109e6	−1.94415	−0.972076	−	0.234668i	$-0.924600\pi$
$233$	−1.61109e6	−1.94415	−0.972076	+	0.234668i	$0.924600\pi$
$234$	0	0
$235$	−55000.0	−0.0649670
$236$	0	0
$237$	839592.	0.970951
$238$	0	0
$239$	898296.	1.01724	0.508622	−	0.860990i	$-0.330155\pi$
$239$	898296.	1.01724	0.508622	+	0.860990i	$0.330155\pi$
$240$	0	0
$241$	−343102.	−0.380523	−0.190261	−	0.981733i	$-0.560934\pi$
$241$	−343102.	−0.380523	−0.190261	+	0.981733i	$0.560934\pi$
$242$	0	0
$243$	59049.0	0.0641500
$244$	0	0
$245$	170175.	0.181126
$246$	0	0
$247$	−65272.0	−0.0680745
$248$	0	0
$249$	209484.	0.214118
$250$	0	0
$251$	−20400.0	−0.0204384	−0.0102192	−	0.999948i	$-0.503253\pi$
$251$	−20400.0	−0.0204384	−0.0102192	+	0.999948i	$0.503253\pi$
$252$	0	0
$253$	−66368.0	−0.0651865
$254$	0	0
$255$	−80550.0	−0.0775738
$256$	0	0
$257$	−117522.	−0.110991	−0.0554953	−	0.998459i	$-0.517674\pi$
$257$	−117522.	−0.110991	−0.0554953	+	0.998459i	$0.517674\pi$
$258$	0	0
$259$	779400.	0.721956
$260$	0	0
$261$	604746.	0.549505
$262$	0	0
$263$	1.75615e6	1.56557	0.782785	−	0.622292i	$-0.213798\pi$
$263$	1.75615e6	1.56557	0.782785	+	0.622292i	$0.213798\pi$
$264$	0	0
$265$	−253050.	−0.221356
$266$	0	0
$267$	921186.	0.790805
$268$	0	0
$269$	548170.	0.461886	0.230943	−	0.972967i	$-0.425819\pi$
$269$	548170.	0.461886	0.230943	+	0.972967i	$0.425819\pi$
$270$	0	0
$271$	−1.96445e6	−1.62487	−0.812433	−	0.583055i	$-0.801857\pi$
$271$	−1.96445e6	−1.62487	−0.812433	+	0.583055i	$0.801857\pi$
$272$	0	0
$273$	73800.0	0.0599308
$274$	0	0
$275$	85000.0	0.0677778
$276$	0	0
$277$	1.42527e6	1.11608	0.558042	−	0.829813i	$-0.311553\pi$
$277$	1.42527e6	1.11608	0.558042	+	0.829813i	$0.311553\pi$
$278$	0	0
$279$	−220968.	−0.169949
$280$	0	0
$281$	−1.52001e6	−1.14837	−0.574185	−	0.818726i	$-0.694681\pi$
$281$	−1.52001e6	−1.14837	−0.574185	+	0.818726i	$0.694681\pi$
$282$	0	0
$283$	−1.10395e6	−0.819375	−0.409687	−	0.912226i	$-0.634362\pi$
$283$	−1.10395e6	−0.819375	−0.409687	+	0.912226i	$0.634362\pi$
$284$	0	0
$285$	179100.	0.130612
$286$	0	0
$287$	1.82340e6	1.30670
$288$	0	0
$289$	−1.29169e6	−0.909735
$290$	0	0
$291$	−445518.	−0.308413
$292$	0	0
$293$	1.24126e6	0.844682	0.422341	−	0.906437i	$-0.361209\pi$
$293$	1.24126e6	0.844682	0.422341	+	0.906437i	$0.361209\pi$
$294$	0	0
$295$	−169400.	−0.113334
$296$	0	0
$297$	99144.0	0.0652192
$298$	0	0
$299$	−40016.0	−0.0258854
$300$	0	0
$301$	244400.	0.155484
$302$	0	0
$303$	969138.	0.606428
$304$	0	0
$305$	−584950.	−0.360055
$306$	0	0
$307$	772772.	0.467956	0.233978	−	0.972242i	$-0.424826\pi$
$307$	772772.	0.467956	0.233978	+	0.972242i	$0.424826\pi$
$308$	0	0
$309$	1.93208e6	1.15114
$310$	0	0
$311$	−1.31498e6	−0.770933	−0.385467	−	0.922722i	$-0.625960\pi$
$311$	−1.31498e6	−0.770933	−0.385467	+	0.922722i	$0.625960\pi$
$312$	0	0
$313$	693986.	0.400396	0.200198	−	0.979755i	$-0.435841\pi$
$313$	693986.	0.400396	0.200198	+	0.979755i	$0.435841\pi$
$314$	0	0
$315$	−202500.	−0.114987
$316$	0	0
$317$	1.79219e6	1.00170	0.500849	−	0.865535i	$-0.333021\pi$
$317$	1.79219e6	1.00170	0.500849	+	0.865535i	$0.333021\pi$
$318$	0	0
$319$	1.01538e6	0.558663
$320$	0	0
$321$	−458028.	−0.248102
$322$	0	0
$323$	−284968.	−0.151981
$324$	0	0
$325$	51250.0	0.0269144
$326$	0	0
$327$	−155178.	−0.0802529
$328$	0	0
$329$	220000.	0.112055
$330$	0	0
$331$	−1.05378e6	−0.528664	−0.264332	−	0.964432i	$-0.585152\pi$
$331$	−1.05378e6	−0.528664	−0.264332	+	0.964432i	$0.585152\pi$
$332$	0	0
$333$	631314.	0.311986
$334$	0	0
$335$	−241900.	−0.117767
$336$	0	0
$337$	2.92700e6	1.40394	0.701970	−	0.712207i	$-0.252304\pi$
$337$	2.92700e6	1.40394	0.701970	+	0.712207i	$0.252304\pi$
$338$	0	0
$339$	−363042.	−0.171576
$340$	0	0
$341$	−371008.	−0.172782
$342$	0	0
$343$	−2.36140e6	−1.08376
$344$	0	0
$345$	109800.	0.0496655
$346$	0	0
$347$	1.26907e6	0.565798	0.282899	−	0.959150i	$-0.408704\pi$
$347$	1.26907e6	0.565798	0.282899	+	0.959150i	$0.408704\pi$
$348$	0	0
$349$	302790.	0.133069	0.0665347	−	0.997784i	$-0.478806\pi$
$349$	302790.	0.133069	0.0665347	+	0.997784i	$0.478806\pi$
$350$	0	0
$351$	59778.0	0.0258984
$352$	0	0
$353$	2.90292e6	1.23993	0.619966	−	0.784629i	$-0.287146\pi$
$353$	2.90292e6	1.23993	0.619966	+	0.784629i	$0.287146\pi$
$354$	0	0
$355$	343200.	0.144536
$356$	0	0
$357$	322200.	0.133800
$358$	0	0
$359$	−1.75582e6	−0.719023	−0.359512	−	0.933141i	$-0.617057\pi$
$359$	−1.75582e6	−0.719023	−0.359512	+	0.933141i	$0.617057\pi$
$360$	0	0
$361$	−1.84248e6	−0.744107
$362$	0	0
$363$	−1.28300e6	−0.511044
$364$	0	0
$365$	684750.	0.269029
$366$	0	0
$367$	1.20809e6	0.468204	0.234102	−	0.972212i	$-0.424785\pi$
$367$	1.20809e6	0.468204	0.234102	+	0.972212i	$0.424785\pi$
$368$	0	0
$369$	1.47695e6	0.564678
$370$	0	0
$371$	1.01220e6	0.381796
$372$	0	0
$373$	3.92449e6	1.46053	0.730266	−	0.683163i	$-0.239396\pi$
$373$	3.92449e6	1.46053	0.730266	+	0.683163i	$0.239396\pi$
$374$	0	0
$375$	−140625.	−0.0516398
$376$	0	0
$377$	612212.	0.221844
$378$	0	0
$379$	3.34034e6	1.19452	0.597259	−	0.802048i	$-0.296256\pi$
$379$	3.34034e6	1.19452	0.597259	+	0.802048i	$0.296256\pi$
$380$	0	0
$381$	−2.19445e6	−0.774486
$382$	0	0
$383$	3.10020e6	1.07992	0.539961	−	0.841690i	$-0.318439\pi$
$383$	3.10020e6	1.07992	0.539961	+	0.841690i	$0.318439\pi$
$384$	0	0
$385$	−340000.	−0.116903
$386$	0	0
$387$	197964.	0.0671906
$388$	0	0
$389$	1.34750e6	0.451496	0.225748	−	0.974186i	$-0.427517\pi$
$389$	1.34750e6	0.451496	0.225748	+	0.974186i	$0.427517\pi$
$390$	0	0
$391$	−174704.	−0.0577911
$392$	0	0
$393$	−2.73002e6	−0.891631
$394$	0	0
$395$	−2.33220e6	−0.752096
$396$	0	0
$397$	1.79123e6	0.570393	0.285196	−	0.958469i	$-0.407941\pi$
$397$	1.79123e6	0.570393	0.285196	+	0.958469i	$0.407941\pi$
$398$	0	0
$399$	−716400.	−0.225280
$400$	0	0
$401$	−5.44503e6	−1.69098	−0.845492	−	0.533989i	$-0.820693\pi$
$401$	−5.44503e6	−1.69098	−0.845492	+	0.533989i	$0.820693\pi$
$402$	0	0
$403$	−223696.	−0.0686113
$404$	0	0
$405$	−164025.	−0.0496904
$406$	0	0
$407$	1.05998e6	0.317185
$408$	0	0
$409$	−3.64353e6	−1.07699	−0.538497	−	0.842627i	$-0.681008\pi$
$409$	−3.64353e6	−1.07699	−0.538497	+	0.842627i	$0.681008\pi$
$410$	0	0
$411$	2.02037e6	0.589966
$412$	0	0
$413$	677600.	0.195478
$414$	0	0
$415$	−581900.	−0.165855
$416$	0	0
$417$	−2.15665e6	−0.607351
$418$	0	0
$419$	−3.28735e6	−0.914768	−0.457384	−	0.889269i	$-0.651214\pi$
$419$	−3.28735e6	−0.914768	−0.457384	+	0.889269i	$0.651214\pi$
$420$	0	0
$421$	−5.50905e6	−1.51486	−0.757428	−	0.652918i	$-0.773544\pi$
$421$	−5.50905e6	−1.51486	−0.757428	+	0.652918i	$0.773544\pi$
$422$	0	0
$423$	178200.	0.0484236
$424$	0	0
$425$	223750.	0.0600884
$426$	0	0
$427$	2.33980e6	0.621025
$428$	0	0
$429$	100368.	0.0263301
$430$	0	0
$431$	372368.	0.0965560	0.0482780	−	0.998834i	$-0.484627\pi$
$431$	372368.	0.0965560	0.0482780	+	0.998834i	$0.484627\pi$
$432$	0	0
$433$	3.18271e6	0.815789	0.407895	−	0.913029i	$-0.366263\pi$
$433$	3.18271e6	0.815789	0.407895	+	0.913029i	$0.366263\pi$
$434$	0	0
$435$	−1.67985e6	−0.425645
$436$	0	0
$437$	388448.	0.0973037
$438$	0	0
$439$	5.20652e6	1.28940	0.644698	−	0.764437i	$-0.276983\pi$
$439$	5.20652e6	1.28940	0.644698	+	0.764437i	$0.276983\pi$
$440$	0	0
$441$	−551367.	−0.135003
$442$	0	0
$443$	−5.32410e6	−1.28895	−0.644476	−	0.764624i	$-0.722925\pi$
$443$	−5.32410e6	−1.28895	−0.644476	+	0.764624i	$0.722925\pi$
$444$	0	0
$445$	−2.55885e6	−0.612555
$446$	0	0
$447$	3.48979e6	0.826095
$448$	0	0
$449$	1.28563e6	0.300953	0.150477	−	0.988614i	$-0.451919\pi$
$449$	1.28563e6	0.300953	0.150477	+	0.988614i	$0.451919\pi$
$450$	0	0
$451$	2.47982e6	0.574089
$452$	0	0
$453$	−4.78966e6	−1.09663
$454$	0	0
$455$	−205000.	−0.0464222
$456$	0	0
$457$	−6.07156e6	−1.35991	−0.679954	−	0.733255i	$-0.738000\pi$
$457$	−6.07156e6	−1.35991	−0.679954	+	0.733255i	$0.738000\pi$
$458$	0	0
$459$	260982.	0.0578201
$460$	0	0
$461$	−5.59141e6	−1.22537	−0.612687	−	0.790326i	$-0.709911\pi$
$461$	−5.59141e6	−1.22537	−0.612687	+	0.790326i	$0.709911\pi$
$462$	0	0
$463$	−6.05881e6	−1.31351	−0.656757	−	0.754102i	$-0.728072\pi$
$463$	−6.05881e6	−1.31351	−0.656757	+	0.754102i	$0.728072\pi$
$464$	0	0
$465$	613800.	0.131642
$466$	0	0
$467$	−2.66636e6	−0.565752	−0.282876	−	0.959157i	$-0.591288\pi$
$467$	−2.66636e6	−0.565752	−0.282876	+	0.959157i	$0.591288\pi$
$468$	0	0
$469$	967600.	0.203125
$470$	0	0
$471$	415458.	0.0862929
$472$	0	0
$473$	332384.	0.0683105
$474$	0	0
$475$	−497500.	−0.101172
$476$	0	0
$477$	819882.	0.164989
$478$	0	0
$479$	−1.76578e6	−0.351640	−0.175820	−	0.984422i	$-0.556258\pi$
$479$	−1.76578e6	−0.351640	−0.175820	+	0.984422i	$0.556258\pi$
$480$	0	0
$481$	639108.	0.125954
$482$	0	0
$483$	−439200.	−0.0856632
$484$	0	0
$485$	1.23755e6	0.238896
$486$	0	0
$487$	1.27339e6	0.243298	0.121649	−	0.992573i	$-0.461182\pi$
$487$	1.27339e6	0.243298	0.121649	+	0.992573i	$0.461182\pi$
$488$	0	0
$489$	−1.66669e6	−0.315198
$490$	0	0
$491$	−6.07997e6	−1.13814	−0.569072	−	0.822287i	$-0.692698\pi$
$491$	−6.07997e6	−1.13814	−0.569072	+	0.822287i	$0.692698\pi$
$492$	0	0
$493$	2.67283e6	0.495283
$494$	0	0
$495$	−275400.	−0.0505186
$496$	0	0
$497$	−1.37280e6	−0.249297
$498$	0	0
$499$	9.53655e6	1.71451	0.857255	−	0.514893i	$-0.172168\pi$
$499$	9.53655e6	1.71451	0.857255	+	0.514893i	$0.172168\pi$
$500$	0	0
$501$	−4.11026e6	−0.731603
$502$	0	0
$503$	−1.97458e6	−0.347980	−0.173990	−	0.984747i	$-0.555666\pi$
$503$	−1.97458e6	−0.347980	−0.173990	+	0.984747i	$0.555666\pi$
$504$	0	0
$505$	−2.69205e6	−0.469737
$506$	0	0
$507$	−3.28112e6	−0.566895
$508$	0	0
$509$	2.47755e6	0.423865	0.211932	−	0.977284i	$-0.432024\pi$
$509$	2.47755e6	0.423865	0.211932	+	0.977284i	$0.432024\pi$
$510$	0	0
$511$	−2.73900e6	−0.464023
$512$	0	0
$513$	−580284.	−0.0973525
$514$	0	0
$515$	−5.36690e6	−0.891673
$516$	0	0
$517$	299200.	0.0492306
$518$	0	0
$519$	−1.82273e6	−0.297033
$520$	0	0
$521$	−4.01025e6	−0.647258	−0.323629	−	0.946184i	$-0.604903\pi$
$521$	−4.01025e6	−0.647258	−0.323629	+	0.946184i	$0.604903\pi$
$522$	0	0
$523$	−1.00486e7	−1.60640	−0.803199	−	0.595711i	$-0.796870\pi$
$523$	−1.00486e7	−1.60640	−0.803199	+	0.595711i	$0.796870\pi$
$524$	0	0
$525$	562500.	0.0890685
$526$	0	0
$527$	−976624.	−0.153180
$528$	0	0
$529$	−6.19820e6	−0.963000
$530$	0	0
$531$	548856.	0.0844738
$532$	0	0
$533$	1.49519e6	0.227970
$534$	0	0
$535$	1.27230e6	0.192179
$536$	0	0
$537$	70272.0	0.0105159
$538$	0	0
$539$	−925752.	−0.137253
$540$	0	0
$541$	4.52474e6	0.664662	0.332331	−	0.943163i	$-0.392165\pi$
$541$	4.52474e6	0.664662	0.332331	+	0.943163i	$0.392165\pi$
$542$	0	0
$543$	1.74929e6	0.254603
$544$	0	0
$545$	431050.	0.0621636
$546$	0	0
$547$	1.06567e7	1.52284	0.761422	−	0.648257i	$-0.224502\pi$
$547$	1.06567e7	1.52284	0.761422	+	0.648257i	$0.224502\pi$
$548$	0	0
$549$	1.89524e6	0.268369
$550$	0	0
$551$	−5.94294e6	−0.833916
$552$	0	0
$553$	9.32880e6	1.29722
$554$	0	0
$555$	−1.75365e6	−0.241663
$556$	0	0
$557$	−8.09545e6	−1.10561	−0.552807	−	0.833310i	$-0.686443\pi$
$557$	−8.09545e6	−1.10561	−0.552807	+	0.833310i	$0.686443\pi$
$558$	0	0
$559$	200408.	0.0271260
$560$	0	0
$561$	438192.	0.0587838
$562$	0	0
$563$	5.55903e6	0.739142	0.369571	−	0.929202i	$-0.379505\pi$
$563$	5.55903e6	0.739142	0.369571	+	0.929202i	$0.379505\pi$
$564$	0	0
$565$	1.00845e6	0.132903
$566$	0	0
$567$	656100.	0.0857062
$568$	0	0
$569$	4.10005e6	0.530895	0.265447	−	0.964125i	$-0.414480\pi$
$569$	4.10005e6	0.530895	0.265447	+	0.964125i	$0.414480\pi$
$570$	0	0
$571$	5.76076e6	0.739418	0.369709	−	0.929148i	$-0.379457\pi$
$571$	5.76076e6	0.739418	0.369709	+	0.929148i	$0.379457\pi$
$572$	0	0
$573$	−3.45204e6	−0.439227
$574$	0	0
$575$	−305000.	−0.0384707
$576$	0	0
$577$	1.13430e7	1.41836	0.709182	−	0.705026i	$-0.249065\pi$
$577$	1.13430e7	1.41836	0.709182	+	0.705026i	$0.249065\pi$
$578$	0	0
$579$	−6.46436e6	−0.801362
$580$	0	0
$581$	2.32760e6	0.286067
$582$	0	0
$583$	1.37659e6	0.167739
$584$	0	0
$585$	−166050.	−0.0200608
$586$	0	0
$587$	−6.67652e6	−0.799752	−0.399876	−	0.916569i	$-0.630947\pi$
$587$	−6.67652e6	−0.799752	−0.399876	+	0.916569i	$0.630947\pi$
$588$	0	0
$589$	2.17149e6	0.257911
$590$	0	0
$591$	3.07996e6	0.362724
$592$	0	0
$593$	1.06401e7	1.24254	0.621268	−	0.783598i	$-0.286618\pi$
$593$	1.06401e7	1.24254	0.621268	+	0.783598i	$0.286618\pi$
$594$	0	0
$595$	−895000.	−0.103641
$596$	0	0
$597$	−2.80202e6	−0.321763
$598$	0	0
$599$	−2.23082e6	−0.254038	−0.127019	−	0.991900i	$-0.540541\pi$
$599$	−2.23082e6	−0.254038	−0.127019	+	0.991900i	$0.540541\pi$
$600$	0	0
$601$	1.28844e7	1.45505	0.727523	−	0.686083i	$-0.240671\pi$
$601$	1.28844e7	1.45505	0.727523	+	0.686083i	$0.240671\pi$
$602$	0	0
$603$	783756.	0.0877784
$604$	0	0
$605$	3.56388e6	0.395853
$606$	0	0
$607$	−3.03342e6	−0.334165	−0.167082	−	0.985943i	$-0.553435\pi$
$607$	−3.03342e6	−0.334165	−0.167082	+	0.985943i	$0.553435\pi$
$608$	0	0
$609$	6.71940e6	0.734154
$610$	0	0
$611$	180400.	0.0195494
$612$	0	0
$613$	6.54520e6	0.703513	0.351756	−	0.936092i	$-0.385585\pi$
$613$	6.54520e6	0.703513	0.351756	+	0.936092i	$0.385585\pi$
$614$	0	0
$615$	−4.10265e6	−0.437398
$616$	0	0
$617$	8.45360e6	0.893982	0.446991	−	0.894539i	$-0.352496\pi$
$617$	8.45360e6	0.893982	0.446991	+	0.894539i	$0.352496\pi$
$618$	0	0
$619$	1.38643e7	1.45436	0.727180	−	0.686447i	$-0.240830\pi$
$619$	1.38643e7	1.45436	0.727180	+	0.686447i	$0.240830\pi$
$620$	0	0
$621$	−355752.	−0.0370185
$622$	0	0
$623$	1.02354e7	1.05654
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	−974304.	−0.0989750
$628$	0	0
$629$	2.79025e6	0.281201
$630$	0	0
$631$	−1.35281e7	−1.35258	−0.676290	−	0.736635i	$-0.736414\pi$
$631$	−1.35281e7	−1.35258	−0.676290	+	0.736635i	$0.736414\pi$
$632$	0	0
$633$	−6.16050e6	−0.611092
$634$	0	0
$635$	6.09570e6	0.599914
$636$	0	0
$637$	−558174.	−0.0545031
$638$	0	0
$639$	−1.11197e6	−0.107731
$640$	0	0
$641$	−1.20292e7	−1.15636	−0.578179	−	0.815910i	$-0.696236\pi$
$641$	−1.20292e7	−1.15636	−0.578179	+	0.815910i	$0.696236\pi$
$642$	0	0
$643$	5.92393e6	0.565044	0.282522	−	0.959261i	$-0.408829\pi$
$643$	5.92393e6	0.565044	0.282522	+	0.959261i	$0.408829\pi$
$644$	0	0
$645$	−549900.	−0.0520456
$646$	0	0
$647$	1.26269e6	0.118587	0.0592933	−	0.998241i	$-0.481115\pi$
$647$	1.26269e6	0.118587	0.0592933	+	0.998241i	$0.481115\pi$
$648$	0	0
$649$	921536.	0.0858817
$650$	0	0
$651$	−2.45520e6	−0.227057
$652$	0	0
$653$	−1.87108e7	−1.71716	−0.858579	−	0.512681i	$-0.828653\pi$
$653$	−1.87108e7	−1.71716	−0.858579	+	0.512681i	$0.828653\pi$
$654$	0	0
$655$	7.58340e6	0.690654
$656$	0	0
$657$	−2.21859e6	−0.200523
$658$	0	0
$659$	−952872.	−0.0854714	−0.0427357	−	0.999086i	$-0.513607\pi$
$659$	−952872.	−0.0854714	−0.0427357	+	0.999086i	$0.513607\pi$
$660$	0	0
$661$	5.16771e6	0.460039	0.230019	−	0.973186i	$-0.426121\pi$
$661$	5.16771e6	0.460039	0.230019	+	0.973186i	$0.426121\pi$
$662$	0	0
$663$	264204.	0.0233429
$664$	0	0
$665$	1.99000e6	0.174501
$666$	0	0
$667$	−3.64341e6	−0.317098
$668$	0	0
$669$	−294372.	−0.0254291
$670$	0	0
$671$	3.18213e6	0.272842
$672$	0	0
$673$	3.34195e6	0.284421	0.142211	−	0.989836i	$-0.454579\pi$
$673$	3.34195e6	0.284421	0.142211	+	0.989836i	$0.454579\pi$
$674$	0	0
$675$	455625.	0.0384900
$676$	0	0
$677$	−1.94248e7	−1.62886	−0.814430	−	0.580261i	$-0.802950\pi$
$677$	−1.94248e7	−1.62886	−0.814430	+	0.580261i	$0.802950\pi$
$678$	0	0
$679$	−4.95020e6	−0.412048
$680$	0	0
$681$	1.08271e7	0.894633
$682$	0	0
$683$	1.56262e7	1.28175	0.640874	−	0.767646i	$-0.278572\pi$
$683$	1.56262e7	1.28175	0.640874	+	0.767646i	$0.278572\pi$
$684$	0	0
$685$	−5.61215e6	−0.456986
$686$	0	0
$687$	810198.	0.0654937
$688$	0	0
$689$	830004.	0.0666089
$690$	0	0
$691$	2.19643e7	1.74994	0.874969	−	0.484179i	$-0.160882\pi$
$691$	2.19643e7	1.74994	0.874969	+	0.484179i	$0.160882\pi$
$692$	0	0
$693$	1.10160e6	0.0871346
$694$	0	0
$695$	5.99070e6	0.470452
$696$	0	0
$697$	6.52777e6	0.508959
$698$	0	0
$699$	−1.44998e7	−1.12246
$700$	0	0
$701$	−6.16069e6	−0.473516	−0.236758	−	0.971569i	$-0.576085\pi$
$701$	−6.16069e6	−0.473516	−0.236758	+	0.971569i	$0.576085\pi$
$702$	0	0
$703$	−6.20402e6	−0.473462
$704$	0	0
$705$	−495000.	−0.0375087
$706$	0	0
$707$	1.07682e7	0.810204
$708$	0	0
$709$	−2.09832e7	−1.56768	−0.783838	−	0.620965i	$-0.786741\pi$
$709$	−2.09832e7	−1.56768	−0.783838	+	0.620965i	$0.786741\pi$
$710$	0	0
$711$	7.55633e6	0.560579
$712$	0	0
$713$	1.33126e6	0.0980709
$714$	0	0
$715$	−278800.	−0.0203952
$716$	0	0
$717$	8.08466e6	0.587306
$718$	0	0
$719$	1.02479e7	0.739284	0.369642	−	0.929174i	$-0.379480\pi$
$719$	1.02479e7	0.739284	0.369642	+	0.929174i	$0.379480\pi$
$720$	0	0
$721$	2.14676e7	1.53796
$722$	0	0
$723$	−3.08792e6	−0.219695
$724$	0	0
$725$	4.66625e6	0.329703
$726$	0	0
$727$	−1.59746e7	−1.12097	−0.560485	−	0.828164i	$-0.689385\pi$
$727$	−1.59746e7	−1.12097	−0.560485	+	0.828164i	$0.689385\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	874952.	0.0605607
$732$	0	0
$733$	−2.03547e7	−1.39928	−0.699640	−	0.714496i	$-0.746656\pi$
$733$	−2.03547e7	−1.39928	−0.699640	+	0.714496i	$0.746656\pi$
$734$	0	0
$735$	1.53158e6	0.104573
$736$	0	0
$737$	1.31594e6	0.0892413
$738$	0	0
$739$	1.19986e7	0.808204	0.404102	−	0.914714i	$-0.367584\pi$
$739$	1.19986e7	0.808204	0.404102	+	0.914714i	$0.367584\pi$
$740$	0	0
$741$	−587448.	−0.0393028
$742$	0	0
$743$	2.41346e7	1.60387	0.801933	−	0.597414i	$-0.203805\pi$
$743$	2.41346e7	1.60387	0.801933	+	0.597414i	$0.203805\pi$
$744$	0	0
$745$	−9.69385e6	−0.639890
$746$	0	0
$747$	1.88536e6	0.123621
$748$	0	0
$749$	−5.08920e6	−0.331471
$750$	0	0
$751$	1.15150e6	0.0745011	0.0372505	−	0.999306i	$-0.488140\pi$
$751$	1.15150e6	0.0745011	0.0372505	+	0.999306i	$0.488140\pi$
$752$	0	0
$753$	−183600.	−0.0118001
$754$	0	0
$755$	1.33046e7	0.849443
$756$	0	0
$757$	1.19330e7	0.756853	0.378426	−	0.925631i	$-0.376465\pi$
$757$	1.19330e7	0.756853	0.378426	+	0.925631i	$0.376465\pi$
$758$	0	0
$759$	−597312.	−0.0376354
$760$	0	0
$761$	1.38917e7	0.869548	0.434774	−	0.900540i	$-0.356828\pi$
$761$	1.38917e7	0.869548	0.434774	+	0.900540i	$0.356828\pi$
$762$	0	0
$763$	−1.72420e6	−0.107220
$764$	0	0
$765$	−724950.	−0.0447873
$766$	0	0
$767$	555632.	0.0341035
$768$	0	0
$769$	−1.06970e7	−0.652296	−0.326148	−	0.945319i	$-0.605751\pi$
$769$	−1.06970e7	−0.652296	−0.326148	+	0.945319i	$0.605751\pi$
$770$	0	0
$771$	−1.05770e6	−0.0640805
$772$	0	0
$773$	−1.05827e7	−0.637010	−0.318505	−	0.947921i	$-0.603181\pi$
$773$	−1.05827e7	−0.637010	−0.318505	+	0.947921i	$0.603181\pi$
$774$	0	0
$775$	−1.70500e6	−0.101969
$776$	0	0
$777$	7.01460e6	0.416822
$778$	0	0
$779$	−1.45143e7	−0.856942
$780$	0	0
$781$	−1.86701e6	−0.109526
$782$	0	0
$783$	5.44271e6	0.317257
$784$	0	0
$785$	−1.15405e6	−0.0668422
$786$	0	0
$787$	−6.23781e6	−0.359001	−0.179500	−	0.983758i	$-0.557448\pi$
$787$	−6.23781e6	−0.359001	−0.179500	+	0.983758i	$0.557448\pi$
$788$	0	0
$789$	1.58054e7	0.903883
$790$	0	0
$791$	−4.03380e6	−0.229231
$792$	0	0
$793$	1.91864e6	0.108345
$794$	0	0
$795$	−2.27745e6	−0.127800
$796$	0	0
$797$	4.59266e6	0.256105	0.128053	−	0.991767i	$-0.459127\pi$
$797$	4.59266e6	0.256105	0.128053	+	0.991767i	$0.459127\pi$
$798$	0	0
$799$	787600.	0.0436454
$800$	0	0
$801$	8.29067e6	0.456571
$802$	0	0
$803$	−3.72504e6	−0.203865
$804$	0	0
$805$	1.22000e6	0.0663545
$806$	0	0
$807$	4.93353e6	0.266670
$808$	0	0
$809$	−13974.0	−0.000750671 0	−0.000375335	−	1.00000i	$-0.500119\pi$
$809$	−13974.0	−0.000750671 0	−0.000375335		1.00000i	$0.500119\pi$
$810$	0	0
$811$	−2.05971e7	−1.09965	−0.549824	−	0.835281i	$-0.685305\pi$
$811$	−2.05971e7	−1.09965	−0.549824	+	0.835281i	$0.685305\pi$
$812$	0	0
$813$	−1.76800e7	−0.938116
$814$	0	0
$815$	4.62970e6	0.244151
$816$	0	0
$817$	−1.94542e6	−0.101967
$818$	0	0
$819$	664200.	0.0346010
$820$	0	0
$821$	−6.28819e6	−0.325588	−0.162794	−	0.986660i	$-0.552051\pi$
$821$	−6.28819e6	−0.325588	−0.162794	+	0.986660i	$0.552051\pi$
$822$	0	0
$823$	−2.51673e7	−1.29520	−0.647601	−	0.761980i	$-0.724227\pi$
$823$	−2.51673e7	−1.29520	−0.647601	+	0.761980i	$0.724227\pi$
$824$	0	0
$825$	765000.	0.0391315
$826$	0	0
$827$	−2.81270e7	−1.43008	−0.715040	−	0.699084i	$-0.753591\pi$
$827$	−2.81270e7	−1.43008	−0.715040	+	0.699084i	$0.753591\pi$
$828$	0	0
$829$	8.41903e6	0.425477	0.212738	−	0.977109i	$-0.431762\pi$
$829$	8.41903e6	0.425477	0.212738	+	0.977109i	$0.431762\pi$
$830$	0	0
$831$	1.28274e7	0.644371
$832$	0	0
$833$	−2.43691e6	−0.121682
$834$	0	0
$835$	1.14174e7	0.566697
$836$	0	0
$837$	−1.98871e6	−0.0981202
$838$	0	0
$839$	−1.89551e7	−0.929653	−0.464827	−	0.885402i	$-0.653883\pi$
$839$	−1.89551e7	−0.929653	−0.464827	+	0.885402i	$0.653883\pi$
$840$	0	0
$841$	3.52300e7	1.71760
$842$	0	0
$843$	−1.36801e7	−0.663012
$844$	0	0
$845$	9.11422e6	0.439115
$846$	0	0
$847$	−1.42555e7	−0.682769
$848$	0	0
$849$	−9.93553e6	−0.473066
$850$	0	0
$851$	−3.80347e6	−0.180035
$852$	0	0
$853$	−4.02367e7	−1.89343	−0.946715	−	0.322071i	$-0.895621\pi$
$853$	−4.02367e7	−1.89343	−0.946715	+	0.322071i	$0.895621\pi$
$854$	0	0
$855$	1.61190e6	0.0754089
$856$	0	0
$857$	−1.79800e6	−0.0836254	−0.0418127	−	0.999125i	$-0.513313\pi$
$857$	−1.79800e6	−0.0836254	−0.0418127	+	0.999125i	$0.513313\pi$
$858$	0	0
$859$	−3.05419e7	−1.41225	−0.706127	−	0.708085i	$-0.749559\pi$
$859$	−3.05419e7	−1.41225	−0.706127	+	0.708085i	$0.749559\pi$
$860$	0	0
$861$	1.64106e7	0.754426
$862$	0	0
$863$	2.66441e7	1.21780	0.608898	−	0.793249i	$-0.291612\pi$
$863$	2.66441e7	1.21780	0.608898	+	0.793249i	$0.291612\pi$
$864$	0	0
$865$	5.06315e6	0.230081
$866$	0	0
$867$	−1.16252e7	−0.525235
$868$	0	0
$869$	1.26872e7	0.569922
$870$	0	0
$871$	793432.	0.0354376
$872$	0	0
$873$	−4.00966e6	−0.178062
$874$	0	0
$875$	−1.56250e6	−0.0689922
$876$	0	0
$877$	−2.10934e7	−0.926079	−0.463040	−	0.886338i	$-0.653241\pi$
$877$	−2.10934e7	−0.926079	−0.463040	+	0.886338i	$0.653241\pi$
$878$	0	0
$879$	1.11713e7	0.487677
$880$	0	0
$881$	1.38507e7	0.601219	0.300610	−	0.953747i	$-0.402810\pi$
$881$	1.38507e7	0.601219	0.300610	+	0.953747i	$0.402810\pi$
$882$	0	0
$883$	−856484.	−0.0369673	−0.0184836	−	0.999829i	$-0.505884\pi$
$883$	−856484.	−0.0369673	−0.0184836	+	0.999829i	$0.505884\pi$
$884$	0	0
$885$	−1.52460e6	−0.0654331
$886$	0	0
$887$	−3.03117e7	−1.29360	−0.646801	−	0.762659i	$-0.723894\pi$
$887$	−3.03117e7	−1.29360	−0.646801	+	0.762659i	$0.723894\pi$
$888$	0	0
$889$	−2.43828e7	−1.03474
$890$	0	0
$891$	892296.	0.0376543
$892$	0	0
$893$	−1.75120e6	−0.0734864
$894$	0	0
$895$	−195200.	−0.00814558
$896$	0	0
$897$	−360144.	−0.0149450
$898$	0	0
$899$	−2.03672e7	−0.840491
$900$	0	0
$901$	3.62368e6	0.148709
$902$	0	0
$903$	2.19960e6	0.0897686
$904$	0	0
$905$	−4.85915e6	−0.197215
$906$	0	0
$907$	1.96327e7	0.792431	0.396216	−	0.918158i	$-0.370323\pi$
$907$	1.96327e7	0.792431	0.396216	+	0.918158i	$0.370323\pi$
$908$	0	0
$909$	8.72224e6	0.350121
$910$	0	0
$911$	−2.84250e6	−0.113476	−0.0567380	−	0.998389i	$-0.518070\pi$
$911$	−2.84250e6	−0.113476	−0.0567380	+	0.998389i	$0.518070\pi$
$912$	0	0
$913$	3.16554e6	0.125681
$914$	0	0
$915$	−5.26455e6	−0.207878
$916$	0	0
$917$	−3.03336e7	−1.19124
$918$	0	0
$919$	−4.20686e7	−1.64312	−0.821560	−	0.570123i	$-0.806896\pi$
$919$	−4.20686e7	−1.64312	−0.821560	+	0.570123i	$0.806896\pi$
$920$	0	0
$921$	6.95495e6	0.270175
$922$	0	0
$923$	−1.12570e6	−0.0434928
$924$	0	0
$925$	4.87125e6	0.187191
$926$	0	0
$927$	1.73888e7	0.664614
$928$	0	0
$929$	−3.50094e7	−1.33090	−0.665449	−	0.746443i	$-0.731760\pi$
$929$	−3.50094e7	−1.33090	−0.665449	+	0.746443i	$0.731760\pi$
$930$	0	0
$931$	5.41837e6	0.204878
$932$	0	0
$933$	−1.18348e7	−0.445099
$934$	0	0
$935$	−1.21720e6	−0.0455337
$936$	0	0
$937$	−1.36631e7	−0.508395	−0.254198	−	0.967152i	$-0.581811\pi$
$937$	−1.36631e7	−0.508395	−0.254198	+	0.967152i	$0.581811\pi$
$938$	0	0
$939$	6.24587e6	0.231169
$940$	0	0
$941$	3.00244e7	1.10535	0.552675	−	0.833397i	$-0.313607\pi$
$941$	3.00244e7	1.10535	0.552675	+	0.833397i	$0.313607\pi$
$942$	0	0
$943$	−8.89819e6	−0.325854
$944$	0	0
$945$	−1.82250e6	−0.0663878
$946$	0	0
$947$	−1.02465e7	−0.371279	−0.185640	−	0.982618i	$-0.559436\pi$
$947$	−1.02465e7	−0.371279	−0.185640	+	0.982618i	$0.559436\pi$
$948$	0	0
$949$	−2.24598e6	−0.0809544
$950$	0	0
$951$	1.61297e7	0.578331
$952$	0	0
$953$	4.96937e7	1.77243	0.886216	−	0.463273i	$-0.153325\pi$
$953$	4.96937e7	1.77243	0.886216	+	0.463273i	$0.153325\pi$
$954$	0	0
$955$	9.58900e6	0.340224
$956$	0	0
$957$	9.13838e6	0.322544
$958$	0	0
$959$	2.24486e7	0.788211
$960$	0	0
$961$	−2.11872e7	−0.740056
$962$	0	0
$963$	−4.12225e6	−0.143241
$964$	0	0
$965$	1.79566e7	0.620733
$966$	0	0
$967$	−3.60558e7	−1.23996	−0.619982	−	0.784616i	$-0.712860\pi$
$967$	−3.60558e7	−1.23996	−0.619982	+	0.784616i	$0.712860\pi$
$968$	0	0
$969$	−2.56471e6	−0.0877464
$970$	0	0
$971$	−4.64940e7	−1.58252	−0.791260	−	0.611480i	$-0.790574\pi$
$971$	−4.64940e7	−1.58252	−0.791260	+	0.611480i	$0.790574\pi$
$972$	0	0
$973$	−2.39628e7	−0.811438
$974$	0	0
$975$	461250.	0.0155391
$976$	0	0
$977$	−4.39457e6	−0.147292	−0.0736461	−	0.997284i	$-0.523464\pi$
$977$	−4.39457e6	−0.147292	−0.0736461	+	0.997284i	$0.523464\pi$
$978$	0	0
$979$	1.39201e7	0.464181
$980$	0	0
$981$	−1.39660e6	−0.0463340
$982$	0	0
$983$	2.36602e6	0.0780969	0.0390485	−	0.999237i	$-0.487567\pi$
$983$	2.36602e6	0.0780969	0.0390485	+	0.999237i	$0.487567\pi$
$984$	0	0
$985$	−8.55545e6	−0.280965
$986$	0	0
$987$	1.98000e6	0.0646952
$988$	0	0
$989$	−1.19267e6	−0.0387731
$990$	0	0
$991$	1.48398e7	0.480004	0.240002	−	0.970772i	$-0.422852\pi$
$991$	1.48398e7	0.480004	0.240002	+	0.970772i	$0.422852\pi$
$992$	0	0
$993$	−9.48402e6	−0.305224
$994$	0	0
$995$	7.78340e6	0.249237
$996$	0	0
$997$	−4.88909e7	−1.55772	−0.778862	−	0.627195i	$-0.784203\pi$
$997$	−4.88909e7	−1.55772	−0.778862	+	0.627195i	$0.784203\pi$
$998$	0	0
$999$	5.68183e6	0.180125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.6.a.j.1.1		1
3.2	odd	2		720.6.a.u.1.1		1
4.3	odd	2		120.6.a.a.1.1	✓	1
8.3	odd	2		960.6.a.w.1.1		1
8.5	even	2		960.6.a.l.1.1		1
12.11	even	2		360.6.a.e.1.1		1
20.3	even	4		600.6.f.e.49.1		2
20.7	even	4		600.6.f.e.49.2		2
20.19	odd	2		600.6.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.6.a.a.1.1	✓	1	4.3	odd	2
240.6.a.j.1.1		1	1.1	even	1	trivial
360.6.a.e.1.1		1	12.11	even	2
600.6.a.h.1.1		1	20.19	odd	2
600.6.f.e.49.1		2	20.3	even	4
600.6.f.e.49.2		2	20.7	even	4
720.6.a.u.1.1		1	3.2	odd	2
960.6.a.l.1.1		1	8.5	even	2
960.6.a.w.1.1		1	8.3	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	240.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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