LMFDB - Embedded newform 354.5.d.a.235.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,5,Mod(235,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	354.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$36.5929669317$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.11
Character	$\chi$	$=$	354.235
Dual form			354.5.d.a.235.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +0.345303 q^{5} +14.6969i q^{6} +29.1133 q^{7} +22.6274i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +0.345303 q^{5} +14.6969i q^{6} +29.1133 q^{7} +22.6274i q^{8} +27.0000 q^{9} -0.976665i q^{10} +119.336i q^{11} +41.5692 q^{12} -304.514i q^{13} -82.3449i q^{14} -1.79425 q^{15} +64.0000 q^{16} -229.594 q^{17} -76.3675i q^{18} -43.2841 q^{19} -2.76243 q^{20} -151.277 q^{21} +337.535 q^{22} +559.546i q^{23} -117.576i q^{24} -624.881 q^{25} -861.295 q^{26} -140.296 q^{27} -232.906 q^{28} -303.900 q^{29} +5.07490i q^{30} +487.779i q^{31} -181.019i q^{32} -620.091i q^{33} +649.390i q^{34} +10.0529 q^{35} -216.000 q^{36} -59.5851i q^{37} +122.426i q^{38} +1582.30i q^{39} +7.81332i q^{40} +2970.49 q^{41} +427.876i q^{42} +556.297i q^{43} -954.692i q^{44} +9.32319 q^{45} +1582.63 q^{46} +880.855i q^{47} -332.554 q^{48} -1553.42 q^{49} +1767.43i q^{50} +1193.01 q^{51} +2436.11i q^{52} -913.151 q^{53} +396.817i q^{54} +41.2073i q^{55} +658.759i q^{56} +224.911 q^{57} +859.558i q^{58} +(2730.34 + 2159.31i) q^{59} +14.3540 q^{60} +2119.11i q^{61} +1379.65 q^{62} +786.059 q^{63} -512.000 q^{64} -105.150i q^{65} -1753.88 q^{66} +5970.68i q^{67} +1836.75 q^{68} -2907.49i q^{69} -28.4340i q^{70} +3795.02 q^{71} +610.940i q^{72} +8963.57i q^{73} -168.532 q^{74} +3246.98 q^{75} +346.273 q^{76} +3474.28i q^{77} +4475.42 q^{78} +2347.21 q^{79} +22.0994 q^{80} +729.000 q^{81} -8401.81i q^{82} +193.448i q^{83} +1210.22 q^{84} -79.2796 q^{85} +1573.44 q^{86} +1579.11 q^{87} -2700.28 q^{88} -769.166i q^{89} -26.3700i q^{90} -8865.40i q^{91} -4476.37i q^{92} -2534.57i q^{93} +2491.43 q^{94} -14.9461 q^{95} +940.604i q^{96} +3332.34i q^{97} +4393.72i q^{98} +3222.09i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) $ 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9	$ 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} - 144 q^{15} + 2560 q^{16} + 480 q^{17} - 792 q^{19} - 1024 q^{22} + 3400 q^{25} + 768 q^{26} + 640 q^{28} + 1608 q^{29} - 5760 q^{35} - 8640 q^{36} + 6264 q^{41} + 7040 q^{46} + 17912 q^{49} + 1296 q^{51} - 1104 q^{53} + 5040 q^{57} + 13584 q^{59} + 1152 q^{60} - 12288 q^{62} - 2160 q^{63} - 20480 q^{64} + 1152 q^{66} - 3840 q^{68} + 35352 q^{71} + 4608 q^{74} + 3168 q^{75} + 6336 q^{76} - 12672 q^{78} - 15720 q^{79} + 29160 q^{81} - 26872 q^{85} + 18432 q^{86} + 7776 q^{87} + 8192 q^{88} - 18432 q^{94} - 19128 q^{95}+O(q^{100}) $ 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9 - 144 * q^15 + 2560 * q^16 + 480 * q^17 - 792 * q^19 - 1024 * q^22 + 3400 * q^25 + 768 * q^26 + 640 * q^28 + 1608 * q^29 - 5760 * q^35 - 8640 * q^36 + 6264 * q^41 + 7040 * q^46 + 17912 * q^49 + 1296 * q^51 - 1104 * q^53 + 5040 * q^57 + 13584 * q^59 + 1152 * q^60 - 12288 * q^62 - 2160 * q^63 - 20480 * q^64 + 1152 * q^66 - 3840 * q^68 + 35352 * q^71 + 4608 * q^74 + 3168 * q^75 + 6336 * q^76 - 12672 * q^78 - 15720 * q^79 + 29160 * q^81 - 26872 * q^85 + 18432 * q^86 + 7776 * q^87 + 8192 * q^88 - 18432 * q^94 - 19128 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	−8.00000			−0.500000
$5$	0.345303			0.0138121			0.00690607	−	0.999976i	$-0.497802\pi$
$5$	0.345303			0.0138121			0.00690607	+	0.999976i	$0.497802\pi$
$6$			14.6969i			0.408248i
$7$	29.1133			0.594149			0.297075	−	0.954854i	$-0.403989\pi$
$7$	29.1133			0.594149			0.297075	+	0.954854i	$0.403989\pi$
$8$			22.6274i			0.353553i
$9$	27.0000			0.333333
$10$		−	0.976665i		−	0.00976665i
$11$			119.336i			0.986252i	0.869958	+	0.493126i	$0.164146\pi$
$11$			119.336i			0.986252i	−0.869958	+	0.493126i	$0.835854\pi$
$12$	41.5692			0.288675
$13$		−	304.514i		−	1.80186i	−0.433968	−	0.900928i	$-0.642887\pi$
$13$		−	304.514i		−	1.80186i	0.433968	−	0.900928i	$-0.357113\pi$
$14$		−	82.3449i		−	0.420127i
$15$	−1.79425			−0.00797444
$16$	64.0000			0.250000
$17$	−229.594			−0.794443			−0.397222	−	0.917723i	$-0.630026\pi$
$17$	−229.594			−0.794443			−0.397222	+	0.917723i	$0.630026\pi$
$18$		−	76.3675i		−	0.235702i
$19$	−43.2841			−0.119901			−0.0599503	−	0.998201i	$-0.519094\pi$
$19$	−43.2841			−0.119901			−0.0599503	+	0.998201i	$0.519094\pi$
$20$	−2.76243			−0.00690607
$21$	−151.277			−0.343032
$22$	337.535			0.697385
$23$			559.546i			1.05774i	0.848702	+	0.528871i	$0.177385\pi$
$23$			559.546i			1.05774i	−0.848702	+	0.528871i	$0.822615\pi$
$24$		−	117.576i		−	0.204124i
$25$	−624.881			−0.999809
$26$	−861.295			−1.27410
$27$	−140.296			−0.192450
$28$	−232.906			−0.297075
$29$	−303.900			−0.361355			−0.180678	−	0.983542i	$-0.557829\pi$
$29$	−303.900			−0.361355			−0.180678	+	0.983542i	$0.557829\pi$
$30$			5.07490i			0.00563878i
$31$			487.779i			0.507574i	0.967260	+	0.253787i	$0.0816762\pi$
$31$			487.779i			0.507574i	−0.967260	+	0.253787i	$0.918324\pi$
$32$		−	181.019i		−	0.176777i
$33$		−	620.091i		−	0.569413i
$34$			649.390i			0.561756i
$35$	10.0529			0.00820647
$36$	−216.000			−0.166667
$37$		−	59.5851i		−	0.0435245i	−0.999763	−	0.0217623i	$-0.993072\pi$
$37$		−	59.5851i		−	0.0435245i	0.999763	−	0.0217623i	$-0.00692769\pi$
$38$			122.426i			0.0847825i
$39$			1582.30i			1.04030i
$40$			7.81332i			0.00488333i
$41$	2970.49			1.76710			0.883548	−	0.468341i	$-0.155148\pi$
$41$	2970.49			1.76710			0.883548	+	0.468341i	$0.155148\pi$
$42$			427.876i			0.242560i
$43$			556.297i			0.300864i	0.988620	+	0.150432i	$0.0480664\pi$
$43$			556.297i			0.300864i	−0.988620	+	0.150432i	$0.951934\pi$
$44$		−	954.692i		−	0.493126i
$45$	9.32319			0.00460404
$46$	1582.63			0.747937
$47$			880.855i			0.398757i	0.979923	+	0.199379i	$0.0638924\pi$
$47$			880.855i			0.398757i	−0.979923	+	0.199379i	$0.936108\pi$
$48$	−332.554			−0.144338
$49$	−1553.42			−0.646987
$50$			1767.43i			0.706972i
$51$	1193.01			0.458672
$52$			2436.11i			0.900928i
$53$	−913.151			−0.325081			−0.162540	−	0.986702i	$-0.551969\pi$
$53$	−913.151			−0.325081			−0.162540	+	0.986702i	$0.551969\pi$
$54$			396.817i			0.136083i
$55$			41.2073i			0.0136222i
$56$			658.759i			0.210063i
$57$	224.911			0.0692246
$58$			859.558i			0.255517i
$59$	2730.34	+	2159.31i	0.784355	+	0.620312i
$59$	2730.34	+	2159.31i	0.784355	+	0.620312i
$60$	14.3540			0.00398722
$61$			2119.11i			0.569500i	0.958602	+	0.284750i	$0.0919105\pi$
$61$			2119.11i			0.569500i	−0.958602	+	0.284750i	$0.908089\pi$
$62$	1379.65			0.358909
$63$	786.059			0.198050
$64$	−512.000			−0.125000
$65$		−	105.150i		−	0.0248875i
$66$	−1753.88			−0.402636
$67$			5970.68i			1.33007i	0.746813	+	0.665034i	$0.231583\pi$
$67$			5970.68i			1.33007i	−0.746813	+	0.665034i	$0.768417\pi$
$68$	1836.75			0.397222
$69$		−	2907.49i		−	0.610688i
$70$		−	28.4340i		−	0.00580285i
$71$	3795.02			0.752832			0.376416	−	0.926451i	$-0.377156\pi$
$71$	3795.02			0.752832			0.376416	+	0.926451i	$0.377156\pi$
$72$			610.940i			0.117851i
$73$			8963.57i			1.68204i	0.541007	+	0.841018i	$0.318043\pi$
$73$			8963.57i			1.68204i	−0.541007	+	0.841018i	$0.681957\pi$
$74$	−168.532			−0.0307765
$75$	3246.98			0.577240
$76$	346.273			0.0599503
$77$			3474.28i			0.585981i
$78$	4475.42			0.735605
$79$	2347.21			0.376095			0.188047	−	0.982160i	$-0.439784\pi$
$79$	2347.21			0.376095			0.188047	+	0.982160i	$0.439784\pi$
$80$	22.0994			0.00345303
$81$	729.000			0.111111
$82$		−	8401.81i		−	1.24952i
$83$			193.448i			0.0280807i	0.999901	+	0.0140403i	$0.00446933\pi$
$83$			193.448i			0.0280807i	−0.999901	+	0.0140403i	$0.995531\pi$
$84$	1210.22			0.171516
$85$	−79.2796			−0.0109730
$86$	1573.44			0.212743
$87$	1579.11			0.208629
$88$	−2700.28			−0.348693
$89$		−	769.166i		−	0.0971047i	−0.998821	−	0.0485523i	$-0.984539\pi$
$89$		−	769.166i		−	0.0971047i	0.998821	−	0.0485523i	$-0.0154608\pi$
$90$		−	26.3700i		−	0.00325555i
$91$		−	8865.40i		−	1.07057i
$92$		−	4476.37i		−	0.528871i
$93$		−	2534.57i		−	0.293048i
$94$	2491.43			0.281964
$95$	−14.9461			−0.00165608
$96$			940.604i			0.102062i
$97$			3332.34i			0.354166i	0.984196	+	0.177083i	$0.0566660\pi$
$97$			3332.34i			0.354166i	−0.984196	+	0.177083i	$0.943334\pi$
$98$			4393.72i			0.457489i
$99$			3222.09i			0.328751i
$100$	4999.05			0.499905
$101$		−	567.019i		−	0.0555847i	−0.999614	−	0.0277923i	$-0.991152\pi$
$101$		−	567.019i		−	0.0555847i	0.999614	−	0.0277923i	$-0.00884772\pi$
$102$		−	3374.33i		−	0.324330i
$103$			10647.0i			1.00358i	0.864989	+	0.501790i	$0.167325\pi$
$103$			10647.0i			1.00358i	−0.864989	+	0.501790i	$0.832675\pi$
$104$	6890.36			0.637052
$105$	−52.2365			−0.00473801
$106$			2582.78i			0.229867i
$107$	−2700.26			−0.235851			−0.117925	−	0.993022i	$-0.537624\pi$
$107$	−2700.26			−0.235851			−0.117925	+	0.993022i	$0.537624\pi$
$108$	1122.37			0.0962250
$109$			3409.15i			0.286941i	0.989655	+	0.143471i	$0.0458263\pi$
$109$			3409.15i			0.286941i	−0.989655	+	0.143471i	$0.954174\pi$
$110$	116.552			0.00963238
$111$			309.613i			0.0251289i
$112$	1863.25			0.148537
$113$			19110.5i			1.49663i	0.663344	+	0.748314i	$0.269137\pi$
$113$			19110.5i			1.49663i	−0.663344	+	0.748314i	$0.730863\pi$
$114$		−	636.144i		−	0.0489492i
$115$			193.213i			0.0146097i
$116$	2431.20			0.180678
$117$		−	8221.87i		−	0.600619i
$118$	6107.44	−	7722.57i	0.438627	−	0.554623i
$119$	−6684.24			−0.472018
$120$		−	40.5992i		−	0.00281939i
$121$	399.803			0.0273071
$122$	5993.74			0.402697
$123$	−15435.1			−1.02023
$124$		−	3902.23i		−	0.253787i
$125$	−431.588			−0.0276216
$126$		−	2223.31i		−	0.140042i
$127$	−8527.84			−0.528727			−0.264364	−	0.964423i	$-0.585162\pi$
$127$	−8527.84			−0.528727			−0.264364	+	0.964423i	$0.585162\pi$
$128$			1448.15i			0.0883883i
$129$		−	2890.60i		−	0.173704i
$130$	−297.408			−0.0175981
$131$		−	15700.1i		−	0.914872i	−0.889242	−	0.457436i	$-0.848768\pi$
$131$		−	15700.1i		−	0.914872i	0.889242	−	0.457436i	$-0.151232\pi$
$132$			4960.72i			0.284706i
$133$	−1260.14			−0.0712388
$134$	16887.6			0.940500
$135$	−48.4447			−0.00265815
$136$		−	5195.12i		−	0.280878i
$137$	14785.4			0.787758			0.393879	−	0.919162i	$-0.371133\pi$
$137$	14785.4			0.787758			0.393879	+	0.919162i	$0.371133\pi$
$138$	−8223.61			−0.431822
$139$	−32415.5			−1.67773			−0.838867	−	0.544336i	$-0.816782\pi$
$139$	−32415.5			−1.67773			−0.838867	+	0.544336i	$0.816782\pi$
$140$	−80.4234			−0.00410323
$141$		−	4577.06i		−	0.230223i
$142$		−	10733.9i		−	0.532332i
$143$	36339.6			1.77708
$144$	1728.00			0.0833333
$145$	−104.938			−0.00499109
$146$	25352.8			1.18938
$147$	8071.78			0.373538
$148$			476.681i			0.0217623i
$149$			14683.3i			0.661379i	0.943740	+	0.330690i	$0.107281\pi$
$149$			14683.3i			0.661379i	−0.943740	+	0.330690i	$0.892719\pi$
$150$		−	9183.83i		−	0.408170i
$151$		−	18534.9i		−	0.812899i	−0.913673	−	0.406450i	$-0.866767\pi$
$151$		−	18534.9i		−	0.812899i	0.913673	−	0.406450i	$-0.133233\pi$
$152$		−	979.407i		−	0.0423912i
$153$	−6199.04			−0.264814
$154$	9826.75			0.414351
$155$			168.432i			0.00701068i
$156$		−	12658.4i		−	0.520151i
$157$			25038.4i			1.01580i	0.861417	+	0.507899i	$0.169578\pi$
$157$			25038.4i			1.01580i	−0.861417	+	0.507899i	$0.830422\pi$
$158$		−	6638.90i		−	0.265939i
$159$	4744.87			0.187685
$160$		−	62.5066i		−	0.00244166i
$161$			16290.2i			0.628457i
$162$		−	2061.92i		−	0.0785674i
$163$	−34771.0			−1.30871			−0.654353	−	0.756189i	$-0.727059\pi$
$163$	−34771.0			−1.30871			−0.654353	+	0.756189i	$0.727059\pi$
$164$	−23763.9			−0.883548
$165$		−	214.119i		−	0.00786481i
$166$	547.153			0.0198561
$167$	−5171.96			−0.185448			−0.0927239	−	0.995692i	$-0.529557\pi$
$167$	−5171.96			−0.185448			−0.0927239	+	0.995692i	$0.529557\pi$
$168$		−	3423.01i		−	0.121280i
$169$	−64167.6			−2.24669
$170$			224.237i			0.00775905i
$171$	−1168.67			−0.0399668
$172$		−	4450.37i		−	0.150432i
$173$			26548.2i			0.887041i	0.896264	+	0.443520i	$0.146271\pi$
$173$			26548.2i			0.887041i	−0.896264	+	0.443520i	$0.853729\pi$
$174$		−	4466.40i		−	0.147523i
$175$	−18192.3			−0.594036
$176$			7637.54i			0.246563i
$177$	−14187.3	−	11220.1i	−0.452848	−	0.358137i
$178$	−2175.53			−0.0686634
$179$			16799.7i			0.524319i	0.965025	+	0.262160i	$0.0844347\pi$
$179$			16799.7i			0.524319i	−0.965025	+	0.262160i	$0.915565\pi$
$180$	−74.5855			−0.00230202
$181$	35844.6			1.09412			0.547062	−	0.837092i	$-0.315746\pi$
$181$	35844.6			1.09412			0.547062	+	0.837092i	$0.315746\pi$
$182$	−25075.1			−0.757008
$183$		−	11011.2i		−	0.328801i
$184$	−12661.1			−0.373968
$185$		−	20.5749i		−	0.000601167i
$186$	−7168.85			−0.207216
$187$		−	27398.9i		−	0.783521i
$188$		−	7046.84i		−	0.199379i
$189$	−4084.48			−0.114344
$190$			42.2741i			0.00117103i
$191$			47215.5i			1.29425i	0.762385	+	0.647124i	$0.224028\pi$
$191$			47215.5i			1.29425i	−0.762385	+	0.647124i	$0.775972\pi$
$192$	2660.43			0.0721688
$193$	−70854.2			−1.90218			−0.951089	−	0.308918i	$-0.900033\pi$
$193$	−70854.2			−1.90218			−0.951089	+	0.308918i	$0.900033\pi$
$194$	9425.29			0.250433
$195$			546.373i			0.0143688i
$196$	12427.3			0.323493
$197$	−25965.9			−0.669070			−0.334535	−	0.942383i	$-0.608579\pi$
$197$	−25965.9			−0.669070			−0.334535	+	0.942383i	$0.608579\pi$
$198$	9113.43			0.232462
$199$	62151.9			1.56945			0.784726	−	0.619843i	$-0.212804\pi$
$199$	62151.9			1.56945			0.784726	+	0.619843i	$0.212804\pi$
$200$		−	14139.4i		−	0.353486i
$201$		−	31024.5i		−	0.767915i
$202$	−1603.77			−0.0393043
$203$	−8847.53			−0.214699
$204$	−9544.05			−0.229336
$205$	1025.72			0.0244074
$206$	30114.2			0.709638
$207$			15107.7i			0.352581i
$208$		−	19488.9i		−	0.450464i
$209$		−	5165.37i		−	0.118252i
$210$			147.747i			0.00335028i
$211$		−	63638.5i		−	1.42940i	−0.699429	−	0.714702i	$-0.746562\pi$
$211$		−	63638.5i		−	1.42940i	0.699429	−	0.714702i	$-0.253438\pi$
$212$	7305.21			0.162540
$213$	−19719.5			−0.434648
$214$			7637.48i			0.166772i
$215$			192.091i			0.00415557i
$216$		−	3174.54i		−	0.0680414i
$217$			14200.8i			0.301575i
$218$	9642.53			0.202898
$219$		−	46576.1i		−	0.971124i
$220$		−	329.658i		−	0.00681112i
$221$			69914.5i			1.43147i
$222$	875.719			0.0177688
$223$	−52958.8			−1.06495			−0.532474	−	0.846446i	$-0.678738\pi$
$223$	−52958.8			−1.06495			−0.532474	+	0.846446i	$0.678738\pi$
$224$		−	5270.07i		−	0.105032i
$225$	−16871.8			−0.333270
$226$	54052.5			1.05828
$227$			28531.2i			0.553693i	0.960914	+	0.276846i	$0.0892893\pi$
$227$			28531.2i			0.553693i	−0.960914	+	0.276846i	$0.910711\pi$
$228$	−1799.29			−0.0346123
$229$		−	52400.1i		−	0.999220i	−0.866251	−	0.499610i	$-0.833477\pi$
$229$		−	52400.1i		−	0.999220i	0.866251	−	0.499610i	$-0.166523\pi$
$230$	546.489			0.0103306
$231$		−	18052.9i		−	0.338316i
$232$		−	6876.47i		−	0.127758i
$233$		−	82040.4i		−	1.51118i	−0.655046	−	0.755589i	$-0.727351\pi$
$233$		−	82040.4i		−	1.51118i	0.655046	−	0.755589i	$-0.272649\pi$
$234$	−23255.0			−0.424702
$235$			304.162i			0.00550769i
$236$	−21842.7	−	17274.4i	−0.392178	−	0.310156i
$237$	−12196.4			−0.217138
$238$			18905.9i			0.333767i
$239$	−37747.8			−0.660839			−0.330420	−	0.943834i	$-0.607190\pi$
$239$	−37747.8			−0.660839			−0.330420	+	0.943834i	$0.607190\pi$
$240$	−114.832			−0.00199361
$241$	−29181.0			−0.502418			−0.251209	−	0.967933i	$-0.580828\pi$
$241$	−29181.0			−0.502418			−0.251209	+	0.967933i	$0.580828\pi$
$242$		−	1130.81i		−	0.0193090i
$243$	−3788.00			−0.0641500
$244$		−	16952.9i		−	0.284750i
$245$	−536.400			−0.00893627
$246$			43657.1i			0.721414i
$247$			13180.6i			0.216044i
$248$	−11037.2			−0.179454
$249$		−	1005.18i		−	0.0162124i
$250$			1220.72i			0.0195314i
$251$	22064.7			0.350228			0.175114	−	0.984548i	$-0.443971\pi$
$251$	22064.7			0.350228			0.175114	+	0.984548i	$0.443971\pi$
$252$	−6288.47			−0.0990248
$253$	−66774.2			−1.04320
$254$			24120.4i			0.373867i
$255$	411.949			0.00633524
$256$	4096.00			0.0625000
$257$	3793.21			0.0574302			0.0287151	−	0.999588i	$-0.490858\pi$
$257$	3793.21			0.0574302			0.0287151	+	0.999588i	$0.490858\pi$
$258$	−8175.86			−0.122827
$259$		−	1734.72i		−	0.0258601i
$260$			841.197i			0.0124437i
$261$	−8205.29			−0.120452
$262$	−44406.7			−0.646913
$263$	56116.8			0.811301			0.405650	−	0.914028i	$-0.367045\pi$
$263$	56116.8			0.811301			0.405650	+	0.914028i	$0.367045\pi$
$264$	14031.0			0.201318
$265$	−315.314			−0.00449006
$266$			3564.22i			0.0503734i
$267$			3996.70i			0.0560634i
$268$		−	47765.4i		−	0.665034i
$269$		−	48707.5i		−	0.673117i	−0.941662	−	0.336559i	$-0.890737\pi$
$269$		−	48707.5i		−	0.673117i	0.941662	−	0.336559i	$-0.109263\pi$
$270$			137.022i			0.00187959i
$271$	114277.			1.55603			0.778017	−	0.628244i	$-0.216226\pi$
$271$	114277.			1.55603			0.778017	+	0.628244i	$0.216226\pi$
$272$	−14694.0			−0.198611
$273$			46066.0i			0.618095i
$274$		−	41819.5i		−	0.557029i
$275$		−	74571.1i		−	0.986064i
$276$			23259.9i			0.305344i
$277$	−4230.31			−0.0551332			−0.0275666	−	0.999620i	$-0.508776\pi$
$277$	−4230.31			−0.0551332			−0.0275666	+	0.999620i	$0.508776\pi$
$278$			91684.9i			1.18634i
$279$			13170.0i			0.169191i
$280$			227.472i			0.00290142i
$281$	−74894.7			−0.948502			−0.474251	−	0.880390i	$-0.657281\pi$
$281$	−74894.7			−0.948502			−0.474251	+	0.880390i	$0.657281\pi$
$282$	−12945.9			−0.162792
$283$		−	10199.3i		−	0.127349i	−0.997971	−	0.0636747i	$-0.979718\pi$
$283$		−	10199.3i		−	0.127349i	0.997971	−	0.0636747i	$-0.0202820\pi$
$284$	−30360.2			−0.376416
$285$	77.6624			0.000956139
$286$		−	102784.i		−	1.25659i
$287$	86480.7			1.04992
$288$		−	4887.52i		−	0.0589256i
$289$	−30807.6			−0.368860
$290$			296.808i			0.00352923i
$291$		−	17315.4i		−	0.204478i
$292$		−	71708.5i		−	0.841018i
$293$	75241.2			0.876437			0.438218	−	0.898869i	$-0.355610\pi$
$293$	75241.2			0.876437			0.438218	+	0.898869i	$0.355610\pi$
$294$		−	22830.5i		−	0.264131i
$295$	942.796	+	745.616i	0.0108336	+	0.00856783i
$296$	1348.26			0.0153883
$297$		−	16742.4i		−	0.189804i
$298$	41530.6			0.467666
$299$	170389.			1.90590
$300$	−25975.8			−0.288620
$301$			16195.6i			0.178758i
$302$	−52424.6			−0.574806
$303$			2946.32i			0.0320918i
$304$	−2770.18			−0.0299751
$305$			731.735i			0.00786600i
$306$			17533.5i			0.187252i
$307$	135267.			1.43521			0.717606	−	0.696449i	$-0.245238\pi$
$307$	135267.			1.43521			0.717606	+	0.696449i	$0.245238\pi$
$308$		−	27794.2i		−	0.292990i
$309$		−	55323.4i		−	0.579417i
$310$	476.396			0.00495730
$311$	−63636.5			−0.657938			−0.328969	−	0.944341i	$-0.606701\pi$
$311$	−63636.5			−0.657938			−0.328969	+	0.944341i	$0.606701\pi$
$312$	−35803.4			−0.367802
$313$			10716.1i			0.109383i	0.998503	+	0.0546913i	$0.0174175\pi$
$313$			10716.1i			0.109383i	−0.998503	+	0.0546913i	$0.982583\pi$
$314$	70819.3			0.718277
$315$	271.429			0.00273549
$316$	−18777.6			−0.188047
$317$	46383.2			0.461575			0.230787	−	0.973004i	$-0.425870\pi$
$317$	46383.2			0.461575			0.230787	+	0.973004i	$0.425870\pi$
$318$		−	13420.5i		−	0.132714i
$319$		−	36266.3i		−	0.356387i
$320$	−176.795			−0.00172652
$321$	14030.9			0.136169
$322$	46075.7			0.444386
$323$	9937.77			0.0952541
$324$	−5832.00			−0.0555556
$325$			190285.i			1.80151i
$326$			98347.3i			0.925395i
$327$		−	17714.5i		−	0.165666i
$328$			67214.4i			0.624762i
$329$			25644.6i			0.236921i
$330$	−605.621			−0.00556126
$331$	77389.4			0.706359			0.353179	−	0.935556i	$-0.385101\pi$
$331$	77389.4			0.706359			0.353179	+	0.935556i	$0.385101\pi$
$332$		−	1547.58i		−	0.0140403i
$333$		−	1608.80i		−	0.0145082i
$334$			14628.5i			0.131131i
$335$			2061.69i			0.0183711i
$336$	−9681.74			−0.0857580
$337$		−	27283.2i		−	0.240234i	−0.992760	−	0.120117i	$-0.961673\pi$
$337$		−	27283.2i		−	0.240234i	0.992760	−	0.120117i	$-0.0383270\pi$
$338$			181493.i			1.58865i
$339$		−	99300.8i		−	0.864079i
$340$	634.237			0.00548648
$341$	−58209.8			−0.500596
$342$			3305.50i			0.0282608i
$343$	−115126.			−0.978556
$344$	−12587.6			−0.106371
$345$		−	1003.96i		−	0.00843490i
$346$	75089.8			0.627233
$347$		−	23270.3i		−	0.193260i	−0.995320	−	0.0966302i	$-0.969194\pi$
$347$		−	23270.3i		−	0.193260i	0.995320	−	0.0966302i	$-0.0308064\pi$
$348$	−12632.9			−0.104314
$349$		−	127246.i		−	1.04471i	−0.852729	−	0.522354i	$-0.825054\pi$
$349$		−	127246.i		−	1.04471i	0.852729	−	0.522354i	$-0.174946\pi$
$350$			51455.7i			0.420047i
$351$			42722.1i			0.346767i
$352$	21602.2			0.174346
$353$			233504.i			1.87390i	0.349469	+	0.936948i	$0.386362\pi$
$353$			233504.i			1.87390i	−0.349469	+	0.936948i	$0.613638\pi$
$354$	−31735.2	+	40127.6i	−0.253241	+	0.320212i
$355$	1310.43			0.0103982
$356$			6153.33i			0.0485523i
$357$	34732.3			0.272519
$358$	47516.7			0.370750
$359$	−155352.			−1.20539			−0.602697	−	0.797970i	$-0.705907\pi$
$359$	−155352.			−1.20539			−0.602697	+	0.797970i	$0.705907\pi$
$360$			210.960i			0.00162778i
$361$	−128447.			−0.985624
$362$		−	101384.i		−	0.773662i
$363$	−2077.44			−0.0157658
$364$			70923.2i			0.535286i
$365$			3095.15i			0.0232325i
$366$	−31144.4			−0.232497
$367$			69140.9i			0.513337i	0.966499	+	0.256669i	$0.0826249\pi$
$367$			69140.9i			0.513337i	−0.966499	+	0.256669i	$0.917375\pi$
$368$			35810.9i			0.264436i
$369$	80203.1			0.589032
$370$	−58.1947			−0.000425089
$371$	−26584.9			−0.193146
$372$			20276.6i			0.146524i
$373$	143374.			1.03051			0.515254	−	0.857038i	$-0.327698\pi$
$373$	143374.			1.03051			0.515254	+	0.857038i	$0.327698\pi$
$374$	−77495.9			−0.554033
$375$	2242.60			0.0159474
$376$	−19931.5			−0.140982
$377$			92541.7i			0.651110i
$378$			11552.7i			0.0808534i
$379$	−354.370			−0.00246705			−0.00123353	−	0.999999i	$-0.500393\pi$
$379$	−354.370			−0.00246705			−0.00123353	+	0.999999i	$0.500393\pi$
$380$	119.569			0.000828041
$381$	44312.0			0.305261
$382$	133545.			0.915171
$383$	265162.			1.80764			0.903822	−	0.427908i	$-0.140749\pi$
$383$	265162.			1.80764			0.903822	+	0.427908i	$0.140749\pi$
$384$		−	7524.83i		−	0.0510310i
$385$			1199.68i			0.00809364i
$386$			200406.i			1.34504i
$387$			15020.0i			0.100288i
$388$		−	26658.8i		−	0.177083i
$389$	239961.			1.58577			0.792887	−	0.609369i	$-0.208577\pi$
$389$	239961.			1.58577			0.792887	+	0.609369i	$0.208577\pi$
$390$	1545.38			0.0101603
$391$		−	128468.i		−	0.840316i
$392$		−	35149.8i		−	0.228744i
$393$			81580.3i			0.528202i
$394$			73442.7i			0.473104i
$395$	810.498			0.00519467
$396$		−	25776.7i		−	0.164375i
$397$		−	5595.42i		−	0.0355019i	−0.999842	−	0.0177510i	$-0.994349\pi$
$397$		−	5595.42i		−	0.0355019i	0.999842	−	0.0177510i	$-0.00565060\pi$
$398$		−	175792.i		−	1.10977i
$399$	6547.89			0.0411297
$400$	−39992.4			−0.249952
$401$			140372.i			0.872953i	0.899716	+	0.436477i	$0.143774\pi$
$401$			140372.i			0.872953i	−0.899716	+	0.436477i	$0.856226\pi$
$402$	−87750.7			−0.542998
$403$	148535.			0.914575
$404$			4536.16i			0.0277923i
$405$	251.726			0.00153468
$406$			25024.6i			0.151815i
$407$	7110.68			0.0429262
$408$			26994.6i			0.162165i
$409$		−	132134.i		−	0.789895i	−0.918704	−	0.394948i	$-0.870763\pi$
$409$		−	132134.i		−	0.789895i	0.918704	−	0.394948i	$-0.129237\pi$
$410$		−	2901.17i		−	0.0172586i
$411$	−76827.4			−0.454813
$412$		−	85175.9i		−	0.501790i
$413$	79489.2	+	62864.5i	0.466024	+	0.368558i
$414$	42731.1			0.249312
$415$			66.7982i			0.000387854i
$416$	−55122.9			−0.318526
$417$	168436.			0.968640
$418$	−14609.9			−0.0836169
$419$		−	124560.i		−	0.709496i	−0.934962	−	0.354748i	$-0.884567\pi$
$419$		−	124560.i		−	0.709496i	0.934962	−	0.354748i	$-0.115433\pi$
$420$	417.892			0.00236900
$421$			223604.i			1.26158i	0.775953	+	0.630791i	$0.217269\pi$
$421$			223604.i			1.26158i	−0.775953	+	0.630791i	$0.782731\pi$
$422$	−179997.			−1.01074
$423$			23783.1i			0.132919i
$424$		−	20662.3i		−	0.114933i
$425$	143469.			0.794292
$426$			55775.2i			0.307342i
$427$			61694.2i			0.338368i
$428$	21602.0			0.117925
$429$	−188826.			−1.02600
$430$	543.316			0.00293843
$431$			75329.6i			0.405519i	0.979229	+	0.202759i	$0.0649909\pi$
$431$			75329.6i			0.405519i	−0.979229	+	0.202759i	$0.935009\pi$
$432$	−8978.95			−0.0481125
$433$	−296476.			−1.58130			−0.790650	−	0.612269i	$-0.790257\pi$
$433$	−296476.			−1.58130			−0.790650	+	0.612269i	$0.790257\pi$
$434$	40166.1			0.213245
$435$	545.272			0.00288161
$436$		−	27273.2i		−	0.143471i
$437$		−	24219.4i		−	0.126824i
$438$	−131737.			−0.686688
$439$	−68945.6			−0.357748			−0.178874	−	0.983872i	$-0.557245\pi$
$439$	−68945.6			−0.357748			−0.178874	+	0.983872i	$0.557245\pi$
$440$	−932.414			−0.00481619
$441$	−41942.2			−0.215662
$442$	197748.			1.01220
$443$		−	132200.i		−	0.673633i	−0.941570	−	0.336817i	$-0.890650\pi$
$443$		−	132200.i		−	0.673633i	0.941570	−	0.336817i	$-0.109350\pi$
$444$		−	2476.91i		−	0.0125645i
$445$		−	265.596i		−	0.00134122i
$446$			149790.i			0.753032i
$447$		−	76296.5i		−	0.381847i
$448$	−14906.0			−0.0742686
$449$	7000.95			0.0347267			0.0173634	−	0.999849i	$-0.494473\pi$
$449$	7000.95			0.0347267			0.0173634	+	0.999849i	$0.494473\pi$
$450$			47720.6i			0.235657i
$451$			354487.i			1.74280i
$452$		−	152884.i		−	0.748314i
$453$			96310.2i			0.469327i
$454$	80698.5			0.391520
$455$		−	3061.25i		−	0.0147869i
$456$			5089.15i			0.0244746i
$457$			111384.i			0.533325i	0.963790	+	0.266662i	$0.0859209\pi$
$457$			111384.i			0.533325i	−0.963790	+	0.266662i	$0.914079\pi$
$458$	−148210.			−0.706555
$459$	32211.2			0.152891
$460$		−	1545.70i		−	0.00730484i
$461$	−64288.5			−0.302504			−0.151252	−	0.988495i	$-0.548331\pi$
$461$	−64288.5			−0.302504			−0.151252	+	0.988495i	$0.548331\pi$
$462$	−51061.3			−0.239226
$463$		−	181610.i		−	0.847184i	−0.905853	−	0.423592i	$-0.860769\pi$
$463$		−	181610.i		−	0.847184i	0.905853	−	0.423592i	$-0.139231\pi$
$464$	−19449.6			−0.0903388
$465$		−	875.196i		−	0.00404762i
$466$	−232045.			−1.06856
$467$			328713.i			1.50724i	0.657310	+	0.753620i	$0.271694\pi$
$467$			328713.i			1.50724i	−0.657310	+	0.753620i	$0.728306\pi$
$468$			65775.0i			0.300309i
$469$			173826.i			0.790259i
$470$	860.301			0.00389453
$471$		−	130103.i		−	0.586471i
$472$	−48859.5	+	61780.6i	−0.219313	+	0.277311i
$473$	−66386.5			−0.296727
$474$			34496.7i			0.153540i
$475$	27047.4			0.119878
$476$	53473.9			0.236009
$477$	−24655.1			−0.108360
$478$			106767.i			0.467284i
$479$	−98111.5			−0.427611			−0.213806	−	0.976876i	$-0.568586\pi$
$479$	−98111.5			−0.427611			−0.213806	+	0.976876i	$0.568586\pi$
$480$			324.794i			0.00140969i
$481$	−18144.5			−0.0784250
$482$			82536.2i			0.355263i
$483$		−	84646.5i		−	0.362840i
$484$	−3198.43			−0.0136535
$485$			1150.67i			0.00489178i
$486$			10714.1i			0.0453609i
$487$	91025.1			0.383798			0.191899	−	0.981415i	$-0.438535\pi$
$487$	91025.1			0.383798			0.191899	+	0.981415i	$0.438535\pi$
$488$	−47949.9			−0.201348
$489$	180675.			0.755582
$490$			1517.17i			0.00631890i
$491$	268985.			1.11575			0.557873	−	0.829926i	$-0.311617\pi$
$491$	268985.			1.11575			0.557873	+	0.829926i	$0.311617\pi$
$492$	123481.			0.510116
$493$	69773.6			0.287076
$494$	37280.4			0.152766
$495$			1112.60i			0.00454075i
$496$			31217.8i			0.126893i
$497$	110486.			0.447294
$498$	−2843.09			−0.0114639
$499$	−290634.			−1.16720			−0.583601	−	0.812041i	$-0.698357\pi$
$499$	−290634.			−1.16720			−0.583601	+	0.812041i	$0.698357\pi$
$500$	3452.70			0.0138108
$501$	26874.3			0.107068
$502$		−	62408.5i		−	0.247649i
$503$		−	346973.i		−	1.37139i	−0.727890	−	0.685693i	$-0.759499\pi$
$503$		−	346973.i		−	1.37139i	0.727890	−	0.685693i	$-0.240501\pi$
$504$			17786.5i			0.0700211i
$505$		−	195.794i		−	0.000767743i
$506$			188866.i			0.737654i
$507$	333425.			1.29713
$508$	68222.7			0.264364
$509$		−	486734.i		−	1.87869i	−0.342970	−	0.939346i	$-0.611433\pi$
$509$		−	486734.i		−	1.87869i	0.342970	−	0.939346i	$-0.388567\pi$
$510$		−	1165.17i		−	0.00447969i
$511$			260959.i			0.999380i
$512$		−	11585.2i		−	0.0441942i
$513$	6072.59			0.0230749
$514$		−	10728.8i		−	0.0406093i
$515$			3676.44i			0.0138616i
$516$			23124.8i			0.0868518i
$517$	−105118.			−0.393275
$518$	−4906.53			−0.0182858
$519$		−	137949.i		−	0.512133i
$520$	2379.26			0.00879905
$521$	−494832.			−1.82298			−0.911490	−	0.411322i	$-0.865067\pi$
$521$	−494832.			−1.82298			−0.911490	+	0.411322i	$0.865067\pi$
$522$			23208.1i			0.0851723i
$523$	−216797.			−0.792591			−0.396296	−	0.918123i	$-0.629704\pi$
$523$	−216797.			−0.792591			−0.396296	+	0.918123i	$0.629704\pi$
$524$			125601.i			0.457436i
$525$	94530.2			0.342967
$526$		−	158722.i		−	0.573676i
$527$		−	111991.i		−	0.403239i
$528$		−	39685.8i		−	0.142353i
$529$	−33250.5			−0.118819
$530$			891.843i			0.00317495i
$531$	73719.2	+	58301.3i	0.261452	+	0.206771i
$532$	10081.1			0.0356194
$533$		−	904554.i		−	3.18405i
$534$	11304.4			0.0396428
$535$	−932.407			−0.00325760
$536$	−135101.			−0.470250
$537$		−	87293.8i		−	0.302716i
$538$	−137765.			−0.475966
$539$		−	185379.i		−	0.638092i
$540$	387.558			0.00132907
$541$		−	311287.i		−	1.06357i	−0.846879	−	0.531785i	$-0.821521\pi$
$541$		−	311287.i		−	1.06357i	0.846879	−	0.531785i	$-0.178479\pi$
$542$		−	323223.i		−	1.10028i
$543$	−186254.			−0.631692
$544$			41561.0i			0.140439i
$545$			1177.19i			0.00396327i
$546$	130294.			0.437059
$547$	318117.			1.06319			0.531597	−	0.846998i	$-0.321592\pi$
$547$	318117.			1.06319			0.531597	+	0.846998i	$0.321592\pi$
$548$	−118283.			−0.393879
$549$			57215.9i			0.189833i
$550$	−210919.			−0.697252
$551$	13154.0			0.0433267
$552$	65788.9			0.215911
$553$	68334.9			0.223456
$554$			11965.1i			0.0389850i
$555$			106.910i			0.000347084i
$556$	259324.			0.838867
$557$	−458615.			−1.47822			−0.739108	−	0.673587i	$-0.764753\pi$
$557$	−458615.			−1.47822			−0.739108	+	0.673587i	$0.764753\pi$
$558$	37250.4			0.119636
$559$	169400.			0.542113
$560$	643.387			0.00205162
$561$			142369.i			0.452366i
$562$			211834.i			0.670692i
$563$		−	218018.i		−	0.687821i	−0.939003	−	0.343910i	$-0.888248\pi$
$563$		−	218018.i		−	0.687821i	0.939003	−	0.343910i	$-0.111752\pi$
$564$			36616.5i			0.115111i
$565$			6598.90i			0.0206716i
$566$	−28848.0			−0.0900497
$567$	21223.6			0.0660166
$568$			85871.6i			0.266166i
$569$			180447.i			0.557347i	0.960386	+	0.278674i	$0.0898948\pi$
$569$			180447.i			0.557347i	−0.960386	+	0.278674i	$0.910105\pi$
$570$		−	219.663i		−	0.000676093i
$571$			73565.0i			0.225631i	0.993616	+	0.112816i	$0.0359869\pi$
$571$			73565.0i			0.225631i	−0.993616	+	0.112816i	$0.964013\pi$
$572$	−290717.			−0.888542
$573$		−	245339.i		−	0.747234i
$574$		−	244604.i		−	0.742404i
$575$		−	349649.i		−	1.05754i
$576$	−13824.0			−0.0416667
$577$	74461.1			0.223654			0.111827	−	0.993728i	$-0.464330\pi$
$577$	74461.1			0.223654			0.111827	+	0.993728i	$0.464330\pi$
$578$			87137.0i			0.260824i
$579$	368169.			1.09822
$580$	839.501			0.00249554
$581$			5631.91i			0.0166841i
$582$	−48975.3			−0.144588
$583$		−	108972.i		−	0.320611i
$584$	−202822.			−0.594689
$585$		−	2839.04i		−	0.00829583i
$586$		−	212814.i		−	0.619734i
$587$			68909.0i			0.199986i	0.994988	+	0.0999930i	$0.0318820\pi$
$587$			68909.0i			0.199986i	−0.994988	+	0.0999930i	$0.968118\pi$
$588$	−64574.3			−0.186769
$589$		−	21113.1i		−	0.0608584i
$590$	2108.92	−	2666.63i	0.00605837	−	0.00766053i
$591$	134923.			0.386288
$592$		−	3813.45i		−	0.0108811i
$593$	−103260.			−0.293645			−0.146823	−	0.989163i	$-0.546905\pi$
$593$	−103260.			−0.293645			−0.146823	+	0.989163i	$0.546905\pi$
$594$	−47354.8			−0.134212
$595$	−2308.09			−0.00651957
$596$		−	117466.i		−	0.330690i
$597$	−322951.			−0.906124
$598$		−	481934.i		−	1.34767i
$599$	425655.			1.18633			0.593163	−	0.805083i	$-0.297879\pi$
$599$	425655.			1.18633			0.593163	+	0.805083i	$0.297879\pi$
$600$			73470.7i			0.204085i
$601$		−	534156.i		−	1.47883i	−0.673249	−	0.739416i	$-0.735102\pi$
$601$		−	534156.i		−	1.47883i	0.673249	−	0.739416i	$-0.264898\pi$
$602$	45808.2			0.126401
$603$			161208.i			0.443356i
$604$			148279.i			0.406450i
$605$	138.053			0.000377169
$606$	8333.45			0.0226924
$607$	−632185.			−1.71580			−0.857901	−	0.513816i	$-0.828231\pi$
$607$	−632185.			−1.71580			−0.857901	+	0.513816i	$0.828231\pi$
$608$			7835.26i			0.0211956i
$609$	45973.1			0.123956
$610$	2069.66			0.00556210
$611$	268233.			0.718504
$612$	49592.3			0.132407
$613$			427346.i			1.13726i	0.822595	+	0.568628i	$0.192526\pi$
$613$			427346.i			1.13726i	−0.822595	+	0.568628i	$0.807474\pi$
$614$		−	382594.i		−	1.01485i
$615$	−5329.79			−0.0140916
$616$	−78614.0			−0.207175
$617$	−524329.			−1.37732			−0.688658	−	0.725087i	$-0.741800\pi$
$617$	−524329.			−1.37732			−0.688658	+	0.725087i	$0.741800\pi$
$618$	−156478.			−0.409710
$619$	−215064.			−0.561289			−0.280645	−	0.959812i	$-0.590548\pi$
$619$	−215064.			−0.561289			−0.280645	+	0.959812i	$0.590548\pi$
$620$		−	1347.45i		−	0.00350534i
$621$		−	78502.1i		−	0.203563i
$622$			179991.i			0.465233i
$623$		−	22393.0i		−	0.0576947i
$624$			101267.i			0.260076i
$625$	390401.			0.999428
$626$	30309.7			0.0773452
$627$			26840.1i			0.0682729i
$628$		−	200307.i		−	0.507899i
$629$			13680.4i			0.0345778i
$630$		−	767.717i		−	0.00193428i
$631$	399375.			1.00305			0.501525	−	0.865143i	$-0.332773\pi$
$631$	399375.			1.00305			0.501525	+	0.865143i	$0.332773\pi$
$632$			53111.2i			0.132970i
$633$			330675.i			0.825267i
$634$		−	131191.i		−	0.326383i
$635$	−2944.69			−0.00730285
$636$	−37959.0			−0.0938427
$637$			473036.i			1.16578i
$638$	−102577.			−0.252004
$639$	102466.			0.250944
$640$			500.053i			0.00122083i
$641$	121848.			0.296553			0.148277	−	0.988946i	$-0.452627\pi$
$641$	121848.			0.296553			0.148277	+	0.988946i	$0.452627\pi$
$642$		−	39685.5i		−	0.0962857i
$643$	−435859.			−1.05420			−0.527102	−	0.849802i	$-0.676721\pi$
$643$	−435859.			−1.05420			−0.527102	+	0.849802i	$0.676721\pi$
$644$		−	130322.i		−	0.314228i
$645$		−	998.135i		−	0.00239922i
$646$		−	28108.3i		−	0.0673549i
$647$	271725.			0.649113			0.324557	−	0.945866i	$-0.394785\pi$
$647$	271725.			0.649113			0.324557	+	0.945866i	$0.394785\pi$
$648$			16495.4i			0.0392837i
$649$	−257684.	+	325829.i	−0.611784	+	0.773572i
$650$	538207.			1.27386
$651$		−	73789.8i		−	0.174114i
$652$	278168.			0.654353
$653$	−237640.			−0.557306			−0.278653	−	0.960392i	$-0.589888\pi$
$653$	−237640.			−0.557306			−0.278653	+	0.960392i	$0.589888\pi$
$654$	−50104.1			−0.117143
$655$		−	5421.31i		−	0.0126363i
$656$	190111.			0.441774
$657$			242016.i			0.560679i
$658$	72533.9			0.167529
$659$		−	796099.i		−	1.83314i	−0.399870	−	0.916572i	$-0.630945\pi$
$659$		−	796099.i		−	1.83314i	0.399870	−	0.916572i	$-0.369055\pi$
$660$			1712.95i			0.00393240i
$661$	92808.8			0.212416			0.106208	−	0.994344i	$-0.466129\pi$
$661$	92808.8			0.212416			0.106208	+	0.994344i	$0.466129\pi$
$662$		−	218890.i		−	0.499471i
$663$		−	363287.i		−	0.826461i
$664$	−4377.23			−0.00992803
$665$	−435.132			−0.000983960
$666$	−4550.37			−0.0102588
$667$		−	170046.i		−	0.382221i
$668$	41375.6			0.0927239
$669$	275182.			0.614848
$670$	5831.35			0.0129903
$671$	−252887.			−0.561670
$672$			27384.1i			0.0606401i
$673$			434666.i			0.959678i	0.877356	+	0.479839i	$0.159305\pi$
$673$			434666.i			0.959678i	−0.877356	+	0.479839i	$0.840695\pi$
$674$	−77168.4			−0.169871
$675$	87668.3			0.192413
$676$	513341.			1.12334
$677$	−468389.			−1.02195			−0.510975	−	0.859596i	$-0.670716\pi$
$677$	−468389.			−1.02195			−0.510975	+	0.859596i	$0.670716\pi$
$678$	−280865.			−0.610996
$679$			97015.5i			0.210427i
$680$		−	1793.89i		−	0.00387952i
$681$		−	148253.i		−	0.319675i
$682$			164642.i			0.353975i
$683$		−	529417.i		−	1.13490i	−0.823409	−	0.567449i	$-0.807931\pi$
$683$		−	529417.i		−	1.13490i	0.823409	−	0.567449i	$-0.192069\pi$
$684$	9349.36			0.0199834
$685$	5105.46			0.0108806
$686$			325626.i			0.691943i
$687$			272279.i			0.576900i
$688$			35603.0i			0.0752159i
$689$			278067.i			0.585749i
$690$	−2839.64			−0.00596438
$691$			398171.i			0.833898i	0.908930	+	0.416949i	$0.136901\pi$
$691$			398171.i			0.833898i	−0.908930	+	0.416949i	$0.863099\pi$
$692$		−	212386.i		−	0.443520i
$693$			93805.5i			0.195327i
$694$	−65818.3			−0.136656
$695$	−11193.2			−0.0231731
$696$			35731.2i			0.0737613i
$697$	−682006.			−1.40386
$698$	−359907.			−0.738720
$699$			426294.i			0.872479i
$700$	145539.			0.297018
$701$		−	400569.i		−	0.815156i	−0.913170	−	0.407578i	$-0.866373\pi$
$701$		−	400569.i		−	0.815156i	0.913170	−	0.407578i	$-0.133627\pi$
$702$	120836.			0.245202
$703$			2579.09i			0.00521862i
$704$		−	61100.3i		−	0.123281i
$705$		−	1580.47i		−	0.00317987i
$706$	660450.			1.32504
$707$		−	16507.8i		−	0.0330256i
$708$	113498.	+	89760.7i	0.226424	+	0.179069i
$709$	−282000.			−0.560992			−0.280496	−	0.959855i	$-0.590499\pi$
$709$	−282000.			−0.560992			−0.280496	+	0.959855i	$0.590499\pi$
$710$		−	3706.47i		−	0.00735264i
$711$	63374.6			0.125365
$712$	17404.2			0.0343317
$713$	−272934.			−0.536883
$714$		−	98237.9i		−	0.192700i
$715$	12548.2			0.0245453
$716$		−	134398.i		−	0.262160i
$717$	196143.			0.381536
$718$			439403.i			0.852342i
$719$			632803.i			1.22408i	0.790825	+	0.612042i	$0.209652\pi$
$719$			632803.i			1.22408i	−0.790825	+	0.612042i	$0.790348\pi$
$720$	596.684			0.00115101
$721$			309969.i			0.596276i
$722$			363304.i			0.696941i
$723$	151629.			0.290071
$724$	−286757.			−0.547062
$725$	189901.			0.361286
$726$			5875.88i			0.0111481i
$727$	−1.02381e6			−1.93708			−0.968542	−	0.248850i	$-0.919947\pi$
$727$	−1.02381e6			−1.93708			−0.968542	+	0.248850i	$0.919947\pi$
$728$	200601.			0.378504
$729$	19683.0			0.0370370
$730$	8754.41			0.0164279
$731$		−	127722.i		−	0.239019i
$732$			88089.7i			0.164400i
$733$	−187550.			−0.349067			−0.174534	−	0.984651i	$-0.555842\pi$
$733$	−187550.			−0.349067			−0.174534	+	0.984651i	$0.555842\pi$
$734$	195560.			0.362984
$735$	2787.21			0.00515936
$736$	101289.			0.186984
$737$	−712520.			−1.31178
$738$		−	226849.i		−	0.416508i
$739$		−	709560.i		−	1.29927i	−0.760245	−	0.649636i	$-0.774921\pi$
$739$		−	709560.i		−	1.29927i	0.760245	−	0.649636i	$-0.225079\pi$
$740$			164.599i			0.000300583i
$741$		−	68488.4i		−	0.124733i
$742$			75193.3i			0.136575i
$743$	−889169.			−1.61067			−0.805335	−	0.592820i	$-0.798015\pi$
$743$	−889169.			−1.61067			−0.805335	+	0.592820i	$0.798015\pi$
$744$	57350.8			0.103608
$745$			5070.18i			0.00913506i
$746$		−	405522.i		−	0.728679i
$747$			5223.09i			0.00936023i
$748$			219192.i			0.391761i
$749$	−78613.4			−0.140131
$750$		−	6343.02i		−	0.0112765i
$751$			362232.i			0.642254i	0.947036	+	0.321127i	$0.104062\pi$
$751$			362232.i			0.642254i	−0.947036	+	0.321127i	$0.895938\pi$
$752$			56374.7i			0.0996894i
$753$	−114652.			−0.202204
$754$	261747.			0.460405
$755$		−	6400.17i		−	0.0112279i
$756$	32675.9			0.0571720
$757$	617075.			1.07683			0.538413	−	0.842681i	$-0.319024\pi$
$757$	617075.			1.07683			0.538413	+	0.842681i	$0.319024\pi$
$758$			1002.31i			0.00174447i
$759$	346969.			0.602292
$760$		−	338.193i		−	0.000585513i
$761$	84132.5			0.145276			0.0726381	−	0.997358i	$-0.476858\pi$
$761$	84132.5			0.145276			0.0726381	+	0.997358i	$0.476858\pi$
$762$		−	125333.i		−	0.215852i
$763$			99251.6i			0.170486i
$764$		−	377724.i		−	0.647124i
$765$	−2140.55			−0.00365765
$766$		−	749990.i		−	1.27820i
$767$	657538.	−	831426.i	1.11771	−	1.41330i
$768$	−21283.4			−0.0360844
$769$			487601.i			0.824540i	0.911062	+	0.412270i	$0.135264\pi$
$769$			487601.i			0.824540i	−0.911062	+	0.412270i	$0.864736\pi$
$770$	3393.21			0.00572307
$771$	−19710.1			−0.0331573
$772$	566834.			0.951089
$773$			887763.i			1.48572i	0.669444	+	0.742862i	$0.266532\pi$
$773$			887763.i			1.48572i	−0.669444	+	0.742862i	$0.733468\pi$
$774$	42483.0			0.0709142
$775$		−	304803.i		−	0.507477i
$776$	−75402.3			−0.125216
$777$			9013.87i			0.0149303i
$778$		−	678712.i		−	1.12131i
$779$	−128575.			−0.211876
$780$		−	4370.99i		−	0.00718440i
$781$			452885.i			0.742482i
$782$	−363363.			−0.594193
$783$	42636.0			0.0695429
$784$	−99418.6			−0.161747
$785$			8645.84i			0.0140303i
$786$	230744.			0.373495
$787$	99407.6			0.160498			0.0802491	−	0.996775i	$-0.474428\pi$
$787$	99407.6			0.160498			0.0802491	+	0.996775i	$0.474428\pi$
$788$	207727.			0.334535
$789$	−291592.			−0.468405
$790$		−	2292.43i		−	0.00367318i
$791$			556368.i			0.889221i
$792$	−72907.5			−0.116231
$793$	645297.			1.02616
$794$	−15826.2			−0.0251037
$795$	1638.42			0.00259233
$796$	−497215.			−0.784726
$797$			578171.i			0.910206i	0.890439	+	0.455103i	$0.150398\pi$
$797$			578171.i			0.910206i	−0.890439	+	0.455103i	$0.849602\pi$
$798$		−	18520.2i		−	0.0290831i
$799$		−	202239.i		−	0.316790i
$800$			113116.i			0.176743i
$801$		−	20767.5i		−	0.0323682i
$802$	397031.			0.617271
$803$	−1.06968e6			−1.65891
$804$			248196.i			0.383958i
$805$			5625.07i			0.00868033i
$806$		−	420121.i		−	0.646702i
$807$			253091.i			0.388625i
$808$	12830.2			0.0196522
$809$			306114.i			0.467720i	0.972270	+	0.233860i	$0.0751358\pi$
$809$			306114.i			0.467720i	−0.972270	+	0.233860i	$0.924864\pi$
$810$		−	711.989i		−	0.00108518i
$811$			1.15116e6i			1.75023i	0.483914	+	0.875116i	$0.339215\pi$
$811$			1.15116e6i			1.75023i	−0.483914	+	0.875116i	$0.660785\pi$
$812$	70780.2			0.107349
$813$	−593799.			−0.898376
$814$		−	20112.0i		−	0.0303534i
$815$	−12006.5			−0.0180760
$816$	76352.4			0.114668
$817$		−	24078.8i		−	0.0360737i
$818$	−373733.			−0.558540
$819$		−	239366.i		−	0.356857i
$820$	−8205.75			−0.0122037
$821$			387597.i			0.575035i	0.957775	+	0.287517i	$0.0928299\pi$
$821$			387597.i			0.575035i	−0.957775	+	0.287517i	$0.907170\pi$
$822$			217301.i			0.321601i
$823$		−	584601.i		−	0.863097i	−0.902090	−	0.431549i	$-0.857967\pi$
$823$		−	584601.i		−	0.863097i	0.902090	−	0.431549i	$-0.142033\pi$
$824$	−240914.			−0.354819
$825$			387483.i			0.569304i
$826$	177808.	−	224829.i	0.260610	−	0.329529i
$827$	993463.			1.45258			0.726291	−	0.687388i	$-0.241243\pi$
$827$	993463.			1.45258			0.726291	+	0.687388i	$0.241243\pi$
$828$		−	120862.i		−	0.176290i
$829$	277889.			0.404355			0.202177	−	0.979349i	$-0.435198\pi$
$829$	277889.			0.404355			0.202177	+	0.979349i	$0.435198\pi$
$830$	188.934			0.000274254
$831$	21981.4			0.0318312
$832$			155911.i			0.225232i
$833$	356655.			0.513994
$834$		−	476409.i		−	0.684932i
$835$	−1785.89			−0.00256143
$836$			41323.0i			0.0591261i
$837$		−	68433.4i		−	0.0976827i
$838$	−352309.			−0.501690
$839$			715635.i			1.01664i	0.861168	+	0.508320i	$0.169733\pi$
$839$			715635.i			1.01664i	−0.861168	+	0.508320i	$0.830267\pi$
$840$		−	1181.98i		−	0.00167514i
$841$	−614926.			−0.869422
$842$	632448.			0.892073
$843$	389164.			0.547618
$844$			509108.i			0.714702i
$845$	−22157.3			−0.0310315
$846$	67268.7			0.0939880
$847$	11639.6			0.0162245
$848$	−58441.7			−0.0812701
$849$			52997.1i			0.0735253i
$850$		−	405791.i		−	0.561649i
$851$	33340.6			0.0460378
$852$	157756.			0.217324
$853$	214771.			0.295173			0.147587	−	0.989049i	$-0.452850\pi$
$853$	214771.			0.295173			0.147587	+	0.989049i	$0.452850\pi$
$854$	174498.			0.239262
$855$	−403.546			−0.000552027
$856$		−	61099.8i		−	0.0833858i
$857$		−	178905.i		−	0.243591i	−0.992555	−	0.121796i	$-0.961135\pi$
$857$		−	178905.i		−	0.243591i	0.992555	−	0.121796i	$-0.0388653\pi$
$858$			534081.i			0.725492i
$859$			170699.i			0.231337i	0.993288	+	0.115668i	$0.0369010\pi$
$859$			170699.i			0.231337i	−0.993288	+	0.115668i	$0.963099\pi$
$860$		−	1536.73i		−	0.00207778i
$861$	−449367.			−0.606170
$862$	213064.			0.286745
$863$			793327.i			1.06520i	0.846367	+	0.532600i	$0.178785\pi$
$863$			793327.i			1.06520i	−0.846367	+	0.532600i	$0.821215\pi$
$864$			25396.3i			0.0340207i
$865$			9167.20i			0.0122519i
$866$			838561.i			1.11815i
$867$	160081.			0.212962
$868$		−	113607.i		−	0.150787i
$869$			280107.i			0.370924i
$870$		−	1542.26i		−	0.00203760i
$871$	1.81815e6			2.39659
$872$	−77140.3			−0.101449
$873$			89973.3i			0.118055i
$874$	−68502.9			−0.0896780
$875$	−12565.0			−0.0164114
$876$			372609.i			0.485562i
$877$	−1.39963e6			−1.81976			−0.909878	−	0.414876i	$-0.863825\pi$
$877$	−1.39963e6			−1.81976			−0.909878	+	0.414876i	$0.863825\pi$
$878$			195008.i			0.252966i
$879$	−390965.			−0.506011
$880$			2637.27i			0.00340556i
$881$			147593.i			0.190158i	0.995470	+	0.0950790i	$0.0303104\pi$
$881$			147593.i			0.190158i	−0.995470	+	0.0950790i	$0.969690\pi$
$882$			118631.i			0.152496i
$883$	561869.			0.720633			0.360316	−	0.932830i	$-0.382669\pi$
$883$	561869.			0.720633			0.360316	+	0.932830i	$0.382669\pi$
$884$		−	559316.i		−	0.715736i
$885$	−4898.91	−	3874.33i	−0.00625479	−	0.00494664i
$886$	−373918.			−0.476331
$887$		−	446523.i		−	0.567541i	−0.958892	−	0.283770i	$-0.908415\pi$
$887$		−	446523.i		−	0.567541i	0.958892	−	0.283770i	$-0.0915853\pi$
$888$	−7005.75			−0.00888441
$889$	−248274.			−0.314143
$890$	−751.218			−0.000948388
$891$			86996.3i			0.109584i
$892$	423670.			0.532474
$893$		−	38127.0i		−	0.0478112i
$894$	−215799.			−0.270007
$895$			5800.99i			0.00724196i
$896$			42160.6i			0.0525159i
$897$	−885369.			−1.10037
$898$		−	19801.7i		−	0.0245555i
$899$		−	148236.i		−	0.183415i
$900$	134974.			0.166635
$901$	209654.			0.258258
$902$	1.00264e6			1.23235
$903$		−	84155.0i		−	0.103206i
$904$	−432420.			−0.529138
$905$	12377.2			0.0151122
$906$	272406.			0.331865
$907$	946148.			1.15012			0.575062	−	0.818110i	$-0.304978\pi$
$907$	946148.			1.15012			0.575062	+	0.818110i	$0.304978\pi$
$908$		−	228250.i		−	0.276846i
$909$		−	15309.5i		−	0.0185282i
$910$	−8658.53			−0.0104559
$911$	1.06764e6			1.28644			0.643219	−	0.765683i	$-0.277599\pi$
$911$	1.06764e6			1.28644			0.643219	+	0.765683i	$0.277599\pi$
$912$	14394.3			0.0173062
$913$	−23085.4			−0.0276946
$914$	315043.			0.377118
$915$		−	3802.21i		−	0.00454144i
$916$			419201.i			0.499610i
$917$		−	457083.i		−	0.543571i
$918$		−	91106.9i		−	0.108110i
$919$		−	954937.i		−	1.13069i	−0.824854	−	0.565345i	$-0.808743\pi$
$919$		−	954937.i		−	1.13069i	0.824854	−	0.565345i	$-0.191257\pi$
$920$	−4371.91			−0.00516530
$921$	−702869.			−0.828620
$922$			181835.i			0.213903i
$923$		−	1.15564e6i		−	1.35649i
$924$			144423.i			0.169158i
$925$			37233.6i			0.0435162i
$926$	−513671.			−0.599050
$927$			287469.i			0.334527i
$928$			55011.7i			0.0638792i
$929$			139772.i			0.161952i	0.996716	+	0.0809762i	$0.0258038\pi$
$929$			139772.i			0.161952i	−0.996716	+	0.0809762i	$0.974196\pi$
$930$	−2475.43			−0.00286210
$931$	67238.2			0.0775741
$932$			656323.i			0.755589i
$933$	330665.			0.379861
$934$	929740.			1.06578
$935$		−	9460.95i		−	0.0108221i
$936$	186040.			0.212351
$937$		−	1.40914e6i		−	1.60500i	−0.596654	−	0.802498i	$-0.703504\pi$
$937$		−	1.40914e6i		−	1.60500i	0.596654	−	0.802498i	$-0.296496\pi$
$938$	491654.			0.558797
$939$		−	55682.5i		−	0.0631521i
$940$		−	2433.30i		−	0.00275385i
$941$			1.13063e6i			1.27686i	0.769682	+	0.638428i	$0.220415\pi$
$941$			1.13063e6i			1.27686i	−0.769682	+	0.638428i	$0.779585\pi$
$942$	−367988.			−0.414698
$943$			1.66212e6i			1.86913i
$944$	174742.	+	138196.i	0.196089	+	0.155078i
$945$	−1410.39			−0.00157934
$946$			187769.i			0.209818i
$947$	−1.52196e6			−1.69708			−0.848542	−	0.529128i	$-0.822519\pi$
$947$	−1.52196e6			−1.69708			−0.848542	+	0.529128i	$0.822519\pi$
$948$	97571.5			0.108569
$949$	2.72953e6			3.03079
$950$		−	76501.6i		−	0.0847663i
$951$	−241014.			−0.266490
$952$		−	151247.i		−	0.166883i
$953$	1.28184e6			1.41139			0.705696	−	0.708515i	$-0.250634\pi$
$953$	1.28184e6			1.41139			0.705696	+	0.708515i	$0.250634\pi$
$954$			69735.1i			0.0766222i
$955$			16303.7i			0.0178763i
$956$	301982.			0.330420
$957$			188445.i			0.205760i
$958$			277501.i			0.302367i
$959$	430453.			0.468046
$960$	918.655			0.000996805
$961$	685593.			0.742369
$962$			51320.3i			0.0554548i
$963$	−72906.9			−0.0786169
$964$	233448.			0.251209
$965$	−24466.2			−0.0262731
$966$	−239416.			−0.256566
$967$		−	553590.i		−	0.592018i	−0.955185	−	0.296009i	$-0.904344\pi$
$967$		−	553590.i		−	0.592018i	0.955185	−	0.296009i	$-0.0956559\pi$
$968$			9046.51i			0.00965452i
$969$	−51638.2			−0.0549950
$970$	3254.58			0.00345901
$971$	135852.			0.144088			0.0720442	−	0.997401i	$-0.477048\pi$
$971$	135852.			0.144088			0.0720442	+	0.997401i	$0.477048\pi$
$972$	30304.0			0.0320750
$973$	−943722.			−0.996824
$974$		−	257458.i		−	0.271386i
$975$		−	988749.i		−	1.04010i
$976$			135623.i			0.142375i
$977$			1.45788e6i			1.52733i	0.645610	+	0.763667i	$0.276603\pi$
$977$			1.45788e6i			1.52733i	−0.645610	+	0.763667i	$0.723397\pi$
$978$		−	511027.i		−	0.534277i
$979$	91789.6			0.0957697
$980$	4291.20			0.00446813
$981$			92047.1i			0.0956471i
$982$		−	760805.i		−	0.788952i
$983$			1.31374e6i			1.35958i	0.733409	+	0.679788i	$0.237928\pi$
$983$			1.31374e6i			1.35958i	−0.733409	+	0.679788i	$0.762072\pi$
$984$		−	349257.i		−	0.360707i
$985$	−8966.12			−0.00924128
$986$		−	197350.i		−	0.202994i
$987$		−	133253.i		−	0.136787i
$988$		−	105445.i		−	0.108022i
$989$	−311273.			−0.318236
$990$	3146.90			0.00321079
$991$			922836.i			0.939674i	0.882753	+	0.469837i	$0.155687\pi$
$991$			922836.i			0.939674i	−0.882753	+	0.469837i	$0.844313\pi$
$992$	88297.4			0.0897272
$993$	−402127.			−0.407816
$994$		−	312501.i		−	0.316285i
$995$	21461.2			0.0216775
$996$			8041.48i			0.00810620i
$997$	−11980.4			−0.0120526			−0.00602629	−	0.999982i	$-0.501918\pi$
$997$	−11980.4			−0.0120526			−0.00602629	+	0.999982i	$0.501918\pi$
$998$			822038.i			0.825336i
$999$			8359.56i			0.00837630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.d.a.235.11	✓	40
3.2	odd	2		1062.5.d.b.235.22		40
59.58	odd	2	inner	354.5.d.a.235.12	yes	40
177.176	even	2		1062.5.d.b.235.21		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.d.a.235.11	✓	40	1.1	even	1	trivial
354.5.d.a.235.12	yes	40	59.58	odd	2	inner
1062.5.d.b.235.21		40	177.176	even	2
1062.5.d.b.235.22		40	3.2	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +0.345303 q^{5} +14.6969i q^{6} +29.1133 q^{7} +22.6274i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +0.345303 q^{5} +14.6969i q^{6} +29.1133 q^{7} +22.6274i q^{8} +27.0000 q^{9} -0.976665i q^{10} +119.336i q^{11} +41.5692 q^{12} -304.514i q^{13} -82.3449i q^{14} -1.79425 q^{15} +64.0000 q^{16} -229.594 q^{17} -76.3675i q^{18} -43.2841 q^{19} -2.76243 q^{20} -151.277 q^{21} +337.535 q^{22} +559.546i q^{23} -117.576i q^{24} -624.881 q^{25} -861.295 q^{26} -140.296 q^{27} -232.906 q^{28} -303.900 q^{29} +5.07490i q^{30} +487.779i q^{31} -181.019i q^{32} -620.091i q^{33} +649.390i q^{34} +10.0529 q^{35} -216.000 q^{36} -59.5851i q^{37} +122.426i q^{38} +1582.30i q^{39} +7.81332i q^{40} +2970.49 q^{41} +427.876i q^{42} +556.297i q^{43} -954.692i q^{44} +9.32319 q^{45} +1582.63 q^{46} +880.855i q^{47} -332.554 q^{48} -1553.42 q^{49} +1767.43i q^{50} +1193.01 q^{51} +2436.11i q^{52} -913.151 q^{53} +396.817i q^{54} +41.2073i q^{55} +658.759i q^{56} +224.911 q^{57} +859.558i q^{58} +(2730.34 + 2159.31i) q^{59} +14.3540 q^{60} +2119.11i q^{61} +1379.65 q^{62} +786.059 q^{63} -512.000 q^{64} -105.150i q^{65} -1753.88 q^{66} +5970.68i q^{67} +1836.75 q^{68} -2907.49i q^{69} -28.4340i q^{70} +3795.02 q^{71} +610.940i q^{72} +8963.57i q^{73} -168.532 q^{74} +3246.98 q^{75} +346.273 q^{76} +3474.28i q^{77} +4475.42 q^{78} +2347.21 q^{79} +22.0994 q^{80} +729.000 q^{81} -8401.81i q^{82} +193.448i q^{83} +1210.22 q^{84} -79.2796 q^{85} +1573.44 q^{86} +1579.11 q^{87} -2700.28 q^{88} -769.166i q^{89} -26.3700i q^{90} -8865.40i q^{91} -4476.37i q^{92} -2534.57i q^{93} +2491.43 q^{94} -14.9461 q^{95} +940.604i q^{96} +3332.34i q^{97} +4393.72i q^{98} +3222.09i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) \) 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} - 144 q^{15} + 2560 q^{16} + 480 q^{17} - 792 q^{19} - 1024 q^{22} + 3400 q^{25} + 768 q^{26} + 640 q^{28} + 1608 q^{29} - 5760 q^{35} - 8640 q^{36} + 6264 q^{41} + 7040 q^{46} + 17912 q^{49} + 1296 q^{51} - 1104 q^{53} + 5040 q^{57} + 13584 q^{59} + 1152 q^{60} - 12288 q^{62} - 2160 q^{63} - 20480 q^{64} + 1152 q^{66} - 3840 q^{68} + 35352 q^{71} + 4608 q^{74} + 3168 q^{75} + 6336 q^{76} - 12672 q^{78} - 15720 q^{79} + 29160 q^{81} - 26872 q^{85} + 18432 q^{86} + 7776 q^{87} + 8192 q^{88} - 18432 q^{94} - 19128 q^{95}+O(q^{100}) \) 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9 - 144 * q^15 + 2560 * q^16 + 480 * q^17 - 792 * q^19 - 1024 * q^22 + 3400 * q^25 + 768 * q^26 + 640 * q^28 + 1608 * q^29 - 5760 * q^35 - 8640 * q^36 + 6264 * q^41 + 7040 * q^46 + 17912 * q^49 + 1296 * q^51 - 1104 * q^53 + 5040 * q^57 + 13584 * q^59 + 1152 * q^60 - 12288 * q^62 - 2160 * q^63 - 20480 * q^64 + 1152 * q^66 - 3840 * q^68 + 35352 * q^71 + 4608 * q^74 + 3168 * q^75 + 6336 * q^76 - 12672 * q^78 - 15720 * q^79 + 29160 * q^81 - 26872 * q^85 + 18432 * q^86 + 7776 * q^87 + 8192 * q^88 - 18432 * q^94 - 19128 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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