LMFDB - Embedded newform 338.10.a.p.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,10,Mod(1,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	338.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,192,-399,3072,-562] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$174.082112623$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 136646 x^{10} - 2261265 x^{9} + 6422687308 x^{8} + 214352365700 x^{7} + \cdots - 14\!\cdots\!24 $ x^12 - x^11 - 136646x^10 - 2261265x^9 + 6422687308x^8 + 214352365700x^7 - 113292049988480x^6 - 5422180918282688x^5 + 449225802381939008x^4 + 23649776612717976832x^3 - 253873801835065913984x^2 - 19616063257504031524864x - 140050093578719428109824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{3}\cdot 7\cdot 13^{8} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$230.287$ of defining polynomial
Character	$\chi$	$=$	338.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+16.0000 q^{2} +171.780 q^{3} +256.000 q^{4} +407.110 q^{5} +2748.49 q^{6} -743.867 q^{7} +4096.00 q^{8} +9825.53 q^{9} +6513.76 q^{10} -30721.0 q^{11} +43975.8 q^{12} -11901.9 q^{14} +69933.5 q^{15} +65536.0 q^{16} -161987. q^{17} +157208. q^{18} -473972. q^{19} +104220. q^{20} -127782. q^{21} -491536. q^{22} -1.55493e6 q^{23} +703613. q^{24} -1.78739e6 q^{25} -1.69332e6 q^{27} -190430. q^{28} +2.77798e6 q^{29} +1.11894e6 q^{30} -2.33732e6 q^{31} +1.04858e6 q^{32} -5.27727e6 q^{33} -2.59179e6 q^{34} -302836. q^{35} +2.51533e6 q^{36} -1.34796e6 q^{37} -7.58356e6 q^{38} +1.66752e6 q^{40} -4.99968e6 q^{41} -2.04451e6 q^{42} -1.99295e6 q^{43} -7.86457e6 q^{44} +4.00007e6 q^{45} -2.48788e7 q^{46} +6.42621e6 q^{47} +1.12578e7 q^{48} -3.98003e7 q^{49} -2.85982e7 q^{50} -2.78262e7 q^{51} -2.02717e7 q^{53} -2.70931e7 q^{54} -1.25068e7 q^{55} -3.04688e6 q^{56} -8.14192e7 q^{57} +4.44477e7 q^{58} -7.38949e7 q^{59} +1.79030e7 q^{60} +1.00486e8 q^{61} -3.73970e7 q^{62} -7.30889e6 q^{63} +1.67772e7 q^{64} -8.44362e7 q^{66} +5.30164e7 q^{67} -4.14687e7 q^{68} -2.67106e8 q^{69} -4.84537e6 q^{70} +7.37635e7 q^{71} +4.02454e7 q^{72} +2.27741e8 q^{73} -2.15674e7 q^{74} -3.07038e8 q^{75} -1.21337e8 q^{76} +2.28523e7 q^{77} -5.63682e8 q^{79} +2.66804e7 q^{80} -4.84275e8 q^{81} -7.99948e7 q^{82} +5.36015e8 q^{83} -3.27122e7 q^{84} -6.59466e7 q^{85} -3.18872e7 q^{86} +4.77203e8 q^{87} -1.25833e8 q^{88} -1.03608e9 q^{89} +6.40011e7 q^{90} -3.98061e8 q^{92} -4.01505e8 q^{93} +1.02819e8 q^{94} -1.92959e8 q^{95} +1.80125e8 q^{96} +1.36454e9 q^{97} -6.36804e8 q^{98} -3.01850e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 192 q^{2} - 399 q^{3} + 3072 q^{4} - 562 q^{5} - 6384 q^{6} + 3161 q^{7} + 49152 q^{8} + 54783 q^{9} - 8992 q^{10} - 164271 q^{11} - 102144 q^{12} + 50576 q^{14} + 434244 q^{15} + 786432 q^{16} - 649529 q^{17}+ \cdots - 4431369848 q^{99}+O(q^{100}) $ 12 * q + 192 * q^2 - 399 * q^3 + 3072 * q^4 - 562 * q^5 - 6384 * q^6 + 3161 * q^7 + 49152 * q^8 + 54783 * q^9 - 8992 * q^10 - 164271 * q^11 - 102144 * q^12 + 50576 * q^14 + 434244 * q^15 + 786432 * q^16 - 649529 * q^17 + 876528 * q^18 - 228567 * q^19 - 143872 * q^20 - 3321918 * q^21 - 2628336 * q^22 - 3365321 * q^23 - 1634304 * q^24 + 1357734 * q^25 - 7310211 * q^27 + 809216 * q^28 + 1210855 * q^29 + 6947904 * q^30 + 2031015 * q^31 + 12582912 * q^32 - 3709742 * q^33 - 10392464 * q^34 - 16818664 * q^35 + 14024448 * q^36 + 21152418 * q^37 - 3657072 * q^38 - 2301952 * q^40 - 20819170 * q^41 - 53150688 * q^42 - 37183522 * q^43 - 42053376 * q^44 - 51849705 * q^45 - 53845136 * q^46 + 20020222 * q^47 - 26148864 * q^48 - 79988801 * q^49 + 21723744 * q^50 - 72774687 * q^51 - 74983469 * q^53 - 116963376 * q^54 - 19133432 * q^55 + 12947456 * q^56 - 13760507 * q^57 + 19373680 * q^58 - 136123112 * q^59 + 111166464 * q^60 - 112790708 * q^61 + 32496240 * q^62 + 659441340 * q^63 + 201326592 * q^64 - 59355872 * q^66 - 61165134 * q^67 - 166279424 * q^68 - 69902864 * q^69 - 269098624 * q^70 + 212025009 * q^71 + 224391168 * q^72 + 71937292 * q^73 + 338438688 * q^74 - 628692958 * q^75 - 58513152 * q^76 - 527155758 * q^77 - 1146472537 * q^79 - 36831232 * q^80 + 1297690908 * q^81 - 333106720 * q^82 - 1318830968 * q^83 - 850411008 * q^84 - 1737694467 * q^85 - 594936352 * q^86 - 1405133144 * q^87 - 672854016 * q^88 - 3175197052 * q^89 - 829595280 * q^90 - 861522176 * q^92 - 2432770524 * q^93 + 320323552 * q^94 + 1551319209 * q^95 - 418381824 * q^96 - 5161204312 * q^97 - 1279820816 * q^98 - 4431369848 * q^99

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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	171.780	1.22441	0.612207	−	0.790698i	$-0.290282\pi$
$3$	171.780	1.22441	0.612207	+	0.790698i	$0.290282\pi$
$4$	256.000	0.500000
$5$	407.110	0.291304	0.145652	−	0.989336i	$-0.453472\pi$
$5$	407.110	0.291304	0.145652	+	0.989336i	$0.453472\pi$
$6$	2748.49	0.865791
$7$	−743.867	−0.117099	−0.0585497	−	0.998284i	$-0.518648\pi$
$7$	−743.867	−0.117099	−0.0585497	+	0.998284i	$0.518648\pi$
$8$	4096.00	0.353553
$9$	9825.53	0.499188
$10$	6513.76	0.205983
$11$	−30721.0	−0.632657	−0.316328	−	0.948650i	$-0.602450\pi$
$11$	−30721.0	−0.632657	−0.316328	+	0.948650i	$0.602450\pi$
$12$	43975.8	0.612207
$13$	0	0
$13$	0	0
$14$	−11901.9	−0.0828017
$15$	69933.5	0.356677
$16$	65536.0	0.250000
$17$	−161987.	−0.470393	−0.235196	−	0.971948i	$-0.575573\pi$
$17$	−161987.	−0.470393	−0.235196	+	0.971948i	$0.575573\pi$
$18$	157208.	0.352980
$19$	−473972.	−0.834376	−0.417188	−	0.908820i	$-0.636984\pi$
$19$	−473972.	−0.834376	−0.417188	+	0.908820i	$0.636984\pi$
$20$	104220.	0.145652
$21$	−127782.	−0.143378
$22$	−491536.	−0.447356
$23$	−1.55493e6	−1.15860	−0.579301	−	0.815113i	$-0.696675\pi$
$23$	−1.55493e6	−1.15860	−0.579301	+	0.815113i	$0.696675\pi$
$24$	703613.	0.432896
$25$	−1.78739e6	−0.915142
$26$	0	0
$27$	−1.69332e6	−0.613200
$28$	−190430.	−0.0585497
$29$	2.77798e6	0.729354	0.364677	−	0.931134i	$-0.381179\pi$
$29$	2.77798e6	0.729354	0.364677	+	0.931134i	$0.381179\pi$
$30$	1.11894e6	0.252209
$31$	−2.33732e6	−0.454558	−0.227279	−	0.973830i	$-0.572983\pi$
$31$	−2.33732e6	−0.454558	−0.227279	+	0.973830i	$0.572983\pi$
$32$	1.04858e6	0.176777
$33$	−5.27727e6	−0.774633
$34$	−2.59179e6	−0.332618
$35$	−302836.	−0.0341115
$36$	2.51533e6	0.249594
$37$	−1.34796e6	−0.118242	−0.0591208	−	0.998251i	$-0.518830\pi$
$37$	−1.34796e6	−0.118242	−0.0591208	+	0.998251i	$0.518830\pi$
$38$	−7.58356e6	−0.589993
$39$	0	0
$40$	1.66752e6	0.102992
$41$	−4.99968e6	−0.276321	−0.138161	−	0.990410i	$-0.544119\pi$
$41$	−4.99968e6	−0.276321	−0.138161	+	0.990410i	$0.544119\pi$
$42$	−2.04451e6	−0.101384
$43$	−1.99295e6	−0.0888974	−0.0444487	−	0.999012i	$-0.514153\pi$
$43$	−1.99295e6	−0.0888974	−0.0444487	+	0.999012i	$0.514153\pi$
$44$	−7.86457e6	−0.316328
$45$	4.00007e6	0.145416
$46$	−2.48788e7	−0.819256
$47$	6.42621e6	0.192094	0.0960472	−	0.995377i	$-0.469380\pi$
$47$	6.42621e6	0.192094	0.0960472	+	0.995377i	$0.469380\pi$
$48$	1.12578e7	0.306103
$49$	−3.98003e7	−0.986288
$50$	−2.85982e7	−0.647103
$51$	−2.78262e7	−0.575955
$52$	0	0
$53$	−2.02717e7	−0.352897	−0.176449	−	0.984310i	$-0.556461\pi$
$53$	−2.02717e7	−0.352897	−0.176449	+	0.984310i	$0.556461\pi$
$54$	−2.70931e7	−0.433598
$55$	−1.25068e7	−0.184296
$56$	−3.04688e6	−0.0414009
$57$	−8.14192e7	−1.02162
$58$	4.44477e7	0.515731
$59$	−7.38949e7	−0.793926	−0.396963	−	0.917835i	$-0.629936\pi$
$59$	−7.38949e7	−0.793926	−0.396963	+	0.917835i	$0.629936\pi$
$60$	1.79030e7	0.178338
$61$	1.00486e8	0.929228	0.464614	−	0.885513i	$-0.346193\pi$
$61$	1.00486e8	0.929228	0.464614	+	0.885513i	$0.346193\pi$
$62$	−3.73970e7	−0.321421
$63$	−7.30889e6	−0.0584546
$64$	1.67772e7	0.125000
$65$	0	0
$66$	−8.44362e7	−0.547748
$67$	5.30164e7	0.321421	0.160710	−	0.987002i	$-0.448622\pi$
$67$	5.30164e7	0.321421	0.160710	+	0.987002i	$0.448622\pi$
$68$	−4.14687e7	−0.235196
$69$	−2.67106e8	−1.41861
$70$	−4.84537e6	−0.0241205
$71$	7.37635e7	0.344492	0.172246	−	0.985054i	$-0.444898\pi$
$71$	7.37635e7	0.344492	0.172246	+	0.985054i	$0.444898\pi$
$72$	4.02454e7	0.176490
$73$	2.27741e8	0.938615	0.469308	−	0.883035i	$-0.344504\pi$
$73$	2.27741e8	0.938615	0.469308	+	0.883035i	$0.344504\pi$
$74$	−2.15674e7	−0.0836095
$75$	−3.07038e8	−1.12051
$76$	−1.21337e8	−0.417188
$77$	2.28523e7	0.0740837
$78$	0	0
$79$	−5.63682e8	−1.62822	−0.814108	−	0.580714i	$-0.802774\pi$
$79$	−5.63682e8	−1.62822	−0.814108	+	0.580714i	$0.802774\pi$
$80$	2.66804e7	0.0728261
$81$	−4.84275e8	−1.25000
$82$	−7.99948e7	−0.195389
$83$	5.36015e8	1.23973	0.619863	−	0.784710i	$-0.287188\pi$
$83$	5.36015e8	1.23973	0.619863	+	0.784710i	$0.287188\pi$
$84$	−3.27122e7	−0.0716890
$85$	−6.59466e7	−0.137027
$86$	−3.18872e7	−0.0628599
$87$	4.77203e8	0.893030
$88$	−1.25833e8	−0.223678
$89$	−1.03608e9	−1.75041	−0.875203	−	0.483756i	$-0.839272\pi$
$89$	−1.03608e9	−1.75041	−0.875203	+	0.483756i	$0.839272\pi$
$90$	6.40011e7	0.102824
$91$	0	0
$92$	−3.98061e8	−0.579301
$93$	−4.01505e8	−0.556567
$94$	1.02819e8	0.135831
$95$	−1.92959e8	−0.243057
$96$	1.80125e8	0.216448
$97$	1.36454e9	1.56500	0.782500	−	0.622650i	$-0.213944\pi$
$97$	1.36454e9	1.56500	0.782500	+	0.622650i	$0.213944\pi$
$98$	−6.36804e8	−0.697411
$99$	−3.01850e8	−0.315815
$100$	−4.57571e8	−0.457571
$101$	−1.36473e9	−1.30497	−0.652485	−	0.757801i	$-0.726274\pi$
$101$	−1.36473e9	−1.30497	−0.652485	+	0.757801i	$0.726274\pi$
$102$	−4.45220e8	−0.407262
$103$	1.16578e9	1.02058	0.510292	−	0.860001i	$-0.329537\pi$
$103$	1.16578e9	1.02058	0.510292	+	0.860001i	$0.329537\pi$
$104$	0	0
$105$	−5.20213e7	−0.0417666
$106$	−3.24347e8	−0.249536
$107$	−8.41266e8	−0.620450	−0.310225	−	0.950663i	$-0.600404\pi$
$107$	−8.41266e8	−0.620450	−0.310225	+	0.950663i	$0.600404\pi$
$108$	−4.33490e8	−0.306600
$109$	−6.13020e8	−0.415963	−0.207982	−	0.978133i	$-0.566689\pi$
$109$	−6.13020e8	−0.415963	−0.207982	+	0.978133i	$0.566689\pi$
$110$	−2.00109e8	−0.130317
$111$	−2.31554e8	−0.144777
$112$	−4.87501e7	−0.0292748
$113$	1.02536e9	0.591594	0.295797	−	0.955251i	$-0.404415\pi$
$113$	1.02536e9	0.591594	0.295797	+	0.955251i	$0.404415\pi$
$114$	−1.30271e9	−0.722395
$115$	−6.33026e8	−0.337506
$116$	7.11163e8	0.364677
$117$	0	0
$118$	−1.18232e9	−0.561391
$119$	1.20497e8	0.0550826
$120$	2.86448e8	0.126104
$121$	−1.41417e9	−0.599746
$122$	1.60778e9	0.657063
$123$	−8.58846e8	−0.338332
$124$	−5.98353e8	−0.227279
$125$	−1.52280e9	−0.557889
$126$	−1.16942e8	−0.0413337
$127$	−3.19992e9	−1.09150	−0.545749	−	0.837949i	$-0.683755\pi$
$127$	−3.19992e9	−1.09150	−0.545749	+	0.837949i	$0.683755\pi$
$128$	2.68435e8	0.0883883
$129$	−3.42350e8	−0.108847
$130$	0	0
$131$	6.26836e9	1.85966	0.929830	−	0.367990i	$-0.119954\pi$
$131$	6.26836e9	1.85966	0.929830	+	0.367990i	$0.119954\pi$
$132$	−1.35098e9	−0.387317
$133$	3.52573e8	0.0977049
$134$	8.48263e8	0.227279
$135$	−6.89368e8	−0.178628
$136$	−6.63499e8	−0.166309
$137$	−4.13958e7	−0.0100395	−0.00501976	−	0.999987i	$-0.501598\pi$
$137$	−4.13958e7	−0.0100395	−0.00501976	+	0.999987i	$0.501598\pi$
$138$	−4.27369e9	−1.00311
$139$	2.33474e9	0.530484	0.265242	−	0.964182i	$-0.414548\pi$
$139$	2.33474e9	0.530484	0.265242	+	0.964182i	$0.414548\pi$
$140$	−7.75260e7	−0.0170558
$141$	1.10390e9	0.235203
$142$	1.18022e9	0.243592
$143$	0	0
$144$	6.43926e8	0.124797
$145$	1.13094e9	0.212464
$146$	3.64385e9	0.663701
$147$	−6.83691e9	−1.20762
$148$	−3.45079e8	−0.0591208
$149$	2.84125e9	0.472250	0.236125	−	0.971723i	$-0.424123\pi$
$149$	2.84125e9	0.472250	0.236125	+	0.971723i	$0.424123\pi$
$150$	−4.91261e9	−0.792322
$151$	−1.03576e10	−1.62130	−0.810649	−	0.585532i	$-0.800886\pi$
$151$	−1.03576e10	−1.62130	−0.810649	+	0.585532i	$0.800886\pi$
$152$	−1.94139e9	−0.294997
$153$	−1.59161e9	−0.234815
$154$	3.65637e8	0.0523851
$155$	−9.51544e8	−0.132415
$156$	0	0
$157$	7.32184e9	0.961772	0.480886	−	0.876783i	$-0.340315\pi$
$157$	7.32184e9	0.961772	0.480886	+	0.876783i	$0.340315\pi$
$158$	−9.01890e9	−1.15132
$159$	−3.48228e9	−0.432092
$160$	4.26886e8	0.0514958
$161$	1.15666e9	0.135672
$162$	−7.74841e9	−0.883883
$163$	1.48972e10	1.65295	0.826475	−	0.562974i	$-0.190343\pi$
$163$	1.48972e10	1.65295	0.826475	+	0.562974i	$0.190343\pi$
$164$	−1.27992e9	−0.138161
$165$	−2.14843e9	−0.225654
$166$	8.57624e9	0.876619
$167$	3.34802e9	0.333092	0.166546	−	0.986034i	$-0.446739\pi$
$167$	3.34802e9	0.333092	0.166546	+	0.986034i	$0.446739\pi$
$168$	−5.23395e8	−0.0506918
$169$	0	0
$170$	−1.05515e9	−0.0968929
$171$	−4.65703e9	−0.416511
$172$	−5.10196e8	−0.0444487
$173$	−1.66055e10	−1.40943	−0.704715	−	0.709491i	$-0.748925\pi$
$173$	−1.66055e10	−1.40943	−0.704715	+	0.709491i	$0.748925\pi$
$174$	7.63524e9	0.631468
$175$	1.32958e9	0.107162
$176$	−2.01333e9	−0.158164
$177$	−1.26937e10	−0.972094
$178$	−1.65773e10	−1.23772
$179$	2.25158e10	1.63926	0.819631	−	0.572892i	$-0.194179\pi$
$179$	2.25158e10	1.63926	0.819631	+	0.572892i	$0.194179\pi$
$180$	1.02402e9	0.0727078
$181$	−4.01508e8	−0.0278062	−0.0139031	−	0.999903i	$-0.504426\pi$
$181$	−4.01508e8	−0.0278062	−0.0139031	+	0.999903i	$0.504426\pi$
$182$	0	0
$183$	1.72616e10	1.13776
$184$	−6.36898e9	−0.409628
$185$	−5.48770e8	−0.0344443
$186$	−6.42408e9	−0.393553
$187$	4.97640e9	0.297597
$188$	1.64511e9	0.0960472
$189$	1.25961e9	0.0718053
$190$	−3.08734e9	−0.171867
$191$	−1.13978e10	−0.619684	−0.309842	−	0.950788i	$-0.600276\pi$
$191$	−1.13978e10	−0.619684	−0.309842	+	0.950788i	$0.600276\pi$
$192$	2.88200e9	0.153052
$193$	2.17344e10	1.12756	0.563780	−	0.825925i	$-0.309347\pi$
$193$	2.17344e10	1.12756	0.563780	+	0.825925i	$0.309347\pi$
$194$	2.18327e10	1.10662
$195$	0	0
$196$	−1.01889e10	−0.493144
$197$	9.57836e9	0.453099	0.226550	−	0.974000i	$-0.427255\pi$
$197$	9.57836e9	0.453099	0.226550	+	0.974000i	$0.427255\pi$
$198$	−4.82960e9	−0.223315
$199$	−3.06708e10	−1.38639	−0.693196	−	0.720749i	$-0.743798\pi$
$199$	−3.06708e10	−1.38639	−0.693196	+	0.720749i	$0.743798\pi$
$200$	−7.32113e9	−0.323552
$201$	9.10718e9	0.393552
$202$	−2.18357e10	−0.922753
$203$	−2.06645e9	−0.0854068
$204$	−7.12351e9	−0.287977
$205$	−2.03542e9	−0.0804936
$206$	1.86525e10	0.721661
$207$	−1.52780e10	−0.578361
$208$	0	0
$209$	1.45609e10	0.527874
$210$	−8.32341e8	−0.0295335
$211$	−2.69897e10	−0.937405	−0.468703	−	0.883356i	$-0.655278\pi$
$211$	−2.69897e10	−0.937405	−0.468703	+	0.883356i	$0.655278\pi$
$212$	−5.18955e9	−0.176449
$213$	1.26711e10	0.421800
$214$	−1.34603e10	−0.438724
$215$	−8.11351e8	−0.0258962
$216$	−6.93584e9	−0.216799
$217$	1.73865e9	0.0532285
$218$	−9.80832e9	−0.294131
$219$	3.91214e10	1.14925
$220$	−3.20175e9	−0.0921478
$221$	0	0
$222$	−3.70486e9	−0.102373
$223$	1.58759e10	0.429898	0.214949	−	0.976625i	$-0.431041\pi$
$223$	1.58759e10	0.429898	0.214949	+	0.976625i	$0.431041\pi$
$224$	−7.80002e8	−0.0207004
$225$	−1.75620e10	−0.456828
$226$	1.64058e10	0.418320
$227$	7.00470e10	1.75095	0.875474	−	0.483265i	$-0.160549\pi$
$227$	7.00470e10	1.75095	0.875474	+	0.483265i	$0.160549\pi$
$228$	−2.08433e10	−0.510811
$229$	−2.13198e10	−0.512299	−0.256149	−	0.966637i	$-0.582454\pi$
$229$	−2.13198e10	−0.512299	−0.256149	+	0.966637i	$0.582454\pi$
$230$	−1.01284e10	−0.238653
$231$	3.92559e9	0.0907090
$232$	1.13786e10	0.257865
$233$	−4.25668e10	−0.946170	−0.473085	−	0.881017i	$-0.656860\pi$
$233$	−4.25668e10	−0.946170	−0.473085	+	0.881017i	$0.656860\pi$
$234$	0	0
$235$	2.61618e9	0.0559579
$236$	−1.89171e10	−0.396963
$237$	−9.68295e10	−1.99361
$238$	1.92795e9	0.0389493
$239$	1.57721e10	0.312680	0.156340	−	0.987703i	$-0.450030\pi$
$239$	1.57721e10	0.312680	0.156340	+	0.987703i	$0.450030\pi$
$240$	4.58316e9	0.0891692
$241$	−8.87866e10	−1.69540	−0.847698	−	0.530480i	$-0.822012\pi$
$241$	−8.87866e10	−1.69540	−0.847698	+	0.530480i	$0.822012\pi$
$242$	−2.26267e10	−0.424084
$243$	−4.98594e10	−0.917316
$244$	2.57245e10	0.464614
$245$	−1.62031e10	−0.287310
$246$	−1.37415e10	−0.239237
$247$	0	0
$248$	−9.57364e9	−0.160711
$249$	9.20769e10	1.51794
$250$	−2.43648e10	−0.394487
$251$	−1.50754e10	−0.239739	−0.119869	−	0.992790i	$-0.538248\pi$
$251$	−1.50754e10	−0.239739	−0.119869	+	0.992790i	$0.538248\pi$
$252$	−1.87108e9	−0.0292273
$253$	4.77689e10	0.732998
$254$	−5.11988e10	−0.771805
$255$	−1.13283e10	−0.167778
$256$	4.29497e9	0.0625000
$257$	−8.79773e10	−1.25797	−0.628987	−	0.777416i	$-0.716530\pi$
$257$	−8.79773e10	−1.25797	−0.628987	+	0.777416i	$0.716530\pi$
$258$	−5.47760e9	−0.0769665
$259$	1.00271e9	0.0138460
$260$	0	0
$261$	2.72951e10	0.364085
$262$	1.00294e11	1.31498
$263$	−7.02242e10	−0.905077	−0.452539	−	0.891745i	$-0.649482\pi$
$263$	−7.02242e10	−0.905077	−0.452539	+	0.891745i	$0.649482\pi$
$264$	−2.16157e10	−0.273874
$265$	−8.25281e9	−0.102801
$266$	5.64116e9	0.0690878
$267$	−1.77978e11	−2.14322
$268$	1.35722e10	0.160710
$269$	−1.23994e11	−1.44382	−0.721912	−	0.691985i	$-0.756736\pi$
$269$	−1.23994e11	−1.44382	−0.721912	+	0.691985i	$0.756736\pi$
$270$	−1.10299e10	−0.126309
$271$	1.89556e10	0.213489	0.106745	−	0.994286i	$-0.465957\pi$
$271$	1.89556e10	0.213489	0.106745	+	0.994286i	$0.465957\pi$
$272$	−1.06160e10	−0.117598
$273$	0	0
$274$	−6.62332e8	−0.00709902
$275$	5.49103e10	0.578971
$276$	−6.83791e10	−0.709304
$277$	−4.12889e10	−0.421381	−0.210690	−	0.977553i	$-0.567571\pi$
$277$	−4.12889e10	−0.421381	−0.210690	+	0.977553i	$0.567571\pi$
$278$	3.73559e10	0.375109
$279$	−2.29654e10	−0.226910
$280$	−1.24042e9	−0.0120602
$281$	1.95250e10	0.186816	0.0934079	−	0.995628i	$-0.470224\pi$
$281$	1.95250e10	0.186816	0.0934079	+	0.995628i	$0.470224\pi$
$282$	1.76624e10	0.166314
$283$	−4.18914e10	−0.388227	−0.194114	−	0.980979i	$-0.562183\pi$
$283$	−4.18914e10	−0.388227	−0.194114	+	0.980979i	$0.562183\pi$
$284$	1.88835e10	0.172246
$285$	−3.31466e10	−0.297603
$286$	0	0
$287$	3.71910e9	0.0323570
$288$	1.03028e10	0.0882449
$289$	−9.23480e10	−0.778731
$290$	1.80951e10	0.150235
$291$	2.34402e11	1.91621
$292$	5.83016e10	0.469308
$293$	−1.37947e11	−1.09347	−0.546736	−	0.837305i	$-0.684130\pi$
$293$	−1.37947e11	−1.09347	−0.546736	+	0.837305i	$0.684130\pi$
$294$	−1.09391e11	−0.853919
$295$	−3.00833e10	−0.231274
$296$	−5.52126e9	−0.0418047
$297$	5.20205e10	0.387945
$298$	4.54600e10	0.333931
$299$	0	0
$300$	−7.86017e10	−0.560256
$301$	1.48249e9	0.0104098
$302$	−1.65722e11	−1.14643
$303$	−2.34434e11	−1.59782
$304$	−3.10623e10	−0.208594
$305$	4.09089e10	0.270688
$306$	−2.54657e10	−0.166039
$307$	5.96149e10	0.383029	0.191515	−	0.981490i	$-0.438660\pi$
$307$	5.96149e10	0.383029	0.191515	+	0.981490i	$0.438660\pi$
$308$	5.85020e9	0.0370418
$309$	2.00258e11	1.24962
$310$	−1.52247e10	−0.0936314
$311$	1.71576e11	1.04000	0.520001	−	0.854166i	$-0.325932\pi$
$311$	1.71576e11	1.04000	0.520001	+	0.854166i	$0.325932\pi$
$312$	0	0
$313$	3.69157e9	0.0217401	0.0108700	−	0.999941i	$-0.496540\pi$
$313$	3.69157e9	0.0217401	0.0108700	+	0.999941i	$0.496540\pi$
$314$	1.17149e11	0.680075
$315$	−2.97552e9	−0.0170281
$316$	−1.44302e11	−0.814108
$317$	1.65466e11	0.920324	0.460162	−	0.887835i	$-0.347791\pi$
$317$	1.65466e11	0.920324	0.460162	+	0.887835i	$0.347791\pi$
$318$	−5.57165e10	−0.305535
$319$	−8.53423e10	−0.461430
$320$	6.83017e9	0.0364130
$321$	−1.44513e11	−0.759687
$322$	1.85065e10	0.0959343
$323$	7.67774e10	0.392484
$324$	−1.23974e11	−0.625000
$325$	0	0
$326$	2.38355e11	1.16881
$327$	−1.05305e11	−0.509311
$328$	−2.04787e10	−0.0976943
$329$	−4.78025e9	−0.0224941
$330$	−3.43748e10	−0.159561
$331$	1.01805e11	0.466168	0.233084	−	0.972457i	$-0.425118\pi$
$331$	1.01805e11	0.466168	0.233084	+	0.972457i	$0.425118\pi$
$332$	1.37220e11	0.619863
$333$	−1.32445e10	−0.0590249
$334$	5.35684e10	0.235532
$335$	2.15835e10	0.0936312
$336$	−8.37431e9	−0.0358445
$337$	−1.79113e10	−0.0756470	−0.0378235	−	0.999284i	$-0.512042\pi$
$337$	−1.79113e10	−0.0756470	−0.0378235	+	0.999284i	$0.512042\pi$
$338$	0	0
$339$	1.76137e11	0.724356
$340$	−1.68823e10	−0.0685137
$341$	7.18046e10	0.287579
$342$	−7.45125e10	−0.294518
$343$	5.96239e10	0.232593
$344$	−8.16313e9	−0.0314300
$345$	−1.08741e11	−0.413247
$346$	−2.65687e11	−0.996617
$347$	−1.16861e11	−0.432699	−0.216349	−	0.976316i	$-0.569415\pi$
$347$	−1.16861e11	−0.432699	−0.216349	+	0.976316i	$0.569415\pi$
$348$	1.22164e11	0.446515
$349$	4.41747e11	1.59389	0.796947	−	0.604050i	$-0.206447\pi$
$349$	4.41747e11	1.59389	0.796947	+	0.604050i	$0.206447\pi$
$350$	2.12733e10	0.0757753
$351$	0	0
$352$	−3.22133e10	−0.111839
$353$	−3.80388e11	−1.30389	−0.651945	−	0.758266i	$-0.726047\pi$
$353$	−3.80388e11	−1.30389	−0.651945	+	0.758266i	$0.726047\pi$
$354$	−2.03099e11	−0.687374
$355$	3.00298e10	0.100352
$356$	−2.65237e11	−0.875203
$357$	2.06990e10	0.0674439
$358$	3.60252e11	1.15913
$359$	−4.62611e11	−1.46991	−0.734956	−	0.678115i	$-0.762797\pi$
$359$	−4.62611e11	−1.46991	−0.734956	+	0.678115i	$0.762797\pi$
$360$	1.63843e10	0.0514122
$361$	−9.80378e10	−0.303816
$362$	−6.42413e9	−0.0196619
$363$	−2.42927e11	−0.734337
$364$	0	0
$365$	9.27155e10	0.273423
$366$	2.76185e11	0.804517
$367$	1.46833e11	0.422501	0.211250	−	0.977432i	$-0.432246\pi$
$367$	1.46833e11	0.422501	0.211250	+	0.977432i	$0.432246\pi$
$368$	−1.01904e11	−0.289651
$369$	−4.91244e10	−0.137936
$370$	−8.78032e9	−0.0243558
$371$	1.50794e10	0.0413240
$372$	−1.02785e11	−0.278284
$373$	−5.69730e11	−1.52398	−0.761990	−	0.647589i	$-0.775777\pi$
$373$	−5.69730e11	−1.52398	−0.761990	+	0.647589i	$0.775777\pi$
$374$	7.96225e10	0.210433
$375$	−2.61587e11	−0.683087
$376$	2.63218e10	0.0679156
$377$	0	0
$378$	2.01537e10	0.0507740
$379$	−5.10729e11	−1.27149	−0.635747	−	0.771898i	$-0.719308\pi$
$379$	−5.10729e11	−1.27149	−0.635747	+	0.771898i	$0.719308\pi$
$380$	−4.93975e10	−0.121529
$381$	−5.49684e11	−1.33644
$382$	−1.82364e11	−0.438182
$383$	1.30775e11	0.310548	0.155274	−	0.987871i	$-0.450374\pi$
$383$	1.30775e11	0.310548	0.155274	+	0.987871i	$0.450374\pi$
$384$	4.61120e10	0.108224
$385$	9.30342e9	0.0215809
$386$	3.47750e11	0.797305
$387$	−1.95818e10	−0.0443765
$388$	3.49323e11	0.782500
$389$	1.94359e11	0.430359	0.215179	−	0.976575i	$-0.430966\pi$
$389$	1.94359e11	0.430359	0.215179	+	0.976575i	$0.430966\pi$
$390$	0	0
$391$	2.51878e11	0.544998
$392$	−1.63022e11	−0.348705
$393$	1.07678e12	2.27699
$394$	1.53254e11	0.320390
$395$	−2.29480e11	−0.474306
$396$	−7.72736e10	−0.157907
$397$	3.39169e11	0.685265	0.342633	−	0.939469i	$-0.388681\pi$
$397$	3.39169e11	0.685265	0.342633	+	0.939469i	$0.388681\pi$
$398$	−4.90733e11	−0.980328
$399$	6.05651e10	0.119631
$400$	−1.17138e11	−0.228785
$401$	2.96624e11	0.572870	0.286435	−	0.958100i	$-0.407530\pi$
$401$	2.96624e11	0.572870	0.286435	+	0.958100i	$0.407530\pi$
$402$	1.45715e11	0.278283
$403$	0	0
$404$	−3.49371e11	−0.652485
$405$	−1.97153e11	−0.364130
$406$	−3.30632e10	−0.0603917
$407$	4.14108e10	0.0748064
$408$	−1.13976e11	−0.203631
$409$	−3.83507e11	−0.677670	−0.338835	−	0.940846i	$-0.610033\pi$
$409$	−3.83507e11	−0.677670	−0.338835	+	0.940846i	$0.610033\pi$
$410$	−3.25667e10	−0.0569175
$411$	−7.11098e9	−0.0122925
$412$	2.98439e11	0.510292
$413$	5.49680e10	0.0929682
$414$	−2.44447e11	−0.408963
$415$	2.18217e11	0.361137
$416$	0	0
$417$	4.01063e11	0.649532
$418$	2.32974e11	0.373263
$419$	2.78496e11	0.441424	0.220712	−	0.975339i	$-0.429162\pi$
$419$	2.78496e11	0.441424	0.220712	+	0.975339i	$0.429162\pi$
$420$	−1.33174e10	−0.0208833
$421$	3.12942e11	0.485506	0.242753	−	0.970088i	$-0.421949\pi$
$421$	3.12942e11	0.485506	0.242753	+	0.970088i	$0.421949\pi$
$422$	−4.31835e11	−0.662845
$423$	6.31409e10	0.0958913
$424$	−8.30328e10	−0.124768
$425$	2.89534e11	0.430476
$426$	2.02738e11	0.298258
$427$	−7.47484e10	−0.108812
$428$	−2.15364e11	−0.310225
$429$	0	0
$430$	−1.29816e10	−0.0183114
$431$	−1.02866e12	−1.43591	−0.717953	−	0.696091i	$-0.754921\pi$
$431$	−1.02866e12	−1.43591	−0.717953	+	0.696091i	$0.754921\pi$
$432$	−1.10974e11	−0.153300
$433$	7.13458e11	0.975378	0.487689	−	0.873017i	$-0.337840\pi$
$433$	7.13458e11	0.975378	0.487689	+	0.873017i	$0.337840\pi$
$434$	2.78184e10	0.0376382
$435$	1.94274e11	0.260143
$436$	−1.56933e11	−0.207982
$437$	7.36992e11	0.966710
$438$	6.25942e11	0.812645
$439$	−1.03174e12	−1.32581	−0.662903	−	0.748705i	$-0.730676\pi$
$439$	−1.03174e12	−1.32581	−0.662903	+	0.748705i	$0.730676\pi$
$440$	−5.12279e10	−0.0651583
$441$	−3.91059e11	−0.492343
$442$	0	0
$443$	−2.25083e11	−0.277668	−0.138834	−	0.990316i	$-0.544335\pi$
$443$	−2.25083e11	−0.277668	−0.138834	+	0.990316i	$0.544335\pi$
$444$	−5.92778e10	−0.0723884
$445$	−4.21799e11	−0.509900
$446$	2.54014e11	0.303984
$447$	4.88072e11	0.578229
$448$	−1.24800e10	−0.0146374
$449$	3.50928e11	0.407483	0.203741	−	0.979025i	$-0.434690\pi$
$449$	3.50928e11	0.407483	0.203741	+	0.979025i	$0.434690\pi$
$450$	−2.80992e11	−0.323026
$451$	1.53595e11	0.174817
$452$	2.62492e11	0.295797
$453$	−1.77923e12	−1.98514
$454$	1.12075e12	1.23811
$455$	0	0
$456$	−3.33493e11	−0.361198
$457$	1.12300e12	1.20436	0.602180	−	0.798361i	$-0.294299\pi$
$457$	1.12300e12	1.20436	0.602180	+	0.798361i	$0.294299\pi$
$458$	−3.41117e11	−0.362250
$459$	2.74296e11	0.288445
$460$	−1.62055e11	−0.168753
$461$	7.79501e11	0.803826	0.401913	−	0.915678i	$-0.368345\pi$
$461$	7.79501e11	0.803826	0.401913	+	0.915678i	$0.368345\pi$
$462$	6.28094e10	0.0641410
$463$	1.57235e12	1.59014	0.795068	−	0.606521i	$-0.207435\pi$
$463$	1.57235e12	1.59014	0.795068	+	0.606521i	$0.207435\pi$
$464$	1.82058e11	0.182338
$465$	−1.63457e11	−0.162130
$466$	−6.81068e11	−0.669043
$467$	4.59549e11	0.447101	0.223550	−	0.974692i	$-0.428235\pi$
$467$	4.59549e11	0.447101	0.223550	+	0.974692i	$0.428235\pi$
$468$	0	0
$469$	−3.94372e10	−0.0376381
$470$	4.18588e10	0.0395682
$471$	1.25775e12	1.17761
$472$	−3.02673e11	−0.280695
$473$	6.12255e10	0.0562415
$474$	−1.54927e12	−1.40969
$475$	8.47172e11	0.763573
$476$	3.08472e10	0.0275413
$477$	−1.99180e11	−0.176162
$478$	2.52354e11	0.221098
$479$	−1.26363e12	−1.09676	−0.548378	−	0.836231i	$-0.684755\pi$
$479$	−1.26363e12	−1.09676	−0.548378	+	0.836231i	$0.684755\pi$
$480$	7.33306e10	0.0630521
$481$	0	0
$482$	−1.42059e12	−1.19883
$483$	1.98691e11	0.166118
$484$	−3.62027e11	−0.299873
$485$	5.55519e11	0.455891
$486$	−7.97750e11	−0.648640
$487$	5.57232e11	0.448906	0.224453	−	0.974485i	$-0.427940\pi$
$487$	5.57232e11	0.448906	0.224453	+	0.974485i	$0.427940\pi$
$488$	4.11591e11	0.328532
$489$	2.55904e12	2.02389
$490$	−2.59249e11	−0.203159
$491$	−1.63350e12	−1.26839	−0.634193	−	0.773175i	$-0.718668\pi$
$491$	−1.63350e12	−1.26839	−0.634193	+	0.773175i	$0.718668\pi$
$492$	−2.19865e11	−0.169166
$493$	−4.49997e11	−0.343082
$494$	0	0
$495$	−1.22886e11	−0.0919982
$496$	−1.53178e11	−0.113640
$497$	−5.48702e10	−0.0403397
$498$	1.47323e12	1.07334
$499$	2.09366e11	0.151166	0.0755830	−	0.997140i	$-0.475918\pi$
$499$	2.09366e11	0.151166	0.0755830	+	0.997140i	$0.475918\pi$
$500$	−3.89837e11	−0.278944
$501$	5.75125e11	0.407843
$502$	−2.41207e11	−0.169521
$503$	2.51323e12	1.75055	0.875277	−	0.483621i	$-0.160679\pi$
$503$	2.51323e12	1.75055	0.875277	+	0.483621i	$0.160679\pi$
$504$	−2.99372e10	−0.0206668
$505$	−5.55595e11	−0.380143
$506$	7.64302e11	0.518308
$507$	0	0
$508$	−8.19180e11	−0.545749
$509$	1.58384e12	1.04588	0.522940	−	0.852370i	$-0.324835\pi$
$509$	1.58384e12	1.04588	0.522940	+	0.852370i	$0.324835\pi$
$510$	−1.81253e11	−0.118637
$511$	−1.69409e11	−0.109911
$512$	6.87195e10	0.0441942
$513$	8.02588e11	0.511640
$514$	−1.40764e12	−0.889522
$515$	4.74600e11	0.297300
$516$	−8.76417e10	−0.0544236
$517$	−1.97420e11	−0.121530
$518$	1.60433e10	0.00979062
$519$	−2.85249e12	−1.72572
$520$	0	0
$521$	4.07598e11	0.242361	0.121181	−	0.992630i	$-0.461332\pi$
$521$	4.07598e11	0.242361	0.121181	+	0.992630i	$0.461332\pi$
$522$	4.36722e11	0.257447
$523$	1.83075e12	1.06997	0.534985	−	0.844862i	$-0.320317\pi$
$523$	1.83075e12	1.06997	0.534985	+	0.844862i	$0.320317\pi$
$524$	1.60470e12	0.929830
$525$	2.28396e11	0.131211
$526$	−1.12359e12	−0.639986
$527$	3.78615e11	0.213821
$528$	−3.45851e11	−0.193658
$529$	6.16643e11	0.342360
$530$	−1.32045e11	−0.0726909
$531$	−7.26056e11	−0.396319
$532$	9.02586e10	0.0488524
$533$	0	0
$534$	−2.84766e12	−1.51549
$535$	−3.42488e11	−0.180740
$536$	2.17155e11	0.113639
$537$	3.86777e12	2.00713
$538$	−1.98390e12	−1.02094
$539$	1.22270e12	0.623981
$540$	−1.76478e11	−0.0893139
$541$	3.70914e12	1.86160	0.930798	−	0.365534i	$-0.119114\pi$
$541$	3.70914e12	1.86160	0.930798	+	0.365534i	$0.119114\pi$
$542$	3.03290e11	0.150960
$543$	−6.89713e10	−0.0340462
$544$	−1.69856e11	−0.0831544
$545$	−2.49566e11	−0.121172
$546$	0	0
$547$	6.53711e11	0.312207	0.156104	−	0.987741i	$-0.450107\pi$
$547$	6.53711e11	0.312207	0.156104	+	0.987741i	$0.450107\pi$
$548$	−1.05973e10	−0.00501976
$549$	9.87330e11	0.463860
$550$	8.78564e11	0.409394
$551$	−1.31669e12	−0.608555
$552$	−1.09407e12	−0.501554
$553$	4.19304e11	0.190663
$554$	−6.60623e11	−0.297961
$555$	−9.42679e10	−0.0421741
$556$	5.97694e11	0.265242
$557$	3.67485e12	1.61768	0.808838	−	0.588031i	$-0.200097\pi$
$557$	3.67485e12	1.61768	0.808838	+	0.588031i	$0.200097\pi$
$558$	−3.67446e11	−0.160450
$559$	0	0
$560$	−1.98467e10	−0.00852788
$561$	8.54849e11	0.364382
$562$	3.12401e11	0.132099
$563$	1.05942e12	0.444406	0.222203	−	0.975000i	$-0.428675\pi$
$563$	1.05942e12	0.444406	0.222203	+	0.975000i	$0.428675\pi$
$564$	2.82598e11	0.117602
$565$	4.17435e11	0.172334
$566$	−6.70263e11	−0.274518
$567$	3.60237e11	0.146374
$568$	3.02135e11	0.121796
$569$	8.80266e11	0.352053	0.176027	−	0.984385i	$-0.443675\pi$
$569$	8.80266e11	0.352053	0.176027	+	0.984385i	$0.443675\pi$
$570$	−5.30345e11	−0.210437
$571$	1.68787e12	0.664473	0.332237	−	0.943196i	$-0.392197\pi$
$571$	1.68787e12	0.664473	0.332237	+	0.943196i	$0.392197\pi$
$572$	0	0
$573$	−1.95792e12	−0.758749
$574$	5.95055e10	0.0228799
$575$	2.77925e12	1.06029
$576$	1.64845e11	0.0623986
$577$	−3.43447e12	−1.28994	−0.644968	−	0.764210i	$-0.723129\pi$
$577$	−3.43447e12	−1.28994	−0.644968	+	0.764210i	$0.723129\pi$
$578$	−1.47757e12	−0.550646
$579$	3.73354e12	1.38060
$580$	2.89521e11	0.106232
$581$	−3.98724e11	−0.145171
$582$	3.75043e12	1.35496
$583$	6.22766e11	0.223263
$584$	9.32826e11	0.331851
$585$	0	0
$586$	−2.20715e12	−0.773201
$587$	−2.96761e12	−1.03166	−0.515828	−	0.856692i	$-0.672516\pi$
$587$	−2.96761e12	−1.03166	−0.515828	+	0.856692i	$0.672516\pi$
$588$	−1.75025e12	−0.603812
$589$	1.10782e12	0.379273
$590$	−4.81333e11	−0.163535
$591$	1.64538e12	0.554781
$592$	−8.83402e10	−0.0295604
$593$	5.26715e12	1.74916	0.874580	−	0.484881i	$-0.161137\pi$
$593$	5.26715e12	1.74916	0.874580	+	0.484881i	$0.161137\pi$
$594$	8.32328e11	0.274319
$595$	4.90555e10	0.0160458
$596$	7.27361e11	0.236125
$597$	−5.26864e12	−1.69752
$598$	0	0
$599$	5.86654e12	1.86192	0.930960	−	0.365120i	$-0.118972\pi$
$599$	5.86654e12	1.86192	0.930960	+	0.365120i	$0.118972\pi$
$600$	−1.25763e12	−0.396161
$601$	−1.71503e11	−0.0536212	−0.0268106	−	0.999641i	$-0.508535\pi$
$601$	−1.71503e11	−0.0536212	−0.0268106	+	0.999641i	$0.508535\pi$
$602$	2.37199e10	0.00736086
$603$	5.20914e11	0.160449
$604$	−2.65155e12	−0.810649
$605$	−5.75722e11	−0.174708
$606$	−3.75094e12	−1.12983
$607$	−1.41459e12	−0.422942	−0.211471	−	0.977384i	$-0.567825\pi$
$607$	−1.41459e12	−0.422942	−0.211471	+	0.977384i	$0.567825\pi$
$608$	−4.96996e11	−0.147498
$609$	−3.54976e11	−0.104573
$610$	6.54543e11	0.191405
$611$	0	0
$612$	−4.07452e11	−0.117407
$613$	5.12682e10	0.0146648	0.00733239	−	0.999973i	$-0.497666\pi$
$613$	5.12682e10	0.0146648	0.00733239	+	0.999973i	$0.497666\pi$
$614$	9.53838e11	0.270843
$615$	−3.49645e11	−0.0985574
$616$	9.36032e10	0.0261925
$617$	−1.01857e12	−0.282947	−0.141474	−	0.989942i	$-0.545184\pi$
$617$	−1.01857e12	−0.282947	−0.141474	+	0.989942i	$0.545184\pi$
$618$	3.20413e12	0.883612
$619$	1.19561e12	0.327326	0.163663	−	0.986516i	$-0.447669\pi$
$619$	1.19561e12	0.327326	0.163663	+	0.986516i	$0.447669\pi$
$620$	−2.43595e11	−0.0662074
$621$	2.63299e12	0.710456
$622$	2.74521e12	0.735392
$623$	7.70707e11	0.204971
$624$	0	0
$625$	2.87104e12	0.752626
$626$	5.90651e10	0.0153726
$627$	2.50128e12	0.646336
$628$	1.87439e12	0.480886
$629$	2.18353e11	0.0556200
$630$	−4.76084e10	−0.0120407
$631$	5.01180e12	1.25853	0.629263	−	0.777193i	$-0.283357\pi$
$631$	5.01180e12	1.25853	0.629263	+	0.777193i	$0.283357\pi$
$632$	−2.30884e12	−0.575661
$633$	−4.63631e12	−1.14777
$634$	2.64745e12	0.650768
$635$	−1.30272e12	−0.317958
$636$	−8.91464e11	−0.216046
$637$	0	0
$638$	−1.36548e12	−0.326281
$639$	7.24765e11	0.171966
$640$	1.09283e11	0.0257479
$641$	−8.80050e11	−0.205895	−0.102948	−	0.994687i	$-0.532827\pi$
$641$	−8.80050e11	−0.205895	−0.102948	+	0.994687i	$0.532827\pi$
$642$	−2.31221e12	−0.537180
$643$	−3.00684e12	−0.693684	−0.346842	−	0.937924i	$-0.612746\pi$
$643$	−3.00684e12	−0.693684	−0.346842	+	0.937924i	$0.612746\pi$
$644$	2.96105e11	0.0678358
$645$	−1.39374e11	−0.0317076
$646$	1.22844e12	0.277528
$647$	2.12776e12	0.477369	0.238684	−	0.971097i	$-0.423284\pi$
$647$	2.12776e12	0.477369	0.238684	+	0.971097i	$0.423284\pi$
$648$	−1.98359e12	−0.441942
$649$	2.27012e12	0.502283
$650$	0	0
$651$	2.98667e11	0.0651737
$652$	3.81368e12	0.826475
$653$	3.63853e12	0.783099	0.391550	−	0.920157i	$-0.371939\pi$
$653$	3.63853e12	0.783099	0.391550	+	0.920157i	$0.371939\pi$
$654$	−1.68488e12	−0.360137
$655$	2.55191e12	0.541727
$656$	−3.27659e11	−0.0690803
$657$	2.23767e12	0.468546
$658$	−7.64840e10	−0.0159057
$659$	1.53357e12	0.316752	0.158376	−	0.987379i	$-0.449374\pi$
$659$	1.53357e12	0.316752	0.158376	+	0.987379i	$0.449374\pi$
$660$	−5.49997e11	−0.112827
$661$	3.04283e12	0.619970	0.309985	−	0.950741i	$-0.399676\pi$
$661$	3.04283e12	0.619970	0.309985	+	0.950741i	$0.399676\pi$
$662$	1.62888e12	0.329631
$663$	0	0
$664$	2.19552e12	0.438309
$665$	1.43536e11	0.0284618
$666$	−2.11911e11	−0.0417369
$667$	−4.31955e12	−0.845031
$668$	8.57094e11	0.166546
$669$	2.72717e12	0.526373
$670$	3.45336e11	0.0662072
$671$	−3.08703e12	−0.587882
$672$	−1.33989e11	−0.0253459
$673$	3.20634e12	0.602479	0.301240	−	0.953548i	$-0.402600\pi$
$673$	3.20634e12	0.602479	0.301240	+	0.953548i	$0.402600\pi$
$674$	−2.86580e11	−0.0534905
$675$	3.02662e12	0.561165
$676$	0	0
$677$	1.74076e12	0.318486	0.159243	−	0.987239i	$-0.449095\pi$
$677$	1.74076e12	0.318486	0.159243	+	0.987239i	$0.449095\pi$
$678$	2.81819e12	0.512197
$679$	−1.01504e12	−0.183260
$680$	−2.70117e11	−0.0484465
$681$	1.20327e13	2.14388
$682$	1.14887e12	0.203349
$683$	−4.26370e12	−0.749711	−0.374855	−	0.927083i	$-0.622308\pi$
$683$	−4.26370e12	−0.749711	−0.374855	+	0.927083i	$0.622308\pi$
$684$	−1.19220e12	−0.208255
$685$	−1.68526e10	−0.00292456
$686$	9.53982e11	0.164468
$687$	−3.66232e12	−0.627265
$688$	−1.30610e11	−0.0222243
$689$	0	0
$690$	−1.73986e12	−0.292210
$691$	−1.11120e13	−1.85413	−0.927064	−	0.374904i	$-0.877676\pi$
$691$	−1.11120e13	−1.85413	−0.927064	+	0.374904i	$0.877676\pi$
$692$	−4.25100e12	−0.704715
$693$	2.24536e11	0.0369817
$694$	−1.86977e12	−0.305964
$695$	9.50497e11	0.154532
$696$	1.95462e12	0.315734
$697$	8.09883e11	0.129979
$698$	7.06795e12	1.12705
$699$	−7.31214e12	−1.15850
$700$	3.40372e11	0.0535812
$701$	−6.22216e12	−0.973218	−0.486609	−	0.873620i	$-0.661766\pi$
$701$	−6.22216e12	−0.973218	−0.486609	+	0.873620i	$0.661766\pi$
$702$	0	0
$703$	6.38898e11	0.0986580
$704$	−5.15413e11	−0.0790821
$705$	4.49408e11	0.0685156
$706$	−6.08621e12	−0.921989
$707$	1.01518e12	0.152811
$708$	−3.24959e12	−0.486047
$709$	−1.16269e13	−1.72805	−0.864023	−	0.503452i	$-0.832063\pi$
$709$	−1.16269e13	−1.72805	−0.864023	+	0.503452i	$0.832063\pi$
$710$	4.80478e11	0.0709595
$711$	−5.53847e12	−0.812786
$712$	−4.24379e12	−0.618862
$713$	3.63435e12	0.526652
$714$	3.31184e11	0.0476901
$715$	0	0
$716$	5.76404e12	0.819631
$717$	2.70935e12	0.382850
$718$	−7.40178e12	−1.03938
$719$	−4.28622e12	−0.598128	−0.299064	−	0.954233i	$-0.596674\pi$
$719$	−4.28622e12	−0.598128	−0.299064	+	0.954233i	$0.596674\pi$
$720$	2.62149e11	0.0363539
$721$	−8.67185e11	−0.119510
$722$	−1.56861e12	−0.214831
$723$	−1.52518e13	−2.07586
$724$	−1.02786e11	−0.0139031
$725$	−4.96532e12	−0.667462
$726$	−3.88682e12	−0.519254
$727$	1.07312e13	1.42476	0.712381	−	0.701792i	$-0.247617\pi$
$727$	1.07312e13	1.42476	0.712381	+	0.701792i	$0.247617\pi$
$728$	0	0
$729$	9.67121e11	0.126826
$730$	1.48345e12	0.193339
$731$	3.22833e11	0.0418167
$732$	4.41896e12	0.568879
$733$	−6.78526e12	−0.868158	−0.434079	−	0.900875i	$-0.642926\pi$
$733$	−6.78526e12	−0.868158	−0.434079	+	0.900875i	$0.642926\pi$
$734$	2.34934e12	0.298753
$735$	−2.78337e12	−0.351786
$736$	−1.63046e12	−0.204814
$737$	−1.62872e12	−0.203349
$738$	−7.85991e11	−0.0975358
$739$	−4.24403e12	−0.523453	−0.261727	−	0.965142i	$-0.584292\pi$
$739$	−4.24403e12	−0.523453	−0.261727	+	0.965142i	$0.584292\pi$
$740$	−1.40485e11	−0.0172221
$741$	0	0
$742$	2.41271e11	0.0292205
$743$	−8.58861e12	−1.03389	−0.516944	−	0.856019i	$-0.672930\pi$
$743$	−8.58861e12	−1.03389	−0.516944	+	0.856019i	$0.672930\pi$
$744$	−1.64456e12	−0.196776
$745$	1.15670e12	0.137568
$746$	−9.11567e12	−1.07762
$747$	5.26663e12	0.618857
$748$	1.27396e12	0.148798
$749$	6.25791e11	0.0726542
$750$	−4.18540e12	−0.483015
$751$	−1.70411e13	−1.95487	−0.977433	−	0.211244i	$-0.932248\pi$
$751$	−1.70411e13	−1.95487	−0.977433	+	0.211244i	$0.932248\pi$
$752$	4.21148e11	0.0480236
$753$	−2.58967e12	−0.293539
$754$	0	0
$755$	−4.21668e12	−0.472291
$756$	3.22459e11	0.0359027
$757$	−6.27839e12	−0.694891	−0.347446	−	0.937700i	$-0.612951\pi$
$757$	−6.27839e12	−0.694891	−0.347446	+	0.937700i	$0.612951\pi$
$758$	−8.17166e12	−0.899082
$759$	8.20576e12	0.897492
$760$	−7.90360e11	−0.0859337
$761$	−1.79803e13	−1.94342	−0.971710	−	0.236177i	$-0.924106\pi$
$761$	−1.79803e13	−1.94342	−0.971710	+	0.236177i	$0.924106\pi$
$762$	−8.79495e12	−0.945009
$763$	4.56005e11	0.0487090
$764$	−2.91783e12	−0.309842
$765$	−6.47960e11	−0.0684025
$766$	2.09239e12	0.219591
$767$	0	0
$768$	7.37791e11	0.0765258
$769$	9.02747e12	0.930888	0.465444	−	0.885077i	$-0.345895\pi$
$769$	9.02747e12	0.930888	0.465444	+	0.885077i	$0.345895\pi$
$770$	1.48855e11	0.0152600
$771$	−1.51128e13	−1.54028
$772$	5.56400e12	0.563780
$773$	3.88617e12	0.391484	0.195742	−	0.980655i	$-0.437288\pi$
$773$	3.88617e12	0.391484	0.195742	+	0.980655i	$0.437288\pi$
$774$	−3.13309e11	−0.0313790
$775$	4.17769e12	0.415985
$776$	5.58917e12	0.553311
$777$	1.72245e11	0.0169533
$778$	3.10974e12	0.304310
$779$	2.36971e12	0.230556
$780$	0	0
$781$	−2.26609e12	−0.217945
$782$	4.03005e12	0.385372
$783$	−4.70401e12	−0.447240
$784$	−2.60835e12	−0.246572
$785$	2.98080e12	0.280168
$786$	1.72285e13	1.61008
$787$	−1.00929e13	−0.937842	−0.468921	−	0.883240i	$-0.655357\pi$
$787$	−1.00929e13	−0.937842	−0.468921	+	0.883240i	$0.655357\pi$
$788$	2.45206e12	0.226550
$789$	−1.20631e13	−1.10819
$790$	−3.67169e12	−0.335385
$791$	−7.62733e11	−0.0692753
$792$	−1.23638e12	−0.111657
$793$	0	0
$794$	5.42670e12	0.484556
$795$	−1.41767e12	−0.125870
$796$	−7.85172e12	−0.693196
$797$	1.97702e12	0.173559	0.0867796	−	0.996228i	$-0.472342\pi$
$797$	1.97702e12	0.173559	0.0867796	+	0.996228i	$0.472342\pi$
$798$	9.69041e11	0.0845920
$799$	−1.04096e12	−0.0903598
$800$	−1.87421e12	−0.161776
$801$	−1.01800e13	−0.873782
$802$	4.74598e12	0.405080
$803$	−6.99642e12	−0.593821
$804$	2.33144e12	0.196776
$805$	4.70887e11	0.0395217
$806$	0	0
$807$	−2.12997e13	−1.76784
$808$	−5.58994e12	−0.461377
$809$	−1.78254e13	−1.46309	−0.731546	−	0.681793i	$-0.761201\pi$
$809$	−1.78254e13	−1.46309	−0.731546	+	0.681793i	$0.761201\pi$
$810$	−3.15445e12	−0.257479
$811$	8.70377e12	0.706503	0.353251	−	0.935528i	$-0.385076\pi$
$811$	8.70377e12	0.706503	0.353251	+	0.935528i	$0.385076\pi$
$812$	−5.29011e11	−0.0427034
$813$	3.25620e12	0.261399
$814$	6.62573e11	0.0528961
$815$	6.06479e12	0.481511
$816$	−1.82362e12	−0.143989
$817$	9.44605e11	0.0741738
$818$	−6.13611e12	−0.479185
$819$	0	0
$820$	−5.21067e11	−0.0402468
$821$	−2.22094e12	−0.170605	−0.0853027	−	0.996355i	$-0.527186\pi$
$821$	−2.22094e12	−0.170605	−0.0853027	+	0.996355i	$0.527186\pi$
$822$	−1.13776e11	−0.00869213
$823$	−2.41858e13	−1.83765	−0.918823	−	0.394671i	$-0.870859\pi$
$823$	−2.41858e13	−1.83765	−0.918823	+	0.394671i	$0.870859\pi$
$824$	4.77503e12	0.360831
$825$	9.43251e12	0.708899
$826$	8.79488e11	0.0657385
$827$	−9.09741e12	−0.676306	−0.338153	−	0.941091i	$-0.609802\pi$
$827$	−9.09741e12	−0.676306	−0.338153	+	0.941091i	$0.609802\pi$
$828$	−3.91116e12	−0.289181
$829$	1.87063e13	1.37560	0.687799	−	0.725901i	$-0.258577\pi$
$829$	1.87063e13	1.37560	0.687799	+	0.725901i	$0.258577\pi$
$830$	3.49147e12	0.255363
$831$	−7.09263e12	−0.515944
$832$	0	0
$833$	6.44713e12	0.463942
$834$	6.41701e12	0.459289
$835$	1.36301e12	0.0970312
$836$	3.72759e12	0.263937
$837$	3.95783e12	0.278735
$838$	4.45594e12	0.312134
$839$	−1.92142e12	−0.133873	−0.0669366	−	0.997757i	$-0.521323\pi$
$839$	−1.92142e12	−0.133873	−0.0669366	+	0.997757i	$0.521323\pi$
$840$	−2.13079e11	−0.0147667
$841$	−6.78997e12	−0.468043
$842$	5.00708e12	0.343305
$843$	3.35402e12	0.228740
$844$	−6.90937e12	−0.468703
$845$	0	0
$846$	1.01025e12	0.0678054
$847$	1.05195e12	0.0702298
$848$	−1.32853e12	−0.0882244
$849$	−7.19613e12	−0.475351
$850$	4.63254e12	0.304392
$851$	2.09598e12	0.136995
$852$	3.24381e12	0.210900
$853$	6.12511e12	0.396135	0.198067	−	0.980188i	$-0.436534\pi$
$853$	6.12511e12	0.396135	0.198067	+	0.980188i	$0.436534\pi$
$854$	−1.19597e12	−0.0769417
$855$	−1.89592e12	−0.121331
$856$	−3.44583e12	−0.219362
$857$	6.56017e12	0.415434	0.207717	−	0.978189i	$-0.433397\pi$
$857$	6.56017e12	0.415434	0.207717	+	0.978189i	$0.433397\pi$
$858$	0	0
$859$	1.35590e13	0.849688	0.424844	−	0.905267i	$-0.360329\pi$
$859$	1.35590e13	0.849688	0.424844	+	0.905267i	$0.360329\pi$
$860$	−2.07706e11	−0.0129481
$861$	6.38868e11	0.0396184
$862$	−1.64586e13	−1.01534
$863$	−1.64847e13	−1.01165	−0.505827	−	0.862635i	$-0.668812\pi$
$863$	−1.64847e13	−1.01165	−0.505827	+	0.862635i	$0.668812\pi$
$864$	−1.77558e12	−0.108400
$865$	−6.76025e12	−0.410573
$866$	1.14153e13	0.689696
$867$	−1.58636e13	−0.953489
$868$	4.45095e11	0.0266142
$869$	1.73169e13	1.03010
$870$	3.10838e12	0.183949
$871$	0	0
$872$	−2.51093e12	−0.147065
$873$	1.34074e13	0.781230
$874$	1.17919e13	0.683567
$875$	1.13276e12	0.0653284
$876$	1.00151e13	0.574627
$877$	−6.70037e12	−0.382473	−0.191236	−	0.981544i	$-0.561250\pi$
$877$	−6.70037e12	−0.382473	−0.191236	+	0.981544i	$0.561250\pi$
$878$	−1.65078e13	−0.937487
$879$	−2.36966e13	−1.33886
$880$	−8.19647e11	−0.0460739
$881$	1.85549e13	1.03769	0.518846	−	0.854868i	$-0.326362\pi$
$881$	1.85549e13	1.03769	0.518846	+	0.854868i	$0.326362\pi$
$882$	−6.25694e12	−0.348139
$883$	1.04252e13	0.577111	0.288555	−	0.957463i	$-0.406825\pi$
$883$	1.04252e13	0.577111	0.288555	+	0.957463i	$0.406825\pi$
$884$	0	0
$885$	−5.16773e12	−0.283175
$886$	−3.60133e12	−0.196341
$887$	−2.46187e13	−1.33539	−0.667696	−	0.744434i	$-0.732719\pi$
$887$	−2.46187e13	−1.33539	−0.667696	+	0.744434i	$0.732719\pi$
$888$	−9.48445e11	−0.0511863
$889$	2.38032e12	0.127814
$890$	−6.74878e12	−0.360554
$891$	1.48774e13	0.790820
$892$	4.06422e12	0.214949
$893$	−3.04585e12	−0.160279
$894$	7.80915e12	0.408870
$895$	9.16639e12	0.477524
$896$	−1.99680e11	−0.0103502
$897$	0	0
$898$	5.61485e12	0.288134
$899$	−6.49301e12	−0.331534
$900$	−4.49588e12	−0.228414
$901$	3.28375e12	0.166000
$902$	2.45752e12	0.123614
$903$	2.54663e11	0.0127459
$904$	4.19988e12	0.209160
$905$	−1.63458e11	−0.00810005
$906$	−2.84677e13	−1.40371
$907$	1.94672e13	0.955147	0.477573	−	0.878592i	$-0.341516\pi$
$907$	1.94672e13	0.955147	0.477573	+	0.878592i	$0.341516\pi$
$908$	1.79320e13	0.875474
$909$	−1.34092e13	−0.651426
$910$	0	0
$911$	3.61012e13	1.73656	0.868279	−	0.496076i	$-0.165226\pi$
$911$	3.61012e13	1.73656	0.868279	+	0.496076i	$0.165226\pi$
$912$	−5.33589e12	−0.255405
$913$	−1.64669e13	−0.784321
$914$	1.79680e13	0.851611
$915$	7.02736e12	0.331434
$916$	−5.45786e12	−0.256149
$917$	−4.66283e12	−0.217765
$918$	4.38874e12	0.203961
$919$	1.77605e13	0.821361	0.410681	−	0.911779i	$-0.365291\pi$
$919$	1.77605e13	0.821361	0.410681	+	0.911779i	$0.365291\pi$
$920$	−2.59287e12	−0.119326
$921$	1.02407e13	0.468986
$922$	1.24720e13	0.568391
$923$	0	0
$924$	1.00495e12	0.0453545
$925$	2.40933e12	0.108208
$926$	2.51576e13	1.12440
$927$	1.14544e13	0.509463
$928$	2.91292e12	0.128933
$929$	−3.62715e13	−1.59770	−0.798849	−	0.601532i	$-0.794557\pi$
$929$	−3.62715e13	−1.59770	−0.798849	+	0.601532i	$0.794557\pi$
$930$	−2.61531e12	−0.114644
$931$	1.88642e13	0.822935
$932$	−1.08971e13	−0.473085
$933$	2.94734e13	1.27339
$934$	7.35278e12	0.316148
$935$	2.02594e12	0.0866912
$936$	0	0
$937$	−3.55731e12	−0.150763	−0.0753813	−	0.997155i	$-0.524017\pi$
$937$	−3.55731e12	−0.150763	−0.0753813	+	0.997155i	$0.524017\pi$
$938$	−6.30995e11	−0.0266142
$939$	6.34139e11	0.0266189
$940$	6.69741e11	0.0279790
$941$	−2.27004e13	−0.943801	−0.471901	−	0.881652i	$-0.656432\pi$
$941$	−2.27004e13	−0.943801	−0.471901	+	0.881652i	$0.656432\pi$
$942$	2.01240e13	0.832693
$943$	7.77413e12	0.320147
$944$	−4.84277e12	−0.198482
$945$	5.12798e11	0.0209172
$946$	9.79607e11	0.0397688
$947$	1.23091e13	0.497339	0.248670	−	0.968588i	$-0.420007\pi$
$947$	1.23091e13	0.497339	0.248670	+	0.968588i	$0.420007\pi$
$948$	−2.47883e13	−0.996805
$949$	0	0
$950$	1.35548e13	0.539927
$951$	2.84238e13	1.12686
$952$	4.93556e11	0.0194747
$953$	9.51428e12	0.373644	0.186822	−	0.982394i	$-0.440181\pi$
$953$	9.51428e12	0.373644	0.186822	+	0.982394i	$0.440181\pi$
$954$	−3.18688e12	−0.124566
$955$	−4.64015e12	−0.180516
$956$	4.03767e12	0.156340
$957$	−1.46601e13	−0.564982
$958$	−2.02181e13	−0.775524
$959$	3.07930e10	0.00117562
$960$	1.17329e12	0.0445846
$961$	−2.09766e13	−0.793377
$962$	0	0
$963$	−8.26588e12	−0.309721
$964$	−2.27294e13	−0.847698
$965$	8.84829e12	0.328463
$966$	3.17906e12	0.117463
$967$	−2.33888e13	−0.860179	−0.430089	−	0.902786i	$-0.641518\pi$
$967$	−2.33888e13	−0.860179	−0.430089	+	0.902786i	$0.641518\pi$
$968$	−5.79244e12	−0.212042
$969$	1.31889e13	0.480563
$970$	8.88831e12	0.322364
$971$	2.42023e12	0.0873716	0.0436858	−	0.999045i	$-0.486090\pi$
$971$	2.42023e12	0.0873716	0.0436858	+	0.999045i	$0.486090\pi$
$972$	−1.27640e13	−0.458658
$973$	−1.73674e12	−0.0621193
$974$	8.91571e12	0.317424
$975$	0	0
$976$	6.58546e12	0.232307
$977$	3.69666e13	1.29803	0.649014	−	0.760776i	$-0.275182\pi$
$977$	3.69666e13	1.29803	0.649014	+	0.760776i	$0.275182\pi$
$978$	4.09447e13	1.43111
$979$	3.18294e13	1.10741
$980$	−4.14799e12	−0.143655
$981$	−6.02324e12	−0.207644
$982$	−2.61359e13	−0.896885
$983$	−3.70914e13	−1.26702	−0.633508	−	0.773736i	$-0.718386\pi$
$983$	−3.70914e13	−1.26702	−0.633508	+	0.773736i	$0.718386\pi$
$984$	−3.51784e12	−0.119618
$985$	3.89945e12	0.131990
$986$	−7.19995e12	−0.242596
$987$	−8.21154e11	−0.0275421
$988$	0	0
$989$	3.09889e12	0.102997
$990$	−1.96618e12	−0.0650526
$991$	1.09766e13	0.361524	0.180762	−	0.983527i	$-0.442144\pi$
$991$	1.09766e13	0.361524	0.180762	+	0.983527i	$0.442144\pi$
$992$	−2.45085e12	−0.0803553
$993$	1.74881e13	0.570782
$994$	−8.77924e11	−0.0285245
$995$	−1.24864e13	−0.403862
$996$	2.35717e13	0.758969
$997$	5.35667e13	1.71698	0.858492	−	0.512827i	$-0.171402\pi$
$997$	5.35667e13	1.71698	0.858492	+	0.512827i	$0.171402\pi$
$998$	3.34986e12	0.106891
$999$	2.28254e12	0.0725058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.p.1.11	yes	12
13.12	even	2		338.10.a.o.1.11	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.10.a.o.1.11	✓	12	13.12	even	2
338.10.a.p.1.11	yes	12	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	338.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +171.780 q^{3} +256.000 q^{4} +407.110 q^{5} +2748.49 q^{6} -743.867 q^{7} +4096.00 q^{8} +9825.53 q^{9} +6513.76 q^{10} -30721.0 q^{11} +43975.8 q^{12} -11901.9 q^{14} +69933.5 q^{15} +65536.0 q^{16} -161987. q^{17} +157208. q^{18} -473972. q^{19} +104220. q^{20} -127782. q^{21} -491536. q^{22} -1.55493e6 q^{23} +703613. q^{24} -1.78739e6 q^{25} -1.69332e6 q^{27} -190430. q^{28} +2.77798e6 q^{29} +1.11894e6 q^{30} -2.33732e6 q^{31} +1.04858e6 q^{32} -5.27727e6 q^{33} -2.59179e6 q^{34} -302836. q^{35} +2.51533e6 q^{36} -1.34796e6 q^{37} -7.58356e6 q^{38} +1.66752e6 q^{40} -4.99968e6 q^{41} -2.04451e6 q^{42} -1.99295e6 q^{43} -7.86457e6 q^{44} +4.00007e6 q^{45} -2.48788e7 q^{46} +6.42621e6 q^{47} +1.12578e7 q^{48} -3.98003e7 q^{49} -2.85982e7 q^{50} -2.78262e7 q^{51} -2.02717e7 q^{53} -2.70931e7 q^{54} -1.25068e7 q^{55} -3.04688e6 q^{56} -8.14192e7 q^{57} +4.44477e7 q^{58} -7.38949e7 q^{59} +1.79030e7 q^{60} +1.00486e8 q^{61} -3.73970e7 q^{62} -7.30889e6 q^{63} +1.67772e7 q^{64} -8.44362e7 q^{66} +5.30164e7 q^{67} -4.14687e7 q^{68} -2.67106e8 q^{69} -4.84537e6 q^{70} +7.37635e7 q^{71} +4.02454e7 q^{72} +2.27741e8 q^{73} -2.15674e7 q^{74} -3.07038e8 q^{75} -1.21337e8 q^{76} +2.28523e7 q^{77} -5.63682e8 q^{79} +2.66804e7 q^{80} -4.84275e8 q^{81} -7.99948e7 q^{82} +5.36015e8 q^{83} -3.27122e7 q^{84} -6.59466e7 q^{85} -3.18872e7 q^{86} +4.77203e8 q^{87} -1.25833e8 q^{88} -1.03608e9 q^{89} +6.40011e7 q^{90} -3.98061e8 q^{92} -4.01505e8 q^{93} +1.02819e8 q^{94} -1.92959e8 q^{95} +1.80125e8 q^{96} +1.36454e9 q^{97} -6.36804e8 q^{98} -3.01850e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 192 q^{2} - 399 q^{3} + 3072 q^{4} - 562 q^{5} - 6384 q^{6} + 3161 q^{7} + 49152 q^{8} + 54783 q^{9} - 8992 q^{10} - 164271 q^{11} - 102144 q^{12} + 50576 q^{14} + 434244 q^{15} + 786432 q^{16} - 649529 q^{17}+ \cdots - 4431369848 q^{99}+O(q^{100}) \) 12 * q + 192 * q^2 - 399 * q^3 + 3072 * q^4 - 562 * q^5 - 6384 * q^6 + 3161 * q^7 + 49152 * q^8 + 54783 * q^9 - 8992 * q^10 - 164271 * q^11 - 102144 * q^12 + 50576 * q^14 + 434244 * q^15 + 786432 * q^16 - 649529 * q^17 + 876528 * q^18 - 228567 * q^19 - 143872 * q^20 - 3321918 * q^21 - 2628336 * q^22 - 3365321 * q^23 - 1634304 * q^24 + 1357734 * q^25 - 7310211 * q^27 + 809216 * q^28 + 1210855 * q^29 + 6947904 * q^30 + 2031015 * q^31 + 12582912 * q^32 - 3709742 * q^33 - 10392464 * q^34 - 16818664 * q^35 + 14024448 * q^36 + 21152418 * q^37 - 3657072 * q^38 - 2301952 * q^40 - 20819170 * q^41 - 53150688 * q^42 - 37183522 * q^43 - 42053376 * q^44 - 51849705 * q^45 - 53845136 * q^46 + 20020222 * q^47 - 26148864 * q^48 - 79988801 * q^49 + 21723744 * q^50 - 72774687 * q^51 - 74983469 * q^53 - 116963376 * q^54 - 19133432 * q^55 + 12947456 * q^56 - 13760507 * q^57 + 19373680 * q^58 - 136123112 * q^59 + 111166464 * q^60 - 112790708 * q^61 + 32496240 * q^62 + 659441340 * q^63 + 201326592 * q^64 - 59355872 * q^66 - 61165134 * q^67 - 166279424 * q^68 - 69902864 * q^69 - 269098624 * q^70 + 212025009 * q^71 + 224391168 * q^72 + 71937292 * q^73 + 338438688 * q^74 - 628692958 * q^75 - 58513152 * q^76 - 527155758 * q^77 - 1146472537 * q^79 - 36831232 * q^80 + 1297690908 * q^81 - 333106720 * q^82 - 1318830968 * q^83 - 850411008 * q^84 - 1737694467 * q^85 - 594936352 * q^86 - 1405133144 * q^87 - 672854016 * q^88 - 3175197052 * q^89 - 829595280 * q^90 - 861522176 * q^92 - 2432770524 * q^93 + 320323552 * q^94 + 1551319209 * q^95 - 418381824 * q^96 - 5161204312 * q^97 - 1279820816 * q^98 - 4431369848 * q^99

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