LMFDB - Embedded newform 338.10.a.q.1.7

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 = [15,-240,324,3840,-2164] 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:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 4 x^{14} - 189447 x^{13} - 2075910 x^{12} + 13427724566 x^{11} + 240902663602 x^{10} + \cdots - 13\!\cdots\!64 $ x^15 - 4x^14 - 189447x^13 - 2075910x^12 + 13427724566x^11 + 240902663602x^10 - 443655654567001x^9 - 6615893817054688x^8 + 7115286003316448188x^7 + 24277759902481977312x^6 - 51707718239515932824096x^5 + 542415804353313005652352x^4 + 123474200669609970033074304x^3 - 1840146860618814818678953344x^2 - 54256006845924411243904364032x - 138658441142855576538884248064
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 13^{13} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.89394$ 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)

$f(q)$	$=$	\(q-16.0000 q^{2} -28.8911 q^{3} +256.000 q^{4} -815.982 q^{5} +462.257 q^{6} +7673.39 q^{7} -4096.00 q^{8} -18848.3 q^{9} +13055.7 q^{10} +38192.3 q^{11} -7396.11 q^{12} -122774. q^{14} +23574.6 q^{15} +65536.0 q^{16} -341529. q^{17} +301573. q^{18} +348100. q^{19} -208891. q^{20} -221692. q^{21} -611077. q^{22} -200977. q^{23} +118338. q^{24} -1.28730e6 q^{25} +1.11321e6 q^{27} +1.96439e6 q^{28} +6.49458e6 q^{29} -377193. q^{30} +5.56460e6 q^{31} -1.04858e6 q^{32} -1.10342e6 q^{33} +5.46446e6 q^{34} -6.26134e6 q^{35} -4.82517e6 q^{36} -1.70812e7 q^{37} -5.56960e6 q^{38} +3.34226e6 q^{40} -1.21887e7 q^{41} +3.54708e6 q^{42} +1.52205e6 q^{43} +9.77723e6 q^{44} +1.53799e7 q^{45} +3.21563e6 q^{46} +2.38449e7 q^{47} -1.89341e6 q^{48} +1.85272e7 q^{49} +2.05968e7 q^{50} +9.86713e6 q^{51} +7.97086e7 q^{53} -1.78114e7 q^{54} -3.11642e7 q^{55} -3.14302e7 q^{56} -1.00570e7 q^{57} -1.03913e8 q^{58} -8.94548e7 q^{59} +6.03509e6 q^{60} +7.49352e7 q^{61} -8.90335e7 q^{62} -1.44630e8 q^{63} +1.67772e7 q^{64} +1.76547e7 q^{66} +1.88079e8 q^{67} -8.74313e7 q^{68} +5.80643e6 q^{69} +1.00181e8 q^{70} -1.03633e8 q^{71} +7.72027e7 q^{72} -3.04172e8 q^{73} +2.73299e8 q^{74} +3.71914e7 q^{75} +8.91137e7 q^{76} +2.93064e8 q^{77} -3.28625e8 q^{79} -5.34762e7 q^{80} +3.38829e8 q^{81} +1.95019e8 q^{82} -2.55837e8 q^{83} -5.67532e7 q^{84} +2.78681e8 q^{85} -2.43529e7 q^{86} -1.87635e8 q^{87} -1.56436e8 q^{88} -6.14853e8 q^{89} -2.46078e8 q^{90} -5.14500e7 q^{92} -1.60767e8 q^{93} -3.81519e8 q^{94} -2.84043e8 q^{95} +3.02945e7 q^{96} +6.50813e8 q^{97} -2.96436e8 q^{98} -7.19860e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 240 q^{2} + 324 q^{3} + 3840 q^{4} - 2164 q^{5} - 5184 q^{6} - 4227 q^{7} - 61440 q^{8} + 112199 q^{9} + 34624 q^{10} + 58782 q^{11} + 82944 q^{12} + 67632 q^{14} - 488672 q^{15} + 983040 q^{16}+ \cdots - 3437295177 q^{99}+O(q^{100}) $ 15 * q - 240 * q^2 + 324 * q^3 + 3840 * q^4 - 2164 * q^5 - 5184 * q^6 - 4227 * q^7 - 61440 * q^8 + 112199 * q^9 + 34624 * q^10 + 58782 * q^11 + 82944 * q^12 + 67632 * q^14 - 488672 * q^15 + 983040 * q^16 + 47308 * q^17 - 1795184 * q^18 - 1027864 * q^19 - 553984 * q^20 + 1332838 * q^21 - 940512 * q^22 - 697897 * q^23 - 1327104 * q^24 + 12121163 * q^25 + 11934723 * q^27 - 1082112 * q^28 + 4970557 * q^29 + 7818752 * q^30 - 8962601 * q^31 - 15728640 * q^32 - 3541482 * q^33 - 756928 * q^34 - 5785412 * q^35 + 28722944 * q^36 - 25045552 * q^37 + 16445824 * q^38 + 8863744 * q^40 - 26390985 * q^41 - 21325408 * q^42 + 11355145 * q^43 + 15048192 * q^44 - 221235525 * q^45 + 11166352 * q^46 - 79882208 * q^47 + 21233664 * q^48 + 150275074 * q^49 - 193938608 * q^50 + 118779121 * q^51 - 21678349 * q^53 - 190955568 * q^54 + 290281352 * q^55 + 17313792 * q^56 + 617732541 * q^57 - 79528912 * q^58 + 264523979 * q^59 - 125100032 * q^60 + 379367976 * q^61 + 143401616 * q^62 - 270769230 * q^63 + 251658240 * q^64 + 56663712 * q^66 + 250185789 * q^67 + 12110848 * q^68 + 281627650 * q^69 + 92566592 * q^70 - 173178579 * q^71 - 459567104 * q^72 - 153358293 * q^73 + 400728832 * q^74 + 20980603 * q^75 - 263133184 * q^76 + 1172911296 * q^77 + 217644101 * q^79 - 141819904 * q^80 + 2373566723 * q^81 + 422255760 * q^82 + 76435497 * q^83 + 341206528 * q^84 - 2676674151 * q^85 - 181682320 * q^86 + 4874616750 * q^87 - 240771072 * q^88 - 2250224949 * q^89 + 3539768400 * q^90 - 178661632 * q^92 - 2915972474 * q^93 + 1278115328 * q^94 + 3329480199 * q^95 - 339738624 * q^96 - 2720440815 * q^97 - 2404401184 * q^98 - 3437295177 * 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
$3$	−28.8911	−0.205929	−0.102965	−	0.994685i	$-0.532833\pi$
$3$	−28.8911	−0.205929	−0.102965	+	0.994685i	$0.532833\pi$
$4$	256.000	0.500000
$5$	−815.982	−0.583869	−0.291934	−	0.956438i	$-0.594299\pi$
$5$	−815.982	−0.583869	−0.291934	+	0.956438i	$0.594299\pi$
$6$	462.257	0.145614
$7$	7673.39	1.20794	0.603971	−	0.797007i	$-0.293584\pi$
$7$	7673.39	1.20794	0.603971	+	0.797007i	$0.293584\pi$
$8$	−4096.00	−0.353553
$9$	−18848.3	−0.957593
$10$	13055.7	0.412858
$11$	38192.3	0.786518	0.393259	−	0.919428i	$-0.371348\pi$
$11$	38192.3	0.786518	0.393259	+	0.919428i	$0.371348\pi$
$12$	−7396.11	−0.102965
$13$	0	0
$13$	0	0
$14$	−122774.	−0.854143
$15$	23574.6	0.120236
$16$	65536.0	0.250000
$17$	−341529.	−0.991761	−0.495880	−	0.868391i	$-0.665155\pi$
$17$	−341529.	−0.991761	−0.495880	+	0.868391i	$0.665155\pi$
$18$	301573.	0.677121
$19$	348100.	0.612792	0.306396	−	0.951904i	$-0.400877\pi$
$19$	348100.	0.612792	0.306396	+	0.951904i	$0.400877\pi$
$20$	−208891.	−0.291934
$21$	−221692.	−0.248750
$22$	−611077.	−0.556152
$23$	−200977.	−0.149751	−0.0748756	−	0.997193i	$-0.523856\pi$
$23$	−200977.	−0.149751	−0.0748756	+	0.997193i	$0.523856\pi$
$24$	118338.	0.0728070
$25$	−1.28730e6	−0.659097
$26$	0	0
$27$	1.11321e6	0.403126
$28$	1.96439e6	0.603971
$29$	6.49458e6	1.70514	0.852570	−	0.522613i	$-0.175043\pi$
$29$	6.49458e6	1.70514	0.852570	+	0.522613i	$0.175043\pi$
$30$	−377193.	−0.0850195
$31$	5.56460e6	1.08220	0.541098	−	0.840959i	$-0.318009\pi$
$31$	5.56460e6	1.08220	0.541098	+	0.840959i	$0.318009\pi$
$32$	−1.04858e6	−0.176777
$33$	−1.10342e6	−0.161967
$34$	5.46446e6	0.701281
$35$	−6.26134e6	−0.705279
$36$	−4.82517e6	−0.478797
$37$	−1.70812e7	−1.49834	−0.749171	−	0.662377i	$-0.769548\pi$
$37$	−1.70812e7	−1.49834	−0.749171	+	0.662377i	$0.769548\pi$
$38$	−5.56960e6	−0.433309
$39$	0	0
$40$	3.34226e6	0.206429
$41$	−1.21887e7	−0.673642	−0.336821	−	0.941569i	$-0.609352\pi$
$41$	−1.21887e7	−0.673642	−0.336821	+	0.941569i	$0.609352\pi$
$42$	3.54708e6	0.175893
$43$	1.52205e6	0.0678925	0.0339463	−	0.999424i	$-0.489192\pi$
$43$	1.52205e6	0.0678925	0.0339463	+	0.999424i	$0.489192\pi$
$44$	9.77723e6	0.393259
$45$	1.53799e7	0.559109
$46$	3.21563e6	0.105890
$47$	2.38449e7	0.712781	0.356390	−	0.934337i	$-0.384007\pi$
$47$	2.38449e7	0.712781	0.356390	+	0.934337i	$0.384007\pi$
$48$	−1.89341e6	−0.0514823
$49$	1.85272e7	0.459122
$50$	2.05968e7	0.466052
$51$	9.86713e6	0.204233
$52$	0	0
$53$	7.97086e7	1.38760	0.693799	−	0.720168i	$-0.255936\pi$
$53$	7.97086e7	1.38760	0.693799	+	0.720168i	$0.255936\pi$
$54$	−1.78114e7	−0.285053
$55$	−3.11642e7	−0.459224
$56$	−3.14302e7	−0.427072
$57$	−1.00570e7	−0.126192
$58$	−1.03913e8	−1.20572
$59$	−8.94548e7	−0.961103	−0.480551	−	0.876967i	$-0.659563\pi$
$59$	−8.94548e7	−0.961103	−0.480551	+	0.876967i	$0.659563\pi$
$60$	6.03509e6	0.0601178
$61$	7.49352e7	0.692950	0.346475	−	0.938059i	$-0.387379\pi$
$61$	7.49352e7	0.692950	0.346475	+	0.938059i	$0.387379\pi$
$62$	−8.90335e7	−0.765228
$63$	−1.44630e8	−1.15672
$64$	1.67772e7	0.125000
$65$	0	0
$66$	1.76547e7	0.114528
$67$	1.88079e8	1.14026	0.570128	−	0.821556i	$-0.306893\pi$
$67$	1.88079e8	1.14026	0.570128	+	0.821556i	$0.306893\pi$
$68$	−8.74313e7	−0.495880
$69$	5.80643e6	0.0308381
$70$	1.00181e8	0.498708
$71$	−1.03633e8	−0.483988	−0.241994	−	0.970278i	$-0.577801\pi$
$71$	−1.03633e8	−0.483988	−0.241994	+	0.970278i	$0.577801\pi$
$72$	7.72027e7	0.338560
$73$	−3.04172e8	−1.25362	−0.626812	−	0.779171i	$-0.715640\pi$
$73$	−3.04172e8	−1.25362	−0.626812	+	0.779171i	$0.715640\pi$
$74$	2.73299e8	1.05949
$75$	3.71914e7	0.135727
$76$	8.91137e7	0.306396
$77$	2.93064e8	0.950068
$78$	0	0
$79$	−3.28625e8	−0.949246	−0.474623	−	0.880189i	$-0.657416\pi$
$79$	−3.28625e8	−0.949246	−0.474623	+	0.880189i	$0.657416\pi$
$80$	−5.34762e7	−0.145967
$81$	3.38829e8	0.874578
$82$	1.95019e8	0.476337
$83$	−2.55837e8	−0.591715	−0.295857	−	0.955232i	$-0.595605\pi$
$83$	−2.55837e8	−0.591715	−0.295857	+	0.955232i	$0.595605\pi$
$84$	−5.67532e7	−0.124375
$85$	2.78681e8	0.579058
$86$	−2.43529e7	−0.0480073
$87$	−1.87635e8	−0.351138
$88$	−1.56436e8	−0.278076
$89$	−6.14853e8	−1.03876	−0.519381	−	0.854543i	$-0.673837\pi$
$89$	−6.14853e8	−1.03876	−0.519381	+	0.854543i	$0.673837\pi$
$90$	−2.46078e8	−0.395350
$91$	0	0
$92$	−5.14500e7	−0.0748756
$93$	−1.60767e8	−0.222856
$94$	−3.81519e8	−0.504012
$95$	−2.84043e8	−0.357790
$96$	3.02945e7	0.0364035
$97$	6.50813e8	0.746420	0.373210	−	0.927747i	$-0.378257\pi$
$97$	6.50813e8	0.746420	0.373210	+	0.927747i	$0.378257\pi$
$98$	−2.96436e8	−0.324648
$99$	−7.19860e8	−0.753165
$100$	−3.29549e8	−0.329549
$101$	−1.42733e9	−1.36483	−0.682416	−	0.730964i	$-0.739071\pi$
$101$	−1.42733e9	−1.36483	−0.682416	+	0.730964i	$0.739071\pi$
$102$	−1.57874e8	−0.144414
$103$	1.57282e8	0.137693	0.0688465	−	0.997627i	$-0.478068\pi$
$103$	1.57282e8	0.137693	0.0688465	+	0.997627i	$0.478068\pi$
$104$	0	0
$105$	1.80897e8	0.145238
$106$	−1.27534e9	−0.981180
$107$	1.01227e9	0.746565	0.373282	−	0.927718i	$-0.378232\pi$
$107$	1.01227e9	0.746565	0.373282	+	0.927718i	$0.378232\pi$
$108$	2.84982e8	0.201563
$109$	1.09459e9	0.742732	0.371366	−	0.928487i	$-0.378890\pi$
$109$	1.09459e9	0.742732	0.371366	+	0.928487i	$0.378890\pi$
$110$	4.98628e8	0.324720
$111$	4.93495e8	0.308552
$112$	5.02883e8	0.301985
$113$	−7.62256e7	−0.0439792	−0.0219896	−	0.999758i	$-0.507000\pi$
$113$	−7.62256e7	−0.0439792	−0.0219896	+	0.999758i	$0.507000\pi$
$114$	1.60912e8	0.0892311
$115$	1.63993e8	0.0874350
$116$	1.66261e9	0.852570
$117$	0	0
$118$	1.43128e9	0.679602
$119$	−2.62068e9	−1.19799
$120$	−9.65615e7	−0.0425097
$121$	−8.99295e8	−0.381389
$122$	−1.19896e9	−0.489990
$123$	3.52144e8	0.138723
$124$	1.42454e9	0.541098
$125$	2.64413e9	0.968695
$126$	2.31408e9	0.817922
$127$	−2.67334e9	−0.911879	−0.455939	−	0.890011i	$-0.650697\pi$
$127$	−2.67334e9	−0.911879	−0.455939	+	0.890011i	$0.650697\pi$
$128$	−2.68435e8	−0.0883883
$129$	−4.39738e7	−0.0139811
$130$	0	0
$131$	−3.38556e9	−1.00441	−0.502203	−	0.864750i	$-0.667477\pi$
$131$	−3.38556e9	−1.00441	−0.502203	+	0.864750i	$0.667477\pi$
$132$	−2.82475e8	−0.0809836
$133$	2.67111e9	0.740217
$134$	−3.00926e9	−0.806283
$135$	−9.08359e8	−0.235373
$136$	1.39890e9	0.350640
$137$	4.00232e9	0.970664	0.485332	−	0.874330i	$-0.338699\pi$
$137$	4.00232e9	0.970664	0.485332	+	0.874330i	$0.338699\pi$
$138$	−9.29029e7	−0.0218059
$139$	6.07493e9	1.38030	0.690152	−	0.723664i	$-0.257543\pi$
$139$	6.07493e9	1.38030	0.690152	+	0.723664i	$0.257543\pi$
$140$	−1.60290e9	−0.352640
$141$	−6.88906e8	−0.146782
$142$	1.65813e9	0.342231
$143$	0	0
$144$	−1.23524e9	−0.239398
$145$	−5.29946e9	−0.995578
$146$	4.86676e9	0.886446
$147$	−5.35272e8	−0.0945466
$148$	−4.37279e9	−0.749171
$149$	−5.82004e9	−0.967360	−0.483680	−	0.875245i	$-0.660700\pi$
$149$	−5.82004e9	−0.967360	−0.483680	+	0.875245i	$0.660700\pi$
$150$	−5.95063e8	−0.0959737
$151$	−8.12500e9	−1.27182	−0.635912	−	0.771762i	$-0.719376\pi$
$151$	−8.12500e9	−1.27182	−0.635912	+	0.771762i	$0.719376\pi$
$152$	−1.42582e9	−0.216655
$153$	6.43724e9	0.949703
$154$	−4.68903e9	−0.671800
$155$	−4.54061e9	−0.631861
$156$	0	0
$157$	2.22705e9	0.292537	0.146268	−	0.989245i	$-0.453274\pi$
$157$	2.22705e9	0.292537	0.146268	+	0.989245i	$0.453274\pi$
$158$	5.25800e9	0.671218
$159$	−2.30287e9	−0.285747
$160$	8.55619e8	0.103214
$161$	−1.54217e9	−0.180891
$162$	−5.42127e9	−0.618420
$163$	5.24174e9	0.581609	0.290804	−	0.956783i	$-0.406077\pi$
$163$	5.24174e9	0.581609	0.290804	+	0.956783i	$0.406077\pi$
$164$	−3.12030e9	−0.336821
$165$	9.00368e8	0.0945676
$166$	4.09340e9	0.418405
$167$	−1.86372e10	−1.85420	−0.927100	−	0.374814i	$-0.877707\pi$
$167$	−1.86372e10	−1.85420	−0.927100	+	0.374814i	$0.877707\pi$
$168$	9.08052e8	0.0879465
$169$	0	0
$170$	−4.45890e9	−0.409456
$171$	−6.56110e9	−0.586805
$172$	3.89646e8	0.0339463
$173$	7.29382e9	0.619081	0.309541	−	0.950886i	$-0.399825\pi$
$173$	7.29382e9	0.619081	0.309541	+	0.950886i	$0.399825\pi$
$174$	3.00216e9	0.248292
$175$	−9.87794e9	−0.796151
$176$	2.50297e9	0.196630
$177$	2.58445e9	0.197919
$178$	9.83765e9	0.734516
$179$	−1.61500e10	−1.17580	−0.587900	−	0.808933i	$-0.700045\pi$
$179$	−1.61500e10	−1.17580	−0.587900	+	0.808933i	$0.700045\pi$
$180$	3.93725e9	0.279554
$181$	1.30952e10	0.906899	0.453450	−	0.891282i	$-0.350193\pi$
$181$	1.30952e10	0.906899	0.453450	+	0.891282i	$0.350193\pi$
$182$	0	0
$183$	−2.16496e9	−0.142699
$184$	8.23200e8	0.0529450
$185$	1.39380e10	0.874835
$186$	2.57227e9	0.157583
$187$	−1.30438e10	−0.780038
$188$	6.10431e9	0.356390
$189$	8.54209e9	0.486952
$190$	4.54469e9	0.252996
$191$	−2.68447e9	−0.145951	−0.0729756	−	0.997334i	$-0.523250\pi$
$191$	−2.68447e9	−0.145951	−0.0729756	+	0.997334i	$0.523250\pi$
$192$	−4.84712e8	−0.0257412
$193$	4.17224e9	0.216452	0.108226	−	0.994126i	$-0.465483\pi$
$193$	4.17224e9	0.216452	0.108226	+	0.994126i	$0.465483\pi$
$194$	−1.04130e10	−0.527798
$195$	0	0
$196$	4.74297e9	0.229561
$197$	−2.04253e10	−0.966207	−0.483103	−	0.875563i	$-0.660490\pi$
$197$	−2.04253e10	−0.966207	−0.483103	+	0.875563i	$0.660490\pi$
$198$	1.15178e10	0.532568
$199$	3.71251e10	1.67814	0.839071	−	0.544022i	$-0.183099\pi$
$199$	3.71251e10	1.67814	0.839071	+	0.544022i	$0.183099\pi$
$200$	5.27278e9	0.233026
$201$	−5.43379e9	−0.234812
$202$	2.28373e10	0.965082
$203$	4.98354e10	2.05971
$204$	2.52598e9	0.102116
$205$	9.94574e9	0.393319
$206$	−2.51652e9	−0.0973637
$207$	3.78807e9	0.143401
$208$	0	0
$209$	1.32948e10	0.481972
$210$	−2.89435e9	−0.102699
$211$	5.25381e10	1.82475	0.912375	−	0.409355i	$-0.134246\pi$
$211$	5.25381e10	1.82475	0.912375	+	0.409355i	$0.134246\pi$
$212$	2.04054e10	0.693799
$213$	2.99406e9	0.0996673
$214$	−1.61962e10	−0.527901
$215$	−1.24197e9	−0.0396403
$216$	−4.55971e9	−0.142526
$217$	4.26993e10	1.30723
$218$	−1.75134e10	−0.525191
$219$	8.78787e9	0.258158
$220$	−7.97804e9	−0.229612
$221$	0	0
$222$	−7.89591e9	−0.218180
$223$	6.55392e10	1.77472	0.887359	−	0.461078i	$-0.152537\pi$
$223$	6.55392e10	1.77472	0.887359	+	0.461078i	$0.152537\pi$
$224$	−8.04613e9	−0.213536
$225$	2.42634e10	0.631147
$226$	1.21961e9	0.0310980
$227$	2.97318e10	0.743199	0.371600	−	0.928393i	$-0.378809\pi$
$227$	2.97318e10	0.743199	0.371600	+	0.928393i	$0.378809\pi$
$228$	−2.57459e9	−0.0630959
$229$	6.46117e10	1.55257	0.776286	−	0.630381i	$-0.217102\pi$
$229$	6.46117e10	1.55257	0.776286	+	0.630381i	$0.217102\pi$
$230$	−2.62389e9	−0.0618259
$231$	−8.46694e9	−0.195647
$232$	−2.66018e10	−0.602858
$233$	5.29218e10	1.17634	0.588170	−	0.808737i	$-0.299849\pi$
$233$	5.29218e10	1.17634	0.588170	+	0.808737i	$0.299849\pi$
$234$	0	0
$235$	−1.94570e10	−0.416171
$236$	−2.29004e10	−0.480551
$237$	9.49433e9	0.195478
$238$	4.19309e10	0.847106
$239$	−2.47807e10	−0.491274	−0.245637	−	0.969362i	$-0.578997\pi$
$239$	−2.47807e10	−0.491274	−0.245637	+	0.969362i	$0.578997\pi$
$240$	1.54498e9	0.0300589
$241$	6.69599e10	1.27861	0.639305	−	0.768953i	$-0.279222\pi$
$241$	6.69599e10	1.27861	0.639305	+	0.768953i	$0.279222\pi$
$242$	1.43887e10	0.269683
$243$	−3.17005e10	−0.583227
$244$	1.91834e10	0.346475
$245$	−1.51179e10	−0.268067
$246$	−5.63430e9	−0.0980917
$247$	0	0
$248$	−2.27926e10	−0.382614
$249$	7.39141e9	0.121851
$250$	−4.23060e10	−0.684971
$251$	9.58602e10	1.52443	0.762214	−	0.647325i	$-0.224113\pi$
$251$	9.58602e10	1.52443	0.762214	+	0.647325i	$0.224113\pi$
$252$	−3.70254e10	−0.578358
$253$	−7.67576e9	−0.117782
$254$	4.27734e10	0.644796
$255$	−8.05139e9	−0.119245
$256$	4.29497e9	0.0625000
$257$	8.61439e10	1.23176	0.615879	−	0.787841i	$-0.288801\pi$
$257$	8.61439e10	1.23176	0.615879	+	0.787841i	$0.288801\pi$
$258$	7.03580e8	0.00988610
$259$	−1.31071e11	−1.80991
$260$	0	0
$261$	−1.22412e11	−1.63283
$262$	5.41689e10	0.710222
$263$	1.06196e11	1.36870	0.684352	−	0.729152i	$-0.260085\pi$
$263$	1.06196e11	1.36870	0.684352	+	0.729152i	$0.260085\pi$
$264$	4.51960e9	0.0572640
$265$	−6.50408e10	−0.810176
$266$	−4.27377e10	−0.523412
$267$	1.77638e10	0.213911
$268$	4.81481e10	0.570128
$269$	1.11963e11	1.30373	0.651866	−	0.758334i	$-0.273987\pi$
$269$	1.11963e11	1.30373	0.651866	+	0.758334i	$0.273987\pi$
$270$	1.45337e10	0.166433
$271$	−9.81374e10	−1.10528	−0.552641	−	0.833420i	$-0.686380\pi$
$271$	−9.81374e10	−1.10528	−0.552641	+	0.833420i	$0.686380\pi$
$272$	−2.23824e10	−0.247940
$273$	0	0
$274$	−6.40371e10	−0.686363
$275$	−4.91649e10	−0.518392
$276$	1.48645e9	0.0154191
$277$	1.15497e11	1.17872	0.589362	−	0.807869i	$-0.299379\pi$
$277$	1.15497e11	1.17872	0.589362	+	0.807869i	$0.299379\pi$
$278$	−9.71989e10	−0.976023
$279$	−1.04883e11	−1.03630
$280$	2.56465e10	0.249354
$281$	1.88548e11	1.80403	0.902015	−	0.431704i	$-0.142087\pi$
$281$	1.88548e11	1.80403	0.902015	+	0.431704i	$0.142087\pi$
$282$	1.10225e10	0.103791
$283$	−3.54780e10	−0.328792	−0.164396	−	0.986394i	$-0.552567\pi$
$283$	−3.54780e10	−0.328792	−0.164396	+	0.986394i	$0.552567\pi$
$284$	−2.65300e10	−0.241994
$285$	8.20632e9	0.0736795
$286$	0	0
$287$	−9.35284e10	−0.813720
$288$	1.97639e10	0.169280
$289$	−1.94607e9	−0.0164104
$290$	8.47913e10	0.703980
$291$	−1.88027e10	−0.153710
$292$	−7.78682e10	−0.626812
$293$	2.08674e10	0.165411	0.0827054	−	0.996574i	$-0.473644\pi$
$293$	2.08674e10	0.165411	0.0827054	+	0.996574i	$0.473644\pi$
$294$	8.56434e9	0.0668546
$295$	7.29935e10	0.561158
$296$	6.99647e10	0.529744
$297$	4.25161e10	0.317066
$298$	9.31207e10	0.684027
$299$	0	0
$300$	9.52101e9	0.0678637
$301$	1.16793e10	0.0820102
$302$	1.30000e11	0.899315
$303$	4.12372e10	0.281059
$304$	2.28131e10	0.153198
$305$	−6.11458e10	−0.404592
$306$	−1.02996e11	−0.671542
$307$	1.94493e11	1.24963	0.624815	−	0.780772i	$-0.285174\pi$
$307$	1.94493e11	1.24963	0.624815	+	0.780772i	$0.285174\pi$
$308$	7.50245e10	0.475034
$309$	−4.54405e9	−0.0283550
$310$	7.26497e10	0.446793
$311$	−1.37275e11	−0.832091	−0.416045	−	0.909344i	$-0.636584\pi$
$311$	−1.37275e11	−0.832091	−0.416045	+	0.909344i	$0.636584\pi$
$312$	0	0
$313$	2.20790e11	1.30026	0.650129	−	0.759824i	$-0.274715\pi$
$313$	2.20790e11	1.30026	0.650129	+	0.759824i	$0.274715\pi$
$314$	−3.56327e10	−0.206855
$315$	1.18016e11	0.675371
$316$	−8.41280e10	−0.474623
$317$	5.96826e10	0.331956	0.165978	−	0.986129i	$-0.446922\pi$
$317$	5.96826e10	0.331956	0.165978	+	0.986129i	$0.446922\pi$
$318$	3.68459e10	0.202054
$319$	2.48043e11	1.34112
$320$	−1.36899e10	−0.0729836
$321$	−2.92454e10	−0.153739
$322$	2.46747e10	0.127909
$323$	−1.18886e11	−0.607743
$324$	8.67403e10	0.437289
$325$	0	0
$326$	−8.38678e10	−0.411260
$327$	−3.16238e10	−0.152950
$328$	4.99248e10	0.238169
$329$	1.82971e11	0.860997
$330$	−1.44059e10	−0.0668694
$331$	2.40129e11	1.09956	0.549779	−	0.835310i	$-0.314712\pi$
$331$	2.40129e11	1.09956	0.549779	+	0.835310i	$0.314712\pi$
$332$	−6.54943e10	−0.295857
$333$	3.21952e11	1.43480
$334$	2.98195e11	1.31112
$335$	−1.53469e11	−0.665760
$336$	−1.45288e10	−0.0621876
$337$	−9.68586e10	−0.409075	−0.204538	−	0.978859i	$-0.565569\pi$
$337$	−9.68586e10	−0.409075	−0.204538	+	0.978859i	$0.565569\pi$
$338$	0	0
$339$	2.20224e9	0.00905661
$340$	7.13424e10	0.289529
$341$	2.12525e11	0.851167
$342$	1.04978e11	0.414934
$343$	−1.67482e11	−0.653349
$344$	−6.23433e9	−0.0240036
$345$	−4.73794e9	−0.0180054
$346$	−1.16701e11	−0.437757
$347$	−4.30745e11	−1.59492	−0.797458	−	0.603374i	$-0.793823\pi$
$347$	−4.30745e11	−1.59492	−0.797458	+	0.603374i	$0.793823\pi$
$348$	−4.80346e10	−0.175569
$349$	−1.95307e11	−0.704700	−0.352350	−	0.935868i	$-0.614617\pi$
$349$	−1.95307e11	−0.704700	−0.352350	+	0.935868i	$0.614617\pi$
$350$	1.58047e11	0.562964
$351$	0	0
$352$	−4.00475e10	−0.139038
$353$	−4.01046e11	−1.37470	−0.687349	−	0.726327i	$-0.741226\pi$
$353$	−4.01046e11	−1.37470	−0.687349	+	0.726327i	$0.741226\pi$
$354$	−4.13511e10	−0.139950
$355$	8.45625e10	0.282586
$356$	−1.57402e11	−0.519381
$357$	7.57143e10	0.246701
$358$	2.58400e11	0.831417
$359$	−2.81095e11	−0.893156	−0.446578	−	0.894745i	$-0.647358\pi$
$359$	−2.81095e11	−0.893156	−0.446578	+	0.894745i	$0.647358\pi$
$360$	−6.29959e10	−0.197675
$361$	−2.01514e11	−0.624486
$362$	−2.09523e11	−0.641275
$363$	2.59816e10	0.0785391
$364$	0	0
$365$	2.48199e11	0.731952
$366$	3.46393e10	0.100903
$367$	2.18648e11	0.629142	0.314571	−	0.949234i	$-0.398139\pi$
$367$	2.18648e11	0.629142	0.314571	+	0.949234i	$0.398139\pi$
$368$	−1.31712e10	−0.0374378
$369$	2.29736e11	0.645075
$370$	−2.23007e11	−0.618602
$371$	6.11635e11	1.67614
$372$	−4.11564e10	−0.111428
$373$	4.99475e11	1.33605	0.668027	−	0.744137i	$-0.267139\pi$
$373$	4.99475e11	1.33605	0.668027	+	0.744137i	$0.267139\pi$
$374$	2.08700e11	0.551570
$375$	−7.63916e10	−0.199483
$376$	−9.76689e10	−0.252006
$377$	0	0
$378$	−1.36674e11	−0.344327
$379$	3.58093e11	0.891496	0.445748	−	0.895158i	$-0.352938\pi$
$379$	3.58093e11	0.891496	0.445748	+	0.895158i	$0.352938\pi$
$380$	−7.27151e10	−0.178895
$381$	7.72356e10	0.187782
$382$	4.29515e10	0.103203
$383$	−4.93579e11	−1.17209	−0.586047	−	0.810277i	$-0.699317\pi$
$383$	−4.93579e11	−1.17209	−0.586047	+	0.810277i	$0.699317\pi$
$384$	7.75539e9	0.0182017
$385$	−2.39135e11	−0.554715
$386$	−6.67558e10	−0.153055
$387$	−2.86881e10	−0.0650134
$388$	1.66608e11	0.373210
$389$	5.35975e11	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$389$	5.35975e11	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$390$	0	0
$391$	6.86393e10	0.148517
$392$	−7.58875e10	−0.162324
$393$	9.78124e10	0.206837
$394$	3.26804e11	0.683211
$395$	2.68152e11	0.554235
$396$	−1.84284e11	−0.376582
$397$	−2.04946e11	−0.414078	−0.207039	−	0.978333i	$-0.566383\pi$
$397$	−2.04946e11	−0.414078	−0.207039	+	0.978333i	$0.566383\pi$
$398$	−5.94001e11	−1.18663
$399$	−7.71711e10	−0.152432
$400$	−8.43644e10	−0.164774
$401$	−1.92115e10	−0.0371032	−0.0185516	−	0.999828i	$-0.505905\pi$
$401$	−1.92115e10	−0.0371032	−0.0185516	+	0.999828i	$0.505905\pi$
$402$	8.69406e10	0.166037
$403$	0	0
$404$	−3.65397e11	−0.682416
$405$	−2.76479e11	−0.510639
$406$	−7.97366e11	−1.45643
$407$	−6.52371e11	−1.17847
$408$	−4.04158e10	−0.0722071
$409$	1.05664e12	1.86712	0.933560	−	0.358422i	$-0.116685\pi$
$409$	1.05664e12	1.86712	0.933560	+	0.358422i	$0.116685\pi$
$410$	−1.59132e11	−0.278118
$411$	−1.15631e11	−0.199888
$412$	4.02643e10	0.0688465
$413$	−6.86421e11	−1.16096
$414$	−6.06091e10	−0.101400
$415$	2.08758e11	0.345484
$416$	0	0
$417$	−1.75511e11	−0.284245
$418$	−2.12716e11	−0.340806
$419$	1.70461e11	0.270185	0.135092	−	0.990833i	$-0.456867\pi$
$419$	1.70461e11	0.270185	0.135092	+	0.990833i	$0.456867\pi$
$420$	4.63096e10	0.0726188
$421$	2.08001e11	0.322698	0.161349	−	0.986897i	$-0.448416\pi$
$421$	2.08001e11	0.322698	0.161349	+	0.986897i	$0.448416\pi$
$422$	−8.40610e11	−1.29029
$423$	−4.49437e11	−0.682554
$424$	−3.26486e11	−0.490590
$425$	4.39650e11	0.653667
$426$	−4.79050e10	−0.0704754
$427$	5.75007e11	0.837043
$428$	2.59140e11	0.373282
$429$	0	0
$430$	1.98715e10	0.0280300
$431$	−4.80660e11	−0.670950	−0.335475	−	0.942049i	$-0.608897\pi$
$431$	−4.80660e11	−0.670950	−0.335475	+	0.942049i	$0.608897\pi$
$432$	7.29554e10	0.100781
$433$	−1.11441e12	−1.52353	−0.761763	−	0.647856i	$-0.775666\pi$
$433$	−1.11441e12	−1.52353	−0.761763	+	0.647856i	$0.775666\pi$
$434$	−6.83189e11	−0.924351
$435$	1.53107e11	0.205019
$436$	2.80215e11	0.371366
$437$	−6.99600e10	−0.0917663
$438$	−1.40606e11	−0.182545
$439$	7.67141e11	0.985791	0.492896	−	0.870088i	$-0.335938\pi$
$439$	7.67141e11	0.985791	0.492896	+	0.870088i	$0.335938\pi$
$440$	1.27649e11	0.162360
$441$	−3.49207e11	−0.439652
$442$	0	0
$443$	8.64963e11	1.06704	0.533520	−	0.845787i	$-0.320869\pi$
$443$	8.64963e11	1.06704	0.533520	+	0.845787i	$0.320869\pi$
$444$	1.26335e11	0.154276
$445$	5.01709e11	0.606501
$446$	−1.04863e12	−1.25492
$447$	1.68147e11	0.199208
$448$	1.28738e11	0.150993
$449$	−1.32420e12	−1.53761	−0.768805	−	0.639483i	$-0.779148\pi$
$449$	−1.32420e12	−1.53761	−0.768805	+	0.639483i	$0.779148\pi$
$450$	−3.88215e11	−0.446288
$451$	−4.65514e11	−0.529832
$452$	−1.95137e10	−0.0219896
$453$	2.34740e11	0.261906
$454$	−4.75709e11	−0.525521
$455$	0	0
$456$	4.11934e10	0.0446155
$457$	−4.86188e11	−0.521412	−0.260706	−	0.965418i	$-0.583955\pi$
$457$	−4.86188e11	−0.521412	−0.260706	+	0.965418i	$0.583955\pi$
$458$	−1.03379e12	−1.09783
$459$	−3.80193e11	−0.399804
$460$	4.19823e10	0.0437175
$461$	5.88880e11	0.607257	0.303629	−	0.952790i	$-0.401802\pi$
$461$	5.88880e11	0.607257	0.303629	+	0.952790i	$0.401802\pi$
$462$	1.35471e11	0.138343
$463$	1.75155e12	1.77136	0.885680	−	0.464296i	$-0.153693\pi$
$463$	1.75155e12	1.77136	0.885680	+	0.464296i	$0.153693\pi$
$464$	4.25629e11	0.426285
$465$	1.31183e11	0.130119
$466$	−8.46749e11	−0.831798
$467$	2.03830e11	0.198309	0.0991544	−	0.995072i	$-0.468386\pi$
$467$	2.03830e11	0.198309	0.0991544	+	0.995072i	$0.468386\pi$
$468$	0	0
$469$	1.44320e12	1.37736
$470$	3.11313e11	0.294277
$471$	−6.43417e10	−0.0602419
$472$	3.66407e11	0.339801
$473$	5.81308e10	0.0533987
$474$	−1.51909e11	−0.138223
$475$	−4.48109e11	−0.403889
$476$	−6.70894e11	−0.598994
$477$	−1.50237e12	−1.32875
$478$	3.96492e11	0.347383
$479$	−5.74049e11	−0.498241	−0.249120	−	0.968473i	$-0.580141\pi$
$479$	−5.74049e11	−0.498241	−0.249120	+	0.968473i	$0.580141\pi$
$480$	−2.47197e10	−0.0212549
$481$	0	0
$482$	−1.07136e12	−0.904114
$483$	4.45550e10	0.0372507
$484$	−2.30219e11	−0.190694
$485$	−5.31051e11	−0.435811
$486$	5.07207e11	0.412404
$487$	1.61943e12	1.30461	0.652307	−	0.757955i	$-0.273801\pi$
$487$	1.61943e12	1.30461	0.652307	+	0.757955i	$0.273801\pi$
$488$	−3.06935e11	−0.244995
$489$	−1.51439e11	−0.119770
$490$	2.41886e11	0.189552
$491$	−2.15980e12	−1.67705	−0.838526	−	0.544861i	$-0.816582\pi$
$491$	−2.15980e12	−1.67705	−0.838526	+	0.544861i	$0.816582\pi$
$492$	9.01489e10	0.0693613
$493$	−2.21808e12	−1.69109
$494$	0	0
$495$	5.87393e11	0.439749
$496$	3.64681e11	0.270549
$497$	−7.95215e11	−0.584629
$498$	−1.18263e11	−0.0861619
$499$	1.86557e12	1.34698	0.673488	−	0.739198i	$-0.264795\pi$
$499$	1.86557e12	1.34698	0.673488	+	0.739198i	$0.264795\pi$
$500$	6.76896e11	0.484348
$501$	5.38449e11	0.381834
$502$	−1.53376e12	−1.07793
$503$	−2.04860e12	−1.42693	−0.713464	−	0.700692i	$-0.752875\pi$
$503$	−2.04860e12	−1.42693	−0.713464	+	0.700692i	$0.752875\pi$
$504$	5.92406e11	0.408961
$505$	1.16468e12	0.796883
$506$	1.22812e11	0.0832845
$507$	0	0
$508$	−6.84375e11	−0.455939
$509$	7.21209e11	0.476246	0.238123	−	0.971235i	$-0.423468\pi$
$509$	7.21209e11	0.476246	0.238123	+	0.971235i	$0.423468\pi$
$510$	1.28822e11	0.0843190
$511$	−2.33403e12	−1.51430
$512$	−6.87195e10	−0.0441942
$513$	3.87509e11	0.247032
$514$	−1.37830e12	−0.870984
$515$	−1.28339e11	−0.0803947
$516$	−1.12573e10	−0.00699053
$517$	9.10694e11	0.560615
$518$	2.09713e12	1.27980
$519$	−2.10726e11	−0.127487
$520$	0	0
$521$	4.04211e11	0.240347	0.120173	−	0.992753i	$-0.461655\pi$
$521$	4.04211e11	0.240347	0.120173	+	0.992753i	$0.461655\pi$
$522$	1.95859e12	1.15459
$523$	−2.44658e12	−1.42989	−0.714944	−	0.699181i	$-0.753548\pi$
$523$	−2.44658e12	−1.42989	−0.714944	+	0.699181i	$0.753548\pi$
$524$	−8.66703e11	−0.502203
$525$	2.85384e11	0.163951
$526$	−1.69914e12	−0.967819
$527$	−1.90047e12	−1.07328
$528$	−7.23135e10	−0.0404918
$529$	−1.76076e12	−0.977575
$530$	1.04065e12	0.572881
$531$	1.68607e12	0.920345
$532$	6.83803e11	0.370108
$533$	0	0
$534$	−2.84220e11	−0.151258
$535$	−8.25990e11	−0.435896
$536$	−7.70370e11	−0.403142
$537$	4.66591e11	0.242132
$538$	−1.79140e12	−0.921877
$539$	7.07598e11	0.361108
$540$	−2.32540e11	−0.117686
$541$	−1.63374e12	−0.819967	−0.409984	−	0.912093i	$-0.634466\pi$
$541$	−1.63374e12	−0.819967	−0.409984	+	0.912093i	$0.634466\pi$
$542$	1.57020e12	0.781552
$543$	−3.78335e11	−0.186757
$544$	3.58119e11	0.175320
$545$	−8.93164e11	−0.433658
$546$	0	0
$547$	−1.38347e11	−0.0660735	−0.0330367	−	0.999454i	$-0.510518\pi$
$547$	−1.38347e11	−0.0660735	−0.0330367	+	0.999454i	$0.510518\pi$
$548$	1.02459e12	0.485332
$549$	−1.41240e12	−0.663564
$550$	7.86639e11	0.366559
$551$	2.26076e12	1.04490
$552$	−2.37831e10	−0.0109029
$553$	−2.52167e12	−1.14663
$554$	−1.84795e12	−0.833483
$555$	−4.02682e11	−0.180154
$556$	1.55518e12	0.690152
$557$	5.83560e11	0.256884	0.128442	−	0.991717i	$-0.459002\pi$
$557$	5.83560e11	0.256884	0.128442	+	0.991717i	$0.459002\pi$
$558$	1.67813e12	0.732777
$559$	0	0
$560$	−4.10343e11	−0.176320
$561$	3.76848e11	0.160633
$562$	−3.01677e12	−1.27564
$563$	5.33198e11	0.223666	0.111833	−	0.993727i	$-0.464328\pi$
$563$	5.33198e11	0.223666	0.111833	+	0.993727i	$0.464328\pi$
$564$	−1.76360e11	−0.0733912
$565$	6.21986e10	0.0256781
$566$	5.67649e11	0.232491
$567$	2.59997e12	1.05644
$568$	4.24480e11	0.171116
$569$	−1.82651e11	−0.0730494	−0.0365247	−	0.999333i	$-0.511629\pi$
$569$	−1.82651e11	−0.0730494	−0.0365247	+	0.999333i	$0.511629\pi$
$570$	−1.31301e11	−0.0520992
$571$	2.65065e12	1.04349	0.521746	−	0.853101i	$-0.325281\pi$
$571$	2.65065e12	1.04349	0.521746	+	0.853101i	$0.325281\pi$
$572$	0	0
$573$	7.75571e10	0.0300556
$574$	1.49645e12	0.575387
$575$	2.58717e11	0.0987006
$576$	−3.16222e11	−0.119699
$577$	3.32134e12	1.24745	0.623724	−	0.781645i	$-0.285619\pi$
$577$	3.32134e12	1.24745	0.623724	+	0.781645i	$0.285619\pi$
$578$	3.11371e10	0.0116039
$579$	−1.20540e11	−0.0445738
$580$	−1.35666e12	−0.497789
$581$	−1.96314e12	−0.714756
$582$	3.00843e11	0.108689
$583$	3.04426e12	1.09137
$584$	1.24589e12	0.443223
$585$	0	0
$586$	−3.33878e11	−0.116963
$587$	2.68083e12	0.931960	0.465980	−	0.884795i	$-0.345702\pi$
$587$	2.68083e12	0.931960	0.465980	+	0.884795i	$0.345702\pi$
$588$	−1.37030e11	−0.0472733
$589$	1.93704e12	0.663161
$590$	−1.16790e12	−0.396799
$591$	5.90108e11	0.198970
$592$	−1.11943e12	−0.374586
$593$	−1.08037e12	−0.358780	−0.179390	−	0.983778i	$-0.557412\pi$
$593$	−1.08037e12	−0.358780	−0.179390	+	0.983778i	$0.557412\pi$
$594$	−6.80257e11	−0.224199
$595$	2.13843e12	0.699468
$596$	−1.48993e12	−0.483680
$597$	−1.07258e12	−0.345578
$598$	0	0
$599$	5.79175e12	1.83818	0.919092	−	0.394043i	$-0.128924\pi$
$599$	5.79175e12	1.83818	0.919092	+	0.394043i	$0.128924\pi$
$600$	−1.52336e11	−0.0479869
$601$	2.08361e12	0.651452	0.325726	−	0.945464i	$-0.394391\pi$
$601$	2.08361e12	0.651452	0.325726	+	0.945464i	$0.394391\pi$
$602$	−1.86869e11	−0.0579900
$603$	−3.54496e12	−1.09190
$604$	−2.08000e12	−0.635912
$605$	7.33808e11	0.222681
$606$	−6.59795e11	−0.198739
$607$	−2.97950e12	−0.890830	−0.445415	−	0.895324i	$-0.646944\pi$
$607$	−2.97950e12	−0.890830	−0.445415	+	0.895324i	$0.646944\pi$
$608$	−3.65010e11	−0.108327
$609$	−1.43980e12	−0.424154
$610$	9.78332e11	0.286090
$611$	0	0
$612$	1.64793e12	0.474852
$613$	−4.05649e11	−0.116032	−0.0580160	−	0.998316i	$-0.518477\pi$
$613$	−4.05649e11	−0.116032	−0.0580160	+	0.998316i	$0.518477\pi$
$614$	−3.11189e12	−0.883622
$615$	−2.87343e11	−0.0809958
$616$	−1.20039e12	−0.335900
$617$	4.28512e12	1.19036	0.595182	−	0.803591i	$-0.297080\pi$
$617$	4.28512e12	1.19036	0.595182	+	0.803591i	$0.297080\pi$
$618$	7.27048e10	0.0200500
$619$	2.19256e12	0.600266	0.300133	−	0.953897i	$-0.402969\pi$
$619$	2.19256e12	0.600266	0.300133	+	0.953897i	$0.402969\pi$
$620$	−1.16240e12	−0.315930
$621$	−2.23729e11	−0.0603685
$622$	2.19641e12	0.588377
$623$	−4.71800e12	−1.25476
$624$	0	0
$625$	3.56698e11	0.0935062
$626$	−3.53264e12	−0.919421
$627$	−3.84100e11	−0.0992522
$628$	5.70124e11	0.146268
$629$	5.83372e12	1.48600
$630$	−1.88825e12	−0.477559
$631$	−4.55941e12	−1.14492	−0.572462	−	0.819931i	$-0.694012\pi$
$631$	−4.55941e12	−1.14492	−0.572462	+	0.819931i	$0.694012\pi$
$632$	1.34605e12	0.335609
$633$	−1.51788e12	−0.375769
$634$	−9.54921e11	−0.234728
$635$	2.18139e12	0.532418
$636$	−5.89534e11	−0.142874
$637$	0	0
$638$	−3.96869e12	−0.948318
$639$	1.95330e12	0.463464
$640$	2.19038e11	0.0516072
$641$	−6.53353e12	−1.52857	−0.764287	−	0.644876i	$-0.776909\pi$
$641$	−6.53353e12	−1.52857	−0.764287	+	0.644876i	$0.776909\pi$
$642$	4.67927e11	0.108710
$643$	4.54044e12	1.04749	0.523743	−	0.851876i	$-0.324535\pi$
$643$	4.54044e12	1.04749	0.523743	+	0.851876i	$0.324535\pi$
$644$	−3.94796e11	−0.0904453
$645$	3.58818e10	0.00816310
$646$	1.90218e12	0.429739
$647$	−2.63894e12	−0.592053	−0.296026	−	0.955180i	$-0.595662\pi$
$647$	−2.63894e12	−0.592053	−0.296026	+	0.955180i	$0.595662\pi$
$648$	−1.38785e12	−0.309210
$649$	−3.41649e12	−0.755925
$650$	0	0
$651$	−1.23363e12	−0.269197
$652$	1.34188e12	0.290804
$653$	8.35055e12	1.79724	0.898620	−	0.438728i	$-0.144571\pi$
$653$	8.35055e12	1.79724	0.898620	+	0.438728i	$0.144571\pi$
$654$	5.05982e11	0.108152
$655$	2.76255e12	0.586441
$656$	−7.98797e11	−0.168411
$657$	5.73314e12	1.20046
$658$	−2.92754e12	−0.608817
$659$	4.16775e12	0.860830	0.430415	−	0.902631i	$-0.358367\pi$
$659$	4.16775e12	0.860830	0.430415	+	0.902631i	$0.358367\pi$
$660$	2.30494e11	0.0472838
$661$	−4.65565e12	−0.948580	−0.474290	−	0.880369i	$-0.657295\pi$
$661$	−4.65565e12	−0.948580	−0.474290	+	0.880369i	$0.657295\pi$
$662$	−3.84206e12	−0.777505
$663$	0	0
$664$	1.04791e12	0.209203
$665$	−2.17957e12	−0.432190
$666$	−5.15123e12	−1.01456
$667$	−1.30526e12	−0.255347
$668$	−4.77112e12	−0.927100
$669$	−1.89350e12	−0.365466
$670$	2.45550e12	0.470764
$671$	2.86195e12	0.545018
$672$	2.32461e11	0.0439733
$673$	7.92962e11	0.148999	0.0744997	−	0.997221i	$-0.476264\pi$
$673$	7.92962e11	0.148999	0.0744997	+	0.997221i	$0.476264\pi$
$674$	1.54974e12	0.289260
$675$	−1.43304e12	−0.265699
$676$	0	0
$677$	5.94620e12	1.08790	0.543952	−	0.839116i	$-0.316927\pi$
$677$	5.94620e12	1.08790	0.543952	+	0.839116i	$0.316927\pi$
$678$	−3.52358e10	−0.00640399
$679$	4.99394e12	0.901631
$680$	−1.14148e12	−0.204728
$681$	−8.58984e11	−0.153046
$682$	−3.40040e12	−0.601866
$683$	3.42571e11	0.0602362	0.0301181	−	0.999546i	$-0.490412\pi$
$683$	3.42571e11	0.0602362	0.0301181	+	0.999546i	$0.490412\pi$
$684$	−1.67964e12	−0.293403
$685$	−3.26582e12	−0.566740
$686$	2.67972e12	0.461987
$687$	−1.86670e12	−0.319720
$688$	9.97493e10	0.0169731
$689$	0	0
$690$	7.58070e10	0.0127318
$691$	−7.76689e12	−1.29597	−0.647986	−	0.761652i	$-0.724389\pi$
$691$	−7.76689e12	−1.29597	−0.647986	+	0.761652i	$0.724389\pi$
$692$	1.86722e12	0.309541
$693$	−5.52377e12	−0.909779
$694$	6.89193e12	1.12778
$695$	−4.95703e12	−0.805917
$696$	7.68554e11	0.124146
$697$	4.16278e12	0.668092
$698$	3.12492e12	0.498298
$699$	−1.52897e12	−0.242243
$700$	−2.52875e12	−0.398075
$701$	9.74048e12	1.52352	0.761762	−	0.647857i	$-0.224335\pi$
$701$	9.74048e12	1.52352	0.761762	+	0.647857i	$0.224335\pi$
$702$	0	0
$703$	−5.94598e12	−0.918172
$704$	6.40761e11	0.0983148
$705$	5.62135e11	0.0857017
$706$	6.41673e12	0.972059
$707$	−1.09525e13	−1.64864
$708$	6.61618e11	0.0989596
$709$	1.76320e12	0.262055	0.131027	−	0.991379i	$-0.458172\pi$
$709$	1.76320e12	0.262055	0.131027	+	0.991379i	$0.458172\pi$
$710$	−1.35300e12	−0.199818
$711$	6.19403e12	0.908992
$712$	2.51844e12	0.367258
$713$	−1.11835e12	−0.162060
$714$	−1.21143e12	−0.174444
$715$	0	0
$716$	−4.13440e12	−0.587900
$717$	7.15942e11	0.101168
$718$	4.49751e12	0.631557
$719$	1.16806e13	1.62999	0.814993	−	0.579471i	$-0.196741\pi$
$719$	1.16806e13	1.62999	0.814993	+	0.579471i	$0.196741\pi$
$720$	1.00794e12	0.139777
$721$	1.20689e12	0.166325
$722$	3.22422e12	0.441578
$723$	−1.93454e12	−0.263303
$724$	3.35237e12	0.453450
$725$	−8.36046e12	−1.12385
$726$	−4.15705e11	−0.0555355
$727$	9.17677e12	1.21839	0.609193	−	0.793022i	$-0.291493\pi$
$727$	9.17677e12	1.21839	0.609193	+	0.793022i	$0.291493\pi$
$728$	0	0
$729$	−5.75332e12	−0.754474
$730$	−3.97119e12	−0.517568
$731$	−5.19825e11	−0.0673332
$732$	−5.54230e11	−0.0713493
$733$	−9.38950e12	−1.20136	−0.600682	−	0.799488i	$-0.705104\pi$
$733$	−9.38950e12	−1.20136	−0.600682	+	0.799488i	$0.705104\pi$
$734$	−3.49837e12	−0.444871
$735$	4.36772e11	0.0552028
$736$	2.10739e11	0.0264725
$737$	7.18315e12	0.896833
$738$	−3.67578e12	−0.456137
$739$	−5.47910e12	−0.675786	−0.337893	−	0.941184i	$-0.609714\pi$
$739$	−5.47910e12	−0.675786	−0.337893	+	0.941184i	$0.609714\pi$
$740$	3.56812e12	0.437418
$741$	0	0
$742$	−9.78616e12	−1.18521
$743$	−5.75985e12	−0.693364	−0.346682	−	0.937983i	$-0.612692\pi$
$743$	−5.75985e12	−0.693364	−0.346682	+	0.937983i	$0.612692\pi$
$744$	6.58502e11	0.0787914
$745$	4.74905e12	0.564811
$746$	−7.99160e12	−0.944733
$747$	4.82210e12	0.566622
$748$	−3.33920e12	−0.390019
$749$	7.76750e12	0.901806
$750$	1.22227e12	0.141056
$751$	4.48697e12	0.514723	0.257361	−	0.966315i	$-0.417147\pi$
$751$	4.48697e12	0.514723	0.257361	+	0.966315i	$0.417147\pi$
$752$	1.56270e12	0.178195
$753$	−2.76950e12	−0.313924
$754$	0	0
$755$	6.62985e12	0.742578
$756$	2.18678e12	0.243476
$757$	−7.23491e12	−0.800759	−0.400380	−	0.916349i	$-0.631122\pi$
$757$	−7.23491e12	−0.800759	−0.400380	+	0.916349i	$0.631122\pi$
$758$	−5.72949e12	−0.630383
$759$	2.21761e11	0.0242548
$760$	1.16344e12	0.126498
$761$	9.84424e12	1.06402	0.532012	−	0.846737i	$-0.321436\pi$
$761$	9.84424e12	1.06402	0.532012	+	0.846737i	$0.321436\pi$
$762$	−1.23577e12	−0.132782
$763$	8.39920e12	0.897176
$764$	−6.87223e11	−0.0729756
$765$	−5.25267e12	−0.554502
$766$	7.89727e12	0.828796
$767$	0	0
$768$	−1.24086e11	−0.0128706
$769$	−1.01086e13	−1.04237	−0.521186	−	0.853443i	$-0.674510\pi$
$769$	−1.01086e13	−1.04237	−0.521186	+	0.853443i	$0.674510\pi$
$770$	3.82616e12	0.392243
$771$	−2.48879e12	−0.253655
$772$	1.06809e12	0.108226
$773$	−6.85077e12	−0.690131	−0.345065	−	0.938579i	$-0.612143\pi$
$773$	−6.85077e12	−0.690131	−0.345065	+	0.938579i	$0.612143\pi$
$774$	4.59010e11	0.0459714
$775$	−7.16330e12	−0.713273
$776$	−2.66573e12	−0.263899
$777$	3.78677e12	0.372713
$778$	−8.57560e12	−0.839182
$779$	−4.24288e12	−0.412803
$780$	0	0
$781$	−3.95798e12	−0.380666
$782$	−1.09823e12	−0.105018
$783$	7.22983e12	0.687385
$784$	1.21420e12	0.114781
$785$	−1.81723e12	−0.170803
$786$	−1.56500e12	−0.146256
$787$	1.48436e13	1.37928	0.689642	−	0.724150i	$-0.257768\pi$
$787$	1.48436e13	1.37928	0.689642	+	0.724150i	$0.257768\pi$
$788$	−5.22887e12	−0.483103
$789$	−3.06813e12	−0.281856
$790$	−4.29043e12	−0.391904
$791$	−5.84908e11	−0.0531243
$792$	2.94855e12	0.266284
$793$	0	0
$794$	3.27914e12	0.292798
$795$	1.87910e12	0.166839
$796$	9.50402e12	0.839071
$797$	1.35901e13	1.19306	0.596529	−	0.802591i	$-0.296546\pi$
$797$	1.35901e13	1.19306	0.596529	+	0.802591i	$0.296546\pi$
$798$	1.23474e12	0.107786
$799$	−8.14373e12	−0.706908
$800$	1.34983e12	0.116513
$801$	1.15889e13	0.994712
$802$	3.07384e11	0.0262359
$803$	−1.16171e13	−0.985998
$804$	−1.39105e12	−0.117406
$805$	1.25838e12	0.105616
$806$	0	0
$807$	−3.23472e12	−0.268476
$808$	5.84636e12	0.482541
$809$	8.74933e12	0.718135	0.359068	−	0.933312i	$-0.383095\pi$
$809$	8.74933e12	0.718135	0.359068	+	0.933312i	$0.383095\pi$
$810$	4.42366e12	0.361076
$811$	1.93959e13	1.57441	0.787203	−	0.616694i	$-0.211529\pi$
$811$	1.93959e13	1.57441	0.787203	+	0.616694i	$0.211529\pi$
$812$	1.27579e13	1.02985
$813$	2.83530e12	0.227610
$814$	1.04379e13	0.833307
$815$	−4.27716e12	−0.339583
$816$	6.46652e11	0.0510581
$817$	5.29827e11	0.0416040
$818$	−1.69062e13	−1.32025
$819$	0	0
$820$	2.54611e12	0.196659
$821$	1.16762e13	0.896926	0.448463	−	0.893801i	$-0.351972\pi$
$821$	1.16762e13	0.896926	0.448463	+	0.893801i	$0.351972\pi$
$822$	1.85010e12	0.141342
$823$	1.98052e13	1.50481	0.752404	−	0.658702i	$-0.228894\pi$
$823$	1.98052e13	1.50481	0.752404	+	0.658702i	$0.228894\pi$
$824$	−6.44228e11	−0.0486819
$825$	1.42043e12	0.106752
$826$	1.09827e13	0.820919
$827$	5.97356e12	0.444077	0.222039	−	0.975038i	$-0.428729\pi$
$827$	5.97356e12	0.444077	0.222039	+	0.975038i	$0.428729\pi$
$828$	9.69746e11	0.0717003
$829$	−1.84814e13	−1.35906	−0.679532	−	0.733646i	$-0.737817\pi$
$829$	−1.84814e13	−1.35906	−0.679532	+	0.733646i	$0.737817\pi$
$830$	−3.34013e12	−0.244294
$831$	−3.33683e12	−0.242734
$832$	0	0
$833$	−6.32758e12	−0.455339
$834$	2.80818e12	0.200992
$835$	1.52076e13	1.08261
$836$	3.40346e12	0.240986
$837$	6.19457e12	0.436261
$838$	−2.72737e12	−0.191049
$839$	6.40888e12	0.446533	0.223266	−	0.974757i	$-0.428328\pi$
$839$	6.40888e12	0.446533	0.223266	+	0.974757i	$0.428328\pi$
$840$	−7.40953e11	−0.0513493
$841$	2.76724e13	1.90750
$842$	−3.32802e12	−0.228182
$843$	−5.44736e12	−0.371503
$844$	1.34498e13	0.912375
$845$	0	0
$846$	7.19099e12	0.482639
$847$	−6.90064e12	−0.460695
$848$	5.22378e12	0.346900
$849$	1.02500e12	0.0677078
$850$	−7.03439e12	−0.462212
$851$	3.43292e12	0.224378
$852$	7.66480e11	0.0498337
$853$	7.28518e12	0.471162	0.235581	−	0.971855i	$-0.424301\pi$
$853$	7.28518e12	0.471162	0.235581	+	0.971855i	$0.424301\pi$
$854$	−9.20011e12	−0.591879
$855$	5.35374e12	0.342617
$856$	−4.14624e12	−0.263950
$857$	1.86647e12	0.118197	0.0590987	−	0.998252i	$-0.481177\pi$
$857$	1.86647e12	0.118197	0.0590987	+	0.998252i	$0.481177\pi$
$858$	0	0
$859$	8.88125e12	0.556551	0.278276	−	0.960501i	$-0.410237\pi$
$859$	8.88125e12	0.556551	0.278276	+	0.960501i	$0.410237\pi$
$860$	−3.17944e11	−0.0198202
$861$	2.70214e12	0.167569
$862$	7.69055e12	0.474433
$863$	−1.79949e13	−1.10434	−0.552168	−	0.833733i	$-0.686199\pi$
$863$	−1.79949e13	−1.10434	−0.552168	+	0.833733i	$0.686199\pi$
$864$	−1.16729e12	−0.0712632
$865$	−5.95163e12	−0.361462
$866$	1.78306e13	1.07730
$867$	5.62241e10	0.00337937
$868$	1.09310e13	0.653615
$869$	−1.25510e13	−0.746600
$870$	−2.44971e12	−0.144970
$871$	0	0
$872$	−4.48344e12	−0.262595
$873$	−1.22667e13	−0.714766
$874$	1.11936e12	0.0648886
$875$	2.02894e13	1.17013
$876$	2.24969e12	0.129079
$877$	−2.11553e13	−1.20759	−0.603797	−	0.797138i	$-0.706346\pi$
$877$	−2.11553e13	−1.20759	−0.603797	+	0.797138i	$0.706346\pi$
$878$	−1.22743e13	−0.697060
$879$	−6.02882e11	−0.0340629
$880$	−2.04238e12	−0.114806
$881$	1.86075e13	1.04063	0.520315	−	0.853974i	$-0.325815\pi$
$881$	1.86075e13	1.04063	0.520315	+	0.853974i	$0.325815\pi$
$882$	5.58731e12	0.310881
$883$	−2.69048e13	−1.48938	−0.744691	−	0.667410i	$-0.767403\pi$
$883$	−2.69048e13	−1.48938	−0.744691	+	0.667410i	$0.767403\pi$
$884$	0	0
$885$	−2.10886e12	−0.115559
$886$	−1.38394e13	−0.754512
$887$	−2.00183e12	−0.108585	−0.0542927	−	0.998525i	$-0.517290\pi$
$887$	−2.00183e12	−0.108585	−0.0542927	+	0.998525i	$0.517290\pi$
$888$	−2.02135e12	−0.109090
$889$	−2.05136e13	−1.10150
$890$	−8.02734e12	−0.428861
$891$	1.29407e13	0.687872
$892$	1.67780e13	0.887359
$893$	8.30043e12	0.436786
$894$	−2.69036e12	−0.140861
$895$	1.31781e13	0.686513
$896$	−2.05981e12	−0.106768
$897$	0	0
$898$	2.11873e13	1.08725
$899$	3.61397e13	1.84530
$900$	6.21143e12	0.315573
$901$	−2.72228e13	−1.37617
$902$	7.44822e12	0.374648
$903$	−3.37428e11	−0.0168883
$904$	3.12220e11	0.0155490
$905$	−1.06855e13	−0.529510
$906$	−3.75584e12	−0.185195
$907$	2.68431e13	1.31704	0.658522	−	0.752561i	$-0.271182\pi$
$907$	2.68431e13	1.31704	0.658522	+	0.752561i	$0.271182\pi$
$908$	7.61135e12	0.371600
$909$	2.69028e13	1.30695
$910$	0	0
$911$	−3.41130e13	−1.64092	−0.820459	−	0.571705i	$-0.806282\pi$
$911$	−3.41130e13	−1.64092	−0.820459	+	0.571705i	$0.806282\pi$
$912$	−6.59095e11	−0.0315479
$913$	−9.77101e12	−0.465394
$914$	7.77900e12	0.368694
$915$	1.76657e12	0.0833173
$916$	1.65406e13	0.776286
$917$	−2.59787e13	−1.21326
$918$	6.08309e12	0.282704
$919$	−1.94780e13	−0.900792	−0.450396	−	0.892829i	$-0.648717\pi$
$919$	−1.94780e13	−0.900792	−0.450396	+	0.892829i	$0.648717\pi$
$920$	−6.71716e11	−0.0309130
$921$	−5.61912e12	−0.257336
$922$	−9.42208e12	−0.429396
$923$	0	0
$924$	−2.16754e12	−0.0978234
$925$	2.19886e13	0.987553
$926$	−2.80247e13	−1.25254
$927$	−2.96450e12	−0.131854
$928$	−6.81006e12	−0.301429
$929$	−2.59976e13	−1.14515	−0.572575	−	0.819852i	$-0.694056\pi$
$929$	−2.59976e13	−1.14515	−0.572575	+	0.819852i	$0.694056\pi$
$930$	−2.09893e12	−0.0920077
$931$	6.44933e12	0.281346
$932$	1.35480e13	0.588170
$933$	3.96603e12	0.171352
$934$	−3.26128e12	−0.140225
$935$	1.06435e13	0.455440
$936$	0	0
$937$	1.79203e12	0.0759483	0.0379741	−	0.999279i	$-0.487910\pi$
$937$	1.79203e12	0.0759483	0.0379741	+	0.999279i	$0.487910\pi$
$938$	−2.30912e13	−0.973943
$939$	−6.37885e12	−0.267761
$940$	−4.98100e12	−0.208085
$941$	−2.98098e13	−1.23938	−0.619692	−	0.784845i	$-0.712743\pi$
$941$	−2.98098e13	−1.23938	−0.619692	+	0.784845i	$0.712743\pi$
$942$	1.02947e12	0.0425975
$943$	2.44964e12	0.100879
$944$	−5.86251e12	−0.240276
$945$	−6.97019e12	−0.284316
$946$	−9.30092e11	−0.0377586
$947$	−6.69825e12	−0.270637	−0.135318	−	0.990802i	$-0.543206\pi$
$947$	−6.69825e12	−0.270637	−0.135318	+	0.990802i	$0.543206\pi$
$948$	2.43055e12	0.0977388
$949$	0	0
$950$	7.16975e12	0.285593
$951$	−1.72429e12	−0.0683595
$952$	1.07343e13	0.423553
$953$	4.18156e13	1.64218	0.821090	−	0.570799i	$-0.193366\pi$
$953$	4.18156e13	1.64218	0.821090	+	0.570799i	$0.193366\pi$
$954$	2.40380e13	0.939572
$955$	2.19047e12	0.0852164
$956$	−6.34387e12	−0.245637
$957$	−7.16623e12	−0.276177
$958$	9.18479e12	0.352309
$959$	3.07113e13	1.17250
$960$	3.95516e11	0.0150295
$961$	4.52511e12	0.171149
$962$	0	0
$963$	−1.90795e13	−0.714905
$964$	1.71417e13	0.639305
$965$	−3.40447e12	−0.126380
$966$	−7.12879e11	−0.0263402
$967$	1.10527e13	0.406489	0.203244	−	0.979128i	$-0.434851\pi$
$967$	1.10527e13	0.406489	0.203244	+	0.979128i	$0.434851\pi$
$968$	3.68351e12	0.134841
$969$	3.43475e12	0.125152
$970$	8.49682e12	0.308165
$971$	6.36275e12	0.229699	0.114849	−	0.993383i	$-0.463361\pi$
$971$	6.36275e12	0.229699	0.114849	+	0.993383i	$0.463361\pi$
$972$	−8.11532e12	−0.291613
$973$	4.66153e13	1.66733
$974$	−2.59109e13	−0.922501
$975$	0	0
$976$	4.91096e12	0.173237
$977$	−2.24005e12	−0.0786559	−0.0393279	−	0.999226i	$-0.512522\pi$
$977$	−2.24005e12	−0.0786559	−0.0393279	+	0.999226i	$0.512522\pi$
$978$	2.42303e12	0.0846904
$979$	−2.34827e13	−0.817006
$980$	−3.87018e12	−0.134034
$981$	−2.06311e13	−0.711235
$982$	3.45568e13	1.18586
$983$	−3.13907e13	−1.07228	−0.536142	−	0.844128i	$-0.680119\pi$
$983$	−3.13907e13	−1.07228	−0.536142	+	0.844128i	$0.680119\pi$
$984$	−1.44238e12	−0.0490459
$985$	1.66667e13	0.564138
$986$	3.54893e13	1.19578
$987$	−5.28624e12	−0.177305
$988$	0	0
$989$	−3.05897e11	−0.0101670
$990$	−9.39828e12	−0.310950
$991$	−2.85083e13	−0.938943	−0.469472	−	0.882948i	$-0.655556\pi$
$991$	−2.85083e13	−0.938943	−0.469472	+	0.882948i	$0.655556\pi$
$992$	−5.83490e12	−0.191307
$993$	−6.93757e12	−0.226431
$994$	1.27234e13	0.413395
$995$	−3.02934e13	−0.979815
$996$	1.89220e12	0.0609257
$997$	−2.38039e13	−0.762993	−0.381496	−	0.924370i	$-0.624591\pi$
$997$	−2.38039e13	−0.762993	−0.381496	+	0.924370i	$0.624591\pi$
$998$	−2.98492e13	−0.952456
$999$	−1.90150e13	−0.604020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.q.1.7	✓	15
13.12	even	2		338.10.a.r.1.7	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.10.a.q.1.7	✓	15	1.1	even	1	trivial
338.10.a.r.1.7	yes	15	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -28.8911 q^{3} +256.000 q^{4} -815.982 q^{5} +462.257 q^{6} +7673.39 q^{7} -4096.00 q^{8} -18848.3 q^{9} +13055.7 q^{10} +38192.3 q^{11} -7396.11 q^{12} -122774. q^{14} +23574.6 q^{15} +65536.0 q^{16} -341529. q^{17} +301573. q^{18} +348100. q^{19} -208891. q^{20} -221692. q^{21} -611077. q^{22} -200977. q^{23} +118338. q^{24} -1.28730e6 q^{25} +1.11321e6 q^{27} +1.96439e6 q^{28} +6.49458e6 q^{29} -377193. q^{30} +5.56460e6 q^{31} -1.04858e6 q^{32} -1.10342e6 q^{33} +5.46446e6 q^{34} -6.26134e6 q^{35} -4.82517e6 q^{36} -1.70812e7 q^{37} -5.56960e6 q^{38} +3.34226e6 q^{40} -1.21887e7 q^{41} +3.54708e6 q^{42} +1.52205e6 q^{43} +9.77723e6 q^{44} +1.53799e7 q^{45} +3.21563e6 q^{46} +2.38449e7 q^{47} -1.89341e6 q^{48} +1.85272e7 q^{49} +2.05968e7 q^{50} +9.86713e6 q^{51} +7.97086e7 q^{53} -1.78114e7 q^{54} -3.11642e7 q^{55} -3.14302e7 q^{56} -1.00570e7 q^{57} -1.03913e8 q^{58} -8.94548e7 q^{59} +6.03509e6 q^{60} +7.49352e7 q^{61} -8.90335e7 q^{62} -1.44630e8 q^{63} +1.67772e7 q^{64} +1.76547e7 q^{66} +1.88079e8 q^{67} -8.74313e7 q^{68} +5.80643e6 q^{69} +1.00181e8 q^{70} -1.03633e8 q^{71} +7.72027e7 q^{72} -3.04172e8 q^{73} +2.73299e8 q^{74} +3.71914e7 q^{75} +8.91137e7 q^{76} +2.93064e8 q^{77} -3.28625e8 q^{79} -5.34762e7 q^{80} +3.38829e8 q^{81} +1.95019e8 q^{82} -2.55837e8 q^{83} -5.67532e7 q^{84} +2.78681e8 q^{85} -2.43529e7 q^{86} -1.87635e8 q^{87} -1.56436e8 q^{88} -6.14853e8 q^{89} -2.46078e8 q^{90} -5.14500e7 q^{92} -1.60767e8 q^{93} -3.81519e8 q^{94} -2.84043e8 q^{95} +3.02945e7 q^{96} +6.50813e8 q^{97} -2.96436e8 q^{98} -7.19860e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 240 q^{2} + 324 q^{3} + 3840 q^{4} - 2164 q^{5} - 5184 q^{6} - 4227 q^{7} - 61440 q^{8} + 112199 q^{9} + 34624 q^{10} + 58782 q^{11} + 82944 q^{12} + 67632 q^{14} - 488672 q^{15} + 983040 q^{16}+ \cdots - 3437295177 q^{99}+O(q^{100}) \) 15 * q - 240 * q^2 + 324 * q^3 + 3840 * q^4 - 2164 * q^5 - 5184 * q^6 - 4227 * q^7 - 61440 * q^8 + 112199 * q^9 + 34624 * q^10 + 58782 * q^11 + 82944 * q^12 + 67632 * q^14 - 488672 * q^15 + 983040 * q^16 + 47308 * q^17 - 1795184 * q^18 - 1027864 * q^19 - 553984 * q^20 + 1332838 * q^21 - 940512 * q^22 - 697897 * q^23 - 1327104 * q^24 + 12121163 * q^25 + 11934723 * q^27 - 1082112 * q^28 + 4970557 * q^29 + 7818752 * q^30 - 8962601 * q^31 - 15728640 * q^32 - 3541482 * q^33 - 756928 * q^34 - 5785412 * q^35 + 28722944 * q^36 - 25045552 * q^37 + 16445824 * q^38 + 8863744 * q^40 - 26390985 * q^41 - 21325408 * q^42 + 11355145 * q^43 + 15048192 * q^44 - 221235525 * q^45 + 11166352 * q^46 - 79882208 * q^47 + 21233664 * q^48 + 150275074 * q^49 - 193938608 * q^50 + 118779121 * q^51 - 21678349 * q^53 - 190955568 * q^54 + 290281352 * q^55 + 17313792 * q^56 + 617732541 * q^57 - 79528912 * q^58 + 264523979 * q^59 - 125100032 * q^60 + 379367976 * q^61 + 143401616 * q^62 - 270769230 * q^63 + 251658240 * q^64 + 56663712 * q^66 + 250185789 * q^67 + 12110848 * q^68 + 281627650 * q^69 + 92566592 * q^70 - 173178579 * q^71 - 459567104 * q^72 - 153358293 * q^73 + 400728832 * q^74 + 20980603 * q^75 - 263133184 * q^76 + 1172911296 * q^77 + 217644101 * q^79 - 141819904 * q^80 + 2373566723 * q^81 + 422255760 * q^82 + 76435497 * q^83 + 341206528 * q^84 - 2676674151 * q^85 - 181682320 * q^86 + 4874616750 * q^87 - 240771072 * q^88 - 2250224949 * q^89 + 3539768400 * q^90 - 178661632 * q^92 - 2915972474 * q^93 + 1278115328 * q^94 + 3329480199 * q^95 - 339738624 * q^96 - 2720440815 * q^97 - 2404401184 * q^98 - 3437295177 * q^99

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