LMFDB - Embedded newform 151.12.a.b.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [151,12,Mod(1,151)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("151.1"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(151, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	151.a (trivial)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$116.019820264$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-74.0388 q^{2} -482.351 q^{3} +3433.74 q^{4} +9798.61 q^{5} +35712.7 q^{6} +4473.40 q^{7} -102599. q^{8} +55515.2 q^{9} -725478. q^{10} -1.02682e6 q^{11} -1.65627e6 q^{12} +965114. q^{13} -331205. q^{14} -4.72637e6 q^{15} +563981. q^{16} -5.54116e6 q^{17} -4.11028e6 q^{18} -2.02324e7 q^{19} +3.36459e7 q^{20} -2.15775e6 q^{21} +7.60242e7 q^{22} -5.24663e6 q^{23} +4.94886e7 q^{24} +4.71847e7 q^{25} -7.14559e7 q^{26} +5.86692e7 q^{27} +1.53605e7 q^{28} -8.97842e7 q^{29} +3.49935e8 q^{30} -1.20783e7 q^{31} +1.68366e8 q^{32} +4.95285e8 q^{33} +4.10261e8 q^{34} +4.38331e7 q^{35} +1.90625e8 q^{36} -2.90183e8 q^{37} +1.49798e9 q^{38} -4.65523e8 q^{39} -1.00533e9 q^{40} +6.31516e8 q^{41} +1.59757e8 q^{42} -1.09157e9 q^{43} -3.52582e9 q^{44} +5.43972e8 q^{45} +3.88454e8 q^{46} -2.06224e9 q^{47} -2.72037e8 q^{48} -1.95732e9 q^{49} -3.49350e9 q^{50} +2.67278e9 q^{51} +3.31395e9 q^{52} +4.96957e9 q^{53} -4.34379e9 q^{54} -1.00614e10 q^{55} -4.58965e8 q^{56} +9.75910e9 q^{57} +6.64751e9 q^{58} -6.55157e9 q^{59} -1.62291e10 q^{60} +6.65185e8 q^{61} +8.94266e8 q^{62} +2.48342e8 q^{63} -1.36206e10 q^{64} +9.45678e9 q^{65} -3.66703e10 q^{66} -9.28229e9 q^{67} -1.90269e10 q^{68} +2.53072e9 q^{69} -3.24535e9 q^{70} +1.00053e10 q^{71} -5.69579e9 q^{72} +2.14204e9 q^{73} +2.14848e10 q^{74} -2.27596e10 q^{75} -6.94727e10 q^{76} -4.59336e9 q^{77} +3.44668e10 q^{78} +2.49752e10 q^{79} +5.52623e9 q^{80} -3.81335e10 q^{81} -4.67567e10 q^{82} +2.93270e10 q^{83} -7.40916e9 q^{84} -5.42957e10 q^{85} +8.08187e10 q^{86} +4.33075e10 q^{87} +1.05350e11 q^{88} -9.03337e10 q^{89} -4.02751e10 q^{90} +4.31734e9 q^{91} -1.80156e10 q^{92} +5.82600e9 q^{93} +1.52686e11 q^{94} -1.98249e11 q^{95} -8.12113e10 q^{96} +7.67242e10 q^{97} +1.44917e11 q^{98} -5.70039e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 96 q^{2} + 719 q^{3} + 76800 q^{4} + 32669 q^{5} + 62208 q^{6} + 48045 q^{7} + 332331 q^{8} + 5218827 q^{9} + 326849 q^{10} + 1825499 q^{11} + 2261853 q^{12} + 1312687 q^{13} + 8226356 q^{14} + 613376 q^{15}+ \cdots + 723642496724 q^{99}+O(q^{100}) $ 72 * q + 96 * q^2 + 719 * q^3 + 76800 * q^4 + 32669 * q^5 + 62208 * q^6 + 48045 * q^7 + 332331 * q^8 + 5218827 * q^9 + 326849 * q^10 + 1825499 * q^11 + 2261853 * q^12 + 1312687 * q^13 + 8226356 * q^14 + 613376 * q^15 + 84812296 * q^16 + 40931638 * q^17 + 13122715 * q^18 + 29375013 * q^19 + 84918219 * q^20 + 46372635 * q^21 + 58791436 * q^22 + 63373752 * q^23 + 208042693 * q^24 + 822098007 * q^25 + 432475855 * q^26 + 279380906 * q^27 + 199223712 * q^28 + 51987647 * q^29 + 32799172 * q^30 + 148980151 * q^31 + 840145879 * q^32 + 1349677131 * q^33 + 1022459895 * q^34 + 1271864483 * q^35 + 6069158248 * q^36 + 810903761 * q^37 - 2120563014 * q^38 - 2355029258 * q^39 - 3320389733 * q^40 + 5859782715 * q^41 + 6554723872 * q^42 + 3919513748 * q^43 + 14612470209 * q^44 + 10929057031 * q^45 + 15665409299 * q^46 + 3875062355 * q^47 + 29410144241 * q^48 + 37248222741 * q^49 + 16504097391 * q^50 + 12516522585 * q^51 + 567334931 * q^52 + 14672884898 * q^53 + 9414903427 * q^54 - 2982579193 * q^55 + 19920696363 * q^56 + 2875970526 * q^57 - 48084192512 * q^58 + 17257084239 * q^59 - 93407696365 * q^60 + 1422999895 * q^61 - 22829643062 * q^62 - 32319999932 * q^63 + 66529030631 * q^64 + 34355567339 * q^65 - 38790557894 * q^66 - 10815985001 * q^67 - 25606248436 * q^68 - 54498950277 * q^69 - 144393130061 * q^70 + 27421632954 * q^71 - 128042048589 * q^72 + 21697968943 * q^73 - 101715174833 * q^74 - 83292842880 * q^75 - 70562325614 * q^76 + 45959714583 * q^77 - 187146337248 * q^78 + 1132036389 * q^79 + 59865281599 * q^80 + 463311030968 * q^81 + 24896564876 * q^82 + 116660670941 * q^83 + 30259089579 * q^84 + 108598686344 * q^85 + 137406150133 * q^86 + 37420541026 * q^87 + 169139986803 * q^88 + 558676234986 * q^89 + 208795168870 * q^90 + 147594184277 * q^91 + 207339666618 * q^92 + 333952966703 * q^93 + 601254931179 * q^94 + 292495837940 * q^95 + 632965316684 * q^96 + 204273411870 * q^97 + 541340673550 * q^98 + 723642496724 * 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 $

$2$	−74.0388	−1.63604	−0.818021	−	0.575189i	$-0.804929\pi$
$2$	−74.0388	−1.63604	−0.818021	+	0.575189i	$0.804929\pi$
$3$	−482.351	−1.14603	−0.573015	−	0.819545i	$-0.694226\pi$
$3$	−482.351	−1.14603	−0.573015	+	0.819545i	$0.694226\pi$
$4$	3433.74	1.67663
$5$	9798.61	1.40226	0.701132	−	0.713032i	$-0.252678\pi$
$5$	9798.61	1.40226	0.701132	+	0.713032i	$0.252678\pi$
$6$	35712.7	1.87495
$7$	4473.40	0.100600	0.0503001	−	0.998734i	$-0.483982\pi$
$7$	4473.40	0.100600	0.0503001	+	0.998734i	$0.483982\pi$
$8$	−102599.	−1.10700
$9$	55515.2	0.313385
$10$	−725478.	−2.29416
$11$	−1.02682e6	−1.92235	−0.961176	−	0.275937i	$-0.911012\pi$
$11$	−1.02682e6	−1.92235	−0.961176	+	0.275937i	$0.911012\pi$
$12$	−1.65627e6	−1.92147
$13$	965114.	0.720925	0.360463	−	0.932774i	$-0.382619\pi$
$13$	965114.	0.720925	0.360463	+	0.932774i	$0.382619\pi$
$14$	−331205.	−0.164586
$15$	−4.72637e6	−1.60704
$16$	563981.	0.134464
$17$	−5.54116e6	−0.946524	−0.473262	−	0.880922i	$-0.656924\pi$
$17$	−5.54116e6	−0.946524	−0.473262	+	0.880922i	$0.656924\pi$
$18$	−4.11028e6	−0.512711
$19$	−2.02324e7	−1.87457	−0.937285	−	0.348563i	$-0.886670\pi$
$19$	−2.02324e7	−1.87457	−0.937285	+	0.348563i	$0.886670\pi$
$20$	3.36459e7	2.35108
$21$	−2.15775e6	−0.115291
$22$	7.60242e7	3.14505
$23$	−5.24663e6	−0.169972	−0.0849860	−	0.996382i	$-0.527085\pi$
$23$	−5.24663e6	−0.169972	−0.0849860	+	0.996382i	$0.527085\pi$
$24$	4.94886e7	1.26865
$25$	4.71847e7	0.966343
$26$	−7.14559e7	−1.17946
$27$	5.86692e7	0.786881
$28$	1.53605e7	0.168670
$29$	−8.97842e7	−0.812851	−0.406425	−	0.913684i	$-0.633225\pi$
$29$	−8.97842e7	−0.812851	−0.406425	+	0.913684i	$0.633225\pi$
$30$	3.49935e8	2.62918
$31$	−1.20783e7	−0.0757737	−0.0378868	−	0.999282i	$-0.512063\pi$
$31$	−1.20783e7	−0.0757737	−0.0378868	+	0.999282i	$0.512063\pi$
$32$	1.68366e8	0.887011
$33$	4.95285e8	2.20307
$34$	4.10261e8	1.54855
$35$	4.38331e7	0.141068
$36$	1.90625e8	0.525432
$37$	−2.90183e8	−0.687958	−0.343979	−	0.938977i	$-0.611775\pi$
$37$	−2.90183e8	−0.687958	−0.343979	+	0.938977i	$0.611775\pi$
$38$	1.49798e9	3.06688
$39$	−4.65523e8	−0.826202
$40$	−1.00533e9	−1.55230
$41$	6.31516e8	0.851281	0.425641	−	0.904892i	$-0.360049\pi$
$41$	6.31516e8	0.851281	0.425641	+	0.904892i	$0.360049\pi$
$42$	1.59757e8	0.188621
$43$	−1.09157e9	−1.13234	−0.566169	−	0.824289i	$-0.691575\pi$
$43$	−1.09157e9	−1.13234	−0.566169	+	0.824289i	$0.691575\pi$
$44$	−3.52582e9	−3.22308
$45$	5.43972e8	0.439449
$46$	3.88454e8	0.278081
$47$	−2.06224e9	−1.31160	−0.655798	−	0.754936i	$-0.727668\pi$
$47$	−2.06224e9	−1.31160	−0.655798	+	0.754936i	$0.727668\pi$
$48$	−2.72037e8	−0.154099
$49$	−1.95732e9	−0.989880
$50$	−3.49350e9	−1.58098
$51$	2.67278e9	1.08474
$52$	3.31395e9	1.20873
$53$	4.96957e9	1.63231	0.816153	−	0.577836i	$-0.196103\pi$
$53$	4.96957e9	1.63231	0.816153	+	0.577836i	$0.196103\pi$
$54$	−4.34379e9	−1.28737
$55$	−1.00614e10	−2.69564
$56$	−4.58965e8	−0.111364
$57$	9.75910e9	2.14831
$58$	6.64751e9	1.32986
$59$	−6.55157e9	−1.19305	−0.596526	−	0.802594i	$-0.703453\pi$
$59$	−6.55157e9	−1.19305	−0.596526	+	0.802594i	$0.703453\pi$
$60$	−1.62291e10	−2.69441
$61$	6.65185e8	0.100839	0.0504195	−	0.998728i	$-0.483944\pi$
$61$	6.65185e8	0.100839	0.0504195	+	0.998728i	$0.483944\pi$
$62$	8.94266e8	0.123969
$63$	2.48342e8	0.0315266
$64$	−1.36206e10	−1.58565
$65$	9.45678e9	1.01093
$66$	−3.66703e10	−3.60432
$67$	−9.28229e9	−0.839931	−0.419965	−	0.907540i	$-0.637958\pi$
$67$	−9.28229e9	−0.839931	−0.419965	+	0.907540i	$0.637958\pi$
$68$	−1.90269e10	−1.58697
$69$	2.53072e9	0.194793
$70$	−3.24535e9	−0.230793
$71$	1.00053e10	0.658129	0.329064	−	0.944308i	$-0.393267\pi$
$71$	1.00053e10	0.658129	0.329064	+	0.944308i	$0.393267\pi$
$72$	−5.69579e9	−0.346917
$73$	2.14204e9	0.120935	0.0604675	−	0.998170i	$-0.480741\pi$
$73$	2.14204e9	0.120935	0.0604675	+	0.998170i	$0.480741\pi$
$74$	2.14848e10	1.12553
$75$	−2.27596e10	−1.10746
$76$	−6.94727e10	−3.14297
$77$	−4.59336e9	−0.193389
$78$	3.44668e10	1.35170
$79$	2.49752e10	0.913186	0.456593	−	0.889676i	$-0.349070\pi$
$79$	2.49752e10	0.913186	0.456593	+	0.889676i	$0.349070\pi$
$80$	5.52623e9	0.188553
$81$	−3.81335e10	−1.21517
$82$	−4.67567e10	−1.39273
$83$	2.93270e10	0.817219	0.408610	−	0.912709i	$-0.366014\pi$
$83$	2.93270e10	0.817219	0.408610	+	0.912709i	$0.366014\pi$
$84$	−7.40916e9	−0.193300
$85$	−5.42957e10	−1.32728
$86$	8.08187e10	1.85255
$87$	4.33075e10	0.931551
$88$	1.05350e11	2.12804
$89$	−9.03337e10	−1.71477	−0.857383	−	0.514679i	$-0.827911\pi$
$89$	−9.03337e10	−1.71477	−0.857383	+	0.514679i	$0.827911\pi$
$90$	−4.02751e10	−0.718956
$91$	4.31734e9	0.0725252
$92$	−1.80156e10	−0.284981
$93$	5.82600e9	0.0868389
$94$	1.52686e11	2.14583
$95$	−1.98249e11	−2.62864
$96$	−8.12113e10	−1.01654
$97$	7.67242e10	0.907169	0.453584	−	0.891213i	$-0.350145\pi$
$97$	7.67242e10	0.907169	0.453584	+	0.891213i	$0.350145\pi$
$98$	1.44917e11	1.61948
$99$	−5.70039e10	−0.602436
$100$	1.62020e11	1.62020
$101$	5.87052e10	0.555787	0.277894	−	0.960612i	$-0.410364\pi$
$101$	5.87052e10	0.555787	0.277894	+	0.960612i	$0.410364\pi$
$102$	−1.97890e11	−1.77469
$103$	1.51543e11	1.28805	0.644023	−	0.765006i	$-0.277264\pi$
$103$	1.51543e11	1.28805	0.644023	+	0.765006i	$0.277264\pi$
$104$	−9.90195e10	−0.798063
$105$	−2.11429e10	−0.161668
$106$	−3.67941e11	−2.67052
$107$	−2.03583e11	−1.40324	−0.701620	−	0.712552i	$-0.747539\pi$
$107$	−2.03583e11	−1.40324	−0.701620	+	0.712552i	$0.747539\pi$
$108$	2.01455e11	1.31931
$109$	1.52809e10	0.0951271	0.0475636	−	0.998868i	$-0.484854\pi$
$109$	1.52809e10	0.0951271	0.0475636	+	0.998868i	$0.484854\pi$
$110$	7.44932e11	4.41018
$111$	1.39970e11	0.788421
$112$	2.52292e9	0.0135271
$113$	−1.79874e11	−0.918411	−0.459205	−	0.888330i	$-0.651866\pi$
$113$	−1.79874e11	−0.918411	−0.459205	+	0.888330i	$0.651866\pi$
$114$	−7.22552e11	−3.51473
$115$	−5.14097e10	−0.238346
$116$	−3.08296e11	−1.36285
$117$	5.35785e10	0.225927
$118$	4.85071e11	1.95188
$119$	−2.47878e10	−0.0952204
$120$	4.84919e11	1.77899
$121$	7.69039e11	2.69544
$122$	−4.92495e10	−0.164977
$123$	−3.04612e11	−0.975594
$124$	−4.14739e10	−0.127045
$125$	−1.61032e10	−0.0471963
$126$	−1.83869e10	−0.0515788
$127$	−4.40877e11	−1.18412	−0.592062	−	0.805892i	$-0.701686\pi$
$127$	−4.40877e11	−1.18412	−0.592062	+	0.805892i	$0.701686\pi$
$128$	6.63642e11	1.70718
$129$	5.26521e11	1.29769
$130$	−7.00169e11	−1.65392
$131$	−8.10088e10	−0.183459	−0.0917297	−	0.995784i	$-0.529240\pi$
$131$	−8.10088e10	−0.183459	−0.0917297	+	0.995784i	$0.529240\pi$
$132$	1.70068e12	3.69374
$133$	−9.05075e10	−0.188582
$134$	6.87249e11	1.37416
$135$	5.74877e11	1.10341
$136$	5.68516e11	1.04780
$137$	6.00311e11	1.06271	0.531353	−	0.847150i	$-0.321684\pi$
$137$	6.00311e11	1.06271	0.531353	+	0.847150i	$0.321684\pi$
$138$	−1.87371e11	−0.318690
$139$	−8.69288e10	−0.142096	−0.0710481	−	0.997473i	$-0.522634\pi$
$139$	−8.69288e10	−0.142096	−0.0710481	+	0.997473i	$0.522634\pi$
$140$	1.50512e11	0.236519
$141$	9.94721e11	1.50313
$142$	−7.40783e11	−1.07673
$143$	−9.90994e11	−1.38587
$144$	3.13096e10	0.0421389
$145$	−8.79760e11	−1.13983
$146$	−1.58594e11	−0.197855
$147$	9.44113e11	1.13443
$148$	−9.96413e11	−1.15345
$149$	−1.05777e12	−1.17996	−0.589979	−	0.807419i	$-0.700864\pi$
$149$	−1.05777e12	−1.17996	−0.589979	+	0.807419i	$0.700864\pi$
$150$	1.68509e12	1.81185
$151$	−7.85027e10	−0.0813788
$151$	−7.85027e10	−0.0813788
$152$	2.07581e12	2.07515
$153$	−3.07619e11	−0.296626
$154$	3.40087e11	0.316392
$155$	−1.18351e11	−0.106255
$156$	−1.59849e12	−1.38524
$157$	−1.94141e12	−1.62431	−0.812157	−	0.583439i	$-0.801707\pi$
$157$	−1.94141e12	−1.62431	−0.812157	+	0.583439i	$0.801707\pi$
$158$	−1.84913e12	−1.49401
$159$	−2.39708e12	−1.87067
$160$	1.64975e12	1.24382
$161$	−2.34703e10	−0.0170992
$162$	2.82336e12	1.98808
$163$	−2.06392e12	−1.40495	−0.702477	−	0.711707i	$-0.747922\pi$
$163$	−2.06392e12	−1.40495	−0.702477	+	0.711707i	$0.747922\pi$
$164$	2.16846e12	1.42729
$165$	4.85311e12	3.08929
$166$	−2.17134e12	−1.33700
$167$	2.42022e12	1.44183	0.720914	−	0.693024i	$-0.243722\pi$
$167$	2.42022e12	1.44183	0.720914	+	0.693024i	$0.243722\pi$
$168$	2.21382e11	0.127627
$169$	−8.60715e11	−0.480267
$170$	4.01999e12	2.17148
$171$	−1.12320e12	−0.587463
$172$	−3.74818e12	−1.89851
$173$	9.85540e11	0.483527	0.241764	−	0.970335i	$-0.422274\pi$
$173$	9.85540e11	0.483527	0.241764	+	0.970335i	$0.422274\pi$
$174$	−3.20643e12	−1.52406
$175$	2.11076e11	0.0972143
$176$	−5.79105e11	−0.258486
$177$	3.16016e12	1.36727
$178$	6.68820e12	2.80543
$179$	2.99293e12	1.21732	0.608659	−	0.793432i	$-0.291708\pi$
$179$	2.99293e12	1.21732	0.608659	+	0.793432i	$0.291708\pi$
$180$	1.86786e12	0.736794
$181$	4.01178e12	1.53499	0.767493	−	0.641057i	$-0.221504\pi$
$181$	4.01178e12	1.53499	0.767493	+	0.641057i	$0.221504\pi$
$182$	−3.19651e11	−0.118654
$183$	−3.20852e11	−0.115564
$184$	5.38298e11	0.188159
$185$	−2.84339e12	−0.964699
$186$	−4.31350e11	−0.142072
$187$	5.68975e12	1.81955
$188$	−7.08119e12	−2.19907
$189$	2.62451e11	0.0791604
$190$	1.46781e13	4.30057
$191$	−3.55463e12	−1.01184	−0.505919	−	0.862581i	$-0.668847\pi$
$191$	−3.55463e12	−1.01184	−0.505919	+	0.862581i	$0.668847\pi$
$192$	6.56992e12	1.81720
$193$	4.09949e12	1.10196	0.550978	−	0.834520i	$-0.314255\pi$
$193$	4.09949e12	1.10196	0.550978	+	0.834520i	$0.314255\pi$
$194$	−5.68057e12	−1.48417
$195$	−4.56148e12	−1.15855
$196$	−6.72092e12	−1.65966
$197$	2.15849e11	0.0518305	0.0259152	−	0.999664i	$-0.491750\pi$
$197$	2.15849e11	0.0518305	0.0259152	+	0.999664i	$0.491750\pi$
$198$	4.22050e12	0.985611
$199$	−4.67028e12	−1.06084	−0.530422	−	0.847734i	$-0.677966\pi$
$199$	−4.67028e12	−1.06084	−0.530422	+	0.847734i	$0.677966\pi$
$200$	−4.84109e12	−1.06974
$201$	4.47732e12	0.962586
$202$	−4.34646e12	−0.909291
$203$	−4.01641e11	−0.0817729
$204$	9.17765e12	1.81872
$205$	6.18798e12	1.19372
$206$	−1.12201e13	−2.10730
$207$	−2.91268e11	−0.0532667
$208$	5.44306e11	0.0969382
$209$	2.07749e13	3.60358
$210$	1.56540e12	0.264496
$211$	8.87852e11	0.146146	0.0730730	−	0.997327i	$-0.476719\pi$
$211$	8.87852e11	0.146146	0.0730730	+	0.997327i	$0.476719\pi$
$212$	1.70642e13	2.73678
$213$	−4.82608e12	−0.754235
$214$	1.50731e13	2.29576
$215$	−1.06959e13	−1.58784
$216$	−6.01938e12	−0.871077
$217$	−5.40313e10	−0.00762284
$218$	−1.13138e12	−0.155632
$219$	−1.03322e12	−0.138595
$220$	−3.45482e13	−4.51960
$221$	−5.34785e12	−0.682373
$222$	−1.03632e13	−1.28989
$223$	−5.83669e12	−0.708744	−0.354372	−	0.935104i	$-0.615305\pi$
$223$	−5.83669e12	−0.708744	−0.354372	+	0.935104i	$0.615305\pi$
$224$	7.53168e11	0.0892334
$225$	2.61947e12	0.302837
$226$	1.33177e13	1.50256
$227$	−1.66716e11	−0.0183584	−0.00917919	−	0.999958i	$-0.502922\pi$
$227$	−1.66716e11	−0.0183584	−0.00917919	+	0.999958i	$0.502922\pi$
$228$	3.35102e13	3.60193
$229$	−1.43907e13	−1.51003	−0.755016	−	0.655706i	$-0.772371\pi$
$229$	−1.43907e13	−1.51003	−0.755016	+	0.655706i	$0.772371\pi$
$230$	3.80631e12	0.389943
$231$	2.21561e12	0.221630
$232$	9.21174e12	0.899825
$233$	2.86220e12	0.273050	0.136525	−	0.990637i	$-0.456407\pi$
$233$	2.86220e12	0.273050	0.136525	+	0.990637i	$0.456407\pi$
$234$	−3.96689e12	−0.369626
$235$	−2.02071e13	−1.83920
$236$	−2.24964e13	−2.00031
$237$	−1.20468e13	−1.04654
$238$	1.83526e12	0.155785
$239$	−7.81633e12	−0.648357	−0.324179	−	0.945996i	$-0.605088\pi$
$239$	−7.81633e12	−0.648357	−0.324179	+	0.945996i	$0.605088\pi$
$240$	−2.66558e12	−0.216088
$241$	−4.67513e12	−0.370425	−0.185212	−	0.982698i	$-0.559297\pi$
$241$	−4.67513e12	−0.370425	−0.185212	+	0.982698i	$0.559297\pi$
$242$	−5.69387e13	−4.40984
$243$	8.00064e12	0.605746
$244$	2.28407e12	0.169070
$245$	−1.91790e13	−1.38807
$246$	2.25531e13	1.59611
$247$	−1.95265e13	−1.35143
$248$	1.23922e12	0.0838813
$249$	−1.41459e13	−0.936558
$250$	1.19226e12	0.0772151
$251$	1.84902e13	1.17148	0.585742	−	0.810498i	$-0.300803\pi$
$251$	1.84902e13	1.17148	0.585742	+	0.810498i	$0.300803\pi$
$252$	8.52743e11	0.0528585
$253$	5.38733e12	0.326746
$254$	3.26420e13	1.93728
$255$	2.61896e13	1.52110
$256$	−2.12402e13	−1.20737
$257$	−4.77841e12	−0.265859	−0.132929	−	0.991126i	$-0.542438\pi$
$257$	−4.77841e12	−0.265859	−0.132929	+	0.991126i	$0.542438\pi$
$258$	−3.89830e13	−2.12308
$259$	−1.29810e12	−0.0692087
$260$	3.24721e13	1.69495
$261$	−4.98439e12	−0.254735
$262$	5.99779e12	0.300147
$263$	−1.86573e13	−0.914306	−0.457153	−	0.889388i	$-0.651131\pi$
$263$	−1.86573e13	−0.914306	−0.457153	+	0.889388i	$0.651131\pi$
$264$	−5.08157e13	−2.43880
$265$	4.86949e13	2.28892
$266$	6.70107e12	0.308528
$267$	4.35725e13	1.96517
$268$	−3.18730e13	−1.40826
$269$	2.66055e13	1.15168	0.575842	−	0.817561i	$-0.304674\pi$
$269$	2.66055e13	1.15168	0.575842	+	0.817561i	$0.304674\pi$
$270$	−4.25632e13	−1.80523
$271$	−1.66167e13	−0.690582	−0.345291	−	0.938496i	$-0.612220\pi$
$271$	−1.66167e13	−0.690582	−0.345291	+	0.938496i	$0.612220\pi$
$272$	−3.12511e12	−0.127273
$273$	−2.08247e12	−0.0831161
$274$	−4.44463e13	−1.73863
$275$	−4.84500e13	−1.85765
$276$	8.68983e12	0.326596
$277$	−1.09987e13	−0.405231	−0.202616	−	0.979258i	$-0.564944\pi$
$277$	−1.09987e13	−0.405231	−0.202616	+	0.979258i	$0.564944\pi$
$278$	6.43610e12	0.232475
$279$	−6.70532e11	−0.0237463
$280$	−4.49723e12	−0.156162
$281$	2.18346e13	0.743464	0.371732	−	0.928340i	$-0.378764\pi$
$281$	2.18346e13	0.743464	0.371732	+	0.928340i	$0.378764\pi$
$282$	−7.36480e13	−2.45918
$283$	2.73834e13	0.896730	0.448365	−	0.893851i	$-0.352007\pi$
$283$	2.73834e13	0.896730	0.448365	+	0.893851i	$0.352007\pi$
$284$	3.43558e13	1.10344
$285$	9.56256e13	3.01250
$286$	7.33720e13	2.26734
$287$	2.82502e12	0.0856391
$288$	9.34686e12	0.277976
$289$	−3.56747e12	−0.104093
$290$	6.51364e13	1.86481
$291$	−3.70080e13	−1.03964
$292$	7.35522e12	0.202764
$293$	−5.42833e13	−1.46857	−0.734284	−	0.678842i	$-0.762482\pi$
$293$	−5.42833e13	−1.46857	−0.734284	+	0.678842i	$0.762482\pi$
$294$	−6.99010e13	−1.85598
$295$	−6.41963e13	−1.67297
$296$	2.97724e13	0.761569
$297$	−6.02424e13	−1.51266
$298$	7.83159e13	1.93046
$299$	−5.06360e12	−0.122537
$300$	−7.81505e13	−1.85680
$301$	−4.88304e12	−0.113913
$302$	5.81225e12	0.133139
$303$	−2.83165e13	−0.636949
$304$	−1.14107e13	−0.252062
$305$	6.51789e12	0.141403
$306$	2.27757e13	0.485293
$307$	−2.66929e13	−0.558644	−0.279322	−	0.960197i	$-0.590110\pi$
$307$	−2.66929e13	−0.558644	−0.279322	+	0.960197i	$0.590110\pi$
$308$	−1.57724e13	−0.324242
$309$	−7.30970e13	−1.47614
$310$	8.76257e12	0.173837
$311$	9.02025e13	1.75807	0.879036	−	0.476756i	$-0.158187\pi$
$311$	9.02025e13	1.75807	0.879036	+	0.476756i	$0.158187\pi$
$312$	4.77621e13	0.914604
$313$	−2.21056e13	−0.415919	−0.207959	−	0.978137i	$-0.566682\pi$
$313$	−2.21056e13	−0.415919	−0.207959	+	0.978137i	$0.566682\pi$
$314$	1.43740e14	2.65744
$315$	2.43341e12	0.0442086
$316$	8.57583e13	1.53108
$317$	5.96625e13	1.04683	0.523414	−	0.852079i	$-0.324658\pi$
$317$	5.96625e13	1.04683	0.523414	+	0.852079i	$0.324658\pi$
$318$	1.77477e14	3.06050
$319$	9.21918e13	1.56258
$320$	−1.33463e14	−2.22350
$321$	9.81986e13	1.60815
$322$	1.73771e12	0.0279750
$323$	1.12111e14	1.77433
$324$	−1.30941e14	−2.03740
$325$	4.55386e13	0.696661
$326$	1.52810e14	2.29856
$327$	−7.37077e12	−0.109019
$328$	−6.47927e13	−0.942367
$329$	−9.22521e12	−0.131947
$330$	−3.59318e14	−5.05420
$331$	4.76333e13	0.658957	0.329478	−	0.944163i	$-0.393127\pi$
$331$	4.76333e13	0.658957	0.329478	+	0.944163i	$0.393127\pi$
$332$	1.00701e14	1.37018
$333$	−1.61096e13	−0.215596
$334$	−1.79190e14	−2.35889
$335$	−9.09535e13	−1.17780
$336$	−1.21693e12	−0.0155024
$337$	1.14824e14	1.43903	0.719513	−	0.694479i	$-0.244365\pi$
$337$	1.14824e14	1.43903	0.719513	+	0.694479i	$0.244365\pi$
$338$	6.37263e13	0.785737
$339$	8.67623e13	1.05253
$340$	−1.86437e14	−2.22535
$341$	1.24022e13	0.145664
$342$	8.31607e13	0.961113
$343$	−1.76012e13	−0.200182
$344$	1.11994e14	1.25350
$345$	2.47975e13	0.273151
$346$	−7.29682e13	−0.791071
$347$	−1.25030e13	−0.133414	−0.0667072	−	0.997773i	$-0.521249\pi$
$347$	−1.25030e13	−0.133414	−0.0667072	+	0.997773i	$0.521249\pi$
$348$	1.48707e14	1.56187
$349$	6.96825e13	0.720417	0.360209	−	0.932872i	$-0.382706\pi$
$349$	6.96825e13	0.720417	0.360209	+	0.932872i	$0.382706\pi$
$350$	−1.56278e13	−0.159047
$351$	5.66224e13	0.567283
$352$	−1.72881e14	−1.70515
$353$	1.99446e14	1.93671	0.968356	−	0.249574i	$-0.0802907\pi$
$353$	1.99446e14	1.93671	0.968356	+	0.249574i	$0.0802907\pi$
$354$	−2.33974e14	−2.23692
$355$	9.80384e13	0.922870
$356$	−3.10183e14	−2.87503
$357$	1.19564e13	0.109126
$358$	−2.21593e14	−1.99158
$359$	2.16924e13	0.191994	0.0959972	−	0.995382i	$-0.469396\pi$
$359$	2.16924e13	0.191994	0.0959972	+	0.995382i	$0.469396\pi$
$360$	−5.58109e13	−0.486469
$361$	2.92858e14	2.51401
$362$	−2.97027e14	−2.51130
$363$	−3.70947e14	−3.08905
$364$	1.48246e13	0.121598
$365$	2.09890e13	0.169583
$366$	2.37555e13	0.189068
$367$	6.85922e12	0.0537788	0.0268894	−	0.999638i	$-0.491440\pi$
$367$	6.85922e12	0.0537788	0.0268894	+	0.999638i	$0.491440\pi$
$368$	−2.95900e12	−0.0228551
$369$	3.50588e13	0.266779
$370$	2.10521e14	1.57829
$371$	2.22309e13	0.164210
$372$	2.00050e13	0.145597
$373$	−2.35819e14	−1.69115	−0.845573	−	0.533860i	$-0.820741\pi$
$373$	−2.35819e14	−1.69115	−0.845573	+	0.533860i	$0.820741\pi$
$374$	−4.21262e14	−2.97686
$375$	7.76740e12	0.0540884
$376$	2.11583e14	1.45194
$377$	−8.66520e13	−0.586005
$378$	−1.94315e13	−0.129510
$379$	4.15952e13	0.273230	0.136615	−	0.990624i	$-0.456378\pi$
$379$	4.15952e13	0.273230	0.136615	+	0.990624i	$0.456378\pi$
$380$	−6.80736e14	−4.40727
$381$	2.12658e14	1.35704
$382$	2.63181e14	1.65541
$383$	2.06017e14	1.27735	0.638674	−	0.769478i	$-0.279483\pi$
$383$	2.06017e14	1.27735	0.638674	+	0.769478i	$0.279483\pi$
$384$	−3.20108e14	−1.95648
$385$	−4.50086e13	−0.271182
$386$	−3.03521e14	−1.80285
$387$	−6.05989e13	−0.354858
$388$	2.63451e14	1.52099
$389$	−1.35093e14	−0.768973	−0.384486	−	0.923131i	$-0.625621\pi$
$389$	−1.35093e14	−0.768973	−0.384486	+	0.923131i	$0.625621\pi$
$390$	3.37727e14	1.89544
$391$	2.90724e13	0.160883
$392$	2.00818e14	1.09580
$393$	3.90746e13	0.210250
$394$	−1.59812e13	−0.0847968
$395$	2.44722e14	1.28053
$396$	−1.95737e14	−1.01006
$397$	−2.61812e14	−1.33242	−0.666212	−	0.745762i	$-0.732085\pi$
$397$	−2.61812e14	−1.33242	−0.666212	+	0.745762i	$0.732085\pi$
$398$	3.45782e14	1.73558
$399$	4.36564e13	0.216121
$400$	2.66113e13	0.129938
$401$	3.61906e14	1.74302	0.871508	−	0.490382i	$-0.163143\pi$
$401$	3.61906e14	1.74302	0.871508	+	0.490382i	$0.163143\pi$
$402$	−3.31495e14	−1.57483
$403$	−1.16570e13	−0.0546271
$404$	2.01578e14	0.931851
$405$	−3.73655e14	−1.70400
$406$	2.97370e13	0.133784
$407$	2.97964e14	1.32250
$408$	−2.74224e14	−1.20081
$409$	3.45776e14	1.49389	0.746943	−	0.664889i	$-0.231521\pi$
$409$	3.45776e14	1.49389	0.746943	+	0.664889i	$0.231521\pi$
$410$	−4.58151e14	−1.95298
$411$	−2.89561e14	−1.21789
$412$	5.20360e14	2.15958
$413$	−2.93078e13	−0.120021
$414$	2.15651e13	0.0871466
$415$	2.87364e14	1.14596
$416$	1.62492e14	0.639468
$417$	4.19302e13	0.162846
$418$	−1.53815e15	−5.89561
$419$	2.72543e14	1.03100	0.515498	−	0.856891i	$-0.327607\pi$
$419$	2.72543e14	1.03100	0.515498	+	0.856891i	$0.327607\pi$
$420$	−7.25995e13	−0.271058
$421$	1.48387e14	0.546821	0.273410	−	0.961897i	$-0.411848\pi$
$421$	1.48387e14	0.546821	0.273410	+	0.961897i	$0.411848\pi$
$422$	−6.57355e13	−0.239101
$423$	−1.14486e14	−0.411035
$424$	−5.09872e14	−1.80696
$425$	−2.61458e14	−0.914666
$426$	3.57317e14	1.23396
$427$	2.97564e12	0.0101444
$428$	−6.99053e14	−2.35272
$429$	4.78007e14	1.58825
$430$	7.91912e14	2.59777
$431$	2.61289e14	0.846245	0.423122	−	0.906073i	$-0.360934\pi$
$431$	2.61289e14	0.846245	0.423122	+	0.906073i	$0.360934\pi$
$432$	3.30883e13	0.105807
$433$	−4.20304e14	−1.32703	−0.663514	−	0.748164i	$-0.730936\pi$
$433$	−4.20304e14	−1.32703	−0.663514	+	0.748164i	$0.730936\pi$
$434$	4.00041e12	0.0124713
$435$	4.24353e14	1.30628
$436$	5.24708e13	0.159493
$437$	1.06152e14	0.318625
$438$	7.64980e13	0.226748
$439$	−1.99630e14	−0.584348	−0.292174	−	0.956365i	$-0.594379\pi$
$439$	−1.99630e14	−0.584348	−0.292174	+	0.956365i	$0.594379\pi$
$440$	1.03228e15	2.98407
$441$	−1.08661e14	−0.310214
$442$	3.95948e14	1.11639
$443$	−1.66596e14	−0.463920	−0.231960	−	0.972725i	$-0.574514\pi$
$443$	−1.66596e14	−0.463920	−0.231960	+	0.972725i	$0.574514\pi$
$444$	4.80621e14	1.32189
$445$	−8.85145e14	−2.40455
$446$	4.32141e14	1.15954
$447$	5.10216e14	1.35227
$448$	−6.09306e13	−0.159517
$449$	5.38002e14	1.39133	0.695663	−	0.718368i	$-0.255111\pi$
$449$	5.38002e14	1.39133	0.695663	+	0.718368i	$0.255111\pi$
$450$	−1.93942e14	−0.495455
$451$	−6.48451e14	−1.63646
$452$	−6.17641e14	−1.53984
$453$	3.78658e13	0.0932626
$454$	1.23434e13	0.0300351
$455$	4.23040e13	0.101699
$456$	−1.00127e15	−2.37818
$457$	−2.94852e14	−0.691935	−0.345968	−	0.938246i	$-0.612449\pi$
$457$	−2.94852e14	−0.691935	−0.345968	+	0.938246i	$0.612449\pi$
$458$	1.06547e15	2.47048
$459$	−3.25095e14	−0.744802
$460$	−1.76528e14	−0.399618
$461$	7.90356e14	1.76794	0.883970	−	0.467543i	$-0.154861\pi$
$461$	7.90356e14	1.76794	0.883970	+	0.467543i	$0.154861\pi$
$462$	−1.64041e14	−0.362595
$463$	−2.53278e14	−0.553224	−0.276612	−	0.960982i	$-0.589212\pi$
$463$	−2.53278e14	−0.553224	−0.276612	+	0.960982i	$0.589212\pi$
$464$	−5.06366e13	−0.109299
$465$	5.70867e13	0.121771
$466$	−2.11914e14	−0.446721
$467$	6.89350e14	1.43614	0.718071	−	0.695970i	$-0.245025\pi$
$467$	6.89350e14	1.43614	0.718071	+	0.695970i	$0.245025\pi$
$468$	1.83975e14	0.378797
$469$	−4.15234e13	−0.0844972
$470$	1.49611e15	3.00901
$471$	9.36442e14	1.86151
$472$	6.72183e14	1.32071
$473$	1.12084e15	2.17675
$474$	8.91930e14	1.71218
$475$	−9.54658e14	−1.81148
$476$	−8.51150e13	−0.159650
$477$	2.75887e14	0.511540
$478$	5.78712e14	1.06074
$479$	−3.46370e14	−0.627618	−0.313809	−	0.949486i	$-0.601605\pi$
$479$	−3.46370e14	−0.627618	−0.313809	+	0.949486i	$0.601605\pi$
$480$	−7.95758e14	−1.42546
$481$	−2.80060e14	−0.495967
$482$	3.46141e14	0.606031
$483$	1.13209e13	0.0195962
$484$	2.64068e15	4.51925
$485$	7.51791e14	1.27209
$486$	−5.92358e14	−0.991025
$487$	3.23381e14	0.534940	0.267470	−	0.963566i	$-0.413812\pi$
$487$	3.23381e14	0.534940	0.267470	+	0.963566i	$0.413812\pi$
$488$	−6.82471e13	−0.111629
$489$	9.95535e14	1.61012
$490$	1.41999e15	2.27094
$491$	−1.05882e15	−1.67445	−0.837226	−	0.546858i	$-0.815824\pi$
$491$	−1.05882e15	−1.67445	−0.837226	+	0.546858i	$0.815824\pi$
$492$	−1.04596e15	−1.63571
$493$	4.97508e14	0.769382
$494$	1.44572e15	2.21099
$495$	−5.58559e14	−0.844775
$496$	−6.81196e12	−0.0101888
$497$	4.47579e13	0.0662079
$498$	1.04735e15	1.53225
$499$	−7.73072e14	−1.11858	−0.559290	−	0.828972i	$-0.688926\pi$
$499$	−7.73072e14	−1.11858	−0.559290	+	0.828972i	$0.688926\pi$
$500$	−5.52943e13	−0.0791308
$501$	−1.16739e15	−1.65238
$502$	−1.36899e15	−1.91660
$503$	−2.14334e14	−0.296802	−0.148401	−	0.988927i	$-0.547413\pi$
$503$	−2.14334e14	−0.296802	−0.148401	+	0.988927i	$0.547413\pi$
$504$	−2.54796e13	−0.0348999
$505$	5.75229e14	0.779360
$506$	−3.98871e14	−0.534570
$507$	4.15167e14	0.550400
$508$	−1.51386e15	−1.98534
$509$	−4.98275e14	−0.646430	−0.323215	−	0.946326i	$-0.604764\pi$
$509$	−4.98275e14	−0.646430	−0.323215	+	0.946326i	$0.604764\pi$
$510$	−1.93904e15	−2.48858
$511$	9.58222e12	0.0121661
$512$	2.13460e14	0.268122
$513$	−1.18702e15	−1.47506
$514$	3.53788e14	0.434956
$515$	1.48491e15	1.80618
$516$	1.80794e15	2.17576
$517$	2.11754e15	2.52135
$518$	9.61101e13	0.113228
$519$	−4.75376e14	−0.554137
$520$	−9.70254e14	−1.11909
$521$	−7.15733e14	−0.816852	−0.408426	−	0.912791i	$-0.633922\pi$
$521$	−7.15733e14	−0.816852	−0.408426	+	0.912791i	$0.633922\pi$
$522$	3.69038e14	0.416758
$523$	9.59715e14	1.07247	0.536233	−	0.844070i	$-0.319847\pi$
$523$	9.59715e14	1.07247	0.536233	+	0.844070i	$0.319847\pi$
$524$	−2.78163e14	−0.307594
$525$	−1.01813e14	−0.111410
$526$	1.38136e15	1.49584
$527$	6.69280e13	0.0717216
$528$	2.79332e14	0.296233
$529$	−9.25283e14	−0.971110
$530$	−3.60531e15	−3.74477
$531$	−3.63712e14	−0.373885
$532$	−3.10779e14	−0.316183
$533$	6.09485e14	0.613710
$534$	−3.22606e15	−3.21510
$535$	−1.99484e15	−1.96771
$536$	9.52351e14	0.929802
$537$	−1.44364e15	−1.39508
$538$	−1.96984e15	−1.88420
$539$	2.00980e15	1.90290
$540$	1.97398e15	1.85002
$541$	−4.19484e14	−0.389162	−0.194581	−	0.980886i	$-0.562335\pi$
$541$	−4.19484e14	−0.389162	−0.194581	+	0.980886i	$0.562335\pi$
$542$	1.23028e15	1.12982
$543$	−1.93508e15	−1.75914
$544$	−9.32941e14	−0.839576
$545$	1.49732e14	0.133393
$546$	1.54184e14	0.135981
$547$	3.93617e14	0.343671	0.171836	−	0.985126i	$-0.445030\pi$
$547$	3.93617e14	0.343671	0.171836	+	0.985126i	$0.445030\pi$
$548$	2.06131e15	1.78177
$549$	3.69279e13	0.0316014
$550$	3.58718e15	3.03919
$551$	1.81655e15	1.52375
$552$	−2.59648e14	−0.215636
$553$	1.11724e14	0.0918667
$554$	8.14331e14	0.662975
$555$	1.37151e15	1.10557
$556$	−2.98491e14	−0.238243
$557$	1.06361e15	0.840579	0.420289	−	0.907390i	$-0.361929\pi$
$557$	1.06361e15	0.840579	0.420289	+	0.907390i	$0.361929\pi$
$558$	4.96454e13	0.0388500
$559$	−1.05349e15	−0.816331
$560$	2.47211e13	0.0189685
$561$	−2.74445e15	−2.08526
$562$	−1.61661e15	−1.21634
$563$	−1.29669e15	−0.966143	−0.483071	−	0.875581i	$-0.660479\pi$
$563$	−1.29669e15	−0.966143	−0.483071	+	0.875581i	$0.660479\pi$
$564$	3.41562e15	2.52020
$565$	−1.76252e15	−1.28785
$566$	−2.02743e15	−1.46709
$567$	−1.70586e14	−0.122247
$568$	−1.02653e15	−0.728548
$569$	1.86023e15	1.30753	0.653763	−	0.756700i	$-0.273189\pi$
$569$	1.86023e15	1.30753	0.653763	+	0.756700i	$0.273189\pi$
$570$	−7.08000e15	−4.92858
$571$	4.22754e14	0.291467	0.145733	−	0.989324i	$-0.453446\pi$
$571$	4.22754e14	0.291467	0.145733	+	0.989324i	$0.453446\pi$
$572$	−3.40282e15	−2.32360
$573$	1.71458e15	1.15960
$574$	−2.09161e14	−0.140109
$575$	−2.47561e14	−0.164251
$576$	−7.56152e14	−0.496919
$577$	2.18314e15	1.42107	0.710534	−	0.703663i	$-0.248453\pi$
$577$	2.18314e15	1.42107	0.710534	+	0.703663i	$0.248453\pi$
$578$	2.64131e14	0.170301
$579$	−1.97739e15	−1.26287
$580$	−3.02087e15	−1.91108
$581$	1.31192e14	0.0822124
$582$	2.74003e15	1.70090
$583$	−5.10283e15	−3.13787
$584$	−2.19771e14	−0.133875
$585$	5.24995e14	0.316810
$586$	4.01907e15	2.40264
$587$	−2.13382e15	−1.26371	−0.631856	−	0.775085i	$-0.717707\pi$
$587$	−2.13382e15	−1.26371	−0.631856	+	0.775085i	$0.717707\pi$
$588$	3.24184e15	1.90203
$589$	2.44374e14	0.142043
$590$	4.75302e15	2.73706
$591$	−1.04115e14	−0.0593993
$592$	−1.63658e14	−0.0925054
$593$	−1.12358e15	−0.629220	−0.314610	−	0.949221i	$-0.601874\pi$
$593$	−1.12358e15	−0.629220	−0.314610	+	0.949221i	$0.601874\pi$
$594$	4.46028e15	2.47478
$595$	−2.42886e14	−0.133524
$596$	−3.63211e15	−1.97835
$597$	2.25271e15	1.21576
$598$	3.74903e14	0.200476
$599$	1.38908e15	0.736001	0.368001	−	0.929826i	$-0.380042\pi$
$599$	1.38908e15	0.736001	0.368001	+	0.929826i	$0.380042\pi$
$600$	2.33510e15	1.22595
$601$	−2.56065e15	−1.33211	−0.666056	−	0.745902i	$-0.732019\pi$
$601$	−2.56065e15	−1.33211	−0.666056	+	0.745902i	$0.732019\pi$
$602$	3.61535e14	0.186367
$603$	−5.15308e14	−0.263222
$604$	−2.69558e14	−0.136442
$605$	7.53552e15	3.77971
$606$	2.09652e15	1.04208
$607$	−2.36783e15	−1.16630	−0.583152	−	0.812363i	$-0.698181\pi$
$607$	−2.36783e15	−1.16630	−0.583152	+	0.812363i	$0.698181\pi$
$608$	−3.40644e15	−1.66276
$609$	1.93732e14	0.0937142
$610$	−4.82577e14	−0.231341
$611$	−1.99029e15	−0.945563
$612$	−1.05628e15	−0.497334
$613$	−9.89216e14	−0.461592	−0.230796	−	0.973002i	$-0.574133\pi$
$613$	−9.89216e14	−0.461592	−0.230796	+	0.973002i	$0.574133\pi$
$614$	1.97631e15	0.913965
$615$	−2.98478e15	−1.36804
$616$	4.71273e14	0.214081
$617$	−5.76537e14	−0.259572	−0.129786	−	0.991542i	$-0.541429\pi$
$617$	−5.76537e14	−0.259572	−0.129786	+	0.991542i	$0.541429\pi$
$618$	5.41201e15	2.41503
$619$	2.36436e15	1.04572	0.522860	−	0.852419i	$-0.324865\pi$
$619$	2.36436e15	1.04572	0.522860	+	0.852419i	$0.324865\pi$
$620$	−4.06387e14	−0.178150
$621$	−3.07816e14	−0.133748
$622$	−6.67849e15	−2.87628
$623$	−4.04099e14	−0.172506
$624$	−2.62547e14	−0.111094
$625$	−2.46173e15	−1.03252
$626$	1.63667e15	0.680461
$627$	−1.00208e16	−4.12982
$628$	−6.66631e15	−2.72338
$629$	1.60795e15	0.651169
$630$	−1.80167e14	−0.0723271
$631$	1.78024e15	0.708461	0.354231	−	0.935158i	$-0.384743\pi$
$631$	1.78024e15	0.708461	0.354231	+	0.935158i	$0.384743\pi$
$632$	−2.56242e15	−1.01090
$633$	−4.28256e14	−0.167488
$634$	−4.41734e15	−1.71265
$635$	−4.31999e15	−1.66045
$636$	−8.23094e15	−3.13643
$637$	−1.88903e15	−0.713629
$638$	−6.82577e15	−2.55645
$639$	5.55449e14	0.206248
$640$	6.50277e15	2.39391
$641$	−2.29926e15	−0.839208	−0.419604	−	0.907707i	$-0.637831\pi$
$641$	−2.29926e15	−0.839208	−0.419604	+	0.907707i	$0.637831\pi$
$642$	−7.27051e15	−2.63101
$643$	−8.41066e14	−0.301766	−0.150883	−	0.988552i	$-0.548212\pi$
$643$	−8.41066e14	−0.301766	−0.150883	+	0.988552i	$0.548212\pi$
$644$	−8.05910e13	−0.0286691
$645$	5.15918e15	1.81971
$646$	−8.30054e15	−2.90287
$647$	2.82359e15	0.979103	0.489552	−	0.871974i	$-0.337160\pi$
$647$	2.82359e15	0.979103	0.489552	+	0.871974i	$0.337160\pi$
$648$	3.91245e15	1.34520
$649$	6.72726e15	2.29347
$650$	−3.37162e15	−1.13977
$651$	2.60620e13	0.00873601
$652$	−7.08699e15	−2.35559
$653$	8.53212e13	0.0281212	0.0140606	−	0.999901i	$-0.495524\pi$
$653$	8.53212e13	0.0281212	0.0140606	+	0.999901i	$0.495524\pi$
$654$	5.45723e14	0.178359
$655$	−7.93774e14	−0.257258
$656$	3.56163e14	0.114466
$657$	1.18916e14	0.0378993
$658$	6.83024e14	0.215871
$659$	1.01213e15	0.317225	0.158613	−	0.987341i	$-0.449298\pi$
$659$	1.01213e15	0.317225	0.158613	+	0.987341i	$0.449298\pi$
$660$	1.66643e16	5.17960
$661$	4.46924e15	1.37761	0.688804	−	0.724947i	$-0.258136\pi$
$661$	4.46924e15	1.37761	0.688804	+	0.724947i	$0.258136\pi$
$662$	−3.52671e15	−1.07808
$663$	2.57954e15	0.782020
$664$	−3.00892e15	−0.904661
$665$	−8.86848e14	−0.264442
$666$	1.19273e15	0.352724
$667$	4.71065e14	0.138162
$668$	8.31040e15	2.41742
$669$	2.81533e15	0.812242
$670$	6.73409e15	1.92694
$671$	−6.83022e14	−0.193848
$672$	−3.63291e14	−0.102264
$673$	−5.78074e15	−1.61399	−0.806995	−	0.590559i	$-0.798907\pi$
$673$	−5.78074e15	−1.61399	−0.806995	+	0.590559i	$0.798907\pi$
$674$	−8.50144e15	−2.35431
$675$	2.76829e15	0.760397
$676$	−2.95548e15	−0.805231
$677$	−2.87753e15	−0.777646	−0.388823	−	0.921312i	$-0.627118\pi$
$677$	−2.87753e15	−0.777646	−0.388823	+	0.921312i	$0.627118\pi$
$678$	−6.42378e15	−1.72198
$679$	3.43218e14	0.0912613
$680$	5.57067e15	1.46929
$681$	8.04154e13	0.0210392
$682$	−9.18247e14	−0.238312
$683$	2.25550e15	0.580669	0.290335	−	0.956925i	$-0.406233\pi$
$683$	2.25550e15	0.580669	0.290335	+	0.956925i	$0.406233\pi$
$684$	−3.85680e15	−0.984959
$685$	5.88222e15	1.49019
$686$	1.30317e15	0.327506
$687$	6.94136e15	1.73054
$688$	−6.15627e14	−0.152258
$689$	4.79620e15	1.17677
$690$	−1.83598e15	−0.446887
$691$	−2.77386e15	−0.669817	−0.334908	−	0.942251i	$-0.608705\pi$
$691$	−2.77386e15	−0.669817	−0.334908	+	0.942251i	$0.608705\pi$
$692$	3.38409e15	0.810697
$693$	−2.55002e14	−0.0606052
$694$	9.25708e14	0.218272
$695$	−8.51782e14	−0.199256
$696$	−4.44329e15	−1.03123
$697$	−3.49933e15	−0.805758
$698$	−5.15921e15	−1.17863
$699$	−1.38058e15	−0.312923
$700$	7.24781e14	0.162993
$701$	−3.43243e15	−0.765865	−0.382932	−	0.923776i	$-0.625086\pi$
$701$	−3.43243e15	−0.765865	−0.382932	+	0.923776i	$0.625086\pi$
$702$	−4.19226e15	−0.928098
$703$	5.87108e15	1.28963
$704$	1.39859e16	3.04818
$705$	9.74689e15	2.10778
$706$	−1.47668e16	−3.16854
$707$	2.62612e14	0.0559123
$708$	1.08512e16	2.29242
$709$	4.64906e15	0.974564	0.487282	−	0.873245i	$-0.337988\pi$
$709$	4.64906e15	0.974564	0.487282	+	0.873245i	$0.337988\pi$
$710$	−7.25865e15	−1.50985
$711$	1.38650e15	0.286179
$712$	9.26812e15	1.89824
$713$	6.33707e13	0.0128794
$714$	−8.85240e14	−0.178534
$715$	−9.71037e15	−1.94336
$716$	1.02769e16	2.04100
$717$	3.77021e15	0.743037
$718$	−1.60608e15	−0.314111
$719$	6.74580e15	1.30926	0.654628	−	0.755951i	$-0.272825\pi$
$719$	6.74580e15	1.30926	0.654628	+	0.755951i	$0.272825\pi$
$720$	3.06790e14	0.0590898
$721$	6.77914e14	0.129578
$722$	−2.16829e16	−4.11303
$723$	2.25505e15	0.424518
$724$	1.37754e16	2.57361
$725$	−4.23644e15	−0.785492
$726$	2.74644e16	5.05381
$727$	3.54614e15	0.647615	0.323808	−	0.946123i	$-0.395037\pi$
$727$	3.54614e15	0.647615	0.323808	+	0.946123i	$0.395037\pi$
$728$	−4.42954e14	−0.0802853
$729$	2.89611e15	0.520972
$730$	−1.55400e15	−0.277445
$731$	6.04858e15	1.07178
$732$	−1.10172e15	−0.193759
$733$	−3.38004e14	−0.0589998	−0.0294999	−	0.999565i	$-0.509391\pi$
$733$	−3.38004e14	−0.0589998	−0.0294999	+	0.999565i	$0.509391\pi$
$734$	−5.07848e14	−0.0879844
$735$	9.25099e15	1.59077
$736$	−8.83353e14	−0.150767
$737$	9.53120e15	1.61464
$738$	−2.59571e15	−0.436461
$739$	4.85789e15	0.810781	0.405390	−	0.914144i	$-0.367136\pi$
$739$	4.85789e15	0.810781	0.405390	+	0.914144i	$0.367136\pi$
$740$	−9.76347e15	−1.61745
$741$	9.41864e15	1.54877
$742$	−1.64595e15	−0.268655
$743$	−4.77142e15	−0.773052	−0.386526	−	0.922278i	$-0.626325\pi$
$743$	−4.77142e15	−0.773052	−0.386526	+	0.922278i	$0.626325\pi$
$744$	−5.97740e14	−0.0961305
$745$	−1.03647e16	−1.65461
$746$	1.74598e16	2.76678
$747$	1.62810e15	0.256104
$748$	1.95371e16	3.05072
$749$	−9.10711e14	−0.141166
$750$	−5.75089e14	−0.0884908
$751$	7.11112e15	1.08622	0.543110	−	0.839661i	$-0.317247\pi$
$751$	7.11112e15	1.08622	0.543110	+	0.839661i	$0.317247\pi$
$752$	−1.16306e15	−0.176362
$753$	−8.91876e15	−1.34256
$754$	6.41561e15	0.958728
$755$	−7.69218e14	−0.114115
$756$	9.01189e14	0.132723
$757$	1.15531e16	1.68917	0.844583	−	0.535425i	$-0.179848\pi$
$757$	1.15531e16	1.68917	0.844583	+	0.535425i	$0.179848\pi$
$758$	−3.07966e15	−0.447015
$759$	−2.59858e15	−0.374461
$760$	2.03401e16	2.90990
$761$	9.18464e15	1.30451	0.652254	−	0.758001i	$-0.273824\pi$
$761$	9.18464e15	1.30451	0.652254	+	0.758001i	$0.273824\pi$
$762$	−1.57449e16	−2.22018
$763$	6.83578e13	0.00956981
$764$	−1.22057e16	−1.69648
$765$	−3.01424e15	−0.415948
$766$	−1.52532e16	−2.08979
$767$	−6.32302e15	−0.860102
$768$	1.02452e16	1.38368
$769$	−1.17471e16	−1.57520	−0.787601	−	0.616186i	$-0.788677\pi$
$769$	−1.17471e16	−1.57520	−0.787601	+	0.616186i	$0.788677\pi$
$770$	3.33238e15	0.443665
$771$	2.30487e15	0.304682
$772$	1.40766e16	1.84757
$773$	−1.09462e16	−1.42651	−0.713254	−	0.700905i	$-0.752780\pi$
$773$	−1.09462e16	−1.42651	−0.713254	+	0.700905i	$0.752780\pi$
$774$	4.48667e15	0.580562
$775$	−5.69913e14	−0.0732233
$776$	−7.87181e15	−1.00423
$777$	6.26142e14	0.0793153
$778$	1.00021e16	1.25807
$779$	−1.27771e16	−1.59579
$780$	−1.56630e16	−1.94247
$781$	−1.02736e16	−1.26515
$782$	−2.15249e15	−0.263211
$783$	−5.26756e15	−0.639617
$784$	−1.10389e15	−0.133103
$785$	−1.90232e16	−2.27772
$786$	−2.89304e15	−0.343978
$787$	−6.23211e15	−0.735824	−0.367912	−	0.929861i	$-0.619927\pi$
$787$	−6.23211e15	−0.735824	−0.367912	+	0.929861i	$0.619927\pi$
$788$	7.41169e14	0.0869007
$789$	8.99935e15	1.04782
$790$	−1.81189e16	−2.09500
$791$	−8.04649e14	−0.0923923
$792$	5.84853e15	0.666896
$793$	6.41979e14	0.0726973
$794$	1.93843e16	2.17990
$795$	−2.34880e16	−2.62317
$796$	−1.60366e16	−1.77864
$797$	−4.59150e15	−0.505748	−0.252874	−	0.967499i	$-0.581376\pi$
$797$	−4.59150e15	−0.505748	−0.252874	+	0.967499i	$0.581376\pi$
$798$	−3.23226e15	−0.353583
$799$	1.14272e16	1.24146
$800$	7.94429e15	0.857156
$801$	−5.01490e15	−0.537382
$802$	−2.67951e16	−2.85165
$803$	−2.19948e15	−0.232480
$804$	1.53740e16	1.61390
$805$	−2.29976e14	−0.0239776
$806$	8.63069e14	0.0893723
$807$	−1.28332e16	−1.31987
$808$	−6.02307e15	−0.615256
$809$	1.23473e16	1.25272	0.626362	−	0.779532i	$-0.284543\pi$
$809$	1.23473e16	1.25272	0.626362	+	0.779532i	$0.284543\pi$
$810$	2.76650e16	2.78781
$811$	−3.10452e15	−0.310727	−0.155364	−	0.987857i	$-0.549655\pi$
$811$	−3.10452e15	−0.310727	−0.155364	+	0.987857i	$0.549655\pi$
$812$	−1.37913e15	−0.137103
$813$	8.01510e15	0.791427
$814$	−2.20609e16	−2.16366
$815$	−2.02236e16	−1.97011
$816$	1.50740e15	0.145859
$817$	2.20851e16	2.12265
$818$	−2.56009e16	−2.44406
$819$	2.39678e14	0.0227283
$820$	2.12479e16	2.00143
$821$	−6.46320e15	−0.604728	−0.302364	−	0.953193i	$-0.597776\pi$
$821$	−6.46320e15	−0.604728	−0.302364	+	0.953193i	$0.597776\pi$
$822$	2.14387e16	1.99253
$823$	−1.35323e16	−1.24931	−0.624657	−	0.780900i	$-0.714761\pi$
$823$	−1.35323e16	−1.24931	−0.624657	+	0.780900i	$0.714761\pi$
$824$	−1.55481e16	−1.42587
$825$	2.33699e16	2.12892
$826$	2.16992e15	0.196360
$827$	1.84767e15	0.166090	0.0830452	−	0.996546i	$-0.473535\pi$
$827$	1.84767e15	0.166090	0.0830452	+	0.996546i	$0.473535\pi$
$828$	−1.00014e15	−0.0893087
$829$	5.45124e14	0.0483554	0.0241777	−	0.999708i	$-0.492303\pi$
$829$	5.45124e14	0.0483554	0.0241777	+	0.999708i	$0.492303\pi$
$830$	−2.12761e16	−1.87483
$831$	5.30523e15	0.464407
$832$	−1.31455e16	−1.14313
$833$	1.08458e16	0.936944
$834$	−3.10446e15	−0.266424
$835$	2.37148e16	2.02182
$836$	7.13357e16	6.04188
$837$	−7.08627e14	−0.0596249
$838$	−2.01787e16	−1.68675
$839$	1.42958e16	1.18718	0.593592	−	0.804766i	$-0.297709\pi$
$839$	1.42958e16	1.18718	0.593592	+	0.804766i	$0.297709\pi$
$840$	2.16924e15	0.178966
$841$	−4.13931e15	−0.339274
$842$	−1.09864e16	−0.894622
$843$	−1.05319e16	−0.852033
$844$	3.04866e15	0.245033
$845$	−8.43382e15	−0.673461
$846$	8.47637e15	0.672470
$847$	3.44022e15	0.271161
$848$	2.80274e15	0.219486
$849$	−1.32084e16	−1.02768
$850$	1.93580e16	1.49643
$851$	1.52248e15	0.116934
$852$	−1.65715e16	−1.26458
$853$	2.96534e15	0.224830	0.112415	−	0.993661i	$-0.464141\pi$
$853$	2.96534e15	0.224830	0.112415	+	0.993661i	$0.464141\pi$
$854$	−2.20313e14	−0.0165967
$855$	−1.10058e16	−0.823777
$856$	2.08874e16	1.55338
$857$	2.19799e16	1.62417	0.812086	−	0.583538i	$-0.198332\pi$
$857$	2.19799e16	1.62417	0.812086	+	0.583538i	$0.198332\pi$
$858$	−3.53911e16	−2.59844
$859$	−1.35313e16	−0.987139	−0.493570	−	0.869706i	$-0.664308\pi$
$859$	−1.35313e16	−0.987139	−0.493570	+	0.869706i	$0.664308\pi$
$860$	−3.67270e16	−2.66222
$861$	−1.36265e15	−0.0981449
$862$	−1.93455e16	−1.38449
$863$	3.26489e15	0.232171	0.116086	−	0.993239i	$-0.462965\pi$
$863$	3.26489e15	0.232171	0.116086	+	0.993239i	$0.462965\pi$
$864$	9.87788e15	0.697972
$865$	9.65693e15	0.678032
$866$	3.11188e16	2.17107
$867$	1.72077e15	0.119294
$868$	−1.85530e14	−0.0127807
$869$	−2.56449e16	−1.75546
$870$	−3.14186e16	−2.13713
$871$	−8.95846e15	−0.605527
$872$	−1.56781e15	−0.105306
$873$	4.25936e15	0.284293
$874$	−7.85935e15	−0.521283
$875$	−7.20362e13	−0.00474795
$876$	−3.54780e15	−0.232373
$877$	2.02513e16	1.31812	0.659060	−	0.752090i	$-0.270954\pi$
$877$	2.02513e16	1.31812	0.659060	+	0.752090i	$0.270954\pi$
$878$	1.47804e16	0.956018
$879$	2.61836e16	1.68302
$880$	−5.67443e15	−0.362466
$881$	−1.49325e16	−0.947908	−0.473954	−	0.880550i	$-0.657174\pi$
$881$	−1.49325e16	−0.947908	−0.473954	+	0.880550i	$0.657174\pi$
$882$	8.04512e15	0.507522
$883$	1.68354e16	1.05545	0.527727	−	0.849414i	$-0.323045\pi$
$883$	1.68354e16	1.05545	0.527727	+	0.849414i	$0.323045\pi$
$884$	−1.83631e16	−1.14409
$885$	3.09652e16	1.91728
$886$	1.23345e16	0.758993
$887$	−1.97975e16	−1.21068	−0.605341	−	0.795966i	$-0.706963\pi$
$887$	−1.97975e16	−1.21068	−0.605341	+	0.795966i	$0.706963\pi$
$888$	−1.43607e16	−0.872781
$889$	−1.97222e15	−0.119123
$890$	6.55351e16	3.93395
$891$	3.91561e16	2.33599
$892$	−2.00417e16	−1.18830
$893$	4.17239e16	2.45868
$894$	−3.77757e16	−2.21236
$895$	2.93265e16	1.70700
$896$	2.96874e15	0.171742
$897$	2.44243e15	0.140431
$898$	−3.98330e16	−2.27627
$899$	1.08444e15	0.0615927
$900$	8.99459e15	0.507747
$901$	−2.75372e16	−1.54502
$902$	4.80105e16	2.67732
$903$	2.35534e15	0.130548
$904$	1.84548e16	1.01668
$905$	3.93099e16	2.15246
$906$	−2.80354e15	−0.152582
$907$	1.79967e16	0.973537	0.486769	−	0.873531i	$-0.338175\pi$
$907$	1.79967e16	0.973537	0.486769	+	0.873531i	$0.338175\pi$
$908$	−5.72459e14	−0.0307802
$909$	3.25903e15	0.174176
$910$	−3.13214e15	−0.166385
$911$	1.01330e16	0.535038	0.267519	−	0.963553i	$-0.413796\pi$
$911$	1.01330e16	0.535038	0.267519	+	0.963553i	$0.413796\pi$
$912$	5.50395e15	0.288870
$913$	−3.01135e16	−1.57098
$914$	2.18305e16	1.13203
$915$	−3.14391e15	−0.162052
$916$	−4.94139e16	−2.53177
$917$	−3.62385e14	−0.0184560
$918$	2.40697e16	1.21853
$919$	−2.52198e16	−1.26913	−0.634566	−	0.772868i	$-0.718821\pi$
$919$	−2.52198e16	−1.26913	−0.634566	+	0.772868i	$0.718821\pi$
$920$	5.27457e15	0.263848
$921$	1.28754e16	0.640223
$922$	−5.85170e16	−2.89243
$923$	9.65629e15	0.474461
$924$	7.60784e15	0.371591
$925$	−1.36922e16	−0.664804
$926$	1.87524e16	0.905098
$927$	8.41296e15	0.403655
$928$	−1.51166e16	−0.721007
$929$	2.48086e16	1.17630	0.588148	−	0.808754i	$-0.299857\pi$
$929$	2.48086e16	1.17630	0.588148	+	0.808754i	$0.299857\pi$
$930$	−4.22663e15	−0.199222
$931$	3.96011e16	1.85560
$932$	9.82805e15	0.457804
$933$	−4.35093e16	−2.01480
$934$	−5.10387e16	−2.34959
$935$	5.57517e16	2.55149
$936$	−5.49709e15	−0.250101
$937$	3.56854e15	0.161407	0.0807035	−	0.996738i	$-0.474283\pi$
$937$	3.56854e15	0.161407	0.0807035	+	0.996738i	$0.474283\pi$
$938$	3.07434e15	0.138241
$939$	1.06627e16	0.476656
$940$	−6.93859e16	−3.08367
$941$	3.76015e16	1.66136	0.830678	−	0.556753i	$-0.187953\pi$
$941$	3.76015e16	1.66136	0.830678	+	0.556753i	$0.187953\pi$
$942$	−6.93330e16	−3.04551
$943$	−3.31333e15	−0.144694
$944$	−3.69497e15	−0.160422
$945$	2.57165e15	0.111004
$946$	−8.29860e16	−3.56126
$947$	−1.85165e15	−0.0790015	−0.0395007	−	0.999220i	$-0.512577\pi$
$947$	−1.85165e15	−0.0790015	−0.0395007	+	0.999220i	$0.512577\pi$
$948$	−4.13656e16	−1.75466
$949$	2.06731e15	0.0871851
$950$	7.06817e16	2.96365
$951$	−2.87782e16	−1.19970
$952$	2.54320e15	0.105409
$953$	2.42250e16	0.998280	0.499140	−	0.866521i	$-0.333649\pi$
$953$	2.42250e16	0.998280	0.499140	+	0.866521i	$0.333649\pi$
$954$	−2.04263e16	−0.836901
$955$	−3.48305e16	−1.41886
$956$	−2.68393e16	−1.08706
$957$	−4.44688e16	−1.79077
$958$	2.56448e16	1.02681
$959$	2.68543e15	0.106908
$960$	6.43761e16	2.54820
$961$	−2.52626e16	−0.994258
$962$	2.07353e16	0.811422
$963$	−1.13020e16	−0.439754
$964$	−1.60532e16	−0.621066
$965$	4.01693e16	1.54523
$966$	−8.38187e14	−0.0320602
$967$	3.81780e16	1.45200	0.726002	−	0.687692i	$-0.241376\pi$
$967$	3.81780e16	1.45200	0.726002	+	0.687692i	$0.241376\pi$
$968$	−7.89024e16	−2.98384
$969$	−5.40767e16	−2.03343
$970$	−5.56617e16	−2.08119
$971$	−1.49006e16	−0.553986	−0.276993	−	0.960872i	$-0.589338\pi$
$971$	−1.49006e16	−0.553986	−0.276993	+	0.960872i	$0.589338\pi$
$972$	2.74722e16	1.01561
$973$	−3.88867e14	−0.0142949
$974$	−2.39427e16	−0.875183
$975$	−2.19656e16	−0.798394
$976$	3.75152e14	0.0135592
$977$	−2.27675e16	−0.818268	−0.409134	−	0.912474i	$-0.634169\pi$
$977$	−2.27675e16	−0.818268	−0.409134	+	0.912474i	$0.634169\pi$
$978$	−7.37082e16	−2.63422
$979$	9.27561e16	3.29638
$980$	−6.58557e16	−2.32729
$981$	8.48325e14	0.0298114
$982$	7.83935e16	2.73947
$983$	3.18572e16	1.10704	0.553520	−	0.832836i	$-0.313284\pi$
$983$	3.18572e16	1.10704	0.553520	+	0.832836i	$0.313284\pi$
$984$	3.12528e16	1.07998
$985$	2.11502e15	0.0726800
$986$	−3.68349e16	−1.25874
$987$	4.44979e15	0.151215
$988$	−6.70491e16	−2.26584
$989$	5.72708e15	0.192466
$990$	4.13551e16	1.38209
$991$	2.73785e16	0.909922	0.454961	−	0.890511i	$-0.349653\pi$
$991$	2.73785e16	0.909922	0.454961	+	0.890511i	$0.349653\pi$
$992$	−2.03358e15	−0.0672120
$993$	−2.29760e16	−0.755184
$994$	−3.31382e15	−0.108319
$995$	−4.57623e16	−1.48758
$996$	−4.85734e16	−1.57026
$997$	−2.28629e16	−0.735036	−0.367518	−	0.930016i	$-0.619792\pi$
$997$	−2.28629e16	−0.735036	−0.367518	+	0.930016i	$0.619792\pi$
$998$	5.72373e16	1.83004
$999$	−1.70248e16	−0.541342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.12.a.b.1.9	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.12.a.b.1.9	✓	72	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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	151.a (trivial)

\(f(q)\)	\(=\)	\(q-74.0388 q^{2} -482.351 q^{3} +3433.74 q^{4} +9798.61 q^{5} +35712.7 q^{6} +4473.40 q^{7} -102599. q^{8} +55515.2 q^{9} -725478. q^{10} -1.02682e6 q^{11} -1.65627e6 q^{12} +965114. q^{13} -331205. q^{14} -4.72637e6 q^{15} +563981. q^{16} -5.54116e6 q^{17} -4.11028e6 q^{18} -2.02324e7 q^{19} +3.36459e7 q^{20} -2.15775e6 q^{21} +7.60242e7 q^{22} -5.24663e6 q^{23} +4.94886e7 q^{24} +4.71847e7 q^{25} -7.14559e7 q^{26} +5.86692e7 q^{27} +1.53605e7 q^{28} -8.97842e7 q^{29} +3.49935e8 q^{30} -1.20783e7 q^{31} +1.68366e8 q^{32} +4.95285e8 q^{33} +4.10261e8 q^{34} +4.38331e7 q^{35} +1.90625e8 q^{36} -2.90183e8 q^{37} +1.49798e9 q^{38} -4.65523e8 q^{39} -1.00533e9 q^{40} +6.31516e8 q^{41} +1.59757e8 q^{42} -1.09157e9 q^{43} -3.52582e9 q^{44} +5.43972e8 q^{45} +3.88454e8 q^{46} -2.06224e9 q^{47} -2.72037e8 q^{48} -1.95732e9 q^{49} -3.49350e9 q^{50} +2.67278e9 q^{51} +3.31395e9 q^{52} +4.96957e9 q^{53} -4.34379e9 q^{54} -1.00614e10 q^{55} -4.58965e8 q^{56} +9.75910e9 q^{57} +6.64751e9 q^{58} -6.55157e9 q^{59} -1.62291e10 q^{60} +6.65185e8 q^{61} +8.94266e8 q^{62} +2.48342e8 q^{63} -1.36206e10 q^{64} +9.45678e9 q^{65} -3.66703e10 q^{66} -9.28229e9 q^{67} -1.90269e10 q^{68} +2.53072e9 q^{69} -3.24535e9 q^{70} +1.00053e10 q^{71} -5.69579e9 q^{72} +2.14204e9 q^{73} +2.14848e10 q^{74} -2.27596e10 q^{75} -6.94727e10 q^{76} -4.59336e9 q^{77} +3.44668e10 q^{78} +2.49752e10 q^{79} +5.52623e9 q^{80} -3.81335e10 q^{81} -4.67567e10 q^{82} +2.93270e10 q^{83} -7.40916e9 q^{84} -5.42957e10 q^{85} +8.08187e10 q^{86} +4.33075e10 q^{87} +1.05350e11 q^{88} -9.03337e10 q^{89} -4.02751e10 q^{90} +4.31734e9 q^{91} -1.80156e10 q^{92} +5.82600e9 q^{93} +1.52686e11 q^{94} -1.98249e11 q^{95} -8.12113e10 q^{96} +7.67242e10 q^{97} +1.44917e11 q^{98} -5.70039e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 96 q^{2} + 719 q^{3} + 76800 q^{4} + 32669 q^{5} + 62208 q^{6} + 48045 q^{7} + 332331 q^{8} + 5218827 q^{9} + 326849 q^{10} + 1825499 q^{11} + 2261853 q^{12} + 1312687 q^{13} + 8226356 q^{14} + 613376 q^{15}+ \cdots + 723642496724 q^{99}+O(q^{100}) \) 72 * q + 96 * q^2 + 719 * q^3 + 76800 * q^4 + 32669 * q^5 + 62208 * q^6 + 48045 * q^7 + 332331 * q^8 + 5218827 * q^9 + 326849 * q^10 + 1825499 * q^11 + 2261853 * q^12 + 1312687 * q^13 + 8226356 * q^14 + 613376 * q^15 + 84812296 * q^16 + 40931638 * q^17 + 13122715 * q^18 + 29375013 * q^19 + 84918219 * q^20 + 46372635 * q^21 + 58791436 * q^22 + 63373752 * q^23 + 208042693 * q^24 + 822098007 * q^25 + 432475855 * q^26 + 279380906 * q^27 + 199223712 * q^28 + 51987647 * q^29 + 32799172 * q^30 + 148980151 * q^31 + 840145879 * q^32 + 1349677131 * q^33 + 1022459895 * q^34 + 1271864483 * q^35 + 6069158248 * q^36 + 810903761 * q^37 - 2120563014 * q^38 - 2355029258 * q^39 - 3320389733 * q^40 + 5859782715 * q^41 + 6554723872 * q^42 + 3919513748 * q^43 + 14612470209 * q^44 + 10929057031 * q^45 + 15665409299 * q^46 + 3875062355 * q^47 + 29410144241 * q^48 + 37248222741 * q^49 + 16504097391 * q^50 + 12516522585 * q^51 + 567334931 * q^52 + 14672884898 * q^53 + 9414903427 * q^54 - 2982579193 * q^55 + 19920696363 * q^56 + 2875970526 * q^57 - 48084192512 * q^58 + 17257084239 * q^59 - 93407696365 * q^60 + 1422999895 * q^61 - 22829643062 * q^62 - 32319999932 * q^63 + 66529030631 * q^64 + 34355567339 * q^65 - 38790557894 * q^66 - 10815985001 * q^67 - 25606248436 * q^68 - 54498950277 * q^69 - 144393130061 * q^70 + 27421632954 * q^71 - 128042048589 * q^72 + 21697968943 * q^73 - 101715174833 * q^74 - 83292842880 * q^75 - 70562325614 * q^76 + 45959714583 * q^77 - 187146337248 * q^78 + 1132036389 * q^79 + 59865281599 * q^80 + 463311030968 * q^81 + 24896564876 * q^82 + 116660670941 * q^83 + 30259089579 * q^84 + 108598686344 * q^85 + 137406150133 * q^86 + 37420541026 * q^87 + 169139986803 * q^88 + 558676234986 * q^89 + 208795168870 * q^90 + 147594184277 * q^91 + 207339666618 * q^92 + 333952966703 * q^93 + 601254931179 * q^94 + 292495837940 * q^95 + 632965316684 * q^96 + 204273411870 * q^97 + 541340673550 * q^98 + 723642496724 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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