LMFDB - Embedded newform 109.16.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [109,16,Mod(1,109)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(109, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("109.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 109 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	109.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$155.535920559$
Analytic rank:	$1$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-353.821 q^{2} +2082.60 q^{3} +92421.0 q^{4} +261489. q^{5} -736868. q^{6} +2.67149e6 q^{7} -2.11065e7 q^{8} -1.00117e7 q^{9} +O(q^{10})$	\(q-353.821 q^{2} +2082.60 q^{3} +92421.0 q^{4} +261489. q^{5} -736868. q^{6} +2.67149e6 q^{7} -2.11065e7 q^{8} -1.00117e7 q^{9} -9.25202e7 q^{10} -6.32397e7 q^{11} +1.92476e8 q^{12} -4.91833e7 q^{13} -9.45229e8 q^{14} +5.44578e8 q^{15} +4.43945e9 q^{16} -1.96264e9 q^{17} +3.54233e9 q^{18} +3.16729e9 q^{19} +2.41671e10 q^{20} +5.56366e9 q^{21} +2.23755e10 q^{22} -1.56935e10 q^{23} -4.39564e10 q^{24} +3.78589e10 q^{25} +1.74020e10 q^{26} -5.07334e10 q^{27} +2.46902e11 q^{28} +1.08912e11 q^{29} -1.92683e11 q^{30} -1.13759e11 q^{31} -8.79153e11 q^{32} -1.31703e11 q^{33} +6.94421e11 q^{34} +6.98566e11 q^{35} -9.25289e11 q^{36} +1.05384e12 q^{37} -1.12065e12 q^{38} -1.02429e11 q^{39} -5.51911e12 q^{40} -1.28088e12 q^{41} -1.96854e12 q^{42} -1.43190e12 q^{43} -5.84468e12 q^{44} -2.61794e12 q^{45} +5.55267e12 q^{46} +1.10408e12 q^{47} +9.24562e12 q^{48} +2.38930e12 q^{49} -1.33953e13 q^{50} -4.08739e12 q^{51} -4.54557e12 q^{52} +1.05235e13 q^{53} +1.79505e13 q^{54} -1.65365e13 q^{55} -5.63857e13 q^{56} +6.59622e12 q^{57} -3.85353e13 q^{58} -3.23789e13 q^{59} +5.03305e13 q^{60} +1.10766e13 q^{61} +4.02502e13 q^{62} -2.67461e13 q^{63} +1.65590e14 q^{64} -1.28609e13 q^{65} +4.65993e13 q^{66} -3.30500e13 q^{67} -1.81389e14 q^{68} -3.26832e13 q^{69} -2.47167e14 q^{70} -5.69920e13 q^{71} +2.11311e14 q^{72} +1.45124e14 q^{73} -3.72869e14 q^{74} +7.88452e13 q^{75} +2.92724e14 q^{76} -1.68944e14 q^{77} +3.62416e13 q^{78} -1.58939e13 q^{79} +1.16087e15 q^{80} +3.79988e13 q^{81} +4.53201e14 q^{82} -2.06072e14 q^{83} +5.14199e14 q^{84} -5.13208e14 q^{85} +5.06635e14 q^{86} +2.26820e14 q^{87} +1.33477e15 q^{88} +2.20525e14 q^{89} +9.26282e14 q^{90} -1.31393e14 q^{91} -1.45040e15 q^{92} -2.36915e14 q^{93} -3.90645e14 q^{94} +8.28212e14 q^{95} -1.83093e15 q^{96} +2.86469e14 q^{97} -8.45384e14 q^{98} +6.33135e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 384 q^{2} - 9775 q^{3} + 1032192 q^{4} - 550760 q^{5} - 1290263 q^{6} - 3953576 q^{7} - 15117261 q^{8} + 286423921 q^{9}+O(q^{10}) $ 66 * q - 384 * q^2 - 9775 * q^3 + 1032192 * q^4 - 550760 * q^5 - 1290263 * q^6 - 3953576 * q^7 - 15117261 * q^8 + 286423921 * q^9	\( 66 q - 384 q^{2} - 9775 q^{3} + 1032192 q^{4} - 550760 q^{5} - 1290263 q^{6} - 3953576 q^{7} - 15117261 q^{8} + 286423921 q^{9} + 6483836 q^{10} - 418640282 q^{11} - 433698156 q^{12} - 251211569 q^{13} - 1592332821 q^{14} - 1067853378 q^{15} + 15344152328 q^{16} - 6669915144 q^{17} - 1130846704 q^{18} - 11923665296 q^{19} - 19811264155 q^{20} - 16836632576 q^{21} - 25066407453 q^{22} - 66240319423 q^{23} - 105321578171 q^{24} + 400217086854 q^{25} - 110366500241 q^{26} - 360361891108 q^{27} + 168304047263 q^{28} - 365318101624 q^{29} - 1696019730217 q^{30} - 581021125356 q^{31} - 945136776447 q^{32} - 80720646410 q^{33} + 509364050231 q^{34} - 1107221269012 q^{35} + 7914914022741 q^{36} + 885376534021 q^{37} - 245887726685 q^{38} - 14886955906 q^{39} + 4617883372968 q^{40} - 5158051651090 q^{41} - 922037781169 q^{42} - 3364734631553 q^{43} - 16009768816826 q^{44} - 13607122605862 q^{45} - 27613809885909 q^{46} - 15436064264767 q^{47} - 58305445438958 q^{48} + 22356385252652 q^{49} - 59201596698313 q^{50} - 31998753555286 q^{51} - 77785825258670 q^{52} - 35536412905909 q^{53} - 72434695159938 q^{54} - 48394117279296 q^{55} - 127390800143296 q^{56} - 41066353710544 q^{57} - 53471659238834 q^{58} - 182936201870706 q^{59} - 34432643772594 q^{60} - 69231508155360 q^{61} - 76728243090752 q^{62} - 989010429598 q^{63} + 206028006415075 q^{64} - 61149791847076 q^{65} + 209354337452312 q^{66} + 49820429470096 q^{67} - 183448493081939 q^{68} + 117351537759646 q^{69} + 488482013120139 q^{70} - 239459552004052 q^{71} + 601977723367037 q^{72} + 110709721135383 q^{73} + 234158962981804 q^{74} - 302768537362063 q^{75} + 418562925992027 q^{76} - 80154467168214 q^{77} + 13\!\cdots\!85 q^{78}+ \cdots - 35\!\cdots\!14 q^{99}+O(q^{100}) \) 66 * q - 384 * q^2 - 9775 * q^3 + 1032192 * q^4 - 550760 * q^5 - 1290263 * q^6 - 3953576 * q^7 - 15117261 * q^8 + 286423921 * q^9 + 6483836 * q^10 - 418640282 * q^11 - 433698156 * q^12 - 251211569 * q^13 - 1592332821 * q^14 - 1067853378 * q^15 + 15344152328 * q^16 - 6669915144 * q^17 - 1130846704 * q^18 - 11923665296 * q^19 - 19811264155 * q^20 - 16836632576 * q^21 - 25066407453 * q^22 - 66240319423 * q^23 - 105321578171 * q^24 + 400217086854 * q^25 - 110366500241 * q^26 - 360361891108 * q^27 + 168304047263 * q^28 - 365318101624 * q^29 - 1696019730217 * q^30 - 581021125356 * q^31 - 945136776447 * q^32 - 80720646410 * q^33 + 509364050231 * q^34 - 1107221269012 * q^35 + 7914914022741 * q^36 + 885376534021 * q^37 - 245887726685 * q^38 - 14886955906 * q^39 + 4617883372968 * q^40 - 5158051651090 * q^41 - 922037781169 * q^42 - 3364734631553 * q^43 - 16009768816826 * q^44 - 13607122605862 * q^45 - 27613809885909 * q^46 - 15436064264767 * q^47 - 58305445438958 * q^48 + 22356385252652 * q^49 - 59201596698313 * q^50 - 31998753555286 * q^51 - 77785825258670 * q^52 - 35536412905909 * q^53 - 72434695159938 * q^54 - 48394117279296 * q^55 - 127390800143296 * q^56 - 41066353710544 * q^57 - 53471659238834 * q^58 - 182936201870706 * q^59 - 34432643772594 * q^60 - 69231508155360 * q^61 - 76728243090752 * q^62 - 989010429598 * q^63 + 206028006415075 * q^64 - 61149791847076 * q^65 + 209354337452312 * q^66 + 49820429470096 * q^67 - 183448493081939 * q^68 + 117351537759646 * q^69 + 488482013120139 * q^70 - 239459552004052 * q^71 + 601977723367037 * q^72 + 110709721135383 * q^73 + 234158962981804 * q^74 - 302768537362063 * q^75 + 418562925992027 * q^76 - 80154467168214 * q^77 + 1323913017253085 * q^78 + 344264682091929 * q^79 - 32065698598171 * q^80 + 1988692250246122 * q^81 + 1270983624769250 * q^82 - 199730025767393 * q^83 + 617489751122564 * q^84 - 296293702359276 * q^85 + 537692257035328 * q^86 + 1240867015034202 * q^87 + 1947480665387314 * q^88 - 1639057373302857 * q^89 + 5020535661304190 * q^90 - 1546657035058086 * q^91 - 962008536423118 * q^92 - 614708405129510 * q^93 + 3330590764725661 * q^94 - 20584796236314 * q^95 - 1119373012440080 * q^96 + 1414025770405407 * q^97 + 2532116291022334 * q^98 - 3534034927854514 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−353.821	−1.95460	−0.977301	−	0.211857i	$-0.932049\pi$
$2$	−353.821	−1.95460	−0.977301	+	0.211857i	$0.932049\pi$
$3$	2082.60	0.549791	0.274895	−	0.961474i	$-0.411357\pi$
$3$	2082.60	0.549791	0.274895	+	0.961474i	$0.411357\pi$
$4$	92421.0	2.82047
$5$	261489.	1.49685	0.748425	−	0.663219i	$-0.230810\pi$
$5$	261489.	1.49685	0.748425	+	0.663219i	$0.230810\pi$
$6$	−736868.	−1.07462
$7$	2.67149e6	1.22608	0.613039	−	0.790052i	$-0.289947\pi$
$7$	2.67149e6	1.22608	0.613039	+	0.790052i	$0.289947\pi$
$8$	−2.11065e7	−3.55828
$9$	−1.00117e7	−0.697730
$10$	−9.25202e7	−2.92575
$11$	−6.32397e7	−0.978464	−0.489232	−	0.872154i	$-0.662723\pi$
$11$	−6.32397e7	−0.978464	−0.489232	+	0.872154i	$0.662723\pi$
$12$	1.92476e8	1.55067
$13$	−4.91833e7	−0.217391	−0.108696	−	0.994075i	$-0.534667\pi$
$13$	−4.91833e7	−0.217391	−0.108696	+	0.994075i	$0.534667\pi$
$14$	−9.45229e8	−2.39650
$15$	5.44578e8	0.822954
$16$	4.43945e9	4.13456
$17$	−1.96264e9	−1.16004	−0.580020	−	0.814602i	$-0.696955\pi$
$17$	−1.96264e9	−1.16004	−0.580020	+	0.814602i	$0.696955\pi$
$18$	3.54233e9	1.36378
$19$	3.16729e9	0.812898	0.406449	−	0.913673i	$-0.366767\pi$
$19$	3.16729e9	0.812898	0.406449	+	0.913673i	$0.366767\pi$
$20$	2.41671e10	4.22182
$21$	5.56366e9	0.674087
$22$	2.23755e10	1.91251
$23$	−1.56935e10	−0.961080	−0.480540	−	0.876973i	$-0.659559\pi$
$23$	−1.56935e10	−0.961080	−0.480540	+	0.876973i	$0.659559\pi$
$24$	−4.39564e10	−1.95631
$25$	3.78589e10	1.24056
$26$	1.74020e10	0.424913
$27$	−5.07334e10	−0.933396
$28$	2.46902e11	3.45811
$29$	1.08912e11	1.17244	0.586220	−	0.810152i	$-0.300616\pi$
$29$	1.08912e11	1.17244	0.586220	+	0.810152i	$0.300616\pi$
$30$	−1.92683e11	−1.60855
$31$	−1.13759e11	−0.742630	−0.371315	−	0.928507i	$-0.621093\pi$
$31$	−1.13759e11	−0.742630	−0.371315	+	0.928507i	$0.621093\pi$
$32$	−8.79153e11	−4.52313
$33$	−1.31703e11	−0.537950
$34$	6.94421e11	2.26742
$35$	6.98566e11	1.83526
$36$	−9.25289e11	−1.96792
$37$	1.05384e12	1.82499	0.912496	−	0.409086i	$-0.134153\pi$
$37$	1.05384e12	1.82499	0.912496	+	0.409086i	$0.134153\pi$
$38$	−1.12065e12	−1.58889
$39$	−1.02429e11	−0.119520
$40$	−5.51911e12	−5.32622
$41$	−1.28088e12	−1.02714	−0.513569	−	0.858048i	$-0.671677\pi$
$41$	−1.28088e12	−1.02714	−0.513569	+	0.858048i	$0.671677\pi$
$42$	−1.96854e12	−1.31757
$43$	−1.43190e12	−0.803338	−0.401669	−	0.915785i	$-0.631570\pi$
$43$	−1.43190e12	−0.803338	−0.401669	+	0.915785i	$0.631570\pi$
$44$	−5.84468e12	−2.75972
$45$	−2.61794e12	−1.04440
$46$	5.55267e12	1.87853
$47$	1.10408e12	0.317882	0.158941	−	0.987288i	$-0.449192\pi$
$47$	1.10408e12	0.317882	0.158941	+	0.987288i	$0.449192\pi$
$48$	9.24562e12	2.27314
$49$	2.38930e12	0.503269
$50$	−1.33953e13	−2.42480
$51$	−4.08739e12	−0.637779
$52$	−4.54557e12	−0.613145
$53$	1.05235e13	1.23053	0.615265	−	0.788321i	$-0.289049\pi$
$53$	1.05235e13	1.23053	0.615265	+	0.788321i	$0.289049\pi$
$54$	1.79505e13	1.82442
$55$	−1.65365e13	−1.46461
$56$	−5.63857e13	−4.36274
$57$	6.59622e12	0.446924
$58$	−3.85353e13	−2.29165
$59$	−3.23789e13	−1.69384	−0.846919	−	0.531722i	$-0.821545\pi$
$59$	−3.23789e13	−1.69384	−0.846919	+	0.531722i	$0.821545\pi$
$60$	5.03305e13	2.32111
$61$	1.10766e13	0.451265	0.225632	−	0.974213i	$-0.427555\pi$
$61$	1.10766e13	0.451265	0.225632	+	0.974213i	$0.427555\pi$
$62$	4.02502e13	1.45155
$63$	−2.67461e13	−0.855472
$64$	1.65590e14	4.70636
$65$	−1.28609e13	−0.325402
$66$	4.65993e13	1.05148
$67$	−3.30500e13	−0.666209	−0.333104	−	0.942890i	$-0.608096\pi$
$67$	−3.30500e13	−0.666209	−0.333104	+	0.942890i	$0.608096\pi$
$68$	−1.81389e14	−3.27185
$69$	−3.26832e13	−0.528393
$70$	−2.47167e14	−3.58720
$71$	−5.69920e13	−0.743663	−0.371832	−	0.928300i	$-0.621270\pi$
$71$	−5.69920e13	−0.743663	−0.371832	+	0.928300i	$0.621270\pi$
$72$	2.11311e14	2.48272
$73$	1.45124e14	1.53751	0.768757	−	0.639541i	$-0.220875\pi$
$73$	1.45124e14	1.53751	0.768757	+	0.639541i	$0.220875\pi$
$74$	−3.72869e14	−3.56713
$75$	7.88452e13	0.682049
$76$	2.92724e14	2.29275
$77$	−1.68944e14	−1.19967
$78$	3.62416e13	0.233613
$79$	−1.58939e13	−0.0931165	−0.0465582	−	0.998916i	$-0.514825\pi$
$79$	−1.58939e13	−0.0931165	−0.0465582	+	0.998916i	$0.514825\pi$
$80$	1.16087e15	6.18882
$81$	3.79988e13	0.184558
$82$	4.53201e14	2.00765
$83$	−2.06072e14	−0.833555	−0.416777	−	0.909009i	$-0.636841\pi$
$83$	−2.06072e14	−0.833555	−0.416777	+	0.909009i	$0.636841\pi$
$84$	5.14199e14	1.90124
$85$	−5.13208e14	−1.73641
$86$	5.06635e14	1.57021
$87$	2.26820e14	0.644596
$88$	1.33477e15	3.48165
$89$	2.20525e14	0.528486	0.264243	−	0.964456i	$-0.414878\pi$
$89$	2.20525e14	0.528486	0.264243	+	0.964456i	$0.414878\pi$
$90$	9.26282e14	2.04138
$91$	−1.31393e14	−0.266539
$92$	−1.45040e15	−2.71069
$93$	−2.36915e14	−0.408291
$94$	−3.90645e14	−0.621332
$95$	8.28212e14	1.21679
$96$	−1.83093e15	−2.48678
$97$	2.86469e14	0.359989	0.179995	−	0.983668i	$-0.442392\pi$
$97$	2.86469e14	0.359989	0.179995	+	0.983668i	$0.442392\pi$
$98$	−8.45384e14	−0.983691
$99$	6.33135e14	0.682704
$100$	3.49896e15	3.49896
$101$	2.28596e14	0.212157	0.106079	−	0.994358i	$-0.466170\pi$
$101$	2.28596e14	0.212157	0.106079	+	0.994358i	$0.466170\pi$
$102$	1.44620e15	1.24660
$103$	−7.32534e14	−0.586879	−0.293440	−	0.955978i	$-0.594800\pi$
$103$	−7.32534e14	−0.586879	−0.293440	+	0.955978i	$0.594800\pi$
$104$	1.03808e15	0.773540
$105$	1.45484e15	1.00901
$106$	−3.72344e15	−2.40519
$107$	−2.03489e15	−1.22507	−0.612536	−	0.790443i	$-0.709851\pi$
$107$	−2.03489e15	−1.22507	−0.612536	+	0.790443i	$0.709851\pi$
$108$	−4.68884e15	−2.63261
$109$	1.82804e14	0.0957826
$109$	1.82804e14	0.0957826
$110$	5.85095e15	2.86274
$111$	2.19473e15	1.00336
$112$	1.18600e16	5.06930
$113$	−3.24253e15	−1.29657	−0.648284	−	0.761399i	$-0.724513\pi$
$113$	−3.24253e15	−1.29657	−0.648284	+	0.761399i	$0.724513\pi$
$114$	−2.33388e15	−0.873558
$115$	−4.10367e15	−1.43859
$116$	1.00657e16	3.30682
$117$	4.92406e14	0.151680
$118$	1.14563e16	3.31078
$119$	−5.24317e15	−1.42230
$120$	−1.14941e16	−2.92831
$121$	−1.77987e14	−0.0426087
$122$	−3.91912e15	−0.882042
$123$	−2.66756e15	−0.564711
$124$	−1.05137e16	−2.09456
$125$	1.91969e15	0.360085
$126$	9.46331e15	1.67211
$127$	−9.52215e15	−1.58565	−0.792825	−	0.609450i	$-0.791390\pi$
$127$	−9.52215e15	−1.58565	−0.792825	+	0.609450i	$0.791390\pi$
$128$	−2.97812e16	−4.67593
$129$	−2.98208e15	−0.441668
$130$	4.55045e15	0.636032
$131$	9.75356e14	0.128715	0.0643574	−	0.997927i	$-0.479500\pi$
$131$	9.75356e14	0.128715	0.0643574	+	0.997927i	$0.479500\pi$
$132$	−1.21722e16	−1.51727
$133$	8.46139e15	0.996677
$134$	1.16938e16	1.30217
$135$	−1.32662e16	−1.39715
$136$	4.14243e16	4.12775
$137$	−2.53667e15	−0.239254	−0.119627	−	0.992819i	$-0.538170\pi$
$137$	−2.53667e15	−0.239254	−0.119627	+	0.992819i	$0.538170\pi$
$138$	1.15640e16	1.03280
$139$	−9.89390e15	−0.837060	−0.418530	−	0.908203i	$-0.637454\pi$
$139$	−9.89390e15	−0.837060	−0.418530	+	0.908203i	$0.637454\pi$
$140$	6.45622e16	5.17628
$141$	2.29936e15	0.174768
$142$	2.01649e16	1.45357
$143$	3.11033e15	0.212709
$144$	−4.44463e16	−2.88481
$145$	2.84793e16	1.75497
$146$	−5.13480e16	−3.00523
$147$	4.97597e15	0.276693
$148$	9.73968e16	5.14733
$149$	−2.03913e16	−1.02459	−0.512293	−	0.858811i	$-0.671204\pi$
$149$	−2.03913e16	−1.02459	−0.512293	+	0.858811i	$0.671204\pi$
$150$	−2.78971e16	−1.33313
$151$	1.31296e16	0.596930	0.298465	−	0.954421i	$-0.403525\pi$
$151$	1.31296e16	0.596930	0.298465	+	0.954421i	$0.403525\pi$
$152$	−6.68504e16	−2.89252
$153$	1.96493e16	0.809395
$154$	5.97760e16	2.34488
$155$	−2.97467e16	−1.11161
$156$	−9.46662e15	−0.337101
$157$	−1.49279e16	−0.506699	−0.253350	−	0.967375i	$-0.581532\pi$
$157$	−1.49279e16	−0.506699	−0.253350	+	0.967375i	$0.581532\pi$
$158$	5.62358e15	0.182006
$159$	2.19163e16	0.676534
$160$	−2.29889e17	−6.77046
$161$	−4.19249e16	−1.17836
$162$	−1.34448e16	−0.360737
$163$	−7.67567e16	−1.96657	−0.983285	−	0.182075i	$-0.941719\pi$
$163$	−7.67567e16	−1.96657	−0.983285	+	0.182075i	$0.941719\pi$
$164$	−1.18380e17	−2.89701
$165$	−3.44390e16	−0.805231
$166$	7.29127e16	1.62927
$167$	7.01088e16	1.49761	0.748805	−	0.662790i	$-0.230628\pi$
$167$	7.01088e16	1.49761	0.748805	+	0.662790i	$0.230628\pi$
$168$	−1.17429e17	−2.39859
$169$	−4.87669e16	−0.952741
$170$	1.81584e17	3.39398
$171$	−3.17099e16	−0.567184
$172$	−1.32337e17	−2.26579
$173$	9.96908e16	1.63422	0.817108	−	0.576485i	$-0.195576\pi$
$173$	9.96908e16	1.63422	0.817108	+	0.576485i	$0.195576\pi$
$174$	−8.02537e16	−1.25993
$175$	1.01140e17	1.52103
$176$	−2.80750e17	−4.04552
$177$	−6.74324e16	−0.931256
$178$	−7.80264e16	−1.03298
$179$	−2.94327e16	−0.373622	−0.186811	−	0.982396i	$-0.559815\pi$
$179$	−2.94327e16	−0.373622	−0.186811	+	0.982396i	$0.559815\pi$
$180$	−2.41953e17	−2.94569
$181$	−1.40713e17	−1.64340	−0.821701	−	0.569918i	$-0.806975\pi$
$181$	−1.40713e17	−1.64340	−0.821701	+	0.569918i	$0.806975\pi$
$182$	4.64894e16	0.520977
$183$	2.30681e16	0.248101
$184$	3.31233e17	3.41980
$185$	2.75567e17	2.73174
$186$	8.38253e16	0.798046
$187$	1.24117e17	1.13506
$188$	1.02040e17	0.896575
$189$	−1.35534e17	−1.14442
$190$	−2.93039e17	−2.37833
$191$	1.72969e17	1.34964	0.674819	−	0.737984i	$-0.264222\pi$
$191$	1.72969e17	1.34964	0.674819	+	0.737984i	$0.264222\pi$
$192$	3.44859e17	2.58751
$193$	−1.32973e17	−0.959586	−0.479793	−	0.877382i	$-0.659288\pi$
$193$	−1.32973e17	−0.959586	−0.479793	+	0.877382i	$0.659288\pi$
$194$	−1.01359e17	−0.703635
$195$	−2.67841e16	−0.178903
$196$	2.20822e17	1.41945
$197$	−3.88609e16	−0.240445	−0.120223	−	0.992747i	$-0.538361\pi$
$197$	−3.88609e16	−0.240445	−0.120223	+	0.992747i	$0.538361\pi$
$198$	−2.24016e17	−1.33441
$199$	−1.98507e17	−1.13862	−0.569308	−	0.822124i	$-0.692789\pi$
$199$	−1.98507e17	−1.13862	−0.569308	+	0.822124i	$0.692789\pi$
$200$	−7.99069e17	−4.41427
$201$	−6.88300e16	−0.366275
$202$	−8.08819e16	−0.414683
$203$	2.90957e17	1.43750
$204$	−3.77761e17	−1.79883
$205$	−3.34936e17	−1.53747
$206$	2.59186e17	1.14711
$207$	1.57118e17	0.670575
$208$	−2.18347e17	−0.898818
$209$	−2.00299e17	−0.795391
$210$	−5.14751e17	−1.97221
$211$	−7.24661e16	−0.267927	−0.133963	−	0.990986i	$-0.542770\pi$
$211$	−7.24661e16	−0.267927	−0.133963	+	0.990986i	$0.542770\pi$
$212$	9.72595e17	3.47067
$213$	−1.18692e17	−0.408859
$214$	7.19984e17	2.39453
$215$	−3.74425e17	−1.20248
$216$	1.07080e18	3.32129
$217$	−3.03906e17	−0.910523
$218$	−6.46798e16	−0.187217
$219$	3.02237e17	0.845311
$220$	−1.52832e18	−4.13089
$221$	9.65289e16	0.252183
$222$	−7.76540e17	−1.96117
$223$	3.80172e17	0.928310	0.464155	−	0.885754i	$-0.346358\pi$
$223$	3.80172e17	0.928310	0.464155	+	0.885754i	$0.346358\pi$
$224$	−2.34865e18	−5.54572
$225$	−3.79031e17	−0.865578
$226$	1.14727e18	2.53427
$227$	−4.14710e17	−0.886238	−0.443119	−	0.896463i	$-0.646128\pi$
$227$	−4.14710e17	−0.886238	−0.443119	+	0.896463i	$0.646128\pi$
$228$	6.09629e17	1.26053
$229$	8.29688e17	1.66015	0.830077	−	0.557648i	$-0.188296\pi$
$229$	8.29688e17	1.66015	0.830077	+	0.557648i	$0.188296\pi$
$230$	1.45196e18	2.81188
$231$	−3.51844e17	−0.659569
$232$	−2.29875e18	−4.17187
$233$	2.76758e17	0.486329	0.243165	−	0.969985i	$-0.421814\pi$
$233$	2.76758e17	0.486329	0.243165	+	0.969985i	$0.421814\pi$
$234$	−1.74224e17	−0.296475
$235$	2.88704e17	0.475822
$236$	−2.99249e18	−4.77741
$237$	−3.31006e16	−0.0511946
$238$	1.85514e18	2.78003
$239$	1.24776e18	1.81196	0.905980	−	0.423321i	$-0.139136\pi$
$239$	1.24776e18	1.81196	0.905980	+	0.423321i	$0.139136\pi$
$240$	2.41763e18	3.40256
$241$	−7.99963e17	−1.09129	−0.545647	−	0.838015i	$-0.683716\pi$
$241$	−7.99963e17	−1.09129	−0.545647	+	0.838015i	$0.683716\pi$
$242$	6.29755e16	0.0832830
$243$	8.07106e17	1.03486
$244$	1.02371e18	1.27278
$245$	6.24776e17	0.753319
$246$	9.43838e17	1.10378
$247$	−1.55778e17	−0.176717
$248$	2.40105e18	2.64249
$249$	−4.29167e17	−0.458281
$250$	−6.79225e17	−0.703823
$251$	5.70033e17	0.573254	0.286627	−	0.958042i	$-0.407466\pi$
$251$	5.70033e17	0.573254	0.286627	+	0.958042i	$0.407466\pi$
$252$	−2.47190e18	−2.41283
$253$	9.92449e17	0.940382
$254$	3.36913e18	3.09931
$255$	−1.06881e18	−0.954660
$256$	5.11114e18	4.43321
$257$	−4.72481e17	−0.398002	−0.199001	−	0.979999i	$-0.563770\pi$
$257$	−4.72481e17	−0.398002	−0.199001	+	0.979999i	$0.563770\pi$
$258$	1.05512e18	0.863285
$259$	2.81532e18	2.23758
$260$	−1.18862e18	−0.917786
$261$	−1.09039e18	−0.818046
$262$	−3.45101e17	−0.251586
$263$	−2.49264e18	−1.76601	−0.883003	−	0.469368i	$-0.844482\pi$
$263$	−2.49264e18	−1.76601	−0.883003	+	0.469368i	$0.844482\pi$
$264$	2.77979e18	1.91418
$265$	2.75179e18	1.84192
$266$	−2.99382e18	−1.94811
$267$	4.59267e17	0.290557
$268$	−3.05451e18	−1.87902
$269$	2.46282e18	1.47330	0.736649	−	0.676275i	$-0.236407\pi$
$269$	2.46282e18	1.47330	0.736649	+	0.676275i	$0.236407\pi$
$270$	4.69387e18	2.73088
$271$	1.97522e18	1.11775	0.558876	−	0.829251i	$-0.311233\pi$
$271$	1.97522e18	1.11775	0.558876	+	0.829251i	$0.311233\pi$
$272$	−8.71303e18	−4.79626
$273$	−2.73639e17	−0.146541
$274$	8.97526e17	0.467647
$275$	−2.39419e18	−1.21384
$276$	−3.02062e18	−1.49031
$277$	−3.55687e18	−1.70793	−0.853964	−	0.520333i	$-0.825808\pi$
$277$	−3.55687e18	−1.70793	−0.853964	+	0.520333i	$0.825808\pi$
$278$	3.50066e18	1.63612
$279$	1.13892e18	0.518156
$280$	−1.47443e19	−6.53037
$281$	−4.09430e18	−1.76556	−0.882779	−	0.469788i	$-0.844330\pi$
$281$	−4.09430e18	−1.76556	−0.882779	+	0.469788i	$0.844330\pi$
$282$	−8.13560e17	−0.341603
$283$	2.58631e18	1.05751	0.528753	−	0.848776i	$-0.322660\pi$
$283$	2.58631e18	1.05751	0.528753	+	0.848776i	$0.322660\pi$
$284$	−5.26726e18	−2.09748
$285$	1.72484e18	0.668978
$286$	−1.10050e18	−0.415762
$287$	−3.42185e18	−1.25935
$288$	8.80178e18	3.15593
$289$	9.89519e17	0.345693
$290$	−1.00766e19	−3.43026
$291$	5.96601e17	0.197919
$292$	1.34126e19	4.33651
$293$	−2.06592e18	−0.651037	−0.325518	−	0.945536i	$-0.605539\pi$
$293$	−2.06592e18	−0.651037	−0.325518	+	0.945536i	$0.605539\pi$
$294$	−1.76060e18	−0.540824
$295$	−8.46672e18	−2.53542
$296$	−2.22428e19	−6.49384
$297$	3.20837e18	0.913294
$298$	7.21488e18	2.00266
$299$	7.71855e17	0.208930
$300$	7.28695e18	1.92370
$301$	−3.82530e18	−0.984956
$302$	−4.64551e18	−1.16676
$303$	4.76075e17	0.116642
$304$	1.40610e19	3.36098
$305$	2.89640e18	0.675476
$306$	−6.95231e18	−1.58204
$307$	6.81865e17	0.151412	0.0757061	−	0.997130i	$-0.475879\pi$
$307$	6.81865e17	0.151412	0.0757061	+	0.997130i	$0.475879\pi$
$308$	−1.56140e19	−3.38364
$309$	−1.52558e18	−0.322661
$310$	1.05250e19	2.17275
$311$	−8.90066e18	−1.79357	−0.896787	−	0.442462i	$-0.854105\pi$
$311$	−8.90066e18	−1.79357	−0.896787	+	0.442462i	$0.854105\pi$
$312$	2.16192e18	0.425285
$313$	6.41278e18	1.23158	0.615792	−	0.787909i	$-0.288836\pi$
$313$	6.41278e18	1.23158	0.615792	+	0.787909i	$0.288836\pi$
$314$	5.28179e18	0.990395
$315$	−6.99381e18	−1.28051
$316$	−1.46893e18	−0.262632
$317$	−2.98527e18	−0.521242	−0.260621	−	0.965441i	$-0.583927\pi$
$317$	−2.98527e18	−0.521242	−0.260621	+	0.965441i	$0.583927\pi$
$318$	−7.75445e18	−1.32235
$319$	−6.88756e18	−1.14719
$320$	4.33001e19	7.04472
$321$	−4.23786e18	−0.673533
$322$	1.48339e19	2.30322
$323$	−6.21624e18	−0.942994
$324$	3.51189e18	0.520539
$325$	−1.86203e18	−0.269687
$326$	2.71581e19	3.84386
$327$	3.80708e17	0.0526604
$328$	2.70348e19	3.65485
$329$	2.94953e18	0.389748
$330$	1.21852e19	1.57391
$331$	−3.49453e18	−0.441244	−0.220622	−	0.975359i	$-0.570809\pi$
$331$	−3.49453e18	−0.441244	−0.220622	+	0.975359i	$0.570809\pi$
$332$	−1.90454e19	−2.35101
$333$	−1.05507e19	−1.27335
$334$	−2.48059e19	−2.92723
$335$	−8.64221e18	−0.997215
$336$	2.46996e19	2.78705
$337$	−1.11623e18	−0.123177	−0.0615886	−	0.998102i	$-0.519617\pi$
$337$	−1.11623e18	−0.123177	−0.0615886	+	0.998102i	$0.519617\pi$
$338$	1.72547e19	1.86223
$339$	−6.75290e18	−0.712841
$340$	−4.74312e19	−4.89748
$341$	7.19408e18	0.726637
$342$	1.12196e19	1.10862
$343$	−6.30007e18	−0.609031
$344$	3.02223e19	2.85851
$345$	−8.54631e18	−0.790925
$346$	−3.52727e19	−3.19424
$347$	4.41029e17	0.0390838	0.0195419	−	0.999809i	$-0.493779\pi$
$347$	4.41029e17	0.0390838	0.0195419	+	0.999809i	$0.493779\pi$
$348$	2.09630e19	1.81806
$349$	6.45557e18	0.547953	0.273977	−	0.961736i	$-0.411661\pi$
$349$	6.45557e18	0.547953	0.273977	+	0.961736i	$0.411661\pi$
$350$	−3.57854e19	−2.97300
$351$	2.49524e18	0.202912
$352$	5.55974e19	4.42572
$353$	−2.52671e19	−1.96899	−0.984497	−	0.175400i	$-0.943878\pi$
$353$	−2.52671e19	−1.96899	−0.984497	+	0.175400i	$0.943878\pi$
$354$	2.38590e19	1.82023
$355$	−1.49028e19	−1.11315
$356$	2.03812e19	1.49058
$357$	−1.09194e19	−0.781967
$358$	1.04139e19	0.730282
$359$	2.12610e19	1.46007	0.730036	−	0.683409i	$-0.239503\pi$
$359$	2.12610e19	1.46007	0.730036	+	0.683409i	$0.239503\pi$
$360$	5.52555e19	3.71627
$361$	−5.14939e18	−0.339197
$362$	4.97871e19	3.21220
$363$	−3.70677e17	−0.0234259
$364$	−1.21434e19	−0.751764
$365$	3.79485e19	2.30143
$366$	−8.16197e18	−0.484939
$367$	−9.10932e18	−0.530262	−0.265131	−	0.964212i	$-0.585415\pi$
$367$	−9.10932e18	−0.530262	−0.265131	+	0.964212i	$0.585415\pi$
$368$	−6.96703e19	−3.97365
$369$	1.28237e19	0.716665
$370$	−9.75013e19	−5.33946
$371$	2.81135e19	1.50873
$372$	−2.18959e19	−1.15157
$373$	3.23195e19	1.66590	0.832948	−	0.553352i	$-0.186651\pi$
$373$	3.23195e19	1.66590	0.832948	+	0.553352i	$0.186651\pi$
$374$	−4.39150e19	−2.21858
$375$	3.99795e18	0.197972
$376$	−2.33032e19	−1.13111
$377$	−5.35664e18	−0.254878
$378$	4.79547e19	2.23688
$379$	1.59509e19	0.729440	0.364720	−	0.931117i	$-0.381165\pi$
$379$	1.59509e19	0.729440	0.364720	+	0.931117i	$0.381165\pi$
$380$	7.65442e19	3.43191
$381$	−1.98309e19	−0.871775
$382$	−6.11999e19	−2.63800
$383$	−2.22292e18	−0.0939580	−0.0469790	−	0.998896i	$-0.514959\pi$
$383$	−2.22292e18	−0.0939580	−0.0469790	+	0.998896i	$0.514959\pi$
$384$	−6.20225e19	−2.57078
$385$	−4.41771e19	−1.79573
$386$	4.70486e19	1.87561
$387$	1.43357e19	0.560513
$388$	2.64757e19	1.01534
$389$	−2.41566e19	−0.908687	−0.454343	−	0.890827i	$-0.650126\pi$
$389$	−2.41566e19	−0.908687	−0.454343	+	0.890827i	$0.650126\pi$
$390$	9.47678e18	0.349684
$391$	3.08005e19	1.11489
$392$	−5.04297e19	−1.79078
$393$	2.03128e18	0.0707662
$394$	1.37498e19	0.469974
$395$	−4.15607e18	−0.139381
$396$	5.85150e19	1.92554
$397$	1.13356e19	0.366031	0.183015	−	0.983110i	$-0.441414\pi$
$397$	1.13356e19	0.366031	0.183015	+	0.983110i	$0.441414\pi$
$398$	7.02358e19	2.22554
$399$	1.76217e19	0.547964
$400$	1.68073e20	5.12918
$401$	−4.15722e19	−1.24515	−0.622573	−	0.782561i	$-0.713913\pi$
$401$	−4.15722e19	−1.24515	−0.622573	+	0.782561i	$0.713913\pi$
$402$	2.43535e19	0.715922
$403$	5.59503e18	0.161441
$404$	2.11271e19	0.598383
$405$	9.93628e18	0.276256
$406$	−1.02947e20	−2.80974
$407$	−6.66444e19	−1.78569
$408$	8.62705e19	2.26940
$409$	−3.44584e19	−0.889959	−0.444979	−	0.895541i	$-0.646789\pi$
$409$	−3.44584e19	−0.889959	−0.444979	+	0.895541i	$0.646789\pi$
$410$	1.18507e20	3.00514
$411$	−5.28288e18	−0.131540
$412$	−6.77016e19	−1.65527
$413$	−8.64999e19	−2.07678
$414$	−5.55914e19	−1.31071
$415$	−5.38857e19	−1.24771
$416$	4.32396e19	0.983290
$417$	−2.06051e19	−0.460207
$418$	7.08698e19	1.55467
$419$	−8.07986e19	−1.74100	−0.870500	−	0.492169i	$-0.836204\pi$
$419$	−8.07986e19	−1.74100	−0.870500	+	0.492169i	$0.836204\pi$
$420$	1.34457e20	2.84587
$421$	6.29500e18	0.130882	0.0654410	−	0.997856i	$-0.479155\pi$
$421$	6.29500e18	0.130882	0.0654410	+	0.997856i	$0.479155\pi$
$422$	2.56400e19	0.523690
$423$	−1.10537e19	−0.221796
$424$	−2.22114e20	−4.37857
$425$	−7.43034e19	−1.43910
$426$	4.19956e19	0.799156
$427$	2.95909e19	0.553286
$428$	−1.88066e20	−3.45527
$429$	6.47760e18	0.116946
$430$	1.32479e20	2.35036
$431$	3.10111e19	0.540677	0.270339	−	0.962765i	$-0.412864\pi$
$431$	3.10111e19	0.540677	0.270339	+	0.962765i	$0.412864\pi$
$432$	−2.25229e20	−3.85918
$433$	−3.63178e19	−0.611589	−0.305795	−	0.952097i	$-0.598922\pi$
$433$	−3.63178e19	−0.611589	−0.305795	+	0.952097i	$0.598922\pi$
$434$	1.07528e20	1.77971
$435$	5.93110e19	0.964864
$436$	1.68949e19	0.270152
$437$	−4.97057e19	−0.781260
$438$	−1.06938e20	−1.65225
$439$	−9.75066e18	−0.148098	−0.0740491	−	0.997255i	$-0.523592\pi$
$439$	−9.75066e18	−0.148098	−0.0740491	+	0.997255i	$0.523592\pi$
$440$	3.49027e20	5.21151
$441$	−2.39209e19	−0.351146
$442$	−3.41539e19	−0.492916
$443$	1.03538e20	1.46917	0.734584	−	0.678518i	$-0.237377\pi$
$443$	1.03538e20	1.46917	0.734584	+	0.678518i	$0.237377\pi$
$444$	2.02839e20	2.82995
$445$	5.76650e19	0.791065
$446$	−1.34513e20	−1.81448
$447$	−4.24671e19	−0.563308
$448$	4.42373e20	5.77037
$449$	7.93769e19	1.01823	0.509116	−	0.860698i	$-0.329973\pi$
$449$	7.93769e19	1.01823	0.509116	+	0.860698i	$0.329973\pi$
$450$	1.34109e20	1.69186
$451$	8.10023e19	1.00502
$452$	−2.99678e20	−3.65693
$453$	2.73437e19	0.328186
$454$	1.46733e20	1.73224
$455$	−3.43577e19	−0.398969
$456$	−1.39223e20	−1.59028
$457$	4.14649e19	0.465917	0.232959	−	0.972487i	$-0.425159\pi$
$457$	4.14649e19	0.465917	0.232959	+	0.972487i	$0.425159\pi$
$458$	−2.93561e20	−3.24494
$459$	9.95713e19	1.08278
$460$	−3.79265e20	−4.05750
$461$	−4.74903e18	−0.0499859	−0.0249930	−	0.999688i	$-0.507956\pi$
$461$	−4.74903e18	−0.0499859	−0.0249930	+	0.999688i	$0.507956\pi$
$462$	1.24490e20	1.28920
$463$	−1.78065e20	−1.81435	−0.907177	−	0.420749i	$-0.861767\pi$
$463$	−1.78065e20	−1.81435	−0.907177	+	0.420749i	$0.861767\pi$
$464$	4.83509e20	4.84752
$465$	−6.19506e19	−0.611151
$466$	−9.79226e19	−0.950579
$467$	−1.87354e20	−1.78973	−0.894864	−	0.446338i	$-0.852728\pi$
$467$	−1.87354e20	−1.78973	−0.894864	+	0.446338i	$0.852728\pi$
$468$	4.55087e19	0.427810
$469$	−8.82927e19	−0.816824
$470$	−1.02149e20	−0.930041
$471$	−3.10888e19	−0.278578
$472$	6.83404e20	6.02716
$473$	9.05528e19	0.786037
$474$	1.17117e19	0.100065
$475$	1.19910e20	1.00845
$476$	−4.84579e20	−4.01155
$477$	−1.05358e20	−0.858578
$478$	−4.41485e20	−3.54166
$479$	−8.70765e19	−0.687677	−0.343839	−	0.939029i	$-0.611727\pi$
$479$	−8.70765e19	−0.687677	−0.343839	+	0.939029i	$0.611727\pi$
$480$	−4.78767e20	−3.72233
$481$	−5.18312e19	−0.396737
$482$	2.83043e20	2.13305
$483$	−8.73130e19	−0.647851
$484$	−1.64498e19	−0.120176
$485$	7.49085e19	0.538850
$486$	−2.85571e20	−2.02275
$487$	1.37878e20	0.961675	0.480838	−	0.876810i	$-0.340333\pi$
$487$	1.37878e20	0.961675	0.480838	+	0.876810i	$0.340333\pi$
$488$	−2.33787e20	−1.60573
$489$	−1.59854e20	−1.08120
$490$	−2.21059e20	−1.47244
$491$	−1.67886e20	−1.10130	−0.550648	−	0.834738i	$-0.685619\pi$
$491$	−1.67886e20	−1.10130	−0.550648	+	0.834738i	$0.685619\pi$
$492$	−2.46539e20	−1.59275
$493$	−2.13754e20	−1.36008
$494$	5.51174e19	0.345411
$495$	1.65558e20	1.02191
$496$	−5.05027e20	−3.07045
$497$	−1.52254e20	−0.911790
$498$	1.51848e20	0.895756
$499$	6.00224e19	0.348786	0.174393	−	0.984676i	$-0.444204\pi$
$499$	6.00224e19	0.348786	0.174393	+	0.984676i	$0.444204\pi$
$500$	1.77420e20	1.01561
$501$	1.46009e20	0.823372
$502$	−2.01690e20	−1.12048
$503$	−1.13659e20	−0.622078	−0.311039	−	0.950397i	$-0.600677\pi$
$503$	−1.13659e20	−0.622078	−0.311039	+	0.950397i	$0.600677\pi$
$504$	5.64515e20	3.04401
$505$	5.97753e19	0.317568
$506$	−3.51149e20	−1.83807
$507$	−1.01562e20	−0.523808
$508$	−8.80047e20	−4.47227
$509$	3.28974e20	1.64732	0.823660	−	0.567084i	$-0.191929\pi$
$509$	3.28974e20	1.64732	0.823660	+	0.567084i	$0.191929\pi$
$510$	3.78167e20	1.86598
$511$	3.87699e20	1.88511
$512$	−8.32557e20	−3.98923
$513$	−1.60688e20	−0.758756
$514$	1.67173e20	0.777936
$515$	−1.91550e20	−0.878470
$516$	−2.75606e20	−1.24571
$517$	−6.98215e19	−0.311036
$518$	−9.96117e20	−4.37358
$519$	2.07617e20	0.898477
$520$	2.71448e20	1.15787
$521$	−2.87704e20	−1.20966	−0.604830	−	0.796355i	$-0.706759\pi$
$521$	−2.87704e20	−1.20966	−0.604830	+	0.796355i	$0.706759\pi$
$522$	3.85802e20	1.59895
$523$	4.18267e20	1.70880	0.854400	−	0.519615i	$-0.173925\pi$
$523$	4.18267e20	1.70880	0.854400	+	0.519615i	$0.173925\pi$
$524$	9.01434e19	0.363036
$525$	2.10634e20	0.836246
$526$	8.81948e20	3.45184
$527$	2.23267e20	0.861481
$528$	−5.84690e20	−2.22419
$529$	−2.03508e19	−0.0763246
$530$	−9.73638e20	−3.60022
$531$	3.24167e20	1.18184
$532$	7.82011e20	2.81109
$533$	6.29977e19	0.223291
$534$	−1.62498e20	−0.567922
$535$	−5.32100e20	−1.83375
$536$	6.97568e20	2.37056
$537$	−6.12967e19	−0.205414
$538$	−8.71397e20	−2.87971
$539$	−1.51099e20	−0.492431
$540$	−1.22608e21	−3.94063
$541$	−7.66624e19	−0.242998	−0.121499	−	0.992592i	$-0.538770\pi$
$541$	−7.66624e19	−0.242998	−0.121499	+	0.992592i	$0.538770\pi$
$542$	−6.98874e20	−2.18476
$543$	−2.93049e20	−0.903527
$544$	1.72546e21	5.24702
$545$	4.78012e19	0.143372
$546$	9.68191e19	0.286428
$547$	−4.93014e19	−0.143865	−0.0719323	−	0.997410i	$-0.522917\pi$
$547$	−4.93014e19	−0.143865	−0.0719323	+	0.997410i	$0.522917\pi$
$548$	−2.34442e20	−0.674809
$549$	−1.10895e20	−0.314861
$550$	8.47113e20	2.37258
$551$	3.44956e20	0.953074
$552$	6.89828e20	1.88017
$553$	−4.24603e19	−0.114168
$554$	1.25849e21	3.33832
$555$	5.73897e20	1.50188
$556$	−9.14404e20	−2.36090
$557$	6.43748e20	1.63984	0.819921	−	0.572477i	$-0.194018\pi$
$557$	6.43748e20	1.63984	0.819921	+	0.572477i	$0.194018\pi$
$558$	−4.02972e20	−1.01279
$559$	7.04254e19	0.174639
$560$	3.10125e21	7.58798
$561$	2.58486e20	0.624044
$562$	1.44865e21	3.45096
$563$	2.70911e20	0.636816	0.318408	−	0.947954i	$-0.396852\pi$
$563$	2.70911e20	0.636816	0.318408	+	0.947954i	$0.396852\pi$
$564$	2.12509e20	0.492928
$565$	−8.47885e20	−1.94077
$566$	−9.15091e20	−2.06700
$567$	1.01514e20	0.226282
$568$	1.20290e21	2.64617
$569$	7.03198e20	1.52664	0.763319	−	0.646022i	$-0.223569\pi$
$569$	7.03198e20	1.52664	0.763319	+	0.646022i	$0.223569\pi$
$570$	−6.10283e20	−1.30759
$571$	−9.48952e19	−0.200666	−0.100333	−	0.994954i	$-0.531991\pi$
$571$	−9.48952e19	−0.200666	−0.100333	+	0.994954i	$0.531991\pi$
$572$	2.87460e20	0.599940
$573$	3.60225e20	0.742018
$574$	1.21072e21	2.46153
$575$	−5.94138e20	−1.19228
$576$	−1.65784e21	−3.28377
$577$	6.19743e20	1.21169	0.605847	−	0.795581i	$-0.292834\pi$
$577$	6.19743e20	1.21169	0.605847	+	0.795581i	$0.292834\pi$
$578$	−3.50112e20	−0.675691
$579$	−2.76930e20	−0.527571
$580$	2.63208e21	4.94982
$581$	−5.50521e20	−1.02200
$582$	−2.11090e20	−0.386852
$583$	−6.65504e20	−1.20403
$584$	−3.06306e21	−5.47091
$585$	1.28759e20	0.227043
$586$	7.30964e20	1.27252
$587$	−2.20301e20	−0.378643	−0.189322	−	0.981915i	$-0.560629\pi$
$587$	−2.20301e20	−0.378643	−0.189322	+	0.981915i	$0.560629\pi$
$588$	4.59884e20	0.780403
$589$	−3.60308e20	−0.603683
$590$	2.99570e21	4.95574
$591$	−8.09318e19	−0.132194
$592$	4.67846e21	7.54554
$593$	−3.60581e20	−0.574239	−0.287119	−	0.957895i	$-0.592698\pi$
$593$	−3.60581e20	−0.574239	−0.287119	+	0.957895i	$0.592698\pi$
$594$	−1.13519e21	−1.78513
$595$	−1.37103e21	−2.12897
$596$	−1.88459e21	−2.88981
$597$	−4.13411e20	−0.626000
$598$	−2.73098e20	−0.408376
$599$	−9.65954e20	−1.42645	−0.713223	−	0.700938i	$-0.752765\pi$
$599$	−9.65954e20	−1.42645	−0.713223	+	0.700938i	$0.752765\pi$
$600$	−1.66414e21	−2.42693
$601$	−7.03434e20	−1.01313	−0.506565	−	0.862202i	$-0.669085\pi$
$601$	−7.03434e20	−1.01313	−0.506565	+	0.862202i	$0.669085\pi$
$602$	1.35347e21	1.92520
$603$	3.30885e20	0.464834
$604$	1.21345e21	1.68362
$605$	−4.65417e19	−0.0637789
$606$	−1.68445e20	−0.227989
$607$	4.14206e20	0.553733	0.276867	−	0.960908i	$-0.410704\pi$
$607$	4.14206e20	0.553733	0.276867	+	0.960908i	$0.410704\pi$
$608$	−2.78453e21	−3.67685
$609$	6.05948e20	0.790326
$610$	−1.02481e21	−1.32029
$611$	−5.43021e19	−0.0691047
$612$	1.81600e21	2.28287
$613$	1.43481e21	1.78172	0.890862	−	0.454275i	$-0.150102\pi$
$613$	1.43481e21	1.78172	0.890862	+	0.454275i	$0.150102\pi$
$614$	−2.41258e20	−0.295950
$615$	−6.97538e20	−0.845288
$616$	3.56582e21	4.26878
$617$	2.91487e20	0.344732	0.172366	−	0.985033i	$-0.444859\pi$
$617$	2.91487e20	0.344732	0.172366	+	0.985033i	$0.444859\pi$
$618$	5.39781e20	0.630673
$619$	−4.58458e20	−0.529200	−0.264600	−	0.964358i	$-0.585240\pi$
$619$	−4.58458e20	−0.529200	−0.264600	+	0.964358i	$0.585240\pi$
$620$	−2.74922e21	−3.13525
$621$	7.96183e20	0.897069
$622$	3.14924e21	3.50572
$623$	5.89132e20	0.647966
$624$	−4.54730e20	−0.494161
$625$	−6.53386e20	−0.701568
$626$	−2.26897e21	−2.40725
$627$	−4.17143e20	−0.437299
$628$	−1.37965e21	−1.42913
$629$	−2.06830e21	−2.11706
$630$	2.47455e21	2.50289
$631$	3.07567e20	0.307411	0.153706	−	0.988117i	$-0.450879\pi$
$631$	3.07567e20	0.307411	0.153706	+	0.988117i	$0.450879\pi$
$632$	3.35464e20	0.331335
$633$	−1.50918e20	−0.147304
$634$	1.05625e21	1.01882
$635$	−2.48994e21	−2.37348
$636$	2.02553e21	1.90814
$637$	−1.17514e20	−0.109406
$638$	2.43696e21	2.24230
$639$	5.70585e20	0.518876
$640$	−7.78746e21	−6.99916
$641$	1.81271e20	0.161025	0.0805124	−	0.996754i	$-0.474344\pi$
$641$	1.81271e20	0.161025	0.0805124	+	0.996754i	$0.474344\pi$
$642$	1.49944e21	1.31649
$643$	4.74792e20	0.412022	0.206011	−	0.978550i	$-0.433952\pi$
$643$	4.74792e20	0.412022	0.206011	+	0.978550i	$0.433952\pi$
$644$	−3.87474e21	−3.32352
$645$	−7.79780e20	−0.661111
$646$	2.19944e21	1.84318
$647$	−1.13149e21	−0.937278	−0.468639	−	0.883390i	$-0.655255\pi$
$647$	−1.13149e21	−0.937278	−0.468639	+	0.883390i	$0.655255\pi$
$648$	−8.02021e20	−0.656709
$649$	2.04763e21	1.65736
$650$	6.58823e20	0.527131
$651$	−6.32916e20	−0.500597
$652$	−7.09393e21	−5.54664
$653$	1.77816e21	1.37443	0.687214	−	0.726455i	$-0.258833\pi$
$653$	1.77816e21	1.37443	0.687214	+	0.726455i	$0.258833\pi$
$654$	−1.34702e20	−0.102930
$655$	2.55045e20	0.192667
$656$	−5.68639e21	−4.24676
$657$	−1.45294e21	−1.07277
$658$	−1.04361e21	−0.761802
$659$	1.93610e20	0.139729	0.0698644	−	0.997556i	$-0.477743\pi$
$659$	1.93610e20	0.139729	0.0698644	+	0.997556i	$0.477743\pi$
$660$	−3.18288e21	−2.27113
$661$	4.57674e20	0.322883	0.161441	−	0.986882i	$-0.448386\pi$
$661$	4.57674e20	0.322883	0.161441	+	0.986882i	$0.448386\pi$
$662$	1.23644e21	0.862457
$663$	2.01031e20	0.138648
$664$	4.34946e21	2.96603
$665$	2.21256e21	1.49188
$666$	3.73305e21	2.48889
$667$	−1.70920e21	−1.12681
$668$	6.47952e21	4.22396
$669$	7.91747e20	0.510376
$670$	3.05779e21	1.94916
$671$	−7.00479e20	−0.441546
$672$	−4.89130e21	−3.04898
$673$	1.69354e21	1.04396	0.521980	−	0.852958i	$-0.325194\pi$
$673$	1.69354e21	1.04396	0.521980	+	0.852958i	$0.325194\pi$
$674$	3.94946e20	0.240762
$675$	−1.92071e21	−1.15794
$676$	−4.50709e21	−2.68717
$677$	1.15361e21	0.680212	0.340106	−	0.940387i	$-0.389537\pi$
$677$	1.15361e21	0.680212	0.340106	+	0.940387i	$0.389537\pi$
$678$	2.38932e21	1.39332
$679$	7.65299e20	0.441375
$680$	1.08320e22	6.17863
$681$	−8.63677e20	−0.487246
$682$	−2.54541e21	−1.42029
$683$	−1.41512e21	−0.780977	−0.390488	−	0.920608i	$-0.627694\pi$
$683$	−1.41512e21	−0.780977	−0.390488	+	0.920608i	$0.627694\pi$
$684$	−2.93066e21	−1.59972
$685$	−6.63312e20	−0.358128
$686$	2.22909e21	1.19041
$687$	1.72791e21	0.912738
$688$	−6.35684e21	−3.32145
$689$	−5.17581e20	−0.267506
$690$	3.02386e21	1.54594
$691$	−9.22602e20	−0.466583	−0.233292	−	0.972407i	$-0.574950\pi$
$691$	−9.22602e20	−0.466583	−0.233292	+	0.972407i	$0.574950\pi$
$692$	9.21353e21	4.60925
$693$	1.69141e21	0.837049
$694$	−1.56045e20	−0.0763932
$695$	−2.58715e21	−1.25295
$696$	−4.78738e21	−2.29366
$697$	2.51390e21	1.19152
$698$	−2.28411e21	−1.07103
$699$	5.76377e20	0.267379
$700$	9.34745e21	4.29000
$701$	−3.48260e21	−1.58131	−0.790657	−	0.612260i	$-0.790261\pi$
$701$	−3.48260e21	−1.58131	−0.790657	+	0.612260i	$0.790261\pi$
$702$	−8.82866e20	−0.396612
$703$	3.33781e21	1.48353
$704$	−1.04719e22	−4.60500
$705$	6.01257e20	0.261602
$706$	8.94001e21	3.84860
$707$	6.10692e20	0.260122
$708$	−6.23217e21	−2.62658
$709$	−6.55052e20	−0.273168	−0.136584	−	0.990629i	$-0.543612\pi$
$709$	−6.55052e20	−0.273168	−0.136584	+	0.990629i	$0.543612\pi$
$710$	5.27291e21	2.17577
$711$	1.59124e20	0.0649702
$712$	−4.65451e21	−1.88050
$713$	1.78527e21	0.713727
$714$	3.86352e21	1.52843
$715$	8.13319e20	0.318394
$716$	−2.72020e21	−1.05379
$717$	2.59860e21	0.996198
$718$	−7.52256e21	−2.85386
$719$	−4.91498e21	−1.84525	−0.922625	−	0.385699i	$-0.873960\pi$
$719$	−4.91498e21	−1.84525	−0.922625	+	0.385699i	$0.873960\pi$
$720$	−1.16222e22	−4.31813
$721$	−1.95696e21	−0.719560
$722$	1.82196e21	0.662994
$723$	−1.66601e21	−0.599984
$724$	−1.30048e22	−4.63516
$725$	4.12329e21	1.45448
$726$	1.31153e20	0.0457882
$727$	2.95920e21	1.02251	0.511254	−	0.859430i	$-0.329181\pi$
$727$	2.95920e21	1.02251	0.511254	+	0.859430i	$0.329181\pi$
$728$	2.77323e21	0.948421
$729$	1.13564e21	0.384401
$730$	−1.34269e22	−4.49838
$731$	2.81029e21	0.931905
$732$	2.13198e21	0.699760
$733$	−1.47249e21	−0.478380	−0.239190	−	0.970973i	$-0.576882\pi$
$733$	−1.47249e21	−0.478380	−0.239190	+	0.970973i	$0.576882\pi$
$734$	3.22307e21	1.03645
$735$	1.30116e21	0.414168
$736$	1.37969e22	4.34710
$737$	2.09007e21	0.651861
$738$	−4.53730e21	−1.40079
$739$	4.68961e21	1.43319	0.716594	−	0.697491i	$-0.245700\pi$
$739$	4.68961e21	1.43319	0.716594	+	0.697491i	$0.245700\pi$
$740$	2.54682e22	7.70478
$741$	−3.24423e20	−0.0971573
$742$	−9.94713e21	−2.94896
$743$	1.53305e20	0.0449925	0.0224963	−	0.999747i	$-0.492839\pi$
$743$	1.53305e20	0.0449925	0.0224963	+	0.999747i	$0.492839\pi$
$744$	5.00043e21	1.45282
$745$	−5.33211e21	−1.53365
$746$	−1.14353e22	−3.25616
$747$	2.06313e21	0.581596
$748$	1.14710e22	3.20139
$749$	−5.43618e21	−1.50203
$750$	−1.41456e21	−0.386955
$751$	−5.48698e21	−1.48605	−0.743025	−	0.669263i	$-0.766610\pi$
$751$	−5.48698e21	−1.48605	−0.743025	+	0.669263i	$0.766610\pi$
$752$	4.90150e21	1.31430
$753$	1.18715e21	0.315170
$754$	1.89529e21	0.498185
$755$	3.43324e21	0.893515
$756$	−1.25262e22	−3.22779
$757$	4.54878e21	1.16058	0.580291	−	0.814409i	$-0.302939\pi$
$757$	4.54878e21	1.16058	0.580291	+	0.814409i	$0.302939\pi$
$758$	−5.64374e21	−1.42577
$759$	2.06688e21	0.517013
$760$	−1.74806e22	−4.32968
$761$	2.47019e21	0.605822	0.302911	−	0.953019i	$-0.402042\pi$
$761$	2.47019e21	0.605822	0.302911	+	0.953019i	$0.402042\pi$
$762$	7.01657e21	1.70397
$763$	4.88359e20	0.117437
$764$	1.59859e22	3.80661
$765$	5.13807e21	1.21154
$766$	7.86516e20	0.183650
$767$	1.59250e21	0.368225
$768$	1.06445e22	2.43734
$769$	−3.03260e20	−0.0687650	−0.0343825	−	0.999409i	$-0.510946\pi$
$769$	−3.03260e20	−0.0687650	−0.0343825	+	0.999409i	$0.510946\pi$
$770$	1.56308e22	3.50994
$771$	−9.83990e20	−0.218818
$772$	−1.22895e22	−2.70648
$773$	4.60747e21	1.00489	0.502443	−	0.864611i	$-0.332435\pi$
$773$	4.60747e21	1.00489	0.502443	+	0.864611i	$0.332435\pi$
$774$	−5.07226e21	−1.09558
$775$	−4.30679e21	−0.921279
$776$	−6.04634e21	−1.28094
$777$	5.86319e21	1.23020
$778$	8.54711e21	1.77612
$779$	−4.05691e21	−0.834959
$780$	−2.47542e21	−0.504590
$781$	3.60416e21	0.727648
$782$	−1.08979e22	−2.17917
$783$	−5.52547e21	−1.09435
$784$	1.06072e22	2.08080
$785$	−3.90347e21	−0.758453
$786$	−7.18709e20	−0.138320
$787$	3.15423e21	0.601288	0.300644	−	0.953736i	$-0.402798\pi$
$787$	3.15423e21	0.601288	0.300644	+	0.953736i	$0.402798\pi$
$788$	−3.59156e21	−0.678167
$789$	−5.19119e21	−0.970933
$790$	1.47050e21	0.272435
$791$	−8.66238e21	−1.58969
$792$	−1.33632e22	−2.42925
$793$	−5.44781e20	−0.0981010
$794$	−4.01078e21	−0.715444
$795$	5.73088e21	1.01267
$796$	−1.83462e22	−3.21143
$797$	4.80984e21	0.834052	0.417026	−	0.908895i	$-0.363072\pi$
$797$	4.80984e21	0.834052	0.417026	+	0.908895i	$0.363072\pi$
$798$	−6.23493e21	−1.07105
$799$	−2.16690e21	−0.368756
$800$	−3.32838e22	−5.61123
$801$	−2.20783e21	−0.368741
$802$	1.47091e22	2.43377
$803$	−9.17763e21	−1.50440
$804$	−6.36134e21	−1.03307
$805$	−1.09629e22	−1.76383
$806$	−1.97964e21	−0.315553
$807$	5.12908e21	0.810006
$808$	−4.82485e21	−0.754916
$809$	9.10872e21	1.41203	0.706015	−	0.708197i	$-0.250491\pi$
$809$	9.10872e21	1.41203	0.706015	+	0.708197i	$0.250491\pi$
$810$	−3.51566e21	−0.539969
$811$	4.91788e21	0.748379	0.374190	−	0.927352i	$-0.377921\pi$
$811$	4.91788e21	0.748379	0.374190	+	0.927352i	$0.377921\pi$
$812$	2.68906e22	4.05443
$813$	4.11360e21	0.614530
$814$	2.35802e22	3.49031
$815$	−2.00710e22	−2.94366
$816$	−1.81458e22	−2.63694
$817$	−4.53524e21	−0.653032
$818$	1.21921e22	1.73951
$819$	1.31546e21	0.185972
$820$	−3.09551e22	−4.33639
$821$	−1.87372e20	−0.0260095	−0.0130047	−	0.999915i	$-0.504140\pi$
$821$	−1.87372e20	−0.0260095	−0.0130047	+	0.999915i	$0.504140\pi$
$822$	1.86919e21	0.257108
$823$	−2.91105e21	−0.396781	−0.198390	−	0.980123i	$-0.563571\pi$
$823$	−2.91105e21	−0.396781	−0.198390	+	0.980123i	$0.563571\pi$
$824$	1.54612e22	2.08828
$825$	−4.98615e21	−0.667361
$826$	3.06054e22	4.05927
$827$	−1.71379e21	−0.225251	−0.112626	−	0.993638i	$-0.535926\pi$
$827$	−1.71379e21	−0.225251	−0.112626	+	0.993638i	$0.535926\pi$
$828$	1.45210e22	1.89133
$829$	9.09215e20	0.117357	0.0586783	−	0.998277i	$-0.481311\pi$
$829$	9.09215e20	0.117357	0.0586783	+	0.998277i	$0.481311\pi$
$830$	1.90659e22	2.43877
$831$	−7.40755e21	−0.939002
$832$	−8.14427e21	−1.02312
$833$	−4.68933e21	−0.583813
$834$	7.29050e21	0.899522
$835$	1.83327e22	2.24170
$836$	−1.85118e22	−2.24337
$837$	5.77138e21	0.693168
$838$	2.85882e22	3.40296
$839$	7.89822e21	0.931783	0.465892	−	0.884842i	$-0.345734\pi$
$839$	7.89822e21	0.931783	0.465892	+	0.884842i	$0.345734\pi$
$840$	−3.07064e22	−3.59033
$841$	3.23261e21	0.374613
$842$	−2.22730e21	−0.255822
$843$	−8.52680e21	−0.970688
$844$	−6.69739e21	−0.755679
$845$	−1.27520e22	−1.42611
$846$	3.91101e21	0.433522
$847$	−4.75491e20	−0.0522416
$848$	4.67187e22	5.08770
$849$	5.38627e21	0.581407
$850$	2.62901e22	2.81287
$851$	−1.65383e22	−1.75396
$852$	−1.09696e22	−1.15317
$853$	8.93704e21	0.931270	0.465635	−	0.884977i	$-0.345826\pi$
$853$	8.93704e21	0.931270	0.465635	+	0.884977i	$0.345826\pi$
$854$	−1.04699e22	−1.08145
$855$	−8.29179e21	−0.848989
$856$	4.29492e22	4.35915
$857$	−1.24927e21	−0.125690	−0.0628449	−	0.998023i	$-0.520017\pi$
$857$	−1.24927e21	−0.125690	−0.0628449	+	0.998023i	$0.520017\pi$
$858$	−2.29191e21	−0.228582
$859$	2.98290e21	0.294910	0.147455	−	0.989069i	$-0.452892\pi$
$859$	2.98290e21	0.294910	0.147455	+	0.989069i	$0.452892\pi$
$860$	−3.46048e22	−3.39155
$861$	−7.12637e21	−0.692380
$862$	−1.09724e22	−1.05681
$863$	1.52342e22	1.45458	0.727290	−	0.686330i	$-0.240780\pi$
$863$	1.52342e22	1.45458	0.727290	+	0.686330i	$0.240780\pi$
$864$	4.46024e22	4.22188
$865$	2.60681e22	2.44618
$866$	1.28500e22	1.19541
$867$	2.06078e21	0.190059
$868$	−2.80873e22	−2.56810
$869$	1.00512e21	0.0911111
$870$	−2.09855e22	−1.88592
$871$	1.62551e21	0.144828
$872$	−3.85835e21	−0.340822
$873$	−2.86803e21	−0.251175
$874$	1.75869e22	1.52705
$875$	5.12843e21	0.441493
$876$	2.79330e22	2.38417
$877$	−1.00951e22	−0.854307	−0.427153	−	0.904179i	$-0.640484\pi$
$877$	−1.00951e22	−0.854307	−0.427153	+	0.904179i	$0.640484\pi$
$878$	3.44998e21	0.289473
$879$	−4.30248e21	−0.357934
$880$	−7.34130e22	−6.05554
$881$	1.58987e22	1.30030	0.650149	−	0.759807i	$-0.274706\pi$
$881$	1.58987e22	1.30030	0.650149	+	0.759807i	$0.274706\pi$
$882$	8.46371e21	0.686351
$883$	1.23882e22	0.996100	0.498050	−	0.867148i	$-0.334050\pi$
$883$	1.23882e22	0.996100	0.498050	+	0.867148i	$0.334050\pi$
$884$	8.92130e21	0.711272
$885$	−1.76328e22	−1.39395
$886$	−3.66338e22	−2.87164
$887$	−2.73283e21	−0.212415	−0.106208	−	0.994344i	$-0.533871\pi$
$887$	−2.73283e21	−0.212415	−0.106208	+	0.994344i	$0.533871\pi$
$888$	−4.63229e22	−3.57025
$889$	−2.54383e22	−1.94413
$890$	−2.04031e22	−1.54622
$891$	−2.40303e21	−0.180583
$892$	3.51358e22	2.61827
$893$	3.49694e21	0.258406
$894$	1.50257e22	1.10104
$895$	−7.69633e21	−0.559256
$896$	−7.95602e22	−5.73305
$897$	1.60747e21	0.114868
$898$	−2.80852e22	−1.99024
$899$	−1.23897e22	−0.870689
$900$	−3.50304e22	−2.44133
$901$	−2.06538e22	−1.42746
$902$	−2.86603e22	−1.96441
$903$	−7.96659e21	−0.541520
$904$	6.84383e22	4.61356
$905$	−3.67948e22	−2.45993
$906$	−9.67476e21	−0.641474
$907$	−6.10132e21	−0.401208	−0.200604	−	0.979672i	$-0.564290\pi$
$907$	−6.10132e21	−0.401208	−0.200604	+	0.979672i	$0.564290\pi$
$908$	−3.83279e22	−2.49961
$909$	−2.28863e21	−0.148029
$910$	1.21565e22	0.779825
$911$	−2.39967e22	−1.52674	−0.763368	−	0.645964i	$-0.776456\pi$
$911$	−2.39967e22	−1.52674	−0.763368	+	0.645964i	$0.776456\pi$
$912$	2.92836e22	1.84783
$913$	1.30320e22	0.815603
$914$	−1.46711e22	−0.910683
$915$	6.03205e21	0.371370
$916$	7.66806e22	4.68241
$917$	2.60566e21	0.157815
$918$	−3.52304e22	−2.11640
$919$	−2.57072e22	−1.53175	−0.765877	−	0.642988i	$-0.777695\pi$
$919$	−2.57072e22	−1.53175	−0.765877	+	0.642988i	$0.777695\pi$
$920$	8.66139e22	5.11893
$921$	1.42006e21	0.0832450
$922$	1.68030e21	0.0977025
$923$	2.80305e21	0.161666
$924$	−3.25178e22	−1.86029
$925$	3.98972e22	2.26401
$926$	6.30032e22	3.54634
$927$	7.33389e21	0.409483
$928$	−9.57502e22	−5.30310
$929$	9.66874e20	0.0531193	0.0265596	−	0.999647i	$-0.491545\pi$
$929$	9.66874e20	0.0531193	0.0265596	+	0.999647i	$0.491545\pi$
$930$	2.19194e22	1.19456
$931$	7.56762e21	0.409107
$932$	2.55782e22	1.37167
$933$	−1.85366e22	−0.986090
$934$	6.62898e22	3.49821
$935$	3.24551e22	1.69901
$936$	−1.03930e22	−0.539722
$937$	−2.23964e22	−1.15380	−0.576900	−	0.816814i	$-0.695738\pi$
$937$	−2.23964e22	−1.15380	−0.576900	+	0.816814i	$0.695738\pi$
$938$	3.12398e22	1.59657
$939$	1.33553e22	0.677113
$940$	2.66823e22	1.34204
$941$	−7.54073e21	−0.376263	−0.188131	−	0.982144i	$-0.560243\pi$
$941$	−7.54073e21	−0.376263	−0.188131	+	0.982144i	$0.560243\pi$
$942$	1.09999e22	0.544510
$943$	2.01014e22	0.987162
$944$	−1.43744e23	−7.00327
$945$	−3.54406e22	−1.71302
$946$	−3.20394e22	−1.53639
$947$	−7.68738e21	−0.365724	−0.182862	−	0.983139i	$-0.558536\pi$
$947$	−7.68738e21	−0.365724	−0.182862	+	0.983139i	$0.558536\pi$
$948$	−3.05920e21	−0.144393
$949$	−7.13769e21	−0.334242
$950$	−4.24268e22	−1.97112
$951$	−6.21714e21	−0.286574
$952$	1.10665e23	5.06095
$953$	−3.26559e22	−1.48172	−0.740858	−	0.671661i	$-0.765581\pi$
$953$	−3.26559e22	−1.48172	−0.740858	+	0.671661i	$0.765581\pi$
$954$	3.72778e22	1.67818
$955$	4.52294e22	2.02021
$956$	1.15320e23	5.11057
$957$	−1.43441e22	−0.630714
$958$	3.08095e22	1.34413
$959$	−6.77669e21	−0.293345
$960$	9.01769e22	3.87312
$961$	−1.05242e22	−0.448500
$962$	1.83389e22	0.775463
$963$	2.03726e22	0.854770
$964$	−7.39334e22	−3.07796
$965$	−3.47710e22	−1.43636
$966$	3.08931e22	1.26629
$967$	−2.57410e22	−1.04695	−0.523475	−	0.852041i	$-0.675365\pi$
$967$	−2.57410e22	−1.04695	−0.523475	+	0.852041i	$0.675365\pi$
$968$	3.75668e21	0.151614
$969$	−1.29460e22	−0.518449
$970$	−2.65042e22	−1.05324
$971$	−1.31122e22	−0.517050	−0.258525	−	0.966005i	$-0.583236\pi$
$971$	−1.31122e22	−0.517050	−0.258525	+	0.966005i	$0.583236\pi$
$972$	7.45935e22	2.91880
$973$	−2.64315e22	−1.02630
$974$	−4.87842e22	−1.87969
$975$	−3.87786e21	−0.148272
$976$	4.91739e22	1.86578
$977$	9.48719e21	0.357214	0.178607	−	0.983920i	$-0.442841\pi$
$977$	9.48719e21	0.357214	0.178607	+	0.983920i	$0.442841\pi$
$978$	5.65596e22	2.11332
$979$	−1.39460e22	−0.517104
$980$	5.77425e22	2.12471
$981$	−1.83017e21	−0.0668304
$982$	5.94016e22	2.15259
$983$	−2.78236e22	−1.00060	−0.500302	−	0.865851i	$-0.666778\pi$
$983$	−2.78236e22	−1.00060	−0.500302	+	0.865851i	$0.666778\pi$
$984$	5.63028e22	2.00940
$985$	−1.01617e22	−0.359910
$986$	7.56307e22	2.65841
$987$	6.14271e21	0.214280
$988$	−1.43971e22	−0.498424
$989$	2.24714e22	0.772073
$990$	−5.85778e22	−1.99742
$991$	−1.65847e22	−0.561247	−0.280624	−	0.959818i	$-0.590541\pi$
$991$	−1.65847e22	−0.561247	−0.280624	+	0.959818i	$0.590541\pi$
$992$	1.00011e23	3.35902
$993$	−7.27773e21	−0.242592
$994$	5.38705e22	1.78219
$995$	−5.19074e22	−1.70434
$996$	−3.96641e22	−1.29256
$997$	−3.03223e22	−0.980726	−0.490363	−	0.871518i	$-0.663136\pi$
$997$	−3.03223e22	−0.980726	−0.490363	+	0.871518i	$0.663136\pi$
$998$	−2.12372e22	−0.681738
$999$	−5.34648e22	−1.70344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	109.16.a.a.1.2	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
109.16.a.a.1.2	✓	66	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 109 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	109.a (trivial)

\(f(q)\)	\(=\)	\(q-353.821 q^{2} +2082.60 q^{3} +92421.0 q^{4} +261489. q^{5} -736868. q^{6} +2.67149e6 q^{7} -2.11065e7 q^{8} -1.00117e7 q^{9} +O(q^{10})\)	\(q-353.821 q^{2} +2082.60 q^{3} +92421.0 q^{4} +261489. q^{5} -736868. q^{6} +2.67149e6 q^{7} -2.11065e7 q^{8} -1.00117e7 q^{9} -9.25202e7 q^{10} -6.32397e7 q^{11} +1.92476e8 q^{12} -4.91833e7 q^{13} -9.45229e8 q^{14} +5.44578e8 q^{15} +4.43945e9 q^{16} -1.96264e9 q^{17} +3.54233e9 q^{18} +3.16729e9 q^{19} +2.41671e10 q^{20} +5.56366e9 q^{21} +2.23755e10 q^{22} -1.56935e10 q^{23} -4.39564e10 q^{24} +3.78589e10 q^{25} +1.74020e10 q^{26} -5.07334e10 q^{27} +2.46902e11 q^{28} +1.08912e11 q^{29} -1.92683e11 q^{30} -1.13759e11 q^{31} -8.79153e11 q^{32} -1.31703e11 q^{33} +6.94421e11 q^{34} +6.98566e11 q^{35} -9.25289e11 q^{36} +1.05384e12 q^{37} -1.12065e12 q^{38} -1.02429e11 q^{39} -5.51911e12 q^{40} -1.28088e12 q^{41} -1.96854e12 q^{42} -1.43190e12 q^{43} -5.84468e12 q^{44} -2.61794e12 q^{45} +5.55267e12 q^{46} +1.10408e12 q^{47} +9.24562e12 q^{48} +2.38930e12 q^{49} -1.33953e13 q^{50} -4.08739e12 q^{51} -4.54557e12 q^{52} +1.05235e13 q^{53} +1.79505e13 q^{54} -1.65365e13 q^{55} -5.63857e13 q^{56} +6.59622e12 q^{57} -3.85353e13 q^{58} -3.23789e13 q^{59} +5.03305e13 q^{60} +1.10766e13 q^{61} +4.02502e13 q^{62} -2.67461e13 q^{63} +1.65590e14 q^{64} -1.28609e13 q^{65} +4.65993e13 q^{66} -3.30500e13 q^{67} -1.81389e14 q^{68} -3.26832e13 q^{69} -2.47167e14 q^{70} -5.69920e13 q^{71} +2.11311e14 q^{72} +1.45124e14 q^{73} -3.72869e14 q^{74} +7.88452e13 q^{75} +2.92724e14 q^{76} -1.68944e14 q^{77} +3.62416e13 q^{78} -1.58939e13 q^{79} +1.16087e15 q^{80} +3.79988e13 q^{81} +4.53201e14 q^{82} -2.06072e14 q^{83} +5.14199e14 q^{84} -5.13208e14 q^{85} +5.06635e14 q^{86} +2.26820e14 q^{87} +1.33477e15 q^{88} +2.20525e14 q^{89} +9.26282e14 q^{90} -1.31393e14 q^{91} -1.45040e15 q^{92} -2.36915e14 q^{93} -3.90645e14 q^{94} +8.28212e14 q^{95} -1.83093e15 q^{96} +2.86469e14 q^{97} -8.45384e14 q^{98} +6.33135e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 384 q^{2} - 9775 q^{3} + 1032192 q^{4} - 550760 q^{5} - 1290263 q^{6} - 3953576 q^{7} - 15117261 q^{8} + 286423921 q^{9}+O(q^{10}) \) 66 * q - 384 * q^2 - 9775 * q^3 + 1032192 * q^4 - 550760 * q^5 - 1290263 * q^6 - 3953576 * q^7 - 15117261 * q^8 + 286423921 * q^9	\( 66 q - 384 q^{2} - 9775 q^{3} + 1032192 q^{4} - 550760 q^{5} - 1290263 q^{6} - 3953576 q^{7} - 15117261 q^{8} + 286423921 q^{9} + 6483836 q^{10} - 418640282 q^{11} - 433698156 q^{12} - 251211569 q^{13} - 1592332821 q^{14} - 1067853378 q^{15} + 15344152328 q^{16} - 6669915144 q^{17} - 1130846704 q^{18} - 11923665296 q^{19} - 19811264155 q^{20} - 16836632576 q^{21} - 25066407453 q^{22} - 66240319423 q^{23} - 105321578171 q^{24} + 400217086854 q^{25} - 110366500241 q^{26} - 360361891108 q^{27} + 168304047263 q^{28} - 365318101624 q^{29} - 1696019730217 q^{30} - 581021125356 q^{31} - 945136776447 q^{32} - 80720646410 q^{33} + 509364050231 q^{34} - 1107221269012 q^{35} + 7914914022741 q^{36} + 885376534021 q^{37} - 245887726685 q^{38} - 14886955906 q^{39} + 4617883372968 q^{40} - 5158051651090 q^{41} - 922037781169 q^{42} - 3364734631553 q^{43} - 16009768816826 q^{44} - 13607122605862 q^{45} - 27613809885909 q^{46} - 15436064264767 q^{47} - 58305445438958 q^{48} + 22356385252652 q^{49} - 59201596698313 q^{50} - 31998753555286 q^{51} - 77785825258670 q^{52} - 35536412905909 q^{53} - 72434695159938 q^{54} - 48394117279296 q^{55} - 127390800143296 q^{56} - 41066353710544 q^{57} - 53471659238834 q^{58} - 182936201870706 q^{59} - 34432643772594 q^{60} - 69231508155360 q^{61} - 76728243090752 q^{62} - 989010429598 q^{63} + 206028006415075 q^{64} - 61149791847076 q^{65} + 209354337452312 q^{66} + 49820429470096 q^{67} - 183448493081939 q^{68} + 117351537759646 q^{69} + 488482013120139 q^{70} - 239459552004052 q^{71} + 601977723367037 q^{72} + 110709721135383 q^{73} + 234158962981804 q^{74} - 302768537362063 q^{75} + 418562925992027 q^{76} - 80154467168214 q^{77} + 13\!\cdots\!85 q^{78}+ \cdots - 35\!\cdots\!14 q^{99}+O(q^{100}) \) 66 * q - 384 * q^2 - 9775 * q^3 + 1032192 * q^4 - 550760 * q^5 - 1290263 * q^6 - 3953576 * q^7 - 15117261 * q^8 + 286423921 * q^9 + 6483836 * q^10 - 418640282 * q^11 - 433698156 * q^12 - 251211569 * q^13 - 1592332821 * q^14 - 1067853378 * q^15 + 15344152328 * q^16 - 6669915144 * q^17 - 1130846704 * q^18 - 11923665296 * q^19 - 19811264155 * q^20 - 16836632576 * q^21 - 25066407453 * q^22 - 66240319423 * q^23 - 105321578171 * q^24 + 400217086854 * q^25 - 110366500241 * q^26 - 360361891108 * q^27 + 168304047263 * q^28 - 365318101624 * q^29 - 1696019730217 * q^30 - 581021125356 * q^31 - 945136776447 * q^32 - 80720646410 * q^33 + 509364050231 * q^34 - 1107221269012 * q^35 + 7914914022741 * q^36 + 885376534021 * q^37 - 245887726685 * q^38 - 14886955906 * q^39 + 4617883372968 * q^40 - 5158051651090 * q^41 - 922037781169 * q^42 - 3364734631553 * q^43 - 16009768816826 * q^44 - 13607122605862 * q^45 - 27613809885909 * q^46 - 15436064264767 * q^47 - 58305445438958 * q^48 + 22356385252652 * q^49 - 59201596698313 * q^50 - 31998753555286 * q^51 - 77785825258670 * q^52 - 35536412905909 * q^53 - 72434695159938 * q^54 - 48394117279296 * q^55 - 127390800143296 * q^56 - 41066353710544 * q^57 - 53471659238834 * q^58 - 182936201870706 * q^59 - 34432643772594 * q^60 - 69231508155360 * q^61 - 76728243090752 * q^62 - 989010429598 * q^63 + 206028006415075 * q^64 - 61149791847076 * q^65 + 209354337452312 * q^66 + 49820429470096 * q^67 - 183448493081939 * q^68 + 117351537759646 * q^69 + 488482013120139 * q^70 - 239459552004052 * q^71 + 601977723367037 * q^72 + 110709721135383 * q^73 + 234158962981804 * q^74 - 302768537362063 * q^75 + 418562925992027 * q^76 - 80154467168214 * q^77 + 1323913017253085 * q^78 + 344264682091929 * q^79 - 32065698598171 * q^80 + 1988692250246122 * q^81 + 1270983624769250 * q^82 - 199730025767393 * q^83 + 617489751122564 * q^84 - 296293702359276 * q^85 + 537692257035328 * q^86 + 1240867015034202 * q^87 + 1947480665387314 * q^88 - 1639057373302857 * q^89 + 5020535661304190 * q^90 - 1546657035058086 * q^91 - 962008536423118 * q^92 - 614708405129510 * q^93 + 3330590764725661 * q^94 - 20584796236314 * q^95 - 1119373012440080 * q^96 + 1414025770405407 * q^97 + 2532116291022334 * q^98 - 3534034927854514 * q^99

Introduction

L-functions

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