LMFDB - Embedded newform 197.10.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,10,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	197.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:	$101.462059724$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-27.2613 q^{2} -2.80973 q^{3} +231.177 q^{4} +1123.40 q^{5} +76.5969 q^{6} -8481.66 q^{7} +7655.60 q^{8} -19675.1 q^{9} -30625.2 q^{10} +79300.8 q^{11} -649.546 q^{12} -97256.2 q^{13} +231221. q^{14} -3156.44 q^{15} -327064. q^{16} -37665.0 q^{17} +536368. q^{18} +584746. q^{19} +259703. q^{20} +23831.2 q^{21} -2.16184e6 q^{22} +1.46262e6 q^{23} -21510.2 q^{24} -691109. q^{25} +2.65133e6 q^{26} +110586. q^{27} -1.96076e6 q^{28} -5.08723e6 q^{29} +86048.6 q^{30} -226476. q^{31} +4.99651e6 q^{32} -222814. q^{33} +1.02680e6 q^{34} -9.52825e6 q^{35} -4.54843e6 q^{36} +7.07236e6 q^{37} -1.59409e7 q^{38} +273264. q^{39} +8.60026e6 q^{40} -2.82852e7 q^{41} -649669. q^{42} +2.12893e7 q^{43} +1.83325e7 q^{44} -2.21029e7 q^{45} -3.98727e7 q^{46} +4.37126e6 q^{47} +918963. q^{48} +3.15849e7 q^{49} +1.88405e7 q^{50} +105829. q^{51} -2.24834e7 q^{52} +8.42582e7 q^{53} -3.01471e6 q^{54} +8.90861e7 q^{55} -6.49321e7 q^{56} -1.64298e6 q^{57} +1.38684e8 q^{58} -4.99543e7 q^{59} -729696. q^{60} +1.38172e8 q^{61} +6.17401e6 q^{62} +1.66878e8 q^{63} +3.12455e7 q^{64} -1.09257e8 q^{65} +6.07420e6 q^{66} -2.30776e7 q^{67} -8.70728e6 q^{68} -4.10956e6 q^{69} +2.59752e8 q^{70} +1.47748e8 q^{71} -1.50625e8 q^{72} +1.64941e8 q^{73} -1.92802e8 q^{74} +1.94183e6 q^{75} +1.35180e8 q^{76} -6.72602e8 q^{77} -7.44953e6 q^{78} +3.82858e8 q^{79} -3.67422e8 q^{80} +3.86954e8 q^{81} +7.71091e8 q^{82} -4.96417e7 q^{83} +5.50922e6 q^{84} -4.23127e7 q^{85} -5.80373e8 q^{86} +1.42938e7 q^{87} +6.07095e8 q^{88} -2.48081e8 q^{89} +6.02554e8 q^{90} +8.24894e8 q^{91} +3.38123e8 q^{92} +636336. q^{93} -1.19166e8 q^{94} +6.56901e8 q^{95} -1.40389e7 q^{96} -1.11825e9 q^{97} -8.61045e8 q^{98} -1.56025e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 32 q^{2} - 892 q^{3} + 16896 q^{4} - 2329 q^{5} - 10272 q^{6} - 37846 q^{7} - 24933 q^{8} + 419903 q^{9} - 138907 q^{10} - 143074 q^{11} - 496640 q^{12} - 433821 q^{13} - 130143 q^{14} - 670126 q^{15}+ \cdots - 6380320552 q^{99}+O(q^{100}) $ 71 * q - 32 * q^2 - 892 * q^3 + 16896 * q^4 - 2329 * q^5 - 10272 * q^6 - 37846 * q^7 - 24933 * q^8 + 419903 * q^9 - 138907 * q^10 - 143074 * q^11 - 496640 * q^12 - 433821 * q^13 - 130143 * q^14 - 670126 * q^15 + 3670016 * q^16 - 226712 * q^17 - 1140455 * q^18 - 4200657 * q^19 - 2522261 * q^20 - 2222620 * q^21 - 5109807 * q^22 - 1576984 * q^23 - 7953747 * q^24 + 20408644 * q^25 - 3606210 * q^26 - 22380322 * q^27 - 28281314 * q^28 - 1600554 * q^29 + 1211083 * q^30 - 27408409 * q^31 - 19842828 * q^32 - 26002786 * q^33 - 33310606 * q^34 - 25745764 * q^35 + 75847738 * q^36 - 56498684 * q^37 - 8523742 * q^38 - 67092176 * q^39 - 69825234 * q^40 - 41524361 * q^41 - 29804525 * q^42 - 103636613 * q^43 - 93059022 * q^44 - 41029851 * q^45 - 35065939 * q^46 - 155481346 * q^47 - 310890046 * q^48 + 274445845 * q^49 - 532508319 * q^50 - 401628576 * q^51 - 638463912 * q^52 - 235002576 * q^53 - 485779441 * q^54 - 274178598 * q^55 - 174143696 * q^56 + 10220750 * q^57 - 54794577 * q^58 - 309204685 * q^59 + 349852813 * q^60 - 172553358 * q^61 + 313207667 * q^62 - 291588072 * q^63 + 1670833437 * q^64 + 394656726 * q^65 + 2405207530 * q^66 - 1034845512 * q^67 + 2160039119 * q^68 + 472060058 * q^69 + 1282221119 * q^70 + 515265617 * q^71 + 1722271619 * q^72 - 667322970 * q^73 + 1111943967 * q^74 - 304507118 * q^75 - 1476894506 * q^76 - 347407724 * q^77 - 99563531 * q^78 - 338475893 * q^79 - 652382330 * q^80 + 1981631951 * q^81 - 2682827483 * q^82 - 2423465319 * q^83 - 1042585800 * q^84 - 2101960924 * q^85 - 2597172884 * q^86 - 2135063354 * q^87 - 5542447545 * q^88 - 2765884440 * q^89 - 6736154529 * q^90 - 6821909968 * q^91 - 4167412114 * q^92 - 4756429190 * q^93 - 5116706209 * q^94 - 4295841932 * q^95 - 14387243887 * q^96 - 6239794299 * q^97 - 8201372742 * q^98 - 6380320552 * 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 $

$2$	−27.2613	−1.20479	−0.602395	−	0.798198i	$-0.705787\pi$
$2$	−27.2613	−1.20479	−0.602395	+	0.798198i	$0.705787\pi$
$3$	−2.80973	−0.0200272	−0.0100136	−	0.999950i	$-0.503187\pi$
$3$	−2.80973	−0.0200272	−0.0100136	+	0.999950i	$0.503187\pi$
$4$	231.177	0.451517
$5$	1123.40	0.803836	0.401918	−	0.915676i	$-0.368344\pi$
$5$	1123.40	0.803836	0.401918	+	0.915676i	$0.368344\pi$
$6$	76.5969	0.0241285
$7$	−8481.66	−1.33518	−0.667590	−	0.744529i	$-0.732674\pi$
$7$	−8481.66	−1.33518	−0.667590	+	0.744529i	$0.732674\pi$
$8$	7655.60	0.660806
$9$	−19675.1	−0.999599
$10$	−30625.2	−0.968453
$11$	79300.8	1.63309	0.816546	−	0.577281i	$-0.195886\pi$
$11$	79300.8	1.63309	0.816546	+	0.577281i	$0.195886\pi$
$12$	−649.546	−0.00904262
$13$	−97256.2	−0.944435	−0.472218	−	0.881482i	$-0.656546\pi$
$13$	−97256.2	−0.944435	−0.472218	+	0.881482i	$0.656546\pi$
$14$	231221.	1.60861
$15$	−3156.44	−0.0160986
$16$	−327064.	−1.24765
$17$	−37665.0	−0.109375	−0.0546875	−	0.998504i	$-0.517416\pi$
$17$	−37665.0	−0.109375	−0.0546875	+	0.998504i	$0.517416\pi$
$18$	536368.	1.20431
$19$	584746.	1.02938	0.514691	−	0.857376i	$-0.327907\pi$
$19$	584746.	1.02938	0.514691	+	0.857376i	$0.327907\pi$
$20$	259703.	0.362946
$21$	23831.2	0.0267399
$22$	−2.16184e6	−1.96753
$23$	1.46262e6	1.08982	0.544910	−	0.838495i	$-0.316564\pi$
$23$	1.46262e6	1.08982	0.544910	+	0.838495i	$0.316564\pi$
$24$	−21510.2	−0.0132341
$25$	−691109.	−0.353848
$26$	2.65133e6	1.13785
$27$	110586.	0.0400463
$28$	−1.96076e6	−0.602857
$29$	−5.08723e6	−1.33564	−0.667822	−	0.744321i	$-0.732773\pi$
$29$	−5.08723e6	−1.33564	−0.667822	+	0.744321i	$0.732773\pi$
$30$	86048.6	0.0193954
$31$	−226476.	−0.0440447	−0.0220224	−	0.999757i	$-0.507011\pi$
$31$	−226476.	−0.0440447	−0.0220224	+	0.999757i	$0.507011\pi$
$32$	4.99651e6	0.842349
$33$	−222814.	−0.0327062
$34$	1.02680e6	0.131774
$35$	−9.52825e6	−1.07327
$36$	−4.54843e6	−0.451336
$37$	7.07236e6	0.620378	0.310189	−	0.950675i	$-0.399608\pi$
$37$	7.07236e6	0.620378	0.310189	+	0.950675i	$0.399608\pi$
$38$	−1.59409e7	−1.24019
$39$	273264.	0.0189144
$40$	8.60026e6	0.531180
$41$	−2.82852e7	−1.56326	−0.781632	−	0.623740i	$-0.785613\pi$
$41$	−2.82852e7	−1.56326	−0.781632	+	0.623740i	$0.785613\pi$
$42$	−649669.	−0.0322159
$43$	2.12893e7	0.949627	0.474813	−	0.880087i	$-0.342516\pi$
$43$	2.12893e7	0.949627	0.474813	+	0.880087i	$0.342516\pi$
$44$	1.83325e7	0.737369
$45$	−2.21029e7	−0.803514
$46$	−3.98727e7	−1.31300
$47$	4.37126e6	0.130667	0.0653335	−	0.997863i	$-0.479189\pi$
$47$	4.37126e6	0.130667	0.0653335	+	0.997863i	$0.479189\pi$
$48$	918963.	0.0249869
$49$	3.15849e7	0.782704
$50$	1.88405e7	0.426312
$51$	105829.	0.00219047
$52$	−2.24834e7	−0.426429
$53$	8.42582e7	1.46680	0.733400	−	0.679797i	$-0.237932\pi$
$53$	8.42582e7	1.46680	0.733400	+	0.679797i	$0.237932\pi$
$54$	−3.01471e6	−0.0482474
$55$	8.90861e7	1.31274
$56$	−6.49321e7	−0.882295
$57$	−1.64298e6	−0.0206156
$58$	1.38684e8	1.60917
$59$	−4.99543e7	−0.536709	−0.268354	−	0.963320i	$-0.586480\pi$
$59$	−4.99543e7	−0.536709	−0.268354	+	0.963320i	$0.586480\pi$
$60$	−729696.	−0.00726878
$61$	1.38172e8	1.27772	0.638860	−	0.769323i	$-0.279406\pi$
$61$	1.38172e8	1.27772	0.638860	+	0.769323i	$0.279406\pi$
$62$	6.17401e6	0.0530646
$63$	1.66878e8	1.33464
$64$	3.12455e7	0.232797
$65$	−1.09257e8	−0.759171
$66$	6.07420e6	0.0394041
$67$	−2.30776e7	−0.139912	−0.0699559	−	0.997550i	$-0.522286\pi$
$67$	−2.30776e7	−0.139912	−0.0699559	+	0.997550i	$0.522286\pi$
$68$	−8.70728e6	−0.0493847
$69$	−4.10956e6	−0.0218260
$70$	2.59752e8	1.29306
$71$	1.47748e8	0.690018	0.345009	−	0.938599i	$-0.387876\pi$
$71$	1.47748e8	0.690018	0.345009	+	0.938599i	$0.387876\pi$
$72$	−1.50625e8	−0.660541
$73$	1.64941e8	0.679791	0.339896	−	0.940463i	$-0.389608\pi$
$73$	1.64941e8	0.679791	0.339896	+	0.940463i	$0.389608\pi$
$74$	−1.92802e8	−0.747425
$75$	1.94183e6	0.00708657
$76$	1.35180e8	0.464783
$77$	−6.72602e8	−2.18047
$78$	−7.44953e6	−0.0227878
$79$	3.82858e8	1.10590	0.552949	−	0.833215i	$-0.313502\pi$
$79$	3.82858e8	1.10590	0.552949	+	0.833215i	$0.313502\pi$
$80$	−3.67422e8	−1.00291
$81$	3.86954e8	0.998797
$82$	7.71091e8	1.88340
$83$	−4.96417e7	−0.114814	−0.0574070	−	0.998351i	$-0.518283\pi$
$83$	−4.96417e7	−0.114814	−0.0574070	+	0.998351i	$0.518283\pi$
$84$	5.50922e6	0.0120735
$85$	−4.23127e7	−0.0879196
$86$	−5.80373e8	−1.14410
$87$	1.42938e7	0.0267492
$88$	6.07095e8	1.07916
$89$	−2.48081e8	−0.419120	−0.209560	−	0.977796i	$-0.567203\pi$
$89$	−2.48081e8	−0.419120	−0.209560	+	0.977796i	$0.567203\pi$
$90$	6.02554e8	0.968065
$91$	8.24894e8	1.26099
$92$	3.38123e8	0.492073
$93$	636336.	0.000882091 0
$94$	−1.19166e8	−0.157426
$95$	6.56901e8	0.827454
$96$	−1.40389e7	−0.0168699
$97$	−1.11825e9	−1.28253	−0.641265	−	0.767319i	$-0.721590\pi$
$97$	−1.11825e9	−1.28253	−0.641265	+	0.767319i	$0.721590\pi$
$98$	−8.61045e8	−0.942993
$99$	−1.56025e9	−1.63244
$100$	−1.59768e8	−0.159768
$101$	−8.40721e7	−0.0803907	−0.0401953	−	0.999192i	$-0.512798\pi$
$101$	−8.40721e7	−0.0803907	−0.0401953	+	0.999192i	$0.512798\pi$
$102$	−2.88503e6	−0.00263906
$103$	1.40068e8	0.122623	0.0613113	−	0.998119i	$-0.480472\pi$
$103$	1.40068e8	0.122623	0.0613113	+	0.998119i	$0.480472\pi$
$104$	−7.44554e8	−0.624089
$105$	2.67719e7	0.0214945
$106$	−2.29699e9	−1.76719
$107$	1.22164e9	0.900985	0.450492	−	0.892780i	$-0.351248\pi$
$107$	1.22164e9	0.900985	0.450492	+	0.892780i	$0.351248\pi$
$108$	2.55649e7	0.0180816
$109$	−2.76698e9	−1.87753	−0.938765	−	0.344559i	$-0.888028\pi$
$109$	−2.76698e9	−1.87753	−0.938765	+	0.344559i	$0.888028\pi$
$110$	−2.42860e9	−1.58157
$111$	−1.98715e7	−0.0124244
$112$	2.77404e9	1.66584
$113$	6.64574e8	0.383434	0.191717	−	0.981450i	$-0.438594\pi$
$113$	6.64574e8	0.383434	0.191717	+	0.981450i	$0.438594\pi$
$114$	4.47898e7	0.0248374
$115$	1.64309e9	0.876037
$116$	−1.17605e9	−0.603066
$117$	1.91353e9	0.944057
$118$	1.36182e9	0.646621
$119$	3.19462e8	0.146035
$120$	−2.41644e7	−0.0106380
$121$	3.93067e9	1.66699
$122$	−3.76674e9	−1.53938
$123$	7.94740e7	0.0313078
$124$	−5.23559e7	−0.0198870
$125$	−2.97052e9	−1.08827
$126$	−4.54929e9	−1.60796
$127$	−1.43263e9	−0.488671	−0.244336	−	0.969691i	$-0.578570\pi$
$127$	−1.43263e9	−0.488671	−0.244336	+	0.969691i	$0.578570\pi$
$128$	−3.41000e9	−1.12282
$129$	−5.98172e7	−0.0190183
$130$	2.97849e9	0.914641
$131$	3.69105e9	1.09504	0.547519	−	0.836793i	$-0.315572\pi$
$131$	3.69105e9	1.09504	0.547519	+	0.836793i	$0.315572\pi$
$132$	−5.15095e7	−0.0147674
$133$	−4.95962e9	−1.37441
$134$	6.29125e8	0.168564
$135$	1.24232e8	0.0321907
$136$	−2.88348e8	−0.0722757
$137$	−3.13654e9	−0.760692	−0.380346	−	0.924844i	$-0.624195\pi$
$137$	−3.13654e9	−0.760692	−0.380346	+	0.924844i	$0.624195\pi$
$138$	1.12032e8	0.0262958
$139$	−3.50593e9	−0.796594	−0.398297	−	0.917257i	$-0.630399\pi$
$139$	−3.50593e9	−0.796594	−0.398297	+	0.917257i	$0.630399\pi$
$140$	−2.20271e9	−0.484598
$141$	−1.22821e7	−0.00261689
$142$	−4.02781e9	−0.831326
$143$	−7.71250e9	−1.54235
$144$	6.43501e9	1.24715
$145$	−5.71497e9	−1.07364
$146$	−4.49650e9	−0.819005
$147$	−8.87453e7	−0.0156753
$148$	1.63497e9	0.280112
$149$	−3.48521e9	−0.579283	−0.289641	−	0.957135i	$-0.593536\pi$
$149$	−3.48521e9	−0.579283	−0.289641	+	0.957135i	$0.593536\pi$
$150$	−5.29368e7	−0.00853782
$151$	9.00940e9	1.41026	0.705131	−	0.709077i	$-0.250888\pi$
$151$	9.00940e9	1.41026	0.705131	+	0.709077i	$0.250888\pi$
$152$	4.47658e9	0.680221
$153$	7.41063e8	0.109331
$154$	1.83360e10	2.62701
$155$	−2.54422e8	−0.0354047
$156$	6.31724e7	0.00854017
$157$	−1.39865e10	−1.83721	−0.918606	−	0.395174i	$-0.870684\pi$
$157$	−1.39865e10	−1.83721	−0.918606	+	0.395174i	$0.870684\pi$
$158$	−1.04372e10	−1.33238
$159$	−2.36743e8	−0.0293759
$160$	5.61305e9	0.677110
$161$	−1.24054e10	−1.45511
$162$	−1.05489e10	−1.20334
$163$	−9.82245e8	−0.108987	−0.0544936	−	0.998514i	$-0.517354\pi$
$163$	−9.82245e8	−0.108987	−0.0544936	+	0.998514i	$0.517354\pi$
$164$	−6.53889e9	−0.705841
$165$	−2.50308e8	−0.0262904
$166$	1.35329e9	0.138327
$167$	−1.90494e10	−1.89521	−0.947606	−	0.319441i	$-0.896505\pi$
$167$	−1.90494e10	−1.89521	−0.947606	+	0.319441i	$0.896505\pi$
$168$	1.82442e8	0.0176699
$169$	−1.14573e9	−0.108042
$170$	1.15350e9	0.105925
$171$	−1.15049e10	−1.02897
$172$	4.92159e9	0.428773
$173$	−1.55325e10	−1.31836	−0.659180	−	0.751985i	$-0.729097\pi$
$173$	−1.55325e10	−1.31836	−0.659180	+	0.751985i	$0.729097\pi$
$174$	−3.89666e8	−0.0322271
$175$	5.86175e9	0.472450
$176$	−2.59364e10	−2.03753
$177$	1.40358e8	0.0107488
$178$	6.76301e9	0.504952
$179$	−7.81980e9	−0.569321	−0.284660	−	0.958628i	$-0.591881\pi$
$179$	−7.81980e9	−0.569321	−0.284660	+	0.958628i	$0.591881\pi$
$180$	−5.10968e9	−0.362800
$181$	−2.49172e10	−1.72562	−0.862811	−	0.505527i	$-0.831298\pi$
$181$	−2.49172e10	−1.72562	−0.862811	+	0.505527i	$0.831298\pi$
$182$	−2.24877e10	−1.51923
$183$	−3.88227e8	−0.0255891
$184$	1.11972e10	0.720160
$185$	7.94505e9	0.498682
$186$	−1.73473e7	−0.00106273
$187$	−2.98687e9	−0.178619
$188$	1.01053e9	0.0589984
$189$	−9.37951e8	−0.0534690
$190$	−1.79080e10	−0.996907
$191$	1.77428e10	0.964655	0.482328	−	0.875991i	$-0.339792\pi$
$191$	1.77428e10	0.964655	0.482328	+	0.875991i	$0.339792\pi$
$192$	−8.77915e7	−0.00466226
$193$	−4.69301e9	−0.243469	−0.121735	−	0.992563i	$-0.538846\pi$
$193$	−4.69301e9	−0.243469	−0.121735	+	0.992563i	$0.538846\pi$
$194$	3.04850e10	1.54518
$195$	3.06984e8	0.0152041
$196$	7.30170e9	0.353404
$197$	−1.50614e9	−0.0712470
$197$	−1.50614e9	−0.0712470
$198$	4.25344e10	1.96674
$199$	−1.32204e10	−0.597594	−0.298797	−	0.954317i	$-0.596585\pi$
$199$	−1.32204e10	−0.597594	−0.298797	+	0.954317i	$0.596585\pi$
$200$	−5.29085e9	−0.233825
$201$	6.48420e7	0.00280204
$202$	2.29191e9	0.0968538
$203$	4.31482e10	1.78332
$204$	2.44652e7	0.000989036 0
$205$	−3.17755e10	−1.25661
$206$	−3.81842e9	−0.147734
$207$	−2.87771e10	−1.08938
$208$	3.18090e10	1.17832
$209$	4.63708e10	1.68107
$210$	−7.29835e8	−0.0258963
$211$	5.71933e10	1.98643	0.993216	−	0.116280i	$-0.0370970\pi$
$211$	5.71933e10	1.98643	0.993216	+	0.116280i	$0.0370970\pi$
$212$	1.94786e10	0.662286
$213$	−4.15134e8	−0.0138191
$214$	−3.33036e10	−1.08550
$215$	2.39163e10	0.763344
$216$	8.46600e8	0.0264629
$217$	1.92089e9	0.0588076
$218$	7.54314e10	2.26203
$219$	−4.63440e8	−0.0136143
$220$	2.05947e10	0.592724
$221$	3.66316e9	0.103298
$222$	5.41721e8	0.0149688
$223$	−5.71649e10	−1.54795	−0.773977	−	0.633214i	$-0.781735\pi$
$223$	−5.71649e10	−1.54795	−0.773977	+	0.633214i	$0.781735\pi$
$224$	−4.23787e10	−1.12469
$225$	1.35976e10	0.353706
$226$	−1.81171e10	−0.461957
$227$	−1.80488e10	−0.451163	−0.225581	−	0.974224i	$-0.572428\pi$
$227$	−1.80488e10	−0.451163	−0.225581	+	0.974224i	$0.572428\pi$
$228$	−3.79819e8	−0.00930830
$229$	5.57660e10	1.34002	0.670008	−	0.742354i	$-0.266291\pi$
$229$	5.57660e10	1.34002	0.670008	+	0.742354i	$0.266291\pi$
$230$	−4.47928e10	−1.05544
$231$	1.88983e9	0.0436687
$232$	−3.89458e10	−0.882601
$233$	−5.29219e10	−1.17634	−0.588172	−	0.808736i	$-0.700152\pi$
$233$	−5.29219e10	−1.17634	−0.588172	+	0.808736i	$0.700152\pi$
$234$	−5.21652e10	−1.13739
$235$	4.91065e9	0.105035
$236$	−1.15483e10	−0.242333
$237$	−1.07573e9	−0.0221480
$238$	−8.70894e9	−0.175942
$239$	1.79804e9	0.0356458	0.0178229	−	0.999841i	$-0.494327\pi$
$239$	1.79804e9	0.0356458	0.0178229	+	0.999841i	$0.494327\pi$
$240$	1.03236e9	0.0200854
$241$	−6.95213e10	−1.32752	−0.663760	−	0.747945i	$-0.731041\pi$
$241$	−6.95213e10	−1.32752	−0.663760	+	0.747945i	$0.731041\pi$
$242$	−1.07155e11	−2.00837
$243$	−3.26390e9	−0.0600494
$244$	3.19422e10	0.576913
$245$	3.54824e10	0.629166
$246$	−2.16656e9	−0.0377193
$247$	−5.68702e10	−0.972184
$248$	−1.73381e9	−0.0291050
$249$	1.39480e8	0.00229940
$250$	8.09801e10	1.31114
$251$	1.13858e11	1.81063	0.905317	−	0.424737i	$-0.139633\pi$
$251$	1.13858e11	1.81063	0.905317	+	0.424737i	$0.139633\pi$
$252$	3.85782e10	0.602615
$253$	1.15987e11	1.77978
$254$	3.90553e10	0.588746
$255$	1.18887e8	0.00176078
$256$	7.69634e10	1.11996
$257$	−6.07005e9	−0.0867947	−0.0433974	−	0.999058i	$-0.513818\pi$
$257$	−6.07005e9	−0.0867947	−0.0433974	+	0.999058i	$0.513818\pi$
$258$	1.63069e9	0.0229131
$259$	−5.99853e10	−0.828316
$260$	−2.52577e10	−0.342779
$261$	1.00092e11	1.33511
$262$	−1.00623e11	−1.31929
$263$	8.09083e10	1.04278	0.521390	−	0.853319i	$-0.325414\pi$
$263$	8.09083e10	1.04278	0.521390	+	0.853319i	$0.325414\pi$
$264$	−1.70578e9	−0.0216125
$265$	9.46553e10	1.17907
$266$	1.35205e11	1.65587
$267$	6.97042e8	0.00839380
$268$	−5.33501e9	−0.0631726
$269$	−7.12863e10	−0.830081	−0.415041	−	0.909803i	$-0.636233\pi$
$269$	−7.12863e10	−0.830081	−0.415041	+	0.909803i	$0.636233\pi$
$270$	−3.38671e9	−0.0387830
$271$	1.47145e11	1.65723	0.828617	−	0.559816i	$-0.189128\pi$
$271$	1.47145e11	1.65723	0.828617	+	0.559816i	$0.189128\pi$
$272$	1.23189e10	0.136462
$273$	−2.31773e9	−0.0252541
$274$	8.55062e10	0.916474
$275$	−5.48055e10	−0.577866
$276$	−9.50035e8	−0.00985482
$277$	2.60482e10	0.265839	0.132919	−	0.991127i	$-0.457565\pi$
$277$	2.60482e10	0.265839	0.132919	+	0.991127i	$0.457565\pi$
$278$	9.55762e10	0.959728
$279$	4.45593e9	0.0440271
$280$	−7.29445e10	−0.709220
$281$	−6.02508e10	−0.576480	−0.288240	−	0.957558i	$-0.593070\pi$
$281$	−6.02508e10	−0.576480	−0.288240	+	0.957558i	$0.593070\pi$
$282$	3.34825e8	0.00315280
$283$	−3.43541e10	−0.318376	−0.159188	−	0.987248i	$-0.550888\pi$
$283$	−3.43541e10	−0.318376	−0.159188	+	0.987248i	$0.550888\pi$
$284$	3.41560e10	0.311555
$285$	−1.84572e9	−0.0165716
$286$	2.10252e11	1.85821
$287$	2.39906e11	2.08724
$288$	−9.83069e10	−0.842011
$289$	−1.17169e11	−0.988037
$290$	1.55797e11	1.29351
$291$	3.14200e9	0.0256855
$292$	3.81305e10	0.306937
$293$	−7.28008e10	−0.577075	−0.288537	−	0.957469i	$-0.593169\pi$
$293$	−7.28008e10	−0.577075	−0.288537	+	0.957469i	$0.593169\pi$
$294$	2.41931e9	0.0188855
$295$	−5.61184e10	−0.431426
$296$	5.41431e10	0.409950
$297$	8.76955e9	0.0653993
$298$	9.50112e10	0.697914
$299$	−1.42248e11	−1.02926
$300$	4.48907e8	0.00319971
$301$	−1.80568e11	−1.26792
$302$	−2.45608e11	−1.69907
$303$	2.36220e8	0.00161000
$304$	−1.91249e11	−1.28431
$305$	1.55222e11	1.02708
$306$	−2.02023e10	−0.131721
$307$	6.54927e10	0.420795	0.210397	−	0.977616i	$-0.432524\pi$
$307$	6.54927e10	0.420795	0.210397	+	0.977616i	$0.432524\pi$
$308$	−1.55490e11	−0.984520
$309$	−3.93553e8	−0.00245578
$310$	6.93586e9	0.0426552
$311$	−1.93043e11	−1.17013	−0.585064	−	0.810987i	$-0.698930\pi$
$311$	−1.93043e11	−1.17013	−0.585064	+	0.810987i	$0.698930\pi$
$312$	2.09200e9	0.0124987
$313$	−2.03390e11	−1.19779	−0.598895	−	0.800828i	$-0.704393\pi$
$313$	−2.03390e11	−1.19779	−0.598895	+	0.800828i	$0.704393\pi$
$314$	3.81289e11	2.21345
$315$	1.87469e11	1.07283
$316$	8.85078e10	0.499332
$317$	−3.09712e11	−1.72263	−0.861314	−	0.508073i	$-0.830358\pi$
$317$	−3.09712e11	−1.72263	−0.861314	+	0.508073i	$0.830358\pi$
$318$	6.45392e9	0.0353917
$319$	−4.03422e11	−2.18123
$320$	3.51010e10	0.187130
$321$	−3.43249e9	−0.0180442
$322$	3.38187e11	1.75310
$323$	−2.20245e10	−0.112589
$324$	8.94549e10	0.450974
$325$	6.72146e10	0.334186
$326$	2.67772e10	0.131307
$327$	7.77448e9	0.0376016
$328$	−2.16540e11	−1.03301
$329$	−3.70755e10	−0.174464
$330$	6.82372e9	0.0316744
$331$	−3.55412e11	−1.62744	−0.813722	−	0.581255i	$-0.802562\pi$
$331$	−3.55412e11	−1.62744	−0.813722	+	0.581255i	$0.802562\pi$
$332$	−1.14760e10	−0.0518405
$333$	−1.39149e11	−0.620129
$334$	5.19312e11	2.28333
$335$	−2.59253e10	−0.112466
$336$	−7.79433e9	−0.0333620
$337$	−3.56501e10	−0.150566	−0.0752829	−	0.997162i	$-0.523986\pi$
$337$	−3.56501e10	−0.150566	−0.0752829	+	0.997162i	$0.523986\pi$
$338$	3.12340e10	0.130168
$339$	−1.86728e9	−0.00767910
$340$	−9.78172e9	−0.0396972
$341$	−1.79597e10	−0.0719291
$342$	3.13639e11	1.23969
$343$	7.43729e10	0.290129
$344$	1.62982e11	0.627519
$345$	−4.61666e9	−0.0175445
$346$	4.23436e11	1.58835
$347$	−2.35582e11	−0.872288	−0.436144	−	0.899877i	$-0.643656\pi$
$347$	−2.35582e11	−0.872288	−0.436144	+	0.899877i	$0.643656\pi$
$348$	3.30439e9	0.0120777
$349$	−1.61378e11	−0.582276	−0.291138	−	0.956681i	$-0.594034\pi$
$349$	−1.61378e11	−0.582276	−0.291138	+	0.956681i	$0.594034\pi$
$350$	−1.59799e11	−0.569203
$351$	−1.07552e10	−0.0378212
$352$	3.96227e11	1.37563
$353$	−3.84760e11	−1.31888	−0.659438	−	0.751759i	$-0.729206\pi$
$353$	−3.84760e11	−1.31888	−0.659438	+	0.751759i	$0.729206\pi$
$354$	−3.82634e9	−0.0129500
$355$	1.65980e11	0.554661
$356$	−5.73506e10	−0.189240
$357$	−8.97603e8	−0.00292467
$358$	2.13178e11	0.685912
$359$	−2.52817e11	−0.803308	−0.401654	−	0.915792i	$-0.631565\pi$
$359$	−2.52817e11	−0.803308	−0.401654	+	0.915792i	$0.631565\pi$
$360$	−1.69211e11	−0.530967
$361$	1.92403e10	0.0596253
$362$	6.79274e11	2.07901
$363$	−1.10441e10	−0.0333851
$364$	1.90696e11	0.569359
$365$	1.85294e11	0.546441
$366$	1.05836e10	0.0308295
$367$	−1.71582e11	−0.493713	−0.246856	−	0.969052i	$-0.579398\pi$
$367$	−1.71582e11	−0.493713	−0.246856	+	0.969052i	$0.579398\pi$
$368$	−4.78368e11	−1.35971
$369$	5.56515e11	1.56264
$370$	−2.16592e11	−0.600807
$371$	−7.14650e11	−1.95844
$372$	1.47106e8	0.000398279 0
$373$	−5.28558e10	−0.141385	−0.0706924	−	0.997498i	$-0.522521\pi$
$373$	−5.28558e10	−0.141385	−0.0706924	+	0.997498i	$0.522521\pi$
$374$	8.14258e10	0.215199
$375$	8.34637e9	0.0217950
$376$	3.34646e10	0.0863455
$377$	4.94765e11	1.26143
$378$	2.55697e10	0.0644189
$379$	−4.80261e11	−1.19564	−0.597821	−	0.801630i	$-0.703967\pi$
$379$	−4.80261e11	−1.19564	−0.597821	+	0.801630i	$0.703967\pi$
$380$	1.51860e11	0.373610
$381$	4.02531e9	0.00978670
$382$	−4.83691e11	−1.16221
$383$	−4.19884e11	−0.997092	−0.498546	−	0.866863i	$-0.666133\pi$
$383$	−4.19884e11	−0.997092	−0.498546	+	0.866863i	$0.666133\pi$
$384$	9.58121e9	0.0224869
$385$	−7.55598e11	−1.75274
$386$	1.27937e11	0.293329
$387$	−4.18869e11	−0.949246
$388$	−2.58515e11	−0.579085
$389$	8.83759e11	1.95686	0.978432	−	0.206569i	$-0.0662297\pi$
$389$	8.83759e11	1.95686	0.978432	+	0.206569i	$0.0662297\pi$
$390$	−8.36876e9	−0.0183177
$391$	−5.50894e10	−0.119199
$392$	2.41801e11	0.517216
$393$	−1.03709e10	−0.0219305
$394$	4.10592e10	0.0858377
$395$	4.30100e11	0.888961
$396$	−3.60694e11	−0.737073
$397$	5.53182e11	1.11766	0.558832	−	0.829281i	$-0.311250\pi$
$397$	5.53182e11	1.11766	0.558832	+	0.829281i	$0.311250\pi$
$398$	3.60405e11	0.719975
$399$	1.39352e10	0.0275255
$400$	2.26037e11	0.441478
$401$	3.82922e11	0.739538	0.369769	−	0.929124i	$-0.379437\pi$
$401$	3.82922e11	0.739538	0.369769	+	0.929124i	$0.379437\pi$
$402$	−1.76767e9	−0.00337587
$403$	2.20262e10	0.0415974
$404$	−1.94355e10	−0.0362978
$405$	4.34703e11	0.802869
$406$	−1.17627e12	−2.14853
$407$	5.60844e11	1.01313
$408$	8.10182e8	0.00144748
$409$	7.80488e11	1.37915	0.689575	−	0.724214i	$-0.257797\pi$
$409$	7.80488e11	1.37915	0.689575	+	0.724214i	$0.257797\pi$
$410$	8.66240e11	1.51395
$411$	8.81286e9	0.0152345
$412$	3.23804e10	0.0553662
$413$	4.23695e11	0.716602
$414$	7.84501e11	1.31248
$415$	−5.57672e10	−0.0922916
$416$	−4.85942e11	−0.795544
$417$	9.85074e9	0.0159535
$418$	−1.26413e12	−2.02534
$419$	−2.67523e11	−0.424032	−0.212016	−	0.977266i	$-0.568003\pi$
$419$	−2.67523e11	−0.424032	−0.212016	+	0.977266i	$0.568003\pi$
$420$	6.18904e9	0.00970513
$421$	−1.20251e11	−0.186560	−0.0932801	−	0.995640i	$-0.529735\pi$
$421$	−1.20251e11	−0.186560	−0.0932801	+	0.995640i	$0.529735\pi$
$422$	−1.55916e12	−2.39323
$423$	−8.60049e10	−0.130615
$424$	6.45047e11	0.969271
$425$	2.60306e10	0.0387021
$426$	1.13171e10	0.0166491
$427$	−1.17193e12	−1.70599
$428$	2.82416e11	0.406810
$429$	2.16701e10	0.0308889
$430$	−6.51988e11	−0.919669
$431$	5.43676e10	0.0758914	0.0379457	−	0.999280i	$-0.487919\pi$
$431$	5.43676e10	0.0758914	0.0379457	+	0.999280i	$0.487919\pi$
$432$	−3.61686e10	−0.0499638
$433$	7.13709e11	0.975721	0.487860	−	0.872922i	$-0.337777\pi$
$433$	7.13709e11	0.975721	0.487860	+	0.872922i	$0.337777\pi$
$434$	−5.23659e10	−0.0708508
$435$	1.60576e10	0.0215019
$436$	−6.39662e11	−0.847737
$437$	8.55259e11	1.12184
$438$	1.26340e10	0.0164024
$439$	−3.91017e10	−0.0502464	−0.0251232	−	0.999684i	$-0.507998\pi$
$439$	−3.91017e10	−0.0502464	−0.0251232	+	0.999684i	$0.507998\pi$
$440$	6.82007e11	0.867465
$441$	−6.21437e11	−0.782390
$442$	−9.98623e10	−0.124452
$443$	9.76650e10	0.120482	0.0602410	−	0.998184i	$-0.480813\pi$
$443$	9.76650e10	0.120482	0.0602410	+	0.998184i	$0.480813\pi$
$444$	−4.59382e9	−0.00560984
$445$	−2.78693e11	−0.336904
$446$	1.55839e12	1.86496
$447$	9.79251e9	0.0116014
$448$	−2.65013e11	−0.310826
$449$	−4.90259e11	−0.569268	−0.284634	−	0.958636i	$-0.591872\pi$
$449$	−4.90259e11	−0.569268	−0.284634	+	0.958636i	$0.591872\pi$
$450$	−3.70689e11	−0.426141
$451$	−2.24304e12	−2.55295
$452$	1.53634e11	0.173127
$453$	−2.53140e10	−0.0282436
$454$	4.92035e11	0.543556
$455$	9.26682e11	1.01363
$456$	−1.25780e10	−0.0136229
$457$	1.12239e12	1.20371	0.601855	−	0.798606i	$-0.294429\pi$
$457$	1.12239e12	1.20371	0.601855	+	0.798606i	$0.294429\pi$
$458$	−1.52025e12	−1.61444
$459$	−4.16522e9	−0.00438007
$460$	3.79845e11	0.395546
$461$	−5.53487e11	−0.570759	−0.285380	−	0.958415i	$-0.592120\pi$
$461$	−5.53487e11	−0.570759	−0.285380	+	0.958415i	$0.592120\pi$
$462$	−5.15193e10	−0.0526115
$463$	−1.15064e12	−1.16366	−0.581829	−	0.813311i	$-0.697663\pi$
$463$	−1.15064e12	−1.16366	−0.581829	+	0.813311i	$0.697663\pi$
$464$	1.66385e12	1.66641
$465$	7.14857e8	0.000709057 0
$466$	1.44272e12	1.41725
$467$	−1.20682e12	−1.17413	−0.587067	−	0.809538i	$-0.699718\pi$
$467$	−1.20682e12	−1.17413	−0.587067	+	0.809538i	$0.699718\pi$
$468$	4.42363e11	0.426258
$469$	1.95736e11	0.186807
$470$	−1.33870e11	−0.126545
$471$	3.92982e10	0.0367942
$472$	−3.82430e11	−0.354660
$473$	1.68826e12	1.55083
$474$	2.93257e10	0.0266837
$475$	−4.04123e11	−0.364244
$476$	7.38522e10	0.0659375
$477$	−1.65779e12	−1.46621
$478$	−4.90167e10	−0.0429456
$479$	−5.88600e11	−0.510870	−0.255435	−	0.966826i	$-0.582219\pi$
$479$	−5.88600e11	−0.510870	−0.255435	+	0.966826i	$0.582219\pi$
$480$	−1.57712e10	−0.0135606
$481$	−6.87831e11	−0.585907
$482$	1.89524e12	1.59938
$483$	3.48559e10	0.0291416
$484$	9.08680e11	0.752674
$485$	−1.25624e12	−1.03094
$486$	8.89781e10	0.0723469
$487$	8.90630e11	0.717492	0.358746	−	0.933435i	$-0.383204\pi$
$487$	8.90630e11	0.717492	0.358746	+	0.933435i	$0.383204\pi$
$488$	1.05779e12	0.844325
$489$	2.75985e9	0.00218271
$490$	−9.67294e11	−0.758012
$491$	−1.75078e11	−0.135946	−0.0679729	−	0.997687i	$-0.521653\pi$
$491$	−1.75078e11	−0.135946	−0.0679729	+	0.997687i	$0.521653\pi$
$492$	1.83726e10	0.0141360
$493$	1.91611e11	0.146086
$494$	1.55035e12	1.17128
$495$	−1.75278e12	−1.31221
$496$	7.40720e10	0.0549524
$497$	−1.25315e12	−0.921298
$498$	−3.80240e9	−0.00277029
$499$	2.13513e12	1.54160	0.770801	−	0.637076i	$-0.219856\pi$
$499$	2.13513e12	1.54160	0.770801	+	0.637076i	$0.219856\pi$
$500$	−6.86715e11	−0.491373
$501$	5.35239e10	0.0379558
$502$	−3.10391e12	−2.18143
$503$	−1.85502e12	−1.29209	−0.646044	−	0.763300i	$-0.723578\pi$
$503$	−1.85502e12	−1.29209	−0.646044	+	0.763300i	$0.723578\pi$
$504$	1.27755e12	0.881941
$505$	−9.44462e10	−0.0646209
$506$	−3.16194e12	−2.14425
$507$	3.21919e9	0.00216377
$508$	−3.31191e11	−0.220644
$509$	−6.25773e11	−0.413225	−0.206613	−	0.978423i	$-0.566244\pi$
$509$	−6.25773e11	−0.413225	−0.206613	+	0.978423i	$0.566244\pi$
$510$	−3.24102e9	−0.00212137
$511$	−1.39897e12	−0.907643
$512$	−3.52197e11	−0.226501
$513$	6.46646e10	0.0412229
$514$	1.65477e11	0.104569
$515$	1.57351e11	0.0985685
$516$	−1.38284e10	−0.00858711
$517$	3.46644e11	0.213391
$518$	1.63528e12	0.997947
$519$	4.36422e10	0.0264030
$520$	−8.36429e11	−0.501665
$521$	−7.06921e11	−0.420341	−0.210170	−	0.977665i	$-0.567402\pi$
$521$	−7.06921e11	−0.420341	−0.210170	+	0.977665i	$0.567402\pi$
$522$	−2.72863e12	−1.60852
$523$	8.82998e11	0.516062	0.258031	−	0.966137i	$-0.416926\pi$
$523$	8.82998e11	0.516062	0.258031	+	0.966137i	$0.416926\pi$
$524$	8.53286e11	0.494429
$525$	−1.64700e10	−0.00946184
$526$	−2.20566e12	−1.25633
$527$	8.53021e9	0.00481739
$528$	7.28745e10	0.0408059
$529$	3.38090e11	0.187708
$530$	−2.58042e12	−1.42053
$531$	9.82856e11	0.536493
$532$	−1.14655e12	−0.620569
$533$	2.75092e12	1.47640
$534$	−1.90023e10	−0.0101128
$535$	1.37239e12	0.724244
$536$	−1.76673e11	−0.0924546
$537$	2.19716e10	0.0114019
$538$	1.94335e12	1.00007
$539$	2.50471e12	1.27823
$540$	2.87195e10	0.0145346
$541$	1.66056e12	0.833427	0.416713	−	0.909038i	$-0.363182\pi$
$541$	1.66056e12	0.833427	0.416713	+	0.909038i	$0.363182\pi$
$542$	−4.01136e12	−1.99662
$543$	7.00107e10	0.0345593
$544$	−1.88194e11	−0.0921319
$545$	−3.10841e12	−1.50923
$546$	6.31844e10	0.0304258
$547$	−2.25202e12	−1.07555	−0.537773	−	0.843090i	$-0.680734\pi$
$547$	−2.25202e12	−1.07555	−0.537773	+	0.843090i	$0.680734\pi$
$548$	−7.25096e11	−0.343466
$549$	−2.71855e12	−1.27721
$550$	1.49407e12	0.696206
$551$	−2.97474e12	−1.37489
$552$	−3.14611e10	−0.0144228
$553$	−3.24727e12	−1.47657
$554$	−7.10106e11	−0.320279
$555$	−2.23235e10	−0.00998720
$556$	−8.10491e11	−0.359676
$557$	2.43310e12	1.07105	0.535527	−	0.844518i	$-0.320113\pi$
$557$	2.43310e12	1.07105	0.535527	+	0.844518i	$0.320113\pi$
$558$	−1.21474e11	−0.0530433
$559$	−2.07051e12	−0.896861
$560$	3.11635e12	1.33906
$561$	8.39230e9	0.00357724
$562$	1.64251e12	0.694537
$563$	−1.87650e12	−0.787154	−0.393577	−	0.919292i	$-0.628763\pi$
$563$	−1.87650e12	−0.787154	−0.393577	+	0.919292i	$0.628763\pi$
$564$	−2.83933e9	−0.00118157
$565$	7.46579e11	0.308218
$566$	9.36536e11	0.383575
$567$	−3.28202e12	−1.33357
$568$	1.13110e12	0.455968
$569$	6.80557e11	0.272182	0.136091	−	0.990696i	$-0.456546\pi$
$569$	6.80557e11	0.272182	0.136091	+	0.990696i	$0.456546\pi$
$570$	5.03166e10	0.0199652
$571$	−1.66287e12	−0.654628	−0.327314	−	0.944916i	$-0.606143\pi$
$571$	−1.66287e12	−0.654628	−0.327314	+	0.944916i	$0.606143\pi$
$572$	−1.78295e12	−0.696397
$573$	−4.98526e10	−0.0193193
$574$	−6.54013e12	−2.51468
$575$	−1.01083e12	−0.385630
$576$	−6.14758e11	−0.232703
$577$	2.72131e12	1.02208	0.511042	−	0.859556i	$-0.329260\pi$
$577$	2.72131e12	1.02208	0.511042	+	0.859556i	$0.329260\pi$
$578$	3.19418e12	1.19038
$579$	1.31861e10	0.00487600
$580$	−1.32117e12	−0.484766
$581$	4.21044e11	0.153297
$582$	−8.56549e10	−0.0309456
$583$	6.68175e12	2.39542
$584$	1.26272e12	0.449210
$585$	2.14965e12	0.758867
$586$	1.98464e12	0.695253
$587$	4.16725e12	1.44870	0.724349	−	0.689433i	$-0.242140\pi$
$587$	4.16725e12	1.44870	0.724349	+	0.689433i	$0.242140\pi$
$588$	−2.05159e10	−0.00707769
$589$	−1.32431e11	−0.0453388
$590$	1.52986e12	0.519777
$591$	4.23185e9	0.00142688
$592$	−2.31311e12	−0.774015
$593$	−3.32259e11	−0.110339	−0.0551696	−	0.998477i	$-0.517570\pi$
$593$	−3.32259e11	−0.110339	−0.0551696	+	0.998477i	$0.517570\pi$
$594$	−2.39069e11	−0.0787924
$595$	3.58882e11	0.117388
$596$	−8.05700e11	−0.261556
$597$	3.71459e10	0.0119681
$598$	3.87787e12	1.24005
$599$	3.49811e12	1.11023	0.555115	−	0.831773i	$-0.312674\pi$
$599$	3.49811e12	1.11023	0.555115	+	0.831773i	$0.312674\pi$
$600$	1.48659e10	0.00468285
$601$	4.68251e12	1.46401	0.732004	−	0.681301i	$-0.238585\pi$
$601$	4.68251e12	1.46401	0.732004	+	0.681301i	$0.238585\pi$
$602$	4.92252e12	1.52758
$603$	4.54054e11	0.139856
$604$	2.08277e12	0.636758
$605$	4.41570e12	1.33998
$606$	−6.43967e9	−0.00193971
$607$	−3.49070e12	−1.04367	−0.521836	−	0.853046i	$-0.674753\pi$
$607$	−3.49070e12	−1.04367	−0.521836	+	0.853046i	$0.674753\pi$
$608$	2.92169e12	0.867098
$609$	−1.21235e11	−0.0357149
$610$	−4.23154e12	−1.23741
$611$	−4.25132e11	−0.123407
$612$	1.71317e11	0.0493649
$613$	3.63680e12	1.04027	0.520136	−	0.854084i	$-0.325881\pi$
$613$	3.63680e12	1.04027	0.520136	+	0.854084i	$0.325881\pi$
$614$	−1.78542e12	−0.506969
$615$	8.92807e10	0.0251663
$616$	−5.14917e12	−1.44087
$617$	6.36043e11	0.176686	0.0883432	−	0.996090i	$-0.471843\pi$
$617$	6.36043e11	0.176686	0.0883432	+	0.996090i	$0.471843\pi$
$618$	1.07288e10	0.00295870
$619$	1.92995e12	0.528369	0.264185	−	0.964472i	$-0.414897\pi$
$619$	1.92995e12	0.528369	0.264185	+	0.964472i	$0.414897\pi$
$620$	−5.88164e10	−0.0159858
$621$	1.61745e11	0.0436433
$622$	5.26261e12	1.40976
$623$	2.10414e12	0.559601
$624$	−8.93748e10	−0.0235985
$625$	−1.98724e12	−0.520944
$626$	5.54468e12	1.44308
$627$	−1.30290e11	−0.0336671
$628$	−3.23335e12	−0.829533
$629$	−2.66381e11	−0.0678539
$630$	−5.11065e12	−1.29254
$631$	−3.98525e11	−0.100075	−0.0500373	−	0.998747i	$-0.515934\pi$
$631$	−3.98525e11	−0.100075	−0.0500373	+	0.998747i	$0.515934\pi$
$632$	2.93100e12	0.730785
$633$	−1.60698e11	−0.0397826
$634$	8.44315e12	2.07540
$635$	−1.60941e12	−0.392812
$636$	−5.47296e10	−0.0132637
$637$	−3.07183e12	−0.739213
$638$	1.09978e13	2.62792
$639$	−2.90697e12	−0.689741
$640$	−3.83078e12	−0.902563
$641$	−5.02329e12	−1.17524	−0.587621	−	0.809136i	$-0.699935\pi$
$641$	−5.02329e12	−1.17524	−0.587621	+	0.809136i	$0.699935\pi$
$642$	9.35742e10	0.0217394
$643$	5.97878e10	0.0137931	0.00689657	−	0.999976i	$-0.497805\pi$
$643$	5.97878e10	0.0137931	0.00689657	+	0.999976i	$0.497805\pi$
$644$	−2.86784e12	−0.657005
$645$	−6.71984e10	−0.0152876
$646$	6.00415e11	0.135646
$647$	−7.37249e12	−1.65404	−0.827018	−	0.562176i	$-0.809964\pi$
$647$	−7.37249e12	−1.65404	−0.827018	+	0.562176i	$0.809964\pi$
$648$	2.96237e12	0.660011
$649$	−3.96141e12	−0.876494
$650$	−1.83236e12	−0.402624
$651$	−5.39719e9	−0.00117775
$652$	−2.27072e11	−0.0492096
$653$	8.15737e12	1.75566	0.877831	−	0.478971i	$-0.158990\pi$
$653$	8.15737e12	1.75566	0.877831	+	0.478971i	$0.158990\pi$
$654$	−2.11942e11	−0.0453020
$655$	4.14651e12	0.880232
$656$	9.25108e12	1.95041
$657$	−3.24523e12	−0.679519
$658$	1.01073e12	0.210192
$659$	6.17339e12	1.27508	0.637542	−	0.770415i	$-0.279951\pi$
$659$	6.17339e12	1.27508	0.637542	+	0.770415i	$0.279951\pi$
$660$	−5.78655e10	−0.0118706
$661$	−1.02154e12	−0.208136	−0.104068	−	0.994570i	$-0.533186\pi$
$661$	−1.02154e12	−0.208136	−0.104068	+	0.994570i	$0.533186\pi$
$662$	9.68898e12	1.96073
$663$	−1.02925e10	−0.00206876
$664$	−3.80036e11	−0.0758698
$665$	−5.57161e12	−1.10480
$666$	3.79339e12	0.747125
$667$	−7.44066e12	−1.45561
$668$	−4.40379e12	−0.855721
$669$	1.60618e11	0.0310011
$670$	7.06756e11	0.135498
$671$	1.09572e13	2.08663
$672$	1.19073e11	0.0225243
$673$	−8.94337e12	−1.68048	−0.840241	−	0.542214i	$-0.817586\pi$
$673$	−8.94337e12	−1.68048	−0.840241	+	0.542214i	$0.817586\pi$
$674$	9.71867e11	0.181400
$675$	−7.64268e10	−0.0141703
$676$	−2.64866e11	−0.0487827
$677$	−6.62513e12	−1.21212	−0.606060	−	0.795419i	$-0.707251\pi$
$677$	−6.62513e12	−1.21212	−0.606060	+	0.795419i	$0.707251\pi$
$678$	5.09044e10	0.00925169
$679$	9.48465e12	1.71241
$680$	−3.23929e11	−0.0580978
$681$	5.07125e10	0.00903551
$682$	4.89604e11	0.0866594
$683$	−4.28043e11	−0.0752653	−0.0376326	−	0.999292i	$-0.511982\pi$
$683$	−4.28043e11	−0.0752653	−0.0376326	+	0.999292i	$0.511982\pi$
$684$	−2.65968e12	−0.464597
$685$	−3.52358e12	−0.611472
$686$	−2.02750e12	−0.349545
$687$	−1.56688e11	−0.0268367
$688$	−6.96295e12	−1.18480
$689$	−8.19464e12	−1.38530
$690$	1.25856e11	0.0211375
$691$	2.03772e12	0.340012	0.170006	−	0.985443i	$-0.445621\pi$
$691$	2.03772e12	0.340012	0.170006	+	0.985443i	$0.445621\pi$
$692$	−3.59076e12	−0.595263
$693$	1.32335e13	2.17960
$694$	6.42227e12	1.05092
$695$	−3.93855e12	−0.640331
$696$	1.09427e11	0.0176760
$697$	1.06536e12	0.170982
$698$	4.39936e12	0.701520
$699$	1.48697e11	0.0235588
$700$	1.35510e12	0.213319
$701$	9.06293e12	1.41755	0.708774	−	0.705436i	$-0.249249\pi$
$701$	9.06293e12	1.41755	0.708774	+	0.705436i	$0.249249\pi$
$702$	2.93199e11	0.0455665
$703$	4.13553e12	0.638606
$704$	2.47779e12	0.380179
$705$	−1.37976e10	−0.00210355
$706$	1.04891e13	1.58897
$707$	7.13071e11	0.107336
$708$	3.24476e10	0.00485325
$709$	−1.97637e12	−0.293738	−0.146869	−	0.989156i	$-0.546920\pi$
$709$	−1.97637e12	−0.293738	−0.146869	+	0.989156i	$0.546920\pi$
$710$	−4.52482e12	−0.668250
$711$	−7.53276e12	−1.10546
$712$	−1.89921e12	−0.276957
$713$	−3.31247e11	−0.0480008
$714$	2.44698e10	0.00352362
$715$	−8.66418e12	−1.23980
$716$	−1.80776e12	−0.257058
$717$	−5.05200e9	−0.000713884 0
$718$	6.89213e12	0.967817
$719$	−1.30533e12	−0.182154	−0.0910771	−	0.995844i	$-0.529031\pi$
$719$	−1.30533e12	−0.182154	−0.0910771	+	0.995844i	$0.529031\pi$
$720$	7.22906e12	1.00250
$721$	−1.18801e12	−0.163723
$722$	−5.24516e11	−0.0718359
$723$	1.95336e11	0.0265865
$724$	−5.76028e12	−0.779148
$725$	3.51583e12	0.472614
$726$	3.01077e11	0.0402220
$727$	1.26168e13	1.67511	0.837557	−	0.546350i	$-0.183983\pi$
$727$	1.26168e13	1.67511	0.837557	+	0.546350i	$0.183983\pi$
$728$	6.31505e12	0.833270
$729$	−7.60725e12	−0.997594
$730$	−5.05134e12	−0.658346
$731$	−8.01861e11	−0.103865
$732$	−8.97490e10	−0.0115539
$733$	−1.05610e13	−1.35125	−0.675627	−	0.737243i	$-0.736127\pi$
$733$	−1.05610e13	−1.35125	−0.675627	+	0.737243i	$0.736127\pi$
$734$	4.67754e12	0.594820
$735$	−9.96960e10	−0.0126004
$736$	7.30797e12	0.918008
$737$	−1.83007e12	−0.228489
$738$	−1.51713e13	−1.88265
$739$	3.02384e12	0.372957	0.186479	−	0.982459i	$-0.440293\pi$
$739$	3.02384e12	0.372957	0.186479	+	0.982459i	$0.440293\pi$
$740$	1.83671e12	0.225164
$741$	1.59790e11	0.0194701
$742$	1.94823e13	2.35951
$743$	1.45200e13	1.74790	0.873952	−	0.486012i	$-0.161549\pi$
$743$	1.45200e13	1.74790	0.873952	+	0.486012i	$0.161549\pi$
$744$	4.87153e9	0.000582891 0
$745$	−3.91527e12	−0.465648
$746$	1.44091e12	0.170339
$747$	9.76705e11	0.114768
$748$	−6.90495e11	−0.0806498
$749$	−1.03616e13	−1.20298
$750$	−2.27533e11	−0.0262584
$751$	4.67153e12	0.535895	0.267948	−	0.963434i	$-0.413655\pi$
$751$	4.67153e12	0.535895	0.267948	+	0.963434i	$0.413655\pi$
$752$	−1.42968e12	−0.163027
$753$	−3.19910e11	−0.0362619
$754$	−1.34879e13	−1.51976
$755$	1.01211e13	1.13362
$756$	−2.16833e11	−0.0241422
$757$	5.33315e12	0.590272	0.295136	−	0.955455i	$-0.404635\pi$
$757$	5.33315e12	0.590272	0.295136	+	0.955455i	$0.404635\pi$
$758$	1.30925e13	1.44050
$759$	−3.25891e11	−0.0356439
$760$	5.02897e12	0.546786
$761$	−2.66730e12	−0.288298	−0.144149	−	0.989556i	$-0.546044\pi$
$761$	−2.66730e12	−0.288298	−0.144149	+	0.989556i	$0.546044\pi$
$762$	−1.09735e11	−0.0117909
$763$	2.34686e13	2.50684
$764$	4.10173e12	0.435558
$765$	8.32507e11	0.0878843
$766$	1.14466e13	1.20129
$767$	4.85836e12	0.506887
$768$	−2.16247e11	−0.0224297
$769$	−1.16350e13	−1.19977	−0.599883	−	0.800087i	$-0.704786\pi$
$769$	−1.16350e13	−1.19977	−0.599883	+	0.800087i	$0.704786\pi$
$770$	2.05986e13	2.11168
$771$	1.70552e10	0.00173825
$772$	−1.08492e12	−0.109930
$773$	−5.34961e12	−0.538908	−0.269454	−	0.963013i	$-0.586843\pi$
$773$	−5.34961e12	−0.538908	−0.269454	+	0.963013i	$0.586843\pi$
$774$	1.14189e13	1.14364
$775$	1.56519e11	0.0155851
$776$	−8.56090e12	−0.847504
$777$	1.68543e11	0.0165888
$778$	−2.40924e13	−2.35761
$779$	−1.65397e13	−1.60919
$780$	7.09675e10	0.00686489
$781$	1.17166e13	1.12686
$782$	1.50181e12	0.143610
$783$	−5.62576e11	−0.0534876
$784$	−1.03303e13	−0.976540
$785$	−1.57123e13	−1.47682
$786$	2.82723e11	0.0264217
$787$	−1.16579e13	−1.08326	−0.541632	−	0.840615i	$-0.682194\pi$
$787$	−1.16579e13	−1.08326	−0.541632	+	0.840615i	$0.682194\pi$
$788$	−3.48184e11	−0.0321693
$789$	−2.27331e11	−0.0208839
$790$	−1.17251e13	−1.07101
$791$	−5.63669e12	−0.511953
$792$	−1.19447e13	−1.07872
$793$	−1.34381e13	−1.20672
$794$	−1.50805e13	−1.34655
$795$	−2.65956e11	−0.0236134
$796$	−3.05625e12	−0.269824
$797$	−1.16078e13	−1.01903	−0.509514	−	0.860463i	$-0.670175\pi$
$797$	−1.16078e13	−1.01903	−0.509514	+	0.860463i	$0.670175\pi$
$798$	−3.79891e11	−0.0331624
$799$	−1.64643e11	−0.0142917
$800$	−3.45313e12	−0.298063
$801$	4.88102e12	0.418952
$802$	−1.04389e13	−0.890988
$803$	1.30799e13	1.11016
$804$	1.49900e10	0.00126517
$805$	−1.39362e13	−1.16967
$806$	−6.00461e11	−0.0501161
$807$	2.00296e11	0.0166242
$808$	−6.43622e11	−0.0531227
$809$	3.30393e12	0.271183	0.135591	−	0.990765i	$-0.456707\pi$
$809$	3.30393e12	0.271183	0.135591	+	0.990765i	$0.456707\pi$
$810$	−1.18505e13	−0.967288
$811$	−3.66102e12	−0.297172	−0.148586	−	0.988899i	$-0.547472\pi$
$811$	−3.66102e12	−0.297172	−0.148586	+	0.988899i	$0.547472\pi$
$812$	9.97486e12	0.805201
$813$	−4.13438e11	−0.0331897
$814$	−1.52893e13	−1.22061
$815$	−1.10345e12	−0.0876078
$816$	−3.46128e10	−0.00273294
$817$	1.24488e13	0.977528
$818$	−2.12771e13	−1.66159
$819$	−1.62299e13	−1.26048
$820$	−7.34576e12	−0.567380
$821$	1.09783e13	0.843321	0.421660	−	0.906754i	$-0.361447\pi$
$821$	1.09783e13	0.843321	0.421660	+	0.906754i	$0.361447\pi$
$822$	−2.40250e11	−0.0183544
$823$	−1.81105e13	−1.37604	−0.688019	−	0.725693i	$-0.741519\pi$
$823$	−1.81105e13	−1.37604	−0.688019	+	0.725693i	$0.741519\pi$
$824$	1.07230e12	0.0810298
$825$	1.53989e11	0.0115730
$826$	−1.15505e13	−0.863355
$827$	−5.02389e12	−0.373478	−0.186739	−	0.982410i	$-0.559792\pi$
$827$	−5.02389e12	−0.373478	−0.186739	+	0.982410i	$0.559792\pi$
$828$	−6.65260e12	−0.491875
$829$	2.49772e13	1.83674	0.918371	−	0.395721i	$-0.129505\pi$
$829$	2.49772e13	1.83674	0.918371	+	0.395721i	$0.129505\pi$
$830$	1.52028e12	0.111192
$831$	−7.31884e10	−0.00532400
$832$	−3.03882e12	−0.219862
$833$	−1.18965e12	−0.0856083
$834$	−2.68544e11	−0.0192206
$835$	−2.14000e13	−1.52344
$836$	1.07199e13	0.759034
$837$	−2.50450e10	−0.00176383
$838$	7.29302e12	0.510869
$839$	−1.68612e13	−1.17479	−0.587393	−	0.809302i	$-0.699846\pi$
$839$	−1.68612e13	−1.17479	−0.587393	+	0.809302i	$0.699846\pi$
$840$	2.04955e11	0.0142037
$841$	1.13728e13	0.783944
$842$	3.27819e12	0.224766
$843$	1.69289e11	0.0115453
$844$	1.32218e13	0.896909
$845$	−1.28711e12	−0.0868479
$846$	2.34460e12	0.157363
$847$	−3.33386e13	−2.22573
$848$	−2.75578e13	−1.83005
$849$	9.65259e10	0.00637616
$850$	−7.09628e11	−0.0466279
$851$	1.03441e13	0.676101
$852$	−9.59694e10	−0.00623957
$853$	−2.96077e12	−0.191485	−0.0957424	−	0.995406i	$-0.530523\pi$
$853$	−2.96077e12	−0.191485	−0.0957424	+	0.995406i	$0.530523\pi$
$854$	3.19482e13	2.05535
$855$	−1.29246e13	−0.827122
$856$	9.35241e12	0.595376
$857$	−2.12923e13	−1.34837	−0.674186	−	0.738562i	$-0.735505\pi$
$857$	−2.12923e13	−1.34837	−0.674186	+	0.738562i	$0.735505\pi$
$858$	−5.90754e11	−0.0372146
$859$	1.10479e13	0.692325	0.346163	−	0.938174i	$-0.387485\pi$
$859$	1.10479e13	0.692325	0.346163	+	0.938174i	$0.387485\pi$
$860$	5.52889e12	0.344663
$861$	−6.74071e11	−0.0418015
$862$	−1.48213e12	−0.0914332
$863$	−5.45410e12	−0.334714	−0.167357	−	0.985896i	$-0.553523\pi$
$863$	−5.45410e12	−0.334714	−0.167357	+	0.985896i	$0.553523\pi$
$864$	5.52543e11	0.0337330
$865$	−1.74491e13	−1.05975
$866$	−1.94566e13	−1.17554
$867$	3.29214e11	0.0197876
$868$	4.44065e11	0.0265526
$869$	3.03609e13	1.80603
$870$	−4.37749e11	−0.0259053
$871$	2.24444e12	0.132138
$872$	−2.11829e13	−1.24068
$873$	2.20018e13	1.28202
$874$	−2.33154e13	−1.35158
$875$	2.51949e13	1.45304
$876$	−1.07137e11	−0.00614709
$877$	−6.93874e12	−0.396079	−0.198040	−	0.980194i	$-0.563458\pi$
$877$	−6.93874e12	−0.396079	−0.198040	+	0.980194i	$0.563458\pi$
$878$	1.06596e12	0.0605363
$879$	2.04551e11	0.0115572
$880$	−2.91368e13	−1.63784
$881$	−1.10273e13	−0.616705	−0.308352	−	0.951272i	$-0.599778\pi$
$881$	−1.10273e13	−0.616705	−0.308352	+	0.951272i	$0.599778\pi$
$882$	1.69412e13	0.942615
$883$	−1.09368e13	−0.605434	−0.302717	−	0.953081i	$-0.597894\pi$
$883$	−1.09368e13	−0.605434	−0.302717	+	0.953081i	$0.597894\pi$
$884$	8.46837e11	0.0466407
$885$	1.57678e11	0.00864024
$886$	−2.66247e12	−0.145155
$887$	−2.59031e13	−1.40506	−0.702532	−	0.711653i	$-0.747947\pi$
$887$	−2.59031e13	−1.40506	−0.702532	+	0.711653i	$0.747947\pi$
$888$	−1.52128e11	−0.00821014
$889$	1.21511e13	0.652464
$890$	7.59753e12	0.405898
$891$	3.06858e13	1.63113
$892$	−1.32152e13	−0.698928
$893$	2.55608e12	0.134506
$894$	−2.66956e11	−0.0139772
$895$	−8.78473e12	−0.457641
$896$	2.89225e13	1.49917
$897$	3.99680e11	0.0206133
$898$	1.33651e13	0.685848
$899$	1.15213e12	0.0588280
$900$	3.14346e12	0.159704
$901$	−3.17359e12	−0.160431
$902$	6.11482e13	3.07577
$903$	5.07349e11	0.0253929
$904$	5.08771e12	0.253375
$905$	−2.79919e13	−1.38712
$906$	6.90093e11	0.0340275
$907$	−1.56389e12	−0.0767316	−0.0383658	−	0.999264i	$-0.512215\pi$
$907$	−1.56389e12	−0.0767316	−0.0383658	+	0.999264i	$0.512215\pi$
$908$	−4.17248e12	−0.203708
$909$	1.65413e12	0.0803585
$910$	−2.52625e13	−1.22121
$911$	2.44644e13	1.17680	0.588398	−	0.808571i	$-0.299759\pi$
$911$	2.44644e13	1.17680	0.588398	+	0.808571i	$0.299759\pi$
$912$	5.37360e11	0.0257210
$913$	−3.93662e12	−0.187502
$914$	−3.05978e13	−1.45022
$915$	−4.36132e11	−0.0205695
$916$	1.28918e13	0.605040
$917$	−3.13063e13	−1.46207
$918$	1.13549e11	0.00527706
$919$	−9.29278e12	−0.429760	−0.214880	−	0.976640i	$-0.568936\pi$
$919$	−9.29278e12	−0.429760	−0.214880	+	0.976640i	$0.568936\pi$
$920$	1.25789e13	0.578890
$921$	−1.84017e11	−0.00842733
$922$	1.50888e13	0.687645
$923$	−1.43695e13	−0.651678
$924$	4.36886e11	0.0197172
$925$	−4.88777e12	−0.219519
$926$	3.13679e13	1.40196
$927$	−2.75585e12	−0.122573
$928$	−2.54184e13	−1.12508
$929$	3.95256e12	0.174104	0.0870518	−	0.996204i	$-0.472255\pi$
$929$	3.95256e12	0.174104	0.0870518	+	0.996204i	$0.472255\pi$
$930$	−1.94879e10	−0.000854264 0
$931$	1.84692e13	0.805701
$932$	−1.22343e13	−0.531139
$933$	5.42401e11	0.0234343
$934$	3.28996e13	1.41459
$935$	−3.35543e12	−0.143581
$936$	1.46492e13	0.623838
$937$	3.11102e12	0.131848	0.0659242	−	0.997825i	$-0.479000\pi$
$937$	3.11102e12	0.131848	0.0659242	+	0.997825i	$0.479000\pi$
$938$	−5.33602e12	−0.225063
$939$	5.71473e11	0.0239884
$940$	1.13523e12	0.0474250
$941$	−2.78496e13	−1.15789	−0.578943	−	0.815368i	$-0.696534\pi$
$941$	−2.78496e13	−1.15789	−0.578943	+	0.815368i	$0.696534\pi$
$942$	−1.07132e12	−0.0443292
$943$	−4.13704e13	−1.70368
$944$	1.63382e13	0.669624
$945$	−1.05369e12	−0.0429803
$946$	−4.60240e13	−1.86842
$947$	4.90336e12	0.198116	0.0990578	−	0.995082i	$-0.468417\pi$
$947$	4.90336e12	0.198116	0.0990578	+	0.995082i	$0.468417\pi$
$948$	−2.48684e11	−0.0100002
$949$	−1.60415e13	−0.642019
$950$	1.10169e13	0.438837
$951$	8.70209e11	0.0344994
$952$	2.44567e12	0.0965010
$953$	3.31980e13	1.30375	0.651875	−	0.758327i	$-0.273983\pi$
$953$	3.31980e13	1.30375	0.651875	+	0.758327i	$0.273983\pi$
$954$	4.51935e13	1.76648
$955$	1.99322e13	0.775425
$956$	4.15664e11	0.0160947
$957$	1.13351e12	0.0436838
$958$	1.60460e13	0.615490
$959$	2.66031e13	1.01566
$960$	−9.86245e10	−0.00374769
$961$	−2.63883e13	−0.998060
$962$	1.87511e13	0.705895
$963$	−2.40360e13	−0.900624
$964$	−1.60717e13	−0.599399
$965$	−5.27211e12	−0.195709
$966$	−9.50216e11	−0.0351095
$967$	−4.01878e13	−1.47800	−0.739001	−	0.673704i	$-0.764702\pi$
$967$	−4.01878e13	−1.47800	−0.739001	+	0.673704i	$0.764702\pi$
$968$	3.00916e13	1.10156
$969$	6.18829e10	0.00225483
$970$	3.42467e13	1.24207
$971$	8.15723e12	0.294480	0.147240	−	0.989101i	$-0.452961\pi$
$971$	8.15723e12	0.294480	0.147240	+	0.989101i	$0.452961\pi$
$972$	−7.54538e11	−0.0271133
$973$	2.97361e13	1.06360
$974$	−2.42797e13	−0.864427
$975$	−1.88855e11	−0.00669281
$976$	−4.51911e13	−1.59415
$977$	9.16012e12	0.321644	0.160822	−	0.986983i	$-0.448585\pi$
$977$	9.16012e12	0.321644	0.160822	+	0.986983i	$0.448585\pi$
$978$	−7.52369e10	−0.00262970
$979$	−1.96730e13	−0.684462
$980$	8.20270e12	0.284079
$981$	5.44406e13	1.87678
$982$	4.77286e12	0.163786
$983$	−3.83289e13	−1.30929	−0.654645	−	0.755937i	$-0.727182\pi$
$983$	−3.83289e13	−1.30929	−0.654645	+	0.755937i	$0.727182\pi$
$984$	6.08421e11	0.0206884
$985$	−1.69199e12	−0.0572709
$986$	−5.22355e12	−0.176003
$987$	1.04172e11	0.00349402
$988$	−1.31471e13	−0.438958
$989$	3.11380e13	1.03492
$990$	4.77830e13	1.58094
$991$	5.86162e13	1.93057	0.965287	−	0.261191i	$-0.0841152\pi$
$991$	5.86162e13	1.93057	0.965287	+	0.261191i	$0.0841152\pi$
$992$	−1.13159e12	−0.0371010
$993$	9.98613e11	0.0325931
$994$	3.41625e13	1.10997
$995$	−1.48518e13	−0.480368
$996$	3.22445e10	0.00103822
$997$	2.00858e13	0.643814	0.321907	−	0.946771i	$-0.395676\pi$
$997$	2.00858e13	0.643814	0.321907	+	0.946771i	$0.395676\pi$
$998$	−5.82064e13	−1.85730
$999$	7.82103e11	0.0248439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.a.1.18	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.a.1.18	✓	71	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-27.2613 q^{2} -2.80973 q^{3} +231.177 q^{4} +1123.40 q^{5} +76.5969 q^{6} -8481.66 q^{7} +7655.60 q^{8} -19675.1 q^{9} -30625.2 q^{10} +79300.8 q^{11} -649.546 q^{12} -97256.2 q^{13} +231221. q^{14} -3156.44 q^{15} -327064. q^{16} -37665.0 q^{17} +536368. q^{18} +584746. q^{19} +259703. q^{20} +23831.2 q^{21} -2.16184e6 q^{22} +1.46262e6 q^{23} -21510.2 q^{24} -691109. q^{25} +2.65133e6 q^{26} +110586. q^{27} -1.96076e6 q^{28} -5.08723e6 q^{29} +86048.6 q^{30} -226476. q^{31} +4.99651e6 q^{32} -222814. q^{33} +1.02680e6 q^{34} -9.52825e6 q^{35} -4.54843e6 q^{36} +7.07236e6 q^{37} -1.59409e7 q^{38} +273264. q^{39} +8.60026e6 q^{40} -2.82852e7 q^{41} -649669. q^{42} +2.12893e7 q^{43} +1.83325e7 q^{44} -2.21029e7 q^{45} -3.98727e7 q^{46} +4.37126e6 q^{47} +918963. q^{48} +3.15849e7 q^{49} +1.88405e7 q^{50} +105829. q^{51} -2.24834e7 q^{52} +8.42582e7 q^{53} -3.01471e6 q^{54} +8.90861e7 q^{55} -6.49321e7 q^{56} -1.64298e6 q^{57} +1.38684e8 q^{58} -4.99543e7 q^{59} -729696. q^{60} +1.38172e8 q^{61} +6.17401e6 q^{62} +1.66878e8 q^{63} +3.12455e7 q^{64} -1.09257e8 q^{65} +6.07420e6 q^{66} -2.30776e7 q^{67} -8.70728e6 q^{68} -4.10956e6 q^{69} +2.59752e8 q^{70} +1.47748e8 q^{71} -1.50625e8 q^{72} +1.64941e8 q^{73} -1.92802e8 q^{74} +1.94183e6 q^{75} +1.35180e8 q^{76} -6.72602e8 q^{77} -7.44953e6 q^{78} +3.82858e8 q^{79} -3.67422e8 q^{80} +3.86954e8 q^{81} +7.71091e8 q^{82} -4.96417e7 q^{83} +5.50922e6 q^{84} -4.23127e7 q^{85} -5.80373e8 q^{86} +1.42938e7 q^{87} +6.07095e8 q^{88} -2.48081e8 q^{89} +6.02554e8 q^{90} +8.24894e8 q^{91} +3.38123e8 q^{92} +636336. q^{93} -1.19166e8 q^{94} +6.56901e8 q^{95} -1.40389e7 q^{96} -1.11825e9 q^{97} -8.61045e8 q^{98} -1.56025e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 32 q^{2} - 892 q^{3} + 16896 q^{4} - 2329 q^{5} - 10272 q^{6} - 37846 q^{7} - 24933 q^{8} + 419903 q^{9} - 138907 q^{10} - 143074 q^{11} - 496640 q^{12} - 433821 q^{13} - 130143 q^{14} - 670126 q^{15}+ \cdots - 6380320552 q^{99}+O(q^{100}) \) 71 * q - 32 * q^2 - 892 * q^3 + 16896 * q^4 - 2329 * q^5 - 10272 * q^6 - 37846 * q^7 - 24933 * q^8 + 419903 * q^9 - 138907 * q^10 - 143074 * q^11 - 496640 * q^12 - 433821 * q^13 - 130143 * q^14 - 670126 * q^15 + 3670016 * q^16 - 226712 * q^17 - 1140455 * q^18 - 4200657 * q^19 - 2522261 * q^20 - 2222620 * q^21 - 5109807 * q^22 - 1576984 * q^23 - 7953747 * q^24 + 20408644 * q^25 - 3606210 * q^26 - 22380322 * q^27 - 28281314 * q^28 - 1600554 * q^29 + 1211083 * q^30 - 27408409 * q^31 - 19842828 * q^32 - 26002786 * q^33 - 33310606 * q^34 - 25745764 * q^35 + 75847738 * q^36 - 56498684 * q^37 - 8523742 * q^38 - 67092176 * q^39 - 69825234 * q^40 - 41524361 * q^41 - 29804525 * q^42 - 103636613 * q^43 - 93059022 * q^44 - 41029851 * q^45 - 35065939 * q^46 - 155481346 * q^47 - 310890046 * q^48 + 274445845 * q^49 - 532508319 * q^50 - 401628576 * q^51 - 638463912 * q^52 - 235002576 * q^53 - 485779441 * q^54 - 274178598 * q^55 - 174143696 * q^56 + 10220750 * q^57 - 54794577 * q^58 - 309204685 * q^59 + 349852813 * q^60 - 172553358 * q^61 + 313207667 * q^62 - 291588072 * q^63 + 1670833437 * q^64 + 394656726 * q^65 + 2405207530 * q^66 - 1034845512 * q^67 + 2160039119 * q^68 + 472060058 * q^69 + 1282221119 * q^70 + 515265617 * q^71 + 1722271619 * q^72 - 667322970 * q^73 + 1111943967 * q^74 - 304507118 * q^75 - 1476894506 * q^76 - 347407724 * q^77 - 99563531 * q^78 - 338475893 * q^79 - 652382330 * q^80 + 1981631951 * q^81 - 2682827483 * q^82 - 2423465319 * q^83 - 1042585800 * q^84 - 2101960924 * q^85 - 2597172884 * q^86 - 2135063354 * q^87 - 5542447545 * q^88 - 2765884440 * q^89 - 6736154529 * q^90 - 6821909968 * q^91 - 4167412114 * q^92 - 4756429190 * q^93 - 5116706209 * q^94 - 4295841932 * q^95 - 14387243887 * q^96 - 6239794299 * q^97 - 8201372742 * q^98 - 6380320552 * q^99

Introduction

L-functions

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