LMFDB - Embedded newform 197.10.a.a.1.5

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			1.5
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)

$f(q)$	$=$	\(q-42.8620 q^{2} +210.134 q^{3} +1325.15 q^{4} +1176.05 q^{5} -9006.77 q^{6} +4058.46 q^{7} -34853.1 q^{8} +24473.5 q^{9} -50407.8 q^{10} -37710.7 q^{11} +278459. q^{12} -132580. q^{13} -173954. q^{14} +247128. q^{15} +815397. q^{16} -236606. q^{17} -1.04898e6 q^{18} +620418. q^{19} +1.55844e6 q^{20} +852822. q^{21} +1.61636e6 q^{22} +611280. q^{23} -7.32384e6 q^{24} -570034. q^{25} +5.68266e6 q^{26} +1.00664e6 q^{27} +5.37806e6 q^{28} +1.33524e6 q^{29} -1.05924e7 q^{30} -7.12238e6 q^{31} -1.71047e7 q^{32} -7.92432e6 q^{33} +1.01414e7 q^{34} +4.77295e6 q^{35} +3.24310e7 q^{36} -2.07938e7 q^{37} -2.65923e7 q^{38} -2.78597e7 q^{39} -4.09890e7 q^{40} -6.99487e6 q^{41} -3.65536e7 q^{42} -2.54778e6 q^{43} -4.99723e7 q^{44} +2.87820e7 q^{45} -2.62007e7 q^{46} -1.66405e7 q^{47} +1.71343e8 q^{48} -2.38825e7 q^{49} +2.44328e7 q^{50} -4.97190e7 q^{51} -1.75689e8 q^{52} +3.28649e7 q^{53} -4.31466e7 q^{54} -4.43497e7 q^{55} -1.41450e8 q^{56} +1.30371e8 q^{57} -5.72312e7 q^{58} +3.05490e7 q^{59} +3.27482e8 q^{60} -2.86018e7 q^{61} +3.05279e8 q^{62} +9.93245e7 q^{63} +3.15659e8 q^{64} -1.55921e8 q^{65} +3.39652e8 q^{66} -1.55918e8 q^{67} -3.13538e8 q^{68} +1.28451e8 q^{69} -2.04578e8 q^{70} +3.94439e7 q^{71} -8.52976e8 q^{72} -1.58793e8 q^{73} +8.91263e8 q^{74} -1.19784e8 q^{75} +8.22145e8 q^{76} -1.53047e8 q^{77} +1.19412e9 q^{78} +4.53571e8 q^{79} +9.58947e8 q^{80} -2.70181e8 q^{81} +2.99814e8 q^{82} -1.57803e8 q^{83} +1.13012e9 q^{84} -2.78260e8 q^{85} +1.09203e8 q^{86} +2.80581e8 q^{87} +1.31434e9 q^{88} +8.31272e7 q^{89} -1.23365e9 q^{90} -5.38073e8 q^{91} +8.10037e8 q^{92} -1.49666e9 q^{93} +7.13243e8 q^{94} +7.29642e8 q^{95} -3.59429e9 q^{96} -1.15900e9 q^{97} +1.02365e9 q^{98} -9.22912e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−42.8620	−1.89425	−0.947125	−	0.320866i	$-0.896026\pi$
$2$	−42.8620	−1.89425	−0.947125	+	0.320866i	$0.896026\pi$
$3$	210.134	1.49779	0.748896	−	0.662688i	$-0.230584\pi$
$3$	210.134	1.49779	0.748896	+	0.662688i	$0.230584\pi$
$4$	1325.15	2.58818
$5$	1176.05	0.841512	0.420756	−	0.907174i	$-0.361765\pi$
$5$	1176.05	0.841512	0.420756	+	0.907174i	$0.361765\pi$
$6$	−9006.77	−2.83719
$7$	4058.46	0.638881	0.319441	−	0.947606i	$-0.396505\pi$
$7$	4058.46	0.638881	0.319441	+	0.947606i	$0.396505\pi$
$8$	−34853.1	−3.00841
$9$	24473.5	1.24338
$10$	−50407.8	−1.59403
$11$	−37710.7	−0.776601	−0.388300	−	0.921533i	$-0.626938\pi$
$11$	−37710.7	−0.776601	−0.388300	+	0.921533i	$0.626938\pi$
$12$	278459.	3.87655
$13$	−132580.	−1.28746	−0.643731	−	0.765252i	$-0.722615\pi$
$13$	−132580.	−1.28746	−0.643731	+	0.765252i	$0.722615\pi$
$14$	−173954.	−1.21020
$15$	247128.	1.26041
$16$	815397.	3.11049
$17$	−236606.	−0.687077	−0.343539	−	0.939139i	$-0.611626\pi$
$17$	−236606.	−0.687077	−0.343539	+	0.939139i	$0.611626\pi$
$18$	−1.04898e6	−2.35527
$19$	620418.	1.09218	0.546088	−	0.837728i	$-0.316116\pi$
$19$	620418.	1.09218	0.546088	+	0.837728i	$0.316116\pi$
$20$	1.55844e6	2.17798
$21$	852822.	0.956911
$22$	1.61636e6	1.47108
$23$	611280.	0.455475	0.227738	−	0.973723i	$-0.426867\pi$
$23$	611280.	0.455475	0.227738	+	0.973723i	$0.426867\pi$
$24$	−7.32384e6	−4.50597
$25$	−570034.	−0.291857
$26$	5.68266e6	2.43877
$27$	1.00664e6	0.364533
$28$	5.37806e6	1.65354
$29$	1.33524e6	0.350566	0.175283	−	0.984518i	$-0.443916\pi$
$29$	1.33524e6	0.350566	0.175283	+	0.984518i	$0.443916\pi$
$30$	−1.05924e7	−2.38753
$31$	−7.12238e6	−1.38515	−0.692576	−	0.721345i	$-0.743524\pi$
$31$	−7.12238e6	−1.38515	−0.692576	+	0.721345i	$0.743524\pi$
$32$	−1.71047e7	−2.88364
$33$	−7.92432e6	−1.16319
$34$	1.01414e7	1.30150
$35$	4.77295e6	0.537626
$36$	3.24310e7	3.21809
$37$	−2.07938e7	−1.82400	−0.912002	−	0.410185i	$-0.865464\pi$
$37$	−2.07938e7	−1.82400	−0.912002	+	0.410185i	$0.865464\pi$
$38$	−2.65923e7	−2.06886
$39$	−2.78597e7	−1.92835
$40$	−4.09890e7	−2.53161
$41$	−6.99487e6	−0.386591	−0.193296	−	0.981141i	$-0.561918\pi$
$41$	−6.99487e6	−0.386591	−0.193296	+	0.981141i	$0.561918\pi$
$42$	−3.65536e7	−1.81263
$43$	−2.54778e6	−0.113646	−0.0568230	−	0.998384i	$-0.518097\pi$
$43$	−2.54778e6	−0.113646	−0.0568230	+	0.998384i	$0.518097\pi$
$44$	−4.99723e7	−2.00998
$45$	2.87820e7	1.04632
$46$	−2.62007e7	−0.862784
$47$	−1.66405e7	−0.497422	−0.248711	−	0.968578i	$-0.580007\pi$
$47$	−1.66405e7	−0.497422	−0.248711	+	0.968578i	$0.580007\pi$
$48$	1.71343e8	4.65887
$49$	−2.38825e7	−0.591831
$50$	2.44328e7	0.552850
$51$	−4.97190e7	−1.02910
$52$	−1.75689e8	−3.33218
$53$	3.28649e7	0.572125	0.286063	−	0.958211i	$-0.407653\pi$
$53$	3.28649e7	0.572125	0.286063	+	0.958211i	$0.407653\pi$
$54$	−4.31466e7	−0.690517
$55$	−4.43497e7	−0.653519
$56$	−1.41450e8	−1.92201
$57$	1.30371e8	1.63585
$58$	−5.72312e7	−0.664059
$59$	3.05490e7	0.328218	0.164109	−	0.986442i	$-0.447525\pi$
$59$	3.05490e7	0.328218	0.164109	+	0.986442i	$0.447525\pi$
$60$	3.27482e8	3.26217
$61$	−2.86018e7	−0.264490	−0.132245	−	0.991217i	$-0.542219\pi$
$61$	−2.86018e7	−0.264490	−0.132245	+	0.991217i	$0.542219\pi$
$62$	3.05279e8	2.62382
$63$	9.93245e7	0.794372
$64$	3.15659e8	2.35184
$65$	−1.55921e8	−1.08342
$66$	3.39652e8	2.20337
$67$	−1.55918e8	−0.945281	−0.472641	−	0.881255i	$-0.656699\pi$
$67$	−1.55918e8	−0.945281	−0.472641	+	0.881255i	$0.656699\pi$
$68$	−3.13538e8	−1.77828
$69$	1.28451e8	0.682207
$70$	−2.04578e8	−1.01840
$71$	3.94439e7	0.184212	0.0921059	−	0.995749i	$-0.470640\pi$
$71$	3.94439e7	0.184212	0.0921059	+	0.995749i	$0.470640\pi$
$72$	−8.52976e8	−3.74060
$73$	−1.58793e8	−0.654452	−0.327226	−	0.944946i	$-0.606114\pi$
$73$	−1.58793e8	−0.654452	−0.327226	+	0.944946i	$0.606114\pi$
$74$	8.91263e8	3.45512
$75$	−1.19784e8	−0.437141
$76$	8.22145e8	2.82675
$77$	−1.53047e8	−0.496156
$78$	1.19412e9	3.65278
$79$	4.53571e8	1.31016	0.655078	−	0.755561i	$-0.272636\pi$
$79$	4.53571e8	1.31016	0.655078	+	0.755561i	$0.272636\pi$
$80$	9.58947e8	2.61752
$81$	−2.70181e8	−0.697385
$82$	2.99814e8	0.732300
$83$	−1.57803e8	−0.364975	−0.182487	−	0.983208i	$-0.558415\pi$
$83$	−1.57803e8	−0.364975	−0.182487	+	0.983208i	$0.558415\pi$
$84$	1.13012e9	2.47666
$85$	−2.78260e8	−0.578184
$86$	1.09203e8	0.215274
$87$	2.80581e8	0.525075
$88$	1.31434e9	2.33633
$89$	8.31272e7	0.140439	0.0702196	−	0.997532i	$-0.477630\pi$
$89$	8.31272e7	0.140439	0.0702196	+	0.997532i	$0.477630\pi$
$90$	−1.23365e9	−1.98199
$91$	−5.38073e8	−0.822535
$92$	8.10037e8	1.17885
$93$	−1.49666e9	−2.07467
$94$	7.13243e8	0.942242
$95$	7.29642e8	0.919080
$96$	−3.59429e9	−4.31910
$97$	−1.15900e9	−1.32927	−0.664633	−	0.747170i	$-0.731412\pi$
$97$	−1.15900e9	−1.32927	−0.664633	+	0.747170i	$0.731412\pi$
$98$	1.02365e9	1.12108
$99$	−9.22912e8	−0.965610
$100$	−7.55379e8	−0.755379
$101$	−8.56510e8	−0.819004	−0.409502	−	0.912309i	$-0.634298\pi$
$101$	−8.56510e8	−0.819004	−0.409502	+	0.912309i	$0.634298\pi$
$102$	2.13106e9	1.94937
$103$	−3.58390e7	−0.0313754	−0.0156877	−	0.999877i	$-0.504994\pi$
$103$	−3.58390e7	−0.0313754	−0.0156877	+	0.999877i	$0.504994\pi$
$104$	4.62084e9	3.87321
$105$	1.00296e9	0.805252
$106$	−1.40866e9	−1.08375
$107$	2.34336e9	1.72827	0.864137	−	0.503257i	$-0.167865\pi$
$107$	2.34336e9	1.72827	0.864137	+	0.503257i	$0.167865\pi$
$108$	1.33395e9	0.943478
$109$	1.14960e9	0.780062	0.390031	−	0.920802i	$-0.372464\pi$
$109$	1.14960e9	0.780062	0.390031	+	0.920802i	$0.372464\pi$
$110$	1.90091e9	1.23793
$111$	−4.36949e9	−2.73198
$112$	3.30926e9	1.98724
$113$	−3.14117e9	−1.81234	−0.906168	−	0.422918i	$-0.861006\pi$
$113$	−3.14117e9	−1.81234	−0.906168	+	0.422918i	$0.861006\pi$
$114$	−5.58796e9	−3.09871
$115$	7.18895e8	0.383288
$116$	1.76940e9	0.907327
$117$	−3.24470e9	−1.60081
$118$	−1.30939e9	−0.621727
$119$	−9.60256e8	−0.438961
$120$	−8.61319e9	−3.79183
$121$	−9.35848e8	−0.396891
$122$	1.22593e9	0.501010
$123$	−1.46986e9	−0.579033
$124$	−9.43821e9	−3.58502
$125$	−2.96736e9	−1.08711
$126$	−4.25725e9	−1.50474
$127$	−5.38024e9	−1.83520	−0.917602	−	0.397500i	$-0.869878\pi$
$127$	−5.38024e9	−1.83520	−0.917602	+	0.397500i	$0.869878\pi$
$128$	−4.77215e9	−1.57134
$129$	−5.35376e8	−0.170218
$130$	6.68309e9	2.05226
$131$	1.95534e9	0.580099	0.290050	−	0.957012i	$-0.406328\pi$
$131$	1.95534e9	0.580099	0.290050	+	0.957012i	$0.406328\pi$
$132$	−1.05009e10	−3.01054
$133$	2.51794e9	0.697771
$134$	6.68297e9	1.79060
$135$	1.18386e9	0.306759
$136$	8.24646e9	2.06701
$137$	6.71394e9	1.62830	0.814151	−	0.580653i	$-0.197203\pi$
$137$	6.71394e9	1.62830	0.814151	+	0.580653i	$0.197203\pi$
$138$	−5.50566e9	−1.29227
$139$	8.16969e9	1.85626	0.928130	−	0.372256i	$-0.121416\pi$
$139$	8.16969e9	1.85626	0.928130	+	0.372256i	$0.121416\pi$
$140$	6.32486e9	1.39147
$141$	−3.49673e9	−0.745035
$142$	−1.69064e9	−0.348943
$143$	4.99971e9	0.999844
$144$	1.99556e10	3.86753
$145$	1.57031e9	0.295005
$146$	6.80617e9	1.23970
$147$	−5.01854e9	−0.886440
$148$	−2.75548e10	−4.72085
$149$	7.06577e8	0.117441	0.0587207	−	0.998274i	$-0.481298\pi$
$149$	7.06577e8	0.117441	0.0587207	+	0.998274i	$0.481298\pi$
$150$	5.13416e9	0.828055
$151$	4.96371e9	0.776980	0.388490	−	0.921453i	$-0.372997\pi$
$151$	4.96371e9	0.776980	0.388490	+	0.921453i	$0.372997\pi$
$152$	−2.16235e10	−3.28571
$153$	−5.79057e9	−0.854298
$154$	6.55992e9	0.939842
$155$	−8.37627e9	−1.16562
$156$	−3.69183e10	−4.99092
$157$	7.30151e9	0.959101	0.479550	−	0.877514i	$-0.340800\pi$
$157$	7.30151e9	0.959101	0.479550	+	0.877514i	$0.340800\pi$
$158$	−1.94409e10	−2.48176
$159$	6.90605e9	0.856925
$160$	−2.01160e10	−2.42662
$161$	2.48086e9	0.290995
$162$	1.15805e10	1.32102
$163$	−5.05122e9	−0.560469	−0.280235	−	0.959932i	$-0.590412\pi$
$163$	−5.05122e9	−0.560469	−0.280235	+	0.959932i	$0.590412\pi$
$164$	−9.26923e9	−1.00057
$165$	−9.31939e9	−0.978836
$166$	6.76373e9	0.691353
$167$	3.33034e8	0.0331333	0.0165667	−	0.999863i	$-0.494726\pi$
$167$	3.33034e8	0.0331333	0.0165667	+	0.999863i	$0.494726\pi$
$168$	−2.97235e10	−2.87878
$169$	6.97309e9	0.657559
$170$	1.19268e10	1.09522
$171$	1.51838e10	1.35799
$172$	−3.37619e9	−0.294136
$173$	−1.18746e10	−1.00788	−0.503941	−	0.863738i	$-0.668117\pi$
$173$	−1.18746e10	−1.00788	−0.503941	+	0.863738i	$0.668117\pi$
$174$	−1.20262e10	−0.994622
$175$	−2.31346e9	−0.186462
$176$	−3.07492e10	−2.41561
$177$	6.41939e9	0.491603
$178$	−3.56299e9	−0.266027
$179$	9.87288e9	0.718795	0.359398	−	0.933185i	$-0.382982\pi$
$179$	9.87288e9	0.718795	0.359398	+	0.933185i	$0.382982\pi$
$180$	3.81404e10	2.70806
$181$	−1.82748e10	−1.26561	−0.632803	−	0.774313i	$-0.718096\pi$
$181$	−1.82748e10	−1.26561	−0.632803	+	0.774313i	$0.718096\pi$
$182$	2.30628e10	1.55809
$183$	−6.01022e9	−0.396151
$184$	−2.13050e10	−1.37026
$185$	−2.44545e10	−1.53492
$186$	6.41497e10	3.92994
$187$	8.92258e9	0.533585
$188$	−2.20511e10	−1.28742
$189$	4.08541e9	0.232894
$190$	−3.12739e10	−1.74097
$191$	−2.70670e10	−1.47160	−0.735800	−	0.677199i	$-0.763193\pi$
$191$	−2.70670e10	−1.47160	−0.735800	+	0.677199i	$0.763193\pi$
$192$	6.63309e10	3.52257
$193$	1.82511e10	0.946850	0.473425	−	0.880834i	$-0.343017\pi$
$193$	1.82511e10	0.946850	0.473425	+	0.880834i	$0.343017\pi$
$194$	4.96771e10	2.51796
$195$	−3.27644e10	−1.62273
$196$	−3.16479e10	−1.53176
$197$	−1.50614e9	−0.0712470
$197$	−1.50614e9	−0.0712470
$198$	3.95578e10	1.82911
$199$	−4.08623e9	−0.184707	−0.0923536	−	0.995726i	$-0.529439\pi$
$199$	−4.08623e9	−0.184707	−0.0923536	+	0.995726i	$0.529439\pi$
$200$	1.98675e10	0.878026
$201$	−3.27638e10	−1.41583
$202$	3.67117e10	1.55140
$203$	5.41903e9	0.223970
$204$	−6.58851e10	−2.66349
$205$	−8.22630e9	−0.325321
$206$	1.53613e9	0.0594328
$207$	1.49601e10	0.566329
$208$	−1.08106e11	−4.00464
$209$	−2.33964e10	−0.848186
$210$	−4.29889e10	−1.52535
$211$	4.59144e10	1.59470	0.797348	−	0.603520i	$-0.206235\pi$
$211$	4.59144e10	1.59470	0.797348	+	0.603520i	$0.206235\pi$
$212$	4.35509e10	1.48076
$213$	8.28852e9	0.275911
$214$	−1.00441e11	−3.27378
$215$	−2.99632e9	−0.0956345
$216$	−3.50846e10	−1.09667
$217$	−2.89059e10	−0.884948
$218$	−4.92743e10	−1.47763
$219$	−3.33678e10	−0.980233
$220$	−5.87699e10	−1.69142
$221$	3.13693e10	0.884586
$222$	1.87285e11	5.17505
$223$	−1.01326e10	−0.274378	−0.137189	−	0.990545i	$-0.543807\pi$
$223$	−1.01326e10	−0.274378	−0.137189	+	0.990545i	$0.543807\pi$
$224$	−6.94189e10	−1.84231
$225$	−1.39507e10	−0.362890
$226$	1.34637e11	3.43302
$227$	4.31431e10	1.07844	0.539218	−	0.842166i	$-0.318720\pi$
$227$	4.31431e10	1.07844	0.539218	+	0.842166i	$0.318720\pi$
$228$	1.72761e11	4.23388
$229$	3.38627e10	0.813695	0.406847	−	0.913496i	$-0.366628\pi$
$229$	3.38627e10	0.813695	0.406847	+	0.913496i	$0.366628\pi$
$230$	−3.08133e10	−0.726043
$231$	−3.21605e10	−0.743138
$232$	−4.65374e10	−1.05465
$233$	−1.75319e10	−0.389697	−0.194849	−	0.980833i	$-0.562422\pi$
$233$	−1.75319e10	−0.389697	−0.194849	+	0.980833i	$0.562422\pi$
$234$	1.39074e11	3.03232
$235$	−1.95700e10	−0.418587
$236$	4.04819e10	0.849488
$237$	9.53108e10	1.96234
$238$	4.11584e10	0.831501
$239$	3.10437e10	0.615435	0.307718	−	0.951478i	$-0.400435\pi$
$239$	3.10437e10	0.615435	0.307718	+	0.951478i	$0.400435\pi$
$240$	2.01508e11	3.92050
$241$	−9.49864e10	−1.81378	−0.906891	−	0.421366i	$-0.861551\pi$
$241$	−9.49864e10	−1.81378	−0.906891	+	0.421366i	$0.861551\pi$
$242$	4.01123e10	0.751811
$243$	−7.65881e10	−1.40907
$244$	−3.79016e10	−0.684547
$245$	−2.80870e10	−0.498033
$246$	6.30012e10	1.09683
$247$	−8.22553e10	−1.40614
$248$	2.48237e11	4.16710
$249$	−3.31597e10	−0.546656
$250$	1.27187e11	2.05926
$251$	7.02548e10	1.11723	0.558617	−	0.829426i	$-0.311332\pi$
$251$	7.02548e10	1.11723	0.558617	+	0.829426i	$0.311332\pi$
$252$	1.31620e11	2.05598
$253$	−2.30518e10	−0.353723
$254$	2.30607e11	3.47633
$255$	−5.84720e10	−0.865999
$256$	4.29261e10	0.624657
$257$	5.32221e10	0.761015	0.380507	−	0.924778i	$-0.375749\pi$
$257$	5.32221e10	0.761015	0.380507	+	0.924778i	$0.375749\pi$
$258$	2.29473e10	0.322435
$259$	−8.43908e10	−1.16532
$260$	−2.06619e11	−2.80407
$261$	3.26780e10	0.435887
$262$	−8.38099e10	−1.09885
$263$	1.14592e11	1.47691	0.738456	−	0.674301i	$-0.235555\pi$
$263$	1.14592e11	1.47691	0.738456	+	0.674301i	$0.235555\pi$
$264$	2.76187e11	3.49934
$265$	3.86508e10	0.481450
$266$	−1.07924e11	−1.32175
$267$	1.74679e10	0.210349
$268$	−2.06615e11	−2.44656
$269$	1.12972e11	1.31549	0.657743	−	0.753243i	$-0.271511\pi$
$269$	1.12972e11	1.31549	0.657743	+	0.753243i	$0.271511\pi$
$270$	−5.07425e10	−0.581079
$271$	−1.12335e11	−1.26519	−0.632593	−	0.774484i	$-0.718010\pi$
$271$	−1.12335e11	−1.26519	−0.632593	+	0.774484i	$0.718010\pi$
$272$	−1.92928e11	−2.13715
$273$	−1.13068e11	−1.23199
$274$	−2.87773e11	−3.08441
$275$	2.14964e10	0.226657
$276$	1.70217e11	1.76568
$277$	1.09513e11	1.11765	0.558825	−	0.829286i	$-0.311252\pi$
$277$	1.09513e11	1.11765	0.558825	+	0.829286i	$0.311252\pi$
$278$	−3.50169e11	−3.51622
$279$	−1.74309e11	−1.72227
$280$	−1.66352e11	−1.61740
$281$	−1.68285e11	−1.61015	−0.805075	−	0.593173i	$-0.797875\pi$
$281$	−1.68285e11	−1.61015	−0.805075	+	0.593173i	$0.797875\pi$
$282$	1.49877e11	1.41128
$283$	−1.08799e11	−1.00829	−0.504146	−	0.863619i	$-0.668193\pi$
$283$	−1.08799e11	−1.00829	−0.504146	+	0.863619i	$0.668193\pi$
$284$	5.22690e10	0.476773
$285$	1.53323e11	1.37659
$286$	−2.14297e11	−1.89395
$287$	−2.83884e10	−0.246986
$288$	−4.18612e11	−3.58547
$289$	−6.26055e10	−0.527925
$290$	−6.73067e10	−0.558814
$291$	−2.43546e11	−1.99096
$292$	−2.10424e11	−1.69384
$293$	1.91945e11	1.52150	0.760750	−	0.649045i	$-0.224831\pi$
$293$	1.91945e11	1.52150	0.760750	+	0.649045i	$0.224831\pi$
$294$	2.15104e11	1.67914
$295$	3.59271e10	0.276200
$296$	7.24728e11	5.48735
$297$	−3.79611e10	−0.283097
$298$	−3.02853e10	−0.222463
$299$	−8.10438e10	−0.586408
$300$	−1.58731e11	−1.13140
$301$	−1.03401e10	−0.0726063
$302$	−2.12754e11	−1.47179
$303$	−1.79982e11	−1.22670
$304$	5.05887e11	3.39721
$305$	−3.36371e10	−0.222571
$306$	2.48195e11	1.61825
$307$	1.20158e11	0.772024	0.386012	−	0.922494i	$-0.373852\pi$
$307$	1.20158e11	0.772024	0.386012	+	0.922494i	$0.373852\pi$
$308$	−2.02811e11	−1.28414
$309$	−7.53102e9	−0.0469938
$310$	3.59023e11	2.20798
$311$	−1.32220e11	−0.801451	−0.400725	−	0.916198i	$-0.631242\pi$
$311$	−1.32220e11	−0.801451	−0.400725	+	0.916198i	$0.631242\pi$
$312$	9.70998e11	5.80127
$313$	−2.63480e11	−1.55167	−0.775834	−	0.630937i	$-0.782670\pi$
$313$	−2.63480e11	−1.55167	−0.775834	+	0.630937i	$0.782670\pi$
$314$	−3.12957e11	−1.81678
$315$	1.16811e11	0.668474
$316$	6.01049e11	3.39092
$317$	−2.04075e11	−1.13507	−0.567536	−	0.823349i	$-0.692103\pi$
$317$	−2.04075e11	−1.13507	−0.567536	+	0.823349i	$0.692103\pi$
$318$	−2.96007e11	−1.62323
$319$	−5.03530e10	−0.272250
$320$	3.71231e11	1.97911
$321$	4.92421e11	2.58859
$322$	−1.06334e11	−0.551216
$323$	−1.46795e11	−0.750410
$324$	−3.58030e11	−1.80496
$325$	7.55754e10	0.375755
$326$	2.16505e11	1.06167
$327$	2.41571e11	1.16837
$328$	2.43793e11	1.16302
$329$	−6.75347e10	−0.317794
$330$	3.99447e11	1.85416
$331$	8.46985e10	0.387838	0.193919	−	0.981018i	$-0.437880\pi$
$331$	8.46985e10	0.387838	0.193919	+	0.981018i	$0.437880\pi$
$332$	−2.09112e11	−0.944620
$333$	−5.08896e11	−2.26793
$334$	−1.42745e10	−0.0627628
$335$	−1.83368e11	−0.795465
$336$	6.95389e11	2.97647
$337$	−2.29023e11	−0.967262	−0.483631	−	0.875272i	$-0.660682\pi$
$337$	−2.29023e11	−0.967262	−0.483631	+	0.875272i	$0.660682\pi$
$338$	−2.98880e11	−1.24558
$339$	−6.60068e11	−2.71450
$340$	−3.68736e11	−1.49644
$341$	2.68590e11	1.07571
$342$	−6.50806e11	−2.57237
$343$	−2.60700e11	−1.01699
$344$	8.87981e10	0.341893
$345$	1.51065e11	0.574086
$346$	5.08967e11	1.90918
$347$	−4.29574e10	−0.159058	−0.0795290	−	0.996833i	$-0.525342\pi$
$347$	−4.29574e10	−0.159058	−0.0795290	+	0.996833i	$0.525342\pi$
$348$	3.71811e11	1.35899
$349$	−4.32584e11	−1.56083	−0.780416	−	0.625261i	$-0.784993\pi$
$349$	−4.32584e11	−1.56083	−0.780416	+	0.625261i	$0.784993\pi$
$350$	9.91594e10	0.353206
$351$	−1.33461e11	−0.469323
$352$	6.45032e11	2.23944
$353$	1.36580e11	0.468167	0.234084	−	0.972216i	$-0.424791\pi$
$353$	1.36580e11	0.468167	0.234084	+	0.972216i	$0.424791\pi$
$354$	−2.75148e11	−0.931218
$355$	4.63880e10	0.155016
$356$	1.10156e11	0.363482
$357$	−2.01783e11	−0.657472
$358$	−4.23171e11	−1.36158
$359$	−5.04925e9	−0.0160436	−0.00802181	−	0.999968i	$-0.502553\pi$
$359$	−5.04925e9	−0.0160436	−0.00802181	+	0.999968i	$0.502553\pi$
$360$	−1.00314e12	−3.14776
$361$	6.22305e10	0.192850
$362$	7.83293e11	2.39737
$363$	−1.96654e11	−0.594460
$364$	−7.13026e11	−2.12887
$365$	−1.86748e11	−0.550730
$366$	2.57610e11	0.750408
$367$	3.69321e11	1.06269	0.531346	−	0.847155i	$-0.321687\pi$
$367$	3.69321e11	1.06269	0.531346	+	0.847155i	$0.321687\pi$
$368$	4.98436e11	1.41675
$369$	−1.71189e11	−0.480680
$370$	1.04817e12	2.90752
$371$	1.33381e11	0.365520
$372$	−1.98329e12	−5.36962
$373$	2.93916e11	0.786202	0.393101	−	0.919495i	$-0.371402\pi$
$373$	2.93916e11	0.786202	0.393101	+	0.919495i	$0.371402\pi$
$374$	−3.82439e11	−1.01074
$375$	−6.23544e11	−1.62827
$376$	5.79972e11	1.49645
$377$	−1.77027e11	−0.451340
$378$	−1.75109e11	−0.441158
$379$	−4.68869e11	−1.16728	−0.583641	−	0.812012i	$-0.698372\pi$
$379$	−4.68869e11	−1.16728	−0.583641	+	0.812012i	$0.698372\pi$
$380$	9.66883e11	2.37874
$381$	−1.13057e12	−2.74875
$382$	1.16014e12	2.78758
$383$	−4.91407e11	−1.16693	−0.583467	−	0.812137i	$-0.698304\pi$
$383$	−4.91407e11	−1.16693	−0.583467	+	0.812137i	$0.698304\pi$
$384$	−1.00279e12	−2.35353
$385$	−1.79991e11	−0.417521
$386$	−7.82278e11	−1.79357
$387$	−6.23530e10	−0.141305
$388$	−1.53585e12	−3.44038
$389$	2.88880e11	0.639653	0.319827	−	0.947476i	$-0.396375\pi$
$389$	2.88880e11	0.639653	0.319827	+	0.947476i	$0.396375\pi$
$390$	1.40435e12	3.07386
$391$	−1.44633e11	−0.312947
$392$	8.32380e11	1.78047
$393$	4.10885e11	0.868868
$394$	6.45561e10	0.134960
$395$	5.33422e11	1.10251
$396$	−1.22300e12	−2.49917
$397$	1.64983e11	0.333336	0.166668	−	0.986013i	$-0.446699\pi$
$397$	1.64983e11	0.333336	0.166668	+	0.986013i	$0.446699\pi$
$398$	1.75144e11	0.349881
$399$	5.29106e11	1.04512
$400$	−4.64804e11	−0.907820
$401$	−2.16368e11	−0.417872	−0.208936	−	0.977929i	$-0.567000\pi$
$401$	−2.16368e11	−0.417872	−0.208936	+	0.977929i	$0.567000\pi$
$402$	1.40432e12	2.68194
$403$	9.44289e11	1.78333
$404$	−1.13500e12	−2.11973
$405$	−3.17747e11	−0.586858
$406$	−2.32270e11	−0.424255
$407$	7.84149e11	1.41652
$408$	1.73286e12	3.09595
$409$	1.07249e11	0.189512	0.0947561	−	0.995501i	$-0.469793\pi$
$409$	1.07249e11	0.189512	0.0947561	+	0.995501i	$0.469793\pi$
$410$	3.52596e11	0.616239
$411$	1.41083e12	2.43886
$412$	−4.74920e10	−0.0812051
$413$	1.23982e11	0.209693
$414$	−6.41221e11	−1.07277
$415$	−1.85584e11	−0.307131
$416$	2.26775e12	3.71258
$417$	1.71673e12	2.78029
$418$	1.00282e12	1.60667
$419$	−8.41829e11	−1.33432	−0.667161	−	0.744914i	$-0.732491\pi$
$419$	−8.41829e11	−1.33432	−0.667161	+	0.744914i	$0.732491\pi$
$420$	1.32907e12	2.08414
$421$	4.95646e11	0.768958	0.384479	−	0.923134i	$-0.374381\pi$
$421$	4.95646e11	0.768958	0.384479	+	0.923134i	$0.374381\pi$
$422$	−1.96798e12	−3.02075
$423$	−4.07250e11	−0.618485
$424$	−1.14545e12	−1.72119
$425$	1.34873e11	0.200528
$426$	−3.55262e11	−0.522644
$427$	−1.16079e11	−0.168978
$428$	3.10530e12	4.47308
$429$	1.05061e12	1.49756
$430$	1.28428e11	0.181155
$431$	−8.92090e11	−1.24526	−0.622631	−	0.782515i	$-0.713936\pi$
$431$	−8.92090e11	−1.24526	−0.622631	+	0.782515i	$0.713936\pi$
$432$	8.20812e11	1.13388
$433$	−1.09828e12	−1.50147	−0.750734	−	0.660605i	$-0.770300\pi$
$433$	−1.09828e12	−1.50147	−0.750734	+	0.660605i	$0.770300\pi$
$434$	1.23896e12	1.67631
$435$	3.29977e11	0.441857
$436$	1.52339e12	2.01894
$437$	3.79249e11	0.497460
$438$	1.43021e12	1.85681
$439$	1.00187e12	1.28742	0.643710	−	0.765269i	$-0.277394\pi$
$439$	1.00187e12	1.28742	0.643710	+	0.765269i	$0.277394\pi$
$440$	1.54572e12	1.96605
$441$	−5.84488e11	−0.735871
$442$	−1.34455e12	−1.67563
$443$	1.15080e12	1.41965	0.709825	−	0.704378i	$-0.248774\pi$
$443$	1.15080e12	1.41965	0.709825	+	0.704378i	$0.248774\pi$
$444$	−5.79022e12	−7.07085
$445$	9.77616e10	0.118181
$446$	4.34304e11	0.519741
$447$	1.48476e11	0.175903
$448$	1.28109e12	1.50255
$449$	1.25582e12	1.45821	0.729105	−	0.684402i	$-0.239936\pi$
$449$	1.25582e12	1.45821	0.729105	+	0.684402i	$0.239936\pi$
$450$	5.97954e11	0.687403
$451$	2.63782e11	0.300227
$452$	−4.16252e12	−4.69065
$453$	1.04305e12	1.16375
$454$	−1.84920e12	−2.04283
$455$	−6.32800e11	−0.692174
$456$	−4.54384e12	−4.92132
$457$	−1.68839e12	−1.81072	−0.905360	−	0.424646i	$-0.860399\pi$
$457$	−1.68839e12	−1.81072	−0.905360	+	0.424646i	$0.860399\pi$
$458$	−1.45142e12	−1.54134
$459$	−2.38177e11	−0.250463
$460$	9.52643e11	0.992019
$461$	−1.16403e12	−1.20035	−0.600176	−	0.799868i	$-0.704903\pi$
$461$	−1.16403e12	−1.20035	−0.600176	+	0.799868i	$0.704903\pi$
$462$	1.37846e12	1.40769
$463$	5.46829e11	0.553015	0.276508	−	0.961012i	$-0.410823\pi$
$463$	5.46829e11	0.553015	0.276508	+	0.961012i	$0.410823\pi$
$464$	1.08875e12	1.09043
$465$	−1.76014e12	−1.74586
$466$	7.51452e11	0.738184
$467$	7.83554e11	0.762330	0.381165	−	0.924507i	$-0.375523\pi$
$467$	7.83554e11	0.762330	0.381165	+	0.924507i	$0.375523\pi$
$468$	−4.29971e12	−4.14317
$469$	−6.32789e11	−0.603922
$470$	8.38809e11	0.792908
$471$	1.53430e12	1.43653
$472$	−1.06473e12	−0.987415
$473$	9.60787e10	0.0882576
$474$	−4.08521e12	−3.71716
$475$	−3.53659e11	−0.318760
$476$	−1.27248e12	−1.13611
$477$	8.04318e11	0.711369
$478$	−1.33059e12	−1.16579
$479$	1.46747e12	1.27368	0.636840	−	0.770996i	$-0.280241\pi$
$479$	1.46747e12	1.27368	0.636840	+	0.770996i	$0.280241\pi$
$480$	−4.22707e12	−3.63457
$481$	2.75685e12	2.34834
$482$	4.07131e12	3.43575
$483$	5.21313e11	0.435849
$484$	−1.24014e12	−1.02723
$485$	−1.36304e12	−1.11859
$486$	3.28272e12	2.66913
$487$	−3.35144e11	−0.269992	−0.134996	−	0.990846i	$-0.543102\pi$
$487$	−3.35144e11	−0.269992	−0.134996	+	0.990846i	$0.543102\pi$
$488$	9.96862e11	0.795693
$489$	−1.06143e12	−0.839466
$490$	1.20386e12	0.943398
$491$	−5.58180e11	−0.433419	−0.216709	−	0.976236i	$-0.569532\pi$
$491$	−5.58180e11	−0.433419	−0.216709	+	0.976236i	$0.569532\pi$
$492$	−1.94778e12	−1.49864
$493$	−3.15927e11	−0.240866
$494$	3.52562e12	2.66357
$495$	−1.08539e12	−0.812573
$496$	−5.80757e12	−4.30851
$497$	1.60081e11	0.117689
$498$	1.42129e12	1.03550
$499$	−6.42247e10	−0.0463713	−0.0231857	−	0.999731i	$-0.507381\pi$
$499$	−6.42247e10	−0.0463713	−0.0231857	+	0.999731i	$0.507381\pi$
$500$	−3.93219e12	−2.81365
$501$	6.99820e10	0.0496268
$502$	−3.01126e12	−2.11632
$503$	1.57337e12	1.09591	0.547955	−	0.836508i	$-0.315406\pi$
$503$	1.57337e12	1.09591	0.547955	+	0.836508i	$0.315406\pi$
$504$	−3.46177e12	−2.38980
$505$	−1.00730e12	−0.689202
$506$	9.88046e11	0.670039
$507$	1.46529e12	0.984887
$508$	−7.12961e12	−4.74984
$509$	−7.06302e11	−0.466402	−0.233201	−	0.972429i	$-0.574920\pi$
$509$	−7.06302e11	−0.466402	−0.233201	+	0.972429i	$0.574920\pi$
$510$	2.50623e12	1.64042
$511$	−6.44454e11	−0.418117
$512$	6.03442e11	0.388080
$513$	6.24538e11	0.398135
$514$	−2.28120e12	−1.44155
$515$	−4.21485e10	−0.0264028
$516$	−7.09453e11	−0.440555
$517$	6.27524e11	0.386299
$518$	3.61715e12	2.20741
$519$	−2.49525e12	−1.50960
$520$	5.43434e12	3.25936
$521$	−2.07529e12	−1.23398	−0.616991	−	0.786970i	$-0.711649\pi$
$521$	−2.07529e12	−1.23398	−0.616991	+	0.786970i	$0.711649\pi$
$522$	−1.40064e12	−0.825678
$523$	−2.14305e12	−1.25249	−0.626246	−	0.779625i	$-0.715410\pi$
$523$	−2.14305e12	−1.25249	−0.626246	+	0.779625i	$0.715410\pi$
$524$	2.59112e12	1.50140
$525$	−4.86137e11	−0.279281
$526$	−4.91165e12	−2.79764
$527$	1.68520e12	0.951707
$528$	−6.46147e12	−3.61809
$529$	−1.42749e12	−0.792542
$530$	−1.65665e12	−0.911987
$531$	7.47640e11	0.408100
$532$	3.33664e12	1.80596
$533$	9.27383e11	0.497722
$534$	−7.48708e11	−0.398453
$535$	2.75591e12	1.45436
$536$	5.43425e12	2.84379
$537$	2.07463e12	1.07661
$538$	−4.84221e12	−2.49186
$539$	9.00627e11	0.459616
$540$	1.56879e12	0.793948
$541$	−1.22119e12	−0.612906	−0.306453	−	0.951886i	$-0.599142\pi$
$541$	−1.22119e12	−0.612906	−0.306453	+	0.951886i	$0.599142\pi$
$542$	4.81491e12	2.39658
$543$	−3.84016e12	−1.89561
$544$	4.04708e12	1.98129
$545$	1.35199e12	0.656431
$546$	4.84630e12	2.33369
$547$	1.11947e12	0.534652	0.267326	−	0.963606i	$-0.413860\pi$
$547$	1.11947e12	0.534652	0.267326	+	0.963606i	$0.413860\pi$
$548$	8.89697e12	4.21434
$549$	−6.99985e11	−0.328862
$550$	−9.21378e11	−0.429344
$551$	8.28409e11	0.382880
$552$	−4.47692e12	−2.05236
$553$	1.84080e12	0.837034
$554$	−4.69393e12	−2.11711
$555$	−5.13873e12	−2.29899
$556$	1.08260e13	4.80434
$557$	−3.36103e12	−1.47953	−0.739766	−	0.672864i	$-0.765064\pi$
$557$	−3.36103e12	−1.47953	−0.739766	+	0.672864i	$0.765064\pi$
$558$	7.47124e12	3.26241
$559$	3.37786e11	0.146315
$560$	3.89185e12	1.67228
$561$	1.87494e12	0.799199
$562$	7.21302e12	3.05003
$563$	−9.42206e11	−0.395237	−0.197619	−	0.980279i	$-0.563321\pi$
$563$	−9.42206e11	−0.395237	−0.197619	+	0.980279i	$0.563321\pi$
$564$	−4.63369e12	−1.92828
$565$	−3.69417e12	−1.52510
$566$	4.66334e12	1.90996
$567$	−1.09652e12	−0.445546
$568$	−1.37474e12	−0.554184
$569$	−4.68472e12	−1.87360	−0.936802	−	0.349859i	$-0.886230\pi$
$569$	−4.68472e12	−1.87360	−0.936802	+	0.349859i	$0.886230\pi$
$570$	−6.57172e12	−2.60761
$571$	3.39870e12	1.33798	0.668992	−	0.743270i	$-0.266726\pi$
$571$	3.39870e12	1.33798	0.668992	+	0.743270i	$0.266726\pi$
$572$	6.62535e12	2.58778
$573$	−5.68770e12	−2.20415
$574$	1.21678e12	0.467853
$575$	−3.48450e11	−0.132934
$576$	7.72527e12	2.92424
$577$	−8.02032e11	−0.301232	−0.150616	−	0.988592i	$-0.548126\pi$
$577$	−8.02032e11	−0.301232	−0.150616	+	0.988592i	$0.548126\pi$
$578$	2.68339e12	1.00002
$579$	3.83519e12	1.41818
$580$	2.08090e12	0.763527
$581$	−6.40435e11	−0.233175
$582$	1.04389e13	3.77138
$583$	−1.23936e12	−0.444313
$584$	5.53443e12	1.96886
$585$	−3.81593e12	−1.34710
$586$	−8.22713e12	−2.88210
$587$	−6.46378e11	−0.224706	−0.112353	−	0.993668i	$-0.535839\pi$
$587$	−6.46378e11	−0.224706	−0.112353	+	0.993668i	$0.535839\pi$
$588$	−6.65030e12	−2.29426
$589$	−4.41885e12	−1.51283
$590$	−1.53991e12	−0.523191
$591$	−3.16491e11	−0.106713
$592$	−1.69552e13	−5.67356
$593$	2.83699e12	0.942133	0.471066	−	0.882098i	$-0.343869\pi$
$593$	2.83699e12	0.942133	0.471066	+	0.882098i	$0.343869\pi$
$594$	1.62709e12	0.536256
$595$	−1.12931e12	−0.369391
$596$	9.36319e11	0.303959
$597$	−8.58657e11	−0.276653
$598$	3.47370e12	1.11080
$599$	3.03613e12	0.963607	0.481803	−	0.876279i	$-0.339982\pi$
$599$	3.03613e12	0.963607	0.481803	+	0.876279i	$0.339982\pi$
$600$	4.17484e12	1.31510
$601$	4.06753e12	1.27173	0.635866	−	0.771800i	$-0.280643\pi$
$601$	4.06753e12	1.27173	0.635866	+	0.771800i	$0.280643\pi$
$602$	4.43196e11	0.137534
$603$	−3.81586e12	−1.17534
$604$	6.57764e12	2.01096
$605$	−1.10060e12	−0.333989
$606$	7.71439e12	2.32367
$607$	−3.69028e12	−1.10334	−0.551670	−	0.834062i	$-0.686009\pi$
$607$	−3.69028e12	−1.10334	−0.551670	+	0.834062i	$0.686009\pi$
$608$	−1.06121e13	−3.14945
$609$	1.13873e12	0.335460
$610$	1.44175e12	0.421606
$611$	2.20620e12	0.640412
$612$	−7.67336e12	−2.21108
$613$	−3.91404e12	−1.11957	−0.559787	−	0.828636i	$-0.689117\pi$
$613$	−3.91404e12	−1.11957	−0.559787	+	0.828636i	$0.689117\pi$
$614$	−5.15022e12	−1.46241
$615$	−1.72863e12	−0.487264
$616$	5.33418e12	1.49264
$617$	3.12063e12	0.866881	0.433441	−	0.901182i	$-0.357299\pi$
$617$	3.12063e12	0.866881	0.433441	+	0.901182i	$0.357299\pi$
$618$	3.22794e11	0.0890179
$619$	5.11729e12	1.40098	0.700490	−	0.713662i	$-0.252965\pi$
$619$	5.11729e12	1.40098	0.700490	+	0.713662i	$0.252965\pi$
$620$	−1.10998e13	−3.01684
$621$	6.15339e11	0.166036
$622$	5.66723e12	1.51815
$623$	3.37368e11	0.0897239
$624$	−2.27167e13	−5.99812
$625$	−2.37641e12	−0.622962
$626$	1.12933e13	2.93924
$627$	−4.91639e12	−1.27041
$628$	9.67558e12	2.48233
$629$	4.91993e12	1.25323
$630$	−5.00673e12	−1.26626
$631$	5.52039e12	1.38624	0.693119	−	0.720823i	$-0.256236\pi$
$631$	5.52039e12	1.38624	0.693119	+	0.720823i	$0.256236\pi$
$632$	−1.58084e13	−3.94149
$633$	9.64820e12	2.38852
$634$	8.74706e12	2.15011
$635$	−6.32742e12	−1.54435
$636$	9.15154e12	2.21787
$637$	3.16636e12	0.761960
$638$	2.15823e12	0.515709
$639$	9.65329e11	0.229045
$640$	−5.61228e12	−1.32230
$641$	1.08626e12	0.254139	0.127070	−	0.991894i	$-0.459443\pi$
$641$	1.08626e12	0.254139	0.127070	+	0.991894i	$0.459443\pi$
$642$	−2.11061e13	−4.90344
$643$	−1.05176e12	−0.242642	−0.121321	−	0.992613i	$-0.538713\pi$
$643$	−1.05176e12	−0.242642	−0.121321	+	0.992613i	$0.538713\pi$
$644$	3.28750e12	0.753146
$645$	−6.29629e11	−0.143241
$646$	6.29190e12	1.42146
$647$	1.60350e12	0.359749	0.179874	−	0.983690i	$-0.442431\pi$
$647$	1.60350e12	0.359749	0.179874	+	0.983690i	$0.442431\pi$
$648$	9.41666e12	2.09802
$649$	−1.15202e12	−0.254895
$650$	−3.23931e12	−0.711774
$651$	−6.07412e12	−1.32547
$652$	−6.69361e12	−1.45060
$653$	7.22552e11	0.155510	0.0777552	−	0.996972i	$-0.475225\pi$
$653$	7.22552e11	0.155510	0.0777552	+	0.996972i	$0.475225\pi$
$654$	−1.03542e13	−2.21318
$655$	2.29958e12	0.488161
$656$	−5.70360e12	−1.20249
$657$	−3.88621e12	−0.813733
$658$	2.89467e12	0.601980
$659$	8.32885e12	1.72029	0.860143	−	0.510052i	$-0.170374\pi$
$659$	8.32885e12	1.72029	0.860143	+	0.510052i	$0.170374\pi$
$660$	−1.23496e13	−2.53340
$661$	−5.03785e12	−1.02645	−0.513226	−	0.858254i	$-0.671550\pi$
$661$	−5.03785e12	−1.02645	−0.513226	+	0.858254i	$0.671550\pi$
$662$	−3.63035e12	−0.734661
$663$	6.59178e12	1.32493
$664$	5.49991e12	1.09799
$665$	2.96122e12	0.587183
$666$	2.18123e13	4.29603
$667$	8.16208e11	0.159674
$668$	4.41320e11	0.0857550
$669$	−2.12921e12	−0.410962
$670$	7.85950e12	1.50681
$671$	1.07859e12	0.205403
$672$	−1.45873e13	−2.75939
$673$	−6.57915e12	−1.23624	−0.618119	−	0.786084i	$-0.712105\pi$
$673$	−6.57915e12	−1.23624	−0.618119	+	0.786084i	$0.712105\pi$
$674$	9.81636e12	1.83223
$675$	−5.73819e11	−0.106392
$676$	9.24037e12	1.70188
$677$	−6.11203e11	−0.111824	−0.0559122	−	0.998436i	$-0.517807\pi$
$677$	−6.11203e11	−0.111824	−0.0559122	+	0.998436i	$0.517807\pi$
$678$	2.82918e13	5.14194
$679$	−4.70377e12	−0.849243
$680$	9.69824e12	1.73941
$681$	9.06584e12	1.61527
$682$	−1.15123e13	−2.03766
$683$	−2.03258e12	−0.357400	−0.178700	−	0.983904i	$-0.557189\pi$
$683$	−2.03258e12	−0.357400	−0.178700	+	0.983904i	$0.557189\pi$
$684$	2.01207e13	3.51473
$685$	7.89593e12	1.37024
$686$	1.11741e13	1.92643
$687$	7.11571e12	1.21875
$688$	−2.07745e12	−0.353495
$689$	−4.35725e12	−0.736590
$690$	−6.47493e12	−1.08746
$691$	−3.00753e12	−0.501832	−0.250916	−	0.968009i	$-0.580732\pi$
$691$	−3.00753e12	−0.501832	−0.250916	+	0.968009i	$0.580732\pi$
$692$	−1.57355e13	−2.60858
$693$	−3.74560e12	−0.616910
$694$	1.84124e12	0.301295
$695$	9.60795e12	1.56207
$696$	−9.77911e12	−1.57964
$697$	1.65503e12	0.265618
$698$	1.85414e13	2.95660
$699$	−3.68406e12	−0.583686
$700$	−3.06568e12	−0.482597
$701$	−5.12180e12	−0.801109	−0.400555	−	0.916273i	$-0.631183\pi$
$701$	−5.12180e12	−0.801109	−0.400555	+	0.916273i	$0.631183\pi$
$702$	5.72040e12	0.889015
$703$	−1.29008e13	−1.99214
$704$	−1.19037e13	−1.82644
$705$	−4.11233e12	−0.626956
$706$	−5.85409e12	−0.886825
$707$	−3.47611e12	−0.523246
$708$	8.50665e12	1.27236
$709$	1.08755e13	1.61637	0.808187	−	0.588925i	$-0.200449\pi$
$709$	1.08755e13	1.61637	0.808187	+	0.588925i	$0.200449\pi$
$710$	−1.98828e12	−0.293640
$711$	1.11004e13	1.62902
$712$	−2.89724e12	−0.422498
$713$	−4.35377e12	−0.630903
$714$	8.64880e12	1.24542
$715$	5.87990e12	0.841381
$716$	1.30830e13	1.86037
$717$	6.52334e12	0.921794
$718$	2.16421e11	0.0303906
$719$	−6.46425e11	−0.0902065	−0.0451033	−	0.998982i	$-0.514362\pi$
$719$	−6.46425e11	−0.0902065	−0.0451033	+	0.998982i	$0.514362\pi$
$720$	2.34688e13	3.25457
$721$	−1.45451e11	−0.0200451
$722$	−2.66732e12	−0.365307
$723$	−1.99599e13	−2.71667
$724$	−2.42168e13	−3.27562
$725$	−7.61134e11	−0.102315
$726$	8.42897e12	1.12606
$727$	−8.79480e12	−1.16767	−0.583836	−	0.811872i	$-0.698449\pi$
$727$	−8.79480e12	−1.16767	−0.583836	+	0.811872i	$0.698449\pi$
$728$	1.87535e13	2.47452
$729$	−1.07758e13	−1.41311
$730$	8.00439e12	1.04322
$731$	6.02820e11	0.0780835
$732$	−7.96443e12	−1.02531
$733$	4.66135e10	0.00596409	0.00298205	−	0.999996i	$-0.499051\pi$
$733$	4.66135e10	0.00596409	0.00298205	+	0.999996i	$0.499051\pi$
$734$	−1.58298e13	−2.01300
$735$	−5.90205e12	−0.745950
$736$	−1.04558e13	−1.31343
$737$	5.87980e12	0.734106
$738$	7.33748e12	0.910528
$739$	7.19559e12	0.887496	0.443748	−	0.896152i	$-0.353649\pi$
$739$	7.19559e12	0.887496	0.443748	+	0.896152i	$0.353649\pi$
$740$	−3.24059e13	−3.97265
$741$	−1.72847e13	−2.10610
$742$	−5.71697e12	−0.692386
$743$	−1.09459e13	−1.31766	−0.658828	−	0.752294i	$-0.728947\pi$
$743$	−1.09459e13	−1.31766	−0.658828	+	0.752294i	$0.728947\pi$
$744$	5.21632e13	6.24146
$745$	8.30969e11	0.0988284
$746$	−1.25978e13	−1.48926
$747$	−3.86197e12	−0.453802
$748$	1.18237e13	1.38101
$749$	9.51044e12	1.10416
$750$	2.67263e13	3.08435
$751$	−4.71876e12	−0.541312	−0.270656	−	0.962676i	$-0.587241\pi$
$751$	−4.71876e12	−0.541312	−0.270656	+	0.962676i	$0.587241\pi$
$752$	−1.35686e13	−1.54723
$753$	1.47629e13	1.67338
$754$	7.58774e12	0.854951
$755$	5.83756e12	0.653838
$756$	5.41377e12	0.602770
$757$	−6.64187e11	−0.0735121	−0.0367561	−	0.999324i	$-0.511702\pi$
$757$	−6.64187e11	−0.0735121	−0.0367561	+	0.999324i	$0.511702\pi$
$758$	2.00967e13	2.21112
$759$	−4.84398e12	−0.529803
$760$	−2.54303e13	−2.76497
$761$	1.27341e12	0.137638	0.0688190	−	0.997629i	$-0.478077\pi$
$761$	1.27341e12	0.137638	0.0688190	+	0.997629i	$0.478077\pi$
$762$	4.84586e13	5.20683
$763$	4.66562e12	0.498367
$764$	−3.58677e13	−3.80876
$765$	−6.80999e12	−0.718902
$766$	2.10627e13	2.21046
$767$	−4.05020e12	−0.422569
$768$	9.02025e12	0.935606
$769$	1.76518e13	1.82020	0.910102	−	0.414385i	$-0.136003\pi$
$769$	1.76518e13	1.82020	0.910102	+	0.414385i	$0.136003\pi$
$770$	7.71478e12	0.790889
$771$	1.11838e13	1.13984
$772$	2.41854e13	2.45062
$773$	3.37474e12	0.339964	0.169982	−	0.985447i	$-0.445629\pi$
$773$	3.37474e12	0.339964	0.169982	+	0.985447i	$0.445629\pi$
$774$	2.67257e12	0.267667
$775$	4.06000e12	0.404267
$776$	4.03949e13	3.99897
$777$	−1.77334e13	−1.74541
$778$	−1.23820e13	−1.21166
$779$	−4.33974e12	−0.422226
$780$	−4.34177e13	−4.19992
$781$	−1.48746e12	−0.143059
$782$	6.19923e12	0.592799
$783$	1.34411e12	0.127793
$784$	−1.94737e13	−1.84089
$785$	8.58693e12	0.807095
$786$	−1.76113e13	−1.64585
$787$	−1.26669e13	−1.17702	−0.588512	−	0.808489i	$-0.700286\pi$
$787$	−1.26669e13	−1.17702	−0.588512	+	0.808489i	$0.700286\pi$
$788$	−1.99586e12	−0.184400
$789$	2.40798e13	2.21211
$790$	−2.28635e13	−2.08843
$791$	−1.27483e13	−1.15787
$792$	3.21664e13	2.90495
$793$	3.79204e12	0.340521
$794$	−7.07149e12	−0.631421
$795$	8.12185e12	0.721113
$796$	−5.41486e12	−0.478055
$797$	1.22477e13	1.07521	0.537604	−	0.843198i	$-0.319330\pi$
$797$	1.22477e13	1.07521	0.537604	+	0.843198i	$0.319330\pi$
$798$	−2.26785e13	−1.97971
$799$	3.93723e12	0.341767
$800$	9.75028e12	0.841612
$801$	2.03441e12	0.174619
$802$	9.27396e12	0.791554
$803$	5.98819e12	0.508248
$804$	−4.34169e13	−3.66443
$805$	2.91761e12	0.244876
$806$	−4.04741e13	−3.37808
$807$	2.37393e13	1.97032
$808$	2.98520e13	2.46390
$809$	−6.41241e12	−0.526324	−0.263162	−	0.964752i	$-0.584765\pi$
$809$	−6.41241e12	−0.526324	−0.263162	+	0.964752i	$0.584765\pi$
$810$	1.36192e13	1.11166
$811$	4.41622e12	0.358473	0.179237	−	0.983806i	$-0.442637\pi$
$811$	4.41622e12	0.358473	0.179237	+	0.983806i	$0.442637\pi$
$812$	7.18102e12	0.579674
$813$	−2.36055e13	−1.89499
$814$	−3.36102e13	−2.68325
$815$	−5.94048e12	−0.471642
$816$	−4.05408e13	−3.20101
$817$	−1.58069e12	−0.124121
$818$	−4.59689e12	−0.358983
$819$	−1.31685e13	−1.02272
$820$	−1.09011e13	−0.841990
$821$	−2.08361e13	−1.60056	−0.800281	−	0.599625i	$-0.795317\pi$
$821$	−2.08361e13	−1.60056	−0.800281	+	0.599625i	$0.795317\pi$
$822$	−6.04710e13	−4.61981
$823$	4.54651e12	0.345445	0.172723	−	0.984971i	$-0.444744\pi$
$823$	4.54651e12	0.345445	0.172723	+	0.984971i	$0.444744\pi$
$824$	1.24910e12	0.0943899
$825$	4.51713e12	0.339484
$826$	−5.31411e12	−0.397210
$827$	7.31038e12	0.543457	0.271729	−	0.962374i	$-0.412405\pi$
$827$	7.31038e12	0.543457	0.271729	+	0.962374i	$0.412405\pi$
$828$	1.98244e13	1.46576
$829$	−1.17691e13	−0.865463	−0.432731	−	0.901523i	$-0.642450\pi$
$829$	−1.17691e13	−0.865463	−0.432731	+	0.901523i	$0.642450\pi$
$830$	7.95447e12	0.581782
$831$	2.30124e13	1.67401
$832$	−4.18503e13	−3.02791
$833$	5.65074e12	0.406634
$834$	−7.35825e13	−5.26656
$835$	3.91665e11	0.0278821
$836$	−3.10037e13	−2.19526
$837$	−7.16968e12	−0.504935
$838$	3.60824e13	2.52754
$839$	8.08551e12	0.563350	0.281675	−	0.959510i	$-0.409110\pi$
$839$	8.08551e12	0.563350	0.281675	+	0.959510i	$0.409110\pi$
$840$	−3.49563e13	−2.42253
$841$	−1.27243e13	−0.877104
$842$	−2.12444e13	−1.45660
$843$	−3.53624e13	−2.41167
$844$	6.08434e13	4.12736
$845$	8.20069e12	0.553344
$846$	1.74555e13	1.17156
$847$	−3.79810e12	−0.253566
$848$	2.67980e13	1.77959
$849$	−2.28624e13	−1.51021
$850$	−5.78094e12	−0.379851
$851$	−1.27108e13	−0.830789
$852$	1.09835e13	0.714107
$853$	−2.08016e13	−1.34532	−0.672660	−	0.739952i	$-0.734848\pi$
$853$	−2.08016e13	−1.34532	−0.672660	+	0.739952i	$0.734848\pi$
$854$	4.97538e12	0.320086
$855$	1.78569e13	1.14277
$856$	−8.16735e13	−5.19935
$857$	1.87346e13	1.18640	0.593199	−	0.805056i	$-0.297865\pi$
$857$	1.87346e13	1.18640	0.593199	+	0.805056i	$0.297865\pi$
$858$	−4.50312e13	−2.83675
$859$	1.33061e13	0.833837	0.416918	−	0.908944i	$-0.363110\pi$
$859$	1.33061e13	0.833837	0.416918	+	0.908944i	$0.363110\pi$
$860$	−3.97056e12	−0.247519
$861$	−5.96537e12	−0.369933
$862$	3.82367e13	2.35884
$863$	−3.57603e12	−0.219459	−0.109729	−	0.993962i	$-0.534998\pi$
$863$	−3.57603e12	−0.219459	−0.109729	+	0.993962i	$0.534998\pi$
$864$	−1.72183e13	−1.05118
$865$	−1.39651e13	−0.848145
$866$	4.70743e13	2.84415
$867$	−1.31556e13	−0.790722
$868$	−3.83046e13	−2.29040
$869$	−1.71045e13	−1.01747
$870$	−1.41434e13	−0.836987
$871$	2.06717e13	1.21701
$872$	−4.00673e13	−2.34674
$873$	−2.83648e13	−1.65278
$874$	−1.62554e13	−0.942313
$875$	−1.20429e13	−0.694536
$876$	−4.42173e13	−2.53702
$877$	−1.59922e13	−0.912873	−0.456437	−	0.889756i	$-0.650875\pi$
$877$	−1.59922e13	−0.912873	−0.456437	+	0.889756i	$0.650875\pi$
$878$	−4.29420e13	−2.43869
$879$	4.03342e13	2.27889
$880$	−3.61626e13	−2.03277
$881$	6.06432e12	0.339149	0.169574	−	0.985517i	$-0.445761\pi$
$881$	6.06432e12	0.339149	0.169574	+	0.985517i	$0.445761\pi$
$882$	2.50523e13	1.39392
$883$	3.18246e13	1.76173	0.880866	−	0.473365i	$-0.156961\pi$
$883$	3.18246e13	1.76173	0.880866	+	0.473365i	$0.156961\pi$
$884$	4.15690e13	2.28947
$885$	7.54952e12	0.413690
$886$	−4.93254e13	−2.68917
$887$	2.25577e13	1.22360	0.611799	−	0.791013i	$-0.290446\pi$
$887$	2.25577e13	1.22360	0.611799	+	0.791013i	$0.290446\pi$
$888$	1.52290e14	8.21891
$889$	−2.18355e13	−1.17248
$890$	−4.19026e12	−0.223865
$891$	1.01887e13	0.541590
$892$	−1.34272e13	−0.710141
$893$	−1.03240e13	−0.543273
$894$	−6.36398e12	−0.333204
$895$	1.16110e13	0.604875
$896$	−1.93676e13	−1.00390
$897$	−1.70301e13	−0.878316
$898$	−5.38271e13	−2.76221
$899$	−9.51012e12	−0.485587
$900$	−1.84867e13	−0.939224
$901$	−7.77604e12	−0.393094
$902$	−1.13062e13	−0.568705
$903$	−2.17280e12	−0.108749
$904$	1.09480e14	5.45225
$905$	−2.14920e13	−1.06502
$906$	−4.47070e13	−2.20444
$907$	2.22307e13	1.09074	0.545368	−	0.838196i	$-0.316390\pi$
$907$	2.22307e13	1.09074	0.545368	+	0.838196i	$0.316390\pi$
$908$	5.71710e13	2.79119
$909$	−2.09618e13	−1.01833
$910$	2.71230e13	1.31115
$911$	1.87529e12	0.0902060	0.0451030	−	0.998982i	$-0.485638\pi$
$911$	1.87529e12	0.0902060	0.0451030	+	0.998982i	$0.485638\pi$
$912$	1.06304e14	5.08831
$913$	5.95085e12	0.283440
$914$	7.23679e13	3.42995
$915$	−7.06831e12	−0.333366
$916$	4.48731e13	2.10599
$917$	7.93569e12	0.370615
$918$	1.02087e13	0.474439
$919$	4.85870e12	0.224699	0.112349	−	0.993669i	$-0.464162\pi$
$919$	4.85870e12	0.224699	0.112349	+	0.993669i	$0.464162\pi$
$920$	−2.50557e13	−1.15309
$921$	2.52494e13	1.15633
$922$	4.98925e13	2.27377
$923$	−5.22949e12	−0.237166
$924$	−4.26175e13	−1.92337
$925$	1.18532e13	0.532349
$926$	−2.34382e13	−1.04755
$927$	−8.77106e11	−0.0390115
$928$	−2.28390e13	−1.01091
$929$	3.37503e13	1.48664	0.743321	−	0.668935i	$-0.233250\pi$
$929$	3.37503e13	1.48664	0.743321	+	0.668935i	$0.233250\pi$
$930$	7.54432e13	3.30709
$931$	−1.48171e13	−0.646384
$932$	−2.32324e13	−1.00861
$933$	−2.77841e13	−1.20041
$934$	−3.35847e13	−1.44404
$935$	1.04934e13	0.449018
$936$	1.13088e14	4.81588
$937$	3.71320e12	0.157369	0.0786846	−	0.996900i	$-0.474928\pi$
$937$	3.71320e12	0.157369	0.0786846	+	0.996900i	$0.474928\pi$
$938$	2.71226e13	1.14398
$939$	−5.53663e13	−2.32407
$940$	−2.59332e13	−1.08338
$941$	−1.83373e13	−0.762397	−0.381199	−	0.924493i	$-0.624489\pi$
$941$	−1.83373e13	−0.762397	−0.381199	+	0.924493i	$0.624489\pi$
$942$	−6.57630e13	−2.72115
$943$	−4.27582e12	−0.176083
$944$	2.49096e13	1.02092
$945$	4.80464e12	0.195983
$946$	−4.11812e12	−0.167182
$947$	−1.15407e13	−0.466290	−0.233145	−	0.972442i	$-0.574902\pi$
$947$	−1.15407e13	−0.466290	−0.233145	+	0.972442i	$0.574902\pi$
$948$	1.26301e14	5.07889
$949$	2.10528e13	0.842583
$950$	1.51585e13	0.603810
$951$	−4.28832e13	−1.70010
$952$	3.34679e13	1.32057
$953$	−4.79972e13	−1.88494	−0.942471	−	0.334287i	$-0.891505\pi$
$953$	−4.79972e13	−1.88494	−0.942471	+	0.334287i	$0.891505\pi$
$954$	−3.44747e13	−1.34751
$955$	−3.18321e13	−1.23837
$956$	4.11374e13	1.59286
$957$	−1.05809e13	−0.407773
$958$	−6.28988e13	−2.41267
$959$	2.72483e13	1.04029
$960$	7.80083e13	2.96429
$961$	2.42887e13	0.918648
$962$	−1.18164e14	−4.44834
$963$	5.73502e13	2.14890
$964$	−1.25871e14	−4.69439
$965$	2.14642e13	0.796786
$966$	−2.23445e13	−0.825607
$967$	2.87883e13	1.05876	0.529379	−	0.848386i	$-0.322425\pi$
$967$	2.87883e13	1.05876	0.529379	+	0.848386i	$0.322425\pi$
$968$	3.26172e13	1.19401
$969$	−3.08466e13	−1.12396
$970$	5.84228e13	2.11889
$971$	9.17107e12	0.331080	0.165540	−	0.986203i	$-0.447063\pi$
$971$	9.17107e12	0.331080	0.165540	+	0.986203i	$0.447063\pi$
$972$	−1.01491e14	−3.64693
$973$	3.31563e13	1.18593
$974$	1.43649e13	0.511432
$975$	1.58810e13	0.562803
$976$	−2.33218e13	−0.822694
$977$	1.82037e13	0.639196	0.319598	−	0.947553i	$-0.396452\pi$
$977$	1.82037e13	0.639196	0.319598	+	0.947553i	$0.396452\pi$
$978$	4.54952e13	1.59016
$979$	−3.13479e12	−0.109065
$980$	−3.72194e13	−1.28900
$981$	2.81348e13	0.969913
$982$	2.39247e13	0.821003
$983$	9.42089e12	0.321811	0.160906	−	0.986970i	$-0.448559\pi$
$983$	9.42089e12	0.321811	0.160906	+	0.986970i	$0.448559\pi$
$984$	5.12293e13	1.74197
$985$	−1.77129e12	−0.0599553
$986$	1.35412e13	0.456260
$987$	−1.41914e13	−0.475989
$988$	−1.09000e14	−3.63933
$989$	−1.55741e12	−0.0517629
$990$	4.65219e13	1.53922
$991$	2.10682e13	0.693898	0.346949	−	0.937884i	$-0.387218\pi$
$991$	2.10682e13	0.693898	0.346949	+	0.937884i	$0.387218\pi$
$992$	1.21827e14	3.99429
$993$	1.77981e13	0.580900
$994$	−6.86141e12	−0.222933
$995$	−4.80560e12	−0.155433
$996$	−4.39416e13	−1.41484
$997$	−9.00550e12	−0.288655	−0.144328	−	0.989530i	$-0.546102\pi$
$997$	−9.00550e12	−0.288655	−0.144328	+	0.989530i	$0.546102\pi$
$998$	2.75280e12	0.0878388
$999$	−2.09319e13	−0.664911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.a.1.5	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.a.1.5	✓	71	1.1	even	1	trivial

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-42.8620 q^{2} +210.134 q^{3} +1325.15 q^{4} +1176.05 q^{5} -9006.77 q^{6} +4058.46 q^{7} -34853.1 q^{8} +24473.5 q^{9} -50407.8 q^{10} -37710.7 q^{11} +278459. q^{12} -132580. q^{13} -173954. q^{14} +247128. q^{15} +815397. q^{16} -236606. q^{17} -1.04898e6 q^{18} +620418. q^{19} +1.55844e6 q^{20} +852822. q^{21} +1.61636e6 q^{22} +611280. q^{23} -7.32384e6 q^{24} -570034. q^{25} +5.68266e6 q^{26} +1.00664e6 q^{27} +5.37806e6 q^{28} +1.33524e6 q^{29} -1.05924e7 q^{30} -7.12238e6 q^{31} -1.71047e7 q^{32} -7.92432e6 q^{33} +1.01414e7 q^{34} +4.77295e6 q^{35} +3.24310e7 q^{36} -2.07938e7 q^{37} -2.65923e7 q^{38} -2.78597e7 q^{39} -4.09890e7 q^{40} -6.99487e6 q^{41} -3.65536e7 q^{42} -2.54778e6 q^{43} -4.99723e7 q^{44} +2.87820e7 q^{45} -2.62007e7 q^{46} -1.66405e7 q^{47} +1.71343e8 q^{48} -2.38825e7 q^{49} +2.44328e7 q^{50} -4.97190e7 q^{51} -1.75689e8 q^{52} +3.28649e7 q^{53} -4.31466e7 q^{54} -4.43497e7 q^{55} -1.41450e8 q^{56} +1.30371e8 q^{57} -5.72312e7 q^{58} +3.05490e7 q^{59} +3.27482e8 q^{60} -2.86018e7 q^{61} +3.05279e8 q^{62} +9.93245e7 q^{63} +3.15659e8 q^{64} -1.55921e8 q^{65} +3.39652e8 q^{66} -1.55918e8 q^{67} -3.13538e8 q^{68} +1.28451e8 q^{69} -2.04578e8 q^{70} +3.94439e7 q^{71} -8.52976e8 q^{72} -1.58793e8 q^{73} +8.91263e8 q^{74} -1.19784e8 q^{75} +8.22145e8 q^{76} -1.53047e8 q^{77} +1.19412e9 q^{78} +4.53571e8 q^{79} +9.58947e8 q^{80} -2.70181e8 q^{81} +2.99814e8 q^{82} -1.57803e8 q^{83} +1.13012e9 q^{84} -2.78260e8 q^{85} +1.09203e8 q^{86} +2.80581e8 q^{87} +1.31434e9 q^{88} +8.31272e7 q^{89} -1.23365e9 q^{90} -5.38073e8 q^{91} +8.10037e8 q^{92} -1.49666e9 q^{93} +7.13243e8 q^{94} +7.29642e8 q^{95} -3.59429e9 q^{96} -1.15900e9 q^{97} +1.02365e9 q^{98} -9.22912e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 32 q^{2} - 892 q^{3} + 16896 q^{4} - 2329 q^{5} - 10272 q^{6} - 37846 q^{7} - 24933 q^{8} + 419903 q^{9} - 138907 q^{10} - 143074 q^{11} - 496640 q^{12} - 433821 q^{13} - 130143 q^{14} - 670126 q^{15}+ \cdots - 6380320552 q^{99}+O(q^{100}) \) 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

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