LMFDB - Embedded newform 197.10.a.a.1.12

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			1.12
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)

$f(q)$	$=$	\(q-30.8011 q^{2} -107.364 q^{3} +436.705 q^{4} -558.513 q^{5} +3306.94 q^{6} -8318.45 q^{7} +2319.16 q^{8} -8155.88 q^{9} +17202.8 q^{10} -77158.5 q^{11} -46886.6 q^{12} +81842.9 q^{13} +256217. q^{14} +59964.4 q^{15} -295026. q^{16} +339216. q^{17} +251210. q^{18} -259370. q^{19} -243905. q^{20} +893106. q^{21} +2.37656e6 q^{22} -1.85438e6 q^{23} -248996. q^{24} -1.64119e6 q^{25} -2.52085e6 q^{26} +2.98891e6 q^{27} -3.63271e6 q^{28} +516651. q^{29} -1.84697e6 q^{30} -4.31210e6 q^{31} +7.89969e6 q^{32} +8.28408e6 q^{33} -1.04482e7 q^{34} +4.64596e6 q^{35} -3.56171e6 q^{36} -247875. q^{37} +7.98886e6 q^{38} -8.78701e6 q^{39} -1.29528e6 q^{40} -1.19189e7 q^{41} -2.75086e7 q^{42} +4.45674e7 q^{43} -3.36955e7 q^{44} +4.55516e6 q^{45} +5.71170e7 q^{46} +2.11544e7 q^{47} +3.16753e7 q^{48} +2.88430e7 q^{49} +5.05503e7 q^{50} -3.64197e7 q^{51} +3.57412e7 q^{52} +2.99273e7 q^{53} -9.20614e7 q^{54} +4.30940e7 q^{55} -1.92918e7 q^{56} +2.78471e7 q^{57} -1.59134e7 q^{58} -7.17560e7 q^{59} +2.61868e7 q^{60} +7.09576e7 q^{61} +1.32817e8 q^{62} +6.78443e7 q^{63} -9.22657e7 q^{64} -4.57103e7 q^{65} -2.55158e8 q^{66} +2.92852e8 q^{67} +1.48137e8 q^{68} +1.99095e8 q^{69} -1.43100e8 q^{70} +9.86093e7 q^{71} -1.89148e7 q^{72} +2.03894e8 q^{73} +7.63482e6 q^{74} +1.76205e8 q^{75} -1.13268e8 q^{76} +6.41839e8 q^{77} +2.70649e8 q^{78} -8.76574e7 q^{79} +1.64776e8 q^{80} -1.60370e8 q^{81} +3.67114e8 q^{82} +4.38233e8 q^{83} +3.90024e8 q^{84} -1.89456e8 q^{85} -1.37272e9 q^{86} -5.54699e7 q^{87} -1.78943e8 q^{88} +7.35999e8 q^{89} -1.40304e8 q^{90} -6.80806e8 q^{91} -8.09819e8 q^{92} +4.62966e8 q^{93} -6.51577e8 q^{94} +1.44861e8 q^{95} -8.48146e8 q^{96} +8.85921e7 q^{97} -8.88396e8 q^{98} +6.29295e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−30.8011	−1.36123	−0.680614	−	0.732643i	$-0.738287\pi$
$2$	−30.8011	−1.36123	−0.680614	+	0.732643i	$0.738287\pi$
$3$	−107.364	−0.765270	−0.382635	−	0.923900i	$-0.624983\pi$
$3$	−107.364	−0.765270	−0.382635	+	0.923900i	$0.624983\pi$
$4$	436.705	0.852940
$5$	−558.513	−0.399639	−0.199820	−	0.979833i	$-0.564036\pi$
$5$	−558.513	−0.399639	−0.199820	+	0.979833i	$0.564036\pi$
$6$	3306.94	1.04171
$7$	−8318.45	−1.30949	−0.654744	−	0.755851i	$-0.727223\pi$
$7$	−8318.45	−1.30949	−0.654744	+	0.755851i	$0.727223\pi$
$8$	2319.16	0.200183
$9$	−8155.88	−0.414361
$10$	17202.8	0.544000
$11$	−77158.5	−1.58897	−0.794487	−	0.607281i	$-0.792260\pi$
$11$	−77158.5	−1.58897	−0.794487	+	0.607281i	$0.792260\pi$
$12$	−46886.6	−0.652729
$13$	81842.9	0.794760	0.397380	−	0.917654i	$-0.369920\pi$
$13$	81842.9	0.794760	0.397380	+	0.917654i	$0.369920\pi$
$14$	256217.	1.78251
$15$	59964.4	0.305832
$16$	−295026.	−1.12543
$17$	339216.	0.985044	0.492522	−	0.870300i	$-0.336075\pi$
$17$	339216.	0.985044	0.492522	+	0.870300i	$0.336075\pi$
$18$	251210.	0.564040
$19$	−259370.	−0.456592	−0.228296	−	0.973592i	$-0.573315\pi$
$19$	−259370.	−0.456592	−0.228296	+	0.973592i	$0.573315\pi$
$20$	−243905.	−0.340868
$21$	893106.	1.00211
$22$	2.37656e6	2.16295
$23$	−1.85438e6	−1.38173	−0.690867	−	0.722982i	$-0.742771\pi$
$23$	−1.85438e6	−1.38173	−0.690867	+	0.722982i	$0.742771\pi$
$24$	−248996.	−0.153194
$25$	−1.64119e6	−0.840289
$26$	−2.52085e6	−1.08185
$27$	2.98891e6	1.08237
$28$	−3.63271e6	−1.11691
$29$	516651.	0.135646	0.0678228	−	0.997697i	$-0.478395\pi$
$29$	516651.	0.135646	0.0678228	+	0.997697i	$0.478395\pi$
$30$	−1.84697e6	−0.416307
$31$	−4.31210e6	−0.838613	−0.419306	−	0.907845i	$-0.637727\pi$
$31$	−4.31210e6	−0.838613	−0.419306	+	0.907845i	$0.637727\pi$
$32$	7.89969e6	1.33179
$33$	8.28408e6	1.21599
$34$	−1.04482e7	−1.34087
$35$	4.64596e6	0.523322
$36$	−3.56171e6	−0.353425
$37$	−247875.	−0.0217433	−0.0108717	−	0.999941i	$-0.503461\pi$
$37$	−247875.	−0.0217433	−0.0108717	+	0.999941i	$0.503461\pi$
$38$	7.98886e6	0.621525
$39$	−8.78701e6	−0.608206
$40$	−1.29528e6	−0.0800008
$41$	−1.19189e7	−0.658731	−0.329366	−	0.944202i	$-0.606835\pi$
$41$	−1.19189e7	−0.658731	−0.329366	+	0.944202i	$0.606835\pi$
$42$	−2.75086e7	−1.36410
$43$	4.45674e7	1.98797	0.993984	−	0.109527i	$-0.0349337\pi$
$43$	4.45674e7	1.98797	0.993984	+	0.109527i	$0.0349337\pi$
$44$	−3.36955e7	−1.35530
$45$	4.55516e6	0.165595
$46$	5.71170e7	1.88085
$47$	2.11544e7	0.632353	0.316177	−	0.948700i	$-0.397601\pi$
$47$	2.11544e7	0.632353	0.316177	+	0.948700i	$0.397601\pi$
$48$	3.16753e7	0.861261
$49$	2.88430e7	0.714758
$50$	5.05503e7	1.14382
$51$	−3.64197e7	−0.753825
$52$	3.57412e7	0.677882
$53$	2.99273e7	0.520987	0.260493	−	0.965476i	$-0.416115\pi$
$53$	2.99273e7	0.520987	0.260493	+	0.965476i	$0.416115\pi$
$54$	−9.20614e7	−1.47335
$55$	4.30940e7	0.635016
$56$	−1.92918e7	−0.262137
$57$	2.78471e7	0.349416
$58$	−1.59134e7	−0.184645
$59$	−7.17560e7	−0.770947	−0.385473	−	0.922719i	$-0.625962\pi$
$59$	−7.17560e7	−0.770947	−0.385473	+	0.922719i	$0.625962\pi$
$60$	2.61868e7	0.260856
$61$	7.09576e7	0.656167	0.328084	−	0.944649i	$-0.393597\pi$
$61$	7.09576e7	0.656167	0.328084	+	0.944649i	$0.393597\pi$
$62$	1.32817e8	1.14154
$63$	6.78443e7	0.542601
$64$	−9.22657e7	−0.687433
$65$	−4.57103e7	−0.317617
$66$	−2.55158e8	−1.65524
$67$	2.92852e8	1.77546	0.887732	−	0.460360i	$-0.152280\pi$
$67$	2.92852e8	1.77546	0.887732	+	0.460360i	$0.152280\pi$
$68$	1.48137e8	0.840183
$69$	1.99095e8	1.05740
$70$	−1.43100e8	−0.712361
$71$	9.86093e7	0.460527	0.230264	−	0.973128i	$-0.426041\pi$
$71$	9.86093e7	0.460527	0.230264	+	0.973128i	$0.426041\pi$
$72$	−1.89148e7	−0.0829480
$73$	2.03894e8	0.840331	0.420166	−	0.907447i	$-0.361972\pi$
$73$	2.03894e8	0.840331	0.420166	+	0.907447i	$0.361972\pi$
$74$	7.63482e6	0.0295976
$75$	1.76205e8	0.643048
$76$	−1.13268e8	−0.389445
$77$	6.41839e8	2.08074
$78$	2.70649e8	0.827906
$79$	−8.76574e7	−0.253202	−0.126601	−	0.991954i	$-0.540407\pi$
$79$	−8.76574e7	−0.253202	−0.126601	+	0.991954i	$0.540407\pi$
$80$	1.64776e8	0.449767
$81$	−1.60370e8	−0.413943
$82$	3.67114e8	0.896683
$83$	4.38233e8	1.01357	0.506785	−	0.862073i	$-0.330834\pi$
$83$	4.38233e8	1.01357	0.506785	+	0.862073i	$0.330834\pi$
$84$	3.90024e8	0.854741
$85$	−1.89456e8	−0.393662
$86$	−1.37272e9	−2.70608
$87$	−5.54699e7	−0.103806
$88$	−1.78943e8	−0.318085
$89$	7.35999e8	1.24343	0.621717	−	0.783242i	$-0.286436\pi$
$89$	7.35999e8	1.24343	0.621717	+	0.783242i	$0.286436\pi$
$90$	−1.40304e8	−0.225412
$91$	−6.80806e8	−1.04073
$92$	−8.09819e8	−1.17854
$93$	4.62966e8	0.641765
$94$	−6.51577e8	−0.860776
$95$	1.44861e8	0.182472
$96$	−8.48146e8	−1.01918
$97$	8.85921e7	0.101607	0.0508033	−	0.998709i	$-0.483822\pi$
$97$	8.85921e7	0.101607	0.0508033	+	0.998709i	$0.483822\pi$
$98$	−8.88396e8	−0.972947
$99$	6.29295e8	0.658410
$100$	−7.16715e8	−0.716715
$101$	1.32225e9	1.26435	0.632174	−	0.774826i	$-0.282163\pi$
$101$	1.32225e9	1.26435	0.632174	+	0.774826i	$0.282163\pi$
$102$	1.12177e9	1.02613
$103$	−1.69416e9	−1.48316	−0.741578	−	0.670867i	$-0.765922\pi$
$103$	−1.69416e9	−1.48316	−0.741578	+	0.670867i	$0.765922\pi$
$104$	1.89807e8	0.159097
$105$	−4.98811e8	−0.400483
$106$	−9.21793e8	−0.709181
$107$	−6.42456e8	−0.473823	−0.236912	−	0.971531i	$-0.576135\pi$
$107$	−6.42456e8	−0.473823	−0.236912	+	0.971531i	$0.576135\pi$
$108$	1.30527e9	0.923195
$109$	5.67111e8	0.384812	0.192406	−	0.981315i	$-0.438371\pi$
$109$	5.67111e8	0.384812	0.192406	+	0.981315i	$0.438371\pi$
$110$	−1.32734e9	−0.864401
$111$	2.66130e7	0.0166395
$112$	2.45416e9	1.47374
$113$	−2.34652e9	−1.35385	−0.676925	−	0.736052i	$-0.736688\pi$
$113$	−2.34652e9	−1.35385	−0.676925	+	0.736052i	$0.736688\pi$
$114$	−8.57720e8	−0.475635
$115$	1.03570e9	0.552195
$116$	2.25624e8	0.115698
$117$	−6.67500e8	−0.329318
$118$	2.21016e9	1.04943
$119$	−2.82175e9	−1.28990
$120$	1.39067e8	0.0612222
$121$	3.59549e9	1.52484
$122$	−2.18557e9	−0.893193
$123$	1.27966e9	0.504107
$124$	−1.88312e9	−0.715286
$125$	2.00747e9	0.735451
$126$	−2.08968e9	−0.738603
$127$	−4.13833e9	−1.41159	−0.705794	−	0.708417i	$-0.749410\pi$
$127$	−4.13833e9	−1.41159	−0.705794	+	0.708417i	$0.749410\pi$
$128$	−1.20276e9	−0.396036
$129$	−4.78495e9	−1.52133
$130$	1.40792e9	0.432349
$131$	−5.29277e8	−0.157023	−0.0785114	−	0.996913i	$-0.525017\pi$
$131$	−5.29277e8	−0.157023	−0.0785114	+	0.996913i	$0.525017\pi$
$132$	3.61770e9	1.03717
$133$	2.15756e9	0.597901
$134$	−9.02016e9	−2.41681
$135$	−1.66934e9	−0.432557
$136$	7.86696e8	0.197189
$137$	3.46052e9	0.839265	0.419633	−	0.907694i	$-0.362159\pi$
$137$	3.46052e9	0.839265	0.419633	+	0.907694i	$0.362159\pi$
$138$	−6.13233e9	−1.43936
$139$	−5.48330e9	−1.24588	−0.622939	−	0.782271i	$-0.714061\pi$
$139$	−5.48330e9	−1.24588	−0.622939	+	0.782271i	$0.714061\pi$
$140$	2.02891e9	0.446362
$141$	−2.27123e9	−0.483921
$142$	−3.03727e9	−0.626882
$143$	−6.31487e9	−1.26285
$144$	2.40619e9	0.466336
$145$	−2.88556e8	−0.0542093
$146$	−6.28014e9	−1.14388
$147$	−3.09672e9	−0.546983
$148$	−1.08248e8	−0.0185457
$149$	−4.78367e8	−0.0795102	−0.0397551	−	0.999209i	$-0.512658\pi$
$149$	−4.78367e8	−0.0795102	−0.0397551	+	0.999209i	$0.512658\pi$
$150$	−5.42731e9	−0.875334
$151$	3.24609e9	0.508118	0.254059	−	0.967189i	$-0.418234\pi$
$151$	3.24609e9	0.508118	0.254059	+	0.967189i	$0.418234\pi$
$152$	−6.01521e8	−0.0914017
$153$	−2.76660e9	−0.408164
$154$	−1.97693e10	−2.83236
$155$	2.40836e9	0.335142
$156$	−3.83733e9	−0.518763
$157$	4.72832e9	0.621096	0.310548	−	0.950558i	$-0.399487\pi$
$157$	4.72832e9	0.621096	0.310548	+	0.950558i	$0.399487\pi$
$158$	2.69994e9	0.344665
$159$	−3.21313e9	−0.398696
$160$	−4.41208e9	−0.532235
$161$	1.54256e10	1.80936
$162$	4.93957e9	0.563471
$163$	−7.60806e9	−0.844170	−0.422085	−	0.906556i	$-0.638702\pi$
$163$	−7.60806e9	−0.844170	−0.422085	+	0.906556i	$0.638702\pi$
$164$	−5.20504e9	−0.561858
$165$	−4.62676e9	−0.485959
$166$	−1.34980e10	−1.37970
$167$	5.32691e9	0.529970	0.264985	−	0.964253i	$-0.414633\pi$
$167$	5.32691e9	0.529970	0.264985	+	0.964253i	$0.414633\pi$
$168$	2.07126e9	0.200605
$169$	−3.90624e9	−0.368357
$170$	5.83545e9	0.535864
$171$	2.11539e9	0.189194
$172$	1.94628e10	1.69562
$173$	6.99208e9	0.593470	0.296735	−	0.954960i	$-0.404102\pi$
$173$	6.99208e9	0.593470	0.296735	+	0.954960i	$0.404102\pi$
$174$	1.70853e9	0.141303
$175$	1.36522e10	1.10035
$176$	2.27637e10	1.78828
$177$	7.70405e9	0.589983
$178$	−2.26696e10	−1.69260
$179$	−7.13352e8	−0.0519356	−0.0259678	−	0.999663i	$-0.508267\pi$
$179$	−7.13352e8	−0.0519356	−0.0259678	+	0.999663i	$0.508267\pi$
$180$	1.98926e9	0.141243
$181$	3.57100e9	0.247307	0.123653	−	0.992325i	$-0.460539\pi$
$181$	3.57100e9	0.247307	0.123653	+	0.992325i	$0.460539\pi$
$182$	2.09695e10	1.41667
$183$	−7.61832e9	−0.502145
$184$	−4.30062e9	−0.276599
$185$	1.38442e8	0.00868948
$186$	−1.42599e10	−0.873589
$187$	−2.61734e10	−1.56521
$188$	9.23822e9	0.539359
$189$	−2.48631e10	−1.41735
$190$	−4.46188e9	−0.248386
$191$	−2.72678e10	−1.48252	−0.741259	−	0.671219i	$-0.765771\pi$
$191$	−2.72678e10	−1.48252	−0.741259	+	0.671219i	$0.765771\pi$
$192$	9.90605e9	0.526072
$193$	−2.27682e10	−1.18119	−0.590596	−	0.806968i	$-0.701107\pi$
$193$	−2.27682e10	−1.18119	−0.590596	+	0.806968i	$0.701107\pi$
$194$	−2.72873e9	−0.138310
$195$	4.90766e9	0.243063
$196$	1.25959e10	0.609645
$197$	−1.50614e9	−0.0712470
$197$	−1.50614e9	−0.0712470
$198$	−1.93830e10	−0.896245
$199$	−1.23454e10	−0.558041	−0.279020	−	0.960285i	$-0.590010\pi$
$199$	−1.23454e10	−0.558041	−0.279020	+	0.960285i	$0.590010\pi$
$200$	−3.80618e9	−0.168211
$201$	−3.14419e10	−1.35871
$202$	−4.07266e10	−1.72107
$203$	−4.29773e9	−0.177626
$204$	−1.59047e10	−0.642967
$205$	6.65685e9	0.263255
$206$	5.21819e10	2.01891
$207$	1.51241e10	0.572537
$208$	−2.41457e10	−0.894449
$209$	2.00126e10	0.725513
$210$	1.53639e10	0.545148
$211$	2.25099e10	0.781811	0.390906	−	0.920431i	$-0.372162\pi$
$211$	2.25099e10	0.781811	0.390906	+	0.920431i	$0.372162\pi$
$212$	1.30694e10	0.444370
$213$	−1.05871e10	−0.352428
$214$	1.97883e10	0.644981
$215$	−2.48915e10	−0.794470
$216$	6.93176e9	0.216671
$217$	3.58700e10	1.09815
$218$	−1.74676e10	−0.523816
$219$	−2.18909e10	−0.643080
$220$	1.88194e10	0.541630
$221$	2.77624e10	0.782873
$222$	−8.19709e8	−0.0226502
$223$	3.77449e10	1.02208	0.511042	−	0.859556i	$-0.329260\pi$
$223$	3.77449e10	1.02208	0.511042	+	0.859556i	$0.329260\pi$
$224$	−6.57132e10	−1.74396
$225$	1.33853e10	0.348183
$226$	7.22752e10	1.84290
$227$	−2.19230e10	−0.548005	−0.274003	−	0.961729i	$-0.588348\pi$
$227$	−2.19230e10	−0.548005	−0.274003	+	0.961729i	$0.588348\pi$
$228$	1.21610e10	0.298031
$229$	3.81665e10	0.917113	0.458557	−	0.888665i	$-0.348367\pi$
$229$	3.81665e10	0.917113	0.458557	+	0.888665i	$0.348367\pi$
$230$	−3.19006e10	−0.751663
$231$	−6.89107e10	−1.59233
$232$	1.19820e9	0.0271539
$233$	−4.89012e10	−1.08697	−0.543486	−	0.839418i	$-0.682896\pi$
$233$	−4.89012e10	−1.08697	−0.543486	+	0.839418i	$0.682896\pi$
$234$	2.05597e10	0.448276
$235$	−1.18150e10	−0.252713
$236$	−3.13362e10	−0.657571
$237$	9.41129e9	0.193768
$238$	8.69129e10	1.75585
$239$	−3.44674e10	−0.683310	−0.341655	−	0.939825i	$-0.610987\pi$
$239$	−3.44674e10	−0.683310	−0.341655	+	0.939825i	$0.610987\pi$
$240$	−1.76910e10	−0.344193
$241$	2.04478e10	0.390454	0.195227	−	0.980758i	$-0.437456\pi$
$241$	2.04478e10	0.390454	0.195227	+	0.980758i	$0.437456\pi$
$242$	−1.10745e11	−2.07565
$243$	−4.16126e10	−0.765590
$244$	3.09875e10	0.559671
$245$	−1.61092e10	−0.285645
$246$	−3.94150e10	−0.686205
$247$	−2.12276e10	−0.362881
$248$	−1.00005e10	−0.167876
$249$	−4.70506e10	−0.775655
$250$	−6.18322e10	−1.00112
$251$	6.84964e10	1.08927	0.544635	−	0.838673i	$-0.316668\pi$
$251$	6.84964e10	1.08927	0.544635	+	0.838673i	$0.316668\pi$
$252$	2.96279e10	0.462806
$253$	1.43081e11	2.19554
$254$	1.27465e11	1.92149
$255$	2.03409e10	0.301258
$256$	8.42863e10	1.22653
$257$	−5.87992e10	−0.840761	−0.420380	−	0.907348i	$-0.638103\pi$
$257$	−5.87992e10	−0.840761	−0.420380	+	0.907348i	$0.638103\pi$
$258$	1.47382e11	2.07088
$259$	2.06194e9	0.0284726
$260$	−1.99619e10	−0.270908
$261$	−4.21374e9	−0.0562063
$262$	1.63023e10	0.213744
$263$	1.08629e11	1.40005	0.700026	−	0.714118i	$-0.253172\pi$
$263$	1.08629e11	1.40005	0.700026	+	0.714118i	$0.253172\pi$
$264$	1.92121e10	0.243421
$265$	−1.67148e10	−0.208207
$266$	−6.64550e10	−0.813880
$267$	−7.90202e10	−0.951562
$268$	1.27890e11	1.51436
$269$	1.62013e11	1.88654	0.943269	−	0.332029i	$-0.107733\pi$
$269$	1.62013e11	1.88654	0.943269	+	0.332029i	$0.107733\pi$
$270$	5.14175e10	0.588808
$271$	−3.17031e10	−0.357059	−0.178530	−	0.983935i	$-0.557134\pi$
$271$	−3.17031e10	−0.357059	−0.178530	+	0.983935i	$0.557134\pi$
$272$	−1.00077e11	−1.10860
$273$	7.30944e10	0.796438
$274$	−1.06588e11	−1.14243
$275$	1.26632e11	1.33520
$276$	8.69457e10	0.901898
$277$	8.43229e10	0.860571	0.430286	−	0.902693i	$-0.358413\pi$
$277$	8.43229e10	0.860571	0.430286	+	0.902693i	$0.358413\pi$
$278$	1.68891e11	1.69592
$279$	3.51690e10	0.347489
$280$	1.07747e10	0.104760
$281$	−5.71170e10	−0.546496	−0.273248	−	0.961944i	$-0.588098\pi$
$281$	−5.71170e10	−0.546496	−0.273248	+	0.961944i	$0.588098\pi$
$282$	6.99562e10	0.658726
$283$	1.60776e10	0.148998	0.0744991	−	0.997221i	$-0.476264\pi$
$283$	1.60776e10	0.148998	0.0744991	+	0.997221i	$0.476264\pi$
$284$	4.30632e10	0.392802
$285$	−1.55530e10	−0.139640
$286$	1.94505e11	1.71903
$287$	9.91467e10	0.862600
$288$	−6.44289e10	−0.551842
$289$	−3.52060e9	−0.0296877
$290$	8.88783e9	0.0737912
$291$	−9.51164e9	−0.0777565
$292$	8.90413e10	0.716752
$293$	7.53770e10	0.597496	0.298748	−	0.954332i	$-0.403431\pi$
$293$	7.53770e10	0.597496	0.298748	+	0.954332i	$0.403431\pi$
$294$	9.53822e10	0.744568
$295$	4.00767e10	0.308100
$296$	−5.74864e8	−0.00435263
$297$	−2.30619e11	−1.71986
$298$	1.47342e10	0.108231
$299$	−1.51768e11	−1.09815
$300$	7.69498e10	0.548481
$301$	−3.70732e11	−2.60322
$302$	−9.99830e10	−0.691664
$303$	−1.41962e11	−0.967568
$304$	7.65207e10	0.513864
$305$	−3.96307e10	−0.262230
$306$	8.52142e10	0.555605
$307$	−7.21713e10	−0.463705	−0.231852	−	0.972751i	$-0.574479\pi$
$307$	−7.21713e10	−0.463705	−0.231852	+	0.972751i	$0.574479\pi$
$308$	2.80295e11	1.77475
$309$	1.81892e11	1.13501
$310$	−7.41801e10	−0.456205
$311$	−1.35249e11	−0.819808	−0.409904	−	0.912129i	$-0.634438\pi$
$311$	−1.35249e11	−0.819808	−0.409904	+	0.912129i	$0.634438\pi$
$312$	−2.03785e10	−0.121752
$313$	7.59766e10	0.447435	0.223718	−	0.974654i	$-0.428181\pi$
$313$	7.59766e10	0.447435	0.223718	+	0.974654i	$0.428181\pi$
$314$	−1.45637e11	−0.845453
$315$	−3.78919e10	−0.216845
$316$	−3.82804e10	−0.215966
$317$	−6.05302e10	−0.336671	−0.168335	−	0.985730i	$-0.553839\pi$
$317$	−6.05302e10	−0.336671	−0.168335	+	0.985730i	$0.553839\pi$
$318$	9.89678e10	0.542715
$319$	−3.98640e10	−0.215537
$320$	5.15315e10	0.274725
$321$	6.89769e10	0.362603
$322$	−4.75125e11	−2.46295
$323$	−8.79823e10	−0.449763
$324$	−7.00344e10	−0.353068
$325$	−1.34320e11	−0.667827
$326$	2.34336e11	1.14911
$327$	−6.08875e10	−0.294485
$328$	−2.76418e10	−0.131867
$329$	−1.75972e11	−0.828058
$330$	1.42509e11	0.661500
$331$	7.04537e9	0.0322610	0.0161305	−	0.999870i	$-0.494865\pi$
$331$	7.04537e9	0.0322610	0.0161305	+	0.999870i	$0.494865\pi$
$332$	1.91379e11	0.864514
$333$	2.02164e9	0.00900959
$334$	−1.64074e11	−0.721409
$335$	−1.63562e11	−0.709545
$336$	−2.63489e11	−1.12781
$337$	−4.14690e11	−1.75142	−0.875708	−	0.482842i	$-0.839605\pi$
$337$	−4.14690e11	−1.75142	−0.875708	+	0.482842i	$0.839605\pi$
$338$	1.20316e11	0.501418
$339$	2.51932e11	1.03606
$340$	−8.27365e10	−0.335770
$341$	3.32715e11	1.33253
$342$	−6.51562e10	−0.257536
$343$	9.57501e10	0.373521
$344$	1.03359e11	0.397957
$345$	−1.11197e11	−0.422578
$346$	−2.15363e11	−0.807848
$347$	2.20530e11	0.816554	0.408277	−	0.912858i	$-0.366130\pi$
$347$	2.20530e11	0.816554	0.408277	+	0.912858i	$0.366130\pi$
$348$	−2.42240e10	−0.0885399
$349$	−3.60181e11	−1.29959	−0.649794	−	0.760110i	$-0.725145\pi$
$349$	−3.60181e11	−1.29959	−0.649794	+	0.760110i	$0.725145\pi$
$350$	−4.20501e11	−1.49782
$351$	2.44621e11	0.860223
$352$	−6.09528e11	−2.11618
$353$	2.08116e11	0.713379	0.356689	−	0.934223i	$-0.383905\pi$
$353$	2.08116e11	0.713379	0.356689	+	0.934223i	$0.383905\pi$
$354$	−2.37293e11	−0.803101
$355$	−5.50745e10	−0.184045
$356$	3.21415e11	1.06057
$357$	3.02956e11	0.987125
$358$	2.19720e10	0.0706962
$359$	−3.47863e11	−1.10531	−0.552654	−	0.833411i	$-0.686385\pi$
$359$	−3.47863e11	−1.10531	−0.552654	+	0.833411i	$0.686385\pi$
$360$	1.05642e10	0.0331492
$361$	−2.55415e11	−0.791524
$362$	−1.09991e11	−0.336641
$363$	−3.86028e11	−1.16691
$364$	−2.97311e11	−0.887678
$365$	−1.13877e11	−0.335829
$366$	2.34652e11	0.683534
$367$	1.48225e11	0.426506	0.213253	−	0.976997i	$-0.431594\pi$
$367$	1.48225e11	0.426506	0.213253	+	0.976997i	$0.431594\pi$
$368$	5.47091e11	1.55505
$369$	9.72089e10	0.272953
$370$	−4.26415e9	−0.0118284
$371$	−2.48949e11	−0.682225
$372$	2.02180e11	0.547387
$373$	2.46971e11	0.660628	0.330314	−	0.943871i	$-0.392845\pi$
$373$	2.46971e11	0.660628	0.330314	+	0.943871i	$0.392845\pi$
$374$	8.06168e11	2.13061
$375$	−2.15531e11	−0.562819
$376$	4.90604e10	0.126586
$377$	4.22842e10	0.107806
$378$	7.65809e11	1.92933
$379$	−9.63616e10	−0.239899	−0.119949	−	0.992780i	$-0.538273\pi$
$379$	−9.63616e10	−0.239899	−0.119949	+	0.992780i	$0.538273\pi$
$380$	6.32617e10	0.155638
$381$	4.44309e11	1.08025
$382$	8.39877e11	2.01804
$383$	−7.12662e9	−0.0169235	−0.00846173	−	0.999964i	$-0.502693\pi$
$383$	−7.12662e9	−0.0169235	−0.00846173	+	0.999964i	$0.502693\pi$
$384$	1.29134e11	0.303074
$385$	−3.58475e11	−0.831546
$386$	7.01284e11	1.60787
$387$	−3.63486e11	−0.823737
$388$	3.86886e10	0.0866643
$389$	5.22248e11	1.15639	0.578194	−	0.815900i	$-0.303758\pi$
$389$	5.22248e11	1.15639	0.578194	+	0.815900i	$0.303758\pi$
$390$	−1.51161e11	−0.330864
$391$	−6.29036e11	−1.36107
$392$	6.68917e10	0.143082
$393$	5.68256e10	0.120165
$394$	4.63907e10	0.0969834
$395$	4.89578e10	0.101189
$396$	2.74816e11	0.561584
$397$	−7.85090e11	−1.58622	−0.793108	−	0.609081i	$-0.791538\pi$
$397$	−7.85090e11	−1.58622	−0.793108	+	0.609081i	$0.791538\pi$
$398$	3.80251e11	0.759620
$399$	−2.31645e11	−0.457556
$400$	4.84193e11	0.945689
$401$	−1.46552e11	−0.283035	−0.141518	−	0.989936i	$-0.545198\pi$
$401$	−1.46552e11	−0.283035	−0.141518	+	0.989936i	$0.545198\pi$
$402$	9.68445e11	1.84951
$403$	−3.52915e11	−0.666496
$404$	5.77433e11	1.07841
$405$	8.95687e10	0.165428
$406$	1.32375e11	0.241790
$407$	1.91257e10	0.0345496
$408$	−8.44632e10	−0.150903
$409$	−6.63688e11	−1.17276	−0.586380	−	0.810036i	$-0.699447\pi$
$409$	−6.63688e11	−1.17276	−0.586380	+	0.810036i	$0.699447\pi$
$410$	−2.05038e11	−0.358349
$411$	−3.71537e11	−0.642265
$412$	−7.39848e11	−1.26504
$413$	5.96899e11	1.00955
$414$	−4.65839e11	−0.779353
$415$	−2.44759e11	−0.405062
$416$	6.46533e11	1.05845
$417$	5.88711e11	0.953433
$418$	−6.16409e11	−0.987587
$419$	7.23699e11	1.14708	0.573541	−	0.819177i	$-0.305569\pi$
$419$	7.23699e11	1.14708	0.573541	+	0.819177i	$0.305569\pi$
$420$	−2.17833e11	−0.341588
$421$	−1.64258e11	−0.254834	−0.127417	−	0.991849i	$-0.540669\pi$
$421$	−1.64258e11	−0.254834	−0.127417	+	0.991849i	$0.540669\pi$
$422$	−6.93328e11	−1.06422
$423$	−1.72532e11	−0.262023
$424$	6.94064e10	0.104292
$425$	−5.56717e11	−0.827722
$426$	3.26095e11	0.479734
$427$	−5.90257e11	−0.859243
$428$	−2.80564e11	−0.404143
$429$	6.77993e11	0.966423
$430$	7.66683e11	1.08145
$431$	4.73374e10	0.0660780	0.0330390	−	0.999454i	$-0.489481\pi$
$431$	4.73374e10	0.0660780	0.0330390	+	0.999454i	$0.489481\pi$
$432$	−8.81804e11	−1.21813
$433$	2.90866e11	0.397647	0.198823	−	0.980035i	$-0.436288\pi$
$433$	2.90866e11	0.397647	0.198823	+	0.980035i	$0.436288\pi$
$434$	−1.10483e12	−1.49484
$435$	3.09806e10	0.0414848
$436$	2.47660e11	0.328221
$437$	4.80971e11	0.630888
$438$	6.74263e11	0.875379
$439$	−1.25818e12	−1.61679	−0.808395	−	0.588640i	$-0.799664\pi$
$439$	−1.25818e12	−1.61679	−0.808395	+	0.588640i	$0.799664\pi$
$440$	9.99420e10	0.127119
$441$	−2.35240e11	−0.296168
$442$	−8.55111e11	−1.06567
$443$	−7.88145e11	−0.972276	−0.486138	−	0.873882i	$-0.661595\pi$
$443$	−7.88145e11	−0.972276	−0.486138	+	0.873882i	$0.661595\pi$
$444$	1.16220e10	0.0141925
$445$	−4.11065e11	−0.496925
$446$	−1.16258e12	−1.39129
$447$	5.13596e10	0.0608468
$448$	7.67508e11	0.900185
$449$	1.56886e12	1.82169	0.910847	−	0.412743i	$-0.135429\pi$
$449$	1.56886e12	1.82169	0.910847	+	0.412743i	$0.135429\pi$
$450$	−4.12282e11	−0.473956
$451$	9.19643e11	1.04671
$452$	−1.02474e12	−1.15475
$453$	−3.48515e11	−0.388847
$454$	6.75253e11	0.745959
$455$	3.80239e11	0.415915
$456$	6.45819e10	0.0699470
$457$	−1.33773e11	−0.143465	−0.0717326	−	0.997424i	$-0.522853\pi$
$457$	−1.33773e11	−0.143465	−0.0717326	+	0.997424i	$0.522853\pi$
$458$	−1.17557e12	−1.24840
$459$	1.01388e12	1.06618
$460$	4.52294e11	0.470989
$461$	5.43676e11	0.560643	0.280321	−	0.959906i	$-0.409559\pi$
$461$	5.43676e11	0.560643	0.280321	+	0.959906i	$0.409559\pi$
$462$	2.12252e12	2.16752
$463$	−1.20020e12	−1.21378	−0.606890	−	0.794786i	$-0.707583\pi$
$463$	−1.20020e12	−1.21378	−0.606890	+	0.794786i	$0.707583\pi$
$464$	−1.52425e11	−0.152660
$465$	−2.58573e11	−0.256475
$466$	1.50621e12	1.47962
$467$	1.94869e12	1.89590	0.947951	−	0.318415i	$-0.103151\pi$
$467$	1.94869e12	1.89590	0.947951	+	0.318415i	$0.103151\pi$
$468$	−2.91501e11	−0.280888
$469$	−2.43608e12	−2.32495
$470$	3.63914e11	0.344000
$471$	−5.07654e11	−0.475306
$472$	−1.66414e11	−0.154330
$473$	−3.43875e12	−3.15883
$474$	−2.89878e11	−0.263762
$475$	4.25675e11	0.383669
$476$	−1.23227e12	−1.10021
$477$	−2.44084e11	−0.215877
$478$	1.06163e12	0.930140
$479$	1.42572e12	1.23744	0.618719	−	0.785612i	$-0.287652\pi$
$479$	1.42572e12	1.23744	0.618719	+	0.785612i	$0.287652\pi$
$480$	4.73700e11	0.407303
$481$	−2.02868e10	−0.0172807
$482$	−6.29813e11	−0.531496
$483$	−1.65616e12	−1.38465
$484$	1.57017e12	1.30059
$485$	−4.94798e10	−0.0406060
$486$	1.28171e12	1.04214
$487$	−2.55347e11	−0.205708	−0.102854	−	0.994696i	$-0.532797\pi$
$487$	−2.55347e11	−0.205708	−0.102854	+	0.994696i	$0.532797\pi$
$488$	1.64562e11	0.131353
$489$	8.16835e11	0.646018
$490$	4.96180e11	0.388828
$491$	−1.86365e11	−0.144710	−0.0723548	−	0.997379i	$-0.523051\pi$
$491$	−1.86365e11	−0.144710	−0.0723548	+	0.997379i	$0.523051\pi$
$492$	5.58836e11	0.429973
$493$	1.75256e11	0.133617
$494$	6.53832e11	0.493963
$495$	−3.51469e11	−0.263126
$496$	1.27218e12	0.943803
$497$	−8.20277e11	−0.603055
$498$	1.44921e12	1.05584
$499$	1.68039e12	1.21327	0.606634	−	0.794981i	$-0.292519\pi$
$499$	1.68039e12	1.21327	0.606634	+	0.794981i	$0.292519\pi$
$500$	8.76672e11	0.627295
$501$	−5.71921e11	−0.405570
$502$	−2.10976e12	−1.48274
$503$	2.45247e12	1.70823	0.854116	−	0.520082i	$-0.174099\pi$
$503$	2.45247e12	1.70823	0.854116	+	0.520082i	$0.174099\pi$
$504$	1.57342e11	0.108619
$505$	−7.38492e11	−0.505283
$506$	−4.40706e12	−2.98863
$507$	4.19392e11	0.281893
$508$	−1.80723e12	−1.20400
$509$	−1.43674e12	−0.948740	−0.474370	−	0.880326i	$-0.657324\pi$
$509$	−1.43674e12	−0.948740	−0.474370	+	0.880326i	$0.657324\pi$
$510$	−6.26520e11	−0.410081
$511$	−1.69608e12	−1.10040
$512$	−1.98029e12	−1.27355
$513$	−7.75232e11	−0.494201
$514$	1.81108e12	1.14447
$515$	9.46209e11	0.592727
$516$	−2.08961e12	−1.29760
$517$	−1.63224e12	−1.00479
$518$	−6.35099e10	−0.0387577
$519$	−7.50701e11	−0.454165
$520$	−1.06010e11	−0.0635814
$521$	2.93064e12	1.74258	0.871289	−	0.490771i	$-0.163285\pi$
$521$	2.93064e12	1.74258	0.871289	+	0.490771i	$0.163285\pi$
$522$	1.29788e11	0.0765096
$523$	6.67888e11	0.390343	0.195171	−	0.980769i	$-0.437474\pi$
$523$	6.67888e11	0.390343	0.195171	+	0.980769i	$0.437474\pi$
$524$	−2.31138e11	−0.133931
$525$	−1.46576e12	−0.842063
$526$	−3.34588e12	−1.90579
$527$	−1.46273e12	−0.826071
$528$	−2.44402e12	−1.36852
$529$	1.63759e12	0.909188
$530$	5.14833e11	0.283416
$531$	5.85233e11	0.319451
$532$	9.42215e11	0.509974
$533$	−9.75476e11	−0.523533
$534$	2.43390e12	1.29529
$535$	3.58820e11	0.189358
$536$	6.79172e11	0.355417
$537$	7.65886e10	0.0397448
$538$	−4.99018e12	−2.56801
$539$	−2.22549e12	−1.13573
$540$	−7.29010e11	−0.368945
$541$	−1.14433e12	−0.574335	−0.287168	−	0.957880i	$-0.592714\pi$
$541$	−1.14433e12	−0.574335	−0.287168	+	0.957880i	$0.592714\pi$
$542$	9.76490e11	0.486039
$543$	−3.83398e11	−0.189257
$544$	2.67970e12	1.31187
$545$	−3.16738e11	−0.153786
$546$	−2.25138e12	−1.08413
$547$	−2.84546e12	−1.35897	−0.679484	−	0.733691i	$-0.737796\pi$
$547$	−2.84546e12	−1.35897	−0.679484	+	0.733691i	$0.737796\pi$
$548$	1.51123e12	0.715843
$549$	−5.78721e11	−0.271890
$550$	−3.90039e12	−1.81751
$551$	−1.34004e11	−0.0619347
$552$	4.61733e11	0.211673
$553$	7.29174e11	0.331565
$554$	−2.59724e12	−1.17143
$555$	−1.48637e10	−0.00664980
$556$	−2.39458e12	−1.06266
$557$	−3.14541e11	−0.138461	−0.0692306	−	0.997601i	$-0.522054\pi$
$557$	−3.14541e11	−0.138461	−0.0692306	+	0.997601i	$0.522054\pi$
$558$	−1.08324e12	−0.473011
$559$	3.64752e12	1.57996
$560$	−1.37068e12	−0.588965
$561$	2.81009e12	1.19781
$562$	1.75927e12	0.743906
$563$	1.85209e12	0.776916	0.388458	−	0.921466i	$-0.373008\pi$
$563$	1.85209e12	0.776916	0.388458	+	0.921466i	$0.373008\pi$
$564$	−9.91856e11	−0.412755
$565$	1.31056e12	0.541051
$566$	−4.95206e11	−0.202821
$567$	1.33403e12	0.542053
$568$	2.28691e11	0.0921896
$569$	2.27961e12	0.911709	0.455854	−	0.890054i	$-0.349334\pi$
$569$	2.27961e12	0.911709	0.455854	+	0.890054i	$0.349334\pi$
$570$	4.79047e11	0.190082
$571$	−3.39014e11	−0.133461	−0.0667307	−	0.997771i	$-0.521257\pi$
$571$	−3.39014e11	−0.133461	−0.0667307	+	0.997771i	$0.521257\pi$
$572$	−2.75774e12	−1.07714
$573$	2.92759e12	1.13453
$574$	−3.05382e12	−1.17419
$575$	3.04339e12	1.16106
$576$	7.52508e11	0.284846
$577$	−1.62294e11	−0.0609552	−0.0304776	−	0.999535i	$-0.509703\pi$
$577$	−1.62294e11	−0.0609552	−0.0304776	+	0.999535i	$0.509703\pi$
$578$	1.08438e11	0.0404117
$579$	2.44449e12	0.903930
$580$	−1.26014e11	−0.0462373
$581$	−3.64542e12	−1.32726
$582$	2.92969e11	0.105844
$583$	−2.30915e12	−0.827834
$584$	4.72862e11	0.168220
$585$	3.72807e11	0.131608
$586$	−2.32169e12	−0.813327
$587$	−3.44991e12	−1.19932	−0.599661	−	0.800254i	$-0.704698\pi$
$587$	−3.44991e12	−1.19932	−0.599661	+	0.800254i	$0.704698\pi$
$588$	−1.35235e12	−0.466543
$589$	1.11843e12	0.382904
$590$	−1.23440e12	−0.419395
$591$	1.61706e11	0.0545232
$592$	7.31296e10	0.0244707
$593$	3.62453e12	1.20366	0.601832	−	0.798623i	$-0.294438\pi$
$593$	3.62453e12	1.20366	0.601832	+	0.798623i	$0.294438\pi$
$594$	7.10332e12	2.34111
$595$	1.57598e12	0.515496
$596$	−2.08905e11	−0.0678174
$597$	1.32546e12	0.427052
$598$	4.67462e12	1.49483
$599$	−5.40443e12	−1.71526	−0.857628	−	0.514270i	$-0.828063\pi$
$599$	−5.40443e12	−1.71526	−0.857628	+	0.514270i	$0.828063\pi$
$600$	4.08649e11	0.128727
$601$	8.26860e11	0.258522	0.129261	−	0.991611i	$-0.458740\pi$
$601$	8.26860e11	0.258522	0.129261	+	0.991611i	$0.458740\pi$
$602$	1.14189e13	3.54357
$603$	−2.38847e12	−0.735684
$604$	1.41758e12	0.433394
$605$	−2.00813e12	−0.609385
$606$	4.37259e12	1.31708
$607$	−2.03173e12	−0.607458	−0.303729	−	0.952759i	$-0.598232\pi$
$607$	−2.03173e12	−0.607458	−0.303729	+	0.952759i	$0.598232\pi$
$608$	−2.04894e12	−0.608084
$609$	4.61424e11	0.135932
$610$	1.22067e12	0.356955
$611$	1.73133e12	0.502569
$612$	−1.20819e12	−0.348140
$613$	−5.07732e12	−1.45232	−0.726160	−	0.687526i	$-0.758697\pi$
$613$	−5.07732e12	−1.45232	−0.726160	+	0.687526i	$0.758697\pi$
$614$	2.22295e12	0.631208
$615$	−7.14708e11	−0.201461
$616$	1.48853e12	0.416528
$617$	6.49891e12	1.80533	0.902667	−	0.430341i	$-0.141607\pi$
$617$	6.49891e12	1.80533	0.902667	+	0.430341i	$0.141607\pi$
$618$	−5.60248e12	−1.54501
$619$	−2.35132e12	−0.643731	−0.321866	−	0.946785i	$-0.604310\pi$
$619$	−2.35132e12	−0.643731	−0.321866	+	0.946785i	$0.604310\pi$
$620$	1.05174e12	0.285856
$621$	−5.54258e12	−1.49555
$622$	4.16581e12	1.11594
$623$	−6.12238e12	−1.62826
$624$	2.59239e12	0.684495
$625$	2.08425e12	0.546374
$626$	−2.34016e12	−0.609061
$627$	−2.14864e12	−0.555213
$628$	2.06488e12	0.529757
$629$	−8.40832e10	−0.0214181
$630$	1.16711e12	0.295175
$631$	7.07159e12	1.77576	0.887881	−	0.460073i	$-0.152177\pi$
$631$	7.07159e12	1.77576	0.887881	+	0.460073i	$0.152177\pi$
$632$	−2.03292e11	−0.0506866
$633$	−2.41676e12	−0.598297
$634$	1.86440e12	0.458286
$635$	2.31131e12	0.564126
$636$	−1.40319e12	−0.340063
$637$	2.36060e12	0.568060
$638$	1.22785e12	0.293395
$639$	−8.04246e11	−0.190825
$640$	6.71757e11	0.158271
$641$	−4.16442e12	−0.974301	−0.487150	−	0.873318i	$-0.661964\pi$
$641$	−4.16442e12	−0.974301	−0.487150	+	0.873318i	$0.661964\pi$
$642$	−2.12456e12	−0.493585
$643$	3.01682e12	0.695986	0.347993	−	0.937497i	$-0.386863\pi$
$643$	3.01682e12	0.695986	0.347993	+	0.937497i	$0.386863\pi$
$644$	6.73644e12	1.54328
$645$	2.67246e12	0.607984
$646$	2.70995e12	0.612230
$647$	5.04362e12	1.13155	0.565774	−	0.824561i	$-0.308578\pi$
$647$	5.04362e12	1.13155	0.565774	+	0.824561i	$0.308578\pi$
$648$	−3.71924e11	−0.0828642
$649$	5.53659e12	1.22501
$650$	4.13719e12	0.909065
$651$	−3.85116e12	−0.840384
$652$	−3.32248e12	−0.720026
$653$	6.48263e12	1.39522	0.697609	−	0.716479i	$-0.254247\pi$
$653$	6.48263e12	1.39522	0.697609	+	0.716479i	$0.254247\pi$
$654$	1.87540e12	0.400861
$655$	2.95608e11	0.0627524
$656$	3.51638e12	0.741358
$657$	−1.66293e12	−0.348201
$658$	5.42011e12	1.12718
$659$	−1.44961e12	−0.299409	−0.149705	−	0.988731i	$-0.547832\pi$
$659$	−1.44961e12	−0.299409	−0.149705	+	0.988731i	$0.547832\pi$
$660$	−2.02053e12	−0.414494
$661$	8.49772e12	1.73139	0.865696	−	0.500569i	$-0.166876\pi$
$661$	8.49772e12	1.73139	0.865696	+	0.500569i	$0.166876\pi$
$662$	−2.17005e11	−0.0439146
$663$	−2.98069e12	−0.599110
$664$	1.01633e12	0.202899
$665$	−1.20502e12	−0.238945
$666$	−6.22687e10	−0.0122641
$667$	−9.58069e11	−0.187426
$668$	2.32629e12	0.452032
$669$	−4.05246e12	−0.782170
$670$	5.03787e12	0.965852
$671$	−5.47498e12	−1.04263
$672$	7.05526e12	1.33460
$673$	7.67840e11	0.144279	0.0721394	−	0.997395i	$-0.477017\pi$
$673$	7.67840e11	0.144279	0.0721394	+	0.997395i	$0.477017\pi$
$674$	1.27729e13	2.38407
$675$	−4.90536e12	−0.909502
$676$	−1.70588e12	−0.314186
$677$	5.59080e12	1.02288	0.511440	−	0.859319i	$-0.329112\pi$
$677$	5.59080e12	1.02288	0.511440	+	0.859319i	$0.329112\pi$
$678$	−7.75979e12	−1.41031
$679$	−7.36949e11	−0.133053
$680$	−4.39380e11	−0.0788043
$681$	2.35376e12	0.419372
$682$	−1.02480e13	−1.81388
$683$	9.35401e12	1.64477	0.822384	−	0.568932i	$-0.192643\pi$
$683$	9.35401e12	1.64477	0.822384	+	0.568932i	$0.192643\pi$
$684$	9.23801e11	0.161371
$685$	−1.93275e12	−0.335403
$686$	−2.94920e12	−0.508448
$687$	−4.09773e12	−0.701839
$688$	−1.31485e13	−2.23733
$689$	2.44934e12	0.414059
$690$	3.42498e12	0.575225
$691$	−8.45371e11	−0.141058	−0.0705288	−	0.997510i	$-0.522469\pi$
$691$	−8.45371e11	−0.141058	−0.0705288	+	0.997510i	$0.522469\pi$
$692$	3.05348e12	0.506194
$693$	−5.23476e12	−0.862179
$694$	−6.79255e12	−1.11152
$695$	3.06249e12	0.497901
$696$	−1.28644e11	−0.0207801
$697$	−4.04307e12	−0.648879
$698$	1.10939e13	1.76904
$699$	5.25025e12	0.831827
$700$	5.96196e12	0.938530
$701$	2.65058e11	0.0414581	0.0207291	−	0.999785i	$-0.493401\pi$
$701$	2.65058e11	0.0414581	0.0207291	+	0.999785i	$0.493401\pi$
$702$	−7.53457e12	−1.17096
$703$	6.42914e10	0.00992782
$704$	7.11908e12	1.09231
$705$	1.26851e12	0.193394
$706$	−6.41021e12	−0.971071
$707$	−1.09991e13	−1.65565
$708$	3.36440e12	0.503220
$709$	−5.43318e12	−0.807507	−0.403753	−	0.914868i	$-0.632295\pi$
$709$	−5.43318e12	−0.807507	−0.403753	+	0.914868i	$0.632295\pi$
$710$	1.69635e12	0.250527
$711$	7.14923e11	0.104917
$712$	1.70690e12	0.248914
$713$	7.99629e12	1.15874
$714$	−9.33135e12	−1.34370
$715$	3.52694e12	0.504685
$716$	−3.11524e11	−0.0442979
$717$	3.70057e12	0.522917
$718$	1.07145e13	1.50458
$719$	1.01516e13	1.41663	0.708315	−	0.705896i	$-0.249456\pi$
$719$	1.01516e13	1.41663	0.708315	+	0.705896i	$0.249456\pi$
$720$	−1.34389e12	−0.186366
$721$	1.40928e13	1.94217
$722$	7.86705e12	1.07744
$723$	−2.19536e12	−0.298802
$724$	1.55947e12	0.210938
$725$	−8.47921e11	−0.113982
$726$	1.18901e13	1.58843
$727$	−4.62553e12	−0.614125	−0.307062	−	0.951689i	$-0.599346\pi$
$727$	−4.62553e12	−0.614125	−0.307062	+	0.951689i	$0.599346\pi$
$728$	−1.57890e12	−0.208336
$729$	7.62428e12	0.999827
$730$	3.50753e12	0.457140
$731$	1.51180e13	1.95824
$732$	−3.32696e12	−0.428300
$733$	8.44064e12	1.07996	0.539980	−	0.841678i	$-0.318432\pi$
$733$	8.44064e12	1.07996	0.539980	+	0.841678i	$0.318432\pi$
$734$	−4.56549e12	−0.580571
$735$	1.72956e12	0.218596
$736$	−1.46491e13	−1.84018
$737$	−2.25961e13	−2.82117
$738$	−2.99414e12	−0.371551
$739$	−7.44300e12	−0.918011	−0.459006	−	0.888433i	$-0.651794\pi$
$739$	−7.44300e12	−0.918011	−0.459006	+	0.888433i	$0.651794\pi$
$740$	6.04581e10	0.00741160
$741$	2.27909e12	0.277702
$742$	7.66789e12	0.928664
$743$	−7.73544e12	−0.931184	−0.465592	−	0.885000i	$-0.654158\pi$
$743$	−7.73544e12	−0.931184	−0.465592	+	0.885000i	$0.654158\pi$
$744$	1.07369e12	0.128470
$745$	2.67174e11	0.0317754
$746$	−7.60698e12	−0.899265
$747$	−3.57417e12	−0.419984
$748$	−1.14300e13	−1.33503
$749$	5.34424e12	0.620466
$750$	6.63858e12	0.766124
$751$	1.28187e13	1.47050	0.735248	−	0.677798i	$-0.237066\pi$
$751$	1.28187e13	1.47050	0.735248	+	0.677798i	$0.237066\pi$
$752$	−6.24108e12	−0.711671
$753$	−7.35407e12	−0.833586
$754$	−1.30240e12	−0.146748
$755$	−1.81298e12	−0.203064
$756$	−1.08578e13	−1.20891
$757$	−2.72804e12	−0.301939	−0.150969	−	0.988538i	$-0.548239\pi$
$757$	−2.72804e12	−0.301939	−0.150969	+	0.988538i	$0.548239\pi$
$758$	2.96804e12	0.326556
$759$	−1.53619e13	−1.68018
$760$	3.35957e11	0.0365277
$761$	1.63243e13	1.76443	0.882213	−	0.470850i	$-0.156053\pi$
$761$	1.63243e13	1.76443	0.882213	+	0.470850i	$0.156053\pi$
$762$	−1.36852e13	−1.47046
$763$	−4.71748e12	−0.503906
$764$	−1.19080e13	−1.26450
$765$	1.54518e12	0.163118
$766$	2.19507e11	0.0230367
$767$	−5.87272e12	−0.612717
$768$	−9.04936e12	−0.938625
$769$	−1.14830e13	−1.18410	−0.592050	−	0.805901i	$-0.701681\pi$
$769$	−1.14830e13	−1.18410	−0.592050	+	0.805901i	$0.701681\pi$
$770$	1.10414e13	1.13192
$771$	6.31294e12	0.643409
$772$	−9.94297e12	−1.00748
$773$	−6.09952e12	−0.614452	−0.307226	−	0.951637i	$-0.599401\pi$
$773$	−6.09952e12	−0.614452	−0.307226	+	0.951637i	$0.599401\pi$
$774$	1.11958e13	1.12129
$775$	7.07697e12	0.704677
$776$	2.05459e11	0.0203399
$777$	−2.21379e11	−0.0217892
$778$	−1.60858e13	−1.57411
$779$	3.09140e12	0.300771
$780$	2.14320e12	0.207318
$781$	−7.60855e12	−0.731766
$782$	1.93750e13	1.85272
$783$	1.54422e12	0.146819
$784$	−8.50944e12	−0.804412
$785$	−2.64083e12	−0.248214
$786$	−1.75029e12	−0.163572
$787$	−2.56411e12	−0.238260	−0.119130	−	0.992879i	$-0.538010\pi$
$787$	−2.56411e12	−0.238260	−0.119130	+	0.992879i	$0.538010\pi$
$788$	−6.57738e11	−0.0607694
$789$	−1.16629e13	−1.07142
$790$	−1.50795e12	−0.137742
$791$	1.95194e13	1.77285
$792$	1.45944e12	0.131802
$793$	5.80737e12	0.521495
$794$	2.41816e13	2.15920
$795$	1.79457e12	0.159334
$796$	−5.39129e12	−0.475975
$797$	4.49245e12	0.394385	0.197192	−	0.980365i	$-0.436818\pi$
$797$	4.49245e12	0.394385	0.197192	+	0.980365i	$0.436818\pi$
$798$	7.13490e12	0.622838
$799$	7.17589e12	0.622896
$800$	−1.29649e13	−1.11909
$801$	−6.00272e12	−0.515231
$802$	4.51394e12	0.385275
$803$	−1.57321e13	−1.33526
$804$	−1.37308e13	−1.15890
$805$	−8.61539e12	−0.723092
$806$	1.08702e13	0.907252
$807$	−1.73945e13	−1.44371
$808$	3.06651e12	0.253101
$809$	−1.08069e13	−0.887015	−0.443508	−	0.896271i	$-0.646266\pi$
$809$	−1.08069e13	−0.887015	−0.443508	+	0.896271i	$0.646266\pi$
$810$	−2.75881e12	−0.225185
$811$	1.18070e13	0.958394	0.479197	−	0.877707i	$-0.340928\pi$
$811$	1.18070e13	0.958394	0.479197	+	0.877707i	$0.340928\pi$
$812$	−1.87684e12	−0.151505
$813$	3.40379e12	0.273247
$814$	−5.89092e11	−0.0470298
$815$	4.24920e12	0.337363
$816$	1.07447e13	0.848380
$817$	−1.15594e13	−0.907690
$818$	2.04423e13	1.59639
$819$	5.55257e12	0.431238
$820$	2.90708e12	0.224540
$821$	−1.91472e13	−1.47082	−0.735412	−	0.677620i	$-0.763011\pi$
$821$	−1.91472e13	−1.47082	−0.735412	+	0.677620i	$0.763011\pi$
$822$	1.14437e13	0.874268
$823$	−1.24811e13	−0.948315	−0.474157	−	0.880440i	$-0.657247\pi$
$823$	−1.24811e13	−0.948315	−0.474157	+	0.880440i	$0.657247\pi$
$824$	−3.92903e12	−0.296902
$825$	−1.35957e13	−1.02179
$826$	−1.83851e13	−1.37422
$827$	−5.92115e12	−0.440181	−0.220090	−	0.975479i	$-0.570635\pi$
$827$	−5.92115e12	−0.440181	−0.220090	+	0.975479i	$0.570635\pi$
$828$	6.60478e12	0.488340
$829$	3.80683e11	0.0279942	0.0139971	−	0.999902i	$-0.495544\pi$
$829$	3.80683e11	0.0279942	0.0139971	+	0.999902i	$0.495544\pi$
$830$	7.53882e12	0.551382
$831$	−9.05328e12	−0.658569
$832$	−7.55129e12	−0.546344
$833$	9.78401e12	0.704068
$834$	−1.81329e13	−1.29784
$835$	−2.97515e12	−0.211797
$836$	8.73960e12	0.618818
$837$	−1.28885e13	−0.907688
$838$	−2.22907e13	−1.56144
$839$	−1.02535e13	−0.714403	−0.357202	−	0.934027i	$-0.616269\pi$
$839$	−1.02535e13	−0.714403	−0.357202	+	0.934027i	$0.616269\pi$
$840$	−1.15682e12	−0.0801697
$841$	−1.42402e13	−0.981600
$842$	5.05932e12	0.346887
$843$	6.13234e12	0.418217
$844$	9.83018e12	0.666838
$845$	2.18169e12	0.147210
$846$	5.31418e12	0.356672
$847$	−2.99089e13	−1.99676
$848$	−8.82933e12	−0.586336
$849$	−1.72616e12	−0.114024
$850$	1.71475e13	1.12672
$851$	4.59656e11	0.0300435
$852$	−4.62346e12	−0.300600
$853$	−2.15574e13	−1.39420	−0.697101	−	0.716973i	$-0.745527\pi$
$853$	−2.15574e13	−1.39420	−0.697101	+	0.716973i	$0.745527\pi$
$854$	1.81805e13	1.16962
$855$	−1.18147e12	−0.0756093
$856$	−1.48996e12	−0.0948512
$857$	−2.58281e13	−1.63560	−0.817802	−	0.575499i	$-0.804808\pi$
$857$	−2.58281e13	−1.63560	−0.817802	+	0.575499i	$0.804808\pi$
$858$	−2.08829e13	−1.31552
$859$	−1.28740e13	−0.806761	−0.403381	−	0.915032i	$-0.632165\pi$
$859$	−1.28740e13	−0.806761	−0.403381	+	0.915032i	$0.632165\pi$
$860$	−1.08702e13	−0.677635
$861$	−1.06448e13	−0.660122
$862$	−1.45804e12	−0.0899472
$863$	−2.84758e13	−1.74754	−0.873771	−	0.486337i	$-0.838333\pi$
$863$	−2.84758e13	−1.74754	−0.873771	+	0.486337i	$0.838333\pi$
$864$	2.36114e13	1.44149
$865$	−3.90517e12	−0.237174
$866$	−8.95898e12	−0.541288
$867$	3.77987e11	0.0227191
$868$	1.56646e13	0.936658
$869$	6.76352e12	0.402331
$870$	−9.54236e11	−0.0564702
$871$	2.39679e13	1.41107
$872$	1.31522e12	0.0770326
$873$	−7.22546e11	−0.0421019
$874$	−1.48144e13	−0.858782
$875$	−1.66990e13	−0.963064
$876$	−9.55987e12	−0.548509
$877$	−2.34209e12	−0.133692	−0.0668461	−	0.997763i	$-0.521294\pi$
$877$	−2.34209e12	−0.133692	−0.0668461	+	0.997763i	$0.521294\pi$
$878$	3.87534e13	2.20082
$879$	−8.09281e12	−0.457246
$880$	−1.27138e13	−0.714668
$881$	2.98326e13	1.66840	0.834198	−	0.551465i	$-0.185931\pi$
$881$	2.98326e13	1.66840	0.834198	+	0.551465i	$0.185931\pi$
$882$	7.24565e12	0.403152
$883$	−2.39921e13	−1.32815	−0.664073	−	0.747668i	$-0.731174\pi$
$883$	−2.39921e13	−1.32815	−0.664073	+	0.747668i	$0.731174\pi$
$884$	1.21240e13	0.667744
$885$	−4.30281e12	−0.235780
$886$	2.42757e13	1.32349
$887$	−4.45226e12	−0.241504	−0.120752	−	0.992683i	$-0.538531\pi$
$887$	−4.45226e12	−0.241504	−0.120752	+	0.992683i	$0.538531\pi$
$888$	6.17199e10	0.00333094
$889$	3.44245e13	1.84846
$890$	1.26612e13	0.676427
$891$	1.23739e13	0.657745
$892$	1.64834e13	0.871776
$893$	−5.48680e12	−0.288727
$894$	−1.58193e12	−0.0828263
$895$	3.98416e11	0.0207555
$896$	1.00051e13	0.518604
$897$	1.62945e13	0.840379
$898$	−4.83225e13	−2.47974
$899$	−2.22785e12	−0.113754
$900$	5.84544e12	0.296979
$901$	1.01518e13	0.513195
$902$	−2.83260e13	−1.42481
$903$	3.98034e13	1.99217
$904$	−5.44195e12	−0.271017
$905$	−1.99445e12	−0.0988335
$906$	1.07346e13	0.529310
$907$	−3.69618e12	−0.181351	−0.0906755	−	0.995880i	$-0.528903\pi$
$907$	−3.69618e12	−0.181351	−0.0906755	+	0.995880i	$0.528903\pi$
$908$	−9.57391e12	−0.467415
$909$	−1.07841e13	−0.523897
$910$	−1.17118e13	−0.566155
$911$	−3.52735e13	−1.69674	−0.848372	−	0.529401i	$-0.822417\pi$
$911$	−3.52735e13	−1.69674	−0.848372	+	0.529401i	$0.822417\pi$
$912$	−8.21561e12	−0.393245
$913$	−3.38134e13	−1.61054
$914$	4.12036e12	0.195289
$915$	4.25493e12	0.200677
$916$	1.66675e13	0.782242
$917$	4.40277e12	0.205619
$918$	−3.12287e13	−1.45131
$919$	3.12212e13	1.44387	0.721937	−	0.691958i	$-0.243252\pi$
$919$	3.12212e13	1.44387	0.721937	+	0.691958i	$0.243252\pi$
$920$	2.40195e12	0.110540
$921$	7.74863e12	0.354860
$922$	−1.67458e13	−0.763162
$923$	8.07047e12	0.366009
$924$	−3.00937e13	−1.35816
$925$	4.06810e11	0.0182707
$926$	3.69675e13	1.65223
$927$	1.38174e13	0.614563
$928$	4.08138e12	0.180651
$929$	8.31874e12	0.366426	0.183213	−	0.983073i	$-0.441350\pi$
$929$	8.31874e12	0.366426	0.183213	+	0.983073i	$0.441350\pi$
$930$	7.96431e12	0.349120
$931$	−7.48101e12	−0.326352
$932$	−2.13554e13	−0.927121
$933$	1.45209e13	0.627374
$934$	−6.00216e13	−2.58075
$935$	1.46182e13	0.625519
$936$	−1.54804e12	−0.0659237
$937$	1.26330e13	0.535400	0.267700	−	0.963502i	$-0.413736\pi$
$937$	1.26330e13	0.535400	0.267700	+	0.963502i	$0.413736\pi$
$938$	7.50338e13	3.16478
$939$	−8.15719e12	−0.342409
$940$	−5.15966e12	−0.215549
$941$	−2.21477e13	−0.920822	−0.460411	−	0.887706i	$-0.652298\pi$
$941$	−2.21477e13	−0.920822	−0.460411	+	0.887706i	$0.652298\pi$
$942$	1.56363e13	0.647000
$943$	2.21022e13	0.910191
$944$	2.11699e13	0.867650
$945$	1.38863e13	0.566428
$946$	1.05917e14	4.29988
$947$	−3.32051e13	−1.34162	−0.670811	−	0.741628i	$-0.734054\pi$
$947$	−3.32051e13	−1.34162	−0.670811	+	0.741628i	$0.734054\pi$
$948$	4.10996e12	0.165272
$949$	1.66872e13	0.667861
$950$	−1.31112e13	−0.522261
$951$	6.49879e12	0.257644
$952$	−6.54410e12	−0.258216
$953$	3.53606e13	1.38868	0.694339	−	0.719648i	$-0.255697\pi$
$953$	3.53606e13	1.38868	0.694339	+	0.719648i	$0.255697\pi$
$954$	7.51803e12	0.293857
$955$	1.52294e13	0.592472
$956$	−1.50521e13	−0.582822
$957$	4.27998e12	0.164944
$958$	−4.39136e13	−1.68444
$959$	−2.87862e13	−1.09901
$960$	−5.53266e12	−0.210239
$961$	−7.84539e12	−0.296729
$962$	6.24856e11	0.0235230
$963$	5.23979e12	0.196334
$964$	8.92965e12	0.333033
$965$	1.27163e13	0.472050
$966$	5.10115e13	1.88483
$967$	1.15684e13	0.425455	0.212728	−	0.977112i	$-0.431765\pi$
$967$	1.15684e13	0.425455	0.212728	+	0.977112i	$0.431765\pi$
$968$	8.33852e12	0.305246
$969$	9.44617e12	0.344190
$970$	1.52403e12	0.0552740
$971$	1.44402e13	0.521299	0.260650	−	0.965433i	$-0.416063\pi$
$971$	1.44402e13	0.521299	0.260650	+	0.965433i	$0.416063\pi$
$972$	−1.81724e13	−0.653002
$973$	4.56126e13	1.63146
$974$	7.86497e12	0.280015
$975$	1.44211e13	0.511068
$976$	−2.09343e13	−0.738473
$977$	5.05890e13	1.77636	0.888180	−	0.459496i	$-0.151970\pi$
$977$	5.05890e13	1.77636	0.888180	+	0.459496i	$0.151970\pi$
$978$	−2.51594e13	−0.879377
$979$	−5.67886e13	−1.97578
$980$	−7.03497e12	−0.243638
$981$	−4.62528e12	−0.159451
$982$	5.74023e12	0.196983
$983$	−2.36354e13	−0.807368	−0.403684	−	0.914898i	$-0.632271\pi$
$983$	−2.36354e13	−0.807368	−0.403684	+	0.914898i	$0.632271\pi$
$984$	2.96775e12	0.100914
$985$	8.41197e11	0.0284731
$986$	−5.39807e12	−0.181883
$987$	1.88931e13	0.633688
$988$	−9.27019e12	−0.309515
$989$	−8.26451e13	−2.74684
$990$	1.08256e13	0.358175
$991$	−3.30463e13	−1.08841	−0.544203	−	0.838953i	$-0.683168\pi$
$991$	−3.30463e13	−1.08841	−0.544203	+	0.838953i	$0.683168\pi$
$992$	−3.40643e13	−1.11685
$993$	−7.56423e11	−0.0246884
$994$	2.52654e13	0.820895
$995$	6.89505e12	0.223015
$996$	−2.05473e13	−0.661587
$997$	−1.63913e13	−0.525395	−0.262697	−	0.964878i	$-0.584612\pi$
$997$	−1.63913e13	−0.525395	−0.262697	+	0.964878i	$0.584612\pi$
$998$	−5.17577e13	−1.65153
$999$	−7.40876e11	−0.0235343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.a.1.12	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.a.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-30.8011 q^{2} -107.364 q^{3} +436.705 q^{4} -558.513 q^{5} +3306.94 q^{6} -8318.45 q^{7} +2319.16 q^{8} -8155.88 q^{9} +17202.8 q^{10} -77158.5 q^{11} -46886.6 q^{12} +81842.9 q^{13} +256217. q^{14} +59964.4 q^{15} -295026. q^{16} +339216. q^{17} +251210. q^{18} -259370. q^{19} -243905. q^{20} +893106. q^{21} +2.37656e6 q^{22} -1.85438e6 q^{23} -248996. q^{24} -1.64119e6 q^{25} -2.52085e6 q^{26} +2.98891e6 q^{27} -3.63271e6 q^{28} +516651. q^{29} -1.84697e6 q^{30} -4.31210e6 q^{31} +7.89969e6 q^{32} +8.28408e6 q^{33} -1.04482e7 q^{34} +4.64596e6 q^{35} -3.56171e6 q^{36} -247875. q^{37} +7.98886e6 q^{38} -8.78701e6 q^{39} -1.29528e6 q^{40} -1.19189e7 q^{41} -2.75086e7 q^{42} +4.45674e7 q^{43} -3.36955e7 q^{44} +4.55516e6 q^{45} +5.71170e7 q^{46} +2.11544e7 q^{47} +3.16753e7 q^{48} +2.88430e7 q^{49} +5.05503e7 q^{50} -3.64197e7 q^{51} +3.57412e7 q^{52} +2.99273e7 q^{53} -9.20614e7 q^{54} +4.30940e7 q^{55} -1.92918e7 q^{56} +2.78471e7 q^{57} -1.59134e7 q^{58} -7.17560e7 q^{59} +2.61868e7 q^{60} +7.09576e7 q^{61} +1.32817e8 q^{62} +6.78443e7 q^{63} -9.22657e7 q^{64} -4.57103e7 q^{65} -2.55158e8 q^{66} +2.92852e8 q^{67} +1.48137e8 q^{68} +1.99095e8 q^{69} -1.43100e8 q^{70} +9.86093e7 q^{71} -1.89148e7 q^{72} +2.03894e8 q^{73} +7.63482e6 q^{74} +1.76205e8 q^{75} -1.13268e8 q^{76} +6.41839e8 q^{77} +2.70649e8 q^{78} -8.76574e7 q^{79} +1.64776e8 q^{80} -1.60370e8 q^{81} +3.67114e8 q^{82} +4.38233e8 q^{83} +3.90024e8 q^{84} -1.89456e8 q^{85} -1.37272e9 q^{86} -5.54699e7 q^{87} -1.78943e8 q^{88} +7.35999e8 q^{89} -1.40304e8 q^{90} -6.80806e8 q^{91} -8.09819e8 q^{92} +4.62966e8 q^{93} -6.51577e8 q^{94} +1.44861e8 q^{95} -8.48146e8 q^{96} +8.85921e7 q^{97} -8.88396e8 q^{98} +6.29295e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 32 q^{2} - 892 q^{3} + 16896 q^{4} - 2329 q^{5} - 10272 q^{6} - 37846 q^{7} - 24933 q^{8} + 419903 q^{9} - 138907 q^{10} - 143074 q^{11} - 496640 q^{12} - 433821 q^{13} - 130143 q^{14} - 670126 q^{15}+ \cdots - 6380320552 q^{99}+O(q^{100}) \) 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

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