LMFDB - Embedded newform 242.10.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,10,Mod(1,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, 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("242.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	242.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:	$124.638672352$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{889}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 222 $ x^2 - x - 222
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$15.4081$ of defining polynomial
Character	$\chi$	$=$	242.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} -2314.76 q^{6} +8664.66 q^{7} +4096.00 q^{8} +1247.12 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} -2314.76 q^{6} +8664.66 q^{7} +4096.00 q^{8} +1247.12 q^{9} -27305.3 q^{10} -37036.2 q^{12} -67852.1 q^{13} +138635. q^{14} +246895. q^{15} +65536.0 q^{16} -249646. q^{17} +19953.9 q^{18} +293189. q^{19} -436885. q^{20} -1.25354e6 q^{21} +1.10315e6 q^{23} -592578. q^{24} +959294. q^{25} -1.08563e6 q^{26} +2.66716e6 q^{27} +2.21815e6 q^{28} +5.23603e6 q^{29} +3.95032e6 q^{30} -8.38378e6 q^{31} +1.04858e6 q^{32} -3.99433e6 q^{34} -1.47869e7 q^{35} +319263. q^{36} +7.34600e6 q^{37} +4.69103e6 q^{38} +9.81632e6 q^{39} -6.99016e6 q^{40} -1.01256e7 q^{41} -2.00566e7 q^{42} +2.56347e7 q^{43} -2.12831e6 q^{45} +1.76505e7 q^{46} +5.88993e7 q^{47} -9.48125e6 q^{48} +3.47227e7 q^{49} +1.53487e7 q^{50} +3.61168e7 q^{51} -1.73701e7 q^{52} +8.68723e7 q^{53} +4.26746e7 q^{54} +3.54904e7 q^{56} -4.24164e7 q^{57} +8.37764e7 q^{58} -1.82302e8 q^{59} +6.32052e7 q^{60} -1.22104e8 q^{61} -1.34141e8 q^{62} +1.08059e7 q^{63} +1.67772e7 q^{64} +1.15795e8 q^{65} -6.80532e7 q^{67} -6.39093e7 q^{68} -1.59596e8 q^{69} -2.36591e8 q^{70} -1.67349e8 q^{71} +5.10821e6 q^{72} +1.51799e8 q^{73} +1.17536e8 q^{74} -1.38783e8 q^{75} +7.50564e7 q^{76} +1.57061e8 q^{78} -2.95735e8 q^{79} -1.11842e8 q^{80} -4.10412e8 q^{81} -1.62010e8 q^{82} -4.61094e8 q^{83} -3.20906e8 q^{84} +4.26040e8 q^{85} +4.10156e8 q^{86} -7.57509e8 q^{87} +4.63623e8 q^{89} -3.40530e7 q^{90} -5.87915e8 q^{91} +2.82407e8 q^{92} +1.21290e9 q^{93} +9.42388e8 q^{94} -5.00351e8 q^{95} -1.51700e8 q^{96} +1.06866e8 q^{97} +5.55563e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} - 336 q^{6} + 7490 q^{7} + 8192 q^{8} - 3141 q^{9}+O(q^{10}) $ 2 * q + 32 * q^2 - 21 * q^3 + 512 * q^4 - 521 * q^5 - 336 * q^6 + 7490 * q^7 + 8192 * q^8 - 3141 * q^9	\( 2 q + 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} - 336 q^{6} + 7490 q^{7} + 8192 q^{8} - 3141 q^{9} - 8336 q^{10} - 5376 q^{12} - 150314 q^{13} + 119840 q^{14} + 393519 q^{15} + 131072 q^{16} - 690472 q^{17} - 50256 q^{18} - 511212 q^{19} - 133376 q^{20} - 1398810 q^{21} + 874751 q^{23} - 86016 q^{24} + 411771 q^{25} - 2405024 q^{26} - 309771 q^{27} + 1917440 q^{28} + 2951058 q^{29} + 6296304 q^{30} - 5818705 q^{31} + 2097152 q^{32} - 11047552 q^{34} - 16179590 q^{35} - 804096 q^{36} + 2658905 q^{37} - 8179392 q^{38} - 381948 q^{39} - 2134016 q^{40} - 13427994 q^{41} - 22380960 q^{42} + 17820762 q^{43} - 7330788 q^{45} + 13996016 q^{46} + 56044104 q^{47} - 1376256 q^{48} - 4251114 q^{49} + 6588336 q^{50} - 18401250 q^{51} - 38480384 q^{52} + 96842752 q^{53} - 4956336 q^{54} + 30679040 q^{56} - 141898680 q^{57} + 47216928 q^{58} - 119136183 q^{59} + 100740864 q^{60} + 90424326 q^{61} - 93099280 q^{62} + 15960420 q^{63} + 33554432 q^{64} + 18029712 q^{65} - 295944891 q^{67} - 176760832 q^{68} - 187843215 q^{69} - 258873440 q^{70} - 322953267 q^{71} - 12865536 q^{72} + 255975514 q^{73} + 42542480 q^{74} - 206496864 q^{75} - 130870272 q^{76} - 6111168 q^{78} + 889658 q^{79} - 34144256 q^{80} - 692205750 q^{81} - 214847904 q^{82} + 277699042 q^{83} - 358095360 q^{84} - 96595042 q^{85} + 285132192 q^{86} - 1040096232 q^{87} + 1363672217 q^{89} - 117292608 q^{90} - 491050280 q^{91} + 223936256 q^{92} + 1530132009 q^{93} + 896705664 q^{94} - 1454033872 q^{95} - 22020096 q^{96} + 1398434043 q^{97} - 68017824 q^{98}+O(q^{100}) \) 2 * q + 32 * q^2 - 21 * q^3 + 512 * q^4 - 521 * q^5 - 336 * q^6 + 7490 * q^7 + 8192 * q^8 - 3141 * q^9 - 8336 * q^10 - 5376 * q^12 - 150314 * q^13 + 119840 * q^14 + 393519 * q^15 + 131072 * q^16 - 690472 * q^17 - 50256 * q^18 - 511212 * q^19 - 133376 * q^20 - 1398810 * q^21 + 874751 * q^23 - 86016 * q^24 + 411771 * q^25 - 2405024 * q^26 - 309771 * q^27 + 1917440 * q^28 + 2951058 * q^29 + 6296304 * q^30 - 5818705 * q^31 + 2097152 * q^32 - 11047552 * q^34 - 16179590 * q^35 - 804096 * q^36 + 2658905 * q^37 - 8179392 * q^38 - 381948 * q^39 - 2134016 * q^40 - 13427994 * q^41 - 22380960 * q^42 + 17820762 * q^43 - 7330788 * q^45 + 13996016 * q^46 + 56044104 * q^47 - 1376256 * q^48 - 4251114 * q^49 + 6588336 * q^50 - 18401250 * q^51 - 38480384 * q^52 + 96842752 * q^53 - 4956336 * q^54 + 30679040 * q^56 - 141898680 * q^57 + 47216928 * q^58 - 119136183 * q^59 + 100740864 * q^60 + 90424326 * q^61 - 93099280 * q^62 + 15960420 * q^63 + 33554432 * q^64 + 18029712 * q^65 - 295944891 * q^67 - 176760832 * q^68 - 187843215 * q^69 - 258873440 * q^70 - 322953267 * q^71 - 12865536 * q^72 + 255975514 * q^73 + 42542480 * q^74 - 206496864 * q^75 - 130870272 * q^76 - 6111168 * q^78 + 889658 * q^79 - 34144256 * q^80 - 692205750 * q^81 - 214847904 * q^82 + 277699042 * q^83 - 358095360 * q^84 - 96595042 * q^85 + 285132192 * q^86 - 1040096232 * q^87 + 1363672217 * q^89 - 117292608 * q^90 - 491050280 * q^91 + 223936256 * q^92 + 1530132009 * q^93 + 896705664 * q^94 - 1454033872 * q^95 - 22020096 * q^96 + 1398434043 * q^97 - 68017824 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	−144.672	−1.03119	−0.515597	−	0.856831i	$-0.672430\pi$
$3$	−144.672	−1.03119	−0.515597	+	0.856831i	$0.672430\pi$
$4$	256.000	0.500000
$5$	−1706.58	−1.22113	−0.610565	−	0.791966i	$-0.709058\pi$
$5$	−1706.58	−1.22113	−0.610565	+	0.791966i	$0.709058\pi$
$6$	−2314.76	−0.729164
$7$	8664.66	1.36399	0.681993	−	0.731358i	$-0.261113\pi$
$7$	8664.66	1.36399	0.681993	+	0.731358i	$0.261113\pi$
$8$	4096.00	0.353553
$9$	1247.12	0.0633603
$10$	−27305.3	−0.863469
$11$	0	0
$11$	0	0
$12$	−37036.2	−0.515597
$13$	−67852.1	−0.658898	−0.329449	−	0.944173i	$-0.606863\pi$
$13$	−67852.1	−0.658898	−0.329449	+	0.944173i	$0.606863\pi$
$14$	138635.	0.964484
$15$	246895.	1.25922
$16$	65536.0	0.250000
$17$	−249646.	−0.724943	−0.362471	−	0.931995i	$-0.618067\pi$
$17$	−249646.	−0.724943	−0.362471	+	0.931995i	$0.618067\pi$
$18$	19953.9	0.0448025
$19$	293189.	0.516127	0.258064	−	0.966128i	$-0.416916\pi$
$19$	293189.	0.516127	0.258064	+	0.966128i	$0.416916\pi$
$20$	−436885.	−0.610565
$21$	−1.25354e6	−1.40653
$22$	0	0
$23$	1.10315e6	0.821979	0.410990	−	0.911640i	$-0.365183\pi$
$23$	1.10315e6	0.821979	0.410990	+	0.911640i	$0.365183\pi$
$24$	−592578.	−0.364582
$25$	959294.	0.491158
$26$	−1.08563e6	−0.465911
$27$	2.66716e6	0.965857
$28$	2.21815e6	0.681993
$29$	5.23603e6	1.37471	0.687354	−	0.726322i	$-0.258772\pi$
$29$	5.23603e6	1.37471	0.687354	+	0.726322i	$0.258772\pi$
$30$	3.95032e6	0.890404
$31$	−8.38378e6	−1.63047	−0.815234	−	0.579131i	$-0.803392\pi$
$31$	−8.38378e6	−1.63047	−0.815234	+	0.579131i	$0.803392\pi$
$32$	1.04858e6	0.176777
$33$	0	0
$34$	−3.99433e6	−0.512612
$35$	−1.47869e7	−1.66561
$36$	319263.	0.0316802
$37$	7.34600e6	0.644382	0.322191	−	0.946675i	$-0.395581\pi$
$37$	7.34600e6	0.644382	0.322191	+	0.946675i	$0.395581\pi$
$38$	4.69103e6	0.364957
$39$	9.81632e6	0.679451
$40$	−6.99016e6	−0.431735
$41$	−1.01256e7	−0.559623	−0.279811	−	0.960055i	$-0.590272\pi$
$41$	−1.01256e7	−0.559623	−0.279811	+	0.960055i	$0.590272\pi$
$42$	−2.00566e7	−0.994570
$43$	2.56347e7	1.14346	0.571730	−	0.820442i	$-0.306273\pi$
$43$	2.56347e7	1.14346	0.571730	+	0.820442i	$0.306273\pi$
$44$	0	0
$45$	−2.12831e6	−0.0773712
$46$	1.76505e7	0.581227
$47$	5.88993e7	1.76064	0.880318	−	0.474385i	$-0.157329\pi$
$47$	5.88993e7	1.76064	0.880318	+	0.474385i	$0.157329\pi$
$48$	−9.48125e6	−0.257798
$49$	3.47227e7	0.860460
$50$	1.53487e7	0.347301
$51$	3.61168e7	0.747556
$52$	−1.73701e7	−0.329449
$53$	8.68723e7	1.51231	0.756153	−	0.654395i	$-0.227076\pi$
$53$	8.68723e7	1.51231	0.756153	+	0.654395i	$0.227076\pi$
$54$	4.26746e7	0.682964
$55$	0	0
$56$	3.54904e7	0.482242
$57$	−4.24164e7	−0.532227
$58$	8.37764e7	0.972066
$59$	−1.82302e8	−1.95865	−0.979326	−	0.202289i	$-0.935162\pi$
$59$	−1.82302e8	−1.95865	−0.979326	+	0.202289i	$0.935162\pi$
$60$	6.32052e7	0.629611
$61$	−1.22104e8	−1.12914	−0.564569	−	0.825386i	$-0.690958\pi$
$61$	−1.22104e8	−1.12914	−0.564569	+	0.825386i	$0.690958\pi$
$62$	−1.34141e8	−1.15292
$63$	1.08059e7	0.0864227
$64$	1.67772e7	0.125000
$65$	1.15795e8	0.804600
$66$	0	0
$67$	−6.80532e7	−0.412584	−0.206292	−	0.978491i	$-0.566140\pi$
$67$	−6.80532e7	−0.412584	−0.206292	+	0.978491i	$0.566140\pi$
$68$	−6.39093e7	−0.362471
$69$	−1.59596e8	−0.847620
$70$	−2.36591e8	−1.17776
$71$	−1.67349e8	−0.781555	−0.390777	−	0.920485i	$-0.627794\pi$
$71$	−1.67349e8	−0.781555	−0.390777	+	0.920485i	$0.627794\pi$
$72$	5.10821e6	0.0224013
$73$	1.51799e8	0.625626	0.312813	−	0.949815i	$-0.398729\pi$
$73$	1.51799e8	0.625626	0.312813	+	0.949815i	$0.398729\pi$
$74$	1.17536e8	0.455647
$75$	−1.38783e8	−0.506479
$76$	7.50564e7	0.258064
$77$	0	0
$78$	1.57061e8	0.480444
$79$	−2.95735e8	−0.854241	−0.427120	−	0.904195i	$-0.640472\pi$
$79$	−2.95735e8	−0.854241	−0.427120	+	0.904195i	$0.640472\pi$
$80$	−1.11842e8	−0.305282
$81$	−4.10412e8	−1.05935
$82$	−1.62010e8	−0.395713
$83$	−4.61094e8	−1.06644	−0.533222	−	0.845975i	$-0.679019\pi$
$83$	−4.61094e8	−1.06644	−0.533222	+	0.845975i	$0.679019\pi$
$84$	−3.20906e8	−0.703267
$85$	4.26040e8	0.885249
$86$	4.10156e8	0.808548
$87$	−7.57509e8	−1.41759
$88$	0	0
$89$	4.63623e8	0.783267	0.391634	−	0.920121i	$-0.371910\pi$
$89$	4.63623e8	0.783267	0.391634	+	0.920121i	$0.371910\pi$
$90$	−3.40530e7	−0.0547097
$91$	−5.87915e8	−0.898728
$92$	2.82407e8	0.410990
$93$	1.21290e9	1.68133
$94$	9.42388e8	1.24496
$95$	−5.00351e8	−0.630258
$96$	−1.51700e8	−0.182291
$97$	1.06866e8	0.122565	0.0612825	−	0.998120i	$-0.480481\pi$
$97$	1.06866e8	0.122565	0.0612825	+	0.998120i	$0.480481\pi$
$98$	5.55563e8	0.608437
$99$	0	0
$100$	2.45579e8	0.245579
$101$	−1.38561e9	−1.32494	−0.662470	−	0.749088i	$-0.730492\pi$
$101$	−1.38561e9	−1.32494	−0.662470	+	0.749088i	$0.730492\pi$
$102$	5.77869e8	0.528602
$103$	−1.45242e9	−1.27152	−0.635760	−	0.771886i	$-0.719313\pi$
$103$	−1.45242e9	−1.27152	−0.635760	+	0.771886i	$0.719313\pi$
$104$	−2.77922e8	−0.232955
$105$	2.13926e9	1.71756
$106$	1.38996e9	1.06936
$107$	−1.44377e9	−1.06481	−0.532405	−	0.846490i	$-0.678712\pi$
$107$	−1.44377e9	−1.06481	−0.532405	+	0.846490i	$0.678712\pi$
$108$	6.82794e8	0.482928
$109$	−2.58675e9	−1.75524	−0.877618	−	0.479361i	$-0.840868\pi$
$109$	−2.58675e9	−1.75524	−0.877618	+	0.479361i	$0.840868\pi$
$110$	0	0
$111$	−1.06276e9	−0.664482
$112$	5.67847e8	0.340997
$113$	1.13601e9	0.655433	0.327717	−	0.944776i	$-0.393721\pi$
$113$	1.13601e9	0.655433	0.327717	+	0.944776i	$0.393721\pi$
$114$	−6.78662e8	−0.376341
$115$	−1.88262e9	−1.00374
$116$	1.34042e9	0.687354
$117$	−8.46198e7	−0.0417480
$118$	−2.91683e9	−1.38498
$119$	−2.16309e9	−0.988812
$120$	1.01128e9	0.445202
$121$	0	0
$122$	−1.95367e9	−0.798422
$123$	1.46490e9	0.577079
$124$	−2.14625e9	−0.815234
$125$	1.69605e9	0.621362
$126$	1.72894e8	0.0611101
$127$	3.27848e9	1.11829	0.559147	−	0.829068i	$-0.311129\pi$
$127$	3.27848e9	1.11829	0.559147	+	0.829068i	$0.311129\pi$
$128$	2.68435e8	0.0883883
$129$	−3.70864e9	−1.17913
$130$	1.85272e9	0.568938
$131$	−1.81056e9	−0.537146	−0.268573	−	0.963259i	$-0.586552\pi$
$131$	−1.81056e9	−0.537146	−0.268573	+	0.963259i	$0.586552\pi$
$132$	0	0
$133$	2.54038e9	0.703991
$134$	−1.08885e9	−0.291741
$135$	−4.55173e9	−1.17944
$136$	−1.02255e9	−0.256306
$137$	−3.19317e9	−0.774425	−0.387213	−	0.921990i	$-0.626562\pi$
$137$	−3.19317e9	−0.774425	−0.387213	+	0.921990i	$0.626562\pi$
$138$	−2.55354e9	−0.599358
$139$	8.30571e8	0.188717	0.0943583	−	0.995538i	$-0.469920\pi$
$139$	8.30571e8	0.188717	0.0943583	+	0.995538i	$0.469920\pi$
$140$	−3.78546e9	−0.832803
$141$	−8.52110e9	−1.81556
$142$	−2.67758e9	−0.552643
$143$	0	0
$144$	8.17314e7	0.0158401
$145$	−8.93570e9	−1.67870
$146$	2.42878e9	0.442384
$147$	−5.02341e9	−0.887301
$148$	1.88058e9	0.322191
$149$	−8.83876e9	−1.46911	−0.734553	−	0.678551i	$-0.762608\pi$
$149$	−8.83876e9	−1.46911	−0.734553	+	0.678551i	$0.762608\pi$
$150$	−2.22053e9	−0.358135
$151$	6.05461e9	0.947742	0.473871	−	0.880594i	$-0.342856\pi$
$151$	6.05461e9	0.947742	0.473871	+	0.880594i	$0.342856\pi$
$152$	1.20090e9	0.182479
$153$	−3.11338e8	−0.0459326
$154$	0	0
$155$	1.43076e10	1.99101
$156$	2.51298e9	0.339726
$157$	−3.21421e9	−0.422208	−0.211104	−	0.977464i	$-0.567706\pi$
$157$	−3.21421e9	−0.422208	−0.211104	+	0.977464i	$0.567706\pi$
$158$	−4.73176e9	−0.604040
$159$	−1.25680e10	−1.55948
$160$	−1.78948e9	−0.215867
$161$	9.55845e9	1.12117
$162$	−6.56660e9	−0.749071
$163$	3.35516e9	0.372279	0.186140	−	0.982523i	$-0.440402\pi$
$163$	3.35516e9	0.372279	0.186140	+	0.982523i	$0.440402\pi$
$164$	−2.59217e9	−0.279811
$165$	0	0
$166$	−7.37750e9	−0.754090
$167$	−1.13205e10	−1.12627	−0.563136	−	0.826364i	$-0.690405\pi$
$167$	−1.13205e10	−1.12627	−0.563136	+	0.826364i	$0.690405\pi$
$168$	−5.13449e9	−0.497285
$169$	−6.00060e9	−0.565854
$170$	6.81665e9	0.625966
$171$	3.65643e8	0.0327020
$172$	6.56249e9	0.571730
$173$	−1.24081e10	−1.05317	−0.526586	−	0.850122i	$-0.676528\pi$
$173$	−1.24081e10	−1.05317	−0.526586	+	0.850122i	$0.676528\pi$
$174$	−1.21201e10	−1.00239
$175$	8.31195e9	0.669934
$176$	0	0
$177$	2.63741e10	2.01975
$178$	7.41797e9	0.553854
$179$	−1.78548e10	−1.29992	−0.649960	−	0.759968i	$-0.725215\pi$
$179$	−1.78548e10	−1.29992	−0.649960	+	0.759968i	$0.725215\pi$
$180$	−5.44848e8	−0.0386856
$181$	2.69794e10	1.86844	0.934220	−	0.356698i	$-0.116098\pi$
$181$	2.69794e10	1.86844	0.934220	+	0.356698i	$0.116098\pi$
$182$	−9.40664e9	−0.635496
$183$	1.76652e10	1.16436
$184$	4.51852e9	0.290614
$185$	−1.25365e10	−0.786874
$186$	1.94064e10	1.18888
$187$	0	0
$188$	1.50782e10	0.880318
$189$	2.31101e10	1.31742
$190$	−8.00562e9	−0.445660
$191$	−1.88704e10	−1.02596	−0.512980	−	0.858400i	$-0.671459\pi$
$191$	−1.88704e10	−1.02596	−0.512980	+	0.858400i	$0.671459\pi$
$192$	−2.42720e9	−0.128899
$193$	1.63769e10	0.849618	0.424809	−	0.905283i	$-0.360341\pi$
$193$	1.63769e10	0.849618	0.424809	+	0.905283i	$0.360341\pi$
$194$	1.70985e9	0.0866665
$195$	−1.67524e10	−0.829698
$196$	8.88900e9	0.430230
$197$	2.41377e10	1.14182	0.570909	−	0.821013i	$-0.306591\pi$
$197$	2.41377e10	1.14182	0.570909	+	0.821013i	$0.306591\pi$
$198$	0	0
$199$	−6.98474e7	−0.00315727	−0.00157863	−	0.999999i	$-0.500502\pi$
$199$	−6.98474e7	−0.00315727	−0.00157863	+	0.999999i	$0.500502\pi$
$200$	3.92927e9	0.173651
$201$	9.84543e9	0.425454
$202$	−2.21698e10	−0.936874
$203$	4.53684e10	1.87508
$204$	9.24591e9	0.373778
$205$	1.72802e10	0.683372
$206$	−2.32387e10	−0.899101
$207$	1.37577e9	0.0520809
$208$	−4.44675e9	−0.164724
$209$	0	0
$210$	3.42282e10	1.21450
$211$	−3.34436e10	−1.16156	−0.580780	−	0.814061i	$-0.697252\pi$
$211$	−3.34436e10	−1.16156	−0.580780	+	0.814061i	$0.697252\pi$
$212$	2.22393e10	0.756153
$213$	2.42107e10	0.805935
$214$	−2.31004e10	−0.752935
$215$	−4.37478e10	−1.39631
$216$	1.09247e10	0.341482
$217$	−7.26426e10	−2.22394
$218$	−4.13880e10	−1.24114
$219$	−2.19611e10	−0.645141
$220$	0	0
$221$	1.69390e10	0.477663
$222$	−1.70042e10	−0.469860
$223$	−1.74786e10	−0.473299	−0.236650	−	0.971595i	$-0.576049\pi$
$223$	−1.74786e10	−0.473299	−0.236650	+	0.971595i	$0.576049\pi$
$224$	9.08555e9	0.241121
$225$	1.19636e9	0.0311200
$226$	1.81761e10	0.463461
$227$	1.99552e10	0.498816	0.249408	−	0.968398i	$-0.419764\pi$
$227$	1.99552e10	0.498816	0.249408	+	0.968398i	$0.419764\pi$
$228$	−1.08586e10	−0.266114
$229$	−7.45741e10	−1.79196	−0.895980	−	0.444095i	$-0.853525\pi$
$229$	−7.45741e10	−1.79196	−0.895980	+	0.444095i	$0.853525\pi$
$230$	−3.01220e10	−0.709754
$231$	0	0
$232$	2.14468e10	0.486033
$233$	4.84331e10	1.07657	0.538283	−	0.842764i	$-0.319073\pi$
$233$	4.84331e10	1.07657	0.538283	+	0.842764i	$0.319073\pi$
$234$	−1.35392e9	−0.0295203
$235$	−1.00516e11	−2.14996
$236$	−4.66693e10	−0.979326
$237$	4.27847e10	0.880888
$238$	−3.46095e10	−0.699196
$239$	2.76719e10	0.548591	0.274295	−	0.961645i	$-0.411555\pi$
$239$	2.76719e10	0.548591	0.274295	+	0.961645i	$0.411555\pi$
$240$	1.61805e10	0.314805
$241$	−5.23953e10	−1.00050	−0.500248	−	0.865882i	$-0.666758\pi$
$241$	−5.23953e10	−1.00050	−0.500248	+	0.865882i	$0.666758\pi$
$242$	0	0
$243$	6.87757e9	0.126534
$244$	−3.12587e10	−0.564569
$245$	−5.92571e10	−1.05073
$246$	2.34384e10	0.408057
$247$	−1.98935e10	−0.340075
$248$	−3.43400e10	−0.576458
$249$	6.67076e10	1.09971
$250$	2.71369e10	0.439369
$251$	5.45608e10	0.867659	0.433829	−	0.900995i	$-0.357162\pi$
$251$	5.45608e10	0.867659	0.433829	+	0.900995i	$0.357162\pi$
$252$	2.76631e9	0.0432113
$253$	0	0
$254$	5.24557e10	0.790754
$255$	−6.16363e10	−0.912863
$256$	4.29497e9	0.0625000
$257$	1.72020e10	0.245969	0.122985	−	0.992409i	$-0.460753\pi$
$257$	1.72020e10	0.245969	0.122985	+	0.992409i	$0.460753\pi$
$258$	−5.93383e10	−0.833770
$259$	6.36506e10	0.878928
$260$	2.96435e10	0.402300
$261$	6.52996e9	0.0871020
$262$	−2.89690e10	−0.379819
$263$	2.32552e10	0.299722	0.149861	−	0.988707i	$-0.452117\pi$
$263$	2.32552e10	0.299722	0.149861	+	0.988707i	$0.452117\pi$
$264$	0	0
$265$	−1.48255e11	−1.84672
$266$	4.06461e10	0.497797
$267$	−6.70735e10	−0.807700
$268$	−1.74216e10	−0.206292
$269$	2.82157e10	0.328554	0.164277	−	0.986414i	$-0.447471\pi$
$269$	2.82157e10	0.328554	0.164277	+	0.986414i	$0.447471\pi$
$270$	−7.28277e10	−0.833988
$271$	−1.37207e11	−1.54530	−0.772651	−	0.634831i	$-0.781070\pi$
$271$	−1.37207e11	−1.54530	−0.772651	+	0.634831i	$0.781070\pi$
$272$	−1.63608e10	−0.181236
$273$	8.50551e10	0.926762
$274$	−5.10907e10	−0.547601
$275$	0	0
$276$	−4.08566e10	−0.423810
$277$	−1.85402e11	−1.89215	−0.946074	−	0.323949i	$-0.894989\pi$
$277$	−1.85402e11	−1.89215	−0.946074	+	0.323949i	$0.894989\pi$
$278$	1.32891e10	0.133443
$279$	−1.04556e10	−0.103307
$280$	−6.05673e10	−0.588880
$281$	5.20765e10	0.498268	0.249134	−	0.968469i	$-0.419854\pi$
$281$	5.20765e10	0.498268	0.249134	+	0.968469i	$0.419854\pi$
$282$	−1.36338e11	−1.28379
$283$	−1.03796e11	−0.961925	−0.480963	−	0.876741i	$-0.659713\pi$
$283$	−1.03796e11	−0.961925	−0.480963	+	0.876741i	$0.659713\pi$
$284$	−4.28412e10	−0.390777
$285$	7.23870e10	0.649918
$286$	0	0
$287$	−8.77352e10	−0.763318
$288$	1.30770e9	0.0112006
$289$	−5.62650e10	−0.474458
$290$	−1.42971e11	−1.18702
$291$	−1.54606e10	−0.126388
$292$	3.88604e10	0.312813
$293$	8.51536e10	0.674992	0.337496	−	0.941327i	$-0.390420\pi$
$293$	8.51536e10	0.674992	0.337496	+	0.941327i	$0.390420\pi$
$294$	−8.03746e10	−0.627417
$295$	3.11113e11	2.39177
$296$	3.00892e10	0.227823
$297$	0	0
$298$	−1.41420e11	−1.03881
$299$	−7.48513e10	−0.541600
$300$	−3.55285e10	−0.253240
$301$	2.22116e11	1.55966
$302$	9.68738e10	0.670155
$303$	2.00460e11	1.36627
$304$	1.92144e10	0.129032
$305$	2.08381e11	1.37882
$306$	−4.98141e9	−0.0324793
$307$	−2.79447e11	−1.79547	−0.897734	−	0.440539i	$-0.854787\pi$
$307$	−2.79447e11	−1.79547	−0.897734	+	0.440539i	$0.854787\pi$
$308$	0	0
$309$	2.10125e11	1.31118
$310$	2.28922e11	1.40786
$311$	2.40111e11	1.45543	0.727714	−	0.685881i	$-0.240583\pi$
$311$	2.40111e11	1.45543	0.727714	+	0.685881i	$0.240583\pi$
$312$	4.02077e10	0.240222
$313$	9.68635e10	0.570441	0.285220	−	0.958462i	$-0.407933\pi$
$313$	9.68635e10	0.570441	0.285220	+	0.958462i	$0.407933\pi$
$314$	−5.14274e10	−0.298546
$315$	−1.84411e10	−0.105533
$316$	−7.57081e10	−0.427120
$317$	−1.70124e11	−0.946237	−0.473118	−	0.880999i	$-0.656872\pi$
$317$	−1.70124e11	−0.946237	−0.473118	+	0.880999i	$0.656872\pi$
$318$	−2.01088e11	−1.10272
$319$	0	0
$320$	−2.86317e10	−0.152641
$321$	2.08874e11	1.09803
$322$	1.52935e11	0.792786
$323$	−7.31934e10	−0.374163
$324$	−1.05066e11	−0.529673
$325$	−6.50900e10	−0.323623
$326$	5.36825e10	0.263241
$327$	3.74232e11	1.80999
$328$	−4.14746e10	−0.197857
$329$	5.10342e11	2.40148
$330$	0	0
$331$	2.45318e10	0.112332	0.0561661	−	0.998421i	$-0.482112\pi$
$331$	2.45318e10	0.112332	0.0561661	+	0.998421i	$0.482112\pi$
$332$	−1.18040e11	−0.533222
$333$	9.16136e9	0.0408282
$334$	−1.81129e11	−0.796394
$335$	1.16138e11	0.503818
$336$	−8.21518e10	−0.351634
$337$	−9.64453e10	−0.407330	−0.203665	−	0.979041i	$-0.565285\pi$
$337$	−9.64453e10	−0.407330	−0.203665	+	0.979041i	$0.565285\pi$
$338$	−9.60096e10	−0.400119
$339$	−1.64349e11	−0.675879
$340$	1.09066e11	0.442625
$341$	0	0
$342$	5.85028e9	0.0231238
$343$	−4.87901e10	−0.190330
$344$	1.05000e11	0.404274
$345$	2.72364e11	1.03505
$346$	−1.98530e11	−0.744704
$347$	1.02569e11	0.379783	0.189891	−	0.981805i	$-0.439186\pi$
$347$	1.02569e11	0.379783	0.189891	+	0.981805i	$0.439186\pi$
$348$	−1.93922e11	−0.708796
$349$	3.59960e11	1.29879	0.649397	−	0.760450i	$-0.275021\pi$
$349$	3.59960e11	1.29879	0.649397	+	0.760450i	$0.275021\pi$
$350$	1.32991e11	0.473715
$351$	−1.80973e11	−0.636401
$352$	0	0
$353$	−6.23410e10	−0.213692	−0.106846	−	0.994276i	$-0.534075\pi$
$353$	−6.23410e10	−0.213692	−0.106846	+	0.994276i	$0.534075\pi$
$354$	4.21985e11	1.42818
$355$	2.85594e11	0.954380
$356$	1.18687e11	0.391634
$357$	3.12940e11	1.01966
$358$	−2.85677e11	−0.919183
$359$	1.12478e11	0.357391	0.178696	−	0.983904i	$-0.442812\pi$
$359$	1.12478e11	0.357391	0.178696	+	0.983904i	$0.442812\pi$
$360$	−8.71758e9	−0.0273549
$361$	−2.36728e11	−0.733613
$362$	4.31671e11	1.32119
$363$	0	0
$364$	−1.50506e11	−0.449364
$365$	−2.59056e11	−0.763970
$366$	2.82642e11	0.823327
$367$	1.51938e11	0.437189	0.218594	−	0.975816i	$-0.429853\pi$
$367$	1.51938e11	0.437189	0.218594	+	0.975816i	$0.429853\pi$
$368$	7.22963e10	0.205495
$369$	−1.26279e10	−0.0354579
$370$	−2.00585e11	−0.556404
$371$	7.52719e11	2.06277
$372$	3.10503e11	0.840664
$373$	−1.79048e11	−0.478938	−0.239469	−	0.970904i	$-0.576973\pi$
$373$	−1.79048e11	−0.478938	−0.239469	+	0.970904i	$0.576973\pi$
$374$	0	0
$375$	−2.45372e11	−0.640744
$376$	2.41251e11	0.622479
$377$	−3.55275e11	−0.905792
$378$	3.69761e11	0.931554
$379$	2.31277e11	0.575780	0.287890	−	0.957663i	$-0.407046\pi$
$379$	2.31277e11	0.575780	0.287890	+	0.957663i	$0.407046\pi$
$380$	−1.28090e11	−0.315129
$381$	−4.74306e11	−1.15318
$382$	−3.01926e11	−0.725463
$383$	3.53920e11	0.840448	0.420224	−	0.907420i	$-0.361951\pi$
$383$	3.53920e11	0.840448	0.420224	+	0.907420i	$0.361951\pi$
$384$	−3.88352e10	−0.0911455
$385$	0	0
$386$	2.62030e11	0.600771
$387$	3.19696e10	0.0724500
$388$	2.73577e10	0.0612825
$389$	4.20470e11	0.931027	0.465513	−	0.885041i	$-0.345870\pi$
$389$	4.20470e11	0.931027	0.465513	+	0.885041i	$0.345870\pi$
$390$	−2.68038e11	−0.586685
$391$	−2.75398e11	−0.595888
$392$	1.42224e11	0.304219
$393$	2.61938e11	0.553901
$394$	3.86203e11	0.807388
$395$	5.04695e11	1.04314
$396$	0	0
$397$	−3.43330e11	−0.693672	−0.346836	−	0.937926i	$-0.612744\pi$
$397$	−3.43330e11	−0.693672	−0.346836	+	0.937926i	$0.612744\pi$
$398$	−1.11756e9	−0.00223253
$399$	−3.67524e11	−0.725951
$400$	6.28683e10	0.122790
$401$	5.15897e11	0.996354	0.498177	−	0.867075i	$-0.334003\pi$
$401$	5.15897e11	0.996354	0.498177	+	0.867075i	$0.334003\pi$
$402$	1.57527e11	0.300841
$403$	5.68857e11	1.07431
$404$	−3.54717e11	−0.662470
$405$	7.00402e11	1.29360
$406$	7.25894e11	1.32589
$407$	0	0
$408$	1.47935e11	0.264301
$409$	4.68357e11	0.827604	0.413802	−	0.910367i	$-0.364201\pi$
$409$	4.68357e11	0.827604	0.413802	+	0.910367i	$0.364201\pi$
$410$	2.76484e11	0.483217
$411$	4.61964e11	0.798582
$412$	−3.71819e11	−0.635760
$413$	−1.57958e12	−2.67158
$414$	2.20123e10	0.0368268
$415$	7.86894e11	1.30227
$416$	−7.11480e10	−0.116478
$417$	−1.20161e11	−0.194603
$418$	0	0
$419$	−1.15054e12	−1.82364	−0.911820	−	0.410590i	$-0.865323\pi$
$419$	−1.15054e12	−1.82364	−0.911820	+	0.410590i	$0.865323\pi$
$420$	5.47651e11	0.858781
$421$	−2.49749e11	−0.387467	−0.193734	−	0.981054i	$-0.562060\pi$
$421$	−2.49749e11	−0.387467	−0.193734	+	0.981054i	$0.562060\pi$
$422$	−5.35097e11	−0.821347
$423$	7.34545e10	0.111554
$424$	3.55829e11	0.534681
$425$	−2.39483e11	−0.356062
$426$	3.87372e11	0.569882
$427$	−1.05799e12	−1.54013
$428$	−3.69606e11	−0.532405
$429$	0	0
$430$	−6.99964e11	−0.987342
$431$	−2.80621e11	−0.391717	−0.195858	−	0.980632i	$-0.562749\pi$
$431$	−2.80621e11	−0.391717	−0.195858	+	0.980632i	$0.562749\pi$
$432$	1.74795e11	0.241464
$433$	1.07421e12	1.46857	0.734285	−	0.678841i	$-0.237518\pi$
$433$	1.07421e12	1.46857	0.734285	+	0.678841i	$0.237518\pi$
$434$	−1.16228e12	−1.57256
$435$	1.29275e12	1.73106
$436$	−6.62208e11	−0.877618
$437$	3.23433e11	0.424246
$438$	−3.51377e11	−0.456184
$439$	−9.45531e11	−1.21503	−0.607513	−	0.794310i	$-0.707833\pi$
$439$	−9.45531e11	−1.21503	−0.607513	+	0.794310i	$0.707833\pi$
$440$	0	0
$441$	4.33034e10	0.0545191
$442$	2.71023e11	0.337759
$443$	1.41348e12	1.74370	0.871852	−	0.489769i	$-0.162919\pi$
$443$	1.41348e12	1.74370	0.871852	+	0.489769i	$0.162919\pi$
$444$	−2.72068e11	−0.332241
$445$	−7.91210e11	−0.956471
$446$	−2.79658e11	−0.334673
$447$	1.27873e12	1.51493
$448$	1.45369e11	0.170498
$449$	3.24374e11	0.376650	0.188325	−	0.982107i	$-0.439694\pi$
$449$	3.24374e11	0.376650	0.188325	+	0.982107i	$0.439694\pi$
$450$	1.91417e10	0.0220051
$451$	0	0
$452$	2.90818e11	0.327717
$453$	−8.75936e11	−0.977305
$454$	3.19284e11	0.352716
$455$	1.00332e12	1.09746
$456$	−1.73738e11	−0.188171
$457$	1.44780e11	0.155269	0.0776344	−	0.996982i	$-0.475263\pi$
$457$	1.44780e11	0.155269	0.0776344	+	0.996982i	$0.475263\pi$
$458$	−1.19319e12	−1.26711
$459$	−6.65846e11	−0.700191
$460$	−4.81951e11	−0.501872
$461$	−2.94094e11	−0.303271	−0.151636	−	0.988436i	$-0.548454\pi$
$461$	−2.94094e11	−0.303271	−0.151636	+	0.988436i	$0.548454\pi$
$462$	0	0
$463$	8.78478e11	0.888416	0.444208	−	0.895924i	$-0.353485\pi$
$463$	8.78478e11	0.888416	0.444208	+	0.895924i	$0.353485\pi$
$464$	3.43148e11	0.343677
$465$	−2.06992e12	−2.05312
$466$	7.74930e11	0.761247
$467$	6.31625e11	0.614516	0.307258	−	0.951626i	$-0.400589\pi$
$467$	6.31625e11	0.614516	0.307258	+	0.951626i	$0.400589\pi$
$468$	−2.16627e10	−0.0208740
$469$	−5.89658e11	−0.562759
$470$	−1.60826e12	−1.52025
$471$	4.65008e11	0.435378
$472$	−7.46709e11	−0.692488
$473$	0	0
$474$	6.84555e11	0.622882
$475$	2.81255e11	0.253500
$476$	−5.53752e11	−0.494406
$477$	1.08340e11	0.0958203
$478$	4.42750e11	0.387912
$479$	1.70132e12	1.47664	0.738321	−	0.674449i	$-0.235619\pi$
$479$	1.70132e12	1.47664	0.738321	+	0.674449i	$0.235619\pi$
$480$	2.58888e11	0.222601
$481$	−4.98441e11	−0.424581
$482$	−8.38324e11	−0.707458
$483$	−1.38284e12	−1.15614
$484$	0	0
$485$	−1.82375e11	−0.149668
$486$	1.10041e11	0.0894729
$487$	2.17815e11	0.175472	0.0877358	−	0.996144i	$-0.472037\pi$
$487$	2.17815e11	0.175472	0.0877358	+	0.996144i	$0.472037\pi$
$488$	−5.00140e11	−0.399211
$489$	−4.85399e11	−0.383892
$490$	−9.48113e11	−0.742981
$491$	−2.45219e11	−0.190409	−0.0952045	−	0.995458i	$-0.530351\pi$
$491$	−2.45219e11	−0.190409	−0.0952045	+	0.995458i	$0.530351\pi$
$492$	3.75015e11	0.288540
$493$	−1.30715e12	−0.996585
$494$	−3.18296e11	−0.240469
$495$	0	0
$496$	−5.49440e11	−0.407617
$497$	−1.45002e12	−1.06603
$498$	1.06732e12	0.777612
$499$	−2.14365e12	−1.54775	−0.773876	−	0.633337i	$-0.781685\pi$
$499$	−2.14365e12	−1.54775	−0.773876	+	0.633337i	$0.781685\pi$
$500$	4.34190e11	0.310681
$501$	1.63777e12	1.16140
$502$	8.72973e11	0.613528
$503$	−7.47725e11	−0.520818	−0.260409	−	0.965498i	$-0.583857\pi$
$503$	−7.47725e11	−0.520818	−0.260409	+	0.965498i	$0.583857\pi$
$504$	4.42609e10	0.0305550
$505$	2.36466e12	1.61792
$506$	0	0
$507$	8.68121e11	0.583505
$508$	8.39292e11	0.559147
$509$	3.60539e11	0.238079	0.119040	−	0.992889i	$-0.462018\pi$
$509$	3.60539e11	0.238079	0.119040	+	0.992889i	$0.462018\pi$
$510$	−9.86181e11	−0.645492
$511$	1.31528e12	0.853345
$512$	6.87195e10	0.0441942
$513$	7.81984e11	0.498505
$514$	2.75232e11	0.173926
$515$	2.47867e12	1.55269
$516$	−9.49412e11	−0.589564
$517$	0	0
$518$	1.01841e12	0.621496
$519$	1.79511e12	1.08602
$520$	4.74296e11	0.284469
$521$	−1.98989e12	−1.18320	−0.591602	−	0.806230i	$-0.701504\pi$
$521$	−1.98989e12	−1.18320	−0.591602	+	0.806230i	$0.701504\pi$
$522$	1.04479e11	0.0615904
$523$	−1.26127e12	−0.737140	−0.368570	−	0.929600i	$-0.620153\pi$
$523$	−1.26127e12	−0.737140	−0.368570	+	0.929600i	$0.620153\pi$
$524$	−4.63503e11	−0.268573
$525$	−1.20251e12	−0.690831
$526$	3.72083e11	0.211936
$527$	2.09297e12	1.18200
$528$	0	0
$529$	−5.84204e11	−0.324350
$530$	−2.37207e12	−1.30583
$531$	−2.27353e11	−0.124101
$532$	6.50338e11	0.351995
$533$	6.87046e11	0.368734
$534$	−1.07318e12	−0.571130
$535$	2.46392e12	1.30027
$536$	−2.78746e11	−0.145870
$537$	2.58310e12	1.34047
$538$	4.51452e11	0.232322
$539$	0	0
$540$	−1.16524e12	−0.589718
$541$	−3.48950e12	−1.75136	−0.875679	−	0.482893i	$-0.839586\pi$
$541$	−3.48950e12	−1.75136	−0.875679	+	0.482893i	$0.839586\pi$
$542$	−2.19531e12	−1.09269
$543$	−3.90318e12	−1.92672
$544$	−2.61772e11	−0.128153
$545$	4.41450e12	2.14337
$546$	1.36088e12	0.655320
$547$	2.03037e12	0.969687	0.484844	−	0.874601i	$-0.338877\pi$
$547$	2.03037e12	0.969687	0.484844	+	0.874601i	$0.338877\pi$
$548$	−8.17452e11	−0.387213
$549$	−1.52279e11	−0.0715426
$550$	0	0
$551$	1.53515e12	0.709525
$552$	−6.53705e11	−0.299679
$553$	−2.56244e12	−1.16517
$554$	−2.96643e12	−1.33795
$555$	1.81369e12	0.811419
$556$	2.12626e11	0.0943583
$557$	−2.94692e12	−1.29724	−0.648620	−	0.761112i	$-0.724654\pi$
$557$	−2.94692e12	−1.29724	−0.648620	+	0.761112i	$0.724654\pi$
$558$	−1.67290e11	−0.0730491
$559$	−1.73937e12	−0.753423
$560$	−9.69077e11	−0.416401
$561$	0	0
$562$	8.33224e11	0.352329
$563$	7.94805e11	0.333405	0.166703	−	0.986007i	$-0.446688\pi$
$563$	7.94805e11	0.333405	0.166703	+	0.986007i	$0.446688\pi$
$564$	−2.18140e12	−0.907778
$565$	−1.93869e12	−0.800369
$566$	−1.66073e12	−0.680184
$567$	−3.55608e12	−1.44493
$568$	−6.85460e11	−0.276321
$569$	−1.51857e12	−0.607338	−0.303669	−	0.952778i	$-0.598212\pi$
$569$	−1.51857e12	−0.607338	−0.303669	+	0.952778i	$0.598212\pi$
$570$	1.15819e12	0.459562
$571$	2.97779e11	0.117228	0.0586140	−	0.998281i	$-0.481332\pi$
$571$	2.97779e11	0.117228	0.0586140	+	0.998281i	$0.481332\pi$
$572$	0	0
$573$	2.73002e12	1.05796
$574$	−1.40376e12	−0.539747
$575$	1.05825e12	0.403722
$576$	2.09232e10	0.00792004
$577$	1.81913e12	0.683241	0.341620	−	0.939838i	$-0.389024\pi$
$577$	1.81913e12	0.683241	0.341620	+	0.939838i	$0.389024\pi$
$578$	−9.00239e11	−0.335492
$579$	−2.36929e12	−0.876121
$580$	−2.28754e12	−0.839349
$581$	−3.99522e12	−1.45462
$582$	−2.47369e11	−0.0893700
$583$	0	0
$584$	6.21767e11	0.221192
$585$	1.44410e11	0.0509797
$586$	1.36246e12	0.477292
$587$	2.78354e12	0.967666	0.483833	−	0.875160i	$-0.339244\pi$
$587$	2.78354e12	0.967666	0.483833	+	0.875160i	$0.339244\pi$
$588$	−1.28599e12	−0.443651
$589$	−2.45803e12	−0.841529
$590$	4.97781e12	1.69124
$591$	−3.49205e12	−1.17744
$592$	4.81427e11	0.161095
$593$	5.56438e11	0.184787	0.0923933	−	0.995723i	$-0.470548\pi$
$593$	5.56438e11	0.184787	0.0923933	+	0.995723i	$0.470548\pi$
$594$	0	0
$595$	3.69149e12	1.20747
$596$	−2.26272e12	−0.734553
$597$	1.01050e10	0.00325576
$598$	−1.19762e12	−0.382969
$599$	−5.73449e12	−1.82001	−0.910006	−	0.414595i	$-0.863923\pi$
$599$	−5.73449e12	−1.82001	−0.910006	+	0.414595i	$0.863923\pi$
$600$	−5.68457e11	−0.179068
$601$	−5.50049e11	−0.171975	−0.0859877	−	0.996296i	$-0.527405\pi$
$601$	−5.50049e11	−0.171975	−0.0859877	+	0.996296i	$0.527405\pi$
$602$	3.55386e12	1.10285
$603$	−8.48707e10	−0.0261415
$604$	1.54998e12	0.473871
$605$	0	0
$606$	3.20736e12	0.966099
$607$	−3.73380e12	−1.11635	−0.558177	−	0.829722i	$-0.688499\pi$
$607$	−3.73380e12	−1.11635	−0.558177	+	0.829722i	$0.688499\pi$
$608$	3.07431e11	0.0912393
$609$	−6.56355e12	−1.93358
$610$	3.33410e12	0.974976
$611$	−3.99644e12	−1.16008
$612$	−7.97026e10	−0.0229663
$613$	−3.83812e12	−1.09786	−0.548929	−	0.835869i	$-0.684964\pi$
$613$	−3.83812e12	−1.09786	−0.548929	+	0.835869i	$0.684964\pi$
$614$	−4.47116e12	−1.26959
$615$	−2.49997e12	−0.704689
$616$	0	0
$617$	−2.53329e12	−0.703723	−0.351861	−	0.936052i	$-0.614451\pi$
$617$	−2.53329e12	−0.703723	−0.351861	+	0.936052i	$0.614451\pi$
$618$	3.36199e12	0.927147
$619$	3.23255e12	0.884988	0.442494	−	0.896772i	$-0.354094\pi$
$619$	3.23255e12	0.884988	0.442494	+	0.896772i	$0.354094\pi$
$620$	3.66275e12	0.995507
$621$	2.94229e12	0.793914
$622$	3.84178e12	1.02914
$623$	4.01713e12	1.06837
$624$	6.43323e11	0.169863
$625$	−4.76807e12	−1.24992
$626$	1.54982e12	0.403363
$627$	0	0
$628$	−8.22838e11	−0.211104
$629$	−1.83390e12	−0.467140
$630$	−2.95058e11	−0.0746233
$631$	3.95011e11	0.0991921	0.0495961	−	0.998769i	$-0.484207\pi$
$631$	3.95011e11	0.0991921	0.0495961	+	0.998769i	$0.484207\pi$
$632$	−1.21133e12	−0.302020
$633$	4.83836e12	1.19779
$634$	−2.72199e12	−0.669090
$635$	−5.59500e12	−1.36558
$636$	−3.21741e12	−0.779740
$637$	−2.35600e12	−0.566955
$638$	0	0
$639$	−2.08704e11	−0.0495196
$640$	−4.58107e11	−0.107934
$641$	−3.96414e12	−0.927444	−0.463722	−	0.885981i	$-0.653486\pi$
$641$	−3.96414e12	−0.927444	−0.463722	+	0.885981i	$0.653486\pi$
$642$	3.34199e12	0.776422
$643$	−7.33426e12	−1.69203	−0.846013	−	0.533163i	$-0.821003\pi$
$643$	−7.33426e12	−1.69203	−0.846013	+	0.533163i	$0.821003\pi$
$644$	2.44696e12	0.560585
$645$	6.32910e12	1.43987
$646$	−1.17109e12	−0.264573
$647$	−1.01763e12	−0.228308	−0.114154	−	0.993463i	$-0.536416\pi$
$647$	−1.01763e12	−0.228308	−0.114154	+	0.993463i	$0.536416\pi$
$648$	−1.68105e12	−0.374535
$649$	0	0
$650$	−1.04144e12	−0.228836
$651$	1.05094e13	2.29331
$652$	8.58921e11	0.186140
$653$	6.78338e12	1.45995	0.729973	−	0.683476i	$-0.239533\pi$
$653$	6.78338e12	1.45995	0.729973	+	0.683476i	$0.239533\pi$
$654$	5.98771e12	1.27985
$655$	3.08987e12	0.655925
$656$	−6.63594e11	−0.139906
$657$	1.89311e11	0.0396399
$658$	8.16547e12	1.69811
$659$	−1.83983e12	−0.380008	−0.190004	−	0.981783i	$-0.560850\pi$
$659$	−1.83983e12	−0.380008	−0.190004	+	0.981783i	$0.560850\pi$
$660$	0	0
$661$	−3.08220e12	−0.627992	−0.313996	−	0.949424i	$-0.601668\pi$
$661$	−3.08220e12	−0.627992	−0.313996	+	0.949424i	$0.601668\pi$
$662$	3.92509e11	0.0794308
$663$	−2.45060e12	−0.492563
$664$	−1.88864e12	−0.377045
$665$	−4.33537e12	−0.859664
$666$	1.46582e11	0.0288699
$667$	5.77614e12	1.12998
$668$	−2.89806e12	−0.563136
$669$	2.52868e12	0.488063
$670$	1.85821e12	0.356253
$671$	0	0
$672$	−1.31443e12	−0.248643
$673$	7.07648e12	1.32969	0.664844	−	0.746983i	$-0.268498\pi$
$673$	7.07648e12	1.32969	0.664844	+	0.746983i	$0.268498\pi$
$674$	−1.54313e12	−0.288026
$675$	2.55859e12	0.474389
$676$	−1.53615e12	−0.282927
$677$	−1.18522e11	−0.0216846	−0.0108423	−	0.999941i	$-0.503451\pi$
$677$	−1.18522e11	−0.0216846	−0.0108423	+	0.999941i	$0.503451\pi$
$678$	−2.62959e12	−0.477918
$679$	9.25956e11	0.167177
$680$	1.74506e12	0.312983
$681$	−2.88697e12	−0.514376
$682$	0	0
$683$	−4.08882e12	−0.718961	−0.359480	−	0.933153i	$-0.617046\pi$
$683$	−4.08882e12	−0.718961	−0.359480	+	0.933153i	$0.617046\pi$
$684$	9.36045e10	0.0163510
$685$	5.44940e12	0.945674
$686$	−7.80642e11	−0.134584
$687$	1.07888e13	1.84786
$688$	1.68000e12	0.285865
$689$	−5.89446e12	−0.996455
$690$	4.35782e12	0.731894
$691$	2.48976e12	0.415438	0.207719	−	0.978189i	$-0.433396\pi$
$691$	2.48976e12	0.415438	0.207719	+	0.978189i	$0.433396\pi$
$692$	−3.17648e12	−0.526586
$693$	0	0
$694$	1.64111e12	0.268547
$695$	−1.41744e12	−0.230447
$696$	−3.10276e12	−0.501194
$697$	2.52782e12	0.405694
$698$	5.75936e12	0.918386
$699$	−7.00694e12	−1.11015
$700$	2.12786e12	0.334967
$701$	−6.94398e12	−1.08612	−0.543059	−	0.839694i	$-0.682734\pi$
$701$	−6.94398e12	−1.08612	−0.543059	+	0.839694i	$0.682734\pi$
$702$	−2.89556e12	−0.450003
$703$	2.15377e12	0.332583
$704$	0	0
$705$	1.45419e13	2.21703
$706$	−9.97457e11	−0.151103
$707$	−1.20059e13	−1.80720
$708$	6.75176e12	1.00987
$709$	−1.00274e13	−1.49032	−0.745159	−	0.666887i	$-0.767626\pi$
$709$	−1.00274e13	−1.49032	−0.745159	+	0.666887i	$0.767626\pi$
$710$	4.56950e12	0.674849
$711$	−3.68817e11	−0.0541250
$712$	1.89900e12	0.276927
$713$	−9.24861e12	−1.34021
$714$	5.00704e12	0.721006
$715$	0	0
$716$	−4.57083e12	−0.649960
$717$	−4.00336e12	−0.565703
$718$	1.79965e12	0.252714
$719$	8.41668e12	1.17452	0.587261	−	0.809398i	$-0.300206\pi$
$719$	8.41668e12	1.17452	0.587261	+	0.809398i	$0.300206\pi$
$720$	−1.39481e11	−0.0193428
$721$	−1.25847e13	−1.73434
$722$	−3.78764e12	−0.518743
$723$	7.58015e12	1.03171
$724$	6.90673e12	0.934220
$725$	5.02289e12	0.675200
$726$	0	0
$727$	−4.69707e10	−0.00623622	−0.00311811	−	0.999995i	$-0.500993\pi$
$727$	−4.69707e10	−0.00623622	−0.00311811	+	0.999995i	$0.500993\pi$
$728$	−2.40810e12	−0.317748
$729$	7.08315e12	0.928865
$730$	−4.14490e12	−0.540209
$731$	−6.39960e12	−0.828943
$732$	4.52228e12	0.582180
$733$	−6.70015e12	−0.857269	−0.428634	−	0.903478i	$-0.641005\pi$
$733$	−6.70015e12	−0.857269	−0.428634	+	0.903478i	$0.641005\pi$
$734$	2.43101e12	0.309139
$735$	8.57286e12	1.08351
$736$	1.15674e12	0.145307
$737$	0	0
$738$	−2.02047e11	−0.0250725
$739$	1.71079e11	0.0211007	0.0105503	−	0.999944i	$-0.496642\pi$
$739$	1.71079e11	0.0211007	0.0105503	+	0.999944i	$0.496642\pi$
$740$	−3.20935e12	−0.393437
$741$	2.87804e12	0.350683
$742$	1.20435e13	1.45860
$743$	−6.82102e12	−0.821106	−0.410553	−	0.911837i	$-0.634664\pi$
$743$	−6.82102e12	−0.821106	−0.410553	+	0.911837i	$0.634664\pi$
$744$	4.96805e12	0.594439
$745$	1.50841e13	1.79397
$746$	−2.86477e12	−0.338661
$747$	−5.75040e11	−0.0675702
$748$	0	0
$749$	−1.25098e13	−1.45239
$750$	−3.92596e12	−0.453075
$751$	5.72654e12	0.656920	0.328460	−	0.944518i	$-0.393470\pi$
$751$	5.72654e12	0.656920	0.328460	+	0.944518i	$0.393470\pi$
$752$	3.86002e12	0.440159
$753$	−7.89345e12	−0.894724
$754$	−5.68440e12	−0.640492
$755$	−1.03327e13	−1.15732
$756$	5.91618e12	0.658708
$757$	2.98205e12	0.330052	0.165026	−	0.986289i	$-0.447229\pi$
$757$	2.98205e12	0.330052	0.165026	+	0.986289i	$0.447229\pi$
$758$	3.70044e12	0.407138
$759$	0	0
$760$	−2.04944e12	−0.222830
$761$	8.46525e12	0.914974	0.457487	−	0.889216i	$-0.348750\pi$
$761$	8.46525e12	0.914974	0.457487	+	0.889216i	$0.348750\pi$
$762$	−7.58890e12	−0.815420
$763$	−2.24133e13	−2.39412
$764$	−4.83082e12	−0.512980
$765$	5.31324e11	0.0560897
$766$	5.66273e12	0.594287
$767$	1.23696e13	1.29055
$768$	−6.21363e11	−0.0644496
$769$	−1.77112e13	−1.82633	−0.913164	−	0.407592i	$-0.866369\pi$
$769$	−1.77112e13	−1.82633	−0.913164	+	0.407592i	$0.866369\pi$
$770$	0	0
$771$	−2.48866e12	−0.253642
$772$	4.19249e12	0.424809
$773$	9.83204e12	0.990458	0.495229	−	0.868763i	$-0.335084\pi$
$773$	9.83204e12	0.990458	0.495229	+	0.868763i	$0.335084\pi$
$774$	5.11514e11	0.0512299
$775$	−8.04251e12	−0.800818
$776$	4.37723e11	0.0433333
$777$	−9.20848e12	−0.906345
$778$	6.72753e12	0.658335
$779$	−2.96873e12	−0.288837
$780$	−4.28860e12	−0.414849
$781$	0	0
$782$	−4.40636e12	−0.421356
$783$	1.39653e13	1.32777
$784$	2.27559e12	0.215115
$785$	5.48531e12	0.515570
$786$	4.19101e12	0.391667
$787$	1.78869e12	0.166207	0.0831036	−	0.996541i	$-0.473517\pi$
$787$	1.78869e12	0.166207	0.0831036	+	0.996541i	$0.473517\pi$
$788$	6.17924e12	0.570909
$789$	−3.36439e12	−0.309072
$790$	8.07512e12	0.737611
$791$	9.84312e12	0.894002
$792$	0	0
$793$	8.28504e12	0.743987
$794$	−5.49328e12	−0.490500
$795$	2.14484e13	1.90433
$796$	−1.78809e10	−0.00157863
$797$	1.04170e13	0.914496	0.457248	−	0.889339i	$-0.348835\pi$
$797$	1.04170e13	0.914496	0.457248	+	0.889339i	$0.348835\pi$
$798$	−5.88038e12	−0.513325
$799$	−1.47039e13	−1.27636
$800$	1.00589e12	0.0868254
$801$	5.78194e11	0.0496281
$802$	8.25436e12	0.704529
$803$	0	0
$804$	2.52043e12	0.212727
$805$	−1.63123e13	−1.36909
$806$	9.10171e12	0.759653
$807$	−4.08204e12	−0.338802
$808$	−5.67548e12	−0.468437
$809$	7.91008e10	0.00649251	0.00324625	−	0.999995i	$-0.498967\pi$
$809$	7.91008e10	0.00649251	0.00324625	+	0.999995i	$0.498967\pi$
$810$	1.12064e13	0.914713
$811$	−7.52015e12	−0.610425	−0.305213	−	0.952284i	$-0.598728\pi$
$811$	−7.52015e12	−0.610425	−0.305213	+	0.952284i	$0.598728\pi$
$812$	1.16143e13	0.937542
$813$	1.98500e13	1.59351
$814$	0	0
$815$	−5.72585e12	−0.454601
$816$	2.36695e12	0.186889
$817$	7.51583e12	0.590171
$818$	7.49372e12	0.585204
$819$	−7.33201e11	−0.0569437
$820$	4.42374e12	0.341686
$821$	−4.67347e12	−0.359000	−0.179500	−	0.983758i	$-0.557448\pi$
$821$	−4.67347e12	−0.359000	−0.179500	+	0.983758i	$0.557448\pi$
$822$	7.39142e12	0.564683
$823$	−4.06045e12	−0.308514	−0.154257	−	0.988031i	$-0.549298\pi$
$823$	−4.06045e12	−0.308514	−0.154257	+	0.988031i	$0.549298\pi$
$824$	−5.94910e12	−0.449551
$825$	0	0
$826$	−2.52733e13	−1.88909
$827$	2.53074e12	0.188136	0.0940682	−	0.995566i	$-0.470013\pi$
$827$	2.53074e12	0.188136	0.0940682	+	0.995566i	$0.470013\pi$
$828$	3.52196e11	0.0260405
$829$	−2.26450e12	−0.166524	−0.0832620	−	0.996528i	$-0.526534\pi$
$829$	−2.26450e12	−0.166524	−0.0832620	+	0.996528i	$0.526534\pi$
$830$	1.25903e13	0.920841
$831$	2.68226e13	1.95117
$832$	−1.13837e12	−0.0823622
$833$	−8.66836e12	−0.623784
$834$	−1.92257e12	−0.137605
$835$	1.93194e13	1.37532
$836$	0	0
$837$	−2.23609e13	−1.57480
$838$	−1.84087e13	−1.28951
$839$	7.42242e12	0.517150	0.258575	−	0.965991i	$-0.416747\pi$
$839$	7.42242e12	0.517150	0.258575	+	0.965991i	$0.416747\pi$
$840$	8.76242e12	0.607250
$841$	1.29088e13	0.889825
$842$	−3.99599e12	−0.273981
$843$	−7.53404e12	−0.513811
$844$	−8.56156e12	−0.580780
$845$	1.02405e13	0.690981
$846$	1.17527e12	0.0788809
$847$	0	0
$848$	5.69326e12	0.378077
$849$	1.50164e13	0.991931
$850$	−3.83173e12	−0.251774
$851$	8.10377e12	0.529668
$852$	6.19795e12	0.402967
$853$	−1.60812e13	−1.04004	−0.520019	−	0.854155i	$-0.674075\pi$
$853$	−1.60812e13	−1.04004	−0.520019	+	0.854155i	$0.674075\pi$
$854$	−1.69279e13	−1.08904
$855$	−6.23999e11	−0.0399334
$856$	−5.91370e12	−0.376467
$857$	−8.68029e11	−0.0549693	−0.0274847	−	0.999622i	$-0.508750\pi$
$857$	−8.68029e11	−0.0549693	−0.0274847	+	0.999622i	$0.508750\pi$
$858$	0	0
$859$	−1.16610e13	−0.730748	−0.365374	−	0.930861i	$-0.619059\pi$
$859$	−1.16610e13	−0.730748	−0.365374	+	0.930861i	$0.619059\pi$
$860$	−1.11994e13	−0.698156
$861$	1.26929e13	0.787129
$862$	−4.48993e12	−0.276986
$863$	2.04030e13	1.25212	0.626060	−	0.779775i	$-0.284666\pi$
$863$	2.04030e13	1.25212	0.626060	+	0.779775i	$0.284666\pi$
$864$	2.79672e12	0.170741
$865$	2.11755e13	1.28606
$866$	1.71874e13	1.03844
$867$	8.13999e12	0.489258
$868$	−1.85965e13	−1.11197
$869$	0	0
$870$	2.06840e13	1.22405
$871$	4.61755e12	0.271850
$872$	−1.05953e13	−0.620570
$873$	1.33275e11	0.00776576
$874$	5.17493e12	0.299987
$875$	1.46957e13	0.847529
$876$	−5.62203e12	−0.322571
$877$	3.26576e13	1.86417	0.932085	−	0.362239i	$-0.117988\pi$
$877$	3.26576e13	1.86417	0.932085	+	0.362239i	$0.117988\pi$
$878$	−1.51285e13	−0.859153
$879$	−1.23194e13	−0.696048
$880$	0	0
$881$	1.89169e13	1.05793	0.528966	−	0.848643i	$-0.322580\pi$
$881$	1.89169e13	1.05793	0.528966	+	0.848643i	$0.322580\pi$
$882$	6.92854e11	0.0385508
$883$	−4.52036e12	−0.250236	−0.125118	−	0.992142i	$-0.539931\pi$
$883$	−4.52036e12	−0.250236	−0.125118	+	0.992142i	$0.539931\pi$
$884$	4.33638e12	0.238832
$885$	−4.50095e13	−2.46638
$886$	2.26157e13	1.23299
$887$	−1.67209e13	−0.906994	−0.453497	−	0.891258i	$-0.649824\pi$
$887$	−1.67209e13	−0.906994	−0.453497	+	0.891258i	$0.649824\pi$
$888$	−4.35308e12	−0.234930
$889$	2.84069e13	1.52534
$890$	−1.26594e13	−0.676327
$891$	0	0
$892$	−4.47453e12	−0.236650
$893$	1.72686e13	0.908712
$894$	2.04596e13	1.07122
$895$	3.04707e13	1.58737
$896$	2.32590e12	0.120561
$897$	1.08289e13	0.558495
$898$	5.18999e12	0.266332
$899$	−4.38977e13	−2.24142
$900$	3.06267e11	0.0155600
$901$	−2.16873e13	−1.09634
$902$	0	0
$903$	−3.21341e13	−1.60832
$904$	4.65309e12	0.231731
$905$	−4.60426e13	−2.28161
$906$	−1.40150e13	−0.691059
$907$	−2.68525e13	−1.31751	−0.658753	−	0.752359i	$-0.728916\pi$
$907$	−2.68525e13	−1.31751	−0.658753	+	0.752359i	$0.728916\pi$
$908$	5.10854e12	0.249408
$909$	−1.72803e12	−0.0839487
$910$	1.60532e13	0.776024
$911$	8.77113e12	0.421913	0.210957	−	0.977495i	$-0.432342\pi$
$911$	8.77113e12	0.421913	0.210957	+	0.977495i	$0.432342\pi$
$912$	−2.77980e12	−0.133057
$913$	0	0
$914$	2.31647e12	0.109792
$915$	−3.01470e13	−1.42184
$916$	−1.90910e13	−0.895980
$917$	−1.56879e13	−0.732660
$918$	−1.06535e13	−0.495110
$919$	8.62159e11	0.0398720	0.0199360	−	0.999801i	$-0.493654\pi$
$919$	8.62159e11	0.0398720	0.0199360	+	0.999801i	$0.493654\pi$
$920$	−7.71122e12	−0.354877
$921$	4.04284e13	1.85147
$922$	−4.70550e12	−0.214445
$923$	1.13549e13	0.514965
$924$	0	0
$925$	7.04697e12	0.316493
$926$	1.40557e13	0.628205
$927$	−1.81134e12	−0.0805640
$928$	5.49037e12	0.243017
$929$	1.65304e12	0.0728138	0.0364069	−	0.999337i	$-0.488409\pi$
$929$	1.65304e12	0.0728138	0.0364069	+	0.999337i	$0.488409\pi$
$930$	−3.31187e13	−1.45178
$931$	1.01803e13	0.444107
$932$	1.23989e13	0.538283
$933$	−3.47375e13	−1.50083
$934$	1.01060e13	0.434529
$935$	0	0
$936$	−3.46603e11	−0.0147601
$937$	2.41842e13	1.02495	0.512476	−	0.858702i	$-0.328728\pi$
$937$	2.41842e13	1.02495	0.512476	+	0.858702i	$0.328728\pi$
$938$	−9.43453e12	−0.397931
$939$	−1.40135e13	−0.588235
$940$	−2.57322e13	−1.07498
$941$	−3.40036e13	−1.41375	−0.706874	−	0.707340i	$-0.749895\pi$
$941$	−3.40036e13	−1.41375	−0.706874	+	0.707340i	$0.749895\pi$
$942$	7.44013e12	0.307859
$943$	−1.11701e13	−0.459998
$944$	−1.19473e13	−0.489663
$945$	−3.94392e13	−1.60874
$946$	0	0
$947$	1.65859e13	0.670138	0.335069	−	0.942194i	$-0.391240\pi$
$947$	1.65859e13	0.670138	0.335069	+	0.942194i	$0.391240\pi$
$948$	1.09529e13	0.440444
$949$	−1.02998e13	−0.412223
$950$	4.50007e12	0.179252
$951$	2.46123e13	0.975753
$952$	−8.86003e12	−0.349598
$953$	2.57430e13	1.01098	0.505489	−	0.862833i	$-0.331312\pi$
$953$	2.57430e13	1.01098	0.505489	+	0.862833i	$0.331312\pi$
$954$	1.73344e12	0.0677552
$955$	3.22038e13	1.25283
$956$	7.08401e12	0.274295
$957$	0	0
$958$	2.72211e13	1.04414
$959$	−2.76677e13	−1.05631
$960$	4.14222e12	0.157403
$961$	4.38482e13	1.65843
$962$	−7.97506e12	−0.300224
$963$	−1.80056e12	−0.0674668
$964$	−1.34132e13	−0.500248
$965$	−2.79485e13	−1.03749
$966$	−2.21255e13	−0.817516
$967$	−4.94862e12	−0.181997	−0.0909986	−	0.995851i	$-0.529006\pi$
$967$	−4.94862e12	−0.181997	−0.0909986	+	0.995851i	$0.529006\pi$
$968$	0	0
$969$	1.05891e13	0.385834
$970$	−2.91801e12	−0.105831
$971$	1.45094e13	0.523799	0.261899	−	0.965095i	$-0.415651\pi$
$971$	1.45094e13	0.523799	0.261899	+	0.965095i	$0.415651\pi$
$972$	1.76066e12	0.0632669
$973$	7.19661e12	0.257407
$974$	3.48504e12	0.124077
$975$	9.41674e12	0.333718
$976$	−8.00224e12	−0.282285
$977$	−8.00736e12	−0.281167	−0.140583	−	0.990069i	$-0.544898\pi$
$977$	−8.00736e12	−0.281167	−0.140583	+	0.990069i	$0.544898\pi$
$978$	−7.76638e12	−0.271453
$979$	0	0
$980$	−1.51698e13	−0.525367
$981$	−3.22599e12	−0.111212
$982$	−3.92351e12	−0.134640
$983$	−3.29697e13	−1.12622	−0.563111	−	0.826381i	$-0.690396\pi$
$983$	−3.29697e13	−1.12622	−0.563111	+	0.826381i	$0.690396\pi$
$984$	6.00024e12	0.204028
$985$	−4.11929e13	−1.39431
$986$	−2.09144e13	−0.704692
$987$	−7.38324e13	−2.47639
$988$	−5.09273e12	−0.170037
$989$	2.82791e13	0.939900
$990$	0	0
$991$	1.22142e12	0.0402286	0.0201143	−	0.999798i	$-0.493597\pi$
$991$	1.22142e12	0.0402286	0.0201143	+	0.999798i	$0.493597\pi$
$992$	−8.79103e12	−0.288229
$993$	−3.54908e12	−0.115836
$994$	−2.32003e13	−0.753798
$995$	1.19200e11	0.00385544
$996$	1.70771e13	0.549855
$997$	3.27455e13	1.04960	0.524800	−	0.851226i	$-0.324140\pi$
$997$	3.27455e13	1.04960	0.524800	+	0.851226i	$0.324140\pi$
$998$	−3.42984e13	−1.09443
$999$	1.95930e13	0.622380

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.10.a.e.1.1		2
11.10	odd	2		22.10.a.d.1.1	✓	2
33.32	even	2		198.10.a.n.1.2		2
44.43	even	2		176.10.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.10.a.d.1.1	✓	2	11.10	odd	2
176.10.a.e.1.2		2	44.43	even	2
198.10.a.n.1.2		2	33.32	even	2
242.10.a.e.1.1		2	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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	242.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} -2314.76 q^{6} +8664.66 q^{7} +4096.00 q^{8} +1247.12 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} -2314.76 q^{6} +8664.66 q^{7} +4096.00 q^{8} +1247.12 q^{9} -27305.3 q^{10} -37036.2 q^{12} -67852.1 q^{13} +138635. q^{14} +246895. q^{15} +65536.0 q^{16} -249646. q^{17} +19953.9 q^{18} +293189. q^{19} -436885. q^{20} -1.25354e6 q^{21} +1.10315e6 q^{23} -592578. q^{24} +959294. q^{25} -1.08563e6 q^{26} +2.66716e6 q^{27} +2.21815e6 q^{28} +5.23603e6 q^{29} +3.95032e6 q^{30} -8.38378e6 q^{31} +1.04858e6 q^{32} -3.99433e6 q^{34} -1.47869e7 q^{35} +319263. q^{36} +7.34600e6 q^{37} +4.69103e6 q^{38} +9.81632e6 q^{39} -6.99016e6 q^{40} -1.01256e7 q^{41} -2.00566e7 q^{42} +2.56347e7 q^{43} -2.12831e6 q^{45} +1.76505e7 q^{46} +5.88993e7 q^{47} -9.48125e6 q^{48} +3.47227e7 q^{49} +1.53487e7 q^{50} +3.61168e7 q^{51} -1.73701e7 q^{52} +8.68723e7 q^{53} +4.26746e7 q^{54} +3.54904e7 q^{56} -4.24164e7 q^{57} +8.37764e7 q^{58} -1.82302e8 q^{59} +6.32052e7 q^{60} -1.22104e8 q^{61} -1.34141e8 q^{62} +1.08059e7 q^{63} +1.67772e7 q^{64} +1.15795e8 q^{65} -6.80532e7 q^{67} -6.39093e7 q^{68} -1.59596e8 q^{69} -2.36591e8 q^{70} -1.67349e8 q^{71} +5.10821e6 q^{72} +1.51799e8 q^{73} +1.17536e8 q^{74} -1.38783e8 q^{75} +7.50564e7 q^{76} +1.57061e8 q^{78} -2.95735e8 q^{79} -1.11842e8 q^{80} -4.10412e8 q^{81} -1.62010e8 q^{82} -4.61094e8 q^{83} -3.20906e8 q^{84} +4.26040e8 q^{85} +4.10156e8 q^{86} -7.57509e8 q^{87} +4.63623e8 q^{89} -3.40530e7 q^{90} -5.87915e8 q^{91} +2.82407e8 q^{92} +1.21290e9 q^{93} +9.42388e8 q^{94} -5.00351e8 q^{95} -1.51700e8 q^{96} +1.06866e8 q^{97} +5.55563e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} - 336 q^{6} + 7490 q^{7} + 8192 q^{8} - 3141 q^{9}+O(q^{10}) \) 2 * q + 32 * q^2 - 21 * q^3 + 512 * q^4 - 521 * q^5 - 336 * q^6 + 7490 * q^7 + 8192 * q^8 - 3141 * q^9	\( 2 q + 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} - 336 q^{6} + 7490 q^{7} + 8192 q^{8} - 3141 q^{9} - 8336 q^{10} - 5376 q^{12} - 150314 q^{13} + 119840 q^{14} + 393519 q^{15} + 131072 q^{16} - 690472 q^{17} - 50256 q^{18} - 511212 q^{19} - 133376 q^{20} - 1398810 q^{21} + 874751 q^{23} - 86016 q^{24} + 411771 q^{25} - 2405024 q^{26} - 309771 q^{27} + 1917440 q^{28} + 2951058 q^{29} + 6296304 q^{30} - 5818705 q^{31} + 2097152 q^{32} - 11047552 q^{34} - 16179590 q^{35} - 804096 q^{36} + 2658905 q^{37} - 8179392 q^{38} - 381948 q^{39} - 2134016 q^{40} - 13427994 q^{41} - 22380960 q^{42} + 17820762 q^{43} - 7330788 q^{45} + 13996016 q^{46} + 56044104 q^{47} - 1376256 q^{48} - 4251114 q^{49} + 6588336 q^{50} - 18401250 q^{51} - 38480384 q^{52} + 96842752 q^{53} - 4956336 q^{54} + 30679040 q^{56} - 141898680 q^{57} + 47216928 q^{58} - 119136183 q^{59} + 100740864 q^{60} + 90424326 q^{61} - 93099280 q^{62} + 15960420 q^{63} + 33554432 q^{64} + 18029712 q^{65} - 295944891 q^{67} - 176760832 q^{68} - 187843215 q^{69} - 258873440 q^{70} - 322953267 q^{71} - 12865536 q^{72} + 255975514 q^{73} + 42542480 q^{74} - 206496864 q^{75} - 130870272 q^{76} - 6111168 q^{78} + 889658 q^{79} - 34144256 q^{80} - 692205750 q^{81} - 214847904 q^{82} + 277699042 q^{83} - 358095360 q^{84} - 96595042 q^{85} + 285132192 q^{86} - 1040096232 q^{87} + 1363672217 q^{89} - 117292608 q^{90} - 491050280 q^{91} + 223936256 q^{92} + 1530132009 q^{93} + 896705664 q^{94} - 1454033872 q^{95} - 22020096 q^{96} + 1398434043 q^{97} - 68017824 q^{98}+O(q^{100}) \) 2 * q + 32 * q^2 - 21 * q^3 + 512 * q^4 - 521 * q^5 - 336 * q^6 + 7490 * q^7 + 8192 * q^8 - 3141 * q^9 - 8336 * q^10 - 5376 * q^12 - 150314 * q^13 + 119840 * q^14 + 393519 * q^15 + 131072 * q^16 - 690472 * q^17 - 50256 * q^18 - 511212 * q^19 - 133376 * q^20 - 1398810 * q^21 + 874751 * q^23 - 86016 * q^24 + 411771 * q^25 - 2405024 * q^26 - 309771 * q^27 + 1917440 * q^28 + 2951058 * q^29 + 6296304 * q^30 - 5818705 * q^31 + 2097152 * q^32 - 11047552 * q^34 - 16179590 * q^35 - 804096 * q^36 + 2658905 * q^37 - 8179392 * q^38 - 381948 * q^39 - 2134016 * q^40 - 13427994 * q^41 - 22380960 * q^42 + 17820762 * q^43 - 7330788 * q^45 + 13996016 * q^46 + 56044104 * q^47 - 1376256 * q^48 - 4251114 * q^49 + 6588336 * q^50 - 18401250 * q^51 - 38480384 * q^52 + 96842752 * q^53 - 4956336 * q^54 + 30679040 * q^56 - 141898680 * q^57 + 47216928 * q^58 - 119136183 * q^59 + 100740864 * q^60 + 90424326 * q^61 - 93099280 * q^62 + 15960420 * q^63 + 33554432 * q^64 + 18029712 * q^65 - 295944891 * q^67 - 176760832 * q^68 - 187843215 * q^69 - 258873440 * q^70 - 322953267 * q^71 - 12865536 * q^72 + 255975514 * q^73 + 42542480 * q^74 - 206496864 * q^75 - 130870272 * q^76 - 6111168 * q^78 + 889658 * q^79 - 34144256 * q^80 - 692205750 * q^81 - 214847904 * q^82 + 277699042 * q^83 - 358095360 * q^84 - 96595042 * q^85 + 285132192 * q^86 - 1040096232 * q^87 + 1363672217 * q^89 - 117292608 * q^90 - 491050280 * q^91 + 223936256 * q^92 + 1530132009 * q^93 + 896705664 * q^94 - 1454033872 * q^95 - 22020096 * q^96 + 1398434043 * q^97 - 68017824 * q^98

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