LMFDB - Embedded newform 22.10.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,10,Mod(1,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, 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("22.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	22.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:	$11.3307883956$
Analytic rank:	$0$
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:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$15.4081$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} +2314.76 q^{6} -8664.66 q^{7} -4096.00 q^{8} +1247.12 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} +2314.76 q^{6} -8664.66 q^{7} -4096.00 q^{8} +1247.12 q^{9} +27305.3 q^{10} +14641.0 q^{11} -37036.2 q^{12} +67852.1 q^{13} +138635. q^{14} +246895. q^{15} +65536.0 q^{16} +249646. q^{17} -19953.9 q^{18} -293189. q^{19} -436885. q^{20} +1.25354e6 q^{21} -234256. q^{22} +1.10315e6 q^{23} +592578. q^{24} +959294. q^{25} -1.08563e6 q^{26} +2.66716e6 q^{27} -2.21815e6 q^{28} -5.23603e6 q^{29} -3.95032e6 q^{30} -8.38378e6 q^{31} -1.04858e6 q^{32} -2.11815e6 q^{33} -3.99433e6 q^{34} +1.47869e7 q^{35} +319263. q^{36} +7.34600e6 q^{37} +4.69103e6 q^{38} -9.81632e6 q^{39} +6.99016e6 q^{40} +1.01256e7 q^{41} -2.00566e7 q^{42} -2.56347e7 q^{43} +3.74810e6 q^{44} -2.12831e6 q^{45} -1.76505e7 q^{46} +5.88993e7 q^{47} -9.48125e6 q^{48} +3.47227e7 q^{49} -1.53487e7 q^{50} -3.61168e7 q^{51} +1.73701e7 q^{52} +8.68723e7 q^{53} -4.26746e7 q^{54} -2.49861e7 q^{55} +3.54904e7 q^{56} +4.24164e7 q^{57} +8.37764e7 q^{58} -1.82302e8 q^{59} +6.32052e7 q^{60} +1.22104e8 q^{61} +1.34141e8 q^{62} -1.08059e7 q^{63} +1.67772e7 q^{64} -1.15795e8 q^{65} +3.38904e7 q^{66} -6.80532e7 q^{67} +6.39093e7 q^{68} -1.59596e8 q^{69} -2.36591e8 q^{70} -1.67349e8 q^{71} -5.10821e6 q^{72} -1.51799e8 q^{73} -1.17536e8 q^{74} -1.38783e8 q^{75} -7.50564e7 q^{76} -1.26859e8 q^{77} +1.57061e8 q^{78} +2.95735e8 q^{79} -1.11842e8 q^{80} -4.10412e8 q^{81} -1.62010e8 q^{82} +4.61094e8 q^{83} +3.20906e8 q^{84} -4.26040e8 q^{85} +4.10156e8 q^{86} +7.57509e8 q^{87} -5.99695e7 q^{88} +4.63623e8 q^{89} +3.40530e7 q^{90} -5.87915e8 q^{91} +2.82407e8 q^{92} +1.21290e9 q^{93} -9.42388e8 q^{94} +5.00351e8 q^{95} +1.51700e8 q^{96} +1.06866e8 q^{97} -5.55563e8 q^{98} +1.82591e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 2 q - 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} + 336 q^{6} - 7490 q^{7} - 8192 q^{8} - 3141 q^{9} + 8336 q^{10} + 29282 q^{11} - 5376 q^{12} + 150314 q^{13} + 119840 q^{14} + 393519 q^{15} + 131072 q^{16} + 690472 q^{17} + 50256 q^{18} + 511212 q^{19} - 133376 q^{20} + 1398810 q^{21} - 468512 q^{22} + 874751 q^{23} + 86016 q^{24} + 411771 q^{25} - 2405024 q^{26} - 309771 q^{27} - 1917440 q^{28} - 2951058 q^{29} - 6296304 q^{30} - 5818705 q^{31} - 2097152 q^{32} - 307461 q^{33} - 11047552 q^{34} + 16179590 q^{35} - 804096 q^{36} + 2658905 q^{37} - 8179392 q^{38} + 381948 q^{39} + 2134016 q^{40} + 13427994 q^{41} - 22380960 q^{42} - 17820762 q^{43} + 7496192 q^{44} - 7330788 q^{45} - 13996016 q^{46} + 56044104 q^{47} - 1376256 q^{48} - 4251114 q^{49} - 6588336 q^{50} + 18401250 q^{51} + 38480384 q^{52} + 96842752 q^{53} + 4956336 q^{54} - 7627961 q^{55} + 30679040 q^{56} + 141898680 q^{57} + 47216928 q^{58} - 119136183 q^{59} + 100740864 q^{60} - 90424326 q^{61} + 93099280 q^{62} - 15960420 q^{63} + 33554432 q^{64} - 18029712 q^{65} + 4919376 q^{66} - 295944891 q^{67} + 176760832 q^{68} - 187843215 q^{69} - 258873440 q^{70} - 322953267 q^{71} + 12865536 q^{72} - 255975514 q^{73} - 42542480 q^{74} - 206496864 q^{75} + 130870272 q^{76} - 109661090 q^{77} - 6111168 q^{78} - 889658 q^{79} - 34144256 q^{80} - 692205750 q^{81} - 214847904 q^{82} - 277699042 q^{83} + 358095360 q^{84} + 96595042 q^{85} + 285132192 q^{86} + 1040096232 q^{87} - 119939072 q^{88} + 1363672217 q^{89} + 117292608 q^{90} - 491050280 q^{91} + 223936256 q^{92} + 1530132009 q^{93} - 896705664 q^{94} + 1454033872 q^{95} + 22020096 q^{96} + 1398434043 q^{97} + 68017824 q^{98} - 45987381 q^{99}+O(q^{100}) \) 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 + 29282 * q^11 - 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 - 468512 * q^22 + 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 - 307461 * q^33 - 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 + 7496192 * q^44 - 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 - 7627961 * q^55 + 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 + 4919376 * q^66 - 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 - 109661090 * q^77 - 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 - 119939072 * q^88 + 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 - 45987381 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−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	$-0.738887\pi$
$7$	−8664.66	−1.36399	−0.681993	+	0.731358i	$0.738887\pi$
$8$	−4096.00	−0.353553
$9$	1247.12	0.0633603
$10$	27305.3	0.863469
$11$	14641.0	0.301511
$11$	14641.0	0.301511
$12$	−37036.2	−0.515597
$13$	67852.1	0.658898	0.329449	−	0.944173i	$-0.393137\pi$
$13$	67852.1	0.658898	0.329449	+	0.944173i	$0.393137\pi$
$14$	138635.	0.964484
$15$	246895.	1.25922
$16$	65536.0	0.250000
$17$	249646.	0.724943	0.362471	−	0.931995i	$-0.381933\pi$
$17$	249646.	0.724943	0.362471	+	0.931995i	$0.381933\pi$
$18$	−19953.9	−0.0448025
$19$	−293189.	−0.516127	−0.258064	−	0.966128i	$-0.583084\pi$
$19$	−293189.	−0.516127	−0.258064	+	0.966128i	$0.583084\pi$
$20$	−436885.	−0.610565
$21$	1.25354e6	1.40653
$22$	−234256.	−0.213201
$23$	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	$-0.741228\pi$
$29$	−5.23603e6	−1.37471	−0.687354	+	0.726322i	$0.741228\pi$
$30$	−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
$33$	−2.11815e6	−0.310917
$34$	−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	$-0.409728\pi$
$41$	1.01256e7	0.559623	0.279811	+	0.960055i	$0.409728\pi$
$42$	−2.00566e7	−0.994570
$43$	−2.56347e7	−1.14346	−0.571730	−	0.820442i	$-0.693727\pi$
$43$	−2.56347e7	−1.14346	−0.571730	+	0.820442i	$0.693727\pi$
$44$	3.74810e6	0.150756
$45$	−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
$55$	−2.49861e7	−0.368185
$56$	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	$-0.309042\pi$
$61$	1.22104e8	1.12914	0.564569	+	0.825386i	$0.309042\pi$
$62$	1.34141e8	1.15292
$63$	−1.08059e7	−0.0864227
$64$	1.67772e7	0.125000
$65$	−1.15795e8	−0.804600
$66$	3.38904e7	0.219851
$67$	−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	$-0.601271\pi$
$73$	−1.51799e8	−0.625626	−0.312813	+	0.949815i	$0.601271\pi$
$74$	−1.17536e8	−0.455647
$75$	−1.38783e8	−0.506479
$76$	−7.50564e7	−0.258064
$77$	−1.26859e8	−0.411258
$78$	1.57061e8	0.480444
$79$	2.95735e8	0.854241	0.427120	−	0.904195i	$-0.359528\pi$
$79$	2.95735e8	0.854241	0.427120	+	0.904195i	$0.359528\pi$
$80$	−1.11842e8	−0.305282
$81$	−4.10412e8	−1.05935
$82$	−1.62010e8	−0.395713
$83$	4.61094e8	1.06644	0.533222	−	0.845975i	$-0.320981\pi$
$83$	4.61094e8	1.06644	0.533222	+	0.845975i	$0.320981\pi$
$84$	3.20906e8	0.703267
$85$	−4.26040e8	−0.885249
$86$	4.10156e8	0.808548
$87$	7.57509e8	1.41759
$88$	−5.99695e7	−0.106600
$89$	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
$99$	1.82591e7	0.0191039
$100$	2.45579e8	0.245579
$101$	1.38561e9	1.32494	0.662470	−	0.749088i	$-0.269508\pi$
$101$	1.38561e9	1.32494	0.662470	+	0.749088i	$0.269508\pi$
$102$	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	$-0.321288\pi$
$107$	1.44377e9	1.06481	0.532405	+	0.846490i	$0.321288\pi$
$108$	6.82794e8	0.482928
$109$	2.58675e9	1.75524	0.877618	−	0.479361i	$-0.159132\pi$
$109$	2.58675e9	1.75524	0.877618	+	0.479361i	$0.159132\pi$
$110$	3.99777e8	0.260346
$111$	−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
$121$	2.14359e8	0.0909091
$122$	−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	$-0.688871\pi$
$127$	−3.27848e9	−1.11829	−0.559147	+	0.829068i	$0.688871\pi$
$128$	−2.68435e8	−0.0883883
$129$	3.70864e9	1.17913
$130$	1.85272e9	0.568938
$131$	1.81056e9	0.537146	0.268573	−	0.963259i	$-0.413448\pi$
$131$	1.81056e9	0.537146	0.268573	+	0.963259i	$0.413448\pi$
$132$	−5.42246e8	−0.155458
$133$	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	$-0.530080\pi$
$139$	−8.30571e8	−0.188717	−0.0943583	+	0.995538i	$0.530080\pi$
$140$	3.78546e9	0.832803
$141$	−8.52110e9	−1.81556
$142$	2.67758e9	0.552643
$143$	9.93422e8	0.198665
$144$	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	$-0.237392\pi$
$149$	8.83876e9	1.46911	0.734553	+	0.678551i	$0.237392\pi$
$150$	2.22053e9	0.358135
$151$	−6.05461e9	−0.947742	−0.473871	−	0.880594i	$-0.657144\pi$
$151$	−6.05461e9	−0.947742	−0.473871	+	0.880594i	$0.657144\pi$
$152$	1.20090e9	0.182479
$153$	3.11338e8	0.0459326
$154$	2.02975e9	0.290803
$155$	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
$165$	3.61479e9	0.379670
$166$	−7.37750e9	−0.754090
$167$	1.13205e10	1.12627	0.563136	−	0.826364i	$-0.309595\pi$
$167$	1.13205e10	1.12627	0.563136	+	0.826364i	$0.309595\pi$
$168$	−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	$-0.323472\pi$
$173$	1.24081e10	1.05317	0.526586	+	0.850122i	$0.323472\pi$
$174$	−1.21201e10	−1.00239
$175$	−8.31195e9	−0.669934
$176$	9.59513e8	0.0753778
$177$	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
$187$	3.65506e9	0.218578
$188$	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	$-0.639659\pi$
$193$	−1.63769e10	−0.849618	−0.424809	+	0.905283i	$0.639659\pi$
$194$	−1.70985e9	−0.0866665
$195$	1.67524e10	0.829698
$196$	8.88900e9	0.430230
$197$	−2.41377e10	−1.14182	−0.570909	−	0.821013i	$-0.693409\pi$
$197$	−2.41377e10	−1.14182	−0.570909	+	0.821013i	$0.693409\pi$
$198$	−2.92146e8	−0.0135085
$199$	−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
$209$	−4.29258e9	−0.155618
$210$	3.42282e10	1.21450
$211$	3.34436e10	1.16156	0.580780	−	0.814061i	$-0.302748\pi$
$211$	3.34436e10	1.16156	0.580780	+	0.814061i	$0.302748\pi$
$212$	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
$220$	−6.39643e9	−0.184092
$221$	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	$-0.580236\pi$
$227$	−1.99552e10	−0.498816	−0.249408	+	0.968398i	$0.580236\pi$
$228$	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
$231$	1.83530e10	0.424086
$232$	2.14468e10	0.486033
$233$	−4.84331e10	−1.07657	−0.538283	−	0.842764i	$-0.680927\pi$
$233$	−4.84331e10	−1.07657	−0.538283	+	0.842764i	$0.680927\pi$
$234$	−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	$-0.588445\pi$
$239$	−2.76719e10	−0.548591	−0.274295	+	0.961645i	$0.588445\pi$
$240$	1.61805e10	0.314805
$241$	5.23953e10	1.00050	0.500248	−	0.865882i	$-0.333242\pi$
$241$	5.23953e10	1.00050	0.500248	+	0.865882i	$0.333242\pi$
$242$	−3.42974e9	−0.0642824
$243$	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
$253$	1.61513e10	0.247836
$254$	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	$-0.547883\pi$
$263$	−2.32552e10	−0.299722	−0.149861	+	0.988707i	$0.547883\pi$
$264$	8.67594e9	0.109926
$265$	−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	$-0.218930\pi$
$271$	1.37207e11	1.54530	0.772651	+	0.634831i	$0.218930\pi$
$272$	1.63608e10	0.181236
$273$	8.50551e10	0.926762
$274$	5.10907e10	0.547601
$275$	1.40450e10	0.148090
$276$	−4.08566e10	−0.423810
$277$	1.85402e11	1.89215	0.946074	−	0.323949i	$-0.105011\pi$
$277$	1.85402e11	1.89215	0.946074	+	0.323949i	$0.105011\pi$
$278$	1.32891e10	0.133443
$279$	−1.04556e10	−0.103307
$280$	−6.05673e10	−0.588880
$281$	−5.20765e10	−0.498268	−0.249134	−	0.968469i	$-0.580146\pi$
$281$	−5.20765e10	−0.498268	−0.249134	+	0.968469i	$0.580146\pi$
$282$	1.36338e11	1.28379
$283$	1.03796e11	0.961925	0.480963	−	0.876741i	$-0.340287\pi$
$283$	1.03796e11	0.961925	0.480963	+	0.876741i	$0.340287\pi$
$284$	−4.28412e10	−0.390777
$285$	−7.23870e10	−0.649918
$286$	−1.58948e10	−0.140477
$287$	−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	$-0.609580\pi$
$293$	−8.51536e10	−0.674992	−0.337496	+	0.941327i	$0.609580\pi$
$294$	8.03746e10	0.627417
$295$	3.11113e11	2.39177
$296$	−3.00892e10	−0.227823
$297$	3.90499e10	0.291217
$298$	−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	$-0.145213\pi$
$307$	2.79447e11	1.79547	0.897734	+	0.440539i	$0.145213\pi$
$308$	−3.24760e10	−0.205629
$309$	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
$319$	−7.66606e10	−0.414490
$320$	−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
$330$	−5.78367e10	−0.268467
$331$	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	$-0.434715\pi$
$337$	9.64453e10	0.407330	0.203665	+	0.979041i	$0.434715\pi$
$338$	9.60096e10	0.400119
$339$	−1.64349e11	−0.675879
$340$	−1.09066e11	−0.442625
$341$	−1.22747e11	−0.491605
$342$	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	$-0.560814\pi$
$347$	−1.02569e11	−0.379783	−0.189891	+	0.981805i	$0.560814\pi$
$348$	1.93922e11	0.708796
$349$	−3.59960e11	−1.29879	−0.649397	−	0.760450i	$-0.724979\pi$
$349$	−3.59960e11	−1.29879	−0.649397	+	0.760450i	$0.724979\pi$
$350$	1.32991e11	0.473715
$351$	1.80973e11	0.636401
$352$	−1.53522e10	−0.0533002
$353$	−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	$-0.557188\pi$
$359$	−1.12478e11	−0.357391	−0.178696	+	0.983904i	$0.557188\pi$
$360$	8.71758e9	0.0273549
$361$	−2.36728e11	−0.733613
$362$	−4.31671e11	−1.32119
$363$	−3.10118e10	−0.0937449
$364$	−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	$-0.423027\pi$
$373$	1.79048e11	0.478938	0.239469	+	0.970904i	$0.423027\pi$
$374$	−5.84810e10	−0.154558
$375$	−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
$385$	2.16496e11	0.502199
$386$	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
$396$	4.67433e9	0.00955193
$397$	−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
$407$	1.07553e11	0.194288
$408$	1.47935e11	0.264301
$409$	−4.68357e11	−0.827604	−0.413802	−	0.910367i	$-0.635799\pi$
$409$	−4.68357e11	−0.827604	−0.413802	+	0.910367i	$0.635799\pi$
$410$	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
$418$	6.86813e10	0.110039
$419$	−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
$429$	−1.43721e11	−0.204862
$430$	−6.99964e11	−0.987342
$431$	2.80621e11	0.391717	0.195858	−	0.980632i	$-0.437251\pi$
$431$	2.80621e11	0.391717	0.195858	+	0.980632i	$0.437251\pi$
$432$	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	$-0.292167\pi$
$439$	9.45531e11	1.21503	0.607513	+	0.794310i	$0.292167\pi$
$440$	1.02343e11	0.130173
$441$	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
$451$	1.48250e11	0.168733
$452$	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	$-0.524737\pi$
$457$	−1.44780e11	−0.155269	−0.0776344	+	0.996982i	$0.524737\pi$
$458$	1.19319e12	1.26711
$459$	6.65846e11	0.700191
$460$	−4.81951e11	−0.501872
$461$	2.94094e11	0.303271	0.151636	−	0.988436i	$-0.451546\pi$
$461$	2.94094e11	0.303271	0.151636	+	0.988436i	$0.451546\pi$
$462$	−2.93649e11	−0.299874
$463$	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
$473$	−3.75318e11	−0.344766
$474$	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	$-0.764381\pi$
$479$	−1.70132e12	−1.47664	−0.738321	+	0.674449i	$0.764381\pi$
$480$	−2.58888e11	−0.222601
$481$	4.98441e11	0.424581
$482$	−8.38324e11	−0.707458
$483$	1.38284e12	1.15614
$484$	5.48759e10	0.0454545
$485$	−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	$-0.469649\pi$
$491$	2.45219e11	0.190409	0.0952045	+	0.995458i	$0.469649\pi$
$492$	−3.75015e11	−0.288540
$493$	−1.30715e12	−0.996585
$494$	3.18296e11	0.240469
$495$	−3.11606e10	−0.0233283
$496$	−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	$-0.416143\pi$
$503$	7.47725e11	0.520818	0.260409	+	0.965498i	$0.416143\pi$
$504$	4.42609e10	0.0305550
$505$	−2.36466e12	−1.61792
$506$	−2.58420e11	−0.175247
$507$	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
$517$	8.62344e11	0.530852
$518$	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	$-0.379847\pi$
$523$	1.26127e12	0.737140	0.368570	+	0.929600i	$0.379847\pi$
$524$	4.63503e11	0.268573
$525$	1.20251e12	0.690831
$526$	3.72083e11	0.211936
$527$	−2.09297e12	−1.18200
$528$	−1.38815e11	−0.0777291
$529$	−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
$539$	5.08375e11	0.259439
$540$	−1.16524e12	−0.589718
$541$	3.48950e12	1.75136	0.875679	−	0.482893i	$-0.160414\pi$
$541$	3.48950e12	1.75136	0.875679	+	0.482893i	$0.160414\pi$
$542$	−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	$-0.661123\pi$
$547$	−2.03037e12	−0.969687	−0.484844	+	0.874601i	$0.661123\pi$
$548$	−8.17452e11	−0.387213
$549$	1.52279e11	0.0715426
$550$	−2.24720e11	−0.104715
$551$	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	$-0.275346\pi$
$557$	2.94692e12	1.29724	0.648620	+	0.761112i	$0.275346\pi$
$558$	1.67290e11	0.0730491
$559$	−1.73937e12	−0.753423
$560$	9.69077e11	0.416401
$561$	−5.28787e11	−0.225397
$562$	8.33224e11	0.352329
$563$	−7.94805e11	−0.333405	−0.166703	−	0.986007i	$-0.553312\pi$
$563$	−7.94805e11	−0.333405	−0.166703	+	0.986007i	$0.553312\pi$
$564$	−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	$-0.401788\pi$
$569$	1.51857e12	0.607338	0.303669	+	0.952778i	$0.401788\pi$
$570$	1.15819e12	0.459562
$571$	−2.97779e11	−0.117228	−0.0586140	−	0.998281i	$-0.518668\pi$
$571$	−2.97779e11	−0.117228	−0.0586140	+	0.998281i	$0.518668\pi$
$572$	2.54316e11	0.0993325
$573$	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
$583$	1.27190e12	0.455978
$584$	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	$-0.529452\pi$
$593$	−5.56438e11	−0.184787	−0.0923933	+	0.995723i	$0.529452\pi$
$594$	−6.24799e11	−0.205921
$595$	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	$-0.472595\pi$
$601$	5.50049e11	0.171975	0.0859877	+	0.996296i	$0.472595\pi$
$602$	−3.55386e12	−1.10285
$603$	−8.48707e10	−0.0261415
$604$	−1.54998e12	−0.473871
$605$	−3.65821e11	−0.111012
$606$	3.20736e12	0.966099
$607$	3.73380e12	1.11635	0.558177	−	0.829722i	$-0.311501\pi$
$607$	3.73380e12	1.11635	0.558177	+	0.829722i	$0.311501\pi$
$608$	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	$-0.315036\pi$
$613$	3.83812e12	1.09786	0.548929	+	0.835869i	$0.315036\pi$
$614$	−4.47116e12	−1.26959
$615$	2.49997e12	0.704689
$616$	5.19615e11	0.145401
$617$	−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
$627$	6.21019e11	0.160473
$628$	−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
$638$	1.22657e12	0.293089
$639$	−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
$649$	−2.66908e12	−0.590556
$650$	−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	$-0.439150\pi$
$659$	1.83983e12	0.380008	0.190004	+	0.981783i	$0.439150\pi$
$660$	9.25387e11	0.189835
$661$	−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
$671$	1.78773e12	0.340448
$672$	−1.31443e12	−0.248643
$673$	−7.07648e12	−1.32969	−0.664844	−	0.746983i	$-0.731502\pi$
$673$	−7.07648e12	−1.32969	−0.664844	+	0.746983i	$0.731502\pi$
$674$	−1.54313e12	−0.288026
$675$	2.55859e12	0.474389
$676$	−1.53615e12	−0.282927
$677$	1.18522e11	0.0216846	0.0108423	−	0.999941i	$-0.496549\pi$
$677$	1.18522e11	0.0216846	0.0108423	+	0.999941i	$0.496549\pi$
$678$	2.62959e12	0.477918
$679$	−9.25956e11	−0.167177
$680$	1.74506e12	0.312983
$681$	2.88697e12	0.514376
$682$	1.96395e12	0.347617
$683$	−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
$693$	−1.58209e11	−0.0260574
$694$	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	$-0.317266\pi$
$701$	6.94398e12	1.08612	0.543059	+	0.839694i	$0.317266\pi$
$702$	−2.89556e12	−0.450003
$703$	−2.15377e12	−0.332583
$704$	2.45635e11	0.0376889
$705$	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
$715$	−1.69535e12	−0.242596
$716$	−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
$726$	4.96189e11	0.0662876
$727$	−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	$-0.358995\pi$
$733$	6.70015e12	0.857269	0.428634	+	0.903478i	$0.358995\pi$
$734$	−2.43101e12	−0.309139
$735$	8.57286e12	1.08351
$736$	−1.15674e12	−0.145307
$737$	−9.96367e11	−0.124399
$738$	−2.02047e11	−0.0250725
$739$	−1.71079e11	−0.0211007	−0.0105503	−	0.999944i	$-0.503358\pi$
$739$	−1.71079e11	−0.0211007	−0.0105503	+	0.999944i	$0.503358\pi$
$740$	−3.20935e12	−0.393437
$741$	2.87804e12	0.350683
$742$	1.20435e13	1.45860
$743$	6.82102e12	0.821106	0.410553	−	0.911837i	$-0.365336\pi$
$743$	6.82102e12	0.821106	0.410553	+	0.911837i	$0.365336\pi$
$744$	−4.96805e12	−0.594439
$745$	−1.50841e13	−1.79397
$746$	−2.86477e12	−0.338661
$747$	5.75040e11	0.0675702
$748$	9.35696e11	0.109289
$749$	−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
$759$	−2.33665e12	−0.255567
$760$	−2.04944e12	−0.222830
$761$	−8.46525e12	−0.914974	−0.457487	−	0.889216i	$-0.651250\pi$
$761$	−8.46525e12	−0.914974	−0.457487	+	0.889216i	$0.651250\pi$
$762$	−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	$-0.133631\pi$
$769$	1.77112e13	1.82633	0.913164	+	0.407592i	$0.133631\pi$
$770$	−3.46393e12	−0.355108
$771$	−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
$781$	−2.45015e12	−0.235648
$782$	−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	$-0.526483\pi$
$787$	−1.78869e12	−0.166207	−0.0831036	+	0.996541i	$0.526483\pi$
$788$	−6.17924e12	−0.570909
$789$	3.36439e12	0.309072
$790$	8.07512e12	0.737611
$791$	−9.84312e12	−0.894002
$792$	−7.47893e10	−0.00675424
$793$	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
$803$	−2.22248e12	−0.188633
$804$	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	$-0.501033\pi$
$809$	−7.91008e10	−0.00649251	−0.00324625	+	0.999995i	$0.501033\pi$
$810$	−1.12064e13	−0.914713
$811$	7.52015e12	0.610425	0.305213	−	0.952284i	$-0.401272\pi$
$811$	7.52015e12	0.610425	0.305213	+	0.952284i	$0.401272\pi$
$812$	1.16143e13	0.937542
$813$	−1.98500e13	−1.59351
$814$	−1.72084e12	−0.137383
$815$	−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	$-0.442552\pi$
$821$	4.67347e12	0.359000	0.179500	+	0.983758i	$0.442552\pi$
$822$	−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
$825$	−2.03193e12	−0.152709
$826$	−2.52733e13	−1.88909
$827$	−2.53074e12	−0.188136	−0.0940682	−	0.995566i	$-0.529987\pi$
$827$	−2.53074e12	−0.188136	−0.0940682	+	0.995566i	$0.529987\pi$
$828$	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
$836$	−1.09890e12	−0.0778091
$837$	−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
$847$	−1.85735e12	−0.123999
$848$	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	$-0.325925\pi$
$853$	1.60812e13	1.04004	0.520019	+	0.854155i	$0.325925\pi$
$854$	1.69279e13	1.08904
$855$	6.23999e11	0.0399334
$856$	−5.91370e12	−0.376467
$857$	8.68029e11	0.0549693	0.0274847	−	0.999622i	$-0.491250\pi$
$857$	8.68029e11	0.0549693	0.0274847	+	0.999622i	$0.491250\pi$
$858$	2.29953e12	0.144859
$859$	−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
$869$	4.32985e12	0.257563
$870$	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	$-0.882012\pi$
$877$	−3.26576e13	−1.86417	−0.932085	+	0.362239i	$0.882012\pi$
$878$	−1.51285e13	−0.859153
$879$	1.23194e13	0.696048
$880$	−1.63749e12	−0.0920461
$881$	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	$-0.350176\pi$
$887$	1.67209e13	0.906994	0.453497	+	0.891258i	$0.350176\pi$
$888$	4.35308e12	0.234930
$889$	2.84069e13	1.52534
$890$	1.26594e13	0.676327
$891$	−6.00885e12	−0.319405
$892$	−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
$902$	−2.37199e12	−0.119312
$903$	−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
$913$	6.75088e12	0.321545
$914$	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	$-0.506346\pi$
$919$	−8.62159e11	−0.0398720	−0.0199360	+	0.999801i	$0.506346\pi$
$920$	7.71122e12	0.354877
$921$	−4.04284e13	−1.85147
$922$	−4.70550e12	−0.214445
$923$	−1.13549e13	−0.514965
$924$	4.69838e12	0.212043
$925$	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
$935$	−6.23766e12	−0.266913
$936$	−3.46603e11	−0.0147601
$937$	−2.41842e13	−1.02495	−0.512476	−	0.858702i	$-0.671272\pi$
$937$	−2.41842e13	−1.02495	−0.512476	+	0.858702i	$0.671272\pi$
$938$	−9.43453e12	−0.397931
$939$	−1.40135e13	−0.588235
$940$	−2.57322e13	−1.07498
$941$	3.40036e13	1.41375	0.706874	−	0.707340i	$-0.250105\pi$
$941$	3.40036e13	1.41375	0.706874	+	0.707340i	$0.250105\pi$
$942$	−7.44013e12	−0.307859
$943$	1.11701e13	0.459998
$944$	−1.19473e13	−0.489663
$945$	3.94392e13	1.60874
$946$	6.00509e12	0.243786
$947$	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	$-0.668688\pi$
$953$	−2.57430e13	−1.01098	−0.505489	+	0.862833i	$0.668688\pi$
$954$	−1.73344e12	−0.0677552
$955$	3.22038e13	1.25283
$956$	−7.08401e12	−0.274295
$957$	1.10907e13	0.427420
$958$	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	$-0.470994\pi$
$967$	4.94862e12	0.181997	0.0909986	+	0.995851i	$0.470994\pi$
$968$	−8.78014e11	−0.0321412
$969$	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
$979$	6.78790e12	0.236164
$980$	−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
$990$	4.98570e11	0.0164956
$991$	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	$-0.675860\pi$
$997$	−3.27455e13	−1.04960	−0.524800	+	0.851226i	$0.675860\pi$
$998$	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	22.10.a.d.1.1	✓	2
3.2	odd	2		198.10.a.n.1.2		2
4.3	odd	2		176.10.a.e.1.2		2
11.10	odd	2		242.10.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.10.a.d.1.1	✓	2	1.1	even	1	trivial
176.10.a.e.1.2		2	4.3	odd	2
198.10.a.n.1.2		2	3.2	odd	2
242.10.a.e.1.1		2	11.10	odd	2

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} +2314.76 q^{6} -8664.66 q^{7} -4096.00 q^{8} +1247.12 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} -144.672 q^{3} +256.000 q^{4} -1706.58 q^{5} +2314.76 q^{6} -8664.66 q^{7} -4096.00 q^{8} +1247.12 q^{9} +27305.3 q^{10} +14641.0 q^{11} -37036.2 q^{12} +67852.1 q^{13} +138635. q^{14} +246895. q^{15} +65536.0 q^{16} +249646. q^{17} -19953.9 q^{18} -293189. q^{19} -436885. q^{20} +1.25354e6 q^{21} -234256. q^{22} +1.10315e6 q^{23} +592578. q^{24} +959294. q^{25} -1.08563e6 q^{26} +2.66716e6 q^{27} -2.21815e6 q^{28} -5.23603e6 q^{29} -3.95032e6 q^{30} -8.38378e6 q^{31} -1.04858e6 q^{32} -2.11815e6 q^{33} -3.99433e6 q^{34} +1.47869e7 q^{35} +319263. q^{36} +7.34600e6 q^{37} +4.69103e6 q^{38} -9.81632e6 q^{39} +6.99016e6 q^{40} +1.01256e7 q^{41} -2.00566e7 q^{42} -2.56347e7 q^{43} +3.74810e6 q^{44} -2.12831e6 q^{45} -1.76505e7 q^{46} +5.88993e7 q^{47} -9.48125e6 q^{48} +3.47227e7 q^{49} -1.53487e7 q^{50} -3.61168e7 q^{51} +1.73701e7 q^{52} +8.68723e7 q^{53} -4.26746e7 q^{54} -2.49861e7 q^{55} +3.54904e7 q^{56} +4.24164e7 q^{57} +8.37764e7 q^{58} -1.82302e8 q^{59} +6.32052e7 q^{60} +1.22104e8 q^{61} +1.34141e8 q^{62} -1.08059e7 q^{63} +1.67772e7 q^{64} -1.15795e8 q^{65} +3.38904e7 q^{66} -6.80532e7 q^{67} +6.39093e7 q^{68} -1.59596e8 q^{69} -2.36591e8 q^{70} -1.67349e8 q^{71} -5.10821e6 q^{72} -1.51799e8 q^{73} -1.17536e8 q^{74} -1.38783e8 q^{75} -7.50564e7 q^{76} -1.26859e8 q^{77} +1.57061e8 q^{78} +2.95735e8 q^{79} -1.11842e8 q^{80} -4.10412e8 q^{81} -1.62010e8 q^{82} +4.61094e8 q^{83} +3.20906e8 q^{84} -4.26040e8 q^{85} +4.10156e8 q^{86} +7.57509e8 q^{87} -5.99695e7 q^{88} +4.63623e8 q^{89} +3.40530e7 q^{90} -5.87915e8 q^{91} +2.82407e8 q^{92} +1.21290e9 q^{93} -9.42388e8 q^{94} +5.00351e8 q^{95} +1.51700e8 q^{96} +1.06866e8 q^{97} -5.55563e8 q^{98} +1.82591e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} + 336 q^{6} - 7490 q^{7} - 8192 q^{8} - 3141 q^{9}+O(q^{10}) \) 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	\( 2 q - 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} + 336 q^{6} - 7490 q^{7} - 8192 q^{8} - 3141 q^{9} + 8336 q^{10} + 29282 q^{11} - 5376 q^{12} + 150314 q^{13} + 119840 q^{14} + 393519 q^{15} + 131072 q^{16} + 690472 q^{17} + 50256 q^{18} + 511212 q^{19} - 133376 q^{20} + 1398810 q^{21} - 468512 q^{22} + 874751 q^{23} + 86016 q^{24} + 411771 q^{25} - 2405024 q^{26} - 309771 q^{27} - 1917440 q^{28} - 2951058 q^{29} - 6296304 q^{30} - 5818705 q^{31} - 2097152 q^{32} - 307461 q^{33} - 11047552 q^{34} + 16179590 q^{35} - 804096 q^{36} + 2658905 q^{37} - 8179392 q^{38} + 381948 q^{39} + 2134016 q^{40} + 13427994 q^{41} - 22380960 q^{42} - 17820762 q^{43} + 7496192 q^{44} - 7330788 q^{45} - 13996016 q^{46} + 56044104 q^{47} - 1376256 q^{48} - 4251114 q^{49} - 6588336 q^{50} + 18401250 q^{51} + 38480384 q^{52} + 96842752 q^{53} + 4956336 q^{54} - 7627961 q^{55} + 30679040 q^{56} + 141898680 q^{57} + 47216928 q^{58} - 119136183 q^{59} + 100740864 q^{60} - 90424326 q^{61} + 93099280 q^{62} - 15960420 q^{63} + 33554432 q^{64} - 18029712 q^{65} + 4919376 q^{66} - 295944891 q^{67} + 176760832 q^{68} - 187843215 q^{69} - 258873440 q^{70} - 322953267 q^{71} + 12865536 q^{72} - 255975514 q^{73} - 42542480 q^{74} - 206496864 q^{75} + 130870272 q^{76} - 109661090 q^{77} - 6111168 q^{78} - 889658 q^{79} - 34144256 q^{80} - 692205750 q^{81} - 214847904 q^{82} - 277699042 q^{83} + 358095360 q^{84} + 96595042 q^{85} + 285132192 q^{86} + 1040096232 q^{87} - 119939072 q^{88} + 1363672217 q^{89} + 117292608 q^{90} - 491050280 q^{91} + 223936256 q^{92} + 1530132009 q^{93} - 896705664 q^{94} + 1454033872 q^{95} + 22020096 q^{96} + 1398434043 q^{97} + 68017824 q^{98} - 45987381 q^{99}+O(q^{100}) \) 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 + 29282 * q^11 - 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 - 468512 * q^22 + 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 - 307461 * q^33 - 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 + 7496192 * q^44 - 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 - 7627961 * q^55 + 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 + 4919376 * q^66 - 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 - 109661090 * q^77 - 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 - 119939072 * q^88 + 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 - 45987381 * q^99

Introduction

L-functions

Modular forms

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