LMFDB - Embedded newform 22.10.a.d.1.2

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			1.2
Root			$-14.4081$ 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)

$f(q)$	$=$	$q-16.0000 q^{2} +123.672 q^{3} +256.000 q^{4} +1185.58 q^{5} -1978.76 q^{6} +1174.66 q^{7} -4096.00 q^{8} -4388.12 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} +123.672 q^{3} +256.000 q^{4} +1185.58 q^{5} -1978.76 q^{6} +1174.66 q^{7} -4096.00 q^{8} -4388.12 q^{9} -18969.3 q^{10} +14641.0 q^{11} +31660.2 q^{12} +82461.9 q^{13} -18794.5 q^{14} +146624. q^{15} +65536.0 q^{16} +440826. q^{17} +70209.9 q^{18} +804401. q^{19} +303509. q^{20} +145273. q^{21} -234256. q^{22} -228403. q^{23} -506562. q^{24} -547523. q^{25} -1.31939e6 q^{26} -2.97693e6 q^{27} +300712. q^{28} +2.28497e6 q^{29} -2.34598e6 q^{30} +2.56508e6 q^{31} -1.04858e6 q^{32} +1.81069e6 q^{33} -7.05322e6 q^{34} +1.39265e6 q^{35} -1.12336e6 q^{36} -4.68709e6 q^{37} -1.28704e7 q^{38} +1.01983e7 q^{39} -4.85614e6 q^{40} +3.30235e6 q^{41} -2.32436e6 q^{42} +7.81398e6 q^{43} +3.74810e6 q^{44} -5.20247e6 q^{45} +3.65445e6 q^{46} -2.85515e6 q^{47} +8.10500e6 q^{48} -3.89738e7 q^{49} +8.76036e6 q^{50} +5.45181e7 q^{51} +2.11103e7 q^{52} +9.97047e6 q^{53} +4.76310e7 q^{54} +1.73581e7 q^{55} -4.81140e6 q^{56} +9.94823e7 q^{57} -3.65595e7 q^{58} +6.31658e7 q^{59} +3.75357e7 q^{60} -2.12529e8 q^{61} -4.10412e7 q^{62} -5.15454e6 q^{63} +1.67772e7 q^{64} +9.77653e7 q^{65} -2.89710e7 q^{66} -2.27892e8 q^{67} +1.12852e8 q^{68} -2.82472e7 q^{69} -2.22824e7 q^{70} -1.55605e8 q^{71} +1.79737e7 q^{72} -1.04177e8 q^{73} +7.49935e7 q^{74} -6.77135e7 q^{75} +2.05927e8 q^{76} +1.71982e7 q^{77} -1.63172e8 q^{78} -2.96624e8 q^{79} +7.76982e7 q^{80} -2.81793e8 q^{81} -5.28376e7 q^{82} -7.38793e8 q^{83} +3.71898e7 q^{84} +5.22635e8 q^{85} -1.25024e8 q^{86} +2.82588e8 q^{87} -5.99695e7 q^{88} +9.00049e8 q^{89} +8.32396e7 q^{90} +9.68645e7 q^{91} -5.84712e7 q^{92} +3.17229e8 q^{93} +4.56823e7 q^{94} +9.53683e8 q^{95} -1.29680e8 q^{96} +1.29157e9 q^{97} +6.23581e8 q^{98} -6.42465e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	123.672	0.881510	0.440755	−	0.897627i	$-0.354711\pi$
$3$	123.672	0.881510	0.440755	+	0.897627i	$0.354711\pi$
$4$	256.000	0.500000
$5$	1185.58	0.848333	0.424166	−	0.905584i	$-0.360567\pi$
$5$	1185.58	0.848333	0.424166	+	0.905584i	$0.360567\pi$
$6$	−1978.76	−0.623322
$7$	1174.66	0.184914	0.0924570	−	0.995717i	$-0.470528\pi$
$7$	1174.66	0.184914	0.0924570	+	0.995717i	$0.470528\pi$
$8$	−4096.00	−0.353553
$9$	−4388.12	−0.222940
$10$	−18969.3	−0.599862
$11$	14641.0	0.301511
$11$	14641.0	0.301511
$12$	31660.2	0.440755
$13$	82461.9	0.800771	0.400386	−	0.916347i	$-0.368876\pi$
$13$	82461.9	0.800771	0.400386	+	0.916347i	$0.368876\pi$
$14$	−18794.5	−0.130754
$15$	146624.	0.747814
$16$	65536.0	0.250000
$17$	440826.	1.28011	0.640055	−	0.768329i	$-0.278911\pi$
$17$	440826.	1.28011	0.640055	+	0.768329i	$0.278911\pi$
$18$	70209.9	0.157642
$19$	804401.	1.41606	0.708030	−	0.706183i	$-0.249584\pi$
$19$	804401.	1.41606	0.708030	+	0.706183i	$0.249584\pi$
$20$	303509.	0.424166
$21$	145273.	0.163004
$22$	−234256.	−0.213201
$23$	−228403.	−0.170187	−0.0850936	−	0.996373i	$-0.527119\pi$
$23$	−228403.	−0.170187	−0.0850936	+	0.996373i	$0.527119\pi$
$24$	−506562.	−0.311661
$25$	−547523.	−0.280332
$26$	−1.31939e6	−0.566231
$27$	−2.97693e6	−1.07803
$28$	300712.	0.0924570
$29$	2.28497e6	0.599914	0.299957	−	0.953953i	$-0.403028\pi$
$29$	2.28497e6	0.599914	0.299957	+	0.953953i	$0.403028\pi$
$30$	−2.34598e6	−0.528784
$31$	2.56508e6	0.498853	0.249427	−	0.968394i	$-0.419758\pi$
$31$	2.56508e6	0.498853	0.249427	+	0.968394i	$0.419758\pi$
$32$	−1.04858e6	−0.176777
$33$	1.81069e6	0.265785
$34$	−7.05322e6	−0.905175
$35$	1.39265e6	0.156869
$36$	−1.12336e6	−0.111470
$37$	−4.68709e6	−0.411146	−0.205573	−	0.978642i	$-0.565906\pi$
$37$	−4.68709e6	−0.411146	−0.205573	+	0.978642i	$0.565906\pi$
$38$	−1.28704e7	−1.00131
$39$	1.01983e7	0.705888
$40$	−4.85614e6	−0.299931
$41$	3.30235e6	0.182514	0.0912569	−	0.995827i	$-0.470912\pi$
$41$	3.30235e6	0.182514	0.0912569	+	0.995827i	$0.470912\pi$
$42$	−2.32436e6	−0.115261
$43$	7.81398e6	0.348549	0.174275	−	0.984697i	$-0.444242\pi$
$43$	7.81398e6	0.348549	0.174275	+	0.984697i	$0.444242\pi$
$44$	3.74810e6	0.150756
$45$	−5.20247e6	−0.189127
$46$	3.65445e6	0.120341
$47$	−2.85515e6	−0.0853470	−0.0426735	−	0.999089i	$-0.513588\pi$
$47$	−2.85515e6	−0.0853470	−0.0426735	+	0.999089i	$0.513588\pi$
$48$	8.10500e6	0.220378
$49$	−3.89738e7	−0.965807
$50$	8.76036e6	0.198224
$51$	5.45181e7	1.12843
$52$	2.11103e7	0.400386
$53$	9.97047e6	0.173570	0.0867849	−	0.996227i	$-0.472341\pi$
$53$	9.97047e6	0.173570	0.0867849	+	0.996227i	$0.472341\pi$
$54$	4.76310e7	0.762285
$55$	1.73581e7	0.255782
$56$	−4.81140e6	−0.0653770
$57$	9.94823e7	1.24827
$58$	−3.65595e7	−0.424203
$59$	6.31658e7	0.678653	0.339326	−	0.940669i	$-0.389801\pi$
$59$	6.31658e7	0.678653	0.339326	+	0.940669i	$0.389801\pi$
$60$	3.75357e7	0.373907
$61$	−2.12529e8	−1.96532	−0.982660	−	0.185414i	$-0.940637\pi$
$61$	−2.12529e8	−1.96532	−0.982660	+	0.185414i	$0.940637\pi$
$62$	−4.10412e7	−0.352743
$63$	−5.15454e6	−0.0412247
$64$	1.67772e7	0.125000
$65$	9.77653e7	0.679320
$66$	−2.89710e7	−0.187939
$67$	−2.27892e8	−1.38163	−0.690815	−	0.723031i	$-0.742748\pi$
$67$	−2.27892e8	−1.38163	−0.690815	+	0.723031i	$0.742748\pi$
$68$	1.12852e8	0.640055
$69$	−2.82472e7	−0.150022
$70$	−2.22824e7	−0.110923
$71$	−1.55605e8	−0.726708	−0.363354	−	0.931651i	$-0.618368\pi$
$71$	−1.55605e8	−0.726708	−0.363354	+	0.931651i	$0.618368\pi$
$72$	1.79737e7	0.0788211
$73$	−1.04177e8	−0.429357	−0.214679	−	0.976685i	$-0.568870\pi$
$73$	−1.04177e8	−0.429357	−0.214679	+	0.976685i	$0.568870\pi$
$74$	7.49935e7	0.290724
$75$	−6.77135e7	−0.247115
$76$	2.05927e8	0.708030
$77$	1.71982e7	0.0557537
$78$	−1.63172e8	−0.499138
$79$	−2.96624e8	−0.856811	−0.428405	−	0.903587i	$-0.640924\pi$
$79$	−2.96624e8	−0.856811	−0.428405	+	0.903587i	$0.640924\pi$
$80$	7.76982e7	0.212083
$81$	−2.81793e8	−0.727358
$82$	−5.28376e7	−0.129057
$83$	−7.38793e8	−1.70872	−0.854361	−	0.519680i	$-0.826051\pi$
$83$	−7.38793e8	−1.70872	−0.854361	+	0.519680i	$0.826051\pi$
$84$	3.71898e7	0.0815018
$85$	5.22635e8	1.08596
$86$	−1.25024e8	−0.246462
$87$	2.82588e8	0.528830
$88$	−5.99695e7	−0.106600
$89$	9.00049e8	1.52059	0.760293	−	0.649580i	$-0.225055\pi$
$89$	9.00049e8	1.52059	0.760293	+	0.649580i	$0.225055\pi$
$90$	8.32396e7	0.133733
$91$	9.68645e7	0.148074
$92$	−5.84712e7	−0.0850936
$93$	3.17229e8	0.439744
$94$	4.56823e7	0.0603494
$95$	9.53683e8	1.20129
$96$	−1.29680e8	−0.155830
$97$	1.29157e9	1.48131	0.740653	−	0.671888i	$-0.234516\pi$
$97$	1.29157e9	1.48131	0.740653	+	0.671888i	$0.234516\pi$
$98$	6.23581e8	0.682929
$99$	−6.42465e7	−0.0672188
$100$	−1.40166e8	−0.140166
$101$	1.45652e9	1.39275	0.696373	−	0.717681i	$-0.254796\pi$
$101$	1.45652e9	1.39275	0.696373	+	0.717681i	$0.254796\pi$
$102$	−8.72289e8	−0.797921
$103$	−1.95971e9	−1.71563	−0.857814	−	0.513960i	$-0.828178\pi$
$103$	−1.95971e9	−1.71563	−0.857814	+	0.513960i	$0.828178\pi$
$104$	−3.37764e8	−0.283115
$105$	1.72233e8	0.138281
$106$	−1.59528e8	−0.122732
$107$	6.07627e8	0.448136	0.224068	−	0.974573i	$-0.428066\pi$
$107$	6.07627e8	0.448136	0.224068	+	0.974573i	$0.428066\pi$
$108$	−7.62095e8	−0.539017
$109$	−1.14761e9	−0.778708	−0.389354	−	0.921088i	$-0.627302\pi$
$109$	−1.14761e9	−0.778708	−0.389354	+	0.921088i	$0.627302\pi$
$110$	−2.77729e8	−0.180865
$111$	−5.79664e8	−0.362429
$112$	7.69823e7	0.0462285
$113$	−2.54053e8	−0.146579	−0.0732895	−	0.997311i	$-0.523350\pi$
$113$	−2.54053e8	−0.146579	−0.0732895	+	0.997311i	$0.523350\pi$
$114$	−1.59172e9	−0.882661
$115$	−2.70790e8	−0.144375
$116$	5.84952e8	0.299957
$117$	−3.61853e8	−0.178524
$118$	−1.01065e9	−0.479880
$119$	5.17820e8	0.236710
$120$	−6.00571e8	−0.264392
$121$	2.14359e8	0.0909091
$122$	3.40046e9	1.38969
$123$	4.08410e8	0.160888
$124$	6.56660e8	0.249427
$125$	−2.96472e9	−1.08615
$126$	8.24726e7	0.0291502
$127$	−1.26227e8	−0.0430561	−0.0215280	−	0.999768i	$-0.506853\pi$
$127$	−1.26227e8	−0.0430561	−0.0215280	+	0.999768i	$0.506853\pi$
$128$	−2.68435e8	−0.0883883
$129$	9.66374e8	0.307250
$130$	−1.56425e9	−0.480352
$131$	−1.87859e9	−0.557328	−0.278664	−	0.960389i	$-0.589892\pi$
$131$	−1.87859e9	−0.557328	−0.278664	+	0.960389i	$0.589892\pi$
$132$	4.63536e8	0.132893
$133$	9.44895e8	0.261849
$134$	3.64627e9	0.976960
$135$	−3.52940e9	−0.914531
$136$	−1.80563e9	−0.452587
$137$	6.32338e9	1.53358	0.766791	−	0.641897i	$-0.221852\pi$
$137$	6.32338e9	1.53358	0.766791	+	0.641897i	$0.221852\pi$
$138$	4.51955e8	0.106081
$139$	−7.82379e9	−1.77767	−0.888833	−	0.458230i	$-0.848483\pi$
$139$	−7.82379e9	−1.77767	−0.888833	+	0.458230i	$0.848483\pi$
$140$	3.56519e8	0.0784343
$141$	−3.53103e8	−0.0752342
$142$	2.48967e9	0.513860
$143$	1.20733e9	0.241442
$144$	−2.87580e8	−0.0557349
$145$	2.70901e9	0.508927
$146$	1.66683e9	0.303602
$147$	−4.81998e9	−0.851369
$148$	−1.19990e9	−0.205573
$149$	−2.69524e8	−0.0447981	−0.0223991	−	0.999749i	$-0.507130\pi$
$149$	−2.69524e8	−0.0447981	−0.0223991	+	0.999749i	$0.507130\pi$
$150$	1.08342e9	0.174737
$151$	1.18223e10	1.85057	0.925286	−	0.379270i	$-0.123825\pi$
$151$	1.18223e10	1.85057	0.925286	+	0.379270i	$0.123825\pi$
$152$	−3.29483e9	−0.500653
$153$	−1.93440e9	−0.285387
$154$	−2.75170e8	−0.0394238
$155$	3.04111e9	0.423194
$156$	2.61076e9	0.352944
$157$	3.66990e9	0.482065	0.241032	−	0.970517i	$-0.422514\pi$
$157$	3.66990e9	0.482065	0.241032	+	0.970517i	$0.422514\pi$
$158$	4.74599e9	0.605857
$159$	1.23307e9	0.153004
$160$	−1.24317e9	−0.149965
$161$	−2.68295e8	−0.0314700
$162$	4.50870e9	0.514320
$163$	−1.30610e10	−1.44921	−0.724605	−	0.689165i	$-0.757978\pi$
$163$	−1.30610e10	−1.44921	−0.724605	+	0.689165i	$0.757978\pi$
$164$	8.45401e8	0.0912569
$165$	2.14672e9	0.225474
$166$	1.18207e10	1.20825
$167$	−1.16911e9	−0.116314	−0.0581571	−	0.998307i	$-0.518522\pi$
$167$	−1.16911e9	−0.116314	−0.0581571	+	0.998307i	$0.518522\pi$
$168$	−5.95037e8	−0.0576305
$169$	−3.80453e9	−0.358765
$170$	−8.36217e9	−0.767889
$171$	−3.52981e9	−0.315696
$172$	2.00038e9	0.174275
$173$	1.90893e10	1.62025	0.810124	−	0.586258i	$-0.199399\pi$
$173$	1.90893e10	1.62025	0.810124	+	0.586258i	$0.199399\pi$
$174$	−4.52140e9	−0.373940
$175$	−6.43151e8	−0.0518373
$176$	9.59513e8	0.0753778
$177$	7.81187e9	0.598240
$178$	−1.44008e10	−1.07522
$179$	−1.99470e10	−1.45224	−0.726122	−	0.687566i	$-0.758679\pi$
$179$	−1.99470e10	−1.45224	−0.726122	+	0.687566i	$0.758679\pi$
$180$	−1.33183e9	−0.0945635
$181$	−8.20947e9	−0.568541	−0.284270	−	0.958744i	$-0.591751\pi$
$181$	−8.20947e9	−0.568541	−0.284270	+	0.958744i	$0.591751\pi$
$182$	−1.54983e9	−0.104704
$183$	−2.62840e10	−1.73245
$184$	9.35539e8	0.0601703
$185$	−5.55693e9	−0.348788
$186$	−5.07567e9	−0.310946
$187$	6.45414e9	0.385968
$188$	−7.30918e8	−0.0426735
$189$	−3.49688e9	−0.199344
$190$	−1.52589e10	−0.849440
$191$	1.24525e10	0.677027	0.338513	−	0.940962i	$-0.390076\pi$
$191$	1.24525e10	0.677027	0.338513	+	0.940962i	$0.390076\pi$
$192$	2.07488e9	0.110189
$193$	1.60846e9	0.0834456	0.0417228	−	0.999129i	$-0.486715\pi$
$193$	1.60846e9	0.0834456	0.0417228	+	0.999129i	$0.486715\pi$
$194$	−2.06651e10	−1.04744
$195$	1.20909e10	0.598828
$196$	−9.97729e9	−0.482903
$197$	4.02780e10	1.90533	0.952664	−	0.304024i	$-0.0983304\pi$
$197$	4.02780e10	1.90533	0.952664	+	0.304024i	$0.0983304\pi$
$198$	1.02794e9	0.0475309
$199$	3.22083e10	1.45589	0.727945	−	0.685636i	$-0.240476\pi$
$199$	3.22083e10	1.45589	0.727945	+	0.685636i	$0.240476\pi$
$200$	2.24265e9	0.0991122
$201$	−2.81839e10	−1.21792
$202$	−2.33044e10	−0.984819
$203$	2.68405e9	0.110933
$204$	1.39566e10	0.564215
$205$	3.91520e9	0.154832
$206$	3.13553e10	1.21313
$207$	1.00226e9	0.0379415
$208$	5.40423e9	0.200193
$209$	1.17772e10	0.426958
$210$	−2.75572e9	−0.0977796
$211$	1.06111e10	0.368544	0.184272	−	0.982875i	$-0.441007\pi$
$211$	1.06111e10	0.368544	0.184272	+	0.982875i	$0.441007\pi$
$212$	2.55244e9	0.0867849
$213$	−1.92440e10	−0.640601
$214$	−9.72203e9	−0.316880
$215$	9.26410e9	0.295686
$216$	1.21935e10	0.381143
$217$	3.01309e9	0.0922450
$218$	1.83618e10	0.550630
$219$	−1.28838e10	−0.378483
$220$	4.44367e9	0.127891
$221$	3.63514e10	1.02508
$222$	9.27463e9	0.256276
$223$	−2.11175e10	−0.571835	−0.285918	−	0.958254i	$-0.592298\pi$
$223$	−2.11175e10	−0.571835	−0.285918	+	0.958254i	$0.592298\pi$
$224$	−1.23172e9	−0.0326885
$225$	2.40260e9	0.0624970
$226$	4.06485e9	0.103647
$227$	−5.33286e9	−0.133304	−0.0666521	−	0.997776i	$-0.521232\pi$
$227$	−5.33286e9	−0.133304	−0.0666521	+	0.997776i	$0.521232\pi$
$228$	2.54675e10	0.624135
$229$	−2.62407e10	−0.630545	−0.315272	−	0.949001i	$-0.602096\pi$
$229$	−2.62407e10	−0.630545	−0.315272	+	0.949001i	$0.602096\pi$
$230$	4.33265e9	0.102089
$231$	2.12694e9	0.0491474
$232$	−9.35923e9	−0.212102
$233$	4.77174e10	1.06066	0.530329	−	0.847792i	$-0.322068\pi$
$233$	4.77174e10	1.06066	0.530329	+	0.847792i	$0.322068\pi$
$234$	5.78965e9	0.126235
$235$	−3.38501e9	−0.0724026
$236$	1.61704e10	0.339326
$237$	−3.66843e10	−0.755287
$238$	−8.28512e9	−0.167380
$239$	−2.64340e10	−0.524050	−0.262025	−	0.965061i	$-0.584390\pi$
$239$	−2.64340e10	−0.524050	−0.262025	+	0.965061i	$0.584390\pi$
$240$	9.60913e9	0.186953
$241$	−4.95287e10	−0.945758	−0.472879	−	0.881127i	$-0.656785\pi$
$241$	−4.95287e10	−0.945758	−0.472879	+	0.881127i	$0.656785\pi$
$242$	−3.42974e9	−0.0642824
$243$	2.37449e10	0.436860
$244$	−5.44074e10	−0.982660
$245$	−4.62066e10	−0.819325
$246$	−6.53455e9	−0.113765
$247$	6.63325e10	1.13394
$248$	−1.05066e10	−0.176371
$249$	−9.13683e10	−1.50626
$250$	4.74355e10	0.768022
$251$	−8.76978e10	−1.39462	−0.697311	−	0.716768i	$-0.745620\pi$
$251$	−8.76978e10	−1.39462	−0.697311	+	0.716768i	$0.745620\pi$
$252$	−1.31956e9	−0.0206123
$253$	−3.34405e9	−0.0513134
$254$	2.01963e9	0.0304453
$255$	6.46356e10	0.957285
$256$	4.29497e9	0.0625000
$257$	−1.09539e11	−1.56628	−0.783140	−	0.621846i	$-0.786383\pi$
$257$	−1.09539e11	−1.56628	−0.783140	+	0.621846i	$0.786383\pi$
$258$	−1.54620e10	−0.217258
$259$	−5.50573e9	−0.0760266
$260$	2.50279e10	0.339660
$261$	−1.00267e10	−0.133745
$262$	3.00574e10	0.394091
$263$	4.08592e9	0.0526610	0.0263305	−	0.999653i	$-0.491618\pi$
$263$	4.08592e9	0.0526610	0.0263305	+	0.999653i	$0.491618\pi$
$264$	−7.41658e9	−0.0939693
$265$	1.18208e10	0.147245
$266$	−1.51183e10	−0.185155
$267$	1.11311e11	1.34041
$268$	−5.83403e10	−0.690815
$269$	−8.48247e10	−0.987727	−0.493864	−	0.869539i	$-0.664416\pi$
$269$	−8.48247e10	−0.987727	−0.493864	+	0.869539i	$0.664416\pi$
$270$	5.64704e10	0.646671
$271$	6.76455e10	0.761864	0.380932	−	0.924603i	$-0.375603\pi$
$271$	6.76455e10	0.761864	0.380932	+	0.924603i	$0.375603\pi$
$272$	2.88900e10	0.320028
$273$	1.19795e10	0.130529
$274$	−1.01174e11	−1.08441
$275$	−8.01628e9	−0.0845232
$276$	−7.23128e9	−0.0750109
$277$	1.22944e11	1.25472	0.627361	−	0.778728i	$-0.284135\pi$
$277$	1.22944e11	1.25472	0.627361	+	0.778728i	$0.284135\pi$
$278$	1.25181e11	1.25700
$279$	−1.12559e10	−0.111214
$280$	−5.70430e9	−0.0554614
$281$	−1.28901e11	−1.23333	−0.616664	−	0.787226i	$-0.711516\pi$
$281$	−1.28901e11	−1.23333	−0.616664	+	0.787226i	$0.711516\pi$
$282$	5.64965e9	0.0531986
$283$	2.08828e10	0.193530	0.0967651	−	0.995307i	$-0.469150\pi$
$283$	2.08828e10	0.193530	0.0967651	+	0.995307i	$0.469150\pi$
$284$	−3.98348e10	−0.363354
$285$	1.17944e11	1.05895
$286$	−1.93172e10	−0.170725
$287$	3.87913e9	0.0337494
$288$	4.60128e9	0.0394105
$289$	7.57401e10	0.638683
$290$	−4.33442e10	−0.359866
$291$	1.59731e11	1.30579
$292$	−2.66693e10	−0.214679
$293$	3.85968e9	0.0305948	0.0152974	−	0.999883i	$-0.495131\pi$
$293$	3.85968e9	0.0305948	0.0152974	+	0.999883i	$0.495131\pi$
$294$	7.71197e10	0.602009
$295$	7.48881e10	0.575723
$296$	1.91983e10	0.145362
$297$	−4.35853e10	−0.325039
$298$	4.31239e9	0.0316770
$299$	−1.88346e10	−0.136281
$300$	−1.73347e10	−0.123558
$301$	9.17874e9	0.0644516
$302$	−1.89157e11	−1.30855
$303$	1.80132e11	1.22772
$304$	5.27172e10	0.354015
$305$	−2.51970e11	−1.66725
$306$	3.09504e10	0.201799
$307$	4.11326e10	0.264279	0.132140	−	0.991231i	$-0.457815\pi$
$307$	4.11326e10	0.264279	0.132140	+	0.991231i	$0.457815\pi$
$308$	4.40273e9	0.0278768
$309$	−2.42362e11	−1.51234
$310$	−4.86577e10	−0.299243
$311$	−2.75638e11	−1.67078	−0.835388	−	0.549661i	$-0.814757\pi$
$311$	−2.75638e11	−1.67078	−0.835388	+	0.549661i	$0.814757\pi$
$312$	−4.17721e10	−0.249569
$313$	3.14160e11	1.85013	0.925064	−	0.379810i	$-0.124011\pi$
$313$	3.14160e11	1.85013	0.925064	+	0.379810i	$0.124011\pi$
$314$	−5.87183e10	−0.340871
$315$	−6.11112e9	−0.0349722
$316$	−7.59358e10	−0.428405
$317$	2.58171e11	1.43595	0.717977	−	0.696067i	$-0.245068\pi$
$317$	2.58171e11	1.43595	0.717977	+	0.696067i	$0.245068\pi$
$318$	−1.97292e10	−0.108190
$319$	3.34542e10	0.180881
$320$	1.98907e10	0.106042
$321$	7.51467e10	0.395037
$322$	4.29273e9	0.0222527
$323$	3.54601e11	1.81271
$324$	−7.21391e10	−0.363679
$325$	−4.51498e10	−0.224482
$326$	2.08975e11	1.02475
$327$	−1.41928e11	−0.686440
$328$	−1.35264e10	−0.0645284
$329$	−3.35382e9	−0.0157819
$330$	−3.43475e10	−0.159434
$331$	−5.94811e10	−0.272366	−0.136183	−	0.990684i	$-0.543484\pi$
$331$	−5.94811e10	−0.272366	−0.136183	+	0.990684i	$0.543484\pi$
$332$	−1.89131e11	−0.854361
$333$	2.05675e10	0.0916607
$334$	1.87058e10	0.0822466
$335$	−2.70184e11	−1.17208
$336$	9.52059e9	0.0407509
$337$	9.61669e10	0.406154	0.203077	−	0.979163i	$-0.434906\pi$
$337$	9.61669e10	0.406154	0.203077	+	0.979163i	$0.434906\pi$
$338$	6.08724e10	0.253685
$339$	−3.14194e10	−0.129211
$340$	1.33795e11	0.542980
$341$	3.75553e10	0.150410
$342$	5.64770e10	0.223231
$343$	−9.31825e10	−0.363505
$344$	−3.20061e10	−0.123231
$345$	−3.34893e10	−0.127268
$346$	−3.05428e11	−1.14569
$347$	−3.65974e11	−1.35509	−0.677543	−	0.735483i	$-0.736955\pi$
$347$	−3.65974e11	−1.35509	−0.677543	+	0.735483i	$0.736955\pi$
$348$	7.23424e10	0.264415
$349$	−4.32258e11	−1.55966	−0.779828	−	0.625993i	$-0.784694\pi$
$349$	−4.32258e11	−1.55966	−0.779828	+	0.625993i	$0.784694\pi$
$350$	1.02904e10	0.0366545
$351$	−2.45484e11	−0.863259
$352$	−1.53522e10	−0.0533002
$353$	−3.67882e11	−1.26102	−0.630511	−	0.776180i	$-0.717155\pi$
$353$	−3.67882e11	−1.26102	−0.630511	+	0.776180i	$0.717155\pi$
$354$	−1.24990e11	−0.423019
$355$	−1.84482e11	−0.616490
$356$	2.30413e11	0.760293
$357$	6.40401e10	0.208663
$358$	3.19152e11	1.02689
$359$	−1.25751e11	−0.399564	−0.199782	−	0.979840i	$-0.564023\pi$
$359$	−1.25751e11	−0.399564	−0.199782	+	0.979840i	$0.564023\pi$
$360$	2.13093e10	0.0668665
$361$	3.24374e11	1.00522
$362$	1.31352e11	0.402019
$363$	2.65103e10	0.0801373
$364$	2.47973e10	0.0740369
$365$	−1.23510e11	−0.364238
$366$	4.20543e11	1.22503
$367$	5.19603e11	1.49511	0.747557	−	0.664197i	$-0.231227\pi$
$367$	5.19603e11	1.49511	0.747557	+	0.664197i	$0.231227\pi$
$368$	−1.49686e10	−0.0425468
$369$	−1.44911e10	−0.0406896
$370$	8.89109e10	0.246631
$371$	1.17119e10	0.0320955
$372$	8.12108e10	0.219872
$373$	4.65238e11	1.24447	0.622237	−	0.782829i	$-0.286224\pi$
$373$	4.65238e11	1.24447	0.622237	+	0.782829i	$0.286224\pi$
$374$	−1.03266e11	−0.272920
$375$	−3.66654e11	−0.957450
$376$	1.16947e10	0.0301747
$377$	1.88423e11	0.480394
$378$	5.59500e10	0.140957
$379$	4.48793e11	1.11730	0.558650	−	0.829404i	$-0.311320\pi$
$379$	4.48793e11	1.11730	0.558650	+	0.829404i	$0.311320\pi$
$380$	2.44143e11	0.600645
$381$	−1.56108e10	−0.0379544
$382$	−1.99240e11	−0.478730
$383$	2.75704e11	0.654710	0.327355	−	0.944901i	$-0.393843\pi$
$383$	2.75704e11	0.654710	0.327355	+	0.944901i	$0.393843\pi$
$384$	−3.31981e10	−0.0779152
$385$	2.03898e10	0.0472977
$386$	−2.57354e10	−0.0590049
$387$	−3.42887e10	−0.0777055
$388$	3.30641e11	0.740653
$389$	8.29663e11	1.83708	0.918540	−	0.395327i	$-0.129369\pi$
$389$	8.29663e11	1.83708	0.918540	+	0.395327i	$0.129369\pi$
$390$	−1.93454e11	−0.423435
$391$	−1.00686e11	−0.217858
$392$	1.59637e11	0.341464
$393$	−2.32330e11	−0.491290
$394$	−6.44448e11	−1.34727
$395$	−3.51672e11	−0.726861
$396$	−1.64471e10	−0.0336094
$397$	1.53152e11	0.309432	0.154716	−	0.987959i	$-0.450554\pi$
$397$	1.53152e11	0.309432	0.154716	+	0.987959i	$0.450554\pi$
$398$	−5.15332e11	−1.02947
$399$	1.16858e11	0.230823
$400$	−3.58824e10	−0.0700829
$401$	2.05461e11	0.396807	0.198404	−	0.980120i	$-0.436424\pi$
$401$	2.05461e11	0.396807	0.198404	+	0.980120i	$0.436424\pi$
$402$	4.50943e11	0.861200
$403$	2.11521e11	0.399467
$404$	3.72870e11	0.696373
$405$	−3.34089e11	−0.617042
$406$	−4.29448e10	−0.0784411
$407$	−6.86237e10	−0.123965
$408$	−2.23306e11	−0.398960
$409$	−6.57635e11	−1.16206	−0.581032	−	0.813880i	$-0.697351\pi$
$409$	−6.57635e11	−1.16206	−0.581032	+	0.813880i	$0.697351\pi$
$410$	−6.26432e10	−0.109483
$411$	7.82029e11	1.35187
$412$	−5.01685e11	−0.857814
$413$	7.41981e10	0.125492
$414$	−1.60362e10	−0.0268287
$415$	−8.75899e11	−1.44956
$416$	−8.64676e10	−0.141558
$417$	−9.67587e11	−1.56703
$418$	−1.88436e11	−0.301905
$419$	−3.79470e11	−0.601471	−0.300735	−	0.953708i	$-0.597232\pi$
$419$	−3.79470e11	−0.601471	−0.300735	+	0.953708i	$0.597232\pi$
$420$	4.40915e10	0.0691407
$421$	9.15367e11	1.42012	0.710061	−	0.704140i	$-0.248667\pi$
$421$	9.15367e11	1.42012	0.710061	+	0.704140i	$0.248667\pi$
$422$	−1.69778e11	−0.260600
$423$	1.25287e10	0.0190272
$424$	−4.08390e10	−0.0613662
$425$	−2.41362e11	−0.358855
$426$	3.07904e11	0.452973
$427$	−2.49648e11	−0.363415
$428$	1.55553e11	0.224068
$429$	1.49313e11	0.212833
$430$	−1.48226e11	−0.209081
$431$	4.90485e11	0.684664	0.342332	−	0.939579i	$-0.388783\pi$
$431$	4.90485e11	0.684664	0.342332	+	0.939579i	$0.388783\pi$
$432$	−1.95096e11	−0.269508
$433$	−5.67227e11	−0.775464	−0.387732	−	0.921772i	$-0.626741\pi$
$433$	−5.67227e11	−0.775464	−0.387732	+	0.921772i	$0.626741\pi$
$434$	−4.82094e10	−0.0652271
$435$	3.35030e11	0.448624
$436$	−2.93788e11	−0.389354
$437$	−1.83728e11	−0.240995
$438$	2.06141e11	0.267628
$439$	−1.15068e12	−1.47865	−0.739323	−	0.673351i	$-0.764854\pi$
$439$	−1.15068e12	−1.47865	−0.739323	+	0.673351i	$0.764854\pi$
$440$	−7.10987e10	−0.0904326
$441$	1.71022e11	0.215317
$442$	−5.81622e11	−0.724838
$443$	−4.44419e11	−0.548247	−0.274123	−	0.961695i	$-0.588388\pi$
$443$	−4.44419e11	−0.548247	−0.274123	+	0.961695i	$0.588388\pi$
$444$	−1.48394e11	−0.181215
$445$	1.06708e12	1.28996
$446$	3.37880e11	0.404349
$447$	−3.33327e10	−0.0394900
$448$	1.97075e10	0.0231143
$449$	6.03886e11	0.701208	0.350604	−	0.936524i	$-0.385976\pi$
$449$	6.03886e11	0.701208	0.350604	+	0.936524i	$0.385976\pi$
$450$	−3.84415e10	−0.0441921
$451$	4.83497e10	0.0550300
$452$	−6.50377e10	−0.0732895
$453$	1.46209e12	1.63130
$454$	8.53258e10	0.0942603
$455$	1.14841e11	0.125616
$456$	−4.07479e11	−0.441330
$457$	−2.80219e11	−0.300521	−0.150260	−	0.988646i	$-0.548011\pi$
$457$	−2.80219e11	−0.300521	−0.150260	+	0.988646i	$0.548011\pi$
$458$	4.19851e11	0.445862
$459$	−1.31231e12	−1.38000
$460$	−6.93224e10	−0.0721877
$461$	1.25259e12	1.29168	0.645838	−	0.763475i	$-0.276508\pi$
$461$	1.25259e12	1.29168	0.645838	+	0.763475i	$0.276508\pi$
$462$	−3.40310e10	−0.0347525
$463$	1.46886e11	0.148548	0.0742739	−	0.997238i	$-0.476336\pi$
$463$	1.46886e11	0.148548	0.0742739	+	0.997238i	$0.476336\pi$
$464$	1.49748e11	0.149979
$465$	3.76101e11	0.373050
$466$	−7.63479e11	−0.749999
$467$	1.49431e12	1.45383	0.726916	−	0.686726i	$-0.240953\pi$
$467$	1.49431e12	1.45383	0.726916	+	0.686726i	$0.240953\pi$
$468$	−9.26344e10	−0.0892618
$469$	−2.67695e11	−0.255483
$470$	5.41601e10	0.0511964
$471$	4.53865e11	0.424945
$472$	−2.58727e11	−0.239940
$473$	1.14404e11	0.105092
$474$	5.86948e11	0.534069
$475$	−4.40428e11	−0.396966
$476$	1.32562e11	0.118355
$477$	−4.37516e10	−0.0386956
$478$	4.22944e11	0.370559
$479$	−1.58007e11	−0.137140	−0.0685702	−	0.997646i	$-0.521844\pi$
$479$	−1.58007e11	−0.137140	−0.0685702	+	0.997646i	$0.521844\pi$
$480$	−1.53746e11	−0.132196
$481$	−3.86507e11	−0.329234
$482$	7.92459e11	0.668752
$483$	−3.31808e10	−0.0277411
$484$	5.48759e10	0.0454545
$485$	1.53126e12	1.25664
$486$	−3.79919e11	−0.308907
$487$	−1.99896e12	−1.61036	−0.805181	−	0.593029i	$-0.797932\pi$
$487$	−1.99896e12	−1.61036	−0.805181	+	0.593029i	$0.797932\pi$
$488$	8.70518e11	0.694846
$489$	−1.61528e12	−1.27749
$490$	7.39305e11	0.579351
$491$	9.33204e11	0.724619	0.362310	−	0.932058i	$-0.381988\pi$
$491$	9.33204e11	0.724619	0.362310	+	0.932058i	$0.381988\pi$
$492$	1.04553e11	0.0804439
$493$	1.00727e12	0.767956
$494$	−1.06132e12	−0.801817
$495$	−7.61694e10	−0.0570239
$496$	1.68105e11	0.124713
$497$	−1.82782e11	−0.134379
$498$	1.46189e12	1.06508
$499$	−1.93508e12	−1.39716	−0.698580	−	0.715532i	$-0.746184\pi$
$499$	−1.93508e12	−1.39716	−0.698580	+	0.715532i	$0.746184\pi$
$500$	−7.58968e11	−0.543074
$501$	−1.44587e11	−0.102532
$502$	1.40316e12	0.986147
$503$	1.50533e12	1.04852	0.524260	−	0.851558i	$-0.324342\pi$
$503$	1.50533e12	1.04852	0.524260	+	0.851558i	$0.324342\pi$
$504$	2.11130e10	0.0145751
$505$	1.72683e12	1.18151
$506$	5.35048e10	0.0362840
$507$	−4.70515e11	−0.316255
$508$	−3.23140e10	−0.0215280
$509$	−1.56888e12	−1.03600	−0.518001	−	0.855380i	$-0.673324\pi$
$509$	−1.56888e12	−1.03600	−0.518001	+	0.855380i	$0.673324\pi$
$510$	−1.03417e12	−0.676902
$511$	−1.22372e11	−0.0793942
$512$	−6.87195e10	−0.0441942
$513$	−2.39465e12	−1.52656
$514$	1.75262e12	1.10753
$515$	−2.32339e12	−1.45542
$516$	2.47392e11	0.153625
$517$	−4.18022e10	−0.0257331
$518$	8.80916e10	0.0537590
$519$	2.36082e12	1.42827
$520$	−4.00447e11	−0.240176
$521$	−8.36119e11	−0.497163	−0.248581	−	0.968611i	$-0.579964\pi$
$521$	−8.36119e11	−0.497163	−0.248581	+	0.968611i	$0.579964\pi$
$522$	1.60427e11	0.0945717
$523$	−1.04380e12	−0.610043	−0.305021	−	0.952345i	$-0.598664\pi$
$523$	−1.04380e12	−0.610043	−0.305021	+	0.952345i	$0.598664\pi$
$524$	−4.80919e11	−0.278664
$525$	−7.95401e10	−0.0456951
$526$	−6.53748e10	−0.0372370
$527$	1.13075e12	0.638587
$528$	1.18665e11	0.0664463
$529$	−1.74898e12	−0.971036
$530$	−1.89133e11	−0.104118
$531$	−2.77179e11	−0.151299
$532$	2.41893e11	0.130925
$533$	2.72318e11	0.146152
$534$	−1.78098e12	−0.947815
$535$	7.20391e11	0.380169
$536$	9.33444e11	0.488480
$537$	−2.46690e12	−1.28017
$538$	1.35719e12	0.698428
$539$	−5.70615e11	−0.291202
$540$	−9.03526e11	−0.457266
$541$	−2.61498e11	−0.131245	−0.0656223	−	0.997845i	$-0.520903\pi$
$541$	−2.61498e11	−0.131245	−0.0656223	+	0.997845i	$0.520903\pi$
$542$	−1.08233e12	−0.538719
$543$	−1.01529e12	−0.501175
$544$	−4.62240e11	−0.226294
$545$	−1.36058e12	−0.660604
$546$	−1.91672e11	−0.0922977
$547$	3.97347e12	1.89770	0.948848	−	0.315734i	$-0.102251\pi$
$547$	3.97347e12	1.89770	0.948848	+	0.315734i	$0.102251\pi$
$548$	1.61879e12	0.766791
$549$	9.32602e11	0.438148
$550$	1.28260e11	0.0597669
$551$	1.83803e12	0.849514
$552$	1.15700e11	0.0530407
$553$	−3.48432e11	−0.158436
$554$	−1.96710e12	−0.887223
$555$	−6.87239e11	−0.307461
$556$	−2.00289e12	−0.888833
$557$	−1.26345e12	−0.556175	−0.278087	−	0.960556i	$-0.589700\pi$
$557$	−1.26345e12	−0.556175	−0.278087	+	0.960556i	$0.589700\pi$
$558$	1.80094e11	0.0786403
$559$	6.44356e11	0.279108
$560$	9.12688e10	0.0392172
$561$	7.98199e11	0.340235
$562$	2.06242e12	0.872095
$563$	2.98705e12	1.25301	0.626505	−	0.779417i	$-0.284485\pi$
$563$	2.98705e12	1.25301	0.626505	+	0.779417i	$0.284485\pi$
$564$	−9.03944e10	−0.0376171
$565$	−3.01201e11	−0.124348
$566$	−3.34124e11	−0.136847
$567$	−3.31011e11	−0.134499
$568$	6.37357e11	0.256930
$569$	−4.48345e11	−0.179311	−0.0896555	−	0.995973i	$-0.528577\pi$
$569$	−4.48345e11	−0.179311	−0.0896555	+	0.995973i	$0.528577\pi$
$570$	−1.88711e12	−0.748790
$571$	1.93797e12	0.762931	0.381466	−	0.924383i	$-0.375420\pi$
$571$	1.93797e12	0.762931	0.381466	+	0.924383i	$0.375420\pi$
$572$	3.09075e11	0.120721
$573$	1.54003e12	0.596806
$574$	−6.20660e10	−0.0238644
$575$	1.25056e11	0.0477089
$576$	−7.36205e10	−0.0278675
$577$	−1.54518e12	−0.580347	−0.290174	−	0.956974i	$-0.593713\pi$
$577$	−1.54518e12	−0.580347	−0.290174	+	0.956974i	$0.593713\pi$
$578$	−1.21184e12	−0.451617
$579$	1.98923e11	0.0735581
$580$	6.93508e11	0.254463
$581$	−8.67828e11	−0.315967
$582$	−2.55570e12	−0.923330
$583$	1.45978e11	0.0523333
$584$	4.26709e11	0.151801
$585$	−4.29006e11	−0.151447
$586$	−6.17549e10	−0.0216338
$587$	−1.73985e10	−0.00604841	−0.00302421	−	0.999995i	$-0.500963\pi$
$587$	−1.73985e10	−0.00604841	−0.00302421	+	0.999995i	$0.500963\pi$
$588$	−1.23392e12	−0.425684
$589$	2.06335e12	0.706406
$590$	−1.19821e12	−0.407098
$591$	4.98128e12	1.67957
$592$	−3.07173e11	−0.102786
$593$	8.05756e10	0.0267582	0.0133791	−	0.999910i	$-0.495741\pi$
$593$	8.05756e10	0.0267582	0.0133791	+	0.999910i	$0.495741\pi$
$594$	6.97365e11	0.229838
$595$	6.13917e11	0.200809
$596$	−6.89982e10	−0.0223991
$597$	3.98327e12	1.28338
$598$	3.01353e11	0.0963652
$599$	4.11009e11	0.130446	0.0652229	−	0.997871i	$-0.479224\pi$
$599$	4.11009e11	0.130446	0.0652229	+	0.997871i	$0.479224\pi$
$600$	2.77354e11	0.0873684
$601$	−3.07127e12	−0.960246	−0.480123	−	0.877201i	$-0.659408\pi$
$601$	−3.07127e12	−0.960246	−0.480123	+	0.877201i	$0.659408\pi$
$602$	−1.46860e11	−0.0455742
$603$	1.00002e12	0.308020
$604$	3.02651e12	0.925286
$605$	2.54140e11	0.0771212
$606$	−2.88211e12	−0.868128
$607$	1.67239e12	0.500021	0.250010	−	0.968243i	$-0.419566\pi$
$607$	1.67239e12	0.500021	0.250010	+	0.968243i	$0.419566\pi$
$608$	−8.43476e11	−0.250326
$609$	3.31943e11	0.0977882
$610$	4.03152e12	1.17892
$611$	−2.35441e11	−0.0683434
$612$	−4.95206e11	−0.142694
$613$	−2.38637e11	−0.0682598	−0.0341299	−	0.999417i	$-0.510866\pi$
$613$	−2.38637e11	−0.0682598	−0.0341299	+	0.999417i	$0.510866\pi$
$614$	−6.58121e11	−0.186874
$615$	4.84203e11	0.136486
$616$	−7.04436e10	−0.0197119
$617$	2.55970e12	0.711060	0.355530	−	0.934665i	$-0.384300\pi$
$617$	2.55970e12	0.711060	0.355530	+	0.934665i	$0.384300\pi$
$618$	3.87779e12	1.06939
$619$	−4.65350e12	−1.27401	−0.637004	−	0.770860i	$-0.719827\pi$
$619$	−4.65350e12	−1.27401	−0.637004	+	0.770860i	$0.719827\pi$
$620$	7.78524e11	0.211597
$621$	6.79941e11	0.183468
$622$	4.41022e12	1.18142
$623$	1.05725e12	0.281178
$624$	6.68354e11	0.176472
$625$	−2.44554e12	−0.641083
$626$	−5.02657e12	−1.30824
$627$	1.45652e12	0.376368
$628$	9.39493e11	0.241032
$629$	−2.06619e12	−0.526312
$630$	9.77780e10	0.0247291
$631$	−2.86910e12	−0.720466	−0.360233	−	0.932862i	$-0.617303\pi$
$631$	−2.86910e12	−0.720466	−0.360233	+	0.932862i	$0.617303\pi$
$632$	1.21497e12	0.302928
$633$	1.31230e12	0.324875
$634$	−4.13073e12	−1.01537
$635$	−1.49652e11	−0.0365259
$636$	3.15667e11	0.0765018
$637$	−3.21385e12	−0.773390
$638$	−5.35267e11	−0.127902
$639$	6.82812e11	0.162012
$640$	−3.18252e11	−0.0749827
$641$	−6.45940e12	−1.51123	−0.755615	−	0.655016i	$-0.772662\pi$
$641$	−6.45940e12	−1.51123	−0.755615	+	0.655016i	$0.772662\pi$
$642$	−1.20235e12	−0.279333
$643$	−2.55823e12	−0.590188	−0.295094	−	0.955468i	$-0.595351\pi$
$643$	−2.55823e12	−0.590188	−0.295094	+	0.955468i	$0.595351\pi$
$644$	−6.86836e10	−0.0157350
$645$	1.14571e12	0.260650
$646$	−5.67362e12	−1.28178
$647$	−9.97781e11	−0.223855	−0.111927	−	0.993716i	$-0.535702\pi$
$647$	−9.97781e11	−0.223855	−0.111927	+	0.993716i	$0.535702\pi$
$648$	1.15423e12	0.257160
$649$	9.24810e11	0.204622
$650$	7.22397e11	0.158732
$651$	3.72636e11	0.0813149
$652$	−3.34361e12	−0.724605
$653$	−7.53538e12	−1.62179	−0.810897	−	0.585188i	$-0.801021\pi$
$653$	−7.53538e12	−1.62179	−0.810897	+	0.585188i	$0.801021\pi$
$654$	2.27084e12	0.485386
$655$	−2.22722e12	−0.472800
$656$	2.16423e11	0.0456284
$657$	4.57141e11	0.0957208
$658$	5.36611e10	0.0111595
$659$	−8.67293e12	−1.79135	−0.895677	−	0.444706i	$-0.853308\pi$
$659$	−8.67293e12	−1.79135	−0.895677	+	0.444706i	$0.853308\pi$
$660$	5.49560e11	0.112737
$661$	4.77055e12	0.971991	0.485995	−	0.873961i	$-0.338457\pi$
$661$	4.77055e12	0.971991	0.485995	+	0.873961i	$0.338457\pi$
$662$	9.51697e11	0.192592
$663$	4.49567e12	0.903615
$664$	3.02610e12	0.604124
$665$	1.12025e12	0.222135
$666$	−3.29081e11	−0.0648139
$667$	−5.21894e11	−0.102098
$668$	−2.99293e11	−0.0581571
$669$	−2.61166e12	−0.504079
$670$	4.32294e12	0.828787
$671$	−3.11163e12	−0.592567
$672$	−1.52329e11	−0.0288152
$673$	−7.71533e12	−1.44973	−0.724864	−	0.688892i	$-0.758098\pi$
$673$	−7.71533e12	−1.44973	−0.724864	+	0.688892i	$0.758098\pi$
$674$	−1.53867e12	−0.287194
$675$	1.62994e12	0.302207
$676$	−9.73959e11	−0.179383
$677$	9.14395e12	1.67296	0.836479	−	0.548000i	$-0.184611\pi$
$677$	9.14395e12	1.67296	0.836479	+	0.548000i	$0.184611\pi$
$678$	5.02711e11	0.0913659
$679$	1.51715e12	0.273914
$680$	−2.14071e12	−0.383945
$681$	−6.59528e11	−0.117509
$682$	−6.00885e11	−0.106356
$683$	8.83407e11	0.155334	0.0776672	−	0.996979i	$-0.475253\pi$
$683$	8.83407e11	0.155334	0.0776672	+	0.996979i	$0.475253\pi$
$684$	−9.03631e11	−0.157848
$685$	7.49688e12	1.30099
$686$	1.49092e12	0.257037
$687$	−3.24525e12	−0.555832
$688$	5.12097e11	0.0871373
$689$	8.22184e11	0.138990
$690$	5.35829e11	0.0899923
$691$	6.58731e12	1.09915	0.549575	−	0.835445i	$-0.314790\pi$
$691$	6.58731e12	1.09915	0.549575	+	0.835445i	$0.314790\pi$
$692$	4.88685e12	0.810124
$693$	−7.54676e10	−0.0124297
$694$	5.85558e12	0.958191
$695$	−9.27573e12	−1.50805
$696$	−1.15748e12	−0.186970
$697$	1.45576e12	0.233638
$698$	6.91613e12	1.10284
$699$	5.90133e12	0.934981
$700$	−1.64647e11	−0.0259186
$701$	6.57894e12	1.02902	0.514512	−	0.857483i	$-0.327973\pi$
$701$	6.57894e12	1.02902	0.514512	+	0.857483i	$0.327973\pi$
$702$	3.92774e12	0.610416
$703$	−3.77030e12	−0.582207
$704$	2.45635e11	0.0376889
$705$	−4.18632e11	−0.0638236
$706$	5.88612e12	0.891678
$707$	1.71092e12	0.257538
$708$	1.99984e12	0.299120
$709$	8.74938e11	0.130038	0.0650188	−	0.997884i	$-0.479289\pi$
$709$	8.74938e11	0.130038	0.0650188	+	0.997884i	$0.479289\pi$
$710$	2.95171e12	0.435924
$711$	1.30162e12	0.191017
$712$	−3.68660e12	−0.537609
$713$	−5.85872e11	−0.0848985
$714$	−1.02464e12	−0.147547
$715$	1.43138e12	0.204823
$716$	−5.10644e12	−0.726122
$717$	−3.26916e12	−0.461955
$718$	2.01202e12	0.282535
$719$	8.46541e12	1.18132	0.590660	−	0.806920i	$-0.298867\pi$
$719$	8.46541e12	1.18132	0.590660	+	0.806920i	$0.298867\pi$
$720$	−3.40949e11	−0.0472818
$721$	−2.30198e12	−0.317244
$722$	−5.18998e12	−0.710801
$723$	−6.12534e12	−0.833696
$724$	−2.10163e12	−0.284270
$725$	−1.25107e12	−0.168175
$726$	−4.24165e11	−0.0566656
$727$	−4.57971e12	−0.608042	−0.304021	−	0.952665i	$-0.598329\pi$
$727$	−4.57971e12	−0.608042	−0.304021	+	0.952665i	$0.598329\pi$
$728$	−3.96757e11	−0.0523520
$729$	8.48313e12	1.11245
$730$	1.97616e12	0.257555
$731$	3.44461e12	0.446182
$732$	−6.72869e12	−0.866225
$733$	2.48940e12	0.318512	0.159256	−	0.987237i	$-0.449090\pi$
$733$	2.48940e12	0.318512	0.159256	+	0.987237i	$0.449090\pi$
$734$	−8.31365e12	−1.05721
$735$	−5.71448e12	−0.722244
$736$	2.39498e11	0.0300851
$737$	−3.33656e12	−0.416577
$738$	2.31858e11	0.0287719
$739$	−8.85822e12	−1.09256	−0.546282	−	0.837602i	$-0.683957\pi$
$739$	−8.85822e12	−1.09256	−0.546282	+	0.837602i	$0.683957\pi$
$740$	−1.42257e12	−0.174394
$741$	8.20350e12	0.999580
$742$	−1.87390e11	−0.0226949
$743$	−1.02362e13	−1.23222	−0.616112	−	0.787659i	$-0.711293\pi$
$743$	−1.02362e13	−1.23222	−0.616112	+	0.787659i	$0.711293\pi$
$744$	−1.29937e12	−0.155473
$745$	−3.19543e11	−0.0380037
$746$	−7.44381e12	−0.879975
$747$	3.24191e12	0.380942
$748$	1.65226e12	0.192984
$749$	7.13753e11	0.0828667
$750$	5.86647e12	0.677019
$751$	3.19150e12	0.366113	0.183056	−	0.983102i	$-0.441401\pi$
$751$	3.19150e12	0.366113	0.183056	+	0.983102i	$0.441401\pi$
$752$	−1.87115e11	−0.0213367
$753$	−1.08458e13	−1.22937
$754$	−3.01477e12	−0.339690
$755$	1.40163e13	1.56990
$756$	−8.95201e11	−0.0996718
$757$	1.65793e13	1.83499	0.917496	−	0.397746i	$-0.130207\pi$
$757$	1.65793e13	1.83499	0.917496	+	0.397746i	$0.130207\pi$
$758$	−7.18069e12	−0.790050
$759$	−4.13567e11	−0.0452333
$760$	−3.90628e12	−0.424720
$761$	8.76788e12	0.947685	0.473842	−	0.880610i	$-0.342867\pi$
$761$	8.76788e12	0.947685	0.473842	+	0.880610i	$0.342867\pi$
$762$	2.49772e11	0.0268378
$763$	−1.34805e12	−0.143994
$764$	3.18784e12	0.338513
$765$	−2.29339e12	−0.242103
$766$	−4.41127e12	−0.462950
$767$	5.20877e12	0.543446
$768$	5.31169e11	0.0550944
$769$	1.02168e13	1.05353	0.526764	−	0.850011i	$-0.323405\pi$
$769$	1.02168e13	1.05353	0.526764	+	0.850011i	$0.323405\pi$
$770$	−3.26237e11	−0.0334445
$771$	−1.35469e13	−1.38069
$772$	4.11767e11	0.0417228
$773$	−4.77737e12	−0.481262	−0.240631	−	0.970617i	$-0.577354\pi$
$773$	−4.77737e12	−0.481262	−0.240631	+	0.970617i	$0.577354\pi$
$774$	5.48619e11	0.0549461
$775$	−1.40444e12	−0.139844
$776$	−5.29026e12	−0.523720
$777$	−6.80907e11	−0.0670183
$778$	−1.32746e13	−1.29901
$779$	2.65641e12	0.258450
$780$	3.09526e12	0.299414
$781$	−2.27821e12	−0.219111
$782$	1.61098e12	0.154049
$783$	−6.80220e12	−0.646728
$784$	−2.55419e12	−0.241452
$785$	4.35096e12	0.408951
$786$	3.71728e12	0.347395
$787$	−1.03319e11	−0.00960053	−0.00480026	−	0.999988i	$-0.501528\pi$
$787$	−1.03319e11	−0.00960053	−0.00480026	+	0.999988i	$0.501528\pi$
$788$	1.03112e13	0.952664
$789$	5.05316e11	0.0464212
$790$	5.62676e12	0.513968
$791$	−2.98426e11	−0.0271045
$792$	2.63154e11	0.0237654
$793$	−1.75255e13	−1.57377
$794$	−2.45043e12	−0.218801
$795$	1.46191e12	0.129798
$796$	8.24531e12	0.727945
$797$	−1.18659e13	−1.04169	−0.520844	−	0.853652i	$-0.674383\pi$
$797$	−1.18659e13	−1.04169	−0.520844	+	0.853652i	$0.674383\pi$
$798$	−1.86972e12	−0.163216
$799$	−1.25862e12	−0.109254
$800$	5.74119e11	0.0495561
$801$	−3.94953e12	−0.338999
$802$	−3.28738e12	−0.280585
$803$	−1.52526e12	−0.129456
$804$	−7.21508e12	−0.608961
$805$	−3.18086e11	−0.0266970
$806$	−3.38434e12	−0.282466
$807$	−1.04905e13	−0.870691
$808$	−5.96592e12	−0.492410
$809$	1.31694e13	1.08093	0.540465	−	0.841367i	$-0.318249\pi$
$809$	1.31694e13	1.08093	0.540465	+	0.841367i	$0.318249\pi$
$810$	5.34542e12	0.436314
$811$	−3.03385e12	−0.246263	−0.123132	−	0.992390i	$-0.539294\pi$
$811$	−3.03385e12	−0.246263	−0.123132	+	0.992390i	$0.539294\pi$
$812$	6.87118e11	0.0554663
$813$	8.36589e12	0.671591
$814$	1.09798e12	0.0876566
$815$	−1.54848e13	−1.22941
$816$	3.57290e12	0.282108
$817$	6.28557e12	0.493566
$818$	1.05222e13	0.821704
$819$	−4.25053e11	−0.0330115
$820$	1.00229e12	0.0774162
$821$	1.60816e13	1.23534	0.617670	−	0.786438i	$-0.288077\pi$
$821$	1.60816e13	1.23534	0.617670	+	0.786438i	$0.288077\pi$
$822$	−1.25125e13	−0.955915
$823$	9.77833e12	0.742960	0.371480	−	0.928441i	$-0.378850\pi$
$823$	9.77833e12	0.742960	0.371480	+	0.928441i	$0.378850\pi$
$824$	8.02695e12	0.606566
$825$	−9.91393e11	−0.0745080
$826$	−1.18717e12	−0.0887366
$827$	1.19955e13	0.891749	0.445874	−	0.895096i	$-0.352893\pi$
$827$	1.19955e13	0.891749	0.445874	+	0.895096i	$0.352893\pi$
$828$	2.56579e11	0.0189707
$829$	1.25391e13	0.922085	0.461043	−	0.887378i	$-0.347475\pi$
$829$	1.25391e13	0.922085	0.461043	+	0.887378i	$0.347475\pi$
$830$	1.40144e13	1.02500
$831$	1.52048e13	1.10605
$832$	1.38348e12	0.100096
$833$	−1.71807e13	−1.23634
$834$	1.54814e13	1.10806
$835$	−1.38608e12	−0.0986732
$836$	3.01497e12	0.213479
$837$	−7.63607e12	−0.537781
$838$	6.07152e12	0.425304
$839$	1.36095e13	0.948233	0.474116	−	0.880462i	$-0.342768\pi$
$839$	1.36095e13	0.948233	0.474116	+	0.880462i	$0.342768\pi$
$840$	−7.05465e11	−0.0488898
$841$	−9.28607e12	−0.640103
$842$	−1.46459e13	−1.00418
$843$	−1.59415e13	−1.08719
$844$	2.71644e12	0.184272
$845$	−4.51057e12	−0.304352
$846$	−2.00460e11	−0.0134543
$847$	2.51798e11	0.0168104
$848$	6.53425e11	0.0433925
$849$	2.58262e12	0.170599
$850$	3.86180e12	0.253749
$851$	1.07055e12	0.0699718
$852$	−4.92647e12	−0.320300
$853$	−5.86443e12	−0.379276	−0.189638	−	0.981854i	$-0.560731\pi$
$853$	−5.86443e12	−0.379276	−0.189638	+	0.981854i	$0.560731\pi$
$854$	3.99437e12	0.256974
$855$	−4.18488e12	−0.267815
$856$	−2.48884e12	−0.158440
$857$	−1.19243e12	−0.0755128	−0.0377564	−	0.999287i	$-0.512021\pi$
$857$	−1.19243e12	−0.0755128	−0.0377564	+	0.999287i	$0.512021\pi$
$858$	−2.38901e12	−0.150496
$859$	1.96633e13	1.23222	0.616108	−	0.787662i	$-0.288709\pi$
$859$	1.96633e13	1.23222	0.616108	+	0.787662i	$0.288709\pi$
$860$	2.37161e12	0.147843
$861$	4.79741e11	0.0297504
$862$	−7.84775e12	−0.484131
$863$	−1.56800e13	−0.962271	−0.481135	−	0.876646i	$-0.659775\pi$
$863$	−1.56800e13	−0.962271	−0.481135	+	0.876646i	$0.659775\pi$
$864$	3.12154e12	0.190571
$865$	2.26319e13	1.37451
$866$	9.07564e12	0.548336
$867$	9.36696e12	0.563006
$868$	7.71350e11	0.0461225
$869$	−4.34288e12	−0.258338
$870$	−5.36049e12	−0.317225
$871$	−1.87924e13	−1.10637
$872$	4.70061e12	0.275315
$873$	−5.66756e12	−0.330242
$874$	2.93964e12	0.170409
$875$	−3.48253e12	−0.200844
$876$	−3.29826e12	−0.189241
$877$	−1.56274e13	−0.892047	−0.446023	−	0.895021i	$-0.647160\pi$
$877$	−1.56274e13	−0.892047	−0.446023	+	0.895021i	$0.647160\pi$
$878$	1.84109e13	1.04556
$879$	4.77336e11	0.0269696
$880$	1.13758e12	0.0639455
$881$	7.19215e12	0.402223	0.201112	−	0.979568i	$-0.435545\pi$
$881$	7.19215e12	0.402223	0.201112	+	0.979568i	$0.435545\pi$
$882$	−2.73635e12	−0.152252
$883$	8.94240e11	0.0495029	0.0247515	−	0.999694i	$-0.492121\pi$
$883$	8.94240e11	0.0495029	0.0247515	+	0.999694i	$0.492121\pi$
$884$	9.30596e12	0.512538
$885$	9.26160e12	0.507506
$886$	7.11071e12	0.387669
$887$	1.98339e13	1.07585	0.537926	−	0.842992i	$-0.319208\pi$
$887$	1.98339e13	1.07585	0.537926	+	0.842992i	$0.319208\pi$
$888$	2.37431e12	0.128138
$889$	−1.48273e11	−0.00796168
$890$	−1.70733e13	−0.912142
$891$	−4.12574e12	−0.219307
$892$	−5.40609e12	−0.285918
$893$	−2.29668e12	−0.120856
$894$	5.33324e11	0.0279236
$895$	−2.36488e13	−1.23199
$896$	−3.15320e11	−0.0163442
$897$	−2.32932e12	−0.120133
$898$	−9.66218e12	−0.495829
$899$	5.86112e12	0.299269
$900$	6.15065e11	0.0312485
$901$	4.39525e12	0.222189
$902$	−7.73595e11	−0.0389121
$903$	1.13516e12	0.0568148
$904$	1.04060e12	0.0518235
$905$	−9.73300e12	−0.482312
$906$	−2.33935e13	−1.15350
$907$	−1.02442e13	−0.502625	−0.251313	−	0.967906i	$-0.580862\pi$
$907$	−1.02442e13	−0.502625	−0.251313	+	0.967906i	$0.580862\pi$
$908$	−1.36521e12	−0.0666521
$909$	−6.39141e12	−0.310498
$910$	−1.83745e12	−0.0888239
$911$	−7.68070e12	−0.369461	−0.184730	−	0.982789i	$-0.559141\pi$
$911$	−7.68070e12	−0.369461	−0.184730	+	0.982789i	$0.559141\pi$
$912$	6.51967e12	0.312068
$913$	−1.08167e13	−0.515199
$914$	4.48350e12	0.212500
$915$	−3.11618e13	−1.46969
$916$	−6.71762e12	−0.315272
$917$	−2.20670e12	−0.103058
$918$	2.09970e13	0.975809
$919$	1.89989e13	0.878633	0.439317	−	0.898332i	$-0.355221\pi$
$919$	1.89989e13	0.878633	0.439317	+	0.898332i	$0.355221\pi$
$920$	1.10916e12	0.0510444
$921$	5.08697e12	0.232965
$922$	−2.00414e13	−0.913352
$923$	−1.28315e13	−0.581927
$924$	5.44496e11	0.0245737
$925$	2.56629e12	0.115257
$926$	−2.35018e12	−0.105039
$927$	8.59943e12	0.382482
$928$	−2.39596e12	−0.106051
$929$	2.17473e13	0.957931	0.478966	−	0.877834i	$-0.341012\pi$
$929$	2.17473e13	0.957931	0.478966	+	0.877834i	$0.341012\pi$
$930$	−6.01762e12	−0.263786
$931$	−3.13506e13	−1.36764
$932$	1.22157e13	0.530329
$933$	−3.40889e13	−1.47281
$934$	−2.39089e13	−1.02802
$935$	7.65191e12	0.327429
$936$	1.48215e12	0.0631177
$937$	3.95881e13	1.67779	0.838893	−	0.544297i	$-0.183203\pi$
$937$	3.95881e13	1.67779	0.838893	+	0.544297i	$0.183203\pi$
$938$	4.28311e12	0.180654
$939$	3.88530e13	1.63091
$940$	−8.66562e11	−0.0362013
$941$	−4.13659e13	−1.71985	−0.859923	−	0.510424i	$-0.829488\pi$
$941$	−4.13659e13	−1.71985	−0.859923	+	0.510424i	$0.829488\pi$
$942$	−7.26184e12	−0.300481
$943$	−7.54267e11	−0.0310615
$944$	4.13963e12	0.169663
$945$	−4.14583e12	−0.169110
$946$	−1.83047e12	−0.0743109
$947$	7.78696e12	0.314625	0.157313	−	0.987549i	$-0.449717\pi$
$947$	7.78696e12	0.314625	0.157313	+	0.987549i	$0.449717\pi$
$948$	−9.39117e12	−0.377644
$949$	−8.59064e12	−0.343817
$950$	7.04685e12	0.280698
$951$	3.19286e13	1.26581
$952$	−2.12099e12	−0.0836898
$953$	1.26501e13	0.496794	0.248397	−	0.968658i	$-0.420096\pi$
$953$	1.26501e13	0.496794	0.248397	+	0.968658i	$0.420096\pi$
$954$	7.00026e11	0.0273619
$955$	1.47634e13	0.574344
$956$	−6.76710e12	−0.262025
$957$	4.13736e12	0.159448
$958$	2.52810e12	0.0969729
$959$	7.42781e12	0.283581
$960$	2.45994e12	0.0934767
$961$	−1.98600e13	−0.751145
$962$	6.18411e12	0.232803
$963$	−2.66634e12	−0.0999074
$964$	−1.26793e13	−0.472879
$965$	1.90696e12	0.0707896
$966$	5.30892e11	0.0196159
$967$	−6.51628e12	−0.239652	−0.119826	−	0.992795i	$-0.538234\pi$
$967$	−6.51628e12	−0.239652	−0.119826	+	0.992795i	$0.538234\pi$
$968$	−8.78014e11	−0.0321412
$969$	4.38544e13	1.59792
$970$	−2.45001e13	−0.888578
$971$	2.06099e13	0.744028	0.372014	−	0.928227i	$-0.378667\pi$
$971$	2.06099e13	0.744028	0.372014	+	0.928227i	$0.378667\pi$
$972$	6.07870e12	0.218430
$973$	−9.19027e12	−0.328716
$974$	3.19833e13	1.13870
$975$	−5.58379e12	−0.197883
$976$	−1.39283e13	−0.491330
$977$	−3.23219e13	−1.13494	−0.567468	−	0.823395i	$-0.692077\pi$
$977$	−3.23219e13	−1.13494	−0.567468	+	0.823395i	$0.692077\pi$
$978$	2.58445e13	0.903324
$979$	1.31776e13	0.458474
$980$	−1.18289e13	−0.409663
$981$	5.03585e12	0.173605
$982$	−1.49313e13	−0.512383
$983$	2.94079e13	1.00455	0.502277	−	0.864707i	$-0.332496\pi$
$983$	2.94079e13	1.00455	0.502277	+	0.864707i	$0.332496\pi$
$984$	−1.67285e12	−0.0568824
$985$	4.77528e13	1.61635
$986$	−1.61164e13	−0.543027
$987$	−4.14775e11	−0.0139119
$988$	1.69811e13	0.566970
$989$	−1.78474e12	−0.0593186
$990$	1.21871e12	0.0403220
$991$	3.67690e13	1.21102	0.605508	−	0.795839i	$-0.292970\pi$
$991$	3.67690e13	1.21102	0.605508	+	0.795839i	$0.292970\pi$
$992$	−2.68968e12	−0.0881857
$993$	−7.35617e12	−0.240093
$994$	2.92451e12	0.0950200
$995$	3.81855e13	1.23508
$996$	−2.33903e13	−0.753128
$997$	−7.67620e12	−0.246047	−0.123024	−	0.992404i	$-0.539259\pi$
$997$	−7.67620e12	−0.246047	−0.123024	+	0.992404i	$0.539259\pi$
$998$	3.09613e13	0.987941
$999$	1.39532e13	0.443229

Twists

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

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

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +123.672 q^{3} +256.000 q^{4} +1185.58 q^{5} -1978.76 q^{6} +1174.66 q^{7} -4096.00 q^{8} -4388.12 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} +123.672 q^{3} +256.000 q^{4} +1185.58 q^{5} -1978.76 q^{6} +1174.66 q^{7} -4096.00 q^{8} -4388.12 q^{9} -18969.3 q^{10} +14641.0 q^{11} +31660.2 q^{12} +82461.9 q^{13} -18794.5 q^{14} +146624. q^{15} +65536.0 q^{16} +440826. q^{17} +70209.9 q^{18} +804401. q^{19} +303509. q^{20} +145273. q^{21} -234256. q^{22} -228403. q^{23} -506562. q^{24} -547523. q^{25} -1.31939e6 q^{26} -2.97693e6 q^{27} +300712. q^{28} +2.28497e6 q^{29} -2.34598e6 q^{30} +2.56508e6 q^{31} -1.04858e6 q^{32} +1.81069e6 q^{33} -7.05322e6 q^{34} +1.39265e6 q^{35} -1.12336e6 q^{36} -4.68709e6 q^{37} -1.28704e7 q^{38} +1.01983e7 q^{39} -4.85614e6 q^{40} +3.30235e6 q^{41} -2.32436e6 q^{42} +7.81398e6 q^{43} +3.74810e6 q^{44} -5.20247e6 q^{45} +3.65445e6 q^{46} -2.85515e6 q^{47} +8.10500e6 q^{48} -3.89738e7 q^{49} +8.76036e6 q^{50} +5.45181e7 q^{51} +2.11103e7 q^{52} +9.97047e6 q^{53} +4.76310e7 q^{54} +1.73581e7 q^{55} -4.81140e6 q^{56} +9.94823e7 q^{57} -3.65595e7 q^{58} +6.31658e7 q^{59} +3.75357e7 q^{60} -2.12529e8 q^{61} -4.10412e7 q^{62} -5.15454e6 q^{63} +1.67772e7 q^{64} +9.77653e7 q^{65} -2.89710e7 q^{66} -2.27892e8 q^{67} +1.12852e8 q^{68} -2.82472e7 q^{69} -2.22824e7 q^{70} -1.55605e8 q^{71} +1.79737e7 q^{72} -1.04177e8 q^{73} +7.49935e7 q^{74} -6.77135e7 q^{75} +2.05927e8 q^{76} +1.71982e7 q^{77} -1.63172e8 q^{78} -2.96624e8 q^{79} +7.76982e7 q^{80} -2.81793e8 q^{81} -5.28376e7 q^{82} -7.38793e8 q^{83} +3.71898e7 q^{84} +5.22635e8 q^{85} -1.25024e8 q^{86} +2.82588e8 q^{87} -5.99695e7 q^{88} +9.00049e8 q^{89} +8.32396e7 q^{90} +9.68645e7 q^{91} -5.84712e7 q^{92} +3.17229e8 q^{93} +4.56823e7 q^{94} +9.53683e8 q^{95} -1.29680e8 q^{96} +1.29157e9 q^{97} +6.23581e8 q^{98} -6.42465e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} - 21 q^{3} + 512 q^{4} - 521 q^{5} + 336 q^{6} - 7490 q^{7} - 8192 q^{8} - 3141 q^{9}+O(q^{10}) \) 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

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