LMFDB - Embedded newform 22.10.a.e.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{463}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 463 $ x^2 - 463
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$21.5174$ 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)

$f(q)$	$=$	$q-16.0000 q^{2} +189.139 q^{3} +256.000 q^{4} -2460.39 q^{5} -3026.23 q^{6} +2204.47 q^{7} -4096.00 q^{8} +16090.7 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} +189.139 q^{3} +256.000 q^{4} -2460.39 q^{5} -3026.23 q^{6} +2204.47 q^{7} -4096.00 q^{8} +16090.7 q^{9} +39366.3 q^{10} -14641.0 q^{11} +48419.7 q^{12} -140322. q^{13} -35271.5 q^{14} -465358. q^{15} +65536.0 q^{16} -343422. q^{17} -257452. q^{18} +188818. q^{19} -629861. q^{20} +416951. q^{21} +234256. q^{22} -2.31035e6 q^{23} -774715. q^{24} +4.10042e6 q^{25} +2.24515e6 q^{26} -679438. q^{27} +564343. q^{28} -363525. q^{29} +7.44572e6 q^{30} -5.09609e6 q^{31} -1.04858e6 q^{32} -2.76919e6 q^{33} +5.49475e6 q^{34} -5.42386e6 q^{35} +4.11923e6 q^{36} +1.24491e7 q^{37} -3.02109e6 q^{38} -2.65405e7 q^{39} +1.00778e7 q^{40} +2.99230e7 q^{41} -6.67122e6 q^{42} +2.52560e7 q^{43} -3.74810e6 q^{44} -3.95896e7 q^{45} +3.69656e7 q^{46} +1.93180e7 q^{47} +1.23954e7 q^{48} -3.54939e7 q^{49} -6.56067e7 q^{50} -6.49546e7 q^{51} -3.59225e7 q^{52} -4.79111e7 q^{53} +1.08710e7 q^{54} +3.60226e7 q^{55} -9.02949e6 q^{56} +3.57129e7 q^{57} +5.81640e6 q^{58} +2.28918e7 q^{59} -1.19132e8 q^{60} +4.69665e7 q^{61} +8.15375e7 q^{62} +3.54715e7 q^{63} +1.67772e7 q^{64} +3.45248e8 q^{65} +4.43071e7 q^{66} -2.94611e8 q^{67} -8.79160e7 q^{68} -4.36978e8 q^{69} +8.67817e7 q^{70} +9.62106e7 q^{71} -6.59077e7 q^{72} +3.14132e8 q^{73} -1.99186e8 q^{74} +7.75551e8 q^{75} +4.83374e7 q^{76} -3.22756e7 q^{77} +4.24647e8 q^{78} +4.72114e8 q^{79} -1.61244e8 q^{80} -4.45223e8 q^{81} -4.78767e8 q^{82} -1.19655e8 q^{83} +1.06740e8 q^{84} +8.44954e8 q^{85} -4.04096e8 q^{86} -6.87569e7 q^{87} +5.99695e7 q^{88} -8.24428e8 q^{89} +6.33433e8 q^{90} -3.09335e8 q^{91} -5.91450e8 q^{92} -9.63873e8 q^{93} -3.09088e8 q^{94} -4.64566e8 q^{95} -1.98327e8 q^{96} -429826. q^{97} +5.67903e8 q^{98} -2.35585e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{2} + 34 q^{3} + 512 q^{4} - 1478 q^{5} - 544 q^{6} + 8196 q^{7} - 8192 q^{8} + 20476 q^{9}+O(q^{10}) $ 2 * q - 32 * q^2 + 34 * q^3 + 512 * q^4 - 1478 * q^5 - 544 * q^6 + 8196 * q^7 - 8192 * q^8 + 20476 * q^9	\( 2 q - 32 q^{2} + 34 q^{3} + 512 q^{4} - 1478 q^{5} - 544 q^{6} + 8196 q^{7} - 8192 q^{8} + 20476 q^{9} + 23648 q^{10} - 29282 q^{11} + 8704 q^{12} - 196296 q^{13} - 131136 q^{14} - 617766 q^{15} + 131072 q^{16} - 548788 q^{17} - 327616 q^{18} - 90928 q^{19} - 378368 q^{20} - 512572 q^{21} + 468512 q^{22} - 3971046 q^{23} - 139264 q^{24} + 3112392 q^{25} + 3140736 q^{26} + 1693846 q^{27} + 2098176 q^{28} - 656128 q^{29} + 9884256 q^{30} - 872214 q^{31} - 2097152 q^{32} - 497794 q^{33} + 8780608 q^{34} + 462196 q^{35} + 5241856 q^{36} - 190722 q^{37} + 1454848 q^{38} - 17856712 q^{39} + 6053888 q^{40} + 3350080 q^{41} + 8201152 q^{42} + 3876012 q^{43} - 7496192 q^{44} - 35281524 q^{45} + 63536736 q^{46} + 38884544 q^{47} + 2228224 q^{48} - 39949062 q^{49} - 49798272 q^{50} - 33094260 q^{51} - 50251776 q^{52} - 134346316 q^{53} - 27101536 q^{54} + 21639398 q^{55} - 33570816 q^{56} + 79112528 q^{57} + 10498048 q^{58} - 125273754 q^{59} - 158148096 q^{60} + 114821880 q^{61} + 13955424 q^{62} + 61745912 q^{63} + 33554432 q^{64} + 290259544 q^{65} + 7964704 q^{66} - 91519714 q^{67} - 140489728 q^{68} - 179338950 q^{69} - 7395136 q^{70} + 411397438 q^{71} - 83869696 q^{72} + 506142392 q^{73} + 3051552 q^{74} + 928832584 q^{75} - 23277568 q^{76} - 119997636 q^{77} + 285707392 q^{78} + 810072516 q^{79} - 96862208 q^{80} - 899727614 q^{81} - 53601280 q^{82} - 718904884 q^{83} - 131218432 q^{84} + 643202972 q^{85} - 62016192 q^{86} - 23362560 q^{87} + 119939072 q^{88} - 810786322 q^{89} + 564504384 q^{90} - 644704528 q^{91} - 1016587776 q^{92} - 1619163382 q^{93} - 622152704 q^{94} - 739387248 q^{95} - 35651584 q^{96} - 230208654 q^{97} + 639184992 q^{98} - 299789116 q^{99}+O(q^{100}) \) 2 * q - 32 * q^2 + 34 * q^3 + 512 * q^4 - 1478 * q^5 - 544 * q^6 + 8196 * q^7 - 8192 * q^8 + 20476 * q^9 + 23648 * q^10 - 29282 * q^11 + 8704 * q^12 - 196296 * q^13 - 131136 * q^14 - 617766 * q^15 + 131072 * q^16 - 548788 * q^17 - 327616 * q^18 - 90928 * q^19 - 378368 * q^20 - 512572 * q^21 + 468512 * q^22 - 3971046 * q^23 - 139264 * q^24 + 3112392 * q^25 + 3140736 * q^26 + 1693846 * q^27 + 2098176 * q^28 - 656128 * q^29 + 9884256 * q^30 - 872214 * q^31 - 2097152 * q^32 - 497794 * q^33 + 8780608 * q^34 + 462196 * q^35 + 5241856 * q^36 - 190722 * q^37 + 1454848 * q^38 - 17856712 * q^39 + 6053888 * q^40 + 3350080 * q^41 + 8201152 * q^42 + 3876012 * q^43 - 7496192 * q^44 - 35281524 * q^45 + 63536736 * q^46 + 38884544 * q^47 + 2228224 * q^48 - 39949062 * q^49 - 49798272 * q^50 - 33094260 * q^51 - 50251776 * q^52 - 134346316 * q^53 - 27101536 * q^54 + 21639398 * q^55 - 33570816 * q^56 + 79112528 * q^57 + 10498048 * q^58 - 125273754 * q^59 - 158148096 * q^60 + 114821880 * q^61 + 13955424 * q^62 + 61745912 * q^63 + 33554432 * q^64 + 290259544 * q^65 + 7964704 * q^66 - 91519714 * q^67 - 140489728 * q^68 - 179338950 * q^69 - 7395136 * q^70 + 411397438 * q^71 - 83869696 * q^72 + 506142392 * q^73 + 3051552 * q^74 + 928832584 * q^75 - 23277568 * q^76 - 119997636 * q^77 + 285707392 * q^78 + 810072516 * q^79 - 96862208 * q^80 - 899727614 * q^81 - 53601280 * q^82 - 718904884 * q^83 - 131218432 * q^84 + 643202972 * q^85 - 62016192 * q^86 - 23362560 * q^87 + 119939072 * q^88 - 810786322 * q^89 + 564504384 * q^90 - 644704528 * q^91 - 1016587776 * q^92 - 1619163382 * q^93 - 622152704 * q^94 - 739387248 * q^95 - 35651584 * q^96 - 230208654 * q^97 + 639184992 * q^98 - 299789116 * 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
$3$	189.139	1.34814	0.674072	−	0.738665i	$-0.264544\pi$
$3$	189.139	1.34814	0.674072	+	0.738665i	$0.264544\pi$
$4$	256.000	0.500000
$5$	−2460.39	−1.76052	−0.880258	−	0.474496i	$-0.842630\pi$
$5$	−2460.39	−1.76052	−0.880258	+	0.474496i	$0.842630\pi$
$6$	−3026.23	−0.953282
$7$	2204.47	0.347026	0.173513	−	0.984832i	$-0.444488\pi$
$7$	2204.47	0.347026	0.173513	+	0.984832i	$0.444488\pi$
$8$	−4096.00	−0.353553
$9$	16090.7	0.817494
$10$	39366.3	1.24487
$11$	−14641.0	−0.301511
$11$	−14641.0	−0.301511
$12$	48419.7	0.674072
$13$	−140322.	−1.36264	−0.681320	−	0.731986i	$-0.738594\pi$
$13$	−140322.	−1.36264	−0.681320	+	0.731986i	$0.738594\pi$
$14$	−35271.5	−0.245385
$15$	−465358.	−2.37343
$16$	65536.0	0.250000
$17$	−343422.	−0.997259	−0.498629	−	0.866815i	$-0.666163\pi$
$17$	−343422.	−0.997259	−0.498629	+	0.866815i	$0.666163\pi$
$18$	−257452.	−0.578056
$19$	188818.	0.332393	0.166196	−	0.986093i	$-0.446851\pi$
$19$	188818.	0.332393	0.166196	+	0.986093i	$0.446851\pi$
$20$	−629861.	−0.880258
$21$	416951.	0.467841
$22$	234256.	0.213201
$23$	−2.31035e6	−1.72148	−0.860741	−	0.509043i	$-0.829999\pi$
$23$	−2.31035e6	−1.72148	−0.860741	+	0.509043i	$0.829999\pi$
$24$	−774715.	−0.476641
$25$	4.10042e6	2.09941
$26$	2.24515e6	0.963532
$27$	−679438.	−0.246044
$28$	564343.	0.173513
$29$	−363525.	−0.0954428	−0.0477214	−	0.998861i	$-0.515196\pi$
$29$	−363525.	−0.0954428	−0.0477214	+	0.998861i	$0.515196\pi$
$30$	7.44572e6	1.67827
$31$	−5.09609e6	−0.991083	−0.495541	−	0.868584i	$-0.665030\pi$
$31$	−5.09609e6	−0.991083	−0.495541	+	0.868584i	$0.665030\pi$
$32$	−1.04858e6	−0.176777
$33$	−2.76919e6	−0.406481
$34$	5.49475e6	0.705168
$35$	−5.42386e6	−0.610945
$36$	4.11923e6	0.408747
$37$	1.24491e7	1.09202	0.546011	−	0.837778i	$-0.316146\pi$
$37$	1.24491e7	1.09202	0.546011	+	0.837778i	$0.316146\pi$
$38$	−3.02109e6	−0.235037
$39$	−2.65405e7	−1.83704
$40$	1.00778e7	0.622436
$41$	2.99230e7	1.65378	0.826889	−	0.562365i	$-0.190109\pi$
$41$	2.99230e7	1.65378	0.826889	+	0.562365i	$0.190109\pi$
$42$	−6.67122e6	−0.330814
$43$	2.52560e7	1.12657	0.563283	−	0.826264i	$-0.309538\pi$
$43$	2.52560e7	1.12657	0.563283	+	0.826264i	$0.309538\pi$
$44$	−3.74810e6	−0.150756
$45$	−3.95896e7	−1.43921
$46$	3.69656e7	1.21727
$47$	1.93180e7	0.577459	0.288730	−	0.957411i	$-0.406767\pi$
$47$	1.93180e7	0.577459	0.288730	+	0.957411i	$0.406767\pi$
$48$	1.23954e7	0.337036
$49$	−3.54939e7	−0.879573
$50$	−6.56067e7	−1.48451
$51$	−6.49546e7	−1.34445
$52$	−3.59225e7	−0.681320
$53$	−4.79111e7	−0.834055	−0.417027	−	0.908894i	$-0.636928\pi$
$53$	−4.79111e7	−0.834055	−0.417027	+	0.908894i	$0.636928\pi$
$54$	1.08710e7	0.173979
$55$	3.60226e7	0.530815
$56$	−9.02949e6	−0.122692
$57$	3.57129e7	0.448114
$58$	5.81640e6	0.0674882
$59$	2.28918e7	0.245950	0.122975	−	0.992410i	$-0.460757\pi$
$59$	2.28918e7	0.245950	0.122975	+	0.992410i	$0.460757\pi$
$60$	−1.19132e8	−1.18671
$61$	4.69665e7	0.434315	0.217157	−	0.976137i	$-0.430322\pi$
$61$	4.69665e7	0.434315	0.217157	+	0.976137i	$0.430322\pi$
$62$	8.15375e7	0.700801
$63$	3.54715e7	0.283692
$64$	1.67772e7	0.125000
$65$	3.45248e8	2.39895
$66$	4.43071e7	0.287425
$67$	−2.94611e8	−1.78613	−0.893063	−	0.449932i	$-0.851448\pi$
$67$	−2.94611e8	−1.78613	−0.893063	+	0.449932i	$0.851448\pi$
$68$	−8.79160e7	−0.498629
$69$	−4.36978e8	−2.32081
$70$	8.67817e7	0.432003
$71$	9.62106e7	0.449325	0.224662	−	0.974437i	$-0.427872\pi$
$71$	9.62106e7	0.449325	0.224662	+	0.974437i	$0.427872\pi$
$72$	−6.59077e7	−0.289028
$73$	3.14132e8	1.29467	0.647336	−	0.762205i	$-0.275883\pi$
$73$	3.14132e8	1.29467	0.647336	+	0.762205i	$0.275883\pi$
$74$	−1.99186e8	−0.772176
$75$	7.75551e8	2.83031
$76$	4.83374e7	0.166196
$77$	−3.22756e7	−0.104632
$78$	4.24647e8	1.29898
$79$	4.72114e8	1.36372	0.681859	−	0.731484i	$-0.261172\pi$
$79$	4.72114e8	1.36372	0.681859	+	0.731484i	$0.261172\pi$
$80$	−1.61244e8	−0.440129
$81$	−4.45223e8	−1.14920
$82$	−4.78767e8	−1.16940
$83$	−1.19655e8	−0.276745	−0.138372	−	0.990380i	$-0.544187\pi$
$83$	−1.19655e8	−0.276745	−0.138372	+	0.990380i	$0.544187\pi$
$84$	1.06740e8	0.233921
$85$	8.44954e8	1.75569
$86$	−4.04096e8	−0.796603
$87$	−6.87569e7	−0.128671
$88$	5.99695e7	0.106600
$89$	−8.24428e8	−1.39283	−0.696414	−	0.717640i	$-0.745222\pi$
$89$	−8.24428e8	−1.39283	−0.696414	+	0.717640i	$0.745222\pi$
$90$	6.33433e8	1.01768
$91$	−3.09335e8	−0.472872
$92$	−5.91450e8	−0.860741
$93$	−9.63873e8	−1.33612
$94$	−3.09088e8	−0.408326
$95$	−4.64566e8	−0.585183
$96$	−1.98327e8	−0.238321
$97$	−429826.	−0.000492970 0	−0.000246485	−	1.00000i	$-0.500078\pi$
$97$	−429826.	−0.000492970 0	−0.000246485		1.00000i	$0.500078\pi$
$98$	5.67903e8	0.621952
$99$	−2.35585e8	−0.246484
$100$	1.04971e9	1.04971
$101$	−1.96236e9	−1.87643	−0.938215	−	0.346053i	$-0.887522\pi$
$101$	−1.96236e9	−1.87643	−0.938215	+	0.346053i	$0.887522\pi$
$102$	1.03927e9	0.950669
$103$	−9.76202e8	−0.854618	−0.427309	−	0.904106i	$-0.640538\pi$
$103$	−9.76202e8	−0.854618	−0.427309	+	0.904106i	$0.640538\pi$
$104$	5.74760e8	0.481766
$105$	−1.02587e9	−0.823642
$106$	7.66578e8	0.589766
$107$	3.83882e8	0.283120	0.141560	−	0.989930i	$-0.454788\pi$
$107$	3.83882e8	0.283120	0.141560	+	0.989930i	$0.454788\pi$
$108$	−1.73936e8	−0.123022
$109$	−6.32006e8	−0.428847	−0.214423	−	0.976741i	$-0.568787\pi$
$109$	−6.32006e8	−0.428847	−0.214423	+	0.976741i	$0.568787\pi$
$110$	−5.76362e8	−0.375343
$111$	2.35462e9	1.47220
$112$	1.44472e8	0.0867565
$113$	2.14453e9	1.23731	0.618657	−	0.785661i	$-0.287677\pi$
$113$	2.14453e9	1.23731	0.618657	+	0.785661i	$0.287677\pi$
$114$	−5.71406e8	−0.316864
$115$	5.68437e9	3.03070
$116$	−9.30623e7	−0.0477214
$117$	−2.25789e9	−1.11395
$118$	−3.66269e8	−0.173913
$119$	−7.57062e8	−0.346075
$120$	1.90611e9	0.839134
$121$	2.14359e8	0.0909091
$122$	−7.51465e8	−0.307107
$123$	5.65961e9	2.22953
$124$	−1.30460e9	−0.495541
$125$	−5.28319e9	−1.93553
$126$	−5.67544e8	−0.200600
$127$	−4.19668e9	−1.43149	−0.715747	−	0.698360i	$-0.753913\pi$
$127$	−4.19668e9	−1.43149	−0.715747	+	0.698360i	$0.753913\pi$
$128$	−2.68435e8	−0.0883883
$129$	4.77691e9	1.51877
$130$	−5.52397e9	−1.69631
$131$	−5.79875e9	−1.72034	−0.860168	−	0.510011i	$-0.829641\pi$
$131$	−5.79875e9	−1.72034	−0.860168	+	0.510011i	$0.829641\pi$
$132$	−7.08913e8	−0.203240
$133$	4.16242e8	0.115349
$134$	4.71377e9	1.26298
$135$	1.67169e9	0.433164
$136$	1.40666e9	0.352584
$137$	3.06342e8	0.0742958	0.0371479	−	0.999310i	$-0.488173\pi$
$137$	3.06342e8	0.0742958	0.0371479	+	0.999310i	$0.488173\pi$
$138$	6.99165e9	1.64106
$139$	2.58649e9	0.587683	0.293842	−	0.955854i	$-0.405066\pi$
$139$	2.58649e9	0.587683	0.293842	+	0.955854i	$0.405066\pi$
$140$	−1.38851e9	−0.305472
$141$	3.65379e9	0.778499
$142$	−1.53937e9	−0.317721
$143$	2.05446e9	0.410851
$144$	1.05452e9	0.204374
$145$	8.94414e8	0.168028
$146$	−5.02612e9	−0.915471
$147$	−6.71330e9	−1.18579
$148$	3.18698e9	0.546011
$149$	2.44788e9	0.406867	0.203433	−	0.979089i	$-0.434790\pi$
$149$	2.44788e9	0.406867	0.203433	+	0.979089i	$0.434790\pi$
$150$	−1.24088e10	−2.00133
$151$	1.23707e9	0.193641	0.0968204	−	0.995302i	$-0.469133\pi$
$151$	1.23707e9	0.193641	0.0968204	+	0.995302i	$0.469133\pi$
$152$	−7.73398e8	−0.117519
$153$	−5.52591e9	−0.815253
$154$	5.16409e8	0.0739862
$155$	1.25384e10	1.74482
$156$	−6.79436e9	−0.918518
$157$	−1.30903e10	−1.71950	−0.859750	−	0.510715i	$-0.829381\pi$
$157$	−1.30903e10	−1.71950	−0.859750	+	0.510715i	$0.829381\pi$
$158$	−7.55382e9	−0.964294
$159$	−9.06188e9	−1.12443
$160$	2.57991e9	0.311218
$161$	−5.09309e9	−0.597399
$162$	7.12356e9	0.812605
$163$	3.43881e9	0.381561	0.190781	−	0.981633i	$-0.438898\pi$
$163$	3.43881e9	0.381561	0.190781	+	0.981633i	$0.438898\pi$
$164$	7.66028e9	0.826889
$165$	6.81330e9	0.715616
$166$	1.91448e9	0.195688
$167$	−6.68004e9	−0.664591	−0.332296	−	0.943175i	$-0.607823\pi$
$167$	−6.68004e9	−0.664591	−0.332296	+	0.943175i	$0.607823\pi$
$168$	−1.70783e9	−0.165407
$169$	9.08581e9	0.856788
$170$	−1.35193e10	−1.24146
$171$	3.03822e9	0.271729
$172$	6.46554e9	0.563283
$173$	5.31351e9	0.450997	0.225498	−	0.974244i	$-0.427599\pi$
$173$	5.31351e9	0.450997	0.225498	+	0.974244i	$0.427599\pi$
$174$	1.10011e9	0.0909839
$175$	9.03923e9	0.728551
$176$	−9.59513e8	−0.0753778
$177$	4.32975e9	0.331576
$178$	1.31908e10	0.984878
$179$	−3.25561e8	−0.0237025	−0.0118512	−	0.999930i	$-0.503772\pi$
$179$	−3.25561e8	−0.0237025	−0.0118512	+	0.999930i	$0.503772\pi$
$180$	−1.01349e10	−0.719606
$181$	−7.60801e8	−0.0526887	−0.0263444	−	0.999653i	$-0.508387\pi$
$181$	−7.60801e8	−0.0526887	−0.0263444	+	0.999653i	$0.508387\pi$
$182$	4.94937e9	0.334371
$183$	8.88323e9	0.585519
$184$	9.46319e9	0.608636
$185$	−3.06298e10	−1.92252
$186$	1.54220e10	0.944782
$187$	5.02804e9	0.300685
$188$	4.94540e9	0.288730
$189$	−1.49780e9	−0.0853837
$190$	7.43306e9	0.413787
$191$	−7.87058e9	−0.427914	−0.213957	−	0.976843i	$-0.568635\pi$
$191$	−7.87058e9	−0.427914	−0.213957	+	0.976843i	$0.568635\pi$
$192$	3.17323e9	0.168518
$193$	−3.90610e9	−0.202645	−0.101322	−	0.994854i	$-0.532307\pi$
$193$	−3.90610e9	−0.202645	−0.101322	+	0.994854i	$0.532307\pi$
$194$	6.87722e6	0.000348582 0
$195$	6.53000e10	3.23413
$196$	−9.08645e9	−0.439786
$197$	6.55841e9	0.310242	0.155121	−	0.987895i	$-0.450423\pi$
$197$	6.55841e9	0.310242	0.155121	+	0.987895i	$0.450423\pi$
$198$	3.76935e9	0.174290
$199$	1.02050e10	0.461290	0.230645	−	0.973038i	$-0.425916\pi$
$199$	1.02050e10	0.461290	0.230645	+	0.973038i	$0.425916\pi$
$200$	−1.67953e10	−0.742255
$201$	−5.57225e10	−2.40796
$202$	3.13977e10	1.32684
$203$	−8.01378e8	−0.0331211
$204$	−1.66284e10	−0.672225
$205$	−7.36223e10	−2.91150
$206$	1.56192e10	0.604306
$207$	−3.71752e10	−1.40730
$208$	−9.19615e9	−0.340660
$209$	−2.76448e9	−0.100220
$210$	1.64138e10	0.582403
$211$	9.82503e9	0.341242	0.170621	−	0.985337i	$-0.445423\pi$
$211$	9.82503e9	0.341242	0.170621	+	0.985337i	$0.445423\pi$
$212$	−1.22652e10	−0.417027
$213$	1.81972e10	0.605755
$214$	−6.14211e9	−0.200196
$215$	−6.21398e10	−1.98334
$216$	2.78298e9	0.0869897
$217$	−1.12342e10	−0.343932
$218$	1.01121e10	0.303240
$219$	5.94148e10	1.74541
$220$	9.22180e9	0.265408
$221$	4.81897e10	1.35890
$222$	−3.76740e10	−1.04101
$223$	−1.49741e10	−0.405481	−0.202740	−	0.979233i	$-0.564985\pi$
$223$	−1.49741e10	−0.405481	−0.202740	+	0.979233i	$0.564985\pi$
$224$	−2.31155e9	−0.0613461
$225$	6.59788e10	1.71626
$226$	−3.43125e10	−0.874913
$227$	−4.32808e10	−1.08188	−0.540940	−	0.841061i	$-0.681931\pi$
$227$	−4.32808e10	−1.08188	−0.540940	+	0.841061i	$0.681931\pi$
$228$	9.14250e9	0.224057
$229$	5.63986e8	0.0135522	0.00677608	−	0.999977i	$-0.497843\pi$
$229$	5.63986e8	0.0135522	0.00677608	+	0.999977i	$0.497843\pi$
$230$	−9.09500e10	−2.14303
$231$	−6.10459e9	−0.141060
$232$	1.48900e9	0.0337441
$233$	5.38441e10	1.19684	0.598421	−	0.801182i	$-0.295795\pi$
$233$	5.38441e10	1.19684	0.598421	+	0.801182i	$0.295795\pi$
$234$	3.61262e10	0.787682
$235$	−4.75299e10	−1.01663
$236$	5.86031e9	0.122975
$237$	8.92953e10	1.83849
$238$	1.21130e10	0.244712
$239$	−3.15456e10	−0.625385	−0.312693	−	0.949854i	$-0.601231\pi$
$239$	−3.15456e10	−0.625385	−0.312693	+	0.949854i	$0.601231\pi$
$240$	−3.04977e10	−0.593357
$241$	3.09267e10	0.590550	0.295275	−	0.955412i	$-0.404589\pi$
$241$	3.09267e10	0.590550	0.295275	+	0.955412i	$0.404589\pi$
$242$	−3.42974e9	−0.0642824
$243$	−7.08358e10	−1.30324
$244$	1.20234e10	0.217157
$245$	8.73291e10	1.54850
$246$	−9.05538e10	−1.57652
$247$	−2.64953e10	−0.452932
$248$	2.08736e10	0.350401
$249$	−2.26315e10	−0.373092
$250$	8.45310e10	1.36863
$251$	2.94849e10	0.468887	0.234443	−	0.972130i	$-0.424673\pi$
$251$	2.94849e10	0.468887	0.234443	+	0.972130i	$0.424673\pi$
$252$	9.08070e9	0.141846
$253$	3.38258e10	0.519046
$254$	6.71469e10	1.01222
$255$	1.59814e11	2.36692
$256$	4.29497e9	0.0625000
$257$	−7.43216e10	−1.06271	−0.531356	−	0.847149i	$-0.678317\pi$
$257$	−7.43216e10	−1.06271	−0.531356	+	0.847149i	$0.678317\pi$
$258$	−7.64306e10	−1.07394
$259$	2.74437e10	0.378960
$260$	8.83835e10	1.19947
$261$	−5.84938e9	−0.0780239
$262$	9.27799e10	1.21646
$263$	−9.14662e10	−1.17885	−0.589426	−	0.807822i	$-0.700646\pi$
$263$	−9.14662e10	−1.17885	−0.589426	+	0.807822i	$0.700646\pi$
$264$	1.13426e10	0.143713
$265$	1.17880e11	1.46837
$266$	−6.65988e9	−0.0815641
$267$	−1.55932e11	−1.87773
$268$	−7.54203e10	−0.893063
$269$	8.70264e10	1.01336	0.506682	−	0.862133i	$-0.330872\pi$
$269$	8.70264e10	1.01336	0.506682	+	0.862133i	$0.330872\pi$
$270$	−2.67470e10	−0.306293
$271$	1.11400e11	1.25465	0.627325	−	0.778758i	$-0.284150\pi$
$271$	1.11400e11	1.25465	0.627325	+	0.778758i	$0.284150\pi$
$272$	−2.25065e10	−0.249315
$273$	−5.85075e10	−0.637500
$274$	−4.90147e9	−0.0525350
$275$	−6.00342e10	−0.632997
$276$	−1.11866e11	−1.16040
$277$	−1.68448e11	−1.71912	−0.859560	−	0.511034i	$-0.829263\pi$
$277$	−1.68448e11	−1.71912	−0.859560	+	0.511034i	$0.829263\pi$
$278$	−4.13838e10	−0.415555
$279$	−8.19999e10	−0.810205
$280$	2.22161e10	0.216002
$281$	2.04491e11	1.95657	0.978284	−	0.207270i	$-0.0664580\pi$
$281$	2.04491e11	1.95657	0.978284	+	0.207270i	$0.0664580\pi$
$282$	−5.84607e10	−0.550482
$283$	−1.77239e11	−1.64256	−0.821279	−	0.570526i	$-0.806739\pi$
$283$	−1.77239e11	−1.64256	−0.821279	+	0.570526i	$0.806739\pi$
$284$	2.46299e10	0.224662
$285$	−8.78678e10	−0.788911
$286$	−3.28713e10	−0.290516
$287$	6.59641e10	0.573904
$288$	−1.68724e10	−0.144514
$289$	−6.49254e8	−0.00547488
$290$	−1.43106e10	−0.118814
$291$	−8.12971e7	−0.000664595 0
$292$	8.04179e10	0.647336
$293$	2.49209e10	0.197542	0.0987710	−	0.995110i	$-0.468509\pi$
$293$	2.49209e10	0.197542	0.0987710	+	0.995110i	$0.468509\pi$
$294$	1.07413e11	0.838481
$295$	−5.63229e10	−0.432998
$296$	−5.09916e10	−0.386088
$297$	9.94765e9	0.0741851
$298$	−3.91661e10	−0.287698
$299$	3.24193e11	2.34576
$300$	1.98541e11	1.41516
$301$	5.56760e10	0.390948
$302$	−1.97931e10	−0.136925
$303$	−3.71160e11	−2.52970
$304$	1.23744e10	0.0830982
$305$	−1.15556e11	−0.764617
$306$	8.84146e10	0.576471
$307$	1.45670e11	0.935941	0.467970	−	0.883744i	$-0.344985\pi$
$307$	1.45670e11	0.935941	0.467970	+	0.883744i	$0.344985\pi$
$308$	−8.26255e9	−0.0523162
$309$	−1.84638e11	−1.15215
$310$	−2.00614e11	−1.23377
$311$	8.11585e10	0.491940	0.245970	−	0.969277i	$-0.420894\pi$
$311$	8.11585e10	0.491940	0.245970	+	0.969277i	$0.420894\pi$
$312$	1.08710e11	0.649490
$313$	−2.11097e11	−1.24318	−0.621589	−	0.783344i	$-0.713512\pi$
$313$	−2.11097e11	−1.24318	−0.621589	+	0.783344i	$0.713512\pi$
$314$	2.09445e11	1.21587
$315$	−8.72739e10	−0.499444
$316$	1.20861e11	0.681859
$317$	1.29844e11	0.722198	0.361099	−	0.932528i	$-0.382402\pi$
$317$	1.29844e11	0.722198	0.361099	+	0.932528i	$0.382402\pi$
$318$	1.44990e11	0.795090
$319$	5.32237e9	0.0287771
$320$	−4.12786e10	−0.220064
$321$	7.26072e10	0.381687
$322$	8.14894e10	0.422425
$323$	−6.48442e10	−0.331482
$324$	−1.13977e11	−0.574599
$325$	−5.75379e11	−2.86075
$326$	−5.50210e10	−0.269804
$327$	−1.19537e11	−0.578148
$328$	−1.22564e11	−0.584699
$329$	4.25858e10	0.200394
$330$	−1.09013e11	−0.506017
$331$	−2.58939e11	−1.18569	−0.592846	−	0.805316i	$-0.701996\pi$
$331$	−2.58939e11	−1.18569	−0.592846	+	0.805316i	$0.701996\pi$
$332$	−3.06317e10	−0.138372
$333$	2.00316e11	0.892722
$334$	1.06881e11	0.469937
$335$	7.24859e11	3.14450
$336$	2.73253e10	0.116960
$337$	1.51821e11	0.641207	0.320604	−	0.947213i	$-0.396114\pi$
$337$	1.51821e11	0.641207	0.320604	+	0.947213i	$0.396114\pi$
$338$	−1.45373e11	−0.605841
$339$	4.05616e11	1.66808
$340$	2.16308e11	0.877845
$341$	7.46119e10	0.298823
$342$	−4.86115e10	−0.192142
$343$	−1.67203e11	−0.652261
$344$	−1.03449e11	−0.398301
$345$	1.07514e12	4.08582
$346$	−8.50161e10	−0.318903
$347$	−3.16156e11	−1.17063	−0.585314	−	0.810807i	$-0.699029\pi$
$347$	−3.16156e11	−1.17063	−0.585314	+	0.810807i	$0.699029\pi$
$348$	−1.76018e10	−0.0643353
$349$	−1.68379e11	−0.607536	−0.303768	−	0.952746i	$-0.598245\pi$
$349$	−1.68379e11	−0.607536	−0.303768	+	0.952746i	$0.598245\pi$
$350$	−1.44628e11	−0.515164
$351$	9.53402e10	0.335269
$352$	1.53522e10	0.0533002
$353$	3.79299e11	1.30015	0.650077	−	0.759868i	$-0.274736\pi$
$353$	3.79299e11	1.30015	0.650077	+	0.759868i	$0.274736\pi$
$354$	−6.92760e10	−0.234460
$355$	−2.36716e11	−0.791043
$356$	−2.11054e11	−0.696414
$357$	−1.43190e11	−0.466559
$358$	5.20897e9	0.0167602
$359$	4.02527e11	1.27900	0.639499	−	0.768792i	$-0.279142\pi$
$359$	4.02527e11	1.27900	0.639499	+	0.768792i	$0.279142\pi$
$360$	1.62159e11	0.508838
$361$	−2.87036e11	−0.889515
$362$	1.21728e10	0.0372565
$363$	4.05437e10	0.122559
$364$	−7.91899e10	−0.236436
$365$	−7.72890e11	−2.27929
$366$	−1.42132e11	−0.414024
$367$	4.34171e11	1.24929	0.624645	−	0.780909i	$-0.285244\pi$
$367$	4.34171e11	1.24929	0.624645	+	0.780909i	$0.285244\pi$
$368$	−1.51411e11	−0.430371
$369$	4.81483e11	1.35195
$370$	4.90076e11	1.35943
$371$	−1.05618e11	−0.289439
$372$	−2.46751e11	−0.668061
$373$	4.50261e10	0.120441	0.0602205	−	0.998185i	$-0.480820\pi$
$373$	4.50261e10	0.120441	0.0602205	+	0.998185i	$0.480820\pi$
$374$	−8.04486e10	−0.212616
$375$	−9.99259e11	−2.60938
$376$	−7.91265e10	−0.204163
$377$	5.10106e10	0.130054
$378$	2.39648e10	0.0603754
$379$	−3.63318e11	−0.904505	−0.452252	−	0.891890i	$-0.649379\pi$
$379$	−3.63318e11	−0.904505	−0.452252	+	0.891890i	$0.649379\pi$
$380$	−1.18929e11	−0.292591
$381$	−7.93758e11	−1.92986
$382$	1.25929e11	0.302581
$383$	4.52314e11	1.07410	0.537051	−	0.843550i	$-0.319538\pi$
$383$	4.52314e11	1.07410	0.537051	+	0.843550i	$0.319538\pi$
$384$	−5.07717e10	−0.119160
$385$	7.94107e10	0.184207
$386$	6.24976e10	0.143291
$387$	4.06388e11	0.920962
$388$	−1.10036e8	−0.000246485 0
$389$	9.40852e10	0.208328	0.104164	−	0.994560i	$-0.466783\pi$
$389$	9.40852e10	0.208328	0.104164	+	0.994560i	$0.466783\pi$
$390$	−1.04480e12	−2.28688
$391$	7.93425e11	1.71676
$392$	1.45383e11	0.310976
$393$	−1.09677e12	−2.31926
$394$	−1.04935e11	−0.219374
$395$	−1.16159e12	−2.40085
$396$	−6.03096e10	−0.123242
$397$	−7.03662e11	−1.42170	−0.710848	−	0.703346i	$-0.751689\pi$
$397$	−7.03662e11	−1.42170	−0.710848	+	0.703346i	$0.751689\pi$
$398$	−1.63280e11	−0.326181
$399$	7.87279e10	0.155507
$400$	2.68725e11	0.524853
$401$	4.92476e11	0.951119	0.475560	−	0.879683i	$-0.342246\pi$
$401$	4.92476e11	0.951119	0.475560	+	0.879683i	$0.342246\pi$
$402$	8.91560e11	1.70268
$403$	7.15095e11	1.35049
$404$	−5.02364e11	−0.938215
$405$	1.09542e12	2.02318
$406$	1.28220e10	0.0234202
$407$	−1.82268e11	−0.329257
$408$	2.66054e11	0.475335
$409$	9.11259e10	0.161023	0.0805113	−	0.996754i	$-0.474345\pi$
$409$	9.11259e10	0.161023	0.0805113	+	0.996754i	$0.474345\pi$
$410$	1.17796e12	2.05874
$411$	5.79414e10	0.100161
$412$	−2.49908e11	−0.427309
$413$	5.04643e10	0.0853510
$414$	5.94804e11	0.995113
$415$	2.94398e11	0.487213
$416$	1.47138e11	0.240883
$417$	4.89206e11	0.792282
$418$	4.42317e10	0.0708664
$419$	3.87900e11	0.614833	0.307416	−	0.951575i	$-0.400536\pi$
$419$	3.87900e11	0.614833	0.307416	+	0.951575i	$0.400536\pi$
$420$	−2.62622e11	−0.411821
$421$	−3.33459e11	−0.517336	−0.258668	−	0.965966i	$-0.583283\pi$
$421$	−3.33459e11	−0.517336	−0.258668	+	0.965966i	$0.583283\pi$
$422$	−1.57201e11	−0.241295
$423$	3.10841e11	0.472070
$424$	1.96244e11	0.294883
$425$	−1.40817e12	−2.09366
$426$	−2.91156e11	−0.428333
$427$	1.03536e11	0.150719
$428$	9.82738e10	0.141560
$429$	3.88579e11	0.553887
$430$	9.94236e11	1.40243
$431$	6.20942e10	0.0866769	0.0433384	−	0.999060i	$-0.486201\pi$
$431$	6.20942e10	0.0866769	0.0433384	+	0.999060i	$0.486201\pi$
$432$	−4.45276e10	−0.0615110
$433$	−4.87435e11	−0.666378	−0.333189	−	0.942860i	$-0.608125\pi$
$433$	−4.87435e11	−0.666378	−0.333189	+	0.942860i	$0.608125\pi$
$434$	1.79747e11	0.243196
$435$	1.69169e11	0.226527
$436$	−1.61794e11	−0.214423
$437$	−4.36235e11	−0.572209
$438$	−9.50637e11	−1.23419
$439$	1.41595e11	0.181952	0.0909761	−	0.995853i	$-0.471001\pi$
$439$	1.41595e11	0.181952	0.0909761	+	0.995853i	$0.471001\pi$
$440$	−1.47549e11	−0.187672
$441$	−5.71124e11	−0.719046
$442$	−7.71035e11	−0.960891
$443$	−8.07817e11	−0.996544	−0.498272	−	0.867021i	$-0.666032\pi$
$443$	−8.07817e11	−0.996544	−0.498272	+	0.867021i	$0.666032\pi$
$444$	6.02783e11	0.736102
$445$	2.02842e12	2.45210
$446$	2.39586e11	0.286718
$447$	4.62991e11	0.548515
$448$	3.69848e10	0.0433783
$449$	−4.90099e11	−0.569083	−0.284542	−	0.958664i	$-0.591841\pi$
$449$	−4.90099e11	−0.569083	−0.284542	+	0.958664i	$0.591841\pi$
$450$	−1.05566e12	−1.21358
$451$	−4.38102e11	−0.498633
$452$	5.49001e11	0.618657
$453$	2.33978e11	0.261056
$454$	6.92492e11	0.765004
$455$	7.61087e11	0.832498
$456$	−1.46280e11	−0.158432
$457$	−5.58083e11	−0.598516	−0.299258	−	0.954172i	$-0.596739\pi$
$457$	−5.58083e11	−0.598516	−0.299258	+	0.954172i	$0.596739\pi$
$458$	−9.02377e9	−0.00958282
$459$	2.33334e11	0.245370
$460$	1.45520e12	1.51535
$461$	−1.86363e12	−1.92179	−0.960895	−	0.276912i	$-0.910689\pi$
$461$	−1.86363e12	−1.92179	−0.960895	+	0.276912i	$0.910689\pi$
$462$	9.76734e10	0.0997441
$463$	2.18349e11	0.220819	0.110410	−	0.993886i	$-0.464784\pi$
$463$	2.18349e11	0.220819	0.110410	+	0.993886i	$0.464784\pi$
$464$	−2.38240e10	−0.0238607
$465$	2.37151e12	2.35226
$466$	−8.61506e11	−0.846295
$467$	5.19773e11	0.505694	0.252847	−	0.967506i	$-0.418633\pi$
$467$	5.19773e11	0.505694	0.252847	+	0.967506i	$0.418633\pi$
$468$	−5.78019e11	−0.556975
$469$	−6.49459e11	−0.619832
$470$	7.60478e11	0.718863
$471$	−2.47590e12	−2.31814
$472$	−9.37649e10	−0.0869564
$473$	−3.69773e11	−0.339673
$474$	−1.42872e12	−1.30001
$475$	7.74232e11	0.697830
$476$	−1.93808e11	−0.173037
$477$	−7.70925e11	−0.681835
$478$	5.04729e11	0.442214
$479$	−6.53191e11	−0.566931	−0.283466	−	0.958982i	$-0.591484\pi$
$479$	−6.53191e11	−0.566931	−0.283466	+	0.958982i	$0.591484\pi$
$480$	4.87963e11	0.419567
$481$	−1.74689e12	−1.48803
$482$	−4.94827e11	−0.417582
$483$	−9.63304e11	−0.805381
$484$	5.48759e10	0.0454545
$485$	1.05754e9	0.000867881 0
$486$	1.13337e12	0.921530
$487$	−1.54196e12	−1.24221	−0.621103	−	0.783729i	$-0.713315\pi$
$487$	−1.54196e12	−1.24221	−0.621103	+	0.783729i	$0.713315\pi$
$488$	−1.92375e11	−0.153553
$489$	6.50415e11	0.514400
$490$	−1.39727e12	−1.09496
$491$	5.70372e11	0.442885	0.221443	−	0.975173i	$-0.428923\pi$
$491$	5.70372e11	0.442885	0.221443	+	0.975173i	$0.428923\pi$
$492$	1.44886e12	1.11477
$493$	1.24842e11	0.0951811
$494$	4.23925e11	0.320271
$495$	5.79631e11	0.433939
$496$	−3.33978e11	−0.247771
$497$	2.12093e11	0.155927
$498$	3.62104e11	0.263816
$499$	1.75816e12	1.26942	0.634712	−	0.772749i	$-0.281119\pi$
$499$	1.75816e12	1.26942	0.634712	+	0.772749i	$0.281119\pi$
$500$	−1.35250e12	−0.967767
$501$	−1.26346e12	−0.895966
$502$	−4.71759e11	−0.331553
$503$	1.44858e11	0.100899	0.0504494	−	0.998727i	$-0.483935\pi$
$503$	1.44858e11	0.100899	0.0504494	+	0.998727i	$0.483935\pi$
$504$	−1.45291e11	−0.100300
$505$	4.82818e12	3.30348
$506$	−5.41213e11	−0.367021
$507$	1.71849e12	1.15507
$508$	−1.07435e12	−0.715747
$509$	−9.44243e11	−0.623525	−0.311762	−	0.950160i	$-0.600919\pi$
$509$	−9.44243e11	−0.623525	−0.311762	+	0.950160i	$0.600919\pi$
$510$	−2.55703e12	−1.67367
$511$	6.92494e11	0.449285
$512$	−6.87195e10	−0.0441942
$513$	−1.28290e11	−0.0817833
$514$	1.18914e12	0.751451
$515$	2.40184e12	1.50457
$516$	1.22289e12	0.759387
$517$	−2.82835e11	−0.174111
$518$	−4.39099e11	−0.267965
$519$	1.00499e12	0.608009
$520$	−1.41414e12	−0.848157
$521$	−2.85515e12	−1.69769	−0.848846	−	0.528641i	$-0.822702\pi$
$521$	−2.85515e12	−1.69769	−0.848846	+	0.528641i	$0.822702\pi$
$522$	9.35901e10	0.0551712
$523$	−1.06535e12	−0.622637	−0.311319	−	0.950306i	$-0.600771\pi$
$523$	−1.06535e12	−0.622637	−0.311319	+	0.950306i	$0.600771\pi$
$524$	−1.48448e12	−0.860168
$525$	1.70968e12	0.982193
$526$	1.46346e12	0.833575
$527$	1.75011e12	0.988366
$528$	−1.81482e11	−0.101620
$529$	3.53657e12	1.96350
$530$	−1.88608e12	−1.03829
$531$	3.68347e11	0.201063
$532$	1.06558e11	0.0576745
$533$	−4.19885e12	−2.25350
$534$	2.49491e12	1.32776
$535$	−9.44501e11	−0.498437
$536$	1.20673e12	0.631491
$537$	−6.15764e10	−0.0319543
$538$	−1.39242e12	−0.716557
$539$	5.19667e11	0.265201
$540$	4.27951e11	0.216582
$541$	1.06296e12	0.533492	0.266746	−	0.963767i	$-0.414051\pi$
$541$	1.06296e12	0.533492	0.266746	+	0.963767i	$0.414051\pi$
$542$	−1.78240e12	−0.887171
$543$	−1.43898e11	−0.0710320
$544$	3.60104e11	0.176292
$545$	1.55498e12	0.754991
$546$	9.36121e11	0.450780
$547$	−3.23462e11	−0.154483	−0.0772414	−	0.997012i	$-0.524611\pi$
$547$	−3.23462e11	−0.154483	−0.0772414	+	0.997012i	$0.524611\pi$
$548$	7.84236e10	0.0371479
$549$	7.55727e11	0.355050
$550$	9.60547e11	0.447597
$551$	−6.86400e10	−0.0317245
$552$	1.78986e12	0.820529
$553$	1.04076e12	0.473246
$554$	2.69517e12	1.21560
$555$	−5.79330e12	−2.59184
$556$	6.62140e11	0.293842
$557$	2.93068e12	1.29009	0.645044	−	0.764145i	$-0.276839\pi$
$557$	2.93068e12	1.29009	0.645044	+	0.764145i	$0.276839\pi$
$558$	1.31200e12	0.572901
$559$	−3.54398e12	−1.53510
$560$	−3.55458e11	−0.152736
$561$	9.51001e11	0.405367
$562$	−3.27185e12	−1.38350
$563$	1.56282e12	0.655573	0.327786	−	0.944752i	$-0.393697\pi$
$563$	1.56282e12	0.655573	0.327786	+	0.944752i	$0.393697\pi$
$564$	9.35371e11	0.389249
$565$	−5.27640e12	−2.17831
$566$	2.83583e12	1.16146
$567$	−9.81478e11	−0.398801
$568$	−3.94079e11	−0.158860
$569$	3.28052e12	1.31201	0.656006	−	0.754756i	$-0.272245\pi$
$569$	3.28052e12	1.31201	0.656006	+	0.754756i	$0.272245\pi$
$570$	1.40589e12	0.557844
$571$	−6.20049e11	−0.244097	−0.122049	−	0.992524i	$-0.538946\pi$
$571$	−6.20049e11	−0.244097	−0.122049	+	0.992524i	$0.538946\pi$
$572$	5.25941e11	0.205426
$573$	−1.48864e12	−0.576890
$574$	−1.05543e12	−0.405811
$575$	−9.47340e12	−3.61410
$576$	2.69958e11	0.102187
$577$	−2.32034e12	−0.871487	−0.435743	−	0.900071i	$-0.643515\pi$
$577$	−2.32034e12	−0.871487	−0.435743	+	0.900071i	$0.643515\pi$
$578$	1.03881e10	0.00387132
$579$	−7.38797e11	−0.273194
$580$	2.28970e11	0.0840142
$581$	−2.63775e11	−0.0960376
$582$	1.30075e9	0.000469939 0
$583$	7.01466e11	0.251477
$584$	−1.28669e12	−0.457736
$585$	5.55530e12	1.96113
$586$	−3.98734e11	−0.139683
$587$	6.88316e11	0.239286	0.119643	−	0.992817i	$-0.461825\pi$
$587$	6.88316e11	0.239286	0.119643	+	0.992817i	$0.461825\pi$
$588$	−1.71861e12	−0.592896
$589$	−9.62234e11	−0.329429
$590$	9.01167e11	0.306176
$591$	1.24045e12	0.418251
$592$	8.15866e11	0.273005
$593$	5.94630e12	1.97470	0.987349	−	0.158564i	$-0.0506865\pi$
$593$	5.94630e12	1.97470	0.987349	+	0.158564i	$0.0506865\pi$
$594$	−1.59162e11	−0.0524568
$595$	1.86267e12	0.609270
$596$	6.26658e11	0.203433
$597$	1.93017e12	0.621886
$598$	−5.18709e12	−1.65870
$599$	5.79992e12	1.84078	0.920389	−	0.391004i	$-0.127872\pi$
$599$	5.79992e12	1.84078	0.920389	+	0.391004i	$0.127872\pi$
$600$	−3.17666e12	−1.00067
$601$	−8.30988e11	−0.259812	−0.129906	−	0.991526i	$-0.541468\pi$
$601$	−8.30988e11	−0.259812	−0.129906	+	0.991526i	$0.541468\pi$
$602$	−8.90816e11	−0.276442
$603$	−4.74051e12	−1.46015
$604$	3.16689e11	0.0968204
$605$	−5.27407e11	−0.160047
$606$	5.93855e12	1.78877
$607$	−3.51569e12	−1.05114	−0.525572	−	0.850749i	$-0.676149\pi$
$607$	−3.51569e12	−1.05114	−0.525572	+	0.850749i	$0.676149\pi$
$608$	−1.97990e11	−0.0587593
$609$	−1.51572e11	−0.0446521
$610$	1.84890e12	0.540666
$611$	−2.71074e12	−0.786870
$612$	−1.41463e12	−0.407627
$613$	−3.60928e12	−1.03240	−0.516200	−	0.856468i	$-0.672654\pi$
$613$	−3.60928e12	−1.03240	−0.516200	+	0.856468i	$0.672654\pi$
$614$	−2.33072e12	−0.661810
$615$	−1.39249e13	−3.92512
$616$	1.32201e11	0.0369931
$617$	−7.62853e10	−0.0211913	−0.0105956	−	0.999944i	$-0.503373\pi$
$617$	−7.62853e10	−0.0211913	−0.0105956	+	0.999944i	$0.503373\pi$
$618$	2.95421e12	0.814692
$619$	3.86697e11	0.105868	0.0529338	−	0.998598i	$-0.483143\pi$
$619$	3.86697e11	0.105868	0.0529338	+	0.998598i	$0.483143\pi$
$620$	3.20983e12	0.872408
$621$	1.56974e12	0.423560
$622$	−1.29854e12	−0.347854
$623$	−1.81742e12	−0.483348
$624$	−1.73936e12	−0.459259
$625$	4.99010e12	1.30812
$626$	3.37756e12	0.879059
$627$	−5.22873e11	−0.135111
$628$	−3.35112e12	−0.859750
$629$	−4.27530e12	−1.08903
$630$	1.39638e12	0.353160
$631$	2.41960e12	0.607590	0.303795	−	0.952737i	$-0.401746\pi$
$631$	2.41960e12	0.607590	0.303795	+	0.952737i	$0.401746\pi$
$632$	−1.93378e12	−0.482147
$633$	1.85830e12	0.460044
$634$	−2.07751e12	−0.510671
$635$	1.03255e13	2.52017
$636$	−2.31984e12	−0.562213
$637$	4.98059e12	1.19854
$638$	−8.51578e10	−0.0203485
$639$	1.54810e12	0.367321
$640$	6.60457e11	0.155609
$641$	4.18228e12	0.978479	0.489240	−	0.872149i	$-0.337274\pi$
$641$	4.18228e12	0.978479	0.489240	+	0.872149i	$0.337274\pi$
$642$	−1.16172e12	−0.269893
$643$	7.26993e12	1.67718	0.838592	−	0.544759i	$-0.183379\pi$
$643$	7.26993e12	1.67718	0.838592	+	0.544759i	$0.183379\pi$
$644$	−1.30383e12	−0.298700
$645$	−1.17531e13	−2.67383
$646$	1.03751e12	0.234393
$647$	−4.26279e12	−0.956367	−0.478184	−	0.878260i	$-0.658705\pi$
$647$	−4.26279e12	−0.956367	−0.478184	+	0.878260i	$0.658705\pi$
$648$	1.82363e12	0.406303
$649$	−3.35159e11	−0.0741566
$650$	9.20607e12	2.02285
$651$	−2.12482e12	−0.463670
$652$	8.80336e11	0.190781
$653$	1.88103e12	0.404842	0.202421	−	0.979299i	$-0.435119\pi$
$653$	1.88103e12	0.404842	0.202421	+	0.979299i	$0.435119\pi$
$654$	1.91260e12	0.408812
$655$	1.42672e13	3.02868
$656$	1.96103e12	0.413444
$657$	5.05462e12	1.05839
$658$	−6.81373e11	−0.141700
$659$	6.17779e11	0.127599	0.0637997	−	0.997963i	$-0.479678\pi$
$659$	6.17779e11	0.127599	0.0637997	+	0.997963i	$0.479678\pi$
$660$	1.74421e12	0.357808
$661$	6.02327e12	1.22723	0.613615	−	0.789606i	$-0.289715\pi$
$661$	6.02327e12	1.22723	0.613615	+	0.789606i	$0.289715\pi$
$662$	4.14303e12	0.838410
$663$	9.11458e12	1.83200
$664$	4.90107e11	0.0978440
$665$	−1.02412e12	−0.203074
$666$	−3.20505e12	−0.631250
$667$	8.39869e11	0.164303
$668$	−1.71009e12	−0.332296
$669$	−2.83220e12	−0.546647
$670$	−1.15977e13	−2.22350
$671$	−6.87637e11	−0.130951
$672$	−4.37205e11	−0.0827035
$673$	−1.39486e12	−0.262098	−0.131049	−	0.991376i	$-0.541835\pi$
$673$	−1.39486e12	−0.262098	−0.131049	+	0.991376i	$0.541835\pi$
$674$	−2.42914e12	−0.453402
$675$	−2.78598e12	−0.516548
$676$	2.32597e12	0.428394
$677$	−6.10159e12	−1.11633	−0.558166	−	0.829729i	$-0.688495\pi$
$677$	−6.10159e12	−1.11633	−0.558166	+	0.829729i	$0.688495\pi$
$678$	−6.48986e12	−1.17951
$679$	−9.47538e8	−0.000171073 0
$680$	−3.46093e12	−0.620730
$681$	−8.18610e12	−1.45853
$682$	−1.19379e12	−0.211300
$683$	−6.10991e12	−1.07434	−0.537170	−	0.843474i	$-0.680507\pi$
$683$	−6.10991e12	−1.07434	−0.537170	+	0.843474i	$0.680507\pi$
$684$	7.77784e11	0.135865
$685$	−7.53722e11	−0.130799
$686$	2.67525e12	0.461218
$687$	1.06672e11	0.0182703
$688$	1.65518e12	0.281642
$689$	6.72299e12	1.13652
$690$	−1.72022e13	−2.88911
$691$	−7.75696e11	−0.129432	−0.0647158	−	0.997904i	$-0.520614\pi$
$691$	−7.75696e11	−0.129432	−0.0647158	+	0.997904i	$0.520614\pi$
$692$	1.36026e12	0.225498
$693$	−5.19338e11	−0.0855363
$694$	5.05850e12	0.827759
$695$	−6.36377e12	−1.03463
$696$	2.81628e11	0.0454919
$697$	−1.02762e13	−1.64924
$698$	2.69406e12	0.429593
$699$	1.01841e13	1.61352
$700$	2.31404e12	0.364276
$701$	−2.09348e12	−0.327444	−0.163722	−	0.986507i	$-0.552350\pi$
$701$	−2.09348e12	−0.327444	−0.163722	+	0.986507i	$0.552350\pi$
$702$	−1.52544e12	−0.237071
$703$	2.35062e12	0.362980
$704$	−2.45635e11	−0.0376889
$705$	−8.98978e12	−1.37056
$706$	−6.06878e12	−0.919348
$707$	−4.32595e12	−0.651170
$708$	1.10842e12	0.165788
$709$	−4.28679e12	−0.637125	−0.318562	−	0.947902i	$-0.603200\pi$
$709$	−4.28679e12	−0.637125	−0.318562	+	0.947902i	$0.603200\pi$
$710$	3.78746e12	0.559352
$711$	7.59666e12	1.11483
$712$	3.37686e12	0.492439
$713$	1.17738e13	1.70613
$714$	2.29104e12	0.329907
$715$	−5.05478e12	−0.723310
$716$	−8.33435e10	−0.0118512
$717$	−5.96651e12	−0.843110
$718$	−6.44043e12	−0.904388
$719$	4.92092e12	0.686699	0.343350	−	0.939208i	$-0.388438\pi$
$719$	4.92092e12	0.686699	0.343350	+	0.939208i	$0.388438\pi$
$720$	−2.59454e12	−0.359803
$721$	−2.15200e12	−0.296575
$722$	4.59257e12	0.628982
$723$	5.84945e12	0.796146
$724$	−1.94765e11	−0.0263444
$725$	−1.49060e12	−0.200374
$726$	−6.48700e11	−0.0866620
$727$	7.19986e12	0.955915	0.477958	−	0.878383i	$-0.341377\pi$
$727$	7.19986e12	0.955915	0.477958	+	0.878383i	$0.341377\pi$
$728$	1.26704e12	0.167185
$729$	−4.63453e12	−0.607759
$730$	1.23662e13	1.61170
$731$	−8.67347e12	−1.12348
$732$	2.27411e12	0.292759
$733$	8.32628e12	1.06533	0.532664	−	0.846327i	$-0.321191\pi$
$733$	8.32628e12	1.06533	0.532664	+	0.846327i	$0.321191\pi$
$734$	−6.94673e12	−0.883382
$735$	1.65174e13	2.08760
$736$	2.42258e12	0.304318
$737$	4.31340e12	0.538537
$738$	−7.70372e12	−0.955976
$739$	−1.25820e13	−1.55185	−0.775927	−	0.630823i	$-0.782717\pi$
$739$	−1.25820e13	−1.55185	−0.775927	+	0.630823i	$0.782717\pi$
$740$	−7.84122e12	−0.961260
$741$	−5.01131e12	−0.610618
$742$	1.68989e12	0.204664
$743$	−7.40687e12	−0.891631	−0.445815	−	0.895125i	$-0.647086\pi$
$743$	−7.40687e12	−0.891631	−0.445815	+	0.895125i	$0.647086\pi$
$744$	3.94802e12	0.472391
$745$	−6.02276e12	−0.716295
$746$	−7.20417e11	−0.0851646
$747$	−1.92534e12	−0.226237
$748$	1.28718e12	0.150342
$749$	8.46255e11	0.0982501
$750$	1.59881e13	1.84511
$751$	3.83379e12	0.439793	0.219897	−	0.975523i	$-0.429428\pi$
$751$	3.83379e12	0.439793	0.219897	+	0.975523i	$0.429428\pi$
$752$	1.26602e12	0.144365
$753$	5.57676e12	0.632127
$754$	−8.16169e11	−0.0919622
$755$	−3.04367e12	−0.340907
$756$	−3.83436e11	−0.0426918
$757$	−6.77747e12	−0.750129	−0.375065	−	0.926999i	$-0.622379\pi$
$757$	−6.77747e12	−0.750129	−0.375065	+	0.926999i	$0.622379\pi$
$758$	5.81309e12	0.639581
$759$	6.39780e12	0.699750
$760$	1.90286e12	0.206893
$761$	1.31604e12	0.142245	0.0711225	−	0.997468i	$-0.477342\pi$
$761$	1.31604e12	0.142245	0.0711225	+	0.997468i	$0.477342\pi$
$762$	1.27001e13	1.36462
$763$	−1.39324e12	−0.148821
$764$	−2.01487e12	−0.213957
$765$	1.35959e13	1.43527
$766$	−7.23703e12	−0.759505
$767$	−3.21223e12	−0.335141
$768$	8.12348e11	0.0842590
$769$	−1.08905e13	−1.12300	−0.561502	−	0.827475i	$-0.689776\pi$
$769$	−1.08905e13	−1.12300	−0.561502	+	0.827475i	$0.689776\pi$
$770$	−1.27057e12	−0.130254
$771$	−1.40571e13	−1.43269
$772$	−9.99961e11	−0.101322
$773$	3.38512e12	0.341009	0.170505	−	0.985357i	$-0.445460\pi$
$773$	3.38512e12	0.341009	0.170505	+	0.985357i	$0.445460\pi$
$774$	−6.50221e12	−0.651218
$775$	−2.08961e13	−2.08069
$776$	1.76057e9	0.000174291 0
$777$	5.19068e12	0.510893
$778$	−1.50536e12	−0.147310
$779$	5.64999e12	0.549704
$780$	1.67168e13	1.61707
$781$	−1.40862e12	−0.135477
$782$	−1.26948e13	−1.21394
$783$	2.46992e11	0.0234831
$784$	−2.32613e12	−0.219893
$785$	3.22074e13	3.02721
$786$	1.75483e13	1.63997
$787$	−1.50098e12	−0.139473	−0.0697363	−	0.997565i	$-0.522216\pi$
$787$	−1.50098e12	−0.139473	−0.0697363	+	0.997565i	$0.522216\pi$
$788$	1.67895e12	0.155121
$789$	−1.72999e13	−1.58926
$790$	1.85854e13	1.69765
$791$	4.72755e12	0.429380
$792$	9.64954e11	0.0871452
$793$	−6.59045e12	−0.591815
$794$	1.12586e13	1.00529
$795$	2.22958e13	1.97957
$796$	2.61248e12	0.230645
$797$	−1.21980e13	−1.07084	−0.535422	−	0.844584i	$-0.679848\pi$
$797$	−1.21980e13	−1.07084	−0.535422	+	0.844584i	$0.679848\pi$
$798$	−1.25965e12	−0.109960
$799$	−6.63422e12	−0.575877
$800$	−4.29960e12	−0.371127
$801$	−1.32657e13	−1.13863
$802$	−7.87961e12	−0.672543
$803$	−4.59921e12	−0.390358
$804$	−1.42650e13	−1.20398
$805$	1.25310e13	1.05173
$806$	−1.14415e13	−0.954940
$807$	1.64601e13	1.36616
$808$	8.03782e12	0.663418
$809$	−1.56863e13	−1.28751	−0.643756	−	0.765231i	$-0.722625\pi$
$809$	−1.56863e13	−1.28751	−0.643756	+	0.765231i	$0.722625\pi$
$810$	−1.75268e13	−1.43060
$811$	3.09157e12	0.250949	0.125474	−	0.992097i	$-0.459955\pi$
$811$	3.09157e12	0.250949	0.125474	+	0.992097i	$0.459955\pi$
$812$	−2.05153e11	−0.0165606
$813$	2.10701e13	1.69145
$814$	2.91628e12	0.232820
$815$	−8.46083e12	−0.671744
$816$	−4.25687e12	−0.336112
$817$	4.76879e12	0.374463
$818$	−1.45801e12	−0.113860
$819$	−4.97744e12	−0.386570
$820$	−1.88473e13	−1.45575
$821$	2.33449e13	1.79328	0.896640	−	0.442760i	$-0.146001\pi$
$821$	2.33449e13	1.79328	0.896640	+	0.442760i	$0.146001\pi$
$822$	−9.27062e11	−0.0708248
$823$	2.00619e13	1.52431	0.762154	−	0.647395i	$-0.224142\pi$
$823$	2.00619e13	1.52431	0.762154	+	0.647395i	$0.224142\pi$
$824$	3.99852e12	0.302153
$825$	−1.13548e13	−0.853372
$826$	−8.07428e11	−0.0603523
$827$	−6.86223e11	−0.0510142	−0.0255071	−	0.999675i	$-0.508120\pi$
$827$	−6.86223e11	−0.0510142	−0.0255071	+	0.999675i	$0.508120\pi$
$828$	−9.51686e12	−0.703651
$829$	5.06613e12	0.372547	0.186273	−	0.982498i	$-0.440359\pi$
$829$	5.06613e12	0.372547	0.186273	+	0.982498i	$0.440359\pi$
$830$	−4.71037e12	−0.344512
$831$	−3.18601e13	−2.31762
$832$	−2.35422e12	−0.170330
$833$	1.21894e13	0.877162
$834$	−7.82730e12	−0.560228
$835$	1.64355e13	1.17002
$836$	−7.07707e11	−0.0501101
$837$	3.46248e12	0.243850
$838$	−6.20640e12	−0.434752
$839$	−5.52927e12	−0.385246	−0.192623	−	0.981273i	$-0.561700\pi$
$839$	−5.52927e12	−0.385246	−0.192623	+	0.981273i	$0.561700\pi$
$840$	4.20194e12	0.291201
$841$	−1.43750e13	−0.990891
$842$	5.33534e12	0.365812
$843$	3.86772e13	2.63774
$844$	2.51521e12	0.170621
$845$	−2.23547e13	−1.50839
$846$	−4.97345e12	−0.333804
$847$	4.72547e11	0.0315478
$848$	−3.13990e12	−0.208514
$849$	−3.35229e13	−2.21441
$850$	2.25308e13	1.48044
$851$	−2.87619e13	−1.87990
$852$	4.65849e12	0.302877
$853$	6.87361e12	0.444543	0.222272	−	0.974985i	$-0.428653\pi$
$853$	6.87361e12	0.444543	0.222272	+	0.974985i	$0.428653\pi$
$854$	−1.65658e12	−0.106574
$855$	−7.47522e12	−0.478384
$856$	−1.57238e12	−0.100098
$857$	−2.49989e13	−1.58310	−0.791549	−	0.611105i	$-0.790725\pi$
$857$	−2.49989e13	−1.58310	−0.791549	+	0.611105i	$0.790725\pi$
$858$	−6.21726e12	−0.391657
$859$	−1.08514e13	−0.680015	−0.340007	−	0.940423i	$-0.610430\pi$
$859$	−1.08514e13	−0.680015	−0.340007	+	0.940423i	$0.610430\pi$
$860$	−1.59078e13	−0.991669
$861$	1.24764e13	0.773706
$862$	−9.93507e11	−0.0612898
$863$	2.71064e13	1.66350	0.831752	−	0.555148i	$-0.187338\pi$
$863$	2.71064e13	1.66350	0.831752	+	0.555148i	$0.187338\pi$
$864$	7.12442e11	0.0434948
$865$	−1.30733e13	−0.793987
$866$	7.79895e12	0.471201
$867$	−1.22800e11	−0.00738093
$868$	−2.87595e12	−0.171966
$869$	−6.91221e12	−0.411176
$870$	−2.70671e12	−0.160179
$871$	4.13404e13	2.43385
$872$	2.58870e12	0.151620
$873$	−6.91623e9	−0.000403000 0
$874$	6.97976e12	0.404613
$875$	−1.16466e13	−0.671681
$876$	1.52102e13	0.872703
$877$	−1.69499e13	−0.967538	−0.483769	−	0.875196i	$-0.660733\pi$
$877$	−1.69499e13	−0.967538	−0.483769	+	0.875196i	$0.660733\pi$
$878$	−2.26552e12	−0.128660
$879$	4.71353e12	0.266315
$880$	2.36078e12	0.132704
$881$	2.93529e11	0.0164157	0.00820786	−	0.999966i	$-0.497387\pi$
$881$	2.93529e11	0.0164157	0.00820786	+	0.999966i	$0.497387\pi$
$882$	9.13798e12	0.508442
$883$	1.76883e13	0.979179	0.489590	−	0.871953i	$-0.337147\pi$
$883$	1.76883e13	0.979179	0.489590	+	0.871953i	$0.337147\pi$
$884$	1.23366e13	0.679452
$885$	−1.06529e13	−0.583744
$886$	1.29251e13	0.704663
$887$	5.09705e12	0.276479	0.138240	−	0.990399i	$-0.455856\pi$
$887$	5.09705e12	0.276479	0.138240	+	0.990399i	$0.455856\pi$
$888$	−9.64453e12	−0.520503
$889$	−9.25144e12	−0.496766
$890$	−3.24547e13	−1.73389
$891$	6.51850e12	0.346496
$892$	−3.83338e12	−0.202740
$893$	3.64758e12	0.191943
$894$	−7.40786e12	−0.387859
$895$	8.01008e11	0.0417285
$896$	−5.91757e11	−0.0306731
$897$	6.13178e13	3.16243
$898$	7.84159e12	0.402403
$899$	1.85256e12	0.0945917
$900$	1.68906e13	0.858129
$901$	1.64537e13	0.831769
$902$	7.00963e12	0.352587
$903$	1.05305e13	0.527055
$904$	−8.78401e12	−0.437457
$905$	1.87187e12	0.0927593
$906$	−3.74365e12	−0.184594
$907$	−9.79174e12	−0.480427	−0.240213	−	0.970720i	$-0.577217\pi$
$907$	−9.79174e12	−0.480427	−0.240213	+	0.970720i	$0.577217\pi$
$908$	−1.10799e13	−0.540940
$909$	−3.15758e13	−1.53397
$910$	−1.21774e13	−0.588665
$911$	1.93322e12	0.0929925	0.0464963	−	0.998918i	$-0.485194\pi$
$911$	1.93322e12	0.0929925	0.0464963	+	0.998918i	$0.485194\pi$
$912$	2.34048e12	0.112028
$913$	1.75187e12	0.0834416
$914$	8.92933e12	0.423215
$915$	−2.18562e13	−1.03081
$916$	1.44380e11	0.00677608
$917$	−1.27831e13	−0.597002
$918$	−3.73334e12	−0.173502
$919$	2.13681e13	0.988202	0.494101	−	0.869405i	$-0.335497\pi$
$919$	2.13681e13	0.988202	0.494101	+	0.869405i	$0.335497\pi$
$920$	−2.32832e13	−1.07151
$921$	2.75520e13	1.26178
$922$	2.98181e13	1.35891
$923$	−1.35005e13	−0.612268
$924$	−1.56277e12	−0.0705298
$925$	5.10466e13	2.29261
$926$	−3.49359e12	−0.156143
$927$	−1.57078e13	−0.698645
$928$	3.81183e11	0.0168721
$929$	2.58137e13	1.13705	0.568526	−	0.822666i	$-0.307514\pi$
$929$	2.58137e13	1.13705	0.568526	+	0.822666i	$0.307514\pi$
$930$	−3.79441e13	−1.66330
$931$	−6.70189e12	−0.292364
$932$	1.37841e13	0.598421
$933$	1.53503e13	0.663206
$934$	−8.31637e12	−0.357580
$935$	−1.23710e13	−0.529360
$936$	9.24831e12	0.393841
$937$	−7.55081e12	−0.320011	−0.160006	−	0.987116i	$-0.551151\pi$
$937$	−7.55081e12	−0.320011	−0.160006	+	0.987116i	$0.551151\pi$
$938$	1.03913e13	0.438288
$939$	−3.99268e13	−1.67598
$940$	−1.21676e13	−0.508313
$941$	3.28851e13	1.36724	0.683622	−	0.729836i	$-0.260404\pi$
$941$	3.28851e13	1.36724	0.683622	+	0.729836i	$0.260404\pi$
$942$	3.96144e13	1.63917
$943$	−6.91325e13	−2.84695
$944$	1.50024e12	0.0614874
$945$	3.68517e12	0.150319
$946$	5.91637e12	0.240185
$947$	7.81276e12	0.315667	0.157834	−	0.987466i	$-0.449549\pi$
$947$	7.81276e12	0.315667	0.157834	+	0.987466i	$0.449549\pi$
$948$	2.28596e13	0.919245
$949$	−4.40797e13	−1.76417
$950$	−1.23877e13	−0.493441
$951$	2.45587e13	0.973627
$952$	3.10093e12	0.122356
$953$	2.01384e13	0.790874	0.395437	−	0.918493i	$-0.370593\pi$
$953$	2.01384e13	0.790874	0.395437	+	0.918493i	$0.370593\pi$
$954$	1.23348e13	0.482130
$955$	1.93647e13	0.753349
$956$	−8.07566e12	−0.312693
$957$	1.00667e12	0.0387957
$958$	1.04511e13	0.400881
$959$	6.75321e11	0.0257826
$960$	−7.80741e12	−0.296679
$961$	−4.69440e11	−0.0177552
$962$	2.79502e13	1.05220
$963$	6.17695e12	0.231449
$964$	7.91723e12	0.295275
$965$	9.61054e12	0.356759
$966$	1.54129e13	0.569490
$967$	5.61159e12	0.206380	0.103190	−	0.994662i	$-0.467095\pi$
$967$	5.61159e12	0.206380	0.103190	+	0.994662i	$0.467095\pi$
$968$	−8.78014e11	−0.0321412
$969$	−1.22646e13	−0.446885
$970$	−1.69207e10	−0.000613684 0
$971$	6.58858e12	0.237851	0.118926	−	0.992903i	$-0.462055\pi$
$971$	6.58858e12	0.237851	0.118926	+	0.992903i	$0.462055\pi$
$972$	−1.81340e13	−0.651620
$973$	5.70182e12	0.203941
$974$	2.46714e13	0.878372
$975$	−1.08827e14	−3.85670
$976$	3.07800e12	0.108579
$977$	−3.61838e13	−1.27054	−0.635270	−	0.772290i	$-0.719111\pi$
$977$	−3.61838e13	−1.27054	−0.635270	+	0.772290i	$0.719111\pi$
$978$	−1.04066e13	−0.363735
$979$	1.20704e13	0.419954
$980$	2.23562e13	0.774251
$981$	−1.01694e13	−0.350580
$982$	−9.12595e12	−0.313167
$983$	−2.35569e13	−0.804687	−0.402343	−	0.915489i	$-0.631804\pi$
$983$	−2.35569e13	−0.804687	−0.402343	+	0.915489i	$0.631804\pi$
$984$	−2.31818e13	−0.788259
$985$	−1.61363e13	−0.546186
$986$	−1.99748e12	−0.0673032
$987$	8.05466e12	0.270159
$988$	−6.78280e12	−0.226466
$989$	−5.83503e13	−1.93936
$990$	−9.27410e12	−0.306841
$991$	−5.79054e13	−1.90716	−0.953581	−	0.301136i	$-0.902634\pi$
$991$	−5.79054e13	−1.90716	−0.953581	+	0.301136i	$0.902634\pi$
$992$	5.34364e12	0.175200
$993$	−4.89756e13	−1.59848
$994$	−3.39349e12	−0.110257
$995$	−2.51083e13	−0.812108
$996$	−5.79366e12	−0.186546
$997$	1.95220e13	0.625742	0.312871	−	0.949796i	$-0.398709\pi$
$997$	1.95220e13	0.625742	0.312871	+	0.949796i	$0.398709\pi$
$998$	−2.81306e13	−0.897619
$999$	−8.45841e12	−0.268685

Twists

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

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

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +189.139 q^{3} +256.000 q^{4} -2460.39 q^{5} -3026.23 q^{6} +2204.47 q^{7} -4096.00 q^{8} +16090.7 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} +189.139 q^{3} +256.000 q^{4} -2460.39 q^{5} -3026.23 q^{6} +2204.47 q^{7} -4096.00 q^{8} +16090.7 q^{9} +39366.3 q^{10} -14641.0 q^{11} +48419.7 q^{12} -140322. q^{13} -35271.5 q^{14} -465358. q^{15} +65536.0 q^{16} -343422. q^{17} -257452. q^{18} +188818. q^{19} -629861. q^{20} +416951. q^{21} +234256. q^{22} -2.31035e6 q^{23} -774715. q^{24} +4.10042e6 q^{25} +2.24515e6 q^{26} -679438. q^{27} +564343. q^{28} -363525. q^{29} +7.44572e6 q^{30} -5.09609e6 q^{31} -1.04858e6 q^{32} -2.76919e6 q^{33} +5.49475e6 q^{34} -5.42386e6 q^{35} +4.11923e6 q^{36} +1.24491e7 q^{37} -3.02109e6 q^{38} -2.65405e7 q^{39} +1.00778e7 q^{40} +2.99230e7 q^{41} -6.67122e6 q^{42} +2.52560e7 q^{43} -3.74810e6 q^{44} -3.95896e7 q^{45} +3.69656e7 q^{46} +1.93180e7 q^{47} +1.23954e7 q^{48} -3.54939e7 q^{49} -6.56067e7 q^{50} -6.49546e7 q^{51} -3.59225e7 q^{52} -4.79111e7 q^{53} +1.08710e7 q^{54} +3.60226e7 q^{55} -9.02949e6 q^{56} +3.57129e7 q^{57} +5.81640e6 q^{58} +2.28918e7 q^{59} -1.19132e8 q^{60} +4.69665e7 q^{61} +8.15375e7 q^{62} +3.54715e7 q^{63} +1.67772e7 q^{64} +3.45248e8 q^{65} +4.43071e7 q^{66} -2.94611e8 q^{67} -8.79160e7 q^{68} -4.36978e8 q^{69} +8.67817e7 q^{70} +9.62106e7 q^{71} -6.59077e7 q^{72} +3.14132e8 q^{73} -1.99186e8 q^{74} +7.75551e8 q^{75} +4.83374e7 q^{76} -3.22756e7 q^{77} +4.24647e8 q^{78} +4.72114e8 q^{79} -1.61244e8 q^{80} -4.45223e8 q^{81} -4.78767e8 q^{82} -1.19655e8 q^{83} +1.06740e8 q^{84} +8.44954e8 q^{85} -4.04096e8 q^{86} -6.87569e7 q^{87} +5.99695e7 q^{88} -8.24428e8 q^{89} +6.33433e8 q^{90} -3.09335e8 q^{91} -5.91450e8 q^{92} -9.63873e8 q^{93} -3.09088e8 q^{94} -4.64566e8 q^{95} -1.98327e8 q^{96} -429826. q^{97} +5.67903e8 q^{98} -2.35585e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} + 34 q^{3} + 512 q^{4} - 1478 q^{5} - 544 q^{6} + 8196 q^{7} - 8192 q^{8} + 20476 q^{9}+O(q^{10}) \) 2 * q - 32 * q^2 + 34 * q^3 + 512 * q^4 - 1478 * q^5 - 544 * q^6 + 8196 * q^7 - 8192 * q^8 + 20476 * q^9	\( 2 q - 32 q^{2} + 34 q^{3} + 512 q^{4} - 1478 q^{5} - 544 q^{6} + 8196 q^{7} - 8192 q^{8} + 20476 q^{9} + 23648 q^{10} - 29282 q^{11} + 8704 q^{12} - 196296 q^{13} - 131136 q^{14} - 617766 q^{15} + 131072 q^{16} - 548788 q^{17} - 327616 q^{18} - 90928 q^{19} - 378368 q^{20} - 512572 q^{21} + 468512 q^{22} - 3971046 q^{23} - 139264 q^{24} + 3112392 q^{25} + 3140736 q^{26} + 1693846 q^{27} + 2098176 q^{28} - 656128 q^{29} + 9884256 q^{30} - 872214 q^{31} - 2097152 q^{32} - 497794 q^{33} + 8780608 q^{34} + 462196 q^{35} + 5241856 q^{36} - 190722 q^{37} + 1454848 q^{38} - 17856712 q^{39} + 6053888 q^{40} + 3350080 q^{41} + 8201152 q^{42} + 3876012 q^{43} - 7496192 q^{44} - 35281524 q^{45} + 63536736 q^{46} + 38884544 q^{47} + 2228224 q^{48} - 39949062 q^{49} - 49798272 q^{50} - 33094260 q^{51} - 50251776 q^{52} - 134346316 q^{53} - 27101536 q^{54} + 21639398 q^{55} - 33570816 q^{56} + 79112528 q^{57} + 10498048 q^{58} - 125273754 q^{59} - 158148096 q^{60} + 114821880 q^{61} + 13955424 q^{62} + 61745912 q^{63} + 33554432 q^{64} + 290259544 q^{65} + 7964704 q^{66} - 91519714 q^{67} - 140489728 q^{68} - 179338950 q^{69} - 7395136 q^{70} + 411397438 q^{71} - 83869696 q^{72} + 506142392 q^{73} + 3051552 q^{74} + 928832584 q^{75} - 23277568 q^{76} - 119997636 q^{77} + 285707392 q^{78} + 810072516 q^{79} - 96862208 q^{80} - 899727614 q^{81} - 53601280 q^{82} - 718904884 q^{83} - 131218432 q^{84} + 643202972 q^{85} - 62016192 q^{86} - 23362560 q^{87} + 119939072 q^{88} - 810786322 q^{89} + 564504384 q^{90} - 644704528 q^{91} - 1016587776 q^{92} - 1619163382 q^{93} - 622152704 q^{94} - 739387248 q^{95} - 35651584 q^{96} - 230208654 q^{97} + 639184992 q^{98} - 299789116 q^{99}+O(q^{100}) \) 2 * q - 32 * q^2 + 34 * q^3 + 512 * q^4 - 1478 * q^5 - 544 * q^6 + 8196 * q^7 - 8192 * q^8 + 20476 * q^9 + 23648 * q^10 - 29282 * q^11 + 8704 * q^12 - 196296 * q^13 - 131136 * q^14 - 617766 * q^15 + 131072 * q^16 - 548788 * q^17 - 327616 * q^18 - 90928 * q^19 - 378368 * q^20 - 512572 * q^21 + 468512 * q^22 - 3971046 * q^23 - 139264 * q^24 + 3112392 * q^25 + 3140736 * q^26 + 1693846 * q^27 + 2098176 * q^28 - 656128 * q^29 + 9884256 * q^30 - 872214 * q^31 - 2097152 * q^32 - 497794 * q^33 + 8780608 * q^34 + 462196 * q^35 + 5241856 * q^36 - 190722 * q^37 + 1454848 * q^38 - 17856712 * q^39 + 6053888 * q^40 + 3350080 * q^41 + 8201152 * q^42 + 3876012 * q^43 - 7496192 * q^44 - 35281524 * q^45 + 63536736 * q^46 + 38884544 * q^47 + 2228224 * q^48 - 39949062 * q^49 - 49798272 * q^50 - 33094260 * q^51 - 50251776 * q^52 - 134346316 * q^53 - 27101536 * q^54 + 21639398 * q^55 - 33570816 * q^56 + 79112528 * q^57 + 10498048 * q^58 - 125273754 * q^59 - 158148096 * q^60 + 114821880 * q^61 + 13955424 * q^62 + 61745912 * q^63 + 33554432 * q^64 + 290259544 * q^65 + 7964704 * q^66 - 91519714 * q^67 - 140489728 * q^68 - 179338950 * q^69 - 7395136 * q^70 + 411397438 * q^71 - 83869696 * q^72 + 506142392 * q^73 + 3051552 * q^74 + 928832584 * q^75 - 23277568 * q^76 - 119997636 * q^77 + 285707392 * q^78 + 810072516 * q^79 - 96862208 * q^80 - 899727614 * q^81 - 53601280 * q^82 - 718904884 * q^83 - 131218432 * q^84 + 643202972 * q^85 - 62016192 * q^86 - 23362560 * q^87 + 119939072 * q^88 - 810786322 * q^89 + 564504384 * q^90 - 644704528 * q^91 - 1016587776 * q^92 - 1619163382 * q^93 - 622152704 * q^94 - 739387248 * q^95 - 35651584 * q^96 - 230208654 * q^97 + 639184992 * q^98 - 299789116 * q^99

Introduction

L-functions

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