LMFDB - Embedded newform 10.26.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,26,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 26, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	10.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:	$39.5996779952$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 6900880 $ x^2 - x - 6900880
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2626.45$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4096.00 q^{2} +1.19926e6 q^{3} +1.67772e7 q^{4} +2.44141e8 q^{5} -4.91217e9 q^{6} -1.32210e10 q^{7} -6.87195e10 q^{8} +5.90937e11 q^{9} -1.00000e12 q^{10} +1.51986e13 q^{11} +2.01203e13 q^{12} +3.15848e12 q^{13} +5.41533e13 q^{14} +2.92788e14 q^{15} +2.81475e14 q^{16} +1.62591e15 q^{17} -2.42048e15 q^{18} +5.64080e15 q^{19} +4.09600e15 q^{20} -1.58554e16 q^{21} -6.22536e16 q^{22} -1.52235e17 q^{23} -8.24125e16 q^{24} +5.96046e16 q^{25} -1.29371e16 q^{26} -3.07432e17 q^{27} -2.21812e17 q^{28} +1.86158e17 q^{29} -1.19926e18 q^{30} +6.41559e18 q^{31} -1.15292e18 q^{32} +1.82271e19 q^{33} -6.65974e18 q^{34} -3.22779e18 q^{35} +9.91428e18 q^{36} +3.10993e19 q^{37} -2.31047e19 q^{38} +3.78784e18 q^{39} -1.67772e19 q^{40} -2.12615e19 q^{41} +6.49439e19 q^{42} +4.45949e20 q^{43} +2.54991e20 q^{44} +1.44272e20 q^{45} +6.23555e20 q^{46} +5.28278e19 q^{47} +3.37562e20 q^{48} -1.16627e21 q^{49} -2.44141e20 q^{50} +1.94989e21 q^{51} +5.29905e19 q^{52} +2.38642e21 q^{53} +1.25924e21 q^{54} +3.71060e21 q^{55} +9.08541e20 q^{56} +6.76479e21 q^{57} -7.62501e20 q^{58} +1.91973e22 q^{59} +4.91217e21 q^{60} +1.98905e21 q^{61} -2.62783e22 q^{62} -7.81279e21 q^{63} +4.72237e21 q^{64} +7.71113e20 q^{65} -7.46583e22 q^{66} -1.03138e23 q^{67} +2.72783e22 q^{68} -1.82570e23 q^{69} +1.32210e22 q^{70} -1.01960e23 q^{71} -4.06089e22 q^{72} +3.26795e23 q^{73} -1.27383e23 q^{74} +7.14815e22 q^{75} +9.46369e22 q^{76} -2.00941e23 q^{77} -1.55150e22 q^{78} +2.14410e23 q^{79} +6.87195e22 q^{80} -8.69386e23 q^{81} +8.70871e22 q^{82} +1.80482e24 q^{83} -2.66010e23 q^{84} +3.96951e23 q^{85} -1.82661e24 q^{86} +2.23251e23 q^{87} -1.04444e24 q^{88} +3.14740e24 q^{89} -5.90937e23 q^{90} -4.17583e22 q^{91} -2.55408e24 q^{92} +7.69396e24 q^{93} -2.16383e23 q^{94} +1.37715e24 q^{95} -1.38265e24 q^{96} +4.10993e24 q^{97} +4.77706e24 q^{98} +8.98144e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8192 q^{2} - 438588 q^{3} + 33554432 q^{4} + 488281250 q^{5} + 1796456448 q^{6} - 34008596636 q^{7} - 137438953472 q^{8} + 2426195859786 q^{9} - 2000000000000 q^{10} + 19344682791984 q^{11} - 7358285611008 q^{12}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 8192 * q^2 - 438588 * q^3 + 33554432 * q^4 + 488281250 * q^5 + 1796456448 * q^6 - 34008596636 * q^7 - 137438953472 * q^8 + 2426195859786 * q^9 - 2000000000000 * q^10 + 19344682791984 * q^11 - 7358285611008 * q^12 - 127796048033588 * q^13 + 139299211821056 * q^14 - 107077148437500 * q^15 + 562949953421312 * q^16 - 2998857935578476 * q^17 - 9937698241683456 * q^18 + 13534782395320 * q^19 + 8192000000000000 * q^20 + 18191471686615584 * q^21 - 79235820715966464 * q^22 - 176800520782624068 * q^23 + 30139537862688768 * q^24 + 119209289550781250 * q^25 + 523452612745576448 * q^26 - 1925577931602663000 * q^27 - 570569571619045376 * q^28 - 1676097487309033380 * q^29 + 438588000000000000 * q^30 + 7125865156346376664 * q^31 - 2305843009213693952 * q^32 + 11436524032432880304 * q^33 + 12283322104129437696 * q^34 - 8302880038085937500 * q^35 + 40704811997935435776 * q^36 + 84009823521808944364 * q^37 - 55438468691230720 * q^38 + 218271507658245788472 * q^39 - 33554432000000000000 * q^40 - 278976945138543009756 * q^41 - 74512268028377432064 * q^42 + 426481602906822493732 * q^43 + 324549921652598636544 * q^44 + 592332973580566406250 * q^45 + 724174933125628182528 * q^46 + 1107620660641184540244 * q^47 - 123451547085573193728 * q^48 - 2075218430900234303166 * q^49 - 488281250000000000000 * q^50 + 9524566337524637542344 * q^51 - 2144061901805881131008 * q^52 + 4105636904637626409852 * q^53 + 7887167207844507648000 * q^54 + 4722822947261718750000 * q^55 + 2337052965351609860096 * q^56 + 15981397362106388525520 * q^57 + 6865295308017800724480 * q^58 - 3765561121989768768360 * q^59 - 1796456448000000000000 * q^60 + 1088840609004402816124 * q^61 - 29187543680394758815744 * q^62 - 45963382166122467752748 * q^63 + 9444732965739290427392 * q^64 - 31200207039450195312500 * q^65 - 46844002436845077725184 * q^66 - 118164954526157928047156 * q^67 - 50312487338514176802816 * q^68 - 142335029641186502306208 * q^69 + 34008596636000000000000 * q^70 + 121487502051587284868424 * q^71 - 166726909943543544938496 * q^72 + 1543159074817774555972 * q^73 - 344104237145329436114944 * q^74 - 26141881942749023437500 * q^75 + 227075967759281029120 * q^76 - 287127672428028283409712 * q^77 - 894040095368174749581312 * q^78 + 821388705533644841730640 * q^79 + 137438953472000000000000 * q^80 + 225897583488924285462402 * q^81 + 1142689567287472167960576 * q^82 + 1078689963931157206149252 * q^83 + 305202249844233961734144 * q^84 - 732143050678338867187500 * q^85 - 1746868645506344934326272 * q^86 + 3273342747249083127820920 * q^87 - 1329356479089044015284224 * q^88 + 5059219929404495720992980 * q^89 - 2426195859786000000000000 * q^90 + 2680469809760336269552184 * q^91 - 2966220526082573035634688 * q^92 + 6530638201511067276729984 * q^93 - 4536814225986291876839424 * q^94 + 3304390233232421875000 * q^95 + 505657536862507801509888 * q^96 + 2393368330790785393982164 * q^97 + 8500094692967359705767936 * q^98 + 16590506333144186236452912 * q^99

Coefficient data

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

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

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

$2$	−4096.00	−0.707107
$2$	−4096.00	−0.707107
$3$	1.19926e6	1.30286	0.651430	−	0.758709i	$-0.274169\pi$
$3$	1.19926e6	1.30286	0.651430	+	0.758709i	$0.274169\pi$
$4$	1.67772e7	0.500000
$5$	2.44141e8	0.447214
$5$	2.44141e8	0.447214
$6$	−4.91217e9	−0.921261
$7$	−1.32210e10	−0.361027	−0.180513	−	0.983573i	$-0.557776\pi$
$7$	−1.32210e10	−0.361027	−0.180513	+	0.983573i	$0.557776\pi$
$8$	−6.87195e10	−0.353553
$9$	5.90937e11	0.697445
$10$	−1.00000e12	−0.316228
$11$	1.51986e13	1.46015	0.730073	−	0.683370i	$-0.239486\pi$
$11$	1.51986e13	1.46015	0.730073	+	0.683370i	$0.239486\pi$
$12$	2.01203e13	0.651430
$13$	3.15848e12	0.0375999	0.0187999	−	0.999823i	$-0.494015\pi$
$13$	3.15848e12	0.0375999	0.0187999	+	0.999823i	$0.494015\pi$
$14$	5.41533e13	0.255284
$15$	2.92788e14	0.582657
$16$	2.81475e14	0.250000
$17$	1.62591e15	0.676840	0.338420	−	0.940995i	$-0.390108\pi$
$17$	1.62591e15	0.676840	0.338420	+	0.940995i	$0.390108\pi$
$18$	−2.42048e15	−0.493168
$19$	5.64080e15	0.584683	0.292342	−	0.956314i	$-0.405566\pi$
$19$	5.64080e15	0.584683	0.292342	+	0.956314i	$0.405566\pi$
$20$	4.09600e15	0.223607
$21$	−1.58554e16	−0.470367
$22$	−6.22536e16	−1.03248
$23$	−1.52235e17	−1.44849	−0.724247	−	0.689540i	$-0.757813\pi$
$23$	−1.52235e17	−1.44849	−0.724247	+	0.689540i	$0.757813\pi$
$24$	−8.24125e16	−0.460631
$25$	5.96046e16	0.200000
$26$	−1.29371e16	−0.0265871
$27$	−3.07432e17	−0.394187
$28$	−2.21812e17	−0.180513
$29$	1.86158e17	0.0977025	0.0488512	−	0.998806i	$-0.484444\pi$
$29$	1.86158e17	0.0977025	0.0488512	+	0.998806i	$0.484444\pi$
$30$	−1.19926e18	−0.412001
$31$	6.41559e18	1.46290	0.731451	−	0.681894i	$-0.238843\pi$
$31$	6.41559e18	1.46290	0.731451	+	0.681894i	$0.238843\pi$
$32$	−1.15292e18	−0.176777
$33$	1.82271e19	1.90236
$34$	−6.65974e18	−0.478598
$35$	−3.22779e18	−0.161456
$36$	9.91428e18	0.348722
$37$	3.10993e19	0.776657	0.388328	−	0.921521i	$-0.373053\pi$
$37$	3.10993e19	0.776657	0.388328	+	0.921521i	$0.373053\pi$
$38$	−2.31047e19	−0.413434
$39$	3.78784e18	0.0489874
$40$	−1.67772e19	−0.158114
$41$	−2.12615e19	−0.147162	−0.0735810	−	0.997289i	$-0.523443\pi$
$41$	−2.12615e19	−0.147162	−0.0735810	+	0.997289i	$0.523443\pi$
$42$	6.49439e19	0.332600
$43$	4.45949e20	1.70188	0.850942	−	0.525260i	$-0.176032\pi$
$43$	4.45949e20	1.70188	0.850942	+	0.525260i	$0.176032\pi$
$44$	2.54991e20	0.730073
$45$	1.44272e20	0.311907
$46$	6.23555e20	1.02424
$47$	5.28278e19	0.0663192	0.0331596	−	0.999450i	$-0.489443\pi$
$47$	5.28278e19	0.0663192	0.0331596	+	0.999450i	$0.489443\pi$
$48$	3.37562e20	0.325715
$49$	−1.16627e21	−0.869660
$50$	−2.44141e20	−0.141421
$51$	1.94989e21	0.881827
$52$	5.29905e19	0.0187999
$53$	2.38642e21	0.667266	0.333633	−	0.942703i	$-0.391725\pi$
$53$	2.38642e21	0.667266	0.333633	+	0.942703i	$0.391725\pi$
$54$	1.25924e21	0.278732
$55$	3.71060e21	0.652997
$56$	9.08541e20	0.127642
$57$	6.76479e21	0.761761
$58$	−7.62501e20	−0.0690861
$59$	1.91973e22	1.40472	0.702361	−	0.711821i	$-0.252129\pi$
$59$	1.91973e22	1.40472	0.702361	+	0.711821i	$0.252129\pi$
$60$	4.91217e21	0.291328
$61$	1.98905e21	0.0959450	0.0479725	−	0.998849i	$-0.484724\pi$
$61$	1.98905e21	0.0959450	0.0479725	+	0.998849i	$0.484724\pi$
$62$	−2.62783e22	−1.03443
$63$	−7.81279e21	−0.251796
$64$	4.72237e21	0.125000
$65$	7.71113e20	0.0168152
$66$	−7.46583e22	−1.34518
$67$	−1.03138e23	−1.53987	−0.769933	−	0.638125i	$-0.779710\pi$
$67$	−1.03138e23	−1.53987	−0.769933	+	0.638125i	$0.779710\pi$
$68$	2.72783e22	0.338420
$69$	−1.82570e23	−1.88719
$70$	1.32210e22	0.114167
$71$	−1.01960e23	−0.737393	−0.368697	−	0.929550i	$-0.620196\pi$
$71$	−1.01960e23	−0.737393	−0.368697	+	0.929550i	$0.620196\pi$
$72$	−4.06089e22	−0.246584
$73$	3.26795e23	1.67009	0.835044	−	0.550183i	$-0.185442\pi$
$73$	3.26795e23	1.67009	0.835044	+	0.550183i	$0.185442\pi$
$74$	−1.27383e23	−0.549179
$75$	7.14815e22	0.260572
$76$	9.46369e22	0.292342
$77$	−2.00941e23	−0.527151
$78$	−1.55150e22	−0.0346393
$79$	2.14410e23	0.408231	0.204115	−	0.978947i	$-0.434568\pi$
$79$	2.14410e23	0.408231	0.204115	+	0.978947i	$0.434568\pi$
$80$	6.87195e22	0.111803
$81$	−8.69386e23	−1.21102
$82$	8.70871e22	0.104059
$83$	1.80482e24	1.85335	0.926674	−	0.375865i	$-0.122654\pi$
$83$	1.80482e24	1.85335	0.926674	+	0.375865i	$0.122654\pi$
$84$	−2.66010e23	−0.235184
$85$	3.96951e23	0.302692
$86$	−1.82661e24	−1.20341
$87$	2.23251e23	0.127293
$88$	−1.04444e24	−0.516239
$89$	3.14740e24	1.35076	0.675378	−	0.737472i	$-0.263981\pi$
$89$	3.14740e24	1.35076	0.675378	+	0.737472i	$0.263981\pi$
$90$	−5.90937e23	−0.220551
$91$	−4.17583e22	−0.0135745
$92$	−2.55408e24	−0.724247
$93$	7.69396e24	1.90596
$94$	−2.16383e23	−0.0468948
$95$	1.37715e24	0.261478
$96$	−1.38265e24	−0.230315
$97$	4.10993e24	0.601433	0.300717	−	0.953714i	$-0.402774\pi$
$97$	4.10993e24	0.601433	0.300717	+	0.953714i	$0.402774\pi$
$98$	4.77706e24	0.614942
$99$	8.98144e24	1.01837
$100$	1.00000e24	0.100000
$101$	7.38400e24	0.652040	0.326020	−	0.945363i	$-0.394292\pi$
$101$	7.38400e24	0.652040	0.326020	+	0.945363i	$0.394292\pi$
$102$	−7.98676e24	−0.623546
$103$	−1.77047e25	−1.22355	−0.611777	−	0.791030i	$-0.709545\pi$
$103$	−1.77047e25	−1.22355	−0.611777	+	0.791030i	$0.709545\pi$
$104$	−2.17049e23	−0.0132936
$105$	−3.87096e24	−0.210355
$106$	−9.77478e24	−0.471828
$107$	−3.05016e25	−1.30926	−0.654630	−	0.755949i	$-0.727176\pi$
$107$	−3.05016e25	−1.30926	−0.654630	+	0.755949i	$0.727176\pi$
$108$	−5.15786e24	−0.197094
$109$	−7.07393e23	−0.0240896	−0.0120448	−	0.999927i	$-0.503834\pi$
$109$	−7.07393e23	−0.0240896	−0.0120448	+	0.999927i	$0.503834\pi$
$110$	−1.51986e25	−0.461738
$111$	3.72962e25	1.01188
$112$	−3.72138e24	−0.0902567
$113$	−4.42998e24	−0.0961437	−0.0480719	−	0.998844i	$-0.515308\pi$
$113$	−4.42998e24	−0.0961437	−0.0480719	+	0.998844i	$0.515308\pi$
$114$	−2.77086e25	−0.538646
$115$	−3.71668e25	−0.647786
$116$	3.12320e24	0.0488512
$117$	1.86646e24	0.0262238
$118$	−7.86322e25	−0.993289
$119$	−2.14962e25	−0.244357
$120$	−2.01203e25	−0.206000
$121$	1.22651e26	1.13202
$122$	−8.14714e24	−0.0678433
$123$	−2.54981e25	−0.191732
$124$	1.07636e26	0.731451
$125$	1.45519e25	0.0894427
$126$	3.20012e25	0.178047
$127$	−3.71403e26	−1.87197	−0.935985	−	0.352040i	$-0.885488\pi$
$127$	−3.71403e26	−1.87197	−0.935985	+	0.352040i	$0.885488\pi$
$128$	−1.93428e25	−0.0883883
$129$	5.34810e26	2.21732
$130$	−3.15848e24	−0.0118901
$131$	1.04713e26	0.358187	0.179093	−	0.983832i	$-0.442684\pi$
$131$	1.04713e26	0.358187	0.179093	+	0.983832i	$0.442684\pi$
$132$	3.05800e26	0.951182
$133$	−7.45771e25	−0.211086
$134$	4.22452e26	1.08885
$135$	−7.50567e25	−0.176286
$136$	−1.11732e26	−0.239299
$137$	5.94307e25	0.116146	0.0580729	−	0.998312i	$-0.481504\pi$
$137$	5.94307e25	0.116146	0.0580729	+	0.998312i	$0.481504\pi$
$138$	7.47805e26	1.33444
$139$	−4.16988e26	−0.679890	−0.339945	−	0.940445i	$-0.610408\pi$
$139$	−4.16988e26	−0.679890	−0.339945	+	0.940445i	$0.610408\pi$
$140$	−5.41533e25	−0.0807280
$141$	6.33543e25	0.0864047
$142$	4.17627e26	0.521416
$143$	4.80046e25	0.0549012
$144$	1.66334e26	0.174361
$145$	4.54486e25	0.0436939
$146$	−1.33855e27	−1.18093
$147$	−1.39867e27	−1.13305
$148$	5.21760e26	0.388328
$149$	−2.31720e27	−1.58539	−0.792693	−	0.609621i	$-0.791322\pi$
$149$	−2.31720e27	−1.58539	−0.792693	+	0.609621i	$0.791322\pi$
$150$	−2.92788e26	−0.184252
$151$	−1.72926e27	−1.00149	−0.500747	−	0.865593i	$-0.666941\pi$
$151$	−1.72926e27	−1.00149	−0.500747	+	0.865593i	$0.666941\pi$
$152$	−3.87633e26	−0.206717
$153$	9.60812e26	0.472058
$154$	8.23056e26	0.372752
$155$	1.56631e27	0.654230
$156$	6.35494e25	0.0244937
$157$	−1.99124e27	−0.708561	−0.354280	−	0.935139i	$-0.615274\pi$
$157$	−1.99124e27	−0.708561	−0.354280	+	0.935139i	$0.615274\pi$
$158$	−8.78222e26	−0.288663
$159$	2.86194e27	0.869354
$160$	−2.81475e26	−0.0790569
$161$	2.01270e27	0.522945
$162$	3.56100e27	0.856317
$163$	5.29799e26	0.117968	0.0589842	−	0.998259i	$-0.481214\pi$
$163$	5.29799e26	0.117968	0.0589842	+	0.998259i	$0.481214\pi$
$164$	−3.56709e26	−0.0735810
$165$	4.44998e27	0.850763
$166$	−7.39253e27	−1.31052
$167$	−8.51848e27	−1.40090	−0.700449	−	0.713703i	$-0.747017\pi$
$167$	−8.51848e27	−1.40090	−0.700449	+	0.713703i	$0.747017\pi$
$168$	1.08958e27	0.166300
$169$	−7.04643e27	−0.998586
$170$	−1.62591e27	−0.214035
$171$	3.33336e27	0.407784
$172$	7.48179e27	0.850942
$173$	−1.49682e28	−1.58341	−0.791705	−	0.610904i	$-0.790806\pi$
$173$	−1.49682e28	−1.58341	−0.791705	+	0.610904i	$0.790806\pi$
$174$	−9.14437e26	−0.0900095
$175$	−7.88034e26	−0.0722053
$176$	4.27804e27	0.365036
$177$	2.30226e28	1.83016
$178$	−1.28917e28	−0.955128
$179$	1.97459e28	1.36400	0.681999	−	0.731353i	$-0.261111\pi$
$179$	1.97459e28	1.36400	0.681999	+	0.731353i	$0.261111\pi$
$180$	2.42048e27	0.155953
$181$	2.28995e28	1.37672	0.688358	−	0.725371i	$-0.258332\pi$
$181$	2.28995e28	1.37672	0.688358	+	0.725371i	$0.258332\pi$
$182$	1.71042e26	0.00959866
$183$	2.38539e27	0.125003
$184$	1.04615e28	0.512120
$185$	7.59261e27	0.347332
$186$	−3.15145e28	−1.34772
$187$	2.47117e28	0.988284
$188$	8.86304e26	0.0331596
$189$	4.06457e27	0.142312
$190$	−5.64080e27	−0.184893
$191$	6.00777e28	1.84415	0.922074	−	0.387013i	$-0.126493\pi$
$191$	6.00777e28	1.84415	0.922074	+	0.387013i	$0.126493\pi$
$192$	5.66335e27	0.162858
$193$	−6.00445e28	−1.61810	−0.809052	−	0.587736i	$-0.800019\pi$
$193$	−6.00445e28	−1.61810	−0.809052	+	0.587736i	$0.800019\pi$
$194$	−1.68343e28	−0.425277
$195$	9.24766e26	0.0219078
$196$	−1.95668e28	−0.434830
$197$	−3.69371e27	−0.0770255	−0.0385128	−	0.999258i	$-0.512262\pi$
$197$	−3.69371e27	−0.0770255	−0.0385128	+	0.999258i	$0.512262\pi$
$198$	−3.67880e28	−0.720097
$199$	−1.22806e28	−0.225713	−0.112856	−	0.993611i	$-0.536000\pi$
$199$	−1.22806e28	−0.225713	−0.112856	+	0.993611i	$0.536000\pi$
$200$	−4.09600e27	−0.0707107
$201$	−1.23689e29	−2.00623
$202$	−3.02448e28	−0.461062
$203$	−2.46119e27	−0.0352732
$204$	3.27138e28	0.440914
$205$	−5.19080e27	−0.0658129
$206$	7.25184e28	0.865183
$207$	−8.99613e28	−1.01024
$208$	8.89033e26	0.00939996
$209$	8.57325e28	0.853723
$210$	1.58554e28	0.148743
$211$	−2.20546e29	−1.94970	−0.974850	−	0.222861i	$-0.928460\pi$
$211$	−2.20546e29	−1.94970	−0.974850	+	0.222861i	$0.928460\pi$
$212$	4.00375e28	0.333633
$213$	−1.22276e29	−0.960720
$214$	1.24935e29	0.925787
$215$	1.08874e29	0.761106
$216$	2.11266e28	0.139366
$217$	−8.48206e28	−0.528147
$218$	2.89748e27	0.0170339
$219$	3.91912e29	2.17589
$220$	6.22536e28	0.326498
$221$	5.13541e27	0.0254491
$222$	−1.52765e29	−0.715504
$223$	−2.23533e27	−0.00989761	−0.00494880	−	0.999988i	$-0.501575\pi$
$223$	−2.23533e27	−0.00989761	−0.00494880	+	0.999988i	$0.501575\pi$
$224$	1.52428e28	0.0638211
$225$	3.52226e28	0.139489
$226$	1.81452e28	0.0679839
$227$	−2.34973e29	−0.833094	−0.416547	−	0.909114i	$-0.636760\pi$
$227$	−2.34973e29	−0.833094	−0.416547	+	0.909114i	$0.636760\pi$
$228$	1.13494e29	0.380880
$229$	3.37494e29	1.07232	0.536158	−	0.844118i	$-0.319875\pi$
$229$	3.37494e29	1.07232	0.536158	+	0.844118i	$0.319875\pi$
$230$	1.52235e29	0.458054
$231$	−2.40981e29	−0.686804
$232$	−1.27926e28	−0.0345430
$233$	2.45486e29	0.628172	0.314086	−	0.949395i	$-0.398302\pi$
$233$	2.45486e29	0.628172	0.314086	+	0.949395i	$0.398302\pi$
$234$	−7.64503e27	−0.0185430
$235$	1.28974e28	0.0296589
$236$	3.22078e29	0.702361
$237$	2.57133e29	0.531868
$238$	8.80485e28	0.172787
$239$	2.75069e29	0.512234	0.256117	−	0.966646i	$-0.417557\pi$
$239$	2.75069e29	0.512234	0.256117	+	0.966646i	$0.417557\pi$
$240$	8.24125e28	0.145664
$241$	−3.54884e29	−0.595489	−0.297744	−	0.954646i	$-0.596234\pi$
$241$	−3.54884e29	−0.595489	−0.297744	+	0.954646i	$0.596234\pi$
$242$	−5.02380e29	−0.800462
$243$	−7.82136e29	−1.18360
$244$	3.33707e28	0.0479725
$245$	−2.84735e29	−0.388924
$246$	1.04440e29	0.135575
$247$	1.78164e28	0.0219840
$248$	−4.40876e29	−0.517214
$249$	2.16445e30	2.41465
$250$	−5.96046e28	−0.0632456
$251$	−1.45056e30	−1.46425	−0.732124	−	0.681171i	$-0.761471\pi$
$251$	−1.45056e30	−1.46425	−0.732124	+	0.681171i	$0.761471\pi$
$252$	−1.31077e29	−0.125898
$253$	−2.31377e30	−2.11501
$254$	1.52127e30	1.32368
$255$	4.76048e29	0.394365
$256$	7.92282e28	0.0625000
$257$	2.49157e28	0.0187201	0.00936006	−	0.999956i	$-0.497021\pi$
$257$	2.49157e28	0.0187201	0.00936006	+	0.999956i	$0.497021\pi$
$258$	−2.19058e30	−1.56788
$259$	−4.11164e29	−0.280394
$260$	1.29371e28	0.00840758
$261$	1.10007e29	0.0681421
$262$	−4.28905e29	−0.253276
$263$	−1.49953e30	−0.844325	−0.422162	−	0.906520i	$-0.638729\pi$
$263$	−1.49953e30	−0.844325	−0.422162	+	0.906520i	$0.638729\pi$
$264$	−1.25256e30	−0.672588
$265$	5.82622e29	0.298410
$266$	3.05468e29	0.149261
$267$	3.77455e30	1.75985
$268$	−1.73036e30	−0.769933
$269$	1.77042e30	0.751920	0.375960	−	0.926636i	$-0.377313\pi$
$269$	1.77042e30	0.751920	0.375960	+	0.926636i	$0.377313\pi$
$270$	3.07432e29	0.124653
$271$	2.89777e30	1.12188	0.560941	−	0.827855i	$-0.310439\pi$
$271$	2.89777e30	1.12188	0.560941	+	0.827855i	$0.310439\pi$
$272$	4.57654e29	0.169210
$273$	−5.00791e28	−0.0176857
$274$	−2.43428e29	−0.0821275
$275$	9.05909e29	0.292029
$276$	−3.06301e30	−0.943593
$277$	−1.66393e30	−0.489935	−0.244968	−	0.969531i	$-0.578777\pi$
$277$	−1.66393e30	−0.489935	−0.244968	+	0.969531i	$0.578777\pi$
$278$	1.70798e30	0.480755
$279$	3.79121e30	1.02029
$280$	2.21812e29	0.0570833
$281$	−2.85222e30	−0.702027	−0.351013	−	0.936370i	$-0.614163\pi$
$281$	−2.85222e30	−0.702027	−0.351013	+	0.936370i	$0.614163\pi$
$282$	−2.59499e29	−0.0610973
$283$	−1.34367e30	−0.302665	−0.151333	−	0.988483i	$-0.548356\pi$
$283$	−1.34367e30	−0.302665	−0.151333	+	0.988483i	$0.548356\pi$
$284$	−1.71060e30	−0.368697
$285$	1.65156e30	0.340670
$286$	−1.96627e29	−0.0388210
$287$	2.81099e29	0.0531294
$288$	−6.81304e29	−0.123292
$289$	−3.12704e30	−0.541888
$290$	−1.86158e29	−0.0308962
$291$	4.92887e30	0.783583
$292$	5.48271e30	0.835044
$293$	1.77083e30	0.258423	0.129212	−	0.991617i	$-0.458755\pi$
$293$	1.77083e30	0.258423	0.129212	+	0.991617i	$0.458755\pi$
$294$	5.72893e30	0.801184
$295$	4.68685e30	0.628211
$296$	−2.13713e30	−0.274590
$297$	−4.67255e30	−0.575571
$298$	9.49125e30	1.12104
$299$	−4.80831e29	−0.0544632
$300$	1.19926e30	0.130286
$301$	−5.89590e30	−0.614425
$302$	7.08305e30	0.708164
$303$	8.85533e30	0.849517
$304$	1.58774e30	0.146171
$305$	4.85607e29	0.0429079
$306$	−3.93549e30	−0.333796
$307$	−1.28750e31	−1.04838	−0.524189	−	0.851602i	$-0.675631\pi$
$307$	−1.28750e31	−1.04838	−0.524189	+	0.851602i	$0.675631\pi$
$308$	−3.37124e30	−0.263576
$309$	−2.12325e31	−1.59412
$310$	−6.41559e30	−0.462610
$311$	−4.08326e29	−0.0282815	−0.0141407	−	0.999900i	$-0.504501\pi$
$311$	−4.08326e29	−0.0282815	−0.0141407	+	0.999900i	$0.504501\pi$
$312$	−2.60298e29	−0.0173196
$313$	−9.20841e30	−0.588682	−0.294341	−	0.955701i	$-0.595100\pi$
$313$	−9.20841e30	−0.588682	−0.294341	+	0.955701i	$0.595100\pi$
$314$	8.15610e30	0.501028
$315$	−1.90742e30	−0.112607
$316$	3.59720e30	0.204115
$317$	−1.73757e31	−0.947764	−0.473882	−	0.880588i	$-0.657148\pi$
$317$	−1.73757e31	−0.947764	−0.473882	+	0.880588i	$0.657148\pi$
$318$	−1.17225e31	−0.614726
$319$	2.82934e30	0.142660
$320$	1.15292e30	0.0559017
$321$	−3.65794e31	−1.70578
$322$	−8.24403e30	−0.369778
$323$	9.17145e30	0.395737
$324$	−1.45859e31	−0.605508
$325$	1.88260e29	0.00751997
$326$	−2.17006e30	−0.0834163
$327$	−8.48349e29	−0.0313854
$328$	1.46108e30	0.0520296
$329$	−6.98437e29	−0.0239430
$330$	−1.82271e31	−0.601581
$331$	5.61759e31	1.78525	0.892627	−	0.450797i	$-0.148860\pi$
$331$	5.61759e31	1.78525	0.892627	+	0.450797i	$0.148860\pi$
$332$	3.02798e31	0.926674
$333$	1.83777e31	0.541675
$334$	3.48917e31	0.990584
$335$	−2.51801e31	−0.688649
$336$	−4.46291e30	−0.117592
$337$	4.19121e31	1.06406	0.532029	−	0.846726i	$-0.321430\pi$
$337$	4.19121e31	1.06406	0.532029	+	0.846726i	$0.321430\pi$
$338$	2.88622e31	0.706107
$339$	−5.31270e30	−0.125262
$340$	6.65974e30	0.151346
$341$	9.75082e31	2.13605
$342$	−1.36534e31	−0.288347
$343$	3.31496e31	0.674997
$344$	−3.06454e31	−0.601707
$345$	−4.45726e31	−0.843975
$346$	6.13098e31	1.11964
$347$	−1.70880e31	−0.301004	−0.150502	−	0.988610i	$-0.548089\pi$
$347$	−1.70880e31	−0.301004	−0.150502	+	0.988610i	$0.548089\pi$
$348$	3.74554e30	0.0636463
$349$	−8.15918e31	−1.33761	−0.668803	−	0.743439i	$-0.733193\pi$
$349$	−8.15918e31	−1.33761	−0.668803	+	0.743439i	$0.733193\pi$
$350$	3.22779e30	0.0510569
$351$	−9.71019e29	−0.0148214
$352$	−1.75228e31	−0.258120
$353$	5.64031e31	0.801899	0.400949	−	0.916100i	$-0.368680\pi$
$353$	5.64031e31	0.801899	0.400949	+	0.916100i	$0.368680\pi$
$354$	−9.43005e31	−1.29412
$355$	−2.48925e31	−0.329772
$356$	5.28046e31	0.675378
$357$	−2.57796e31	−0.318363
$358$	−8.08791e31	−0.964492
$359$	4.12655e31	0.475233	0.237616	−	0.971359i	$-0.423634\pi$
$359$	4.12655e31	0.475233	0.237616	+	0.971359i	$0.423634\pi$
$360$	−9.91428e30	−0.110276
$361$	−6.12579e31	−0.658145
$362$	−9.37965e31	−0.973485
$363$	1.47091e32	1.47487
$364$	−7.00588e29	−0.00678727
$365$	7.97839e31	0.746886
$366$	−9.77054e30	−0.0883904
$367$	1.10522e32	0.966323	0.483161	−	0.875531i	$-0.339488\pi$
$367$	1.10522e32	0.966323	0.483161	+	0.875531i	$0.339488\pi$
$368$	−4.28504e31	−0.362124
$369$	−1.25642e31	−0.102637
$370$	−3.10993e31	−0.245601
$371$	−3.15509e31	−0.240901
$372$	1.29083e32	0.952979
$373$	−1.60774e31	−0.114777	−0.0573885	−	0.998352i	$-0.518277\pi$
$373$	−1.60774e31	−0.114777	−0.0573885	+	0.998352i	$0.518277\pi$
$374$	−1.01219e32	−0.698822
$375$	1.74515e31	0.116531
$376$	−3.63030e30	−0.0234474
$377$	5.87975e29	0.00367360
$378$	−1.66485e31	−0.100630
$379$	−2.27403e32	−1.32986	−0.664930	−	0.746906i	$-0.731539\pi$
$379$	−2.27403e32	−1.32986	−0.664930	+	0.746906i	$0.731539\pi$
$380$	2.31047e31	0.130739
$381$	−4.45409e32	−2.43892
$382$	−2.46078e32	−1.30401
$383$	3.38623e32	1.73673	0.868363	−	0.495929i	$-0.165172\pi$
$383$	3.38623e32	1.73673	0.868363	+	0.495929i	$0.165172\pi$
$384$	−2.31971e31	−0.115158
$385$	−4.90579e31	−0.235749
$386$	2.45942e32	1.14417
$387$	2.63528e32	1.18697
$388$	6.89531e31	0.300717
$389$	−3.10148e32	−1.30978	−0.654890	−	0.755724i	$-0.727285\pi$
$389$	−3.10148e32	−1.30978	−0.654890	+	0.755724i	$0.727285\pi$
$390$	−3.78784e30	−0.0154912
$391$	−2.47521e32	−0.980398
$392$	8.01457e31	0.307471
$393$	1.25578e32	0.466667
$394$	1.51294e31	0.0544653
$395$	5.23461e31	0.182566
$396$	1.50683e32	0.509185
$397$	−3.84570e32	−1.25920	−0.629599	−	0.776920i	$-0.716781\pi$
$397$	−3.84570e32	−1.25920	−0.629599	+	0.776920i	$0.716781\pi$
$398$	5.03013e31	0.159603
$399$	−8.94374e31	−0.275016
$400$	1.67772e31	0.0500000
$401$	3.65396e32	1.05550	0.527751	−	0.849399i	$-0.323035\pi$
$401$	3.65396e32	1.05550	0.527751	+	0.849399i	$0.323035\pi$
$402$	5.06630e32	1.41862
$403$	2.02635e31	0.0550049
$404$	1.23883e32	0.326020
$405$	−2.12252e32	−0.541583
$406$	1.00810e31	0.0249419
$407$	4.72667e32	1.13403
$408$	−1.33996e32	−0.311773
$409$	−1.30167e31	−0.0293737	−0.0146868	−	0.999892i	$-0.504675\pi$
$409$	−1.30167e31	−0.0293737	−0.0146868	+	0.999892i	$0.504675\pi$
$410$	2.12615e31	0.0465367
$411$	7.12729e31	0.151322
$412$	−2.97036e32	−0.611777
$413$	−2.53808e32	−0.507142
$414$	3.68482e32	0.714351
$415$	4.40629e32	0.828843
$416$	−3.64148e30	−0.00664678
$417$	−5.00077e32	−0.885802
$418$	−3.51160e32	−0.603673
$419$	8.70006e32	1.45160	0.725800	−	0.687905i	$-0.241470\pi$
$419$	8.70006e32	1.45160	0.725800	+	0.687905i	$0.241470\pi$
$420$	−6.49439e31	−0.105177
$421$	−5.04763e32	−0.793527	−0.396763	−	0.917921i	$-0.629867\pi$
$421$	−5.04763e32	−0.793527	−0.396763	+	0.917921i	$0.629867\pi$
$422$	9.03355e32	1.37865
$423$	3.12179e31	0.0462540
$424$	−1.63994e32	−0.235914
$425$	9.69120e31	0.135368
$426$	5.00843e32	0.679332
$427$	−2.62972e31	−0.0346387
$428$	−5.11733e32	−0.654630
$429$	5.75700e31	0.0715286
$430$	−4.45949e32	−0.538183
$431$	8.61019e32	1.00936	0.504681	−	0.863306i	$-0.331610\pi$
$431$	8.61019e32	1.00936	0.504681	+	0.863306i	$0.331610\pi$
$432$	−8.65345e31	−0.0985468
$433$	−1.24809e33	−1.38085	−0.690427	−	0.723402i	$-0.742577\pi$
$433$	−1.24809e33	−1.38085	−0.690427	+	0.723402i	$0.742577\pi$
$434$	3.47425e32	0.373456
$435$	5.45047e31	0.0569270
$436$	−1.18681e31	−0.0120448
$437$	−8.58728e32	−0.846910
$438$	−1.60527e33	−1.53859
$439$	3.66479e32	0.341384	0.170692	−	0.985324i	$-0.445400\pi$
$439$	3.66479e32	0.341384	0.170692	+	0.985324i	$0.445400\pi$
$440$	−2.54991e32	−0.230869
$441$	−6.89194e32	−0.606540
$442$	−2.10346e31	−0.0179952
$443$	1.58140e33	1.31521	0.657606	−	0.753362i	$-0.271569\pi$
$443$	1.58140e33	1.31521	0.657606	+	0.753362i	$0.271569\pi$
$444$	6.25726e32	0.505938
$445$	7.68408e32	0.604076
$446$	9.15590e30	0.00699866
$447$	−2.77892e33	−2.06554
$448$	−6.24345e31	−0.0451283
$449$	2.03169e33	1.42817	0.714083	−	0.700061i	$-0.246844\pi$
$449$	2.03169e33	1.42817	0.714083	+	0.700061i	$0.246844\pi$
$450$	−1.44272e32	−0.0986336
$451$	−3.23146e32	−0.214878
$452$	−7.43227e31	−0.0480719
$453$	−2.07383e33	−1.30481
$454$	9.62448e32	0.589086
$455$	−1.01949e31	−0.00607072
$456$	−4.64873e32	−0.269323
$457$	−1.28100e33	−0.722097	−0.361048	−	0.932547i	$-0.617581\pi$
$457$	−1.28100e33	−0.722097	−0.361048	+	0.932547i	$0.617581\pi$
$458$	−1.38238e33	−0.758241
$459$	−4.99858e32	−0.266801
$460$	−6.23555e32	−0.323893
$461$	−1.55893e33	−0.788071	−0.394036	−	0.919095i	$-0.628921\pi$
$461$	−1.55893e33	−0.788071	−0.394036	+	0.919095i	$0.628921\pi$
$462$	9.87058e32	0.485644
$463$	5.69235e32	0.272602	0.136301	−	0.990667i	$-0.456479\pi$
$463$	5.69235e32	0.272602	0.136301	+	0.990667i	$0.456479\pi$
$464$	5.23987e31	0.0244256
$465$	1.87841e33	0.852370
$466$	−1.00551e33	−0.444185
$467$	2.08645e33	0.897321	0.448661	−	0.893702i	$-0.351901\pi$
$467$	2.08645e33	0.897321	0.448661	+	0.893702i	$0.351901\pi$
$468$	3.13140e31	0.0131119
$469$	1.36359e33	0.555932
$470$	−5.28278e31	−0.0209720
$471$	−2.38801e33	−0.923156
$472$	−1.31923e33	−0.496644
$473$	6.77782e33	2.48500
$474$	−1.05322e33	−0.376087
$475$	3.36218e32	0.116937
$476$	−3.60647e32	−0.122179
$477$	1.41022e33	0.465381
$478$	−1.12668e33	−0.362204
$479$	4.90036e33	1.53474	0.767368	−	0.641207i	$-0.221566\pi$
$479$	4.90036e33	1.53474	0.767368	+	0.641207i	$0.221566\pi$
$480$	−3.37562e32	−0.103000
$481$	9.82265e31	0.0292022
$482$	1.45361e33	0.421074
$483$	2.41375e33	0.681324
$484$	2.05775e33	0.566012
$485$	1.00340e33	0.268969
$486$	3.20363e33	0.836929
$487$	−1.04707e33	−0.266603	−0.133302	−	0.991076i	$-0.542558\pi$
$487$	−1.04707e33	−0.266603	−0.133302	+	0.991076i	$0.542558\pi$
$488$	−1.36686e32	−0.0339217
$489$	6.35367e32	0.153696
$490$	1.16627e33	0.275011
$491$	−2.78591e33	−0.640397	−0.320198	−	0.947351i	$-0.603750\pi$
$491$	−2.78591e33	−0.640397	−0.320198	+	0.947351i	$0.603750\pi$
$492$	−4.27787e32	−0.0958658
$493$	3.02676e32	0.0661289
$494$	−7.29758e31	−0.0155450
$495$	2.19273e33	0.455429
$496$	1.80583e33	0.365726
$497$	1.34801e33	0.266219
$498$	−8.86557e33	−1.70742
$499$	−2.70519e33	−0.508090	−0.254045	−	0.967192i	$-0.581761\pi$
$499$	−2.70519e33	−0.508090	−0.254045	+	0.967192i	$0.581761\pi$
$500$	2.44141e32	0.0447214
$501$	−1.02159e34	−1.82517
$502$	5.94150e33	1.03538
$503$	−6.75761e33	−1.14867	−0.574333	−	0.818622i	$-0.694738\pi$
$503$	−6.75761e33	−1.14867	−0.574333	+	0.818622i	$0.694738\pi$
$504$	5.36891e32	0.0890234
$505$	1.80273e33	0.291601
$506$	9.47718e33	1.49554
$507$	−8.45051e33	−1.30102
$508$	−6.23111e33	−0.935985
$509$	−5.92051e33	−0.867734	−0.433867	−	0.900977i	$-0.642851\pi$
$509$	−5.92051e33	−0.867734	−0.433867	+	0.900977i	$0.642851\pi$
$510$	−1.94989e33	−0.278858
$511$	−4.32056e33	−0.602946
$512$	−3.24519e32	−0.0441942
$513$	−1.73416e33	−0.230475
$514$	−1.02055e32	−0.0132371
$515$	−4.32244e33	−0.547190
$516$	8.97261e33	1.10866
$517$	8.02911e32	0.0968357
$518$	1.68413e33	0.198268
$519$	−1.79508e34	−2.06296
$520$	−5.29905e31	−0.00594506
$521$	1.90773e33	0.208951	0.104476	−	0.994527i	$-0.466684\pi$
$521$	1.90773e33	0.208951	0.104476	+	0.994527i	$0.466684\pi$
$522$	−4.50590e32	−0.0481837
$523$	7.03264e33	0.734255	0.367128	−	0.930171i	$-0.380341\pi$
$523$	7.03264e33	0.734255	0.367128	+	0.930171i	$0.380341\pi$
$524$	1.75679e33	0.179093
$525$	−9.45058e32	−0.0940734
$526$	6.14209e33	0.597028
$527$	1.04312e34	0.990150
$528$	5.13048e33	0.475591
$529$	1.21298e34	1.09814
$530$	−2.38642e33	−0.211008
$531$	1.13444e34	0.979716
$532$	−1.25120e33	−0.105543
$533$	−6.71540e31	−0.00553327
$534$	−1.54606e34	−1.24440
$535$	−7.44669e33	−0.585519
$536$	7.08757e33	0.544425
$537$	2.36805e34	1.77710
$538$	−7.25162e33	−0.531688
$539$	−1.77258e34	−1.26983
$540$	−1.25924e33	−0.0881429
$541$	−1.92351e34	−1.31561	−0.657806	−	0.753188i	$-0.728515\pi$
$541$	−1.92351e34	−1.31561	−0.657806	+	0.753188i	$0.728515\pi$
$542$	−1.18693e34	−0.793291
$543$	2.74625e34	1.79367
$544$	−1.87455e33	−0.119649
$545$	−1.72703e32	−0.0107732
$546$	2.05124e32	0.0125057
$547$	−2.85894e33	−0.170358	−0.0851791	−	0.996366i	$-0.527146\pi$
$547$	−2.85894e33	−0.170358	−0.0851791	+	0.996366i	$0.527146\pi$
$548$	9.97082e32	0.0580729
$549$	1.17540e33	0.0669163
$550$	−3.71060e33	−0.206496
$551$	1.05008e33	0.0571250
$552$	1.25461e34	0.667221
$553$	−2.83471e33	−0.147382
$554$	6.81547e33	0.346437
$555$	9.10551e33	0.452524
$556$	−6.99590e33	−0.339945
$557$	−3.74961e34	−1.78154	−0.890770	−	0.454454i	$-0.849834\pi$
$557$	−3.74961e34	−1.78154	−0.890770	+	0.454454i	$0.849834\pi$
$558$	−1.55288e34	−0.721457
$559$	1.40852e33	0.0639906
$560$	−9.08541e32	−0.0403640
$561$	2.96357e34	1.28760
$562$	1.16827e34	0.496408
$563$	3.46228e34	1.43882	0.719410	−	0.694585i	$-0.244412\pi$
$563$	3.46228e34	1.43882	0.719410	+	0.694585i	$0.244412\pi$
$564$	1.06291e33	0.0432023
$565$	−1.08154e33	−0.0429968
$566$	5.50368e33	0.214017
$567$	1.14942e34	0.437209
$568$	7.00661e33	0.260708
$569$	3.03324e34	1.10409	0.552043	−	0.833816i	$-0.313848\pi$
$569$	3.03324e34	1.10409	0.552043	+	0.833816i	$0.313848\pi$
$570$	−6.76479e33	−0.240890
$571$	−2.05373e34	−0.715472	−0.357736	−	0.933823i	$-0.616451\pi$
$571$	−2.05373e34	−0.715472	−0.357736	+	0.933823i	$0.616451\pi$
$572$	8.05383e32	0.0274506
$573$	7.20488e34	2.40267
$574$	−1.15138e33	−0.0375682
$575$	−9.07392e33	−0.289699
$576$	2.79062e33	0.0871806
$577$	−1.73765e34	−0.531209	−0.265604	−	0.964082i	$-0.585571\pi$
$577$	−1.73765e34	−0.531209	−0.265604	+	0.964082i	$0.585571\pi$
$578$	1.28083e34	0.383173
$579$	−7.20090e34	−2.10816
$580$	7.62501e32	0.0218469
$581$	−2.38615e34	−0.669108
$582$	−2.01887e34	−0.554077
$583$	3.62703e34	0.974305
$584$	−2.24572e34	−0.590465
$585$	4.55679e32	0.0117276
$586$	−7.25332e33	−0.182733
$587$	−4.89727e34	−1.20775	−0.603876	−	0.797078i	$-0.706378\pi$
$587$	−4.89727e34	−1.20775	−0.603876	+	0.797078i	$0.706378\pi$
$588$	−2.34657e34	−0.566523
$589$	3.61891e34	0.855335
$590$	−1.91973e34	−0.444212
$591$	−4.42972e33	−0.100353
$592$	8.75368e33	0.194164
$593$	1.10421e34	0.239810	0.119905	−	0.992785i	$-0.461741\pi$
$593$	1.10421e34	0.239810	0.119905	+	0.992785i	$0.461741\pi$
$594$	1.91388e34	0.406990
$595$	−5.24810e33	−0.109280
$596$	−3.88761e34	−0.792693
$597$	−1.47276e34	−0.294072
$598$	1.96949e33	0.0385113
$599$	−1.03520e35	−1.98240	−0.991198	−	0.132391i	$-0.957735\pi$
$599$	−1.03520e35	−1.98240	−0.991198	+	0.132391i	$0.957735\pi$
$600$	−4.91217e33	−0.0921261
$601$	9.90327e34	1.81906	0.909532	−	0.415635i	$-0.136441\pi$
$601$	9.90327e34	1.81906	0.909532	+	0.415635i	$0.136441\pi$
$602$	2.41496e34	0.434464
$603$	−6.09479e34	−1.07397
$604$	−2.90122e34	−0.500747
$605$	2.99442e34	0.506256
$606$	−3.62714e34	−0.600699
$607$	−6.59371e34	−1.06972	−0.534862	−	0.844940i	$-0.679636\pi$
$607$	−6.59371e34	−1.06972	−0.534862	+	0.844940i	$0.679636\pi$
$608$	−6.50340e33	−0.103358
$609$	−2.95161e33	−0.0459560
$610$	−1.98905e33	−0.0303405
$611$	1.66856e32	0.00249359
$612$	1.61198e34	0.236029
$613$	−7.31630e34	−1.04963	−0.524814	−	0.851217i	$-0.675865\pi$
$613$	−7.31630e34	−1.04963	−0.524814	+	0.851217i	$0.675865\pi$
$614$	5.27360e34	0.741315
$615$	−6.22512e33	−0.0857450
$616$	1.38086e34	0.186376
$617$	9.91183e34	1.31096	0.655480	−	0.755213i	$-0.272466\pi$
$617$	9.91183e34	1.31096	0.655480	+	0.755213i	$0.272466\pi$
$618$	8.69685e34	1.12721
$619$	4.22193e34	0.536263	0.268131	−	0.963382i	$-0.413594\pi$
$619$	4.22193e34	0.536263	0.268131	+	0.963382i	$0.413594\pi$
$620$	2.62783e34	0.327115
$621$	4.68020e34	0.570978
$622$	1.67250e33	0.0199980
$623$	−4.16118e34	−0.487659
$624$	1.06618e33	0.0122468
$625$	3.55271e33	0.0400000
$626$	3.77177e34	0.416261
$627$	1.02816e35	1.11228
$628$	−3.34074e34	−0.354280
$629$	5.05648e34	0.525672
$630$	7.81279e33	0.0796249
$631$	8.43792e34	0.843080	0.421540	−	0.906810i	$-0.361490\pi$
$631$	8.43792e34	0.843080	0.421540	+	0.906810i	$0.361490\pi$
$632$	−1.47341e34	−0.144331
$633$	−2.64492e35	−2.54019
$634$	7.11707e34	0.670171
$635$	−9.06746e34	−0.837170
$636$	4.80154e34	0.434677
$637$	−3.68365e33	−0.0326991
$638$	−1.15890e34	−0.100876
$639$	−6.02517e34	−0.514291
$640$	−4.72237e33	−0.0395285
$641$	−1.28702e35	−1.05647	−0.528236	−	0.849097i	$-0.677147\pi$
$641$	−1.28702e35	−1.05647	−0.528236	+	0.849097i	$0.677147\pi$
$642$	1.49829e35	1.20617
$643$	8.92172e34	0.704387	0.352194	−	0.935927i	$-0.385436\pi$
$643$	8.92172e34	0.704387	0.352194	+	0.935927i	$0.385436\pi$
$644$	3.37675e34	0.261473
$645$	1.30569e35	0.991614
$646$	−3.75663e34	−0.279828
$647$	1.63366e33	0.0119360	0.00596800	−	0.999982i	$-0.498100\pi$
$647$	1.63366e33	0.0119360	0.00596800	+	0.999982i	$0.498100\pi$
$648$	5.97437e34	0.428159
$649$	2.91773e35	2.05110
$650$	−7.71113e32	−0.00531742
$651$	−1.01722e35	−0.688101
$652$	8.88855e33	0.0589842
$653$	−1.93507e35	−1.25974	−0.629871	−	0.776700i	$-0.716892\pi$
$653$	−1.93507e35	−1.25974	−0.629871	+	0.776700i	$0.716892\pi$
$654$	3.47484e33	0.0221928
$655$	2.55647e34	0.160186
$656$	−5.98458e33	−0.0367905
$657$	1.93115e35	1.16479
$658$	2.86080e33	0.0169303
$659$	1.10886e35	0.643889	0.321944	−	0.946759i	$-0.395664\pi$
$659$	1.10886e35	0.643889	0.321944	+	0.946759i	$0.395664\pi$
$660$	7.46583e34	0.425382
$661$	−1.40626e35	−0.786224	−0.393112	−	0.919490i	$-0.628602\pi$
$661$	−1.40626e35	−0.786224	−0.393112	+	0.919490i	$0.628602\pi$
$662$	−2.30096e35	−1.26236
$663$	6.15870e33	0.0331566
$664$	−1.24026e35	−0.655258
$665$	−1.82073e34	−0.0944006
$666$	−7.52752e34	−0.383022
$667$	−2.83397e34	−0.141521
$668$	−1.42916e35	−0.700449
$669$	−2.68074e33	−0.0128952
$670$	1.03138e35	0.486948
$671$	3.02308e34	0.140094
$672$	1.82801e34	0.0831500
$673$	−1.02658e35	−0.458358	−0.229179	−	0.973384i	$-0.573604\pi$
$673$	−1.02658e35	−0.458358	−0.229179	+	0.973384i	$0.573604\pi$
$674$	−1.71672e35	−0.752403
$675$	−1.83244e34	−0.0788374
$676$	−1.18220e35	−0.499293
$677$	−3.50696e35	−1.45403	−0.727014	−	0.686622i	$-0.759093\pi$
$677$	−3.50696e35	−1.45403	−0.727014	+	0.686622i	$0.759093\pi$
$678$	2.17608e34	0.0885735
$679$	−5.43374e34	−0.217133
$680$	−2.72783e34	−0.107018
$681$	−2.81793e35	−1.08540
$682$	−3.99394e35	−1.51042
$683$	1.09953e35	0.408270	0.204135	−	0.978943i	$-0.434562\pi$
$683$	1.09953e35	0.408270	0.204135	+	0.978943i	$0.434562\pi$
$684$	5.59245e34	0.203892
$685$	1.45094e34	0.0519420
$686$	−1.35781e35	−0.477295
$687$	4.04743e35	1.39708
$688$	1.25524e35	0.425471
$689$	7.53746e33	0.0250891
$690$	1.82570e35	0.596780
$691$	4.88341e35	1.56764	0.783822	−	0.620985i	$-0.213267\pi$
$691$	4.88341e35	1.56764	0.783822	+	0.620985i	$0.213267\pi$
$692$	−2.51125e35	−0.791705
$693$	−1.18744e35	−0.367659
$694$	6.99924e34	0.212842
$695$	−1.01804e35	−0.304056
$696$	−1.53417e34	−0.0450048
$697$	−3.45694e34	−0.0996051
$698$	3.34200e35	0.945831
$699$	2.94402e35	0.818420
$700$	−1.32210e34	−0.0361027
$701$	−1.82400e35	−0.489270	−0.244635	−	0.969615i	$-0.578668\pi$
$701$	−1.82400e35	−0.489270	−0.244635	+	0.969615i	$0.578668\pi$
$702$	3.97729e33	0.0104803
$703$	1.75425e35	0.454098
$704$	7.17735e34	0.182518
$705$	1.54674e34	0.0386413
$706$	−2.31027e35	−0.567028
$707$	−9.76239e34	−0.235404
$708$	3.86255e35	0.915079
$709$	7.70973e35	1.79457	0.897287	−	0.441447i	$-0.145535\pi$
$709$	7.70973e35	1.79457	0.897287	+	0.441447i	$0.145535\pi$
$710$	1.01960e35	0.233184
$711$	1.26703e35	0.284718
$712$	−2.16288e35	−0.477564
$713$	−9.76678e35	−2.11901
$714$	1.05593e35	0.225117
$715$	1.17199e34	0.0245526
$716$	3.31281e35	0.681999
$717$	3.29880e35	0.667370
$718$	−1.69023e35	−0.336040
$719$	3.81081e35	0.744570	0.372285	−	0.928118i	$-0.378574\pi$
$719$	3.81081e35	0.744570	0.372285	+	0.928118i	$0.378574\pi$
$720$	4.06089e34	0.0779767
$721$	2.34074e35	0.441736
$722$	2.50912e35	0.465379
$723$	−4.25598e35	−0.775838
$724$	3.84190e35	0.688358
$725$	1.10959e34	0.0195405
$726$	−6.02485e35	−1.04289
$727$	2.79252e35	0.475133	0.237567	−	0.971371i	$-0.423650\pi$
$727$	2.79252e35	0.475133	0.237567	+	0.971371i	$0.423650\pi$
$728$	2.86961e33	0.00479933
$729$	−2.01364e35	−0.331046
$730$	−3.26795e35	−0.528128
$731$	7.25075e35	1.15190
$732$	4.00201e34	0.0625015
$733$	9.44086e35	1.44948	0.724739	−	0.689023i	$-0.241960\pi$
$733$	9.44086e35	1.44948	0.724739	+	0.689023i	$0.241960\pi$
$734$	−4.52697e35	−0.683293
$735$	−3.41471e35	−0.506713
$736$	1.75515e35	0.256060
$737$	−1.56755e36	−2.24843
$738$	5.14630e34	0.0725756
$739$	−9.13826e35	−1.26709	−0.633546	−	0.773705i	$-0.718401\pi$
$739$	−9.13826e35	−1.26709	−0.633546	+	0.773705i	$0.718401\pi$
$740$	1.27383e35	0.173666
$741$	2.13664e34	0.0286421
$742$	1.29233e35	0.170342
$743$	3.11791e35	0.404114	0.202057	−	0.979374i	$-0.435237\pi$
$743$	3.11791e35	0.404114	0.202057	+	0.979374i	$0.435237\pi$
$744$	−5.28725e35	−0.673858
$745$	−5.65722e35	−0.709006
$746$	6.58530e34	0.0811597
$747$	1.06653e36	1.29261
$748$	4.14593e35	0.494142
$749$	4.03263e35	0.472678
$750$	−7.14815e34	−0.0824001
$751$	6.99901e35	0.793482	0.396741	−	0.917930i	$-0.370141\pi$
$751$	6.99901e35	0.793482	0.396741	+	0.917930i	$0.370141\pi$
$752$	1.48697e34	0.0165798
$753$	−1.73960e36	−1.90771
$754$	−2.40834e33	−0.00259763
$755$	−4.22183e35	−0.447882
$756$	6.81921e34	0.0711560
$757$	5.56975e35	0.571660	0.285830	−	0.958280i	$-0.407731\pi$
$757$	5.56975e35	0.571660	0.285830	+	0.958280i	$0.407731\pi$
$758$	9.31442e35	0.940353
$759$	−2.77481e36	−2.75556
$760$	−9.46369e34	−0.0924466
$761$	1.53099e36	1.47117	0.735586	−	0.677431i	$-0.236907\pi$
$761$	1.53099e36	1.47117	0.735586	+	0.677431i	$0.236907\pi$
$762$	1.82440e36	1.72457
$763$	9.35246e33	0.00869699
$764$	1.00794e36	0.922074
$765$	2.34573e35	0.211111
$766$	−1.38700e36	−1.22805
$767$	6.06344e34	0.0528174
$768$	9.50152e34	0.0814288
$769$	−1.03936e36	−0.876371	−0.438185	−	0.898885i	$-0.644379\pi$
$769$	−1.03936e36	−0.876371	−0.438185	+	0.898885i	$0.644379\pi$
$770$	2.00941e35	0.166700
$771$	2.98804e34	0.0243897
$772$	−1.00738e36	−0.809052
$773$	−6.50514e34	−0.0514059	−0.0257030	−	0.999670i	$-0.508182\pi$
$773$	−6.50514e34	−0.0514059	−0.0257030	+	0.999670i	$0.508182\pi$
$774$	−1.07941e36	−0.839315
$775$	3.82399e35	0.292580
$776$	−2.82432e35	−0.212639
$777$	−4.93093e35	−0.365314
$778$	1.27036e36	0.926154
$779$	−1.19932e35	−0.0860432
$780$	1.55150e34	0.0109539
$781$	−1.54965e36	−1.07670
$782$	1.01385e36	0.693246
$783$	−5.72308e34	−0.0385131
$784$	−3.28277e35	−0.217415
$785$	−4.86142e35	−0.316878
$786$	−5.14368e35	−0.329984
$787$	−2.59764e36	−1.64019	−0.820097	−	0.572224i	$-0.806081\pi$
$787$	−2.59764e36	−1.64019	−0.820097	+	0.572224i	$0.806081\pi$
$788$	−6.19701e34	−0.0385128
$789$	−1.79833e36	−1.10004
$790$	−2.14410e35	−0.129094
$791$	5.85688e34	0.0347104
$792$	−6.17200e35	−0.360048
$793$	6.28237e33	0.00360752
$794$	1.57520e36	0.890388
$795$	6.98716e35	0.388787
$796$	−2.06034e35	−0.112856
$797$	2.04990e36	1.10536	0.552680	−	0.833394i	$-0.313605\pi$
$797$	2.04990e36	1.10536	0.552680	+	0.833394i	$0.313605\pi$
$798$	3.66335e35	0.194466
$799$	8.58934e34	0.0448875
$800$	−6.87195e34	−0.0353553
$801$	1.85991e36	0.942077
$802$	−1.49666e36	−0.746352
$803$	4.96684e36	2.43857
$804$	−2.07516e36	−1.00311
$805$	4.91382e35	0.233868
$806$	−8.29993e34	−0.0388944
$807$	2.12319e36	0.979647
$808$	−5.07424e35	−0.230531
$809$	3.73106e35	0.166907	0.0834537	−	0.996512i	$-0.473405\pi$
$809$	3.73106e35	0.166907	0.0834537	+	0.996512i	$0.473405\pi$
$810$	8.69386e35	0.382957
$811$	2.01608e36	0.874474	0.437237	−	0.899346i	$-0.355957\pi$
$811$	2.01608e36	0.874474	0.437237	+	0.899346i	$0.355957\pi$
$812$	−4.12919e34	−0.0176366
$813$	3.47518e36	1.46166
$814$	−1.93604e36	−0.801882
$815$	1.29345e35	0.0527571
$816$	5.48846e35	0.220457
$817$	2.51551e36	0.995063
$818$	5.33163e34	0.0207703
$819$	−2.46765e34	−0.00946750
$820$	−8.70871e34	−0.0329064
$821$	−5.48657e35	−0.204179	−0.102090	−	0.994775i	$-0.532553\pi$
$821$	−5.48657e35	−0.204179	−0.102090	+	0.994775i	$0.532553\pi$
$822$	−2.91934e35	−0.107001
$823$	1.67463e36	0.604535	0.302267	−	0.953223i	$-0.402256\pi$
$823$	1.67463e36	0.604535	0.302267	+	0.953223i	$0.402256\pi$
$824$	1.21666e36	0.432592
$825$	1.08642e36	0.380473
$826$	1.03960e36	0.358604
$827$	−2.91183e35	−0.0989345	−0.0494673	−	0.998776i	$-0.515752\pi$
$827$	−2.91183e35	−0.0989345	−0.0494673	+	0.998776i	$0.515752\pi$
$828$	−1.50930e36	−0.505122
$829$	−5.85863e35	−0.193136	−0.0965682	−	0.995326i	$-0.530787\pi$
$829$	−5.85863e35	−0.193136	−0.0965682	+	0.995326i	$0.530787\pi$
$830$	−1.80482e36	−0.586080
$831$	−1.99549e36	−0.638317
$832$	1.49155e34	0.00469998
$833$	−1.89626e36	−0.588620
$834$	2.04832e36	0.626356
$835$	−2.07971e36	−0.626500
$836$	1.43835e36	0.426861
$837$	−1.97236e36	−0.576657
$838$	−3.56355e36	−1.02644
$839$	3.47157e36	0.985147	0.492574	−	0.870271i	$-0.336056\pi$
$839$	3.47157e36	0.985147	0.492574	+	0.870271i	$0.336056\pi$
$840$	2.66010e35	0.0743716
$841$	−3.59571e36	−0.990454
$842$	2.06751e36	0.561108
$843$	−3.42055e36	−0.914643
$844$	−3.70014e36	−0.974850
$845$	−1.72032e36	−0.446581
$846$	−1.27869e35	−0.0327065
$847$	−1.62158e36	−0.408691
$848$	6.71718e35	0.166816
$849$	−1.61141e36	−0.394331
$850$	−3.96951e35	−0.0957196
$851$	−4.73441e36	−1.12498
$852$	−2.05145e36	−0.480360
$853$	3.68459e35	0.0850210	0.0425105	−	0.999096i	$-0.486464\pi$
$853$	3.68459e35	0.0850210	0.0425105	+	0.999096i	$0.486464\pi$
$854$	1.07713e35	0.0244933
$855$	8.13808e35	0.182367
$856$	2.09606e36	0.462893
$857$	2.02730e36	0.441222	0.220611	−	0.975362i	$-0.429195\pi$
$857$	2.02730e36	0.441222	0.220611	+	0.975362i	$0.429195\pi$
$858$	−2.35807e35	−0.0505784
$859$	7.42092e36	1.56871	0.784356	−	0.620311i	$-0.212994\pi$
$859$	7.42092e36	1.56871	0.784356	+	0.620311i	$0.212994\pi$
$860$	1.82661e36	0.380553
$861$	3.37111e35	0.0692202
$862$	−3.52673e36	−0.713726
$863$	−9.61540e36	−1.91793	−0.958965	−	0.283526i	$-0.908496\pi$
$863$	−9.61540e36	−1.91793	−0.958965	+	0.283526i	$0.908496\pi$
$864$	3.54445e35	0.0696831
$865$	−3.65435e36	−0.708123
$866$	5.11218e36	0.976411
$867$	−3.75013e36	−0.706005
$868$	−1.42305e36	−0.264073
$869$	3.25873e36	0.596076
$870$	−2.23251e35	−0.0402535
$871$	−3.25759e35	−0.0578987
$872$	4.86117e34	0.00851696
$873$	2.42871e36	0.419466
$874$	3.51735e36	0.598856
$875$	−1.92391e35	−0.0322912
$876$	6.57519e36	1.08795
$877$	−4.33793e36	−0.707600	−0.353800	−	0.935321i	$-0.615111\pi$
$877$	−4.33793e36	−0.707600	−0.353800	+	0.935321i	$0.615111\pi$
$878$	−1.50110e36	−0.241395
$879$	2.12369e36	0.336690
$880$	1.04444e36	0.163249
$881$	3.45165e36	0.531898	0.265949	−	0.963987i	$-0.414315\pi$
$881$	3.45165e36	0.531898	0.265949	+	0.963987i	$0.414315\pi$
$882$	2.82294e36	0.428888
$883$	−1.53217e36	−0.229509	−0.114754	−	0.993394i	$-0.536608\pi$
$883$	−1.53217e36	−0.229509	−0.114754	+	0.993394i	$0.536608\pi$
$884$	8.61579e34	0.0127245
$885$	5.62075e36	0.818471
$886$	−6.47742e36	−0.929995
$887$	−1.76030e35	−0.0249196	−0.0124598	−	0.999922i	$-0.503966\pi$
$887$	−1.76030e35	−0.0249196	−0.0124598	+	0.999922i	$0.503966\pi$
$888$	−2.56297e36	−0.357752
$889$	4.91032e36	0.675831
$890$	−3.14740e36	−0.427146
$891$	−1.32135e37	−1.76826
$892$	−3.75026e34	−0.00494880
$893$	2.97991e35	0.0387757
$894$	1.13825e37	1.46055
$895$	4.82077e36	0.609998
$896$	2.55732e35	0.0319105
$897$	−5.76642e35	−0.0709579
$898$	−8.32181e36	−1.00987
$899$	1.19431e36	0.142929
$900$	5.90937e35	0.0697445
$901$	3.88011e36	0.451632
$902$	1.32361e36	0.151942
$903$	−7.07072e36	−0.800510
$904$	3.04426e35	0.0339919
$905$	5.59071e36	0.615686
$906$	8.49443e36	0.922638
$907$	4.42056e36	0.473572	0.236786	−	0.971562i	$-0.423906\pi$
$907$	4.42056e36	0.473572	0.236786	+	0.971562i	$0.423906\pi$
$908$	−3.94219e36	−0.416547
$909$	4.36348e36	0.454762
$910$	4.17583e34	0.00429265
$911$	−4.66761e36	−0.473277	−0.236638	−	0.971598i	$-0.576046\pi$
$911$	−4.66761e36	−0.473277	−0.236638	+	0.971598i	$0.576046\pi$
$912$	1.90412e36	0.190440
$913$	2.74308e37	2.70616
$914$	5.24696e36	0.510600
$915$	5.82370e35	0.0559030
$916$	5.66221e36	0.536158
$917$	−1.38441e36	−0.129315
$918$	2.04742e36	0.188657
$919$	−1.51994e36	−0.138160	−0.0690801	−	0.997611i	$-0.522006\pi$
$919$	−1.51994e36	−0.138160	−0.0690801	+	0.997611i	$0.522006\pi$
$920$	2.55408e36	0.229027
$921$	−1.54405e37	−1.36589
$922$	6.38538e36	0.557251
$923$	−3.22038e35	−0.0277259
$924$	−4.04299e36	−0.343402
$925$	1.85366e36	0.155331
$926$	−2.33159e36	−0.192759
$927$	−1.04624e37	−0.853361
$928$	−2.14625e35	−0.0172715
$929$	−1.16057e37	−0.921460	−0.460730	−	0.887540i	$-0.652412\pi$
$929$	−1.16057e37	−0.921460	−0.460730	+	0.887540i	$0.652412\pi$
$930$	−7.69396e36	−0.602717
$931$	−6.57872e36	−0.508476
$932$	4.11858e36	0.314086
$933$	−4.89689e35	−0.0368468
$934$	−8.54612e36	−0.634502
$935$	6.03312e36	0.441974
$936$	−1.28262e35	−0.00927152
$937$	1.23945e36	0.0884062	0.0442031	−	0.999023i	$-0.485925\pi$
$937$	1.23945e36	0.0884062	0.0442031	+	0.999023i	$0.485925\pi$
$938$	−5.58525e36	−0.393104
$939$	−1.10433e37	−0.766970
$940$	2.16383e35	0.0148294
$941$	1.07673e37	0.728176	0.364088	−	0.931365i	$-0.381381\pi$
$941$	1.07673e37	0.728176	0.364088	+	0.931365i	$0.381381\pi$
$942$	9.78129e36	0.652770
$943$	3.23675e36	0.213163
$944$	5.40357e36	0.351181
$945$	9.92326e35	0.0636439
$946$	−2.77620e37	−1.75716
$947$	−2.09189e37	−1.30667	−0.653333	−	0.757071i	$-0.726630\pi$
$947$	−2.09189e37	−1.30667	−0.653333	+	0.757071i	$0.726630\pi$
$948$	4.31398e36	0.265934
$949$	1.03217e36	0.0627951
$950$	−1.37715e36	−0.0826867
$951$	−2.08379e37	−1.23480
$952$	1.47721e36	0.0863933
$953$	7.62955e36	0.440390	0.220195	−	0.975456i	$-0.429331\pi$
$953$	7.62955e36	0.440390	0.220195	+	0.975456i	$0.429331\pi$
$954$	−5.77628e36	−0.329074
$955$	1.46674e37	0.824728
$956$	4.61490e36	0.256117
$957$	3.39312e36	0.185866
$958$	−2.00719e37	−1.08522
$959$	−7.85734e35	−0.0419317
$960$	1.38265e36	0.0728321
$961$	2.19270e37	1.14008
$962$	−4.02336e35	−0.0206491
$963$	−1.80245e37	−0.913137
$964$	−5.95397e36	−0.297744
$965$	−1.46593e37	−0.723639
$966$	−9.88674e36	−0.481769
$967$	2.91319e37	1.40132	0.700661	−	0.713495i	$-0.252889\pi$
$967$	2.91319e37	1.40132	0.700661	+	0.713495i	$0.252889\pi$
$968$	−8.42854e36	−0.400231
$969$	1.09990e37	0.515590
$970$	−4.10993e36	−0.190190
$971$	2.71465e37	1.24015	0.620073	−	0.784544i	$-0.287103\pi$
$971$	2.71465e37	1.24015	0.620073	+	0.784544i	$0.287103\pi$
$972$	−1.31221e37	−0.591798
$973$	5.51300e36	0.245458
$974$	4.28882e36	0.188517
$975$	2.25773e35	0.00979747
$976$	5.59867e35	0.0239862
$977$	1.23101e37	0.520689	0.260344	−	0.965516i	$-0.416164\pi$
$977$	1.23101e37	0.520689	0.260344	+	0.965516i	$0.416164\pi$
$978$	−2.60246e36	−0.108680
$979$	4.78362e37	1.97230
$980$	−4.77706e36	−0.194462
$981$	−4.18025e35	−0.0168012
$982$	1.14111e37	0.452829
$983$	−3.87996e37	−1.52023	−0.760114	−	0.649790i	$-0.774857\pi$
$983$	−3.87996e37	−1.52023	−0.760114	+	0.649790i	$0.774857\pi$
$984$	1.75222e36	0.0677874
$985$	−9.01784e35	−0.0344469
$986$	−1.23976e36	−0.0467602
$987$	−8.37608e35	−0.0311944
$988$	2.98909e35	0.0109920
$989$	−6.78891e37	−2.46517
$990$	−8.98144e36	−0.322037
$991$	2.23853e35	0.00792577	0.00396288	−	0.999992i	$-0.498739\pi$
$991$	2.23853e35	0.00792577	0.00396288	+	0.999992i	$0.498739\pi$
$992$	−7.39667e36	−0.258607
$993$	6.73695e37	2.32594
$994$	−5.52145e36	−0.188245
$995$	−2.99819e36	−0.100942
$996$	3.63134e37	1.20733
$997$	−2.76187e37	−0.906806	−0.453403	−	0.891306i	$-0.649790\pi$
$997$	−2.76187e37	−0.906806	−0.453403	+	0.891306i	$0.649790\pi$
$998$	1.10805e37	0.359274
$999$	−9.56094e36	−0.306148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.a.b.1.2	✓	2
5.2	odd	4		50.26.b.f.49.1		4
5.3	odd	4		50.26.b.f.49.4		4
5.4	even	2		50.26.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.b.1.2	✓	2	1.1	even	1	trivial
50.26.a.f.1.1		2	5.4	even	2
50.26.b.f.49.1		4	5.2	odd	4
50.26.b.f.49.4		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} +1.19926e6 q^{3} +1.67772e7 q^{4} +2.44141e8 q^{5} -4.91217e9 q^{6} -1.32210e10 q^{7} -6.87195e10 q^{8} +5.90937e11 q^{9} -1.00000e12 q^{10} +1.51986e13 q^{11} +2.01203e13 q^{12} +3.15848e12 q^{13} +5.41533e13 q^{14} +2.92788e14 q^{15} +2.81475e14 q^{16} +1.62591e15 q^{17} -2.42048e15 q^{18} +5.64080e15 q^{19} +4.09600e15 q^{20} -1.58554e16 q^{21} -6.22536e16 q^{22} -1.52235e17 q^{23} -8.24125e16 q^{24} +5.96046e16 q^{25} -1.29371e16 q^{26} -3.07432e17 q^{27} -2.21812e17 q^{28} +1.86158e17 q^{29} -1.19926e18 q^{30} +6.41559e18 q^{31} -1.15292e18 q^{32} +1.82271e19 q^{33} -6.65974e18 q^{34} -3.22779e18 q^{35} +9.91428e18 q^{36} +3.10993e19 q^{37} -2.31047e19 q^{38} +3.78784e18 q^{39} -1.67772e19 q^{40} -2.12615e19 q^{41} +6.49439e19 q^{42} +4.45949e20 q^{43} +2.54991e20 q^{44} +1.44272e20 q^{45} +6.23555e20 q^{46} +5.28278e19 q^{47} +3.37562e20 q^{48} -1.16627e21 q^{49} -2.44141e20 q^{50} +1.94989e21 q^{51} +5.29905e19 q^{52} +2.38642e21 q^{53} +1.25924e21 q^{54} +3.71060e21 q^{55} +9.08541e20 q^{56} +6.76479e21 q^{57} -7.62501e20 q^{58} +1.91973e22 q^{59} +4.91217e21 q^{60} +1.98905e21 q^{61} -2.62783e22 q^{62} -7.81279e21 q^{63} +4.72237e21 q^{64} +7.71113e20 q^{65} -7.46583e22 q^{66} -1.03138e23 q^{67} +2.72783e22 q^{68} -1.82570e23 q^{69} +1.32210e22 q^{70} -1.01960e23 q^{71} -4.06089e22 q^{72} +3.26795e23 q^{73} -1.27383e23 q^{74} +7.14815e22 q^{75} +9.46369e22 q^{76} -2.00941e23 q^{77} -1.55150e22 q^{78} +2.14410e23 q^{79} +6.87195e22 q^{80} -8.69386e23 q^{81} +8.70871e22 q^{82} +1.80482e24 q^{83} -2.66010e23 q^{84} +3.96951e23 q^{85} -1.82661e24 q^{86} +2.23251e23 q^{87} -1.04444e24 q^{88} +3.14740e24 q^{89} -5.90937e23 q^{90} -4.17583e22 q^{91} -2.55408e24 q^{92} +7.69396e24 q^{93} -2.16383e23 q^{94} +1.37715e24 q^{95} -1.38265e24 q^{96} +4.10993e24 q^{97} +4.77706e24 q^{98} +8.98144e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8192 q^{2} - 438588 q^{3} + 33554432 q^{4} + 488281250 q^{5} + 1796456448 q^{6} - 34008596636 q^{7} - 137438953472 q^{8} + 2426195859786 q^{9} - 2000000000000 q^{10} + 19344682791984 q^{11} - 7358285611008 q^{12}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 8192 * q^2 - 438588 * q^3 + 33554432 * q^4 + 488281250 * q^5 + 1796456448 * q^6 - 34008596636 * q^7 - 137438953472 * q^8 + 2426195859786 * q^9 - 2000000000000 * q^10 + 19344682791984 * q^11 - 7358285611008 * q^12 - 127796048033588 * q^13 + 139299211821056 * q^14 - 107077148437500 * q^15 + 562949953421312 * q^16 - 2998857935578476 * q^17 - 9937698241683456 * q^18 + 13534782395320 * q^19 + 8192000000000000 * q^20 + 18191471686615584 * q^21 - 79235820715966464 * q^22 - 176800520782624068 * q^23 + 30139537862688768 * q^24 + 119209289550781250 * q^25 + 523452612745576448 * q^26 - 1925577931602663000 * q^27 - 570569571619045376 * q^28 - 1676097487309033380 * q^29 + 438588000000000000 * q^30 + 7125865156346376664 * q^31 - 2305843009213693952 * q^32 + 11436524032432880304 * q^33 + 12283322104129437696 * q^34 - 8302880038085937500 * q^35 + 40704811997935435776 * q^36 + 84009823521808944364 * q^37 - 55438468691230720 * q^38 + 218271507658245788472 * q^39 - 33554432000000000000 * q^40 - 278976945138543009756 * q^41 - 74512268028377432064 * q^42 + 426481602906822493732 * q^43 + 324549921652598636544 * q^44 + 592332973580566406250 * q^45 + 724174933125628182528 * q^46 + 1107620660641184540244 * q^47 - 123451547085573193728 * q^48 - 2075218430900234303166 * q^49 - 488281250000000000000 * q^50 + 9524566337524637542344 * q^51 - 2144061901805881131008 * q^52 + 4105636904637626409852 * q^53 + 7887167207844507648000 * q^54 + 4722822947261718750000 * q^55 + 2337052965351609860096 * q^56 + 15981397362106388525520 * q^57 + 6865295308017800724480 * q^58 - 3765561121989768768360 * q^59 - 1796456448000000000000 * q^60 + 1088840609004402816124 * q^61 - 29187543680394758815744 * q^62 - 45963382166122467752748 * q^63 + 9444732965739290427392 * q^64 - 31200207039450195312500 * q^65 - 46844002436845077725184 * q^66 - 118164954526157928047156 * q^67 - 50312487338514176802816 * q^68 - 142335029641186502306208 * q^69 + 34008596636000000000000 * q^70 + 121487502051587284868424 * q^71 - 166726909943543544938496 * q^72 + 1543159074817774555972 * q^73 - 344104237145329436114944 * q^74 - 26141881942749023437500 * q^75 + 227075967759281029120 * q^76 - 287127672428028283409712 * q^77 - 894040095368174749581312 * q^78 + 821388705533644841730640 * q^79 + 137438953472000000000000 * q^80 + 225897583488924285462402 * q^81 + 1142689567287472167960576 * q^82 + 1078689963931157206149252 * q^83 + 305202249844233961734144 * q^84 - 732143050678338867187500 * q^85 - 1746868645506344934326272 * q^86 + 3273342747249083127820920 * q^87 - 1329356479089044015284224 * q^88 + 5059219929404495720992980 * q^89 - 2426195859786000000000000 * q^90 + 2680469809760336269552184 * q^91 - 2966220526082573035634688 * q^92 + 6530638201511067276729984 * q^93 - 4536814225986291876839424 * q^94 + 3304390233232421875000 * q^95 + 505657536862507801509888 * q^96 + 2393368330790785393982164 * q^97 + 8500094692967359705767936 * q^98 + 16590506333144186236452912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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